diff --git "a/data/track_applied/splits/task9_spatial_patterns_train.json" "b/data/track_applied/splits/task9_spatial_patterns_train.json" new file mode 100644--- /dev/null +++ "b/data/track_applied/splits/task9_spatial_patterns_train.json" @@ -0,0 +1,126482 @@ +[ + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.7, + "lon": 37.26667, + "name": "Finote Selam" + }, + { + "lat": -3.93938, + "lon": 39.74877, + "name": "Mtwapa" + }, + { + "lat": 9.8, + "lon": 35.1, + "name": "Mendī" + }, + { + "lat": -25.81015, + "lon": 28.74248, + "name": "Bronkhorstspruit" + }, + { + "lat": 43.17562, + "lon": -76.11937, + "name": "Cicero" + } + ], + "question": "Which location is the geographic outlier among: Finote Selam, Mtwapa, Mendī, Bronkhorstspruit, Cicero?", + "ground_truth": { + "answer": "Cicero", + "outlier_distance_km": 9416.5, + "second_furthest_km": 4006.0, + "clarity_ratio": 2.35, + "median_distance_km": 3204.9, + "distances_to_centroid": { + "Finote Selam": 2706.9, + "Mtwapa": 3204.9, + "Mendī": 2459.8, + "Bronkhorstspruit": 4006.0, + "Cicero": 9416.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Finote Selam: (10.70°, 37.27°)", + " Mtwapa: (-3.94°, 39.75°)", + " Mendī: (9.80°, 35.10°)", + " Bronkhorstspruit: (-25.81°, 28.74°)", + " Cicero: (43.18°, -76.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cicero: 9416.5 km from centroid", + " Bronkhorstspruit: 4006.0 km from centroid", + " Mtwapa: 3204.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cicero", + "FINAL ANSWER: Cicero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.09028, + "lon": -48.61139, + "name": "Itapema" + }, + { + "lat": -6.00306, + "lon": -40.29278, + "name": "Tauá" + }, + { + "lat": -9.61806, + "lon": -36.76806, + "name": "Craíbas" + }, + { + "lat": -19.41361, + "lon": -42.41944, + "name": "Ipaba" + }, + { + "lat": 7.2, + "lon": 37.66667, + "name": "Hadero" + } + ], + "question": "Which location is the geographic outlier among: Itapema, Tauá, Craíbas, Ipaba, Hadero?", + "ground_truth": { + "answer": "Hadero", + "outlier_distance_km": 7338.1, + "second_furthest_km": 2959.0, + "clarity_ratio": 2.48, + "median_distance_km": 1985.5, + "distances_to_centroid": { + "Itapema": 2959.0, + "Tauá": 1657.2, + "Craíbas": 1178.5, + "Ipaba": 1985.5, + "Hadero": 7338.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itapema: (-27.09°, -48.61°)", + " Tauá: (-6.00°, -40.29°)", + " Craíbas: (-9.62°, -36.77°)", + " Ipaba: (-19.41°, -42.42°)", + " Hadero: (7.20°, 37.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hadero: 7338.1 km from centroid", + " Itapema: 2959.0 km from centroid", + " Ipaba: 1985.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hadero", + "FINAL ANSWER: Hadero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.76667, + "lon": 144.96667, + "name": "Brunswick" + }, + { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + }, + { + "lat": 44.63651, + "lon": -123.10593, + "name": "Albany" + } + ], + "question": "Which location is the geographic outlier among: Brunswick, Manly, Lidcombe, Cessnock, Albany?", + "ground_truth": { + "answer": "Albany", + "outlier_distance_km": 15459.4, + "second_furthest_km": 5777.8, + "clarity_ratio": 2.68, + "median_distance_km": 5774.3, + "distances_to_centroid": { + "Brunswick": 5249.9, + "Manly": 5774.3, + "Lidcombe": 5751.6, + "Cessnock": 5777.8, + "Albany": 15459.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brunswick: (-37.77°, 144.97°)", + " Manly: (-33.80°, 151.29°)", + " Lidcombe: (-33.86°, 151.04°)", + " Cessnock: (-32.83°, 151.36°)", + " Albany: (44.64°, -123.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Albany: 15459.4 km from centroid", + " Cessnock: 5777.8 km from centroid", + " Manly: 5774.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Albany", + "FINAL ANSWER: Albany" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.64083, + "lon": -39.55111, + "name": "Coaraci" + }, + { + "lat": -6.23122, + "lon": -42.68691, + "name": "Regeneração" + }, + { + "lat": -3.36841, + "lon": -64.72054, + "name": "Tefé" + }, + { + "lat": -11.52472, + "lon": -61.01278, + "name": "Espigão dOeste" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + } + ], + "question": "Which location is the geographic outlier among: Coaraci, Regeneração, Tefé, Espigão dOeste, Redbank Plains?", + "ground_truth": { + "answer": "Redbank Plains", + "outlier_distance_km": 15206.0, + "second_furthest_km": 5991.0, + "clarity_ratio": 2.54, + "median_distance_km": 5428.4, + "distances_to_centroid": { + "Coaraci": 3088.2, + "Regeneração": 3543.2, + "Tefé": 5991.0, + "Espigão dOeste": 5428.4, + "Redbank Plains": 15206.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coaraci: (-14.64°, -39.55°)", + " Regeneração: (-6.23°, -42.69°)", + " Tefé: (-3.37°, -64.72°)", + " Espigão dOeste: (-11.52°, -61.01°)", + " Redbank Plains: (-27.65°, 152.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Redbank Plains: 15206.0 km from centroid", + " Tefé: 5991.0 km from centroid", + " Espigão dOeste: 5428.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Redbank Plains", + "FINAL ANSWER: Redbank Plains" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.20279, + "lon": 46.86594, + "name": "Kizilyurt" + }, + { + "lat": 39.94729, + "lon": -0.06313, + "name": "Almassora" + }, + { + "lat": 45.7088, + "lon": 11.47959, + "name": "Thiene" + }, + { + "lat": 55.85, + "lon": 37.65, + "name": "Leonovo" + }, + { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + } + ], + "question": "Which location is the geographic outlier among: Kizilyurt, Almassora, Thiene, Leonovo, West Pennant Hills?", + "ground_truth": { + "answer": "West Pennant Hills", + "outlier_distance_km": 12800.8, + "second_furthest_km": 4569.6, + "clarity_ratio": 2.8, + "median_distance_km": 3698.9, + "distances_to_centroid": { + "Kizilyurt": 1463.9, + "Almassora": 4569.6, + "Thiene": 3698.9, + "Leonovo": 2999.0, + "West Pennant Hills": 12800.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kizilyurt: (43.20°, 46.87°)", + " Almassora: (39.95°, -0.06°)", + " Thiene: (45.71°, 11.48°)", + " Leonovo: (55.85°, 37.65°)", + " West Pennant Hills: (-33.75°, 151.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Pennant Hills: 12800.8 km from centroid", + " Almassora: 4569.6 km from centroid", + " Thiene: 3698.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Pennant Hills", + "FINAL ANSWER: West Pennant Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + }, + { + "lat": -33.41665, + "lon": 149.5806, + "name": "Bathurst" + }, + { + "lat": -33.90741, + "lon": 151.15546, + "name": "Marrickville" + }, + { + "lat": -41.21667, + "lon": 174.91667, + "name": "Lower Hutt" + }, + { + "lat": 53.4614, + "lon": -2.92863, + "name": "Fazakerley" + } + ], + "question": "Which location is the geographic outlier among: Cronulla, Bathurst, Marrickville, Lower Hutt, Fazakerley?", + "ground_truth": { + "answer": "Fazakerley", + "outlier_distance_km": 14048.7, + "second_furthest_km": 5409.5, + "clarity_ratio": 2.6, + "median_distance_km": 3179.5, + "distances_to_centroid": { + "Cronulla": 3179.5, + "Bathurst": 3017.7, + "Marrickville": 3171.9, + "Lower Hutt": 5409.5, + "Fazakerley": 14048.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cronulla: (-34.06°, 151.15°)", + " Bathurst: (-33.42°, 149.58°)", + " Marrickville: (-33.91°, 151.16°)", + " Lower Hutt: (-41.22°, 174.92°)", + " Fazakerley: (53.46°, -2.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fazakerley: 14048.7 km from centroid", + " Lower Hutt: 5409.5 km from centroid", + " Cronulla: 3179.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fazakerley", + "FINAL ANSWER: Fazakerley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8149, + "lon": 144.95052, + "name": "Docklands" + }, + { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + }, + { + "lat": 9.08296, + "lon": -1.81884, + "name": "Damongo" + } + ], + "question": "Which location is the geographic outlier among: Docklands, Wyndham Vale, Cairns, Paraparaumu, Damongo?", + "ground_truth": { + "answer": "Damongo", + "outlier_distance_km": 13803.4, + "second_furthest_km": 5197.8, + "clarity_ratio": 2.66, + "median_distance_km": 2646.5, + "distances_to_centroid": { + "Docklands": 2621.8, + "Wyndham Vale": 2600.0, + "Cairns": 2646.5, + "Paraparaumu": 5197.8, + "Damongo": 13803.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Docklands: (-37.81°, 144.95°)", + " Wyndham Vale: (-37.89°, 144.62°)", + " Cairns: (-16.92°, 145.77°)", + " Paraparaumu: (-40.92°, 175.02°)", + " Damongo: (9.08°, -1.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Damongo: 13803.4 km from centroid", + " Paraparaumu: 5197.8 km from centroid", + " Cairns: 2646.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Damongo", + "FINAL ANSWER: Damongo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.1725, + "lon": -38.46056, + "name": "Pacajus" + }, + { + "lat": -21.79667, + "lon": -50.87861, + "name": "Osvaldo Cruz" + }, + { + "lat": -15.53139, + "lon": -40.90944, + "name": "Encruzilhada" + }, + { + "lat": -4.32222, + "lon": -40.71083, + "name": "Ipu" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + } + ], + "question": "Which location is the geographic outlier among: Pacajus, Osvaldo Cruz, Encruzilhada, Ipu, Port Macquarie?", + "ground_truth": { + "answer": "Port Macquarie", + "outlier_distance_km": 14230.9, + "second_furthest_km": 5011.9, + "clarity_ratio": 2.84, + "median_distance_km": 4239.5, + "distances_to_centroid": { + "Pacajus": 4011.0, + "Osvaldo Cruz": 5011.9, + "Encruzilhada": 3991.6, + "Ipu": 4239.5, + "Port Macquarie": 14230.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacajus: (-4.17°, -38.46°)", + " Osvaldo Cruz: (-21.80°, -50.88°)", + " Encruzilhada: (-15.53°, -40.91°)", + " Ipu: (-4.32°, -40.71°)", + " Port Macquarie: (-31.43°, 152.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Macquarie: 14230.9 km from centroid", + " Osvaldo Cruz: 5011.9 km from centroid", + " Ipu: 4239.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Macquarie", + "FINAL ANSWER: Port Macquarie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.30309, + "lon": 108.7702, + "name": "Zhuoshui" + }, + { + "lat": 12.54288, + "lon": 78.35735, + "name": "Bargūr" + }, + { + "lat": 47.23489, + "lon": 127.10769, + "name": "Suiling" + }, + { + "lat": 33.19133, + "lon": 104.42009, + "name": "Zhongzhai" + }, + { + "lat": 51.40878, + "lon": -0.02526, + "name": "Beckenham" + } + ], + "question": "Which location is the geographic outlier among: Zhuoshui, Bargūr, Suiling, Zhongzhai, Beckenham?", + "ground_truth": { + "answer": "Beckenham", + "outlier_distance_km": 6663.2, + "second_furthest_km": 3839.3, + "clarity_ratio": 1.74, + "median_distance_km": 2526.5, + "distances_to_centroid": { + "Zhuoshui": 2430.1, + "Bargūr": 2526.5, + "Suiling": 3839.3, + "Zhongzhai": 1912.8, + "Beckenham": 6663.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhuoshui: (29.30°, 108.77°)", + " Bargūr: (12.54°, 78.36°)", + " Suiling: (47.23°, 127.11°)", + " Zhongzhai: (33.19°, 104.42°)", + " Beckenham: (51.41°, -0.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Beckenham: 6663.2 km from centroid", + " Suiling: 3839.3 km from centroid", + " Bargūr: 2526.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Beckenham", + "FINAL ANSWER: Beckenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.23126, + "lon": -74.67223, + "name": "Mercerville-Hamilton Square" + }, + { + "lat": 45.07246, + "lon": -93.45579, + "name": "Maple Grove" + }, + { + "lat": 34.86971, + "lon": -117.05615, + "name": "Barstow Heights" + }, + { + "lat": 45.45008, + "lon": -73.46583, + "name": "Brossard" + }, + { + "lat": 9.8, + "lon": 38.73333, + "name": "Fichē" + } + ], + "question": "Which location is the geographic outlier among: Mercerville-Hamilton Square, Maple Grove, Barstow Heights, Brossard, Fichē?", + "ground_truth": { + "answer": "Fichē", + "outlier_distance_km": 10515.7, + "second_furthest_km": 4775.6, + "clarity_ratio": 2.2, + "median_distance_km": 2722.7, + "distances_to_centroid": { + "Mercerville-Hamilton Square": 1100.1, + "Maple Grove": 2722.7, + "Barstow Heights": 4775.6, + "Brossard": 1403.4, + "Fichē": 10515.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mercerville-Hamilton Square: (40.23°, -74.67°)", + " Maple Grove: (45.07°, -93.46°)", + " Barstow Heights: (34.87°, -117.06°)", + " Brossard: (45.45°, -73.47°)", + " Fichē: (9.80°, 38.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fichē: 10515.7 km from centroid", + " Barstow Heights: 4775.6 km from centroid", + " Maple Grove: 2722.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fichē", + "FINAL ANSWER: Fichē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71893, + "lon": -72.24099, + "name": "Mulchén" + }, + { + "lat": -5.81944, + "lon": -46.13861, + "name": "Grajaú" + }, + { + "lat": -3.49444, + "lon": -39.57861, + "name": "Itapipoca" + }, + { + "lat": -27.58504, + "lon": -56.68707, + "name": "Ituzaingó" + }, + { + "lat": 12.6, + "lon": 37.46667, + "name": "Gonder" + } + ], + "question": "Which location is the geographic outlier among: Mulchén, Grajaú, Itapipoca, Ituzaingó, Gonder?", + "ground_truth": { + "answer": "Gonder", + "outlier_distance_km": 8506.9, + "second_furthest_km": 4604.7, + "clarity_ratio": 1.85, + "median_distance_km": 2780.9, + "distances_to_centroid": { + "Mulchén": 4604.7, + "Grajaú": 1383.9, + "Itapipoca": 1090.5, + "Ituzaingó": 2780.9, + "Gonder": 8506.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mulchén: (-37.72°, -72.24°)", + " Grajaú: (-5.82°, -46.14°)", + " Itapipoca: (-3.49°, -39.58°)", + " Ituzaingó: (-27.59°, -56.69°)", + " Gonder: (12.60°, 37.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gonder: 8506.9 km from centroid", + " Mulchén: 4604.7 km from centroid", + " Ituzaingó: 2780.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gonder", + "FINAL ANSWER: Gonder" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.54667, + "lon": -47.43778, + "name": "Votorantim" + }, + { + "lat": -6.21194, + "lon": -38.49694, + "name": "São Miguel" + }, + { + "lat": 10.85953, + "lon": -74.77386, + "name": "Malambo" + }, + { + "lat": -8.28333, + "lon": -35.97611, + "name": "Caruaru" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + } + ], + "question": "Which location is the geographic outlier among: Votorantim, São Miguel, Malambo, Caruaru, Perth?", + "ground_truth": { + "answer": "Perth", + "outlier_distance_km": 12963.6, + "second_furthest_km": 6947.4, + "clarity_ratio": 1.87, + "median_distance_km": 3549.4, + "distances_to_centroid": { + "Votorantim": 3549.4, + "São Miguel": 2529.4, + "Malambo": 6947.4, + "Caruaru": 2203.9, + "Perth": 12963.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Votorantim: (-23.55°, -47.44°)", + " São Miguel: (-6.21°, -38.50°)", + " Malambo: (10.86°, -74.77°)", + " Caruaru: (-8.28°, -35.98°)", + " Perth: (-31.95°, 115.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perth: 12963.6 km from centroid", + " Malambo: 6947.4 km from centroid", + " Votorantim: 3549.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perth", + "FINAL ANSWER: Perth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.58333, + "lon": 145.03333, + "name": "Wollert" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -33.86785, + "lon": 151.20732, + "name": "Sydney" + }, + { + "lat": -37.96667, + "lon": 145.16667, + "name": "Noble Park" + }, + { + "lat": 30.91018, + "lon": 30.17438, + "name": "Abū al Maţāmīr" + } + ], + "question": "Which location is the geographic outlier among: Wollert, Helensvale, Sydney, Noble Park, Abū al Maţāmīr?", + "ground_truth": { + "answer": "Abū al Maţāmīr", + "outlier_distance_km": 11640.3, + "second_furthest_km": 2952.0, + "clarity_ratio": 3.94, + "median_distance_km": 2926.4, + "distances_to_centroid": { + "Wollert": 2644.9, + "Helensvale": 2952.0, + "Sydney": 2926.4, + "Noble Park": 2680.3, + "Abū al Maţāmīr": 11640.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wollert: (-37.58°, 145.03°)", + " Helensvale: (-27.92°, 153.33°)", + " Sydney: (-33.87°, 151.21°)", + " Noble Park: (-37.97°, 145.17°)", + " Abū al Maţāmīr: (30.91°, 30.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Abū al Maţāmīr: 11640.3 km from centroid", + " Helensvale: 2952.0 km from centroid", + " Sydney: 2926.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Abū al Maţāmīr", + "FINAL ANSWER: Abū al Maţāmīr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.4842, + "lon": -88.99369, + "name": "Bloomington" + }, + { + "lat": 19.44506, + "lon": -99.14612, + "name": "Cuauhtémoc" + }, + { + "lat": 25.43333, + "lon": -103.21667, + "name": "San Pedro" + }, + { + "lat": 44.86136, + "lon": -92.62381, + "name": "River Falls" + }, + { + "lat": 43.84369, + "lon": 10.50447, + "name": "Lucca" + } + ], + "question": "Which location is the geographic outlier among: Bloomington, Cuauhtémoc, San Pedro, River Falls, Lucca?", + "ground_truth": { + "answer": "Lucca", + "outlier_distance_km": 7069.3, + "second_furthest_km": 2948.5, + "clarity_ratio": 2.4, + "median_distance_km": 2922.1, + "distances_to_centroid": { + "Bloomington": 1405.6, + "Cuauhtémoc": 2948.5, + "San Pedro": 2922.1, + "River Falls": 1888.2, + "Lucca": 7069.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bloomington: (40.48°, -88.99°)", + " Cuauhtémoc: (19.45°, -99.15°)", + " San Pedro: (25.43°, -103.22°)", + " River Falls: (44.86°, -92.62°)", + " Lucca: (43.84°, 10.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lucca: 7069.3 km from centroid", + " Cuauhtémoc: 2948.5 km from centroid", + " San Pedro: 2922.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lucca", + "FINAL ANSWER: Lucca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.12014, + "lon": 15.28768, + "name": "Lubań" + }, + { + "lat": 55.7163, + "lon": 60.551, + "name": "Kyshtym" + }, + { + "lat": 44.75583, + "lon": 44.9925, + "name": "Neftekumsk" + }, + { + "lat": 55.82885, + "lon": -4.21376, + "name": "Rutherglen" + }, + { + "lat": 22.75923, + "lon": 113.79452, + "name": "Gongheyong" + } + ], + "question": "Which location is the geographic outlier among: Lubań, Kyshtym, Neftekumsk, Rutherglen, Gongheyong?", + "ground_truth": { + "answer": "Gongheyong", + "outlier_distance_km": 6514.3, + "second_furthest_km": 3599.5, + "clarity_ratio": 1.81, + "median_distance_km": 2316.4, + "distances_to_centroid": { + "Lubań": 2316.4, + "Kyshtym": 1473.9, + "Neftekumsk": 165.8, + "Rutherglen": 3599.5, + "Gongheyong": 6514.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lubań: (51.12°, 15.29°)", + " Kyshtym: (55.72°, 60.55°)", + " Neftekumsk: (44.76°, 44.99°)", + " Rutherglen: (55.83°, -4.21°)", + " Gongheyong: (22.76°, 113.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gongheyong: 6514.3 km from centroid", + " Rutherglen: 3599.5 km from centroid", + " Lubań: 2316.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gongheyong", + "FINAL ANSWER: Gongheyong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.9164, + "lon": -118.35257, + "name": "Hawthorne" + }, + { + "lat": 43.4668, + "lon": -80.51639, + "name": "Waterloo" + }, + { + "lat": 19.84073, + "lon": -90.51676, + "name": "Campeche" + }, + { + "lat": 33.0185, + "lon": -80.17565, + "name": "Summerville" + }, + { + "lat": 55.75533, + "lon": 38.09578, + "name": "Zarya" + } + ], + "question": "Which location is the geographic outlier among: Hawthorne, Waterloo, Campeche, Summerville, Zarya?", + "ground_truth": { + "answer": "Zarya", + "outlier_distance_km": 7466.2, + "second_furthest_km": 4664.3, + "clarity_ratio": 1.6, + "median_distance_km": 3037.5, + "distances_to_centroid": { + "Hawthorne": 4664.3, + "Waterloo": 1389.8, + "Campeche": 3037.5, + "Summerville": 1344.1, + "Zarya": 7466.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hawthorne: (33.92°, -118.35°)", + " Waterloo: (43.47°, -80.52°)", + " Campeche: (19.84°, -90.52°)", + " Summerville: (33.02°, -80.18°)", + " Zarya: (55.76°, 38.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zarya: 7466.2 km from centroid", + " Hawthorne: 4664.3 km from centroid", + " Campeche: 3037.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zarya", + "FINAL ANSWER: Zarya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.83841, + "lon": 76.62331, + "name": "Umarga" + }, + { + "lat": 23.80366, + "lon": 72.39101, + "name": "Unjha" + }, + { + "lat": 18.04531, + "lon": 78.26078, + "name": "Medak" + }, + { + "lat": 24.62361, + "lon": 76.70783, + "name": "Chhipa Barod" + }, + { + "lat": 5.89258, + "lon": 7.93534, + "name": "Afikpo" + } + ], + "question": "Which location is the geographic outlier among: Umarga, Unjha, Medak, Chhipa Barod, Afikpo?", + "ground_truth": { + "answer": "Afikpo", + "outlier_distance_km": 6052.1, + "second_furthest_km": 1678.1, + "clarity_ratio": 3.61, + "median_distance_km": 1652.9, + "distances_to_centroid": { + "Umarga": 1506.2, + "Unjha": 1220.4, + "Medak": 1678.1, + "Chhipa Barod": 1652.9, + "Afikpo": 6052.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Umarga: (17.84°, 76.62°)", + " Unjha: (23.80°, 72.39°)", + " Medak: (18.05°, 78.26°)", + " Chhipa Barod: (24.62°, 76.71°)", + " Afikpo: (5.89°, 7.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Afikpo: 6052.1 km from centroid", + " Medak: 1678.1 km from centroid", + " Chhipa Barod: 1652.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Afikpo", + "FINAL ANSWER: Afikpo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.71417, + "lon": 43.00083, + "name": "Aleksandrovskoye" + }, + { + "lat": 53.52189, + "lon": -1.39698, + "name": "Wombwell" + }, + { + "lat": 45.66019, + "lon": 8.79164, + "name": "Gallarate" + }, + { + "lat": 50.7838, + "lon": -0.96869, + "name": "Hayling Island" + }, + { + "lat": -23.35611, + "lon": -46.87694, + "name": "Cajamar" + } + ], + "question": "Which location is the geographic outlier among: Aleksandrovskoye, Wombwell, Gallarate, Hayling Island, Cajamar?", + "ground_truth": { + "answer": "Cajamar", + "outlier_distance_km": 8129.8, + "second_furthest_km": 3779.0, + "clarity_ratio": 2.15, + "median_distance_km": 2146.5, + "distances_to_centroid": { + "Aleksandrovskoye": 3779.0, + "Wombwell": 2146.5, + "Gallarate": 1448.5, + "Hayling Island": 1840.7, + "Cajamar": 8129.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aleksandrovskoye: (44.71°, 43.00°)", + " Wombwell: (53.52°, -1.40°)", + " Gallarate: (45.66°, 8.79°)", + " Hayling Island: (50.78°, -0.97°)", + " Cajamar: (-23.36°, -46.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cajamar: 8129.8 km from centroid", + " Aleksandrovskoye: 3779.0 km from centroid", + " Wombwell: 2146.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cajamar", + "FINAL ANSWER: Cajamar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.18278, + "lon": 124.17701, + "name": "Boroon" + }, + { + "lat": 29.68242, + "lon": 105.93551, + "name": "Wangu" + }, + { + "lat": 16.2838, + "lon": 121.0896, + "name": "Dupax del Sur" + }, + { + "lat": 29.81527, + "lon": 106.42906, + "name": "Longfeng" + }, + { + "lat": 40.39283, + "lon": -3.48194, + "name": "Mejorada del Campo" + } + ], + "question": "Which location is the geographic outlier among: Boroon, Wangu, Dupax del Sur, Longfeng, Mejorada del Campo?", + "ground_truth": { + "answer": "Mejorada del Campo", + "outlier_distance_km": 8590.5, + "second_furthest_km": 3992.1, + "clarity_ratio": 2.15, + "median_distance_km": 3283.1, + "distances_to_centroid": { + "Boroon": 3992.1, + "Wangu": 1584.2, + "Dupax del Sur": 3283.1, + "Longfeng": 1634.1, + "Mejorada del Campo": 8590.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boroon: (8.18°, 124.18°)", + " Wangu: (29.68°, 105.94°)", + " Dupax del Sur: (16.28°, 121.09°)", + " Longfeng: (29.82°, 106.43°)", + " Mejorada del Campo: (40.39°, -3.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mejorada del Campo: 8590.5 km from centroid", + " Boroon: 3992.1 km from centroid", + " Dupax del Sur: 3283.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mejorada del Campo", + "FINAL ANSWER: Mejorada del Campo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.03589, + "lon": 107.11612, + "name": "Gelan" + }, + { + "lat": 37.76354, + "lon": 139.02199, + "name": "Shirone" + }, + { + "lat": -6.28417, + "lon": 107.81056, + "name": "Pamanukan" + }, + { + "lat": 8.96727, + "lon": 76.54188, + "name": "Chavara" + }, + { + "lat": 43.65965, + "lon": -79.37902, + "name": "Church-Yonge Corridor" + } + ], + "question": "Which location is the geographic outlier among: Gelan, Shirone, Pamanukan, Chavara, Church-Yonge Corridor?", + "ground_truth": { + "answer": "Church-Yonge Corridor", + "outlier_distance_km": 11997.4, + "second_furthest_km": 6663.7, + "clarity_ratio": 1.8, + "median_distance_km": 5213.2, + "distances_to_centroid": { + "Gelan": 3743.1, + "Shirone": 6663.7, + "Pamanukan": 5213.2, + "Chavara": 1682.1, + "Church-Yonge Corridor": 11997.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gelan: (30.04°, 107.12°)", + " Shirone: (37.76°, 139.02°)", + " Pamanukan: (-6.28°, 107.81°)", + " Chavara: (8.97°, 76.54°)", + " Church-Yonge Corridor: (43.66°, -79.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Church-Yonge Corridor: 11997.4 km from centroid", + " Shirone: 6663.7 km from centroid", + " Pamanukan: 5213.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Church-Yonge Corridor", + "FINAL ANSWER: Church-Yonge Corridor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.33813, + "lon": -79.97894, + "name": "Baldwin" + }, + { + "lat": 41.66113, + "lon": -91.53017, + "name": "Iowa City" + }, + { + "lat": 37.12005, + "lon": -93.48019, + "name": "Republic" + }, + { + "lat": 49.25, + "lon": -122.88333, + "name": "Cariboo" + }, + { + "lat": 21.84577, + "lon": 71.30544, + "name": "Bābra" + } + ], + "question": "Which location is the geographic outlier among: Baldwin, Iowa City, Republic, Cariboo, Bābra?", + "ground_truth": { + "answer": "Bābra", + "outlier_distance_km": 11843.0, + "second_furthest_km": 4819.8, + "clarity_ratio": 2.46, + "median_distance_km": 2648.6, + "distances_to_centroid": { + "Baldwin": 1456.5, + "Iowa City": 2430.9, + "Republic": 2648.6, + "Cariboo": 4819.8, + "Bābra": 11843.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baldwin: (40.34°, -79.98°)", + " Iowa City: (41.66°, -91.53°)", + " Republic: (37.12°, -93.48°)", + " Cariboo: (49.25°, -122.88°)", + " Bābra: (21.85°, 71.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bābra: 11843.0 km from centroid", + " Cariboo: 4819.8 km from centroid", + " Republic: 2648.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bābra", + "FINAL ANSWER: Bābra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.65689, + "lon": 9.47554, + "name": "Friedrichshafen" + }, + { + "lat": 51.45061, + "lon": 0.05225, + "name": "Eltham" + }, + { + "lat": 49.95542, + "lon": 18.57479, + "name": "Jastrzębie Zdrój" + }, + { + "lat": 51.28635, + "lon": 7.29388, + "name": "Schwelm" + }, + { + "lat": 10.81314, + "lon": 76.62869, + "name": "Puthuppariyāram" + } + ], + "question": "Which location is the geographic outlier among: Friedrichshafen, Eltham, Jastrzębie Zdrój, Schwelm, Puthuppariyāram?", + "ground_truth": { + "answer": "Puthuppariyāram", + "outlier_distance_km": 6287.5, + "second_furthest_km": 1973.3, + "clarity_ratio": 3.19, + "median_distance_km": 1523.9, + "distances_to_centroid": { + "Friedrichshafen": 1180.7, + "Eltham": 1973.3, + "Jastrzębie Zdrój": 907.8, + "Schwelm": 1523.9, + "Puthuppariyāram": 6287.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Friedrichshafen: (47.66°, 9.48°)", + " Eltham: (51.45°, 0.05°)", + " Jastrzębie Zdrój: (49.96°, 18.57°)", + " Schwelm: (51.29°, 7.29°)", + " Puthuppariyāram: (10.81°, 76.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Puthuppariyāram: 6287.5 km from centroid", + " Eltham: 1973.3 km from centroid", + " Schwelm: 1523.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Puthuppariyāram", + "FINAL ANSWER: Puthuppariyāram" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.62142, + "lon": 2.7253, + "name": "Marratxí" + }, + { + "lat": 51.6569, + "lon": 9.63501, + "name": "Uslar" + }, + { + "lat": 57.3438, + "lon": 28.35363, + "name": "Ostrov" + }, + { + "lat": 52.42431, + "lon": 37.59956, + "name": "Livny" + }, + { + "lat": -5.90181, + "lon": -76.12234, + "name": "Yurimaguas" + } + ], + "question": "Which location is the geographic outlier among: Marratxí, Uslar, Ostrov, Livny, Yurimaguas?", + "ground_truth": { + "answer": "Yurimaguas", + "outlier_distance_km": 9274.3, + "second_furthest_km": 3198.5, + "clarity_ratio": 2.9, + "median_distance_km": 2865.2, + "distances_to_centroid": { + "Marratxí": 207.5, + "Uslar": 1574.6, + "Ostrov": 2865.2, + "Livny": 3198.5, + "Yurimaguas": 9274.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marratxí: (39.62°, 2.73°)", + " Uslar: (51.66°, 9.64°)", + " Ostrov: (57.34°, 28.35°)", + " Livny: (52.42°, 37.60°)", + " Yurimaguas: (-5.90°, -76.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yurimaguas: 9274.3 km from centroid", + " Livny: 3198.5 km from centroid", + " Ostrov: 2865.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yurimaguas", + "FINAL ANSWER: Yurimaguas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + { + "lat": 29.2476, + "lon": 107.28443, + "name": "Shuijiang" + } + ], + "question": "Which location is the geographic outlier among: Wollongong city centre, Wollongong, Tuggeranong Administrative District, Orange, Shuijiang?", + "ground_truth": { + "answer": "Shuijiang", + "outlier_distance_km": 6740.4, + "second_furthest_km": 1699.6, + "clarity_ratio": 3.97, + "median_distance_km": 1693.3, + "distances_to_centroid": { + "Wollongong city centre": 1693.3, + "Wollongong": 1693.0, + "Tuggeranong Administrative District": 1699.6, + "Orange": 1495.5, + "Shuijiang": 6740.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Wollongong: (-34.42°, 150.89°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + " Orange: (-33.28°, 149.10°)", + " Shuijiang: (29.25°, 107.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shuijiang: 6740.4 km from centroid", + " Tuggeranong Administrative District: 1699.6 km from centroid", + " Wollongong city centre: 1693.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shuijiang", + "FINAL ANSWER: Shuijiang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + }, + { + "lat": -37.0393, + "lon": 174.92815, + "name": "Takanini" + }, + { + "lat": 19.2366, + "lon": -104.56512, + "name": "Cihuatlán" + } + ], + "question": "Which location is the geographic outlier among: Epsom, Moonee Ponds, Te Atatu Peninsula, Takanini, Cihuatlán?", + "ground_truth": { + "answer": "Cihuatlán", + "outlier_distance_km": 16107.2, + "second_furthest_km": 5907.1, + "clarity_ratio": 2.73, + "median_distance_km": 5895.2, + "distances_to_centroid": { + "Epsom": 5895.2, + "Moonee Ponds": 3277.8, + "Te Atatu Peninsula": 5885.3, + "Takanini": 5907.1, + "Cihuatlán": 16107.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epsom: (-36.89°, 174.77°)", + " Moonee Ponds: (-37.77°, 144.92°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + " Takanini: (-37.04°, 174.93°)", + " Cihuatlán: (19.24°, -104.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cihuatlán: 16107.2 km from centroid", + " Takanini: 5907.1 km from centroid", + " Epsom: 5895.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cihuatlán", + "FINAL ANSWER: Cihuatlán" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.60954, + "lon": -1.42187, + "name": "Grove" + }, + { + "lat": 48.79947, + "lon": 9.79809, + "name": "Schwäbisch Gmünd" + }, + { + "lat": 50.72999, + "lon": -1.1621, + "name": "Ryde" + }, + { + "lat": 36.85868, + "lon": 14.75966, + "name": "Modica" + }, + { + "lat": 6.8773, + "lon": 37.93619, + "name": "Badessa" + } + ], + "question": "Which location is the geographic outlier among: Grove, Schwäbisch Gmünd, Ryde, Modica, Badessa?", + "ground_truth": { + "answer": "Badessa", + "outlier_distance_km": 4415.4, + "second_furthest_km": 1747.1, + "clarity_ratio": 2.53, + "median_distance_km": 1662.8, + "distances_to_centroid": { + "Grove": 1747.1, + "Schwäbisch Gmünd": 1106.2, + "Ryde": 1662.8, + "Modica": 338.7, + "Badessa": 4415.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Grove: (51.61°, -1.42°)", + " Schwäbisch Gmünd: (48.80°, 9.80°)", + " Ryde: (50.73°, -1.16°)", + " Modica: (36.86°, 14.76°)", + " Badessa: (6.88°, 37.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Badessa: 4415.4 km from centroid", + " Grove: 1747.1 km from centroid", + " Ryde: 1662.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Badessa", + "FINAL ANSWER: Badessa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.61841, + "lon": -60.15478, + "name": "Victoria" + }, + { + "lat": -15.32333, + "lon": -58.00361, + "name": "Lambari d'Oeste" + }, + { + "lat": -15.64667, + "lon": -56.1325, + "name": "Várzea Grande" + }, + { + "lat": -16.64944, + "lon": -49.48889, + "name": "Trindade" + }, + { + "lat": 31.41648, + "lon": 31.81332, + "name": "Damietta" + } + ], + "question": "Which location is the geographic outlier among: Victoria, Lambari d'Oeste, Várzea Grande, Trindade, Damietta?", + "ground_truth": { + "answer": "Damietta", + "outlier_distance_km": 8748.1, + "second_furthest_km": 3382.5, + "clarity_ratio": 2.59, + "median_distance_km": 2215.1, + "distances_to_centroid": { + "Victoria": 3382.5, + "Lambari d'Oeste": 2215.1, + "Várzea Grande": 2031.1, + "Trindade": 1423.6, + "Damietta": 8748.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Victoria: (-32.62°, -60.15°)", + " Lambari d'Oeste: (-15.32°, -58.00°)", + " Várzea Grande: (-15.65°, -56.13°)", + " Trindade: (-16.65°, -49.49°)", + " Damietta: (31.42°, 31.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Damietta: 8748.1 km from centroid", + " Victoria: 3382.5 km from centroid", + " Lambari d'Oeste: 2215.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Damietta", + "FINAL ANSWER: Damietta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.26394, + "lon": -56.97304, + "name": "Villa Gesell" + }, + { + "lat": -20.02745, + "lon": -40.74336, + "name": "Santa Maria de Jetibá" + }, + { + "lat": -25.45955, + "lon": -49.53014, + "name": "Campo Largo" + }, + { + "lat": -4.97139, + "lon": -39.01528, + "name": "Quixadá" + }, + { + "lat": 8.39307, + "lon": 8.35544, + "name": "Doma" + } + ], + "question": "Which location is the geographic outlier among: Villa Gesell, Santa Maria de Jetibá, Campo Largo, Quixadá, Doma?", + "ground_truth": { + "answer": "Doma", + "outlier_distance_km": 5538.4, + "second_furthest_km": 3175.6, + "clarity_ratio": 1.74, + "median_distance_km": 1798.8, + "distances_to_centroid": { + "Villa Gesell": 3175.6, + "Santa Maria de Jetibá": 715.6, + "Campo Largo": 1798.8, + "Quixadá": 1268.1, + "Doma": 5538.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Villa Gesell: (-37.26°, -56.97°)", + " Santa Maria de Jetibá: (-20.03°, -40.74°)", + " Campo Largo: (-25.46°, -49.53°)", + " Quixadá: (-4.97°, -39.02°)", + " Doma: (8.39°, 8.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doma: 5538.4 km from centroid", + " Villa Gesell: 3175.6 km from centroid", + " Campo Largo: 1798.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doma", + "FINAL ANSWER: Doma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.79417, + "lon": -52.62278, + "name": "Chapadão do Sul" + }, + { + "lat": -16.03095, + "lon": -48.02929, + "name": "Santa Maria" + }, + { + "lat": -6.79111, + "lon": -50.46694, + "name": "Água Azul do Norte" + }, + { + "lat": -3.87667, + "lon": -38.62556, + "name": "Maracanaú" + }, + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + } + ], + "question": "Which location is the geographic outlier among: Chapadão do Sul, Santa Maria, Água Azul do Norte, Maracanaú, Upper Coomera?", + "ground_truth": { + "answer": "Upper Coomera", + "outlier_distance_km": 14841.5, + "second_furthest_km": 4836.5, + "clarity_ratio": 3.07, + "median_distance_km": 4789.5, + "distances_to_centroid": { + "Chapadão do Sul": 4836.5, + "Santa Maria": 4363.9, + "Água Azul do Norte": 4789.5, + "Maracanaú": 3635.9, + "Upper Coomera": 14841.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chapadão do Sul: (-18.79°, -52.62°)", + " Santa Maria: (-16.03°, -48.03°)", + " Água Azul do Norte: (-6.79°, -50.47°)", + " Maracanaú: (-3.88°, -38.63°)", + " Upper Coomera: (-27.88°, 153.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upper Coomera: 14841.5 km from centroid", + " Chapadão do Sul: 4836.5 km from centroid", + " Água Azul do Norte: 4789.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upper Coomera", + "FINAL ANSWER: Upper Coomera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.72472, + "lon": -52.84972, + "name": "Espumoso" + }, + { + "lat": -20.86361, + "lon": -46.38806, + "name": "Alpinópolis" + }, + { + "lat": -23.5725, + "lon": -46.03861, + "name": "Biritiba Mirim" + }, + { + "lat": -28.6275, + "lon": -53.08972, + "name": "Ibirubá" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + } + ], + "question": "Which location is the geographic outlier among: Espumoso, Alpinópolis, Biritiba Mirim, Ibirubá, Caroline Springs?", + "ground_truth": { + "answer": "Caroline Springs", + "outlier_distance_km": 12280.5, + "second_furthest_km": 4127.5, + "clarity_ratio": 2.98, + "median_distance_km": 4102.7, + "distances_to_centroid": { + "Espumoso": 4102.7, + "Alpinópolis": 3682.0, + "Biritiba Mirim": 3557.4, + "Ibirubá": 4127.5, + "Caroline Springs": 12280.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Espumoso: (-28.72°, -52.85°)", + " Alpinópolis: (-20.86°, -46.39°)", + " Biritiba Mirim: (-23.57°, -46.04°)", + " Ibirubá: (-28.63°, -53.09°)", + " Caroline Springs: (-37.74°, 144.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caroline Springs: 12280.5 km from centroid", + " Ibirubá: 4127.5 km from centroid", + " Espumoso: 4102.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caroline Springs", + "FINAL ANSWER: Caroline Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.65851, + "lon": -17.91821, + "name": "Los Llanos de Aridane" + }, + { + "lat": 46.1165, + "lon": 8.29313, + "name": "Domodossola" + }, + { + "lat": 47.59206, + "lon": 7.55923, + "name": "Saint-Louis" + }, + { + "lat": 49.27732, + "lon": -0.7039, + "name": "Bayeux" + }, + { + "lat": -33.90034, + "lon": 151.05563, + "name": "Greenacre" + } + ], + "question": "Which location is the geographic outlier among: Los Llanos de Aridane, Domodossola, Saint-Louis, Bayeux, Greenacre?", + "ground_truth": { + "answer": "Greenacre", + "outlier_distance_km": 14443.4, + "second_furthest_km": 4636.6, + "clarity_ratio": 3.12, + "median_distance_km": 3539.3, + "distances_to_centroid": { + "Los Llanos de Aridane": 4636.6, + "Domodossola": 2788.8, + "Saint-Louis": 2938.4, + "Bayeux": 3539.3, + "Greenacre": 14443.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Los Llanos de Aridane: (28.66°, -17.92°)", + " Domodossola: (46.12°, 8.29°)", + " Saint-Louis: (47.59°, 7.56°)", + " Bayeux: (49.28°, -0.70°)", + " Greenacre: (-33.90°, 151.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greenacre: 14443.4 km from centroid", + " Los Llanos de Aridane: 4636.6 km from centroid", + " Bayeux: 3539.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greenacre", + "FINAL ANSWER: Greenacre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.42806, + "lon": -60.45944, + "name": "Manaquiri" + }, + { + "lat": -17.29972, + "lon": -48.27944, + "name": "Pires do Rio" + }, + { + "lat": -34.46971, + "lon": -58.52111, + "name": "San Isidro" + }, + { + "lat": -26.89972, + "lon": -48.82722, + "name": "Ilhota" + }, + { + "lat": 49.27738, + "lon": -123.07079, + "name": "Grandview-Woodlands" + } + ], + "question": "Which location is the geographic outlier among: Manaquiri, Pires do Rio, San Isidro, Ilhota, Grandview-Woodlands?", + "ground_truth": { + "answer": "Grandview-Woodlands", + "outlier_distance_km": 8180.3, + "second_furthest_km": 3246.8, + "clarity_ratio": 2.52, + "median_distance_km": 3025.0, + "distances_to_centroid": { + "Manaquiri": 887.9, + "Pires do Rio": 2435.7, + "San Isidro": 3246.8, + "Ilhota": 3025.0, + "Grandview-Woodlands": 8180.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manaquiri: (-3.43°, -60.46°)", + " Pires do Rio: (-17.30°, -48.28°)", + " San Isidro: (-34.47°, -58.52°)", + " Ilhota: (-26.90°, -48.83°)", + " Grandview-Woodlands: (49.28°, -123.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Grandview-Woodlands: 8180.3 km from centroid", + " San Isidro: 3246.8 km from centroid", + " Ilhota: 3025.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Grandview-Woodlands", + "FINAL ANSWER: Grandview-Woodlands" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.18848, + "lon": 28.32078, + "name": "Benoni" + }, + { + "lat": 28.35831, + "lon": 33.07829, + "name": "Ras Gharib" + }, + { + "lat": 11.08333, + "lon": 36.88333, + "name": "Ādīs K’idamē" + }, + { + "lat": -26.33172, + "lon": 26.32065, + "name": "Coligny" + }, + { + "lat": 40.80204, + "lon": -72.84094, + "name": "Mastic" + } + ], + "question": "Which location is the geographic outlier among: Benoni, Ras Gharib, Ādīs K’idamē, Coligny, Mastic?", + "ground_truth": { + "answer": "Mastic", + "outlier_distance_km": 9032.6, + "second_furthest_km": 4025.4, + "clarity_ratio": 2.24, + "median_distance_km": 3940.2, + "distances_to_centroid": { + "Benoni": 4025.4, + "Ras Gharib": 3488.8, + "Ādīs K’idamē": 2981.6, + "Coligny": 3940.2, + "Mastic": 9032.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Benoni: (-26.19°, 28.32°)", + " Ras Gharib: (28.36°, 33.08°)", + " Ādīs K’idamē: (11.08°, 36.88°)", + " Coligny: (-26.33°, 26.32°)", + " Mastic: (40.80°, -72.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mastic: 9032.6 km from centroid", + " Benoni: 4025.4 km from centroid", + " Coligny: 3940.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mastic", + "FINAL ANSWER: Mastic" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": -26.65682, + "lon": 153.07955, + "name": "Sunshine Coast" + }, + { + "lat": -19.30323, + "lon": 146.72531, + "name": "Kirwan" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": 26.39905, + "lon": 87.26525, + "name": "Jogbani" + } + ], + "question": "Which location is the geographic outlier among: Chatswood, Sunshine Coast, Kirwan, Bairnsdale, Jogbani?", + "ground_truth": { + "answer": "Jogbani", + "outlier_distance_km": 7324.8, + "second_furthest_km": 2402.7, + "clarity_ratio": 3.05, + "median_distance_km": 2220.9, + "distances_to_centroid": { + "Chatswood": 2220.9, + "Sunshine Coast": 1881.3, + "Kirwan": 1012.5, + "Bairnsdale": 2402.7, + "Jogbani": 7324.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chatswood: (-33.80°, 151.18°)", + " Sunshine Coast: (-26.66°, 153.08°)", + " Kirwan: (-19.30°, 146.73°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Jogbani: (26.40°, 87.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jogbani: 7324.8 km from centroid", + " Bairnsdale: 2402.7 km from centroid", + " Chatswood: 2220.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jogbani", + "FINAL ANSWER: Jogbani" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.85023, + "lon": 0.47095, + "name": "Bexhill-on-Sea" + }, + { + "lat": 43.92686, + "lon": 11.03718, + "name": "Montemurlo" + }, + { + "lat": 51.97995, + "lon": 7.78293, + "name": "Telgte" + }, + { + "lat": 37.18817, + "lon": -3.60667, + "name": "Granada" + }, + { + "lat": 11.35599, + "lon": 36.95449, + "name": "Gurbetē" + } + ], + "question": "Which location is the geographic outlier among: Bexhill-on-Sea, Montemurlo, Telgte, Granada, Gurbetē?", + "ground_truth": { + "answer": "Gurbetē", + "outlier_distance_km": 4037.7, + "second_furthest_km": 1528.2, + "clarity_ratio": 2.64, + "median_distance_km": 1452.2, + "distances_to_centroid": { + "Bexhill-on-Sea": 1528.2, + "Montemurlo": 542.8, + "Telgte": 1452.2, + "Granada": 1252.5, + "Gurbetē": 4037.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexhill-on-Sea: (50.85°, 0.47°)", + " Montemurlo: (43.93°, 11.04°)", + " Telgte: (51.98°, 7.78°)", + " Granada: (37.19°, -3.61°)", + " Gurbetē: (11.36°, 36.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gurbetē: 4037.7 km from centroid", + " Bexhill-on-Sea: 1528.2 km from centroid", + " Telgte: 1452.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gurbetē", + "FINAL ANSWER: Gurbetē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.15695, + "lon": 133.27331, + "name": "Arsen’yev" + }, + { + "lat": 50.13423, + "lon": 8.91418, + "name": "Hanau am Main" + }, + { + "lat": 59.62056, + "lon": 30.39, + "name": "Kommunar" + }, + { + "lat": 37.49025, + "lon": 14.06216, + "name": "Caltanissetta" + }, + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + } + ], + "question": "Which location is the geographic outlier among: Arsen’yev, Hanau am Main, Kommunar, Caltanissetta, Randwick?", + "ground_truth": { + "answer": "Randwick", + "outlier_distance_km": 11378.4, + "second_furthest_km": 5781.5, + "clarity_ratio": 1.97, + "median_distance_km": 5197.7, + "distances_to_centroid": { + "Arsen’yev": 5781.5, + "Hanau am Main": 5197.7, + "Kommunar": 4160.4, + "Caltanissetta": 4884.1, + "Randwick": 11378.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arsen’yev: (44.16°, 133.27°)", + " Hanau am Main: (50.13°, 8.91°)", + " Kommunar: (59.62°, 30.39°)", + " Caltanissetta: (37.49°, 14.06°)", + " Randwick: (-33.91°, 151.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Randwick: 11378.4 km from centroid", + " Arsen’yev: 5781.5 km from centroid", + " Hanau am Main: 5197.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Randwick", + "FINAL ANSWER: Randwick" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.91667, + "lon": 2.38333, + "name": "Aubervilliers" + }, + { + "lat": 48.07086, + "lon": 1.33783, + "name": "Châteaudun" + }, + { + "lat": 50.29301, + "lon": 2.78186, + "name": "Arras" + }, + { + "lat": 53.63738, + "lon": 9.91973, + "name": "Schnelsen" + }, + { + "lat": 43.11682, + "lon": -79.19958, + "name": "Thorold" + } + ], + "question": "Which location is the geographic outlier among: Aubervilliers, Châteaudun, Arras, Schnelsen, Thorold?", + "ground_truth": { + "answer": "Thorold", + "outlier_distance_km": 5023.5, + "second_furthest_km": 1646.5, + "clarity_ratio": 3.05, + "median_distance_km": 1116.7, + "distances_to_centroid": { + "Aubervilliers": 1091.1, + "Châteaudun": 1026.7, + "Arras": 1116.7, + "Schnelsen": 1646.5, + "Thorold": 5023.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aubervilliers: (48.92°, 2.38°)", + " Châteaudun: (48.07°, 1.34°)", + " Arras: (50.29°, 2.78°)", + " Schnelsen: (53.64°, 9.92°)", + " Thorold: (43.12°, -79.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thorold: 5023.5 km from centroid", + " Schnelsen: 1646.5 km from centroid", + " Arras: 1116.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thorold", + "FINAL ANSWER: Thorold" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.70241, + "lon": 41.72487, + "name": "Proletarsk" + }, + { + "lat": 43.70853, + "lon": 10.4036, + "name": "Pisa" + }, + { + "lat": 50.40959, + "lon": -4.22514, + "name": "Saltash" + }, + { + "lat": 51.16239, + "lon": 54.99157, + "name": "Sol’-Iletsk" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + } + ], + "question": "Which location is the geographic outlier among: Proletarsk, Pisa, Saltash, Sol’-Iletsk, Bracken Ridge?", + "ground_truth": { + "answer": "Bracken Ridge", + "outlier_distance_km": 12647.2, + "second_furthest_km": 4862.5, + "clarity_ratio": 2.6, + "median_distance_km": 3711.4, + "distances_to_centroid": { + "Proletarsk": 1728.2, + "Pisa": 3711.4, + "Saltash": 4862.5, + "Sol’-Iletsk": 2050.5, + "Bracken Ridge": 12647.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Proletarsk: (46.70°, 41.72°)", + " Pisa: (43.71°, 10.40°)", + " Saltash: (50.41°, -4.23°)", + " Sol’-Iletsk: (51.16°, 54.99°)", + " Bracken Ridge: (-27.32°, 153.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bracken Ridge: 12647.2 km from centroid", + " Saltash: 4862.5 km from centroid", + " Pisa: 3711.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bracken Ridge", + "FINAL ANSWER: Bracken Ridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.44203, + "lon": 76.53604, + "name": "Changanācheri" + }, + { + "lat": 9.26877, + "lon": 118.4043, + "name": "Narra" + }, + { + "lat": 39.3895, + "lon": 140.05813, + "name": "Yurihonjō" + }, + { + "lat": 23.07492, + "lon": 88.28637, + "name": "Pandua" + }, + { + "lat": -23.10083, + "lon": -45.70694, + "name": "Caçapava" + } + ], + "question": "Which location is the geographic outlier among: Changanācheri, Narra, Yurihonjō, Pandua, Caçapava?", + "ground_truth": { + "answer": "Caçapava", + "outlier_distance_km": 13687.5, + "second_furthest_km": 7011.2, + "clarity_ratio": 1.95, + "median_distance_km": 4693.1, + "distances_to_centroid": { + "Changanācheri": 266.1, + "Narra": 4693.1, + "Yurihonjō": 7011.2, + "Pandua": 1858.1, + "Caçapava": 13687.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Changanācheri: (9.44°, 76.54°)", + " Narra: (9.27°, 118.40°)", + " Yurihonjō: (39.39°, 140.06°)", + " Pandua: (23.07°, 88.29°)", + " Caçapava: (-23.10°, -45.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caçapava: 13687.5 km from centroid", + " Yurihonjō: 7011.2 km from centroid", + " Narra: 4693.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caçapava", + "FINAL ANSWER: Caçapava" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.33065, + "lon": -71.09116, + "name": "Roxbury Crossing" + }, + { + "lat": 26.10037, + "lon": -80.39977, + "name": "Weston" + }, + { + "lat": 41.70149, + "lon": -71.15505, + "name": "Fall River" + }, + { + "lat": 33.51736, + "lon": -82.07567, + "name": "Martinez" + }, + { + "lat": -29.04912, + "lon": 29.78232, + "name": "Wembesi" + } + ], + "question": "Which location is the geographic outlier among: Roxbury Crossing, Weston, Fall River, Martinez, Wembesi?", + "ground_truth": { + "answer": "Wembesi", + "outlier_distance_km": 10746.4, + "second_furthest_km": 2892.2, + "clarity_ratio": 3.72, + "median_distance_km": 2622.9, + "distances_to_centroid": { + "Roxbury Crossing": 2622.9, + "Weston": 2591.1, + "Fall River": 2572.9, + "Martinez": 2892.2, + "Wembesi": 10746.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Roxbury Crossing: (42.33°, -71.09°)", + " Weston: (26.10°, -80.40°)", + " Fall River: (41.70°, -71.16°)", + " Martinez: (33.52°, -82.08°)", + " Wembesi: (-29.05°, 29.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wembesi: 10746.4 km from centroid", + " Martinez: 2892.2 km from centroid", + " Roxbury Crossing: 2622.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wembesi", + "FINAL ANSWER: Wembesi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.66446, + "lon": 7.63421, + "name": "Werne" + }, + { + "lat": 52.22977, + "lon": 21.01178, + "name": "Warsaw" + }, + { + "lat": 48.83669, + "lon": 2.48255, + "name": "Nogent-sur-Marne" + }, + { + "lat": 50.54114, + "lon": 22.72204, + "name": "Biłgoraj" + }, + { + "lat": 38.70116, + "lon": -90.36234, + "name": "Overland" + } + ], + "question": "Which location is the geographic outlier among: Werne, Warsaw, Nogent-sur-Marne, Biłgoraj, Overland?", + "ground_truth": { + "answer": "Overland", + "outlier_distance_km": 6447.6, + "second_furthest_km": 2167.7, + "clarity_ratio": 2.97, + "median_distance_km": 2041.4, + "distances_to_centroid": { + "Werne": 1124.8, + "Warsaw": 2041.4, + "Nogent-sur-Marne": 720.5, + "Biłgoraj": 2167.7, + "Overland": 6447.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Werne: (51.66°, 7.63°)", + " Warsaw: (52.23°, 21.01°)", + " Nogent-sur-Marne: (48.84°, 2.48°)", + " Biłgoraj: (50.54°, 22.72°)", + " Overland: (38.70°, -90.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Overland: 6447.6 km from centroid", + " Biłgoraj: 2167.7 km from centroid", + " Warsaw: 2041.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Overland", + "FINAL ANSWER: Overland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + }, + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + { + "lat": 41.65726, + "lon": -87.68005, + "name": "Blue Island" + } + ], + "question": "Which location is the geographic outlier among: Bentleigh East, Karori, Glenferrie, Mernda, Blue Island?", + "ground_truth": { + "answer": "Blue Island", + "outlier_distance_km": 17613.1, + "second_furthest_km": 6763.3, + "clarity_ratio": 2.6, + "median_distance_km": 4214.0, + "distances_to_centroid": { + "Bentleigh East": 4214.0, + "Karori": 6763.3, + "Glenferrie": 4211.7, + "Mernda": 4210.4, + "Blue Island": 17613.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bentleigh East: (-37.92°, 145.05°)", + " Karori: (-41.28°, 174.74°)", + " Glenferrie: (-37.83°, 145.05°)", + " Mernda: (-37.60°, 145.10°)", + " Blue Island: (41.66°, -87.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blue Island: 17613.1 km from centroid", + " Karori: 6763.3 km from centroid", + " Bentleigh East: 4214.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blue Island", + "FINAL ANSWER: Blue Island" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.34927, + "lon": -3.0094, + "name": "Algorta" + }, + { + "lat": 55.78874, + "lon": 49.12214, + "name": "Kazan" + }, + { + "lat": 39.48139, + "lon": -0.43937, + "name": "Quart de Poblet" + }, + { + "lat": 50.91234, + "lon": -1.30076, + "name": "Hedge End" + }, + { + "lat": -0.0962, + "lon": 34.27322, + "name": "Bondo" + } + ], + "question": "Which location is the geographic outlier among: Algorta, Kazan, Quart de Poblet, Hedge End, Bondo?", + "ground_truth": { + "answer": "Bondo", + "outlier_distance_km": 4631.3, + "second_furthest_km": 3175.5, + "clarity_ratio": 1.46, + "median_distance_km": 1972.5, + "distances_to_centroid": { + "Algorta": 1689.6, + "Kazan": 3175.5, + "Quart de Poblet": 1412.6, + "Hedge End": 1972.5, + "Bondo": 4631.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Algorta: (43.35°, -3.01°)", + " Kazan: (55.79°, 49.12°)", + " Quart de Poblet: (39.48°, -0.44°)", + " Hedge End: (50.91°, -1.30°)", + " Bondo: (-0.10°, 34.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bondo: 4631.3 km from centroid", + " Kazan: 3175.5 km from centroid", + " Hedge End: 1972.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bondo", + "FINAL ANSWER: Bondo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.85009, + "lon": 8.199, + "name": "Dutsen Wai" + }, + { + "lat": 9.03333, + "lon": 38.15, + "name": "Gīnch’ī" + }, + { + "lat": -34.18307, + "lon": 22.14605, + "name": "Mossel Bay" + }, + { + "lat": 30.59683, + "lon": 30.89931, + "name": "Ash Shuhadā’" + }, + { + "lat": 41.74918, + "lon": -91.59795, + "name": "North Liberty" + } + ], + "question": "Which location is the geographic outlier among: Dutsen Wai, Gīnch’ī, Mossel Bay, Ash Shuhadā’, North Liberty?", + "ground_truth": { + "answer": "North Liberty", + "outlier_distance_km": 9409.4, + "second_furthest_km": 5537.0, + "clarity_ratio": 1.7, + "median_distance_km": 4010.5, + "distances_to_centroid": { + "Dutsen Wai": 729.1, + "Gīnch’ī": 4010.5, + "Mossel Bay": 5537.0, + "Ash Shuhadā’": 3683.9, + "North Liberty": 9409.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dutsen Wai: (10.85°, 8.20°)", + " Gīnch’ī: (9.03°, 38.15°)", + " Mossel Bay: (-34.18°, 22.15°)", + " Ash Shuhadā’: (30.60°, 30.90°)", + " North Liberty: (41.75°, -91.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " North Liberty: 9409.4 km from centroid", + " Mossel Bay: 5537.0 km from centroid", + " Gīnch’ī: 4010.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: North Liberty", + "FINAL ANSWER: North Liberty" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.43569, + "lon": -123.41174, + "name": "Esquimalt" + }, + { + "lat": 31.31716, + "lon": -113.53799, + "name": "Puerto Peñasco" + }, + { + "lat": 19.62749, + "lon": -103.41752, + "name": "Zapotiltic" + }, + { + "lat": 18.86861, + "lon": -99.20833, + "name": "Tres de Mayo" + }, + { + "lat": 50.96983, + "lon": 6.92997, + "name": "Bilderstöckchen" + } + ], + "question": "Which location is the geographic outlier among: Esquimalt, Puerto Peñasco, Zapotiltic, Tres de Mayo, Bilderstöckchen?", + "ground_truth": { + "answer": "Bilderstöckchen", + "outlier_distance_km": 7378.3, + "second_furthest_km": 3443.4, + "clarity_ratio": 2.14, + "median_distance_km": 2538.9, + "distances_to_centroid": { + "Esquimalt": 3443.4, + "Puerto Peñasco": 2538.9, + "Zapotiltic": 2298.3, + "Tres de Mayo": 2086.0, + "Bilderstöckchen": 7378.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Esquimalt: (48.44°, -123.41°)", + " Puerto Peñasco: (31.32°, -113.54°)", + " Zapotiltic: (19.63°, -103.42°)", + " Tres de Mayo: (18.87°, -99.21°)", + " Bilderstöckchen: (50.97°, 6.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bilderstöckchen: 7378.3 km from centroid", + " Esquimalt: 3443.4 km from centroid", + " Puerto Peñasco: 2538.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bilderstöckchen", + "FINAL ANSWER: Bilderstöckchen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.80167, + "lon": 128.50083, + "name": "Hwawŏn" + }, + { + "lat": 30.9525, + "lon": 118.75528, + "name": "Xuancheng" + }, + { + "lat": 35.64595, + "lon": 139.7155, + "name": "Ebisu" + }, + { + "lat": 28.25382, + "lon": 77.85535, + "name": "Khurja" + }, + { + "lat": -27.68806, + "lon": -48.77861, + "name": "Santo Amaro da Imperatriz" + } + ], + "question": "Which location is the geographic outlier among: Hwawŏn, Xuancheng, Ebisu, Khurja, Santo Amaro da Imperatriz?", + "ground_truth": { + "answer": "Santo Amaro da Imperatriz", + "outlier_distance_km": 15109.8, + "second_furthest_km": 5708.1, + "clarity_ratio": 2.65, + "median_distance_km": 4701.3, + "distances_to_centroid": { + "Hwawŏn": 4701.3, + "Xuancheng": 3722.5, + "Ebisu": 5708.1, + "Khurja": 1009.3, + "Santo Amaro da Imperatriz": 15109.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hwawŏn: (35.80°, 128.50°)", + " Xuancheng: (30.95°, 118.76°)", + " Ebisu: (35.65°, 139.72°)", + " Khurja: (28.25°, 77.86°)", + " Santo Amaro da Imperatriz: (-27.69°, -48.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santo Amaro da Imperatriz: 15109.8 km from centroid", + " Ebisu: 5708.1 km from centroid", + " Hwawŏn: 4701.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santo Amaro da Imperatriz", + "FINAL ANSWER: Santo Amaro da Imperatriz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.55877, + "lon": 75.35305, + "name": "Navalgund" + }, + { + "lat": 26.03613, + "lon": 80.57617, + "name": "Bindki" + }, + { + "lat": 25.41961, + "lon": 83.55786, + "name": "Zamānia" + }, + { + "lat": 11.09246, + "lon": 77.31225, + "name": "Andipalayam" + }, + { + "lat": -23.68611, + "lon": -46.62278, + "name": "Diadema" + } + ], + "question": "Which location is the geographic outlier among: Navalgund, Bindki, Zamānia, Andipalayam, Diadema?", + "ground_truth": { + "answer": "Diadema", + "outlier_distance_km": 11565.9, + "second_furthest_km": 3500.3, + "clarity_ratio": 3.3, + "median_distance_km": 3255.7, + "distances_to_centroid": { + "Navalgund": 2364.0, + "Bindki": 3255.7, + "Zamānia": 3500.3, + "Andipalayam": 2540.3, + "Diadema": 11565.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Navalgund: (15.56°, 75.35°)", + " Bindki: (26.04°, 80.58°)", + " Zamānia: (25.42°, 83.56°)", + " Andipalayam: (11.09°, 77.31°)", + " Diadema: (-23.69°, -46.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Diadema: 11565.9 km from centroid", + " Zamānia: 3500.3 km from centroid", + " Bindki: 3255.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Diadema", + "FINAL ANSWER: Diadema" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.56246, + "lon": 76.625, + "name": "Alwar" + }, + { + "lat": -6.93889, + "lon": 107.75278, + "name": "Cileunyi" + }, + { + "lat": 11.4134, + "lon": 76.69521, + "name": "Ooty" + }, + { + "lat": 25.31232, + "lon": 100.27983, + "name": "Miaojie" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + } + ], + "question": "Which location is the geographic outlier among: Alwar, Cileunyi, Ooty, Miaojie, Caroline Springs?", + "ground_truth": { + "answer": "Caroline Springs", + "outlier_distance_km": 6446.9, + "second_furthest_km": 3702.3, + "clarity_ratio": 1.74, + "median_distance_km": 2825.6, + "distances_to_centroid": { + "Alwar": 3702.3, + "Cileunyi": 1408.7, + "Ooty": 2825.6, + "Miaojie": 2380.6, + "Caroline Springs": 6446.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alwar: (27.56°, 76.62°)", + " Cileunyi: (-6.94°, 107.75°)", + " Ooty: (11.41°, 76.70°)", + " Miaojie: (25.31°, 100.28°)", + " Caroline Springs: (-37.74°, 144.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caroline Springs: 6446.9 km from centroid", + " Alwar: 3702.3 km from centroid", + " Ooty: 2825.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caroline Springs", + "FINAL ANSWER: Caroline Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.93726, + "lon": 41.85688, + "name": "Mandera" + }, + { + "lat": 31.32977, + "lon": 31.71507, + "name": "Fāraskūr" + }, + { + "lat": 5.75279, + "lon": 45.64603, + "name": "Kahandhale" + }, + { + "lat": 11.35599, + "lon": 36.95449, + "name": "Gurbetē" + }, + { + "lat": 24.1839, + "lon": 88.27171, + "name": "Murshidābād" + } + ], + "question": "Which location is the geographic outlier among: Mandera, Fāraskūr, Kahandhale, Gurbetē, Murshidābād?", + "ground_truth": { + "answer": "Murshidābād", + "outlier_distance_km": 4223.0, + "second_furthest_km": 2492.5, + "clarity_ratio": 1.69, + "median_distance_km": 1480.5, + "distances_to_centroid": { + "Mandera": 1480.5, + "Fāraskūr": 2492.5, + "Kahandhale": 1120.3, + "Gurbetē": 1363.7, + "Murshidābād": 4223.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mandera: (3.94°, 41.86°)", + " Fāraskūr: (31.33°, 31.72°)", + " Kahandhale: (5.75°, 45.65°)", + " Gurbetē: (11.36°, 36.95°)", + " Murshidābād: (24.18°, 88.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Murshidābād: 4223.0 km from centroid", + " Fāraskūr: 2492.5 km from centroid", + " Mandera: 1480.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Murshidābād", + "FINAL ANSWER: Murshidābād" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.5471, + "lon": 121.972, + "name": "Bungku" + }, + { + "lat": 25.03639, + "lon": 101.54556, + "name": "Chuxiong" + }, + { + "lat": 38.15479, + "lon": 114.80689, + "name": "Beisu" + }, + { + "lat": 20.37175, + "lon": 72.90493, + "name": "Vapi" + }, + { + "lat": -29.91778, + "lon": -51.18361, + "name": "Canoas" + } + ], + "question": "Which location is the geographic outlier among: Bungku, Chuxiong, Beisu, Vapi, Canoas?", + "ground_truth": { + "answer": "Canoas", + "outlier_distance_km": 13759.6, + "second_furthest_km": 5709.8, + "clarity_ratio": 2.41, + "median_distance_km": 5265.8, + "distances_to_centroid": { + "Bungku": 5709.8, + "Chuxiong": 3524.2, + "Beisu": 5265.8, + "Vapi": 1132.9, + "Canoas": 13759.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bungku: (-2.55°, 121.97°)", + " Chuxiong: (25.04°, 101.55°)", + " Beisu: (38.15°, 114.81°)", + " Vapi: (20.37°, 72.90°)", + " Canoas: (-29.92°, -51.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Canoas: 13759.6 km from centroid", + " Bungku: 5709.8 km from centroid", + " Beisu: 5265.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Canoas", + "FINAL ANSWER: Canoas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.93139, + "lon": -48.95889, + "name": "Gaspar" + }, + { + "lat": -23.99306, + "lon": -46.25639, + "name": "Guarujá" + }, + { + "lat": -18.16583, + "lon": -47.94639, + "name": "Catalão" + }, + { + "lat": -30.89083, + "lon": -55.53278, + "name": "Sant'Ana do Livramento" + }, + { + "lat": 51.925, + "lon": 6.58056, + "name": "Aalten" + } + ], + "question": "Which location is the geographic outlier among: Gaspar, Guarujá, Catalão, Sant'Ana do Livramento, Aalten?", + "ground_truth": { + "answer": "Aalten", + "outlier_distance_km": 8076.4, + "second_furthest_km": 2954.7, + "clarity_ratio": 2.73, + "median_distance_km": 2221.2, + "distances_to_centroid": { + "Gaspar": 2221.2, + "Guarujá": 1802.2, + "Catalão": 1399.7, + "Sant'Ana do Livramento": 2954.7, + "Aalten": 8076.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gaspar: (-26.93°, -48.96°)", + " Guarujá: (-23.99°, -46.26°)", + " Catalão: (-18.17°, -47.95°)", + " Sant'Ana do Livramento: (-30.89°, -55.53°)", + " Aalten: (51.92°, 6.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aalten: 8076.4 km from centroid", + " Sant'Ana do Livramento: 2954.7 km from centroid", + " Gaspar: 2221.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aalten", + "FINAL ANSWER: Aalten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.61171, + "lon": 40.65023, + "name": "Gus’-Khrustal’nyy" + }, + { + "lat": 41.60742, + "lon": 12.54158, + "name": "Ardea" + }, + { + "lat": 52.15, + "lon": 11.63333, + "name": "Neue Neustadt" + }, + { + "lat": 52.3475, + "lon": 5.98333, + "name": "Epe" + }, + { + "lat": -26.10639, + "lon": -50.32222, + "name": "Três Barras" + } + ], + "question": "Which location is the geographic outlier among: Gus’-Khrustal’nyy, Ardea, Neue Neustadt, Epe, Três Barras?", + "ground_truth": { + "answer": "Três Barras", + "outlier_distance_km": 8892.1, + "second_furthest_km": 3584.3, + "clarity_ratio": 2.48, + "median_distance_km": 1985.6, + "distances_to_centroid": { + "Gus’-Khrustal’nyy": 3584.3, + "Ardea": 1029.6, + "Neue Neustadt": 1985.6, + "Epe": 1921.2, + "Três Barras": 8892.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gus’-Khrustal’nyy: (55.61°, 40.65°)", + " Ardea: (41.61°, 12.54°)", + " Neue Neustadt: (52.15°, 11.63°)", + " Epe: (52.35°, 5.98°)", + " Três Barras: (-26.11°, -50.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Três Barras: 8892.1 km from centroid", + " Gus’-Khrustal’nyy: 3584.3 km from centroid", + " Neue Neustadt: 1985.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Três Barras", + "FINAL ANSWER: Três Barras" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.02789, + "lon": -74.86905, + "name": "Willingboro" + }, + { + "lat": 49.22219, + "lon": -123.00588, + "name": "Maywood" + }, + { + "lat": 32.45821, + "lon": -83.73157, + "name": "Perry" + }, + { + "lat": 44.05011, + "lon": -79.46631, + "name": "Newmarket" + }, + { + "lat": 6.22482, + "lon": 124.71042, + "name": "Lake Sebu" + } + ], + "question": "Which location is the geographic outlier among: Willingboro, Maywood, Perry, Newmarket, Lake Sebu?", + "ground_truth": { + "answer": "Lake Sebu", + "outlier_distance_km": 15420.3, + "second_furthest_km": 6216.1, + "clarity_ratio": 2.48, + "median_distance_km": 3372.2, + "distances_to_centroid": { + "Willingboro": 2511.7, + "Maywood": 6216.1, + "Perry": 3372.2, + "Newmarket": 2950.6, + "Lake Sebu": 15420.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Willingboro: (40.03°, -74.87°)", + " Maywood: (49.22°, -123.01°)", + " Perry: (32.46°, -83.73°)", + " Newmarket: (44.05°, -79.47°)", + " Lake Sebu: (6.22°, 124.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lake Sebu: 15420.3 km from centroid", + " Maywood: 6216.1 km from centroid", + " Perry: 3372.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lake Sebu", + "FINAL ANSWER: Lake Sebu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.2874, + "lon": 97.7884, + "name": "Singkil" + }, + { + "lat": 17.67023, + "lon": 74.03469, + "name": "Kodoli" + }, + { + "lat": 34.91611, + "lon": 118.63889, + "name": "Xiazhuang" + }, + { + "lat": 8.36972, + "lon": 124.86444, + "name": "Manolo Fortich" + }, + { + "lat": 33.56042, + "lon": -81.71955, + "name": "Aiken" + } + ], + "question": "Which location is the geographic outlier among: Singkil, Kodoli, Xiazhuang, Manolo Fortich, Aiken?", + "ground_truth": { + "answer": "Aiken", + "outlier_distance_km": 13245.5, + "second_furthest_km": 6366.4, + "clarity_ratio": 2.08, + "median_distance_km": 5356.3, + "distances_to_centroid": { + "Singkil": 3874.5, + "Kodoli": 793.6, + "Xiazhuang": 5356.3, + "Manolo Fortich": 6366.4, + "Aiken": 13245.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Singkil: (2.29°, 97.79°)", + " Kodoli: (17.67°, 74.03°)", + " Xiazhuang: (34.92°, 118.64°)", + " Manolo Fortich: (8.37°, 124.86°)", + " Aiken: (33.56°, -81.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aiken: 13245.5 km from centroid", + " Manolo Fortich: 6366.4 km from centroid", + " Xiazhuang: 5356.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aiken", + "FINAL ANSWER: Aiken" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.73542, + "lon": 8.56771, + "name": "Monte Rosello" + }, + { + "lat": 51.61667, + "lon": 5.54861, + "name": "Veghel" + }, + { + "lat": 52.35088, + "lon": 14.56065, + "name": "Słubice" + }, + { + "lat": 41.9908, + "lon": 12.09082, + "name": "Cerveteri" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + } + ], + "question": "Which location is the geographic outlier among: Monte Rosello, Veghel, Słubice, Cerveteri, Bendigo?", + "ground_truth": { + "answer": "Bendigo", + "outlier_distance_km": 13381.1, + "second_furthest_km": 3528.3, + "clarity_ratio": 3.79, + "median_distance_km": 3089.7, + "distances_to_centroid": { + "Monte Rosello": 2825.8, + "Veghel": 3528.3, + "Słubice": 3089.7, + "Cerveteri": 2594.7, + "Bendigo": 13381.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Monte Rosello: (40.74°, 8.57°)", + " Veghel: (51.62°, 5.55°)", + " Słubice: (52.35°, 14.56°)", + " Cerveteri: (41.99°, 12.09°)", + " Bendigo: (-36.76°, 144.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bendigo: 13381.1 km from centroid", + " Veghel: 3528.3 km from centroid", + " Słubice: 3089.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bendigo", + "FINAL ANSWER: Bendigo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.56917, + "lon": -81.54396, + "name": "Ocoee" + }, + { + "lat": 42.8078, + "lon": -87.92425, + "name": "Caledonia" + }, + { + "lat": 32.39091, + "lon": -110.96649, + "name": "Oro Valley" + }, + { + "lat": 33.61983, + "lon": -86.60888, + "name": "Trussville" + }, + { + "lat": -6.96333, + "lon": -35.69167, + "name": "Areia" + } + ], + "question": "Which location is the geographic outlier among: Ocoee, Caledonia, Oro Valley, Trussville, Areia?", + "ground_truth": { + "answer": "Areia", + "outlier_distance_km": 6075.9, + "second_furthest_km": 3022.7, + "clarity_ratio": 2.01, + "median_distance_km": 1976.7, + "distances_to_centroid": { + "Ocoee": 293.3, + "Caledonia": 1976.7, + "Oro Valley": 3022.7, + "Trussville": 1021.1, + "Areia": 6075.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ocoee: (28.57°, -81.54°)", + " Caledonia: (42.81°, -87.92°)", + " Oro Valley: (32.39°, -110.97°)", + " Trussville: (33.62°, -86.61°)", + " Areia: (-6.96°, -35.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Areia: 6075.9 km from centroid", + " Oro Valley: 3022.7 km from centroid", + " Caledonia: 1976.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Areia", + "FINAL ANSWER: Areia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.04159, + "lon": -35.62699, + "name": "Alagoa Grande" + }, + { + "lat": -3.60556, + "lon": -55.33167, + "name": "Aveiro" + }, + { + "lat": -32.43289, + "lon": -63.24811, + "name": "Villa Nueva" + }, + { + "lat": 5.20856, + "lon": -74.73584, + "name": "Honda" + }, + { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + } + ], + "question": "Which location is the geographic outlier among: Alagoa Grande, Aveiro, Villa Nueva, Honda, Paralowie?", + "ground_truth": { + "answer": "Paralowie", + "outlier_distance_km": 14007.0, + "second_furthest_km": 6620.5, + "clarity_ratio": 2.12, + "median_distance_km": 4973.9, + "distances_to_centroid": { + "Alagoa Grande": 2089.2, + "Aveiro": 4260.0, + "Villa Nueva": 4973.9, + "Honda": 6620.5, + "Paralowie": 14007.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alagoa Grande: (-7.04°, -35.63°)", + " Aveiro: (-3.61°, -55.33°)", + " Villa Nueva: (-32.43°, -63.25°)", + " Honda: (5.21°, -74.74°)", + " Paralowie: (-34.76°, 138.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paralowie: 14007.0 km from centroid", + " Honda: 6620.5 km from centroid", + " Villa Nueva: 4973.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paralowie", + "FINAL ANSWER: Paralowie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.91806, + "lon": -54.84417, + "name": "Rio Verde de Mato Grosso" + }, + { + "lat": -22.83917, + "lon": -42.10278, + "name": "São Pedro da Aldeia" + }, + { + "lat": -26.82333, + "lon": -49.27167, + "name": "Timbó" + }, + { + "lat": -23.35611, + "lon": -46.87694, + "name": "Cajamar" + }, + { + "lat": 7.46478, + "lon": 5.42333, + "name": "Ise-Ekiti" + } + ], + "question": "Which location is the geographic outlier among: Rio Verde de Mato Grosso, São Pedro da Aldeia, Timbó, Cajamar, Ise-Ekiti?", + "ground_truth": { + "answer": "Ise-Ekiti", + "outlier_distance_km": 5444.1, + "second_furthest_km": 1844.5, + "clarity_ratio": 2.95, + "median_distance_km": 1637.1, + "distances_to_centroid": { + "Rio Verde de Mato Grosso": 1844.5, + "São Pedro da Aldeia": 815.4, + "Timbó": 1637.1, + "Cajamar": 1210.8, + "Ise-Ekiti": 5444.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rio Verde de Mato Grosso: (-18.92°, -54.84°)", + " São Pedro da Aldeia: (-22.84°, -42.10°)", + " Timbó: (-26.82°, -49.27°)", + " Cajamar: (-23.36°, -46.88°)", + " Ise-Ekiti: (7.46°, 5.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ise-Ekiti: 5444.1 km from centroid", + " Rio Verde de Mato Grosso: 1844.5 km from centroid", + " Timbó: 1637.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ise-Ekiti", + "FINAL ANSWER: Ise-Ekiti" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.86874, + "lon": 6.09317, + "name": "Herzogenrath" + }, + { + "lat": 53.62937, + "lon": 11.41316, + "name": "Schwerin" + }, + { + "lat": 43.60717, + "lon": 13.5103, + "name": "Ancona" + }, + { + "lat": 45.37411, + "lon": 44.2198, + "name": "Arzgir" + }, + { + "lat": 14.11168, + "lon": 78.15982, + "name": "Kadiri" + } + ], + "question": "Which location is the geographic outlier among: Herzogenrath, Schwerin, Ancona, Arzgir, Kadiri?", + "ground_truth": { + "answer": "Kadiri", + "outlier_distance_km": 5479.6, + "second_furthest_km": 2144.7, + "clarity_ratio": 2.55, + "median_distance_km": 1963.6, + "distances_to_centroid": { + "Herzogenrath": 2144.7, + "Schwerin": 1963.6, + "Ancona": 1422.5, + "Arzgir": 1172.4, + "Kadiri": 5479.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Herzogenrath: (50.87°, 6.09°)", + " Schwerin: (53.63°, 11.41°)", + " Ancona: (43.61°, 13.51°)", + " Arzgir: (45.37°, 44.22°)", + " Kadiri: (14.11°, 78.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kadiri: 5479.6 km from centroid", + " Herzogenrath: 2144.7 km from centroid", + " Schwerin: 1963.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kadiri", + "FINAL ANSWER: Kadiri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.27081, + "lon": 99.87203, + "name": "Sam Roi Yot" + }, + { + "lat": 21.85523, + "lon": 70.24791, + "name": "Bhāyāvadar" + }, + { + "lat": 35.36667, + "lon": 136.53333, + "name": "Tarui" + }, + { + "lat": 11.08416, + "lon": 106.78834, + "name": "Uyen Hung" + }, + { + "lat": -6.23169, + "lon": -77.86903, + "name": "Chachapoyas" + } + ], + "question": "Which location is the geographic outlier among: Sam Roi Yot, Bhāyāvadar, Tarui, Uyen Hung, Chachapoyas?", + "ground_truth": { + "answer": "Chachapoyas", + "outlier_distance_km": 16074.5, + "second_furthest_km": 7206.7, + "clarity_ratio": 2.23, + "median_distance_km": 4314.0, + "distances_to_centroid": { + "Sam Roi Yot": 3549.5, + "Bhāyāvadar": 844.2, + "Tarui": 7206.7, + "Uyen Hung": 4314.0, + "Chachapoyas": 16074.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sam Roi Yot: (12.27°, 99.87°)", + " Bhāyāvadar: (21.86°, 70.25°)", + " Tarui: (35.37°, 136.53°)", + " Uyen Hung: (11.08°, 106.79°)", + " Chachapoyas: (-6.23°, -77.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chachapoyas: 16074.5 km from centroid", + " Tarui: 7206.7 km from centroid", + " Uyen Hung: 4314.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chachapoyas", + "FINAL ANSWER: Chachapoyas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.87159, + "lon": -122.27275, + "name": "Berkeley" + }, + { + "lat": 32.50931, + "lon": -92.1193, + "name": "Monroe" + }, + { + "lat": 39.98483, + "lon": -75.14712, + "name": "Hartranft" + }, + { + "lat": 32.94818, + "lon": -96.72972, + "name": "Richardson" + }, + { + "lat": 12.78612, + "lon": 77.63855, + "name": "Jigani" + } + ], + "question": "Which location is the geographic outlier among: Berkeley, Monroe, Hartranft, Richardson, Jigani?", + "ground_truth": { + "answer": "Jigani", + "outlier_distance_km": 13477.9, + "second_furthest_km": 5498.4, + "clarity_ratio": 2.45, + "median_distance_km": 3288.3, + "distances_to_centroid": { + "Berkeley": 5498.4, + "Monroe": 2864.2, + "Hartranft": 1553.3, + "Richardson": 3288.3, + "Jigani": 13477.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Berkeley: (37.87°, -122.27°)", + " Monroe: (32.51°, -92.12°)", + " Hartranft: (39.98°, -75.15°)", + " Richardson: (32.95°, -96.73°)", + " Jigani: (12.79°, 77.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jigani: 13477.9 km from centroid", + " Berkeley: 5498.4 km from centroid", + " Richardson: 3288.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jigani", + "FINAL ANSWER: Jigani" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.59217, + "lon": -70.6996, + "name": "San Bernardo" + }, + { + "lat": -7.11389, + "lon": -34.97806, + "name": "Santa Rita" + }, + { + "lat": -26.96083, + "lon": -50.42694, + "name": "Santa Cecília" + }, + { + "lat": -18.90556, + "lon": -40.07611, + "name": "Jaguaré" + }, + { + "lat": 38.67877, + "lon": -121.35114, + "name": "Foothill Farms" + } + ], + "question": "Which location is the geographic outlier among: San Bernardo, Santa Rita, Santa Cecília, Jaguaré, Foothill Farms?", + "ground_truth": { + "answer": "Foothill Farms", + "outlier_distance_km": 8028.3, + "second_furthest_km": 3149.6, + "clarity_ratio": 2.55, + "median_distance_km": 2769.6, + "distances_to_centroid": { + "San Bernardo": 2769.6, + "Santa Rita": 3149.6, + "Santa Cecília": 2371.2, + "Jaguaré": 2725.8, + "Foothill Farms": 8028.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Bernardo: (-33.59°, -70.70°)", + " Santa Rita: (-7.11°, -34.98°)", + " Santa Cecília: (-26.96°, -50.43°)", + " Jaguaré: (-18.91°, -40.08°)", + " Foothill Farms: (38.68°, -121.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Foothill Farms: 8028.3 km from centroid", + " Santa Rita: 3149.6 km from centroid", + " San Bernardo: 2769.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Foothill Farms", + "FINAL ANSWER: Foothill Farms" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.78438, + "lon": -4.10007, + "name": "High Blantyre" + }, + { + "lat": 53.60554, + "lon": 8.59509, + "name": "Langen" + }, + { + "lat": 51.11357, + "lon": -0.86245, + "name": "Bordon" + }, + { + "lat": 45.22338, + "lon": 11.66379, + "name": "Este" + }, + { + "lat": 6.41919, + "lon": 45.85251, + "name": "Raqo" + } + ], + "question": "Which location is the geographic outlier among: High Blantyre, Langen, Bordon, Este, Raqo?", + "ground_truth": { + "answer": "Raqo", + "outlier_distance_km": 5189.4, + "second_furthest_km": 1892.3, + "clarity_ratio": 2.74, + "median_distance_km": 1384.2, + "distances_to_centroid": { + "High Blantyre": 1892.3, + "Langen": 1271.4, + "Bordon": 1384.2, + "Este": 314.0, + "Raqo": 5189.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " High Blantyre: (55.78°, -4.10°)", + " Langen: (53.61°, 8.60°)", + " Bordon: (51.11°, -0.86°)", + " Este: (45.22°, 11.66°)", + " Raqo: (6.42°, 45.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Raqo: 5189.4 km from centroid", + " High Blantyre: 1892.3 km from centroid", + " Bordon: 1384.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Raqo", + "FINAL ANSWER: Raqo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.20856, + "lon": -74.73584, + "name": "Honda" + }, + { + "lat": -24.65028, + "lon": -50.85056, + "name": "Reserva" + }, + { + "lat": -23.18111, + "lon": -50.64667, + "name": "Cornélio Procópio" + }, + { + "lat": -22.4167, + "lon": -42.97822, + "name": "Teresópolis" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + } + ], + "question": "Which location is the geographic outlier among: Honda, Reserva, Cornélio Procópio, Teresópolis, Mangere East?", + "ground_truth": { + "answer": "Mangere East", + "outlier_distance_km": 13624.4, + "second_furthest_km": 7728.7, + "clarity_ratio": 1.76, + "median_distance_km": 4320.7, + "distances_to_centroid": { + "Honda": 7728.7, + "Reserva": 4320.7, + "Cornélio Procópio": 4309.3, + "Teresópolis": 3529.9, + "Mangere East": 13624.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Honda: (5.21°, -74.74°)", + " Reserva: (-24.65°, -50.85°)", + " Cornélio Procópio: (-23.18°, -50.65°)", + " Teresópolis: (-22.42°, -42.98°)", + " Mangere East: (-36.97°, 174.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mangere East: 13624.4 km from centroid", + " Honda: 7728.7 km from centroid", + " Reserva: 4320.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mangere East", + "FINAL ANSWER: Mangere East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.39028, + "lon": -40.49611, + "name": "Viana" + }, + { + "lat": -29.8175, + "lon": -50.51972, + "name": "Santo Antônio da Patrulha" + }, + { + "lat": -23.57595, + "lon": -46.46298, + "name": "Parque Do Carmo" + }, + { + "lat": -29.46694, + "lon": -51.96139, + "name": "Lajeado" + }, + { + "lat": 47.86278, + "lon": -122.29497, + "name": "Picnic Point-North Lynnwood" + } + ], + "question": "Which location is the geographic outlier among: Viana, Santo Antônio da Patrulha, Parque Do Carmo, Lajeado, Picnic Point-North Lynnwood?", + "ground_truth": { + "answer": "Picnic Point-North Lynnwood", + "outlier_distance_km": 8807.5, + "second_furthest_km": 2553.8, + "clarity_ratio": 3.45, + "median_distance_km": 2416.8, + "distances_to_centroid": { + "Viana": 2553.8, + "Santo Antônio da Patrulha": 2416.8, + "Parque Do Carmo": 2181.3, + "Lajeado": 2310.9, + "Picnic Point-North Lynnwood": 8807.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viana: (-20.39°, -40.50°)", + " Santo Antônio da Patrulha: (-29.82°, -50.52°)", + " Parque Do Carmo: (-23.58°, -46.46°)", + " Lajeado: (-29.47°, -51.96°)", + " Picnic Point-North Lynnwood: (47.86°, -122.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Picnic Point-North Lynnwood: 8807.5 km from centroid", + " Viana: 2553.8 km from centroid", + " Santo Antônio da Patrulha: 2416.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Picnic Point-North Lynnwood", + "FINAL ANSWER: Picnic Point-North Lynnwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.16027, + "lon": 101.51501, + "name": "Denai Alam" + }, + { + "lat": 13.66035, + "lon": 77.21239, + "name": "Madhugiri" + }, + { + "lat": 20.31379, + "lon": 77.34178, + "name": "Mangrūl Pīr" + }, + { + "lat": 25.45887, + "lon": 78.57994, + "name": "Jhānsi" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + } + ], + "question": "Which location is the geographic outlier among: Denai Alam, Madhugiri, Mangrūl Pīr, Jhānsi, Redbank Plains?", + "ground_truth": { + "answer": "Redbank Plains", + "outlier_distance_km": 7081.2, + "second_furthest_km": 2872.5, + "clarity_ratio": 2.47, + "median_distance_km": 2629.1, + "distances_to_centroid": { + "Denai Alam": 615.5, + "Madhugiri": 2338.5, + "Mangrūl Pīr": 2629.1, + "Jhānsi": 2872.5, + "Redbank Plains": 7081.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Denai Alam: (3.16°, 101.52°)", + " Madhugiri: (13.66°, 77.21°)", + " Mangrūl Pīr: (20.31°, 77.34°)", + " Jhānsi: (25.46°, 78.58°)", + " Redbank Plains: (-27.65°, 152.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Redbank Plains: 7081.2 km from centroid", + " Jhānsi: 2872.5 km from centroid", + " Mangrūl Pīr: 2629.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Redbank Plains", + "FINAL ANSWER: Redbank Plains" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.60962, + "lon": 85.48076, + "name": "Mahnar Bazar" + }, + { + "lat": 29.765, + "lon": 105.66645, + "name": "Zhong’ao" + }, + { + "lat": 20.57806, + "lon": 86.56063, + "name": "Patāmundai" + }, + { + "lat": 30.24506, + "lon": 75.84488, + "name": "Sangrūr" + }, + { + "lat": 33.66198, + "lon": -112.34127, + "name": "Sun City West" + } + ], + "question": "Which location is the geographic outlier among: Mahnar Bazar, Zhong’ao, Patāmundai, Sangrūr, Sun City West?", + "ground_truth": { + "answer": "Sun City West", + "outlier_distance_km": 12862.7, + "second_furthest_km": 5536.0, + "clarity_ratio": 2.32, + "median_distance_km": 3953.4, + "distances_to_centroid": { + "Mahnar Bazar": 3691.5, + "Zhong’ao": 5536.0, + "Patāmundai": 3953.4, + "Sangrūr": 2686.9, + "Sun City West": 12862.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mahnar Bazar: (25.61°, 85.48°)", + " Zhong’ao: (29.77°, 105.67°)", + " Patāmundai: (20.58°, 86.56°)", + " Sangrūr: (30.25°, 75.84°)", + " Sun City West: (33.66°, -112.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sun City West: 12862.7 km from centroid", + " Zhong’ao: 5536.0 km from centroid", + " Patāmundai: 3953.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sun City West", + "FINAL ANSWER: Sun City West" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.6083, + "lon": -43.70948, + "name": "Paracambi" + }, + { + "lat": -22.40389, + "lon": -43.6625, + "name": "Vassouras" + }, + { + "lat": -27.00833, + "lon": -51.15167, + "name": "Videira" + }, + { + "lat": -34.59391, + "lon": -60.94644, + "name": "Junín" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + } + ], + "question": "Which location is the geographic outlier among: Paracambi, Vassouras, Videira, Junín, Redbank Plains?", + "ground_truth": { + "answer": "Redbank Plains", + "outlier_distance_km": 13663.2, + "second_furthest_km": 4955.9, + "clarity_ratio": 2.76, + "median_distance_km": 4127.2, + "distances_to_centroid": { + "Paracambi": 3494.3, + "Vassouras": 3495.6, + "Videira": 4127.2, + "Junín": 4955.9, + "Redbank Plains": 13663.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paracambi: (-22.61°, -43.71°)", + " Vassouras: (-22.40°, -43.66°)", + " Videira: (-27.01°, -51.15°)", + " Junín: (-34.59°, -60.95°)", + " Redbank Plains: (-27.65°, 152.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Redbank Plains: 13663.2 km from centroid", + " Junín: 4955.9 km from centroid", + " Videira: 4127.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Redbank Plains", + "FINAL ANSWER: Redbank Plains" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.40148, + "lon": -1.32471, + "name": "Newbury" + }, + { + "lat": 52.30083, + "lon": 4.86389, + "name": "Amstelveen" + }, + { + "lat": 52.8568, + "lon": 19.66913, + "name": "Sierpc" + }, + { + "lat": 61.06919, + "lon": 42.0992, + "name": "Vel’sk" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + } + ], + "question": "Which location is the geographic outlier among: Newbury, Amstelveen, Sierpc, Vel’sk, Sunbury?", + "ground_truth": { + "answer": "Sunbury", + "outlier_distance_km": 13341.1, + "second_furthest_km": 3808.7, + "clarity_ratio": 3.5, + "median_distance_km": 3418.1, + "distances_to_centroid": { + "Newbury": 3808.7, + "Amstelveen": 3418.1, + "Sierpc": 2558.7, + "Vel’sk": 2786.4, + "Sunbury": 13341.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newbury: (51.40°, -1.32°)", + " Amstelveen: (52.30°, 4.86°)", + " Sierpc: (52.86°, 19.67°)", + " Vel’sk: (61.07°, 42.10°)", + " Sunbury: (-37.58°, 144.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunbury: 13341.1 km from centroid", + " Newbury: 3808.7 km from centroid", + " Amstelveen: 3418.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunbury", + "FINAL ANSWER: Sunbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.03333, + "lon": 145.35, + "name": "Berwick" + }, + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": 40.62483, + "lon": -74.14848, + "name": "Graniteville" + } + ], + "question": "Which location is the geographic outlier among: Berwick, Burwood, Maryborough, Tamworth, Graniteville?", + "ground_truth": { + "answer": "Graniteville", + "outlier_distance_km": 17452.3, + "second_furthest_km": 4967.3, + "clarity_ratio": 3.51, + "median_distance_km": 4895.4, + "distances_to_centroid": { + "Berwick": 4507.9, + "Burwood": 4895.4, + "Maryborough": 4967.3, + "Tamworth": 4833.7, + "Graniteville": 17452.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Berwick: (-38.03°, 145.35°)", + " Burwood: (-33.88°, 151.10°)", + " Maryborough: (-25.54°, 152.70°)", + " Tamworth: (-31.09°, 150.93°)", + " Graniteville: (40.62°, -74.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Graniteville: 17452.3 km from centroid", + " Maryborough: 4967.3 km from centroid", + " Burwood: 4895.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Graniteville", + "FINAL ANSWER: Graniteville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.82634, + "lon": 100.21906, + "name": "Huangshan" + }, + { + "lat": 6.5225, + "lon": 124.65917, + "name": "Norala" + }, + { + "lat": 15.0711, + "lon": 120.5423, + "name": "Porac" + }, + { + "lat": 26.00239, + "lon": 78.87658, + "name": "Daboh" + }, + { + "lat": 25.90175, + "lon": -97.49748, + "name": "Brownsville" + } + ], + "question": "Which location is the geographic outlier among: Huangshan, Norala, Porac, Daboh, Brownsville?", + "ground_truth": { + "answer": "Brownsville", + "outlier_distance_km": 14579.1, + "second_furthest_km": 6557.6, + "clarity_ratio": 2.22, + "median_distance_km": 5851.3, + "distances_to_centroid": { + "Huangshan": 3622.8, + "Norala": 6557.6, + "Porac": 5851.3, + "Daboh": 1531.3, + "Brownsville": 14579.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huangshan: (26.83°, 100.22°)", + " Norala: (6.52°, 124.66°)", + " Porac: (15.07°, 120.54°)", + " Daboh: (26.00°, 78.88°)", + " Brownsville: (25.90°, -97.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brownsville: 14579.1 km from centroid", + " Norala: 6557.6 km from centroid", + " Porac: 5851.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brownsville", + "FINAL ANSWER: Brownsville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -41.21667, + "lon": 174.91667, + "name": "Lower Hutt" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -40.81519, + "lon": -63.0004, + "name": "Viedma" + } + ], + "question": "Which location is the geographic outlier among: Newcastle, Cairns, Lower Hutt, Truganina, Viedma?", + "ground_truth": { + "answer": "Viedma", + "outlier_distance_km": 11678.7, + "second_furthest_km": 5576.8, + "clarity_ratio": 2.09, + "median_distance_km": 3956.5, + "distances_to_centroid": { + "Newcastle": 3774.9, + "Cairns": 3956.5, + "Lower Hutt": 5576.8, + "Truganina": 3068.2, + "Viedma": 11678.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newcastle: (-32.93°, 151.78°)", + " Cairns: (-16.92°, 145.77°)", + " Lower Hutt: (-41.22°, 174.92°)", + " Truganina: (-37.82°, 144.75°)", + " Viedma: (-40.82°, -63.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viedma: 11678.7 km from centroid", + " Lower Hutt: 5576.8 km from centroid", + " Cairns: 3956.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viedma", + "FINAL ANSWER: Viedma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.88076, + "lon": 27.39377, + "name": "Qonce" + }, + { + "lat": 6.65581, + "lon": 6.38494, + "name": "Ubiaja" + }, + { + "lat": 10.28969, + "lon": 11.16729, + "name": "Gombe" + }, + { + "lat": 9.86709, + "lon": 11.22594, + "name": "Biliri" + }, + { + "lat": 10.44036, + "lon": 76.09483, + "name": "Talikkulam" + } + ], + "question": "Which location is the geographic outlier among: Qonce, Ubiaja, Gombe, Biliri, Talikkulam?", + "ground_truth": { + "answer": "Talikkulam", + "outlier_distance_km": 5586.7, + "second_furthest_km": 3754.7, + "clarity_ratio": 1.49, + "median_distance_km": 2316.7, + "distances_to_centroid": { + "Qonce": 3754.7, + "Ubiaja": 2316.7, + "Gombe": 1987.7, + "Biliri": 1958.5, + "Talikkulam": 5586.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Qonce: (-32.88°, 27.39°)", + " Ubiaja: (6.66°, 6.38°)", + " Gombe: (10.29°, 11.17°)", + " Biliri: (9.87°, 11.23°)", + " Talikkulam: (10.44°, 76.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Talikkulam: 5586.7 km from centroid", + " Qonce: 3754.7 km from centroid", + " Ubiaja: 2316.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Talikkulam", + "FINAL ANSWER: Talikkulam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.79068, + "lon": 150.6693, + "name": "Glenmore Park" + }, + { + "lat": -33.41665, + "lon": 149.5806, + "name": "Bathurst" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -37.69863, + "lon": 144.78631, + "name": "Taylors Lakes" + }, + { + "lat": 1.01572, + "lon": 35.00622, + "name": "Kitale" + } + ], + "question": "Which location is the geographic outlier among: Glenmore Park, Bathurst, Townsville, Taylors Lakes, Kitale?", + "ground_truth": { + "answer": "Kitale", + "outlier_distance_km": 10091.3, + "second_furthest_km": 2649.1, + "clarity_ratio": 3.81, + "median_distance_km": 2540.7, + "distances_to_centroid": { + "Glenmore Park": 2649.1, + "Bathurst": 2540.7, + "Townsville": 2287.0, + "Taylors Lakes": 2341.9, + "Kitale": 10091.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenmore Park: (-33.79°, 150.67°)", + " Bathurst: (-33.42°, 149.58°)", + " Townsville: (-19.27°, 146.81°)", + " Taylors Lakes: (-37.70°, 144.79°)", + " Kitale: (1.02°, 35.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kitale: 10091.3 km from centroid", + " Glenmore Park: 2649.1 km from centroid", + " Bathurst: 2540.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kitale", + "FINAL ANSWER: Kitale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.92136, + "lon": 8.55183, + "name": "Verbania" + }, + { + "lat": 40.41409, + "lon": -3.66553, + "name": "Estrella" + }, + { + "lat": 55.84244, + "lon": 38.19362, + "name": "Monino" + }, + { + "lat": 51.39894, + "lon": 7.18557, + "name": "Hattingen" + }, + { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + } + ], + "question": "Which location is the geographic outlier among: Verbania, Estrella, Monino, Hattingen, Warwick?", + "ground_truth": { + "answer": "Warwick", + "outlier_distance_km": 13562.9, + "second_furthest_km": 3973.2, + "clarity_ratio": 3.41, + "median_distance_km": 3367.1, + "distances_to_centroid": { + "Verbania": 3059.8, + "Estrella": 3973.2, + "Monino": 2538.1, + "Hattingen": 3367.1, + "Warwick": 13562.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Verbania: (45.92°, 8.55°)", + " Estrella: (40.41°, -3.67°)", + " Monino: (55.84°, 38.19°)", + " Hattingen: (51.40°, 7.19°)", + " Warwick: (-28.22°, 152.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Warwick: 13562.9 km from centroid", + " Estrella: 3973.2 km from centroid", + " Hattingen: 3367.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Warwick", + "FINAL ANSWER: Warwick" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.43054, + "lon": -76.5199, + "name": "Cali" + }, + { + "lat": -43.24895, + "lon": -65.30505, + "name": "Trelew" + }, + { + "lat": -1.8, + "lon": -53.48, + "name": "Prainha" + }, + { + "lat": -22.15214, + "lon": -42.92335, + "name": "São José do Vale do Rio Preto" + }, + { + "lat": 37.28766, + "lon": -6.0541, + "name": "Coria del Río" + } + ], + "question": "Which location is the geographic outlier among: Cali, Trelew, Prainha, São José do Vale do Rio Preto, Coria del Río?", + "ground_truth": { + "answer": "Coria del Río", + "outlier_distance_km": 6483.8, + "second_furthest_km": 4518.7, + "clarity_ratio": 1.43, + "median_distance_km": 3222.2, + "distances_to_centroid": { + "Cali": 3222.2, + "Trelew": 4518.7, + "Prainha": 643.7, + "São José do Vale do Rio Preto": 1979.9, + "Coria del Río": 6483.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cali: (3.43°, -76.52°)", + " Trelew: (-43.25°, -65.31°)", + " Prainha: (-1.80°, -53.48°)", + " São José do Vale do Rio Preto: (-22.15°, -42.92°)", + " Coria del Río: (37.29°, -6.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coria del Río: 6483.8 km from centroid", + " Trelew: 4518.7 km from centroid", + " Cali: 3222.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coria del Río", + "FINAL ANSWER: Coria del Río" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.63006, + "lon": -43.9009, + "name": "Lagoa Santa" + }, + { + "lat": -27.32534, + "lon": -61.28101, + "name": "General Pinedo" + }, + { + "lat": -29.68861, + "lon": -51.46111, + "name": "Montenegro" + }, + { + "lat": -21.13778, + "lon": -48.97278, + "name": "Catanduva" + }, + { + "lat": 26.74906, + "lon": 33.93891, + "name": "Safaga" + } + ], + "question": "Which location is the geographic outlier among: Lagoa Santa, General Pinedo, Montenegro, Catanduva, Safaga?", + "ground_truth": { + "answer": "Safaga", + "outlier_distance_km": 8659.7, + "second_furthest_km": 3147.8, + "clarity_ratio": 2.75, + "median_distance_km": 2460.0, + "distances_to_centroid": { + "Lagoa Santa": 1182.4, + "General Pinedo": 3147.8, + "Montenegro": 2460.0, + "Catanduva": 1730.3, + "Safaga": 8659.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lagoa Santa: (-19.63°, -43.90°)", + " General Pinedo: (-27.33°, -61.28°)", + " Montenegro: (-29.69°, -51.46°)", + " Catanduva: (-21.14°, -48.97°)", + " Safaga: (26.75°, 33.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Safaga: 8659.7 km from centroid", + " General Pinedo: 3147.8 km from centroid", + " Montenegro: 2460.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Safaga", + "FINAL ANSWER: Safaga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.06703, + "lon": 115.61309, + "name": "Huacheng" + }, + { + "lat": 8.6561, + "lon": 123.4227, + "name": "Dapitan" + }, + { + "lat": -8.3939, + "lon": 114.1464, + "name": "Gambiran Satu" + }, + { + "lat": 29.69505, + "lon": 77.67964, + "name": "Deoband" + }, + { + "lat": 40.14477, + "lon": -84.24244, + "name": "Piqua" + } + ], + "question": "Which location is the geographic outlier among: Huacheng, Dapitan, Gambiran Satu, Deoband, Piqua?", + "ground_truth": { + "answer": "Piqua", + "outlier_distance_km": 12908.2, + "second_furthest_km": 5929.6, + "clarity_ratio": 2.18, + "median_distance_km": 5771.3, + "distances_to_centroid": { + "Huacheng": 4805.0, + "Dapitan": 5929.6, + "Gambiran Satu": 5771.3, + "Deoband": 1473.9, + "Piqua": 12908.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huacheng: (24.07°, 115.61°)", + " Dapitan: (8.66°, 123.42°)", + " Gambiran Satu: (-8.39°, 114.15°)", + " Deoband: (29.70°, 77.68°)", + " Piqua: (40.14°, -84.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piqua: 12908.2 km from centroid", + " Dapitan: 5929.6 km from centroid", + " Gambiran Satu: 5771.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piqua", + "FINAL ANSWER: Piqua" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.41648, + "lon": 31.81332, + "name": "Damietta" + }, + { + "lat": 30.12303, + "lon": 31.13571, + "name": "Awsīm" + }, + { + "lat": 12.03219, + "lon": 39.04756, + "name": "Lalibela" + }, + { + "lat": 31.11174, + "lon": 30.93991, + "name": "Kafr ash Shaykh" + }, + { + "lat": 37.6525, + "lon": 127.3075, + "name": "Hwado" + } + ], + "question": "Which location is the geographic outlier among: Damietta, Awsīm, Lalibela, Kafr ash Shaykh, Hwado?", + "ground_truth": { + "answer": "Hwado", + "outlier_distance_km": 6902.7, + "second_furthest_km": 2271.7, + "clarity_ratio": 3.04, + "median_distance_km": 2055.0, + "distances_to_centroid": { + "Damietta": 1974.2, + "Awsīm": 2033.5, + "Lalibela": 2271.7, + "Kafr ash Shaykh": 2055.0, + "Hwado": 6902.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Damietta: (31.42°, 31.81°)", + " Awsīm: (30.12°, 31.14°)", + " Lalibela: (12.03°, 39.05°)", + " Kafr ash Shaykh: (31.11°, 30.94°)", + " Hwado: (37.65°, 127.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hwado: 6902.7 km from centroid", + " Lalibela: 2271.7 km from centroid", + " Kafr ash Shaykh: 2055.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hwado", + "FINAL ANSWER: Hwado" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.96667, + "lon": 140.05, + "name": "Kuroiso" + }, + { + "lat": 14.11356, + "lon": 121.55574, + "name": "Lucban" + }, + { + "lat": -7.54595, + "lon": 112.23307, + "name": "Jombang" + }, + { + "lat": 34.66667, + "lon": 136.46667, + "name": "Hisai-motomachi" + }, + { + "lat": 31.21452, + "lon": 31.35798, + "name": "Bilqās" + } + ], + "question": "Which location is the geographic outlier among: Kuroiso, Lucban, Jombang, Hisai-motomachi, Bilqās?", + "ground_truth": { + "answer": "Bilqās", + "outlier_distance_km": 7579.0, + "second_furthest_km": 3476.0, + "clarity_ratio": 2.18, + "median_distance_km": 3299.9, + "distances_to_centroid": { + "Kuroiso": 3476.0, + "Lucban": 1642.3, + "Jombang": 3299.9, + "Hisai-motomachi": 3085.0, + "Bilqās": 7579.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kuroiso: (36.97°, 140.05°)", + " Lucban: (14.11°, 121.56°)", + " Jombang: (-7.55°, 112.23°)", + " Hisai-motomachi: (34.67°, 136.47°)", + " Bilqās: (31.21°, 31.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bilqās: 7579.0 km from centroid", + " Kuroiso: 3476.0 km from centroid", + " Jombang: 3299.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bilqās", + "FINAL ANSWER: Bilqās" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.58007, + "lon": 10.04067, + "name": "Barmbek-Süd" + }, + { + "lat": 51.36803, + "lon": -0.3065, + "name": "Hook" + }, + { + "lat": 49.04, + "lon": 3.95922, + "name": "Épernay" + }, + { + "lat": 51.47475, + "lon": -0.15547, + "name": "Battersea" + }, + { + "lat": 21.3374, + "lon": -158.09676, + "name": "Makakilo / Kapolei / Honokai Hale" + } + ], + "question": "Which location is the geographic outlier among: Barmbek-Süd, Hook, Épernay, Battersea, Makakilo / Kapolei / Honokai Hale?", + "ground_truth": { + "answer": "Makakilo / Kapolei / Honokai Hale", + "outlier_distance_km": 10996.6, + "second_furthest_km": 2917.4, + "clarity_ratio": 3.77, + "median_distance_km": 2496.7, + "distances_to_centroid": { + "Barmbek-Süd": 2917.4, + "Hook": 2200.1, + "Épernay": 2496.7, + "Battersea": 2211.9, + "Makakilo / Kapolei / Honokai Hale": 10996.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Barmbek-Süd: (53.58°, 10.04°)", + " Hook: (51.37°, -0.31°)", + " Épernay: (49.04°, 3.96°)", + " Battersea: (51.47°, -0.16°)", + " Makakilo / Kapolei / Honokai Hale: (21.34°, -158.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Makakilo / Kapolei / Honokai Hale: 10996.6 km from centroid", + " Barmbek-Süd: 2917.4 km from centroid", + " Épernay: 2496.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Makakilo / Kapolei / Honokai Hale", + "FINAL ANSWER: Makakilo / Kapolei / Honokai Hale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.11982, + "lon": 1.19012, + "name": "Aflao" + }, + { + "lat": 7.63527, + "lon": 4.18156, + "name": "Iwo" + }, + { + "lat": 7.06667, + "lon": 37.7, + "name": "Āreka" + }, + { + "lat": 31.3073, + "lon": 30.2981, + "name": "Idkū" + }, + { + "lat": 42.95947, + "lon": -85.48975, + "name": "Forest Hills" + } + ], + "question": "Which location is the geographic outlier among: Aflao, Iwo, Āreka, Idkū, Forest Hills?", + "ground_truth": { + "answer": "Forest Hills", + "outlier_distance_km": 8028.9, + "second_furthest_km": 4531.7, + "clarity_ratio": 1.77, + "median_distance_km": 3548.0, + "distances_to_centroid": { + "Aflao": 1486.6, + "Iwo": 1452.8, + "Āreka": 4531.7, + "Idkū": 3548.0, + "Forest Hills": 8028.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aflao: (6.12°, 1.19°)", + " Iwo: (7.64°, 4.18°)", + " Āreka: (7.07°, 37.70°)", + " Idkū: (31.31°, 30.30°)", + " Forest Hills: (42.96°, -85.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Forest Hills: 8028.9 km from centroid", + " Āreka: 4531.7 km from centroid", + " Idkū: 3548.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Forest Hills", + "FINAL ANSWER: Forest Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.52526, + "lon": 9.33297, + "name": "Cernusco sul Naviglio" + }, + { + "lat": 40.25038, + "lon": -3.83062, + "name": "Humanes de Madrid" + }, + { + "lat": 43.92686, + "lon": 11.03718, + "name": "Montemurlo" + }, + { + "lat": 41.44809, + "lon": 2.17519, + "name": "les Roquetes" + }, + { + "lat": 33.41477, + "lon": -111.90931, + "name": "Tempe" + } + ], + "question": "Which location is the geographic outlier among: Cernusco sul Naviglio, Humanes de Madrid, Montemurlo, les Roquetes, Tempe?", + "ground_truth": { + "answer": "Tempe", + "outlier_distance_km": 7900.9, + "second_furthest_km": 2445.5, + "clarity_ratio": 3.23, + "median_distance_km": 2311.3, + "distances_to_centroid": { + "Cernusco sul Naviglio": 2311.3, + "Humanes de Madrid": 1251.2, + "Montemurlo": 2445.5, + "les Roquetes": 1738.7, + "Tempe": 7900.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cernusco sul Naviglio: (45.53°, 9.33°)", + " Humanes de Madrid: (40.25°, -3.83°)", + " Montemurlo: (43.93°, 11.04°)", + " les Roquetes: (41.45°, 2.18°)", + " Tempe: (33.41°, -111.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tempe: 7900.9 km from centroid", + " Montemurlo: 2445.5 km from centroid", + " Cernusco sul Naviglio: 2311.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tempe", + "FINAL ANSWER: Tempe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -38.68333, + "lon": 176.08333, + "name": "Taupo" + }, + { + "lat": 33.65983, + "lon": -85.83163, + "name": "Anniston" + } + ], + "question": "Which location is the geographic outlier among: Lidcombe, Seven Hills, Melbourne City Centre, Taupo, Anniston?", + "ground_truth": { + "answer": "Anniston", + "outlier_distance_km": 18187.0, + "second_furthest_km": 6682.8, + "clarity_ratio": 2.72, + "median_distance_km": 4440.7, + "distances_to_centroid": { + "Lidcombe": 4440.7, + "Seven Hills": 4430.1, + "Melbourne City Centre": 3980.1, + "Taupo": 6682.8, + "Anniston": 18187.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lidcombe: (-33.86°, 151.04°)", + " Seven Hills: (-33.78°, 150.93°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Taupo: (-38.68°, 176.08°)", + " Anniston: (33.66°, -85.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Anniston: 18187.0 km from centroid", + " Taupo: 6682.8 km from centroid", + " Lidcombe: 4440.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Anniston", + "FINAL ANSWER: Anniston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.61161, + "lon": -75.45624, + "name": "Aguadas" + }, + { + "lat": -23.56202, + "lon": -46.4913, + "name": "Cidade Lider" + }, + { + "lat": -1.89528, + "lon": -49.38056, + "name": "Limoeiro do Ajuru" + }, + { + "lat": -5.10667, + "lon": -38.3725, + "name": "Morada Nova" + }, + { + "lat": 22.53333, + "lon": 72.9, + "name": "Vallabh Vidyanagar" + } + ], + "question": "Which location is the geographic outlier among: Aguadas, Cidade Lider, Limoeiro do Ajuru, Morada Nova, Vallabh Vidyanagar?", + "ground_truth": { + "answer": "Vallabh Vidyanagar", + "outlier_distance_km": 11081.4, + "second_furthest_km": 5382.6, + "clarity_ratio": 2.06, + "median_distance_km": 3293.3, + "distances_to_centroid": { + "Aguadas": 5382.6, + "Cidade Lider": 3293.3, + "Limoeiro do Ajuru": 2453.0, + "Morada Nova": 1326.4, + "Vallabh Vidyanagar": 11081.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aguadas: (5.61°, -75.46°)", + " Cidade Lider: (-23.56°, -46.49°)", + " Limoeiro do Ajuru: (-1.90°, -49.38°)", + " Morada Nova: (-5.11°, -38.37°)", + " Vallabh Vidyanagar: (22.53°, 72.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vallabh Vidyanagar: 11081.4 km from centroid", + " Aguadas: 5382.6 km from centroid", + " Cidade Lider: 3293.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vallabh Vidyanagar", + "FINAL ANSWER: Vallabh Vidyanagar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.20849, + "lon": 78.26173, + "name": "Dibai" + }, + { + "lat": 39.39528, + "lon": 121.96694, + "name": "Pulandian" + }, + { + "lat": 29.03028, + "lon": 106.97028, + "name": "Conglin" + }, + { + "lat": 10.80268, + "lon": 76.21855, + "name": "Ongallur-I" + }, + { + "lat": -38.18333, + "lon": 145.08333, + "name": "Mount Eliza" + } + ], + "question": "Which location is the geographic outlier among: Dibai, Pulandian, Conglin, Ongallur-I, Mount Eliza?", + "ground_truth": { + "answer": "Mount Eliza", + "outlier_distance_km": 7091.5, + "second_furthest_km": 3256.1, + "clarity_ratio": 2.18, + "median_distance_km": 3252.2, + "distances_to_centroid": { + "Dibai": 3252.2, + "Pulandian": 3256.1, + "Conglin": 1693.0, + "Ongallur-I": 3218.4, + "Mount Eliza": 7091.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dibai: (28.21°, 78.26°)", + " Pulandian: (39.40°, 121.97°)", + " Conglin: (29.03°, 106.97°)", + " Ongallur-I: (10.80°, 76.22°)", + " Mount Eliza: (-38.18°, 145.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Eliza: 7091.5 km from centroid", + " Pulandian: 3256.1 km from centroid", + " Dibai: 3252.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Eliza", + "FINAL ANSWER: Mount Eliza" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -38.04369, + "lon": 145.2923, + "name": "Narre Warren South" + }, + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": 5.30383, + "lon": -1.98956, + "name": "Tarkwa" + } + ], + "question": "Which location is the geographic outlier among: Bexley, Narre Warren South, Newcastle, Altona Meadows, Tarkwa?", + "ground_truth": { + "answer": "Tarkwa", + "outlier_distance_km": 13246.5, + "second_furthest_km": 3268.7, + "clarity_ratio": 4.05, + "median_distance_km": 3212.7, + "distances_to_centroid": { + "Bexley": 3212.7, + "Narre Warren South": 2777.7, + "Newcastle": 3268.7, + "Altona Meadows": 2729.9, + "Tarkwa": 13246.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexley: (-33.95°, 151.12°)", + " Narre Warren South: (-38.04°, 145.29°)", + " Newcastle: (-32.93°, 151.78°)", + " Altona Meadows: (-37.88°, 144.78°)", + " Tarkwa: (5.30°, -1.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tarkwa: 13246.5 km from centroid", + " Newcastle: 3268.7 km from centroid", + " Bexley: 3212.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tarkwa", + "FINAL ANSWER: Tarkwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.3145, + "lon": -81.83569, + "name": "Strongsville" + }, + { + "lat": 25.64724, + "lon": -100.09582, + "name": "Ciudad Benito Juárez" + }, + { + "lat": 41.5067, + "lon": -90.51513, + "name": "Moline" + }, + { + "lat": 19.68028, + "lon": -99.01, + "name": "Ojo de Agua" + }, + { + "lat": -11.78444, + "lon": -38.35306, + "name": "Inhambupe" + } + ], + "question": "Which location is the geographic outlier among: Strongsville, Ciudad Benito Juárez, Moline, Ojo de Agua, Inhambupe?", + "ground_truth": { + "answer": "Inhambupe", + "outlier_distance_km": 6140.1, + "second_furthest_km": 2177.9, + "clarity_ratio": 2.82, + "median_distance_km": 2006.2, + "distances_to_centroid": { + "Strongsville": 2006.2, + "Ciudad Benito Juárez": 1852.8, + "Moline": 2177.9, + "Ojo de Agua": 1807.4, + "Inhambupe": 6140.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Strongsville: (41.31°, -81.84°)", + " Ciudad Benito Juárez: (25.65°, -100.10°)", + " Moline: (41.51°, -90.52°)", + " Ojo de Agua: (19.68°, -99.01°)", + " Inhambupe: (-11.78°, -38.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Inhambupe: 6140.1 km from centroid", + " Moline: 2177.9 km from centroid", + " Strongsville: 2006.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Inhambupe", + "FINAL ANSWER: Inhambupe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": 31.32977, + "lon": 31.71507, + "name": "Fāraskūr" + } + ], + "question": "Which location is the geographic outlier among: Bairnsdale, Perth, Maitland, Tamworth, Fāraskūr?", + "ground_truth": { + "answer": "Fāraskūr", + "outlier_distance_km": 10974.9, + "second_furthest_km": 3446.7, + "clarity_ratio": 3.18, + "median_distance_km": 3344.4, + "distances_to_centroid": { + "Bairnsdale": 3319.4, + "Perth": 1329.8, + "Maitland": 3446.7, + "Tamworth": 3344.4, + "Fāraskūr": 10974.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bairnsdale: (-37.82°, 147.61°)", + " Perth: (-31.95°, 115.86°)", + " Maitland: (-32.73°, 151.56°)", + " Tamworth: (-31.09°, 150.93°)", + " Fāraskūr: (31.33°, 31.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fāraskūr: 10974.9 km from centroid", + " Maitland: 3446.7 km from centroid", + " Tamworth: 3344.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fāraskūr", + "FINAL ANSWER: Fāraskūr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.46355, + "lon": 77.35478, + "name": "Banat" + }, + { + "lat": 36.62554, + "lon": 101.75739, + "name": "Xining" + }, + { + "lat": 3.17822, + "lon": 101.70312, + "name": "Titiwangsa" + }, + { + "lat": 24.7113, + "lon": 98.6532, + "name": "Tuantian" + }, + { + "lat": 44.81135, + "lon": -91.49849, + "name": "Eau Claire" + } + ], + "question": "Which location is the geographic outlier among: Banat, Xining, Titiwangsa, Tuantian, Eau Claire?", + "ground_truth": { + "answer": "Eau Claire", + "outlier_distance_km": 11358.1, + "second_furthest_km": 5413.2, + "clarity_ratio": 2.1, + "median_distance_km": 4232.6, + "distances_to_centroid": { + "Banat": 1936.0, + "Xining": 4232.6, + "Titiwangsa": 5413.2, + "Tuantian": 4090.7, + "Eau Claire": 11358.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banat: (29.46°, 77.35°)", + " Xining: (36.63°, 101.76°)", + " Titiwangsa: (3.18°, 101.70°)", + " Tuantian: (24.71°, 98.65°)", + " Eau Claire: (44.81°, -91.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eau Claire: 11358.1 km from centroid", + " Titiwangsa: 5413.2 km from centroid", + " Xining: 4232.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eau Claire", + "FINAL ANSWER: Eau Claire" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.97631, + "lon": 128.32361, + "name": "Goseong" + }, + { + "lat": 5.83333, + "lon": 100.75, + "name": "Sik" + }, + { + "lat": 20.54875, + "lon": 78.83978, + "name": "Hinganghāt" + }, + { + "lat": 25.05575, + "lon": 98.39993, + "name": "Zhonghe" + }, + { + "lat": -13.255, + "lon": -43.41806, + "name": "Bom Jesus da Lapa" + } + ], + "question": "Which location is the geographic outlier among: Goseong, Sik, Hinganghāt, Zhonghe, Bom Jesus da Lapa?", + "ground_truth": { + "answer": "Bom Jesus da Lapa", + "outlier_distance_km": 13130.1, + "second_furthest_km": 5978.6, + "clarity_ratio": 2.2, + "median_distance_km": 3230.0, + "distances_to_centroid": { + "Goseong": 5978.6, + "Sik": 3230.0, + "Hinganghāt": 934.2, + "Zhonghe": 2931.6, + "Bom Jesus da Lapa": 13130.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Goseong: (34.98°, 128.32°)", + " Sik: (5.83°, 100.75°)", + " Hinganghāt: (20.55°, 78.84°)", + " Zhonghe: (25.06°, 98.40°)", + " Bom Jesus da Lapa: (-13.26°, -43.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bom Jesus da Lapa: 13130.1 km from centroid", + " Goseong: 5978.6 km from centroid", + " Sik: 3230.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bom Jesus da Lapa", + "FINAL ANSWER: Bom Jesus da Lapa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -16.68528, + "lon": -44.365, + "name": "Coração de Jesus" + }, + { + "lat": -25.5302, + "lon": -49.20836, + "name": "São José dos Pinhais" + }, + { + "lat": -1.71464, + "lon": -49.53152, + "name": "São Sebastião da Boa Vista" + }, + { + "lat": -26.30444, + "lon": -48.84556, + "name": "Joinville" + }, + { + "lat": 56.80239, + "lon": 59.93774, + "name": "Revda" + } + ], + "question": "Which location is the geographic outlier among: Coração de Jesus, São José dos Pinhais, São Sebastião da Boa Vista, Joinville, Revda?", + "ground_truth": { + "answer": "Revda", + "outlier_distance_km": 10035.0, + "second_furthest_km": 3553.8, + "clarity_ratio": 2.82, + "median_distance_km": 3521.4, + "distances_to_centroid": { + "Coração de Jesus": 2505.5, + "São José dos Pinhais": 3521.4, + "São Sebastião da Boa Vista": 2572.1, + "Joinville": 3553.8, + "Revda": 10035.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coração de Jesus: (-16.69°, -44.37°)", + " São José dos Pinhais: (-25.53°, -49.21°)", + " São Sebastião da Boa Vista: (-1.71°, -49.53°)", + " Joinville: (-26.30°, -48.85°)", + " Revda: (56.80°, 59.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Revda: 10035.0 km from centroid", + " Joinville: 3553.8 km from centroid", + " São José dos Pinhais: 3521.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Revda", + "FINAL ANSWER: Revda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.91161, + "lon": -15.40558, + "name": "Carrizal" + }, + { + "lat": 50.97221, + "lon": 13.86741, + "name": "Heidenau" + }, + { + "lat": 54.86796, + "lon": -1.69846, + "name": "Stanley" + }, + { + "lat": 48.5498, + "lon": 8.72366, + "name": "Nagold" + }, + { + "lat": 10.27284, + "lon": 76.17475, + "name": "Panangad" + } + ], + "question": "Which location is the geographic outlier among: Carrizal, Heidenau, Stanley, Nagold, Panangad?", + "ground_truth": { + "answer": "Panangad", + "outlier_distance_km": 6687.6, + "second_furthest_km": 3159.5, + "clarity_ratio": 2.12, + "median_distance_km": 2265.6, + "distances_to_centroid": { + "Carrizal": 3159.5, + "Heidenau": 1398.6, + "Stanley": 2265.6, + "Nagold": 1271.8, + "Panangad": 6687.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carrizal: (27.91°, -15.41°)", + " Heidenau: (50.97°, 13.87°)", + " Stanley: (54.87°, -1.70°)", + " Nagold: (48.55°, 8.72°)", + " Panangad: (10.27°, 76.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Panangad: 6687.6 km from centroid", + " Carrizal: 3159.5 km from centroid", + " Stanley: 2265.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Panangad", + "FINAL ANSWER: Panangad" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.96807, + "lon": 174.79875, + "name": "Mangere" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + }, + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + }, + { + "lat": -23.56675, + "lon": -46.66439, + "name": "Jardim Paulista" + } + ], + "question": "Which location is the geographic outlier among: Mangere, Melbourne, Strathfield, Springvale, Jardim Paulista?", + "ground_truth": { + "answer": "Jardim Paulista", + "outlier_distance_km": 13287.3, + "second_furthest_km": 5429.9, + "clarity_ratio": 2.45, + "median_distance_km": 3412.9, + "distances_to_centroid": { + "Mangere": 5429.9, + "Melbourne": 2818.3, + "Strathfield": 3412.9, + "Springvale": 2834.7, + "Jardim Paulista": 13287.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mangere: (-36.97°, 174.80°)", + " Melbourne: (-37.81°, 144.96°)", + " Strathfield: (-33.88°, 151.08°)", + " Springvale: (-37.95°, 145.15°)", + " Jardim Paulista: (-23.57°, -46.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jardim Paulista: 13287.3 km from centroid", + " Mangere: 5429.9 km from centroid", + " Strathfield: 3412.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jardim Paulista", + "FINAL ANSWER: Jardim Paulista" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + { + "lat": -33.41665, + "lon": 149.5806, + "name": "Bathurst" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": 30.41131, + "lon": -88.82781, + "name": "Ocean Springs" + } + ], + "question": "Which location is the geographic outlier among: Bentleigh East, Bathurst, Eight Mile Plains, Mount Martha, Ocean Springs?", + "ground_truth": { + "answer": "Ocean Springs", + "outlier_distance_km": 18624.0, + "second_furthest_km": 5302.0, + "clarity_ratio": 3.51, + "median_distance_km": 4953.8, + "distances_to_centroid": { + "Bentleigh East": 4605.5, + "Bathurst": 4953.8, + "Eight Mile Plains": 5302.0, + "Mount Martha": 4609.7, + "Ocean Springs": 18624.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bentleigh East: (-37.92°, 145.05°)", + " Bathurst: (-33.42°, 149.58°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Mount Martha: (-38.27°, 145.02°)", + " Ocean Springs: (30.41°, -88.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ocean Springs: 18624.0 km from centroid", + " Eight Mile Plains: 5302.0 km from centroid", + " Bathurst: 4953.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ocean Springs", + "FINAL ANSWER: Ocean Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.69863, + "lon": 144.78631, + "name": "Taylors Lakes" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + { + "lat": 43.8361, + "lon": -79.49827, + "name": "Vaughan" + } + ], + "question": "Which location is the geographic outlier among: Taylors Lakes, Port Macquarie, Newcastle, Rockhampton, Vaughan?", + "ground_truth": { + "answer": "Vaughan", + "outlier_distance_km": 16936.8, + "second_furthest_km": 5193.0, + "clarity_ratio": 3.26, + "median_distance_km": 5111.4, + "distances_to_centroid": { + "Taylors Lakes": 4627.4, + "Port Macquarie": 5193.0, + "Newcastle": 5111.4, + "Rockhampton": 4896.6, + "Vaughan": 16936.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taylors Lakes: (-37.70°, 144.79°)", + " Port Macquarie: (-31.43°, 152.91°)", + " Newcastle: (-32.93°, 151.78°)", + " Rockhampton: (-23.38°, 150.51°)", + " Vaughan: (43.84°, -79.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vaughan: 16936.8 km from centroid", + " Port Macquarie: 5193.0 km from centroid", + " Newcastle: 5111.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vaughan", + "FINAL ANSWER: Vaughan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.98567, + "lon": -0.04935, + "name": "Castelló de la Plana" + }, + { + "lat": 45.58882, + "lon": 9.19792, + "name": "Nova Milanese" + }, + { + "lat": 51.4419, + "lon": 6.26639, + "name": "Straelen" + }, + { + "lat": 53.39337, + "lon": -3.01479, + "name": "Birkenhead" + }, + { + "lat": 25.71826, + "lon": 116.74892, + "name": "Liancheng" + } + ], + "question": "Which location is the geographic outlier among: Castelló de la Plana, Nova Milanese, Straelen, Birkenhead, Liancheng?", + "ground_truth": { + "answer": "Liancheng", + "outlier_distance_km": 8155.2, + "second_furthest_km": 2391.2, + "clarity_ratio": 3.41, + "median_distance_km": 2172.7, + "distances_to_centroid": { + "Castelló de la Plana": 2172.7, + "Nova Milanese": 1344.5, + "Straelen": 1726.2, + "Birkenhead": 2391.2, + "Liancheng": 8155.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Castelló de la Plana: (39.99°, -0.05°)", + " Nova Milanese: (45.59°, 9.20°)", + " Straelen: (51.44°, 6.27°)", + " Birkenhead: (53.39°, -3.01°)", + " Liancheng: (25.72°, 116.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Liancheng: 8155.2 km from centroid", + " Birkenhead: 2391.2 km from centroid", + " Castelló de la Plana: 2172.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Liancheng", + "FINAL ANSWER: Liancheng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.62736, + "lon": 104.5637, + "name": "Shawan" + }, + { + "lat": 34.25833, + "lon": 117.88889, + "name": "Yitang" + }, + { + "lat": 29.41607, + "lon": 76.98831, + "name": "Panipat Taraf Makhdum Zadgan" + }, + { + "lat": 18.15662, + "lon": 74.60708, + "name": "Jalochi" + }, + { + "lat": -30.99766, + "lon": 26.32862, + "name": "Burgersdorp" + } + ], + "question": "Which location is the geographic outlier among: Shawan, Yitang, Panipat Taraf Makhdum Zadgan, Jalochi, Burgersdorp?", + "ground_truth": { + "answer": "Burgersdorp", + "outlier_distance_km": 7828.6, + "second_furthest_km": 4221.9, + "clarity_ratio": 1.85, + "median_distance_km": 3072.1, + "distances_to_centroid": { + "Shawan": 3072.1, + "Yitang": 4221.9, + "Panipat Taraf Makhdum Zadgan": 1427.7, + "Jalochi": 596.6, + "Burgersdorp": 7828.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shawan: (33.63°, 104.56°)", + " Yitang: (34.26°, 117.89°)", + " Panipat Taraf Makhdum Zadgan: (29.42°, 76.99°)", + " Jalochi: (18.16°, 74.61°)", + " Burgersdorp: (-31.00°, 26.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Burgersdorp: 7828.6 km from centroid", + " Yitang: 4221.9 km from centroid", + " Shawan: 3072.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Burgersdorp", + "FINAL ANSWER: Burgersdorp" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.71916, + "lon": 40.21603, + "name": "Shakhty" + }, + { + "lat": 55.73321, + "lon": 38.46458, + "name": "Fryazevo" + }, + { + "lat": 51.44337, + "lon": 7.77825, + "name": "Menden" + }, + { + "lat": 53.16532, + "lon": 8.68873, + "name": "Burglesum" + }, + { + "lat": -1.82833, + "lon": -44.86833, + "name": "Cururupu" + } + ], + "question": "Which location is the geographic outlier among: Shakhty, Fryazevo, Menden, Burglesum, Cururupu?", + "ground_truth": { + "answer": "Cururupu", + "outlier_distance_km": 7310.4, + "second_furthest_km": 2610.4, + "clarity_ratio": 2.8, + "median_distance_km": 2480.7, + "distances_to_centroid": { + "Shakhty": 2480.7, + "Fryazevo": 2610.4, + "Menden": 1147.1, + "Burglesum": 1329.3, + "Cururupu": 7310.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shakhty: (47.72°, 40.22°)", + " Fryazevo: (55.73°, 38.46°)", + " Menden: (51.44°, 7.78°)", + " Burglesum: (53.17°, 8.69°)", + " Cururupu: (-1.83°, -44.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cururupu: 7310.4 km from centroid", + " Fryazevo: 2610.4 km from centroid", + " Shakhty: 2480.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cururupu", + "FINAL ANSWER: Cururupu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.57679, + "lon": -60.71114, + "name": "Villa Ángela" + }, + { + "lat": -4.57444, + "lon": -55.94361, + "name": "Trairão" + }, + { + "lat": -3.68611, + "lon": -40.34972, + "name": "Sobral" + }, + { + "lat": -0.98667, + "lon": -49.94, + "name": "Anajás" + }, + { + "lat": 37.60886, + "lon": 15.16577, + "name": "Acireale" + } + ], + "question": "Which location is the geographic outlier among: Villa Ángela, Trairão, Sobral, Anajás, Acireale?", + "ground_truth": { + "answer": "Acireale", + "outlier_distance_km": 6871.2, + "second_furthest_km": 3899.1, + "clarity_ratio": 1.76, + "median_distance_km": 2023.3, + "distances_to_centroid": { + "Villa Ángela": 3899.1, + "Trairão": 2023.3, + "Sobral": 481.4, + "Anajás": 1294.3, + "Acireale": 6871.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Villa Ángela: (-27.58°, -60.71°)", + " Trairão: (-4.57°, -55.94°)", + " Sobral: (-3.69°, -40.35°)", + " Anajás: (-0.99°, -49.94°)", + " Acireale: (37.61°, 15.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Acireale: 6871.2 km from centroid", + " Villa Ángela: 3899.1 km from centroid", + " Trairão: 2023.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Acireale", + "FINAL ANSWER: Acireale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.28917, + "lon": -47.17444, + "name": "Itariri" + }, + { + "lat": -7.51194, + "lon": -39.72417, + "name": "Exu" + }, + { + "lat": -25.40778, + "lon": -52.41611, + "name": "Laranjeiras do Sul" + }, + { + "lat": -22.18556, + "lon": -47.39028, + "name": "Leme" + }, + { + "lat": -25.52297, + "lon": 31.35693, + "name": "Matsulu" + } + ], + "question": "Which location is the geographic outlier among: Itariri, Exu, Laranjeiras do Sul, Leme, Matsulu?", + "ground_truth": { + "answer": "Matsulu", + "outlier_distance_km": 6340.6, + "second_furthest_km": 2233.8, + "clarity_ratio": 2.84, + "median_distance_km": 1763.2, + "distances_to_centroid": { + "Itariri": 1692.1, + "Exu": 1763.2, + "Laranjeiras do Sul": 2233.8, + "Leme": 1692.0, + "Matsulu": 6340.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itariri: (-24.29°, -47.17°)", + " Exu: (-7.51°, -39.72°)", + " Laranjeiras do Sul: (-25.41°, -52.42°)", + " Leme: (-22.19°, -47.39°)", + " Matsulu: (-25.52°, 31.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Matsulu: 6340.6 km from centroid", + " Laranjeiras do Sul: 2233.8 km from centroid", + " Exu: 1763.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Matsulu", + "FINAL ANSWER: Matsulu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.04333, + "lon": -40.82444, + "name": "Marataizes" + }, + { + "lat": -27.58612, + "lon": -48.52335, + "name": "Trindade" + }, + { + "lat": -23.5702, + "lon": -46.72628, + "name": "Butanta" + }, + { + "lat": -5.85833, + "lon": -35.35389, + "name": "Macaíba" + }, + { + "lat": -29.12107, + "lon": 26.214, + "name": "Bloemfontein" + } + ], + "question": "Which location is the geographic outlier among: Marataizes, Trindade, Butanta, Macaíba, Bloemfontein?", + "ground_truth": { + "answer": "Bloemfontein", + "outlier_distance_km": 5572.3, + "second_furthest_km": 2083.2, + "clarity_ratio": 2.67, + "median_distance_km": 1860.6, + "distances_to_centroid": { + "Marataizes": 1221.6, + "Trindade": 2083.2, + "Butanta": 1830.8, + "Macaíba": 1860.6, + "Bloemfontein": 5572.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marataizes: (-21.04°, -40.82°)", + " Trindade: (-27.59°, -48.52°)", + " Butanta: (-23.57°, -46.73°)", + " Macaíba: (-5.86°, -35.35°)", + " Bloemfontein: (-29.12°, 26.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bloemfontein: 5572.3 km from centroid", + " Trindade: 2083.2 km from centroid", + " Macaíba: 1860.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bloemfontein", + "FINAL ANSWER: Bloemfontein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -33.77271, + "lon": 151.08184, + "name": "Epping" + }, + { + "lat": -12.46113, + "lon": 130.84185, + "name": "Darwin" + }, + { + "lat": 23.30521, + "lon": 87.41336, + "name": "Sonāmukhi" + } + ], + "question": "Which location is the geographic outlier among: Wangaratta, Australind, Epping, Darwin, Sonāmukhi?", + "ground_truth": { + "answer": "Sonāmukhi", + "outlier_distance_km": 6278.2, + "second_furthest_km": 2988.2, + "clarity_ratio": 2.1, + "median_distance_km": 2790.2, + "distances_to_centroid": { + "Wangaratta": 2790.2, + "Australind": 1949.4, + "Epping": 2988.2, + "Darwin": 831.9, + "Sonāmukhi": 6278.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wangaratta: (-36.36°, 146.32°)", + " Australind: (-33.28°, 115.72°)", + " Epping: (-33.77°, 151.08°)", + " Darwin: (-12.46°, 130.84°)", + " Sonāmukhi: (23.31°, 87.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sonāmukhi: 6278.2 km from centroid", + " Epping: 2988.2 km from centroid", + " Wangaratta: 2790.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sonāmukhi", + "FINAL ANSWER: Sonāmukhi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.3943, + "lon": 136.66898, + "name": "Mizuho" + }, + { + "lat": 17.51544, + "lon": 78.88563, + "name": "Bhongīr" + }, + { + "lat": 11.11723, + "lon": 77.37256, + "name": "Mannarai" + }, + { + "lat": 34.21024, + "lon": 134.33653, + "name": "Higashikagawa" + }, + { + "lat": -13.4425, + "lon": -42.23889, + "name": "Paramirim" + } + ], + "question": "Which location is the geographic outlier among: Mizuho, Bhongīr, Mannarai, Higashikagawa, Paramirim?", + "ground_truth": { + "answer": "Paramirim", + "outlier_distance_km": 13508.6, + "second_furthest_km": 6199.4, + "clarity_ratio": 2.18, + "median_distance_km": 5979.4, + "distances_to_centroid": { + "Mizuho": 6199.4, + "Bhongīr": 209.1, + "Mannarai": 650.8, + "Higashikagawa": 5979.4, + "Paramirim": 13508.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mizuho: (35.39°, 136.67°)", + " Bhongīr: (17.52°, 78.89°)", + " Mannarai: (11.12°, 77.37°)", + " Higashikagawa: (34.21°, 134.34°)", + " Paramirim: (-13.44°, -42.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paramirim: 13508.6 km from centroid", + " Mizuho: 6199.4 km from centroid", + " Higashikagawa: 5979.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paramirim", + "FINAL ANSWER: Paramirim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + }, + { + "lat": -38.38176, + "lon": 142.48799, + "name": "Warrnambool" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -27.20338, + "lon": 152.95923, + "name": "Narangba" + }, + { + "lat": 6.69903, + "lon": -72.73233, + "name": "Málaga" + } + ], + "question": "Which location is the geographic outlier among: Surfers Paradise, Warrnambool, Canning Vale, Narangba, Málaga?", + "ground_truth": { + "answer": "Málaga", + "outlier_distance_km": 17892.5, + "second_furthest_km": 5477.8, + "clarity_ratio": 3.27, + "median_distance_km": 5445.2, + "distances_to_centroid": { + "Surfers Paradise": 5477.8, + "Warrnambool": 4450.5, + "Canning Vale": 1946.5, + "Narangba": 5445.2, + "Málaga": 17892.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Surfers Paradise: (-28.00°, 153.43°)", + " Warrnambool: (-38.38°, 142.49°)", + " Canning Vale: (-32.06°, 115.92°)", + " Narangba: (-27.20°, 152.96°)", + " Málaga: (6.70°, -72.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Málaga: 17892.5 km from centroid", + " Surfers Paradise: 5477.8 km from centroid", + " Narangba: 5445.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Málaga", + "FINAL ANSWER: Málaga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.8188, + "lon": 151.1062, + "name": "Ryde" + }, + { + "lat": -27.22426, + "lon": 153.02075, + "name": "North Lakes" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -27.94402, + "lon": 153.39815, + "name": "Labrador" + }, + { + "lat": 34.50259, + "lon": -84.95105, + "name": "Calhoun" + } + ], + "question": "Which location is the geographic outlier among: Ryde, North Lakes, Bundoora, Labrador, Calhoun?", + "ground_truth": { + "answer": "Calhoun", + "outlier_distance_km": 18041.5, + "second_furthest_km": 5170.7, + "clarity_ratio": 3.49, + "median_distance_km": 5133.1, + "distances_to_centroid": { + "Ryde": 4998.6, + "North Lakes": 5133.1, + "Bundoora": 4553.3, + "Labrador": 5170.7, + "Calhoun": 18041.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ryde: (-33.82°, 151.11°)", + " North Lakes: (-27.22°, 153.02°)", + " Bundoora: (-37.70°, 145.06°)", + " Labrador: (-27.94°, 153.40°)", + " Calhoun: (34.50°, -84.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Calhoun: 18041.5 km from centroid", + " Labrador: 5170.7 km from centroid", + " North Lakes: 5133.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Calhoun", + "FINAL ANSWER: Calhoun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.81944, + "lon": 3.91731, + "name": "Ijebu Ode" + }, + { + "lat": 5.05127, + "lon": 7.9335, + "name": "Uyo" + }, + { + "lat": -1.19347, + "lon": 34.61967, + "name": "Kihancha" + }, + { + "lat": 2.80922, + "lon": 40.92885, + "name": "El Wak" + }, + { + "lat": 51.72689, + "lon": 36.18457, + "name": "Kursk" + } + ], + "question": "Which location is the geographic outlier among: Ijebu Ode, Uyo, Kihancha, El Wak, Kursk?", + "ground_truth": { + "answer": "Kursk", + "outlier_distance_km": 4422.8, + "second_furthest_km": 2379.4, + "clarity_ratio": 1.86, + "median_distance_km": 2115.0, + "distances_to_centroid": { + "Ijebu Ode": 2379.4, + "Uyo": 2044.4, + "Kihancha": 1923.3, + "El Wak": 2115.0, + "Kursk": 4422.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ijebu Ode: (6.82°, 3.92°)", + " Uyo: (5.05°, 7.93°)", + " Kihancha: (-1.19°, 34.62°)", + " El Wak: (2.81°, 40.93°)", + " Kursk: (51.73°, 36.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kursk: 4422.8 km from centroid", + " Ijebu Ode: 2379.4 km from centroid", + " El Wak: 2115.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kursk", + "FINAL ANSWER: Kursk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75819, + "lon": 145.00583, + "name": "Thornbury" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + }, + { + "lat": 51.5489, + "lon": -0.48211, + "name": "Uxbridge" + } + ], + "question": "Which location is the geographic outlier among: Thornbury, Lidcombe, Glenroy, Malvern East, Uxbridge?", + "ground_truth": { + "answer": "Uxbridge", + "outlier_distance_km": 13556.9, + "second_furthest_km": 3729.3, + "clarity_ratio": 3.64, + "median_distance_km": 3411.0, + "distances_to_centroid": { + "Thornbury": 3401.8, + "Lidcombe": 3729.3, + "Glenroy": 3393.1, + "Malvern East": 3411.0, + "Uxbridge": 13556.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thornbury: (-37.76°, 145.01°)", + " Lidcombe: (-33.86°, 151.04°)", + " Glenroy: (-37.70°, 144.93°)", + " Malvern East: (-37.87°, 145.04°)", + " Uxbridge: (51.55°, -0.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uxbridge: 13556.9 km from centroid", + " Lidcombe: 3729.3 km from centroid", + " Malvern East: 3411.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uxbridge", + "FINAL ANSWER: Uxbridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.0945, + "lon": -79.05671, + "name": "Niagara Falls" + }, + { + "lat": 20.2052, + "lon": -89.28522, + "name": "Tecax" + }, + { + "lat": 19.26757, + "lon": -99.53214, + "name": "San Mateo Atenco" + }, + { + "lat": 34.26783, + "lon": -86.20878, + "name": "Albertville" + }, + { + "lat": -0.9373, + "lon": 37.12275, + "name": "Kenol" + } + ], + "question": "Which location is the geographic outlier among: Niagara Falls, Tecax, San Mateo Atenco, Albertville, Kenol?", + "ground_truth": { + "answer": "Kenol", + "outlier_distance_km": 11122.9, + "second_furthest_km": 3761.8, + "clarity_ratio": 2.96, + "median_distance_km": 2692.1, + "distances_to_centroid": { + "Niagara Falls": 2641.6, + "Tecax": 2692.1, + "San Mateo Atenco": 3761.8, + "Albertville": 2534.9, + "Kenol": 11122.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Niagara Falls: (43.09°, -79.06°)", + " Tecax: (20.21°, -89.29°)", + " San Mateo Atenco: (19.27°, -99.53°)", + " Albertville: (34.27°, -86.21°)", + " Kenol: (-0.94°, 37.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kenol: 11122.9 km from centroid", + " San Mateo Atenco: 3761.8 km from centroid", + " Tecax: 2692.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kenol", + "FINAL ANSWER: Kenol" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -41.33333, + "lon": 173.18333, + "name": "Richmond" + }, + { + "lat": -33.8188, + "lon": 151.1062, + "name": "Ryde" + }, + { + "lat": -33.75881, + "lon": 150.99292, + "name": "Baulkham Hills" + }, + { + "lat": -1.22361, + "lon": -48.29444, + "name": "Santa Bárbara do Pará" + } + ], + "question": "Which location is the geographic outlier among: Eight Mile Plains, Richmond, Ryde, Baulkham Hills, Santa Bárbara do Pará?", + "ground_truth": { + "answer": "Santa Bárbara do Pará", + "outlier_distance_km": 16403.3, + "second_furthest_km": 5360.8, + "clarity_ratio": 3.06, + "median_distance_km": 3641.3, + "distances_to_centroid": { + "Eight Mile Plains": 3641.3, + "Richmond": 5360.8, + "Ryde": 3410.2, + "Baulkham Hills": 3399.4, + "Santa Bárbara do Pará": 16403.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Richmond: (-41.33°, 173.18°)", + " Ryde: (-33.82°, 151.11°)", + " Baulkham Hills: (-33.76°, 150.99°)", + " Santa Bárbara do Pará: (-1.22°, -48.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Bárbara do Pará: 16403.3 km from centroid", + " Richmond: 5360.8 km from centroid", + " Eight Mile Plains: 3641.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Bárbara do Pará", + "FINAL ANSWER: Santa Bárbara do Pará" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.85029, + "lon": 2.14523, + "name": "La Celle-Saint-Cloud" + }, + { + "lat": 52.5511, + "lon": 13.19921, + "name": "Spandau" + }, + { + "lat": 47.75205, + "lon": 7.32866, + "name": "Mulhouse" + }, + { + "lat": 54.54897, + "lon": -3.58412, + "name": "Whitehaven" + }, + { + "lat": 43.78727, + "lon": -79.20636, + "name": "Morningside" + } + ], + "question": "Which location is the geographic outlier among: La Celle-Saint-Cloud, Spandau, Mulhouse, Whitehaven, Morningside?", + "ground_truth": { + "answer": "Morningside", + "outlier_distance_km": 4995.8, + "second_furthest_km": 1786.8, + "clarity_ratio": 2.8, + "median_distance_km": 1431.5, + "distances_to_centroid": { + "La Celle-Saint-Cloud": 1031.0, + "Spandau": 1786.8, + "Mulhouse": 1431.5, + "Whitehaven": 804.5, + "Morningside": 4995.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Celle-Saint-Cloud: (48.85°, 2.15°)", + " Spandau: (52.55°, 13.20°)", + " Mulhouse: (47.75°, 7.33°)", + " Whitehaven: (54.55°, -3.58°)", + " Morningside: (43.79°, -79.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morningside: 4995.8 km from centroid", + " Spandau: 1786.8 km from centroid", + " Mulhouse: 1431.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morningside", + "FINAL ANSWER: Morningside" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.83969, + "lon": -48.02675, + "name": "Águas Claras" + }, + { + "lat": -5.66417, + "lon": -37.79889, + "name": "Apodi" + }, + { + "lat": -9.16972, + "lon": -36.67972, + "name": "Bom Conselho" + }, + { + "lat": -6.98111, + "lon": -34.83389, + "name": "Cabedelo" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + } + ], + "question": "Which location is the geographic outlier among: Águas Claras, Apodi, Bom Conselho, Cabedelo, Glen Iris?", + "ground_truth": { + "answer": "Glen Iris", + "outlier_distance_km": 13219.1, + "second_furthest_km": 4874.7, + "clarity_ratio": 2.71, + "median_distance_km": 3999.0, + "distances_to_centroid": { + "Águas Claras": 4874.7, + "Apodi": 3999.0, + "Bom Conselho": 3774.3, + "Cabedelo": 3642.4, + "Glen Iris": 13219.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Águas Claras: (-15.84°, -48.03°)", + " Apodi: (-5.66°, -37.80°)", + " Bom Conselho: (-9.17°, -36.68°)", + " Cabedelo: (-6.98°, -34.83°)", + " Glen Iris: (-37.87°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glen Iris: 13219.1 km from centroid", + " Águas Claras: 4874.7 km from centroid", + " Apodi: 3999.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glen Iris", + "FINAL ANSWER: Glen Iris" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -38.03333, + "lon": 145.3, + "name": "Narre Warren" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + }, + { + "lat": 26.67479, + "lon": 85.16698, + "name": "Dhāka" + } + ], + "question": "Which location is the geographic outlier among: Armidale, Narre Warren, Maitland, Busselton, Dhāka?", + "ground_truth": { + "answer": "Dhāka", + "outlier_distance_km": 7208.5, + "second_furthest_km": 2471.7, + "clarity_ratio": 2.92, + "median_distance_km": 2389.0, + "distances_to_centroid": { + "Armidale": 2389.0, + "Narre Warren": 2349.1, + "Maitland": 2471.7, + "Busselton": 1947.9, + "Dhāka": 7208.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Armidale: (-30.50°, 151.67°)", + " Narre Warren: (-38.03°, 145.30°)", + " Maitland: (-32.73°, 151.56°)", + " Busselton: (-33.65°, 115.35°)", + " Dhāka: (26.67°, 85.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dhāka: 7208.5 km from centroid", + " Maitland: 2471.7 km from centroid", + " Armidale: 2389.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dhāka", + "FINAL ANSWER: Dhāka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": 41.6292, + "lon": -87.93089, + "name": "Goodings Grove" + } + ], + "question": "Which location is the geographic outlier among: Doreen, Seven Hills, Orange, Baldivis, Goodings Grove?", + "ground_truth": { + "answer": "Goodings Grove", + "outlier_distance_km": 17495.4, + "second_furthest_km": 5768.4, + "clarity_ratio": 3.03, + "median_distance_km": 5596.9, + "distances_to_centroid": { + "Doreen": 5283.9, + "Seven Hills": 5768.4, + "Orange": 5596.9, + "Baldivis": 2578.0, + "Goodings Grove": 17495.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doreen: (-37.60°, 145.15°)", + " Seven Hills: (-33.78°, 150.93°)", + " Orange: (-33.28°, 149.10°)", + " Baldivis: (-32.33°, 115.83°)", + " Goodings Grove: (41.63°, -87.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Goodings Grove: 17495.4 km from centroid", + " Seven Hills: 5768.4 km from centroid", + " Orange: 5596.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Goodings Grove", + "FINAL ANSWER: Goodings Grove" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.47278, + "lon": -47.36306, + "name": "Santa Rosa de Viterbo" + }, + { + "lat": -17.13806, + "lon": -49.98806, + "name": "Indiara" + }, + { + "lat": -10.36083, + "lon": -37.70111, + "name": "Carira" + }, + { + "lat": -35.43247, + "lon": -60.17156, + "name": "Veinticinco de Mayo" + }, + { + "lat": 43.80418, + "lon": -79.27528, + "name": "Agincourt North" + } + ], + "question": "Which location is the geographic outlier among: Santa Rosa de Viterbo, Indiara, Carira, Veinticinco de Mayo, Agincourt North?", + "ground_truth": { + "answer": "Agincourt North", + "outlier_distance_km": 6274.3, + "second_furthest_km": 3084.0, + "clarity_ratio": 2.03, + "median_distance_km": 1903.7, + "distances_to_centroid": { + "Santa Rosa de Viterbo": 1690.4, + "Indiara": 1135.3, + "Carira": 1903.7, + "Veinticinco de Mayo": 3084.0, + "Agincourt North": 6274.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Rosa de Viterbo: (-21.47°, -47.36°)", + " Indiara: (-17.14°, -49.99°)", + " Carira: (-10.36°, -37.70°)", + " Veinticinco de Mayo: (-35.43°, -60.17°)", + " Agincourt North: (43.80°, -79.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Agincourt North: 6274.3 km from centroid", + " Veinticinco de Mayo: 3084.0 km from centroid", + " Carira: 1903.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Agincourt North", + "FINAL ANSWER: Agincourt North" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.95833, + "lon": -38.975, + "name": "Santa Bárbara" + }, + { + "lat": -3.89174, + "lon": -59.09542, + "name": "Nova Olinda do Norte" + }, + { + "lat": -11.71139, + "lon": -40.14889, + "name": "Mairi" + }, + { + "lat": -29.51694, + "lon": -50.77778, + "name": "Três Coroas" + }, + { + "lat": 8.30812, + "lon": 77.22144, + "name": "Marthandam" + } + ], + "question": "Which location is the geographic outlier among: Santa Bárbara, Nova Olinda do Norte, Mairi, Três Coroas, Marthandam?", + "ground_truth": { + "answer": "Marthandam", + "outlier_distance_km": 11204.2, + "second_furthest_km": 4105.6, + "clarity_ratio": 2.73, + "median_distance_km": 3680.5, + "distances_to_centroid": { + "Santa Bárbara": 1831.1, + "Nova Olinda do Norte": 4105.6, + "Mairi": 1955.7, + "Três Coroas": 3680.5, + "Marthandam": 11204.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Bárbara: (-11.96°, -38.98°)", + " Nova Olinda do Norte: (-3.89°, -59.10°)", + " Mairi: (-11.71°, -40.15°)", + " Três Coroas: (-29.52°, -50.78°)", + " Marthandam: (8.31°, 77.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marthandam: 11204.2 km from centroid", + " Nova Olinda do Norte: 4105.6 km from centroid", + " Três Coroas: 3680.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marthandam", + "FINAL ANSWER: Marthandam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.68848, + "lon": -1.62443, + "name": "Kumasi" + }, + { + "lat": 10.85, + "lon": 37.01667, + "name": "Tīlīlī" + }, + { + "lat": 9.27949, + "lon": 12.45819, + "name": "Jimeta" + }, + { + "lat": 6.919, + "lon": 37.529, + "name": "Bale Hawassa" + }, + { + "lat": 20.95361, + "lon": -97.44194, + "name": "Alto Lucero" + } + ], + "question": "Which location is the geographic outlier among: Kumasi, Tīlīlī, Jimeta, Bale Hawassa, Alto Lucero?", + "ground_truth": { + "answer": "Alto Lucero", + "outlier_distance_km": 10087.4, + "second_furthest_km": 4407.0, + "clarity_ratio": 2.29, + "median_distance_km": 4302.1, + "distances_to_centroid": { + "Kumasi": 480.4, + "Tīlīlī": 4302.1, + "Jimeta": 1638.1, + "Bale Hawassa": 4407.0, + "Alto Lucero": 10087.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kumasi: (6.69°, -1.62°)", + " Tīlīlī: (10.85°, 37.02°)", + " Jimeta: (9.28°, 12.46°)", + " Bale Hawassa: (6.92°, 37.53°)", + " Alto Lucero: (20.95°, -97.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alto Lucero: 10087.4 km from centroid", + " Bale Hawassa: 4407.0 km from centroid", + " Tīlīlī: 4302.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alto Lucero", + "FINAL ANSWER: Alto Lucero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.53891, + "lon": 3.3742, + "name": "Shomolu" + }, + { + "lat": 12.79881, + "lon": 39.64448, + "name": "Mehoni" + }, + { + "lat": 6.90412, + "lon": -2.56114, + "name": "Mim" + }, + { + "lat": -1.29996, + "lon": 36.99047, + "name": "Githunguri" + }, + { + "lat": -27.54333, + "lon": 153.20287, + "name": "Capalaba" + } + ], + "question": "Which location is the geographic outlier among: Shomolu, Mehoni, Mim, Githunguri, Capalaba?", + "ground_truth": { + "answer": "Capalaba", + "outlier_distance_km": 11657.5, + "second_furthest_km": 5464.1, + "clarity_ratio": 2.13, + "median_distance_km": 4808.8, + "distances_to_centroid": { + "Shomolu": 4808.8, + "Mehoni": 1644.7, + "Mim": 5464.1, + "Githunguri": 1019.8, + "Capalaba": 11657.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shomolu: (6.54°, 3.37°)", + " Mehoni: (12.80°, 39.64°)", + " Mim: (6.90°, -2.56°)", + " Githunguri: (-1.30°, 36.99°)", + " Capalaba: (-27.54°, 153.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Capalaba: 11657.5 km from centroid", + " Mim: 5464.1 km from centroid", + " Shomolu: 4808.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Capalaba", + "FINAL ANSWER: Capalaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.31649, + "lon": -73.09316, + "name": "Shelton" + }, + { + "lat": 41.50948, + "lon": -90.57875, + "name": "Rock Island" + }, + { + "lat": 40.58654, + "lon": -122.39168, + "name": "Redding" + }, + { + "lat": 19.56233, + "lon": -97.24235, + "name": "Perote" + }, + { + "lat": -22.23, + "lon": -45.93639, + "name": "Pouso Alegre" + } + ], + "question": "Which location is the geographic outlier among: Shelton, Rock Island, Redding, Perote, Pouso Alegre?", + "ground_truth": { + "answer": "Pouso Alegre", + "outlier_distance_km": 6722.3, + "second_furthest_km": 3850.0, + "clarity_ratio": 1.75, + "median_distance_km": 2245.4, + "distances_to_centroid": { + "Shelton": 2245.4, + "Rock Island": 1979.5, + "Redding": 3850.0, + "Perote": 1281.0, + "Pouso Alegre": 6722.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shelton: (41.32°, -73.09°)", + " Rock Island: (41.51°, -90.58°)", + " Redding: (40.59°, -122.39°)", + " Perote: (19.56°, -97.24°)", + " Pouso Alegre: (-22.23°, -45.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pouso Alegre: 6722.3 km from centroid", + " Redding: 3850.0 km from centroid", + " Shelton: 2245.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pouso Alegre", + "FINAL ANSWER: Pouso Alegre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.7275, + "lon": 116.49611, + "name": "Wenshang" + }, + { + "lat": 27.16757, + "lon": 100.92005, + "name": "Xinyingpan" + }, + { + "lat": 13.16667, + "lon": 80.26667, + "name": "Manali" + }, + { + "lat": 29.63116, + "lon": 105.83065, + "name": "Shima" + }, + { + "lat": 41.557, + "lon": -83.62716, + "name": "Perrysburg" + } + ], + "question": "Which location is the geographic outlier among: Wenshang, Xinyingpan, Manali, Shima, Perrysburg?", + "ground_truth": { + "answer": "Perrysburg", + "outlier_distance_km": 11447.1, + "second_furthest_km": 4911.7, + "clarity_ratio": 2.33, + "median_distance_km": 4026.2, + "distances_to_centroid": { + "Wenshang": 4911.7, + "Xinyingpan": 3610.5, + "Manali": 2468.9, + "Shima": 4026.2, + "Perrysburg": 11447.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wenshang: (35.73°, 116.50°)", + " Xinyingpan: (27.17°, 100.92°)", + " Manali: (13.17°, 80.27°)", + " Shima: (29.63°, 105.83°)", + " Perrysburg: (41.56°, -83.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perrysburg: 11447.1 km from centroid", + " Wenshang: 4911.7 km from centroid", + " Shima: 4026.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perrysburg", + "FINAL ANSWER: Perrysburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + { + "lat": -37.8, + "lon": 145.28333, + "name": "Croydon" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + { + "lat": 50.72999, + "lon": -1.1621, + "name": "Ryde" + } + ], + "question": "Which location is the geographic outlier among: Warragul, Yagoona, Croydon, Sunbury, Ryde?", + "ground_truth": { + "answer": "Ryde", + "outlier_distance_km": 13640.0, + "second_furthest_km": 3711.5, + "clarity_ratio": 3.68, + "median_distance_km": 3474.2, + "distances_to_centroid": { + "Warragul": 3474.2, + "Yagoona": 3711.5, + "Croydon": 3405.2, + "Sunbury": 3350.3, + "Ryde": 13640.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warragul: (-38.16°, 145.93°)", + " Yagoona: (-33.90°, 151.02°)", + " Croydon: (-37.80°, 145.28°)", + " Sunbury: (-37.58°, 144.73°)", + " Ryde: (50.73°, -1.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ryde: 13640.0 km from centroid", + " Yagoona: 3711.5 km from centroid", + " Warragul: 3474.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ryde", + "FINAL ANSWER: Ryde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + }, + { + "lat": -7.71361, + "lon": -66.97639, + "name": "Pauini" + } + ], + "question": "Which location is the geographic outlier among: Boronia, Hobart, Melbourne City Centre, Southbank, Pauini?", + "ground_truth": { + "answer": "Pauini", + "outlier_distance_km": 15387.5, + "second_furthest_km": 3990.5, + "clarity_ratio": 3.86, + "median_distance_km": 3833.2, + "distances_to_centroid": { + "Boronia": 3833.2, + "Hobart": 3990.5, + "Melbourne City Centre": 3805.9, + "Southbank": 3805.6, + "Pauini": 15387.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boronia: (-37.87°, 145.28°)", + " Hobart: (-42.88°, 147.33°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Southbank: (-37.82°, 144.96°)", + " Pauini: (-7.71°, -66.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pauini: 15387.5 km from centroid", + " Hobart: 3990.5 km from centroid", + " Boronia: 3833.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pauini", + "FINAL ANSWER: Pauini" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.07381, + "lon": 14.24038, + "name": "Gela" + }, + { + "lat": 51.40878, + "lon": -0.02526, + "name": "Beckenham" + }, + { + "lat": 48.6328, + "lon": 2.44049, + "name": "Évry" + }, + { + "lat": 45.11326, + "lon": 41.0365, + "name": "Novokubansk" + }, + { + "lat": -31.87101, + "lon": 26.97862, + "name": "Queensdale" + } + ], + "question": "Which location is the geographic outlier among: Gela, Beckenham, Évry, Novokubansk, Queensdale?", + "ground_truth": { + "answer": "Queensdale", + "outlier_distance_km": 6968.7, + "second_furthest_km": 2754.6, + "clarity_ratio": 2.53, + "median_distance_km": 2685.1, + "distances_to_centroid": { + "Gela": 817.5, + "Beckenham": 2754.6, + "Évry": 2401.7, + "Novokubansk": 2685.1, + "Queensdale": 6968.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gela: (37.07°, 14.24°)", + " Beckenham: (51.41°, -0.03°)", + " Évry: (48.63°, 2.44°)", + " Novokubansk: (45.11°, 41.04°)", + " Queensdale: (-31.87°, 26.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Queensdale: 6968.7 km from centroid", + " Beckenham: 2754.6 km from centroid", + " Novokubansk: 2685.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Queensdale", + "FINAL ANSWER: Queensdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.92675, + "lon": 6.26764, + "name": "Yenagoa" + }, + { + "lat": 7.54978, + "lon": 37.85374, + "name": "Hosa’ina" + }, + { + "lat": 24.40796, + "lon": 32.92324, + "name": "Darāw" + }, + { + "lat": 9.18059, + "lon": 7.17939, + "name": "Suleja" + }, + { + "lat": 19.26722, + "lon": -103.73778, + "name": "Ciudad de Villa de Álvarez" + } + ], + "question": "Which location is the geographic outlier among: Yenagoa, Hosa’ina, Darāw, Suleja, Ciudad de Villa de Álvarez?", + "ground_truth": { + "answer": "Ciudad de Villa de Álvarez", + "outlier_distance_km": 10533.5, + "second_furthest_km": 4603.8, + "clarity_ratio": 2.29, + "median_distance_km": 4062.8, + "distances_to_centroid": { + "Yenagoa": 1436.8, + "Hosa’ina": 4603.8, + "Darāw": 4062.8, + "Suleja": 1283.7, + "Ciudad de Villa de Álvarez": 10533.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yenagoa: (4.93°, 6.27°)", + " Hosa’ina: (7.55°, 37.85°)", + " Darāw: (24.41°, 32.92°)", + " Suleja: (9.18°, 7.18°)", + " Ciudad de Villa de Álvarez: (19.27°, -103.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciudad de Villa de Álvarez: 10533.5 km from centroid", + " Hosa’ina: 4603.8 km from centroid", + " Darāw: 4062.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciudad de Villa de Álvarez", + "FINAL ANSWER: Ciudad de Villa de Álvarez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.53722, + "lon": -42.98194, + "name": "Guapimirim" + }, + { + "lat": -26.17722, + "lon": -50.39, + "name": "Canoinhas" + }, + { + "lat": -24.6925, + "lon": -48.00222, + "name": "Jacupiranga" + }, + { + "lat": 6.49156, + "lon": -74.40326, + "name": "Puerto Berrío" + }, + { + "lat": 31.55582, + "lon": 31.08918, + "name": "Balţīm" + } + ], + "question": "Which location is the geographic outlier among: Guapimirim, Canoinhas, Jacupiranga, Puerto Berrío, Balţīm?", + "ground_truth": { + "answer": "Balţīm", + "outlier_distance_km": 8384.6, + "second_furthest_km": 4421.3, + "clarity_ratio": 1.9, + "median_distance_km": 2557.8, + "distances_to_centroid": { + "Guapimirim": 1837.5, + "Canoinhas": 2557.8, + "Jacupiranga": 2285.9, + "Puerto Berrío": 4421.3, + "Balţīm": 8384.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guapimirim: (-22.54°, -42.98°)", + " Canoinhas: (-26.18°, -50.39°)", + " Jacupiranga: (-24.69°, -48.00°)", + " Puerto Berrío: (6.49°, -74.40°)", + " Balţīm: (31.56°, 31.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Balţīm: 8384.6 km from centroid", + " Puerto Berrío: 4421.3 km from centroid", + " Canoinhas: 2557.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Balţīm", + "FINAL ANSWER: Balţīm" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.73667, + "lon": 139.32361, + "name": "Fussa" + }, + { + "lat": -7.9797, + "lon": 112.6304, + "name": "Malang" + }, + { + "lat": 38.80898, + "lon": 77.44861, + "name": "Huangdi" + }, + { + "lat": 1.7439, + "lon": 103.3207, + "name": "Kawasan Penempatan Ulu Benut Lima" + }, + { + "lat": 33.41421, + "lon": -111.94348, + "name": "Tempe Junction" + } + ], + "question": "Which location is the geographic outlier among: Fussa, Malang, Huangdi, Kawasan Penempatan Ulu Benut Lima, Tempe Junction?", + "ground_truth": { + "answer": "Tempe Junction", + "outlier_distance_km": 14023.0, + "second_furthest_km": 7400.4, + "clarity_ratio": 1.89, + "median_distance_km": 6164.3, + "distances_to_centroid": { + "Fussa": 7400.4, + "Malang": 6164.3, + "Huangdi": 2416.1, + "Kawasan Penempatan Ulu Benut Lima": 4726.4, + "Tempe Junction": 14023.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fussa: (35.74°, 139.32°)", + " Malang: (-7.98°, 112.63°)", + " Huangdi: (38.81°, 77.45°)", + " Kawasan Penempatan Ulu Benut Lima: (1.74°, 103.32°)", + " Tempe Junction: (33.41°, -111.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tempe Junction: 14023.0 km from centroid", + " Fussa: 7400.4 km from centroid", + " Malang: 6164.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tempe Junction", + "FINAL ANSWER: Tempe Junction" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": 50.3592, + "lon": 11.17463, + "name": "Sonneberg" + } + ], + "question": "Which location is the geographic outlier among: Mornington, Ringwood, Caroline Springs, Ballajura, Sonneberg?", + "ground_truth": { + "answer": "Sonneberg", + "outlier_distance_km": 12414.8, + "second_furthest_km": 3799.2, + "clarity_ratio": 3.27, + "median_distance_km": 3796.2, + "distances_to_centroid": { + "Mornington": 3799.2, + "Ringwood": 3796.2, + "Caroline Springs": 3752.9, + "Ballajura": 1464.1, + "Sonneberg": 12414.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mornington: (-38.22°, 145.04°)", + " Ringwood: (-37.82°, 145.23°)", + " Caroline Springs: (-37.74°, 144.74°)", + " Ballajura: (-31.84°, 115.90°)", + " Sonneberg: (50.36°, 11.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sonneberg: 12414.8 km from centroid", + " Mornington: 3799.2 km from centroid", + " Ringwood: 3796.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sonneberg", + "FINAL ANSWER: Sonneberg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.62867, + "lon": 0.41963, + "name": "Billericay" + }, + { + "lat": 40.37966, + "lon": -3.73909, + "name": "Puerta Bonita" + }, + { + "lat": 49.9, + "lon": 2.3, + "name": "Amiens" + }, + { + "lat": 40.36863, + "lon": -3.71242, + "name": "Orcasitas" + }, + { + "lat": 42.67387, + "lon": 125.52885, + "name": "Dongfeng" + } + ], + "question": "Which location is the geographic outlier among: Billericay, Puerta Bonita, Amiens, Orcasitas, Dongfeng?", + "ground_truth": { + "answer": "Dongfeng", + "outlier_distance_km": 7546.8, + "second_furthest_km": 2324.9, + "clarity_ratio": 3.25, + "median_distance_km": 2323.3, + "distances_to_centroid": { + "Billericay": 1893.7, + "Puerta Bonita": 2324.9, + "Amiens": 1724.8, + "Orcasitas": 2323.3, + "Dongfeng": 7546.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Billericay: (51.63°, 0.42°)", + " Puerta Bonita: (40.38°, -3.74°)", + " Amiens: (49.90°, 2.30°)", + " Orcasitas: (40.37°, -3.71°)", + " Dongfeng: (42.67°, 125.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dongfeng: 7546.8 km from centroid", + " Puerta Bonita: 2324.9 km from centroid", + " Orcasitas: 2323.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dongfeng", + "FINAL ANSWER: Dongfeng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": -37.73261, + "lon": 144.86504, + "name": "Keilor East" + }, + { + "lat": 13.93139, + "lon": 121.61722, + "name": "Lucena" + } + ], + "question": "Which location is the geographic outlier among: Alexandra Hills, Glenferrie, Clayton, Keilor East, Lucena?", + "ground_truth": { + "answer": "Lucena", + "outlier_distance_km": 4899.8, + "second_furthest_km": 1421.1, + "clarity_ratio": 3.45, + "median_distance_km": 1410.8, + "distances_to_centroid": { + "Alexandra Hills": 1144.1, + "Glenferrie": 1410.8, + "Clayton": 1421.1, + "Keilor East": 1396.3, + "Lucena": 4899.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Glenferrie: (-37.83°, 145.05°)", + " Clayton: (-37.92°, 145.12°)", + " Keilor East: (-37.73°, 144.87°)", + " Lucena: (13.93°, 121.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lucena: 4899.8 km from centroid", + " Clayton: 1421.1 km from centroid", + " Glenferrie: 1410.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lucena", + "FINAL ANSWER: Lucena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.66667, + "lon": 145.06667, + "name": "Mill Park" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": -31.83291, + "lon": 115.7759, + "name": "Duncraig" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": 32.54208, + "lon": -97.32085, + "name": "Burleson" + } + ], + "question": "Which location is the geographic outlier among: Mill Park, Willetton, Duncraig, Camberwell, Burleson?", + "ground_truth": { + "answer": "Burleson", + "outlier_distance_km": 18753.7, + "second_furthest_km": 5992.4, + "clarity_ratio": 3.13, + "median_distance_km": 5992.3, + "distances_to_centroid": { + "Mill Park": 5992.3, + "Willetton": 3285.0, + "Duncraig": 3269.1, + "Camberwell": 5992.4, + "Burleson": 18753.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mill Park: (-37.67°, 145.07°)", + " Willetton: (-32.05°, 115.89°)", + " Duncraig: (-31.83°, 115.78°)", + " Camberwell: (-37.84°, 145.07°)", + " Burleson: (32.54°, -97.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Burleson: 18753.7 km from centroid", + " Camberwell: 5992.4 km from centroid", + " Mill Park: 5992.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Burleson", + "FINAL ANSWER: Burleson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.94404, + "lon": 73.83441, + "name": "Deolāli" + }, + { + "lat": 6.37527, + "lon": 124.74521, + "name": "Surallah" + }, + { + "lat": 29.57007, + "lon": 107.04542, + "name": "Dashun" + }, + { + "lat": 35.54651, + "lon": 139.51723, + "name": "Aobadai" + }, + { + "lat": -26.53333, + "lon": 29.06667, + "name": "eMbalenhle" + } + ], + "question": "Which location is the geographic outlier among: Deolāli, Surallah, Dashun, Aobadai, eMbalenhle?", + "ground_truth": { + "answer": "eMbalenhle", + "outlier_distance_km": 8349.1, + "second_furthest_km": 5117.4, + "clarity_ratio": 1.63, + "median_distance_km": 3356.1, + "distances_to_centroid": { + "Deolāli": 2367.6, + "Surallah": 3356.1, + "Dashun": 2232.6, + "Aobadai": 5117.4, + "eMbalenhle": 8349.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deolāli: (19.94°, 73.83°)", + " Surallah: (6.38°, 124.75°)", + " Dashun: (29.57°, 107.05°)", + " Aobadai: (35.55°, 139.52°)", + " eMbalenhle: (-26.53°, 29.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " eMbalenhle: 8349.1 km from centroid", + " Aobadai: 5117.4 km from centroid", + " Surallah: 3356.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: eMbalenhle", + "FINAL ANSWER: eMbalenhle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.0907, + "lon": -80.68618, + "name": "Stallings" + }, + { + "lat": 43.4668, + "lon": -80.51639, + "name": "Waterloo" + }, + { + "lat": 41.42973, + "lon": -97.36838, + "name": "Columbus" + }, + { + "lat": 33.62205, + "lon": -84.36909, + "name": "Forest Park" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + } + ], + "question": "Which location is the geographic outlier among: Stallings, Waterloo, Columbus, Forest Park, Cheltenham?", + "ground_truth": { + "answer": "Cheltenham", + "outlier_distance_km": 18307.0, + "second_furthest_km": 5686.4, + "clarity_ratio": 3.22, + "median_distance_km": 4498.0, + "distances_to_centroid": { + "Stallings": 4175.8, + "Waterloo": 4364.2, + "Columbus": 5686.4, + "Forest Park": 4498.0, + "Cheltenham": 18307.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stallings: (35.09°, -80.69°)", + " Waterloo: (43.47°, -80.52°)", + " Columbus: (41.43°, -97.37°)", + " Forest Park: (33.62°, -84.37°)", + " Cheltenham: (-37.97°, 145.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cheltenham: 18307.0 km from centroid", + " Columbus: 5686.4 km from centroid", + " Forest Park: 4498.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cheltenham", + "FINAL ANSWER: Cheltenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.66314, + "lon": 100.38781, + "name": "Ban Khlong Bang Phran" + }, + { + "lat": 25.8576, + "lon": 83.85487, + "name": "Rasrā" + }, + { + "lat": 3.2594, + "lon": 101.5541, + "name": "Kuang" + }, + { + "lat": 35.19278, + "lon": 128.08472, + "name": "Chinju" + }, + { + "lat": 54.70639, + "lon": 20.51102, + "name": "Kaliningrad" + } + ], + "question": "Which location is the geographic outlier among: Ban Khlong Bang Phran, Rasrā, Kuang, Chinju, Kaliningrad?", + "ground_truth": { + "answer": "Kaliningrad", + "outlier_distance_km": 6129.1, + "second_furthest_km": 4019.0, + "clarity_ratio": 1.53, + "median_distance_km": 3023.8, + "distances_to_centroid": { + "Ban Khlong Bang Phran": 2006.5, + "Rasrā": 311.0, + "Kuang": 3023.8, + "Chinju": 4019.0, + "Kaliningrad": 6129.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ban Khlong Bang Phran: (13.66°, 100.39°)", + " Rasrā: (25.86°, 83.85°)", + " Kuang: (3.26°, 101.55°)", + " Chinju: (35.19°, 128.08°)", + " Kaliningrad: (54.71°, 20.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kaliningrad: 6129.1 km from centroid", + " Chinju: 4019.0 km from centroid", + " Kuang: 3023.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kaliningrad", + "FINAL ANSWER: Kaliningrad" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.27875, + "lon": 3.97267, + "name": "Maubeuge" + }, + { + "lat": 42.69764, + "lon": 2.89541, + "name": "Perpignan" + }, + { + "lat": 52.99505, + "lon": 16.9198, + "name": "Chodzież" + }, + { + "lat": 54.51889, + "lon": 18.53188, + "name": "Gdynia" + }, + { + "lat": 44.82774, + "lon": -92.94382, + "name": "Cottage Grove" + } + ], + "question": "Which location is the geographic outlier among: Maubeuge, Perpignan, Chodzież, Gdynia, Cottage Grove?", + "ground_truth": { + "answer": "Cottage Grove", + "outlier_distance_km": 5981.9, + "second_furthest_km": 2045.8, + "clarity_ratio": 2.92, + "median_distance_km": 1928.7, + "distances_to_centroid": { + "Maubeuge": 1021.9, + "Perpignan": 1228.9, + "Chodzież": 1928.7, + "Gdynia": 2045.8, + "Cottage Grove": 5981.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maubeuge: (50.28°, 3.97°)", + " Perpignan: (42.70°, 2.90°)", + " Chodzież: (53.00°, 16.92°)", + " Gdynia: (54.52°, 18.53°)", + " Cottage Grove: (44.83°, -92.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cottage Grove: 5981.9 km from centroid", + " Gdynia: 2045.8 km from centroid", + " Chodzież: 1928.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cottage Grove", + "FINAL ANSWER: Cottage Grove" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8149, + "lon": 144.95052, + "name": "Docklands" + }, + { + "lat": -37.6, + "lon": 144.95, + "name": "Craigieburn" + }, + { + "lat": -37.88461, + "lon": 145.29539, + "name": "Ferntree Gully" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": 3.5638, + "lon": 101.6581, + "name": "Kuala Kubu Baharu" + } + ], + "question": "Which location is the geographic outlier among: Docklands, Craigieburn, Ferntree Gully, Willetton, Kuala Kubu Baharu?", + "ground_truth": { + "answer": "Kuala Kubu Baharu", + "outlier_distance_km": 4705.1, + "second_furthest_km": 1730.7, + "clarity_ratio": 2.72, + "median_distance_km": 1701.2, + "distances_to_centroid": { + "Docklands": 1701.2, + "Craigieburn": 1687.9, + "Ferntree Gully": 1730.7, + "Willetton": 1466.1, + "Kuala Kubu Baharu": 4705.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Docklands: (-37.81°, 144.95°)", + " Craigieburn: (-37.60°, 144.95°)", + " Ferntree Gully: (-37.88°, 145.30°)", + " Willetton: (-32.05°, 115.89°)", + " Kuala Kubu Baharu: (3.56°, 101.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kuala Kubu Baharu: 4705.1 km from centroid", + " Ferntree Gully: 1730.7 km from centroid", + " Docklands: 1701.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kuala Kubu Baharu", + "FINAL ANSWER: Kuala Kubu Baharu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.6561, + "lon": 123.4227, + "name": "Dapitan" + }, + { + "lat": -6.28417, + "lon": 107.81056, + "name": "Pamanukan" + }, + { + "lat": 31.43224, + "lon": 75.71484, + "name": "Adampur" + }, + { + "lat": 12.93333, + "lon": 100.88333, + "name": "Pattaya" + }, + { + "lat": -21.36, + "lon": -48.22833, + "name": "Guariba" + } + ], + "question": "Which location is the geographic outlier among: Dapitan, Pamanukan, Adampur, Pattaya, Guariba?", + "ground_truth": { + "answer": "Guariba", + "outlier_distance_km": 13329.7, + "second_furthest_km": 5695.7, + "clarity_ratio": 2.34, + "median_distance_km": 4179.4, + "distances_to_centroid": { + "Dapitan": 5695.7, + "Pamanukan": 4179.4, + "Adampur": 2957.4, + "Pattaya": 3295.2, + "Guariba": 13329.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dapitan: (8.66°, 123.42°)", + " Pamanukan: (-6.28°, 107.81°)", + " Adampur: (31.43°, 75.71°)", + " Pattaya: (12.93°, 100.88°)", + " Guariba: (-21.36°, -48.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guariba: 13329.7 km from centroid", + " Dapitan: 5695.7 km from centroid", + " Pamanukan: 4179.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guariba", + "FINAL ANSWER: Guariba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.34982, + "lon": -81.63262, + "name": "Charleston" + }, + { + "lat": 28.53834, + "lon": -81.37924, + "name": "Orlando" + }, + { + "lat": 34.82984, + "lon": -82.60152, + "name": "Easley" + }, + { + "lat": 32.98101, + "lon": -80.03259, + "name": "Goose Creek" + }, + { + "lat": -7.4475, + "lon": -35.24417, + "name": "Ferreiros" + } + ], + "question": "Which location is the geographic outlier among: Charleston, Orlando, Easley, Goose Creek, Ferreiros?", + "ground_truth": { + "answer": "Ferreiros", + "outlier_distance_km": 5415.4, + "second_furthest_km": 1687.1, + "clarity_ratio": 3.21, + "median_distance_km": 1444.7, + "distances_to_centroid": { + "Charleston": 1687.1, + "Orlando": 973.8, + "Easley": 1444.7, + "Goose Creek": 1131.6, + "Ferreiros": 5415.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Charleston: (38.35°, -81.63°)", + " Orlando: (28.54°, -81.38°)", + " Easley: (34.83°, -82.60°)", + " Goose Creek: (32.98°, -80.03°)", + " Ferreiros: (-7.45°, -35.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ferreiros: 5415.4 km from centroid", + " Charleston: 1687.1 km from centroid", + " Easley: 1444.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ferreiros", + "FINAL ANSWER: Ferreiros" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.05266, + "lon": -78.87836, + "name": "Fayetteville" + }, + { + "lat": 45.58344, + "lon": -62.64863, + "name": "New Glasgow" + }, + { + "lat": 20.91154, + "lon": -97.67554, + "name": "Álamo" + }, + { + "lat": 40.74482, + "lon": -73.94875, + "name": "Long Island City" + }, + { + "lat": 7.31667, + "lon": 38.08333, + "name": "K’olīto" + } + ], + "question": "Which location is the geographic outlier among: Fayetteville, New Glasgow, Álamo, Long Island City, K’olīto?", + "ground_truth": { + "answer": "K’olīto", + "outlier_distance_km": 9898.7, + "second_furthest_km": 4374.3, + "clarity_ratio": 2.26, + "median_distance_km": 2303.7, + "distances_to_centroid": { + "Fayetteville": 2303.7, + "New Glasgow": 1864.2, + "Álamo": 4374.3, + "Long Island City": 2089.9, + "K’olīto": 9898.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fayetteville: (35.05°, -78.88°)", + " New Glasgow: (45.58°, -62.65°)", + " Álamo: (20.91°, -97.68°)", + " Long Island City: (40.74°, -73.95°)", + " K’olīto: (7.32°, 38.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " K’olīto: 9898.7 km from centroid", + " Álamo: 4374.3 km from centroid", + " Fayetteville: 2303.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: K’olīto", + "FINAL ANSWER: K’olīto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 23.71667, + "lon": 86.4, + "name": "Jāmadoba" + }, + { + "lat": 25.43596, + "lon": 92.19132, + "name": "Jowai" + }, + { + "lat": 13.16667, + "lon": 123.71667, + "name": "Tagas" + }, + { + "lat": 29.89929, + "lon": 107.46452, + "name": "Zhenxi" + }, + { + "lat": -34.75155, + "lon": 149.72086, + "name": "Goulburn" + } + ], + "question": "Which location is the geographic outlier among: Jāmadoba, Jowai, Tagas, Zhenxi, Goulburn?", + "ground_truth": { + "answer": "Goulburn", + "outlier_distance_km": 6505.4, + "second_furthest_km": 3017.2, + "clarity_ratio": 2.16, + "median_distance_km": 2586.7, + "distances_to_centroid": { + "Jāmadoba": 3017.2, + "Jowai": 2586.7, + "Tagas": 1297.0, + "Zhenxi": 2097.3, + "Goulburn": 6505.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jāmadoba: (23.72°, 86.40°)", + " Jowai: (25.44°, 92.19°)", + " Tagas: (13.17°, 123.72°)", + " Zhenxi: (29.90°, 107.46°)", + " Goulburn: (-34.75°, 149.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Goulburn: 6505.4 km from centroid", + " Jāmadoba: 3017.2 km from centroid", + " Jowai: 2586.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Goulburn", + "FINAL ANSWER: Goulburn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.78341, + "lon": 114.87139, + "name": "Zhangjiakou" + }, + { + "lat": 22.83283, + "lon": 74.25986, + "name": "Dohad" + }, + { + "lat": 17.46885, + "lon": 106.62226, + "name": "Đồng Hới" + }, + { + "lat": 19.66529, + "lon": 82.20629, + "name": "Umarkot" + }, + { + "lat": 39.55388, + "lon": -104.96943, + "name": "Highlands Ranch" + } + ], + "question": "Which location is the geographic outlier among: Zhangjiakou, Dohad, Đồng Hới, Umarkot, Highlands Ranch?", + "ground_truth": { + "answer": "Highlands Ranch", + "outlier_distance_km": 12204.4, + "second_furthest_km": 5594.5, + "clarity_ratio": 2.18, + "median_distance_km": 5422.3, + "distances_to_centroid": { + "Zhangjiakou": 5594.5, + "Dohad": 2055.2, + "Đồng Hới": 5422.3, + "Umarkot": 2950.5, + "Highlands Ranch": 12204.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhangjiakou: (40.78°, 114.87°)", + " Dohad: (22.83°, 74.26°)", + " Đồng Hới: (17.47°, 106.62°)", + " Umarkot: (19.67°, 82.21°)", + " Highlands Ranch: (39.55°, -104.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Highlands Ranch: 12204.4 km from centroid", + " Zhangjiakou: 5594.5 km from centroid", + " Đồng Hới: 5422.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Highlands Ranch", + "FINAL ANSWER: Highlands Ranch" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.10172, + "lon": -80.76452, + "name": "Austintown" + }, + { + "lat": 34.1389, + "lon": -118.35341, + "name": "Universal City" + }, + { + "lat": 32.67811, + "lon": -117.0992, + "name": "National City" + }, + { + "lat": 38.14535, + "lon": -85.8583, + "name": "Pleasure Ridge Park" + }, + { + "lat": -18.775, + "lon": -42.9325, + "name": "Guanhães" + } + ], + "question": "Which location is the geographic outlier among: Austintown, Universal City, National City, Pleasure Ridge Park, Guanhães?", + "ground_truth": { + "answer": "Guanhães", + "outlier_distance_km": 6999.9, + "second_furthest_km": 2979.7, + "clarity_ratio": 2.35, + "median_distance_km": 2836.7, + "distances_to_centroid": { + "Austintown": 1898.3, + "Universal City": 2979.7, + "National City": 2836.7, + "Pleasure Ridge Park": 1441.5, + "Guanhães": 6999.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Austintown: (41.10°, -80.76°)", + " Universal City: (34.14°, -118.35°)", + " National City: (32.68°, -117.10°)", + " Pleasure Ridge Park: (38.15°, -85.86°)", + " Guanhães: (-18.77°, -42.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guanhães: 6999.9 km from centroid", + " Universal City: 2979.7 km from centroid", + " National City: 2836.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guanhães", + "FINAL ANSWER: Guanhães" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.90288, + "lon": -3.52261, + "name": "Livingston" + }, + { + "lat": 40.39061, + "lon": -3.64824, + "name": "Portazgo" + }, + { + "lat": 48.88341, + "lon": 2.23894, + "name": "Puteaux" + }, + { + "lat": 43.94834, + "lon": 4.80892, + "name": "Avignon" + }, + { + "lat": 23.40673, + "lon": 76.7098, + "name": "Shujālpur" + } + ], + "question": "Which location is the geographic outlier among: Livingston, Portazgo, Puteaux, Avignon, Shujālpur?", + "ground_truth": { + "answer": "Shujālpur", + "outlier_distance_km": 5968.5, + "second_furthest_km": 2009.9, + "clarity_ratio": 2.97, + "median_distance_km": 1594.7, + "distances_to_centroid": { + "Livingston": 2009.9, + "Portazgo": 1594.7, + "Puteaux": 1236.1, + "Avignon": 865.7, + "Shujālpur": 5968.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Livingston: (55.90°, -3.52°)", + " Portazgo: (40.39°, -3.65°)", + " Puteaux: (48.88°, 2.24°)", + " Avignon: (43.95°, 4.81°)", + " Shujālpur: (23.41°, 76.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shujālpur: 5968.5 km from centroid", + " Livingston: 2009.9 km from centroid", + " Portazgo: 1594.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shujālpur", + "FINAL ANSWER: Shujālpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + { + "lat": 29.30995, + "lon": 30.8418, + "name": "Al Fayyum" + } + ], + "question": "Which location is the geographic outlier among: Avondale, Dandenong North, Karori, Ballarat, Al Fayyum?", + "ground_truth": { + "answer": "Al Fayyum", + "outlier_distance_km": 12520.2, + "second_furthest_km": 4172.9, + "clarity_ratio": 3.0, + "median_distance_km": 4083.5, + "distances_to_centroid": { + "Avondale": 4083.5, + "Dandenong North": 1806.7, + "Karori": 4172.9, + "Ballarat": 1697.9, + "Al Fayyum": 12520.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Avondale: (-36.88°, 174.70°)", + " Dandenong North: (-37.97°, 145.21°)", + " Karori: (-41.28°, 174.74°)", + " Ballarat: (-37.57°, 143.85°)", + " Al Fayyum: (29.31°, 30.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Fayyum: 12520.2 km from centroid", + " Karori: 4172.9 km from centroid", + " Avondale: 4083.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Fayyum", + "FINAL ANSWER: Al Fayyum" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.50035, + "lon": -79.74949, + "name": "Plum" + }, + { + "lat": 33.49838, + "lon": -112.13432, + "name": "Alhambra" + }, + { + "lat": 47.32232, + "lon": -122.31262, + "name": "Federal Way" + }, + { + "lat": 42.15141, + "lon": -87.95979, + "name": "Buffalo Grove" + }, + { + "lat": 34.23072, + "lon": 74.6472, + "name": "Sumbal" + } + ], + "question": "Which location is the geographic outlier among: Plum, Alhambra, Federal Way, Buffalo Grove, Sumbal?", + "ground_truth": { + "answer": "Sumbal", + "outlier_distance_km": 10846.9, + "second_furthest_km": 4564.0, + "clarity_ratio": 2.38, + "median_distance_km": 4174.0, + "distances_to_centroid": { + "Plum": 1216.6, + "Alhambra": 4174.0, + "Federal Way": 4564.0, + "Buffalo Grove": 1905.6, + "Sumbal": 10846.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Plum: (40.50°, -79.75°)", + " Alhambra: (33.50°, -112.13°)", + " Federal Way: (47.32°, -122.31°)", + " Buffalo Grove: (42.15°, -87.96°)", + " Sumbal: (34.23°, 74.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sumbal: 10846.9 km from centroid", + " Federal Way: 4564.0 km from centroid", + " Alhambra: 4174.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sumbal", + "FINAL ANSWER: Sumbal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": 21.34215, + "lon": -157.82852, + "name": "Nuuanu - Punchbowl" + } + ], + "question": "Which location is the geographic outlier among: Cheltenham, Glen Waverley, Caboolture, Randwick, Nuuanu - Punchbowl?", + "ground_truth": { + "answer": "Nuuanu - Punchbowl", + "outlier_distance_km": 13364.7, + "second_furthest_km": 6549.6, + "clarity_ratio": 2.04, + "median_distance_km": 6264.1, + "distances_to_centroid": { + "Cheltenham": 5677.4, + "Glen Waverley": 5687.8, + "Caboolture": 6549.6, + "Randwick": 6264.1, + "Nuuanu - Punchbowl": 13364.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cheltenham: (-37.97°, 145.05°)", + " Glen Waverley: (-37.88°, 145.16°)", + " Caboolture: (-27.08°, 152.95°)", + " Randwick: (-33.91°, 151.25°)", + " Nuuanu - Punchbowl: (21.34°, -157.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nuuanu - Punchbowl: 13364.7 km from centroid", + " Caboolture: 6549.6 km from centroid", + " Randwick: 6264.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nuuanu - Punchbowl", + "FINAL ANSWER: Nuuanu - Punchbowl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.96176, + "lon": -89.82953, + "name": "Olive Branch" + }, + { + "lat": 38.55185, + "lon": -121.36467, + "name": "Rosemont" + }, + { + "lat": 19.33972, + "lon": -98.95056, + "name": "San Isidro" + }, + { + "lat": 42.35336, + "lon": -88.09341, + "name": "Round Lake" + }, + { + "lat": -23.30246, + "lon": 30.71868, + "name": "Giyani" + } + ], + "question": "Which location is the geographic outlier among: Olive Branch, Rosemont, San Isidro, Round Lake, Giyani?", + "ground_truth": { + "answer": "Giyani", + "outlier_distance_km": 12348.8, + "second_furthest_km": 4863.7, + "clarity_ratio": 2.54, + "median_distance_km": 2662.4, + "distances_to_centroid": { + "Olive Branch": 2114.3, + "Rosemont": 4863.7, + "San Isidro": 2662.4, + "Round Lake": 2600.9, + "Giyani": 12348.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Olive Branch: (34.96°, -89.83°)", + " Rosemont: (38.55°, -121.36°)", + " San Isidro: (19.34°, -98.95°)", + " Round Lake: (42.35°, -88.09°)", + " Giyani: (-23.30°, 30.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Giyani: 12348.8 km from centroid", + " Rosemont: 4863.7 km from centroid", + " San Isidro: 2662.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Giyani", + "FINAL ANSWER: Giyani" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + }, + { + "lat": 33.78417, + "lon": 104.36278, + "name": "Zhouqu Chengguanzhen" + } + ], + "question": "Which location is the geographic outlier among: Tauranga, Epsom, Porirua, Albany, Zhouqu Chengguanzhen?", + "ground_truth": { + "answer": "Zhouqu Chengguanzhen", + "outlier_distance_km": 7956.8, + "second_furthest_km": 3321.4, + "clarity_ratio": 2.4, + "median_distance_km": 3066.0, + "distances_to_centroid": { + "Tauranga": 2982.9, + "Epsom": 2833.6, + "Porirua": 3066.0, + "Albany": 3321.4, + "Zhouqu Chengguanzhen": 7956.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tauranga: (-37.69°, 176.17°)", + " Epsom: (-36.89°, 174.77°)", + " Porirua: (-41.13°, 174.85°)", + " Albany: (-35.03°, 117.88°)", + " Zhouqu Chengguanzhen: (33.78°, 104.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhouqu Chengguanzhen: 7956.8 km from centroid", + " Albany: 3321.4 km from centroid", + " Porirua: 3066.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhouqu Chengguanzhen", + "FINAL ANSWER: Zhouqu Chengguanzhen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.63333, + "lon": -58.41667, + "name": "Boedo" + }, + { + "lat": -9.38861, + "lon": -37.99917, + "name": "Delmiro Gouveia" + }, + { + "lat": -23.08842, + "lon": -47.2119, + "name": "Indaiatuba" + }, + { + "lat": -22.43611, + "lon": -46.82167, + "name": "Itapira" + }, + { + "lat": 42.12753, + "lon": -87.82895, + "name": "Northbrook" + } + ], + "question": "Which location is the geographic outlier among: Boedo, Delmiro Gouveia, Indaiatuba, Itapira, Northbrook?", + "ground_truth": { + "answer": "Northbrook", + "outlier_distance_km": 6607.8, + "second_furthest_km": 2810.6, + "clarity_ratio": 2.35, + "median_distance_km": 1936.6, + "distances_to_centroid": { + "Boedo": 2810.6, + "Delmiro Gouveia": 1936.6, + "Indaiatuba": 1759.5, + "Itapira": 1720.9, + "Northbrook": 6607.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boedo: (-34.63°, -58.42°)", + " Delmiro Gouveia: (-9.39°, -38.00°)", + " Indaiatuba: (-23.09°, -47.21°)", + " Itapira: (-22.44°, -46.82°)", + " Northbrook: (42.13°, -87.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Northbrook: 6607.8 km from centroid", + " Boedo: 2810.6 km from centroid", + " Delmiro Gouveia: 1936.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Northbrook", + "FINAL ANSWER: Northbrook" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.16667, + "lon": 110.56667, + "name": "Serian" + }, + { + "lat": 24.64486, + "lon": 85.50028, + "name": "Rajauli" + }, + { + "lat": 24.9177, + "lon": 79.58871, + "name": "Chhatarpur" + }, + { + "lat": 13.95, + "lon": 108.65, + "name": "An Khê" + }, + { + "lat": 43.2907, + "lon": 5.4384, + "name": "Marseille 11" + } + ], + "question": "Which location is the geographic outlier among: Serian, Rajauli, Chhatarpur, An Khê, Marseille 11?", + "ground_truth": { + "answer": "Marseille 11", + "outlier_distance_km": 6992.7, + "second_furthest_km": 4199.6, + "clarity_ratio": 1.67, + "median_distance_km": 3353.5, + "distances_to_centroid": { + "Serian": 4199.6, + "Rajauli": 843.3, + "Chhatarpur": 405.8, + "An Khê": 3353.5, + "Marseille 11": 6992.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Serian: (1.17°, 110.57°)", + " Rajauli: (24.64°, 85.50°)", + " Chhatarpur: (24.92°, 79.59°)", + " An Khê: (13.95°, 108.65°)", + " Marseille 11: (43.29°, 5.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marseille 11: 6992.7 km from centroid", + " Serian: 4199.6 km from centroid", + " An Khê: 3353.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marseille 11", + "FINAL ANSWER: Marseille 11" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -40.35636, + "lon": 175.61113, + "name": "Palmerston North" + }, + { + "lat": -36.8382, + "lon": 174.61019, + "name": "Massey" + }, + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + { + "lat": -12.93333, + "lon": -74.25, + "name": "Huanta" + } + ], + "question": "Which location is the geographic outlier among: Palmerston North, Massey, Brisbane, Granville, Huanta?", + "ground_truth": { + "answer": "Huanta", + "outlier_distance_km": 15085.5, + "second_furthest_km": 5419.8, + "clarity_ratio": 2.78, + "median_distance_km": 5395.2, + "distances_to_centroid": { + "Palmerston North": 5419.8, + "Massey": 5395.2, + "Brisbane": 3603.1, + "Granville": 3306.4, + "Huanta": 15085.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palmerston North: (-40.36°, 175.61°)", + " Massey: (-36.84°, 174.61°)", + " Brisbane: (-27.47°, 153.03°)", + " Granville: (-33.84°, 151.01°)", + " Huanta: (-12.93°, -74.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huanta: 15085.5 km from centroid", + " Palmerston North: 5419.8 km from centroid", + " Massey: 5395.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huanta", + "FINAL ANSWER: Huanta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": 33.45737, + "lon": 132.4328, + "name": "Yawatahama" + } + ], + "question": "Which location is the geographic outlier among: Maryborough, Earlwood, Rockhampton, Carlton, Yawatahama?", + "ground_truth": { + "answer": "Yawatahama", + "outlier_distance_km": 5848.7, + "second_furthest_km": 2268.3, + "clarity_ratio": 2.58, + "median_distance_km": 1893.7, + "distances_to_centroid": { + "Maryborough": 1115.2, + "Earlwood": 1893.7, + "Rockhampton": 790.2, + "Carlton": 2268.3, + "Yawatahama": 5848.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maryborough: (-25.54°, 152.70°)", + " Earlwood: (-33.92°, 151.13°)", + " Rockhampton: (-23.38°, 150.51°)", + " Carlton: (-37.80°, 144.97°)", + " Yawatahama: (33.46°, 132.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yawatahama: 5848.7 km from centroid", + " Carlton: 2268.3 km from centroid", + " Earlwood: 1893.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yawatahama", + "FINAL ANSWER: Yawatahama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.21197, + "lon": -88.23814, + "name": "Cary" + }, + { + "lat": 32.7668, + "lon": -96.59916, + "name": "Mesquite" + }, + { + "lat": 43.80938, + "lon": -79.22344, + "name": "Malvern" + }, + { + "lat": 34.1064, + "lon": -117.37032, + "name": "Rialto" + }, + { + "lat": 12.01667, + "lon": 39.63333, + "name": "Robīt" + } + ], + "question": "Which location is the geographic outlier among: Cary, Mesquite, Malvern, Rialto, Robīt?", + "ground_truth": { + "answer": "Robīt", + "outlier_distance_km": 10903.1, + "second_furthest_km": 4499.3, + "clarity_ratio": 2.42, + "median_distance_km": 2629.4, + "distances_to_centroid": { + "Cary": 2022.5, + "Mesquite": 2629.4, + "Malvern": 1528.7, + "Rialto": 4499.3, + "Robīt": 10903.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cary: (42.21°, -88.24°)", + " Mesquite: (32.77°, -96.60°)", + " Malvern: (43.81°, -79.22°)", + " Rialto: (34.11°, -117.37°)", + " Robīt: (12.02°, 39.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Robīt: 10903.1 km from centroid", + " Rialto: 4499.3 km from centroid", + " Mesquite: 2629.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Robīt", + "FINAL ANSWER: Robīt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.83333, + "lon": 137.23333, + "name": "Gamagōri" + }, + { + "lat": 28.71753, + "lon": 77.26508, + "name": "Dayal Pur" + }, + { + "lat": 17.75353, + "lon": 106.42355, + "name": "Ba Đồn" + }, + { + "lat": 22.75278, + "lon": 88.34222, + "name": "Shrīrāmpur" + }, + { + "lat": 25.86898, + "lon": -80.21699, + "name": "Pinewood" + } + ], + "question": "Which location is the geographic outlier among: Gamagōri, Dayal Pur, Ba Đồn, Shrīrāmpur, Pinewood?", + "ground_truth": { + "answer": "Pinewood", + "outlier_distance_km": 13194.3, + "second_furthest_km": 6779.2, + "clarity_ratio": 1.95, + "median_distance_km": 4272.2, + "distances_to_centroid": { + "Gamagōri": 6779.2, + "Dayal Pur": 1170.9, + "Ba Đồn": 4272.2, + "Shrīrāmpur": 2307.4, + "Pinewood": 13194.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gamagōri: (34.83°, 137.23°)", + " Dayal Pur: (28.72°, 77.27°)", + " Ba Đồn: (17.75°, 106.42°)", + " Shrīrāmpur: (22.75°, 88.34°)", + " Pinewood: (25.87°, -80.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pinewood: 13194.3 km from centroid", + " Gamagōri: 6779.2 km from centroid", + " Ba Đồn: 4272.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pinewood", + "FINAL ANSWER: Pinewood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.80521, + "lon": 139.71072, + "name": "Kawaguchi" + }, + { + "lat": 13.53671, + "lon": 99.81712, + "name": "Ratchaburi" + }, + { + "lat": 30.81609, + "lon": 108.26216, + "name": "Lihe" + }, + { + "lat": 39.70842, + "lon": 76.17971, + "name": "Artux" + }, + { + "lat": 51.58571, + "lon": 0.60459, + "name": "Rayleigh" + } + ], + "question": "Which location is the geographic outlier among: Kawaguchi, Ratchaburi, Lihe, Artux, Rayleigh?", + "ground_truth": { + "answer": "Rayleigh", + "outlier_distance_km": 6728.0, + "second_furthest_km": 4924.2, + "clarity_ratio": 1.37, + "median_distance_km": 2752.8, + "distances_to_centroid": { + "Kawaguchi": 4924.2, + "Ratchaburi": 2752.8, + "Lihe": 2217.0, + "Artux": 981.4, + "Rayleigh": 6728.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kawaguchi: (35.81°, 139.71°)", + " Ratchaburi: (13.54°, 99.82°)", + " Lihe: (30.82°, 108.26°)", + " Artux: (39.71°, 76.18°)", + " Rayleigh: (51.59°, 0.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rayleigh: 6728.0 km from centroid", + " Kawaguchi: 4924.2 km from centroid", + " Ratchaburi: 2752.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rayleigh", + "FINAL ANSWER: Rayleigh" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.3939, + "lon": 114.1464, + "name": "Gambiran Satu" + }, + { + "lat": 26.25318, + "lon": 108.65785, + "name": "Shangchong" + }, + { + "lat": 17.3381, + "lon": 77.90441, + "name": "Vikārābād" + }, + { + "lat": 21.59556, + "lon": 78.52628, + "name": "Pāndhurnā" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + } + ], + "question": "Which location is the geographic outlier among: Gambiran Satu, Shangchong, Vikārābād, Pāndhurnā, Manukau City?", + "ground_truth": { + "answer": "Manukau City", + "outlier_distance_km": 8019.3, + "second_furthest_km": 3997.8, + "clarity_ratio": 2.01, + "median_distance_km": 3882.7, + "distances_to_centroid": { + "Gambiran Satu": 1422.3, + "Shangchong": 2489.6, + "Vikārābād": 3882.7, + "Pāndhurnā": 3997.8, + "Manukau City": 8019.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gambiran Satu: (-8.39°, 114.15°)", + " Shangchong: (26.25°, 108.66°)", + " Vikārābād: (17.34°, 77.90°)", + " Pāndhurnā: (21.60°, 78.53°)", + " Manukau City: (-36.99°, 174.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manukau City: 8019.3 km from centroid", + " Pāndhurnā: 3997.8 km from centroid", + " Vikārābād: 3882.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manukau City", + "FINAL ANSWER: Manukau City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.73191, + "lon": -93.21772, + "name": "Apple Valley" + }, + { + "lat": 47.76232, + "lon": -122.2054, + "name": "Bothell" + }, + { + "lat": 34.11612, + "lon": -118.15035, + "name": "South Pasadena" + }, + { + "lat": 33.99349, + "lon": -81.07398, + "name": "West Columbia" + }, + { + "lat": 5.55728, + "lon": -0.1864, + "name": "Osu" + } + ], + "question": "Which location is the geographic outlier among: Apple Valley, Bothell, South Pasadena, West Columbia, Osu?", + "ground_truth": { + "answer": "Osu", + "outlier_distance_km": 8998.6, + "second_furthest_km": 3639.3, + "clarity_ratio": 2.47, + "median_distance_km": 3241.1, + "distances_to_centroid": { + "Apple Valley": 1552.9, + "Bothell": 3639.3, + "South Pasadena": 3241.1, + "West Columbia": 194.6, + "Osu": 8998.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Apple Valley: (44.73°, -93.22°)", + " Bothell: (47.76°, -122.21°)", + " South Pasadena: (34.12°, -118.15°)", + " West Columbia: (33.99°, -81.07°)", + " Osu: (5.56°, -0.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Osu: 8998.6 km from centroid", + " Bothell: 3639.3 km from centroid", + " South Pasadena: 3241.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Osu", + "FINAL ANSWER: Osu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.16143, + "lon": 124.37785, + "name": "Siping" + }, + { + "lat": 34.56667, + "lon": 117.82778, + "name": "Xinglou" + }, + { + "lat": 8.16453, + "lon": 99.68039, + "name": "Thung Song" + }, + { + "lat": 34.58333, + "lon": 135.83333, + "name": "Tenri" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + } + ], + "question": "Which location is the geographic outlier among: Siping, Xinglou, Thung Song, Tenri, Epping?", + "ground_truth": { + "answer": "Epping", + "outlier_distance_km": 6397.8, + "second_furthest_km": 2957.4, + "clarity_ratio": 2.16, + "median_distance_km": 2854.7, + "distances_to_centroid": { + "Siping": 2957.4, + "Xinglou": 2110.7, + "Thung Song": 2854.7, + "Tenri": 2297.0, + "Epping": 6397.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Siping: (43.16°, 124.38°)", + " Xinglou: (34.57°, 117.83°)", + " Thung Song: (8.16°, 99.68°)", + " Tenri: (34.58°, 135.83°)", + " Epping: (-37.65°, 145.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Epping: 6397.8 km from centroid", + " Siping: 2957.4 km from centroid", + " Thung Song: 2854.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Epping", + "FINAL ANSWER: Epping" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.9383, + "lon": -0.10087, + "name": "Vila-real" + }, + { + "lat": 51.20219, + "lon": 7.36027, + "name": "Radevormwald" + }, + { + "lat": 47.86825, + "lon": 12.64335, + "name": "Traunstein" + }, + { + "lat": 51.1209, + "lon": 38.5116, + "name": "Rossosh’" + }, + { + "lat": 5.63418, + "lon": 38.23603, + "name": "Hagere Maryam" + } + ], + "question": "Which location is the geographic outlier among: Vila-real, Radevormwald, Traunstein, Rossosh’, Hagere Maryam?", + "ground_truth": { + "answer": "Hagere Maryam", + "outlier_distance_km": 4183.2, + "second_furthest_km": 1997.7, + "clarity_ratio": 2.09, + "median_distance_km": 1665.1, + "distances_to_centroid": { + "Vila-real": 1665.1, + "Radevormwald": 1631.2, + "Traunstein": 1108.0, + "Rossosh’": 1997.7, + "Hagere Maryam": 4183.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vila-real: (39.94°, -0.10°)", + " Radevormwald: (51.20°, 7.36°)", + " Traunstein: (47.87°, 12.64°)", + " Rossosh’: (51.12°, 38.51°)", + " Hagere Maryam: (5.63°, 38.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hagere Maryam: 4183.2 km from centroid", + " Rossosh’: 1997.7 km from centroid", + " Vila-real: 1665.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hagere Maryam", + "FINAL ANSWER: Hagere Maryam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + }, + { + "lat": 50.8567, + "lon": -0.98559, + "name": "Havant" + } + ], + "question": "Which location is the geographic outlier among: Baldivis, Southport, Wahroonga, Paralowie, Havant?", + "ground_truth": { + "answer": "Havant", + "outlier_distance_km": 12923.0, + "second_furthest_km": 4505.9, + "clarity_ratio": 2.87, + "median_distance_km": 4436.8, + "distances_to_centroid": { + "Baldivis": 1910.6, + "Southport": 4505.9, + "Wahroonga": 4436.8, + "Paralowie": 3434.5, + "Havant": 12923.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baldivis: (-32.33°, 115.83°)", + " Southport: (-27.97°, 153.40°)", + " Wahroonga: (-33.72°, 151.12°)", + " Paralowie: (-34.76°, 138.61°)", + " Havant: (50.86°, -0.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Havant: 12923.0 km from centroid", + " Southport: 4505.9 km from centroid", + " Wahroonga: 4436.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Havant", + "FINAL ANSWER: Havant" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.13873, + "lon": -45.11881, + "name": "Olho d’Água das Cunhãs" + }, + { + "lat": -4.90389, + "lon": -80.68528, + "name": "Sullana" + }, + { + "lat": -32.84043, + "lon": -70.95623, + "name": "Llaillay" + }, + { + "lat": -15.46056, + "lon": -55.74972, + "name": "Chapada dos Guimarães" + }, + { + "lat": 47.7742, + "lon": 7.35175, + "name": "Illzach" + } + ], + "question": "Which location is the geographic outlier among: Olho d’Água das Cunhãs, Sullana, Llaillay, Chapada dos Guimarães, Illzach?", + "ground_truth": { + "answer": "Illzach", + "outlier_distance_km": 7748.9, + "second_furthest_km": 4130.5, + "clarity_ratio": 1.88, + "median_distance_km": 3528.6, + "distances_to_centroid": { + "Olho d’Água das Cunhãs": 500.0, + "Sullana": 3528.6, + "Llaillay": 4130.5, + "Chapada dos Guimarães": 1676.8, + "Illzach": 7748.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Olho d’Água das Cunhãs: (-4.14°, -45.12°)", + " Sullana: (-4.90°, -80.69°)", + " Llaillay: (-32.84°, -70.96°)", + " Chapada dos Guimarães: (-15.46°, -55.75°)", + " Illzach: (47.77°, 7.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Illzach: 7748.9 km from centroid", + " Llaillay: 4130.5 km from centroid", + " Sullana: 3528.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Illzach", + "FINAL ANSWER: Illzach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.12242, + "lon": 32.46749, + "name": "Dishnā" + }, + { + "lat": 8.9, + "lon": 39.91667, + "name": "Metahāra" + }, + { + "lat": 12.03219, + "lon": 39.04756, + "name": "Lalibela" + }, + { + "lat": 6.90412, + "lon": -2.56114, + "name": "Mim" + }, + { + "lat": -3.74611, + "lon": -39.78333, + "name": "Irauçuba" + } + ], + "question": "Which location is the geographic outlier among: Dishnā, Metahāra, Lalibela, Mim, Irauçuba?", + "ground_truth": { + "answer": "Irauçuba", + "outlier_distance_km": 6130.5, + "second_furthest_km": 2864.6, + "clarity_ratio": 2.14, + "median_distance_km": 2761.5, + "distances_to_centroid": { + "Dishnā": 2654.4, + "Metahāra": 2864.6, + "Lalibela": 2761.5, + "Mim": 1834.5, + "Irauçuba": 6130.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dishnā: (26.12°, 32.47°)", + " Metahāra: (8.90°, 39.92°)", + " Lalibela: (12.03°, 39.05°)", + " Mim: (6.90°, -2.56°)", + " Irauçuba: (-3.75°, -39.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Irauçuba: 6130.5 km from centroid", + " Metahāra: 2864.6 km from centroid", + " Lalibela: 2761.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Irauçuba", + "FINAL ANSWER: Irauçuba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.74742, + "lon": -0.63489, + "name": "Saintes" + }, + { + "lat": 55.65625, + "lon": 37.48496, + "name": "Troparëvo" + }, + { + "lat": 47.47156, + "lon": -0.55202, + "name": "Angers" + }, + { + "lat": 36.20983, + "lon": -5.38452, + "name": "San Roque" + }, + { + "lat": 11.13333, + "lon": 39.63333, + "name": "Dessie" + } + ], + "question": "Which location is the geographic outlier among: Saintes, Troparëvo, Angers, San Roque, Dessie?", + "ground_truth": { + "answer": "Dessie", + "outlier_distance_km": 4015.3, + "second_furthest_km": 2510.0, + "clarity_ratio": 1.6, + "median_distance_km": 1743.7, + "distances_to_centroid": { + "Saintes": 1405.4, + "Troparëvo": 2510.0, + "Angers": 1493.2, + "San Roque": 1743.7, + "Dessie": 4015.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saintes: (45.75°, -0.63°)", + " Troparëvo: (55.66°, 37.48°)", + " Angers: (47.47°, -0.55°)", + " San Roque: (36.21°, -5.38°)", + " Dessie: (11.13°, 39.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dessie: 4015.3 km from centroid", + " Troparëvo: 2510.0 km from centroid", + " San Roque: 1743.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dessie", + "FINAL ANSWER: Dessie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.6975, + "lon": -38.32417, + "name": "Camaçari" + }, + { + "lat": 6.03131, + "lon": -75.43333, + "name": "La Ceja" + }, + { + "lat": -23.60389, + "lon": -46.91917, + "name": "Cotia" + }, + { + "lat": -7.09167, + "lon": -39.68056, + "name": "Nova Olinda" + }, + { + "lat": 41.07663, + "lon": 1.14163, + "name": "Salou" + } + ], + "question": "Which location is the geographic outlier among: Camaçari, La Ceja, Cotia, Nova Olinda, Salou?", + "ground_truth": { + "answer": "Salou", + "outlier_distance_km": 6084.9, + "second_furthest_km": 3992.4, + "clarity_ratio": 1.52, + "median_distance_km": 2813.2, + "distances_to_centroid": { + "Camaçari": 1503.9, + "La Ceja": 3992.4, + "Cotia": 2813.2, + "Nova Olinda": 871.4, + "Salou": 6084.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Camaçari: (-12.70°, -38.32°)", + " La Ceja: (6.03°, -75.43°)", + " Cotia: (-23.60°, -46.92°)", + " Nova Olinda: (-7.09°, -39.68°)", + " Salou: (41.08°, 1.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Salou: 6084.9 km from centroid", + " La Ceja: 3992.4 km from centroid", + " Cotia: 2813.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Salou", + "FINAL ANSWER: Salou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.32681, + "lon": -2.74757, + "name": "Kendal" + }, + { + "lat": 46.08115, + "lon": 40.87351, + "name": "Belaya Glina" + }, + { + "lat": 40.96836, + "lon": 17.11329, + "name": "Conversano" + }, + { + "lat": 59.84389, + "lon": 30.45111, + "name": "Obukhovo" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + } + ], + "question": "Which location is the geographic outlier among: Kendal, Belaya Glina, Conversano, Obukhovo, Punchbowl?", + "ground_truth": { + "answer": "Punchbowl", + "outlier_distance_km": 13137.2, + "second_furthest_km": 4507.5, + "clarity_ratio": 2.91, + "median_distance_km": 3183.5, + "distances_to_centroid": { + "Kendal": 4507.5, + "Belaya Glina": 1507.4, + "Conversano": 2788.6, + "Obukhovo": 3183.5, + "Punchbowl": 13137.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kendal: (54.33°, -2.75°)", + " Belaya Glina: (46.08°, 40.87°)", + " Conversano: (40.97°, 17.11°)", + " Obukhovo: (59.84°, 30.45°)", + " Punchbowl: (-33.93°, 151.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Punchbowl: 13137.2 km from centroid", + " Kendal: 4507.5 km from centroid", + " Obukhovo: 3183.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Punchbowl", + "FINAL ANSWER: Punchbowl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + }, + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": 30.56482, + "lon": 31.15777, + "name": "Quwaysinā" + } + ], + "question": "Which location is the geographic outlier among: Elwood, Pascoe Vale, Mulgrave, Lara, Quwaysinā?", + "ground_truth": { + "answer": "Quwaysinā", + "outlier_distance_km": 11432.5, + "second_furthest_km": 2661.3, + "clarity_ratio": 4.3, + "median_distance_km": 2643.8, + "distances_to_centroid": { + "Elwood": 2643.8, + "Pascoe Vale": 2632.2, + "Mulgrave": 2661.3, + "Lara": 2607.4, + "Quwaysinā": 11432.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Elwood: (-37.88°, 144.98°)", + " Pascoe Vale: (-37.73°, 144.93°)", + " Mulgrave: (-37.93°, 145.18°)", + " Lara: (-38.02°, 144.41°)", + " Quwaysinā: (30.56°, 31.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Quwaysinā: 11432.5 km from centroid", + " Mulgrave: 2661.3 km from centroid", + " Elwood: 2643.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Quwaysinā", + "FINAL ANSWER: Quwaysinā" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.42524, + "lon": -0.16394, + "name": "Tooting" + }, + { + "lat": 53.56507, + "lon": -2.12267, + "name": "Royton" + }, + { + "lat": 48.97674, + "lon": 2.32722, + "name": "Deuil-la-Barre" + }, + { + "lat": 40.30571, + "lon": -3.73295, + "name": "Getafe" + }, + { + "lat": 39.93819, + "lon": 116.09307, + "name": "Mentougou" + } + ], + "question": "Which location is the geographic outlier among: Tooting, Royton, Deuil-la-Barre, Getafe, Mentougou?", + "ground_truth": { + "answer": "Mentougou", + "outlier_distance_km": 7138.6, + "second_furthest_km": 2220.9, + "clarity_ratio": 3.21, + "median_distance_km": 1891.6, + "distances_to_centroid": { + "Tooting": 1716.5, + "Royton": 1891.6, + "Deuil-la-Barre": 1516.1, + "Getafe": 2220.9, + "Mentougou": 7138.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tooting: (51.43°, -0.16°)", + " Royton: (53.57°, -2.12°)", + " Deuil-la-Barre: (48.98°, 2.33°)", + " Getafe: (40.31°, -3.73°)", + " Mentougou: (39.94°, 116.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mentougou: 7138.6 km from centroid", + " Getafe: 2220.9 km from centroid", + " Royton: 1891.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mentougou", + "FINAL ANSWER: Mentougou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.91528, + "lon": -100.74389, + "name": "San Miguel de Allende" + }, + { + "lat": 36.16284, + "lon": -85.50164, + "name": "Cookeville" + }, + { + "lat": 35.19807, + "lon": -111.65127, + "name": "Flagstaff" + }, + { + "lat": 38.98067, + "lon": -77.10026, + "name": "Bethesda" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + } + ], + "question": "Which location is the geographic outlier among: San Miguel de Allende, Cookeville, Flagstaff, Bethesda, Rockingham?", + "ground_truth": { + "answer": "Rockingham", + "outlier_distance_km": 18156.8, + "second_furthest_km": 6050.0, + "clarity_ratio": 3.0, + "median_distance_km": 5078.3, + "distances_to_centroid": { + "San Miguel de Allende": 5078.3, + "Cookeville": 3744.4, + "Flagstaff": 6050.0, + "Bethesda": 3224.9, + "Rockingham": 18156.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Miguel de Allende: (20.92°, -100.74°)", + " Cookeville: (36.16°, -85.50°)", + " Flagstaff: (35.20°, -111.65°)", + " Bethesda: (38.98°, -77.10°)", + " Rockingham: (-32.28°, 115.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rockingham: 18156.8 km from centroid", + " Flagstaff: 6050.0 km from centroid", + " San Miguel de Allende: 5078.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rockingham", + "FINAL ANSWER: Rockingham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": 26.20437, + "lon": 127.75267, + "name": "Yonabaru" + } + ], + "question": "Which location is the geographic outlier among: Randwick, Seaford, Sunbury, Palmerston, Yonabaru?", + "ground_truth": { + "answer": "Yonabaru", + "outlier_distance_km": 5215.5, + "second_furthest_km": 2162.9, + "clarity_ratio": 2.41, + "median_distance_km": 2097.7, + "distances_to_centroid": { + "Randwick": 1983.0, + "Seaford": 2162.9, + "Sunbury": 2097.7, + "Palmerston": 1214.8, + "Yonabaru": 5215.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Randwick: (-33.91°, 151.25°)", + " Seaford: (-38.10°, 145.13°)", + " Sunbury: (-37.58°, 144.73°)", + " Palmerston: (-12.49°, 130.98°)", + " Yonabaru: (26.20°, 127.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yonabaru: 5215.5 km from centroid", + " Seaford: 2162.9 km from centroid", + " Sunbury: 2097.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yonabaru", + "FINAL ANSWER: Yonabaru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + }, + { + "lat": 34.23072, + "lon": 74.6472, + "name": "Sumbal" + } + ], + "question": "Which location is the geographic outlier among: Robina, Whangarei, Wainuiomata, Griffith, Sumbal?", + "ground_truth": { + "answer": "Sumbal", + "outlier_distance_km": 9613.6, + "second_furthest_km": 3623.9, + "clarity_ratio": 2.65, + "median_distance_km": 3310.3, + "distances_to_centroid": { + "Robina": 1178.9, + "Whangarei": 3310.3, + "Wainuiomata": 3623.9, + "Griffith": 1481.0, + "Sumbal": 9613.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Whangarei: (-35.73°, 174.32°)", + " Wainuiomata: (-41.27°, 174.95°)", + " Griffith: (-34.29°, 146.05°)", + " Sumbal: (34.23°, 74.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sumbal: 9613.6 km from centroid", + " Wainuiomata: 3623.9 km from centroid", + " Whangarei: 3310.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sumbal", + "FINAL ANSWER: Sumbal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -37.87709, + "lon": 145.12939, + "name": "Mount Waverley" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + }, + { + "lat": 41.74753, + "lon": -87.71116, + "name": "Ashburn" + } + ], + "question": "Which location is the geographic outlier among: Porirua, Mount Waverley, Balwyn North, Hamilton, Ashburn?", + "ground_truth": { + "answer": "Ashburn", + "outlier_distance_km": 17289.4, + "second_furthest_km": 6324.8, + "clarity_ratio": 2.73, + "median_distance_km": 6268.0, + "distances_to_centroid": { + "Porirua": 6268.0, + "Mount Waverley": 3705.2, + "Balwyn North": 3699.4, + "Hamilton": 6324.8, + "Ashburn": 17289.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porirua: (-41.13°, 174.85°)", + " Mount Waverley: (-37.88°, 145.13°)", + " Balwyn North: (-37.79°, 145.09°)", + " Hamilton: (-37.78°, 175.28°)", + " Ashburn: (41.75°, -87.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ashburn: 17289.4 km from centroid", + " Hamilton: 6324.8 km from centroid", + " Porirua: 6268.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ashburn", + "FINAL ANSWER: Ashburn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.97782, + "lon": 47.50027, + "name": "Makhachkala" + }, + { + "lat": 39.19042, + "lon": -0.43572, + "name": "Algemesí" + }, + { + "lat": 49.33047, + "lon": 11.02346, + "name": "Schwabach" + }, + { + "lat": 51.10247, + "lon": 17.04827, + "name": "Rejon ulicy Traugutta" + }, + { + "lat": -29.35622, + "lon": -50.81357, + "name": "Canela" + } + ], + "question": "Which location is the geographic outlier among: Makhachkala, Algemesí, Schwabach, Rejon ulicy Traugutta, Canela?", + "ground_truth": { + "answer": "Canela", + "outlier_distance_km": 8900.6, + "second_furthest_km": 3986.2, + "clarity_ratio": 2.23, + "median_distance_km": 2486.7, + "distances_to_centroid": { + "Makhachkala": 3986.2, + "Algemesí": 1065.1, + "Schwabach": 2140.7, + "Rejon ulicy Traugutta": 2486.7, + "Canela": 8900.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Makhachkala: (42.98°, 47.50°)", + " Algemesí: (39.19°, -0.44°)", + " Schwabach: (49.33°, 11.02°)", + " Rejon ulicy Traugutta: (51.10°, 17.05°)", + " Canela: (-29.36°, -50.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Canela: 8900.6 km from centroid", + " Makhachkala: 3986.2 km from centroid", + " Rejon ulicy Traugutta: 2486.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Canela", + "FINAL ANSWER: Canela" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.67675, + "lon": -101.35628, + "name": "Irapuato" + }, + { + "lat": 42.3703, + "lon": -87.90202, + "name": "Gurnee" + }, + { + "lat": 38.1302, + "lon": -121.27245, + "name": "Lodi" + }, + { + "lat": 43.77977, + "lon": -79.29502, + "name": "Tam O'Shanter-Sullivan" + }, + { + "lat": -26.0941, + "lon": 28.00123, + "name": "Randburg" + } + ], + "question": "Which location is the geographic outlier among: Irapuato, Gurnee, Lodi, Tam O'Shanter-Sullivan, Randburg?", + "ground_truth": { + "answer": "Randburg", + "outlier_distance_km": 12117.7, + "second_furthest_km": 4867.7, + "clarity_ratio": 2.49, + "median_distance_km": 2998.8, + "distances_to_centroid": { + "Irapuato": 2998.8, + "Gurnee": 2515.3, + "Lodi": 4867.7, + "Tam O'Shanter-Sullivan": 2312.9, + "Randburg": 12117.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Irapuato: (20.68°, -101.36°)", + " Gurnee: (42.37°, -87.90°)", + " Lodi: (38.13°, -121.27°)", + " Tam O'Shanter-Sullivan: (43.78°, -79.30°)", + " Randburg: (-26.09°, 28.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Randburg: 12117.7 km from centroid", + " Lodi: 4867.7 km from centroid", + " Irapuato: 2998.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Randburg", + "FINAL ANSWER: Randburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.34198, + "lon": 35.35917, + "name": "Zheleznogorsk" + }, + { + "lat": 59.83889, + "lon": 30.17528, + "name": "Uritsk" + }, + { + "lat": 53.58007, + "lon": 10.04067, + "name": "Barmbek-Süd" + }, + { + "lat": 45.74525, + "lon": 4.84197, + "name": "Lyon 07" + }, + { + "lat": 36.16167, + "lon": 119.26306, + "name": "Shiqiaozi" + } + ], + "question": "Which location is the geographic outlier among: Zheleznogorsk, Uritsk, Barmbek-Süd, Lyon 07, Shiqiaozi?", + "ground_truth": { + "answer": "Shiqiaozi", + "outlier_distance_km": 6328.1, + "second_furthest_km": 2638.2, + "clarity_ratio": 2.4, + "median_distance_km": 2098.6, + "distances_to_centroid": { + "Zheleznogorsk": 447.5, + "Uritsk": 1303.3, + "Barmbek-Süd": 2098.6, + "Lyon 07": 2638.2, + "Shiqiaozi": 6328.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zheleznogorsk: (52.34°, 35.36°)", + " Uritsk: (59.84°, 30.18°)", + " Barmbek-Süd: (53.58°, 10.04°)", + " Lyon 07: (45.75°, 4.84°)", + " Shiqiaozi: (36.16°, 119.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shiqiaozi: 6328.1 km from centroid", + " Lyon 07: 2638.2 km from centroid", + " Barmbek-Süd: 2098.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shiqiaozi", + "FINAL ANSWER: Shiqiaozi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.29167, + "lon": -98.46806, + "name": "San Rafael Tlanalapan" + }, + { + "lat": 29.02832, + "lon": -81.30312, + "name": "DeLand" + }, + { + "lat": 44.64969, + "lon": -93.24272, + "name": "Lakeville" + }, + { + "lat": 28.07389, + "lon": -82.43902, + "name": "University" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + } + ], + "question": "Which location is the geographic outlier among: San Rafael Tlanalapan, DeLand, Lakeville, University, Melbourne City Centre?", + "ground_truth": { + "answer": "Melbourne City Centre", + "outlier_distance_km": 17561.8, + "second_furthest_km": 5943.9, + "clarity_ratio": 2.95, + "median_distance_km": 5674.3, + "distances_to_centroid": { + "San Rafael Tlanalapan": 5943.9, + "DeLand": 4224.0, + "Lakeville": 5674.3, + "University": 4316.3, + "Melbourne City Centre": 17561.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Rafael Tlanalapan: (19.29°, -98.47°)", + " DeLand: (29.03°, -81.30°)", + " Lakeville: (44.65°, -93.24°)", + " University: (28.07°, -82.44°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Melbourne City Centre: 17561.8 km from centroid", + " San Rafael Tlanalapan: 5943.9 km from centroid", + " Lakeville: 5674.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Melbourne City Centre", + "FINAL ANSWER: Melbourne City Centre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": -38.14711, + "lon": 144.36069, + "name": "Geelong" + }, + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": 24.93805, + "lon": 73.82392, + "name": "Nāthdwāra" + } + ], + "question": "Which location is the geographic outlier among: West Pennant Hills, Cranbourne East, Geelong, Wangaratta, Nāthdwāra?", + "ground_truth": { + "answer": "Nāthdwāra", + "outlier_distance_km": 8329.6, + "second_furthest_km": 2110.4, + "clarity_ratio": 3.95, + "median_distance_km": 1976.4, + "distances_to_centroid": { + "West Pennant Hills": 2110.4, + "Cranbourne East": 1976.4, + "Geelong": 1924.7, + "Wangaratta": 1905.4, + "Nāthdwāra": 8329.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Pennant Hills: (-33.75°, 151.05°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Geelong: (-38.15°, 144.36°)", + " Wangaratta: (-36.36°, 146.32°)", + " Nāthdwāra: (24.94°, 73.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nāthdwāra: 8329.6 km from centroid", + " West Pennant Hills: 2110.4 km from centroid", + " Cranbourne East: 1976.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nāthdwāra", + "FINAL ANSWER: Nāthdwāra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.49392, + "lon": -99.11075, + "name": "Gustavo Adolfo Madero" + }, + { + "lat": 40.94065, + "lon": -73.99681, + "name": "Dumont" + }, + { + "lat": 34.23087, + "lon": -111.32514, + "name": "Payson" + }, + { + "lat": 42.97086, + "lon": -82.42491, + "name": "Port Huron" + }, + { + "lat": 13.79525, + "lon": 39.60303, + "name": "Wik’ro" + } + ], + "question": "Which location is the geographic outlier among: Gustavo Adolfo Madero, Dumont, Payson, Port Huron, Wik’ro?", + "ground_truth": { + "answer": "Wik’ro", + "outlier_distance_km": 10630.0, + "second_furthest_km": 4299.9, + "clarity_ratio": 2.47, + "median_distance_km": 3584.7, + "distances_to_centroid": { + "Gustavo Adolfo Madero": 3584.7, + "Dumont": 1412.7, + "Payson": 4299.9, + "Port Huron": 2062.2, + "Wik’ro": 10630.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gustavo Adolfo Madero: (19.49°, -99.11°)", + " Dumont: (40.94°, -74.00°)", + " Payson: (34.23°, -111.33°)", + " Port Huron: (42.97°, -82.42°)", + " Wik’ro: (13.80°, 39.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wik’ro: 10630.0 km from centroid", + " Payson: 4299.9 km from centroid", + " Gustavo Adolfo Madero: 3584.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wik’ro", + "FINAL ANSWER: Wik’ro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.75003, + "lon": -87.80422, + "name": "Bridgeview" + }, + { + "lat": 32.25174, + "lon": -110.73731, + "name": "Tanque Verde" + }, + { + "lat": 39.83776, + "lon": -105.00137, + "name": "Sherrelwood" + }, + { + "lat": 28.75888, + "lon": -81.31784, + "name": "Lake Mary" + }, + { + "lat": 7.15181, + "lon": 0.47362, + "name": "Hohoe" + } + ], + "question": "Which location is the geographic outlier among: Bridgeview, Tanque Verde, Sherrelwood, Lake Mary, Hohoe?", + "ground_truth": { + "answer": "Hohoe", + "outlier_distance_km": 8395.0, + "second_furthest_km": 3220.8, + "clarity_ratio": 2.61, + "median_distance_km": 2775.6, + "distances_to_centroid": { + "Bridgeview": 1637.6, + "Tanque Verde": 3220.8, + "Sherrelwood": 2775.6, + "Lake Mary": 450.2, + "Hohoe": 8395.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bridgeview: (41.75°, -87.80°)", + " Tanque Verde: (32.25°, -110.74°)", + " Sherrelwood: (39.84°, -105.00°)", + " Lake Mary: (28.76°, -81.32°)", + " Hohoe: (7.15°, 0.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hohoe: 8395.0 km from centroid", + " Tanque Verde: 3220.8 km from centroid", + " Sherrelwood: 2775.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hohoe", + "FINAL ANSWER: Hohoe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.31419, + "lon": -73.94968, + "name": "Cimitarra" + }, + { + "lat": -7.99, + "lon": -36.49639, + "name": "Jataúba" + }, + { + "lat": -20.14333, + "lon": -44.19972, + "name": "Brumadinho" + }, + { + "lat": -3.89083, + "lon": -38.68556, + "name": "Maranguape" + }, + { + "lat": 14.23333, + "lon": 37.0, + "name": "Abala" + } + ], + "question": "Which location is the geographic outlier among: Cimitarra, Jataúba, Brumadinho, Maranguape, Abala?", + "ground_truth": { + "answer": "Abala", + "outlier_distance_km": 7737.7, + "second_furthest_km": 4834.3, + "clarity_ratio": 1.6, + "median_distance_km": 2431.1, + "distances_to_centroid": { + "Cimitarra": 4834.3, + "Jataúba": 858.0, + "Brumadinho": 2431.1, + "Maranguape": 842.6, + "Abala": 7737.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cimitarra: (6.31°, -73.95°)", + " Jataúba: (-7.99°, -36.50°)", + " Brumadinho: (-20.14°, -44.20°)", + " Maranguape: (-3.89°, -38.69°)", + " Abala: (14.23°, 37.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Abala: 7737.7 km from centroid", + " Cimitarra: 4834.3 km from centroid", + " Brumadinho: 2431.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Abala", + "FINAL ANSWER: Abala" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.56667, + "lon": -73.66667, + "name": "Ahuntsic-Cartierville" + }, + { + "lat": 31.43516, + "lon": -97.74391, + "name": "Gatesville" + }, + { + "lat": 42.40843, + "lon": -71.05366, + "name": "Everett" + }, + { + "lat": 33.03145, + "lon": -111.38734, + "name": "Florence" + }, + { + "lat": -17.01037, + "lon": -46.00851, + "name": "Brasilândia de Minas" + } + ], + "question": "Which location is the geographic outlier among: Ahuntsic-Cartierville, Gatesville, Everett, Florence, Brasilândia de Minas?", + "ground_truth": { + "answer": "Brasilândia de Minas", + "outlier_distance_km": 6120.8, + "second_furthest_km": 3082.7, + "clarity_ratio": 1.99, + "median_distance_km": 2129.4, + "distances_to_centroid": { + "Ahuntsic-Cartierville": 2129.4, + "Gatesville": 1788.2, + "Everett": 1885.9, + "Florence": 3082.7, + "Brasilândia de Minas": 6120.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ahuntsic-Cartierville: (45.57°, -73.67°)", + " Gatesville: (31.44°, -97.74��)", + " Everett: (42.41°, -71.05°)", + " Florence: (33.03°, -111.39°)", + " Brasilândia de Minas: (-17.01°, -46.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brasilândia de Minas: 6120.8 km from centroid", + " Florence: 3082.7 km from centroid", + " Ahuntsic-Cartierville: 2129.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brasilândia de Minas", + "FINAL ANSWER: Brasilândia de Minas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": 23.7, + "lon": 113.03333, + "name": "Qingyuan" + } + ], + "question": "Which location is the geographic outlier among: Glenroy, Hobart, Punchbowl, Corio, Qingyuan?", + "ground_truth": { + "answer": "Qingyuan", + "outlier_distance_km": 6227.4, + "second_furthest_km": 2010.7, + "clarity_ratio": 3.1, + "median_distance_km": 1425.0, + "distances_to_centroid": { + "Glenroy": 1400.2, + "Hobart": 2010.7, + "Punchbowl": 1386.7, + "Corio": 1425.0, + "Qingyuan": 6227.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenroy: (-37.70°, 144.93°)", + " Hobart: (-42.88°, 147.33°)", + " Punchbowl: (-33.93°, 151.05°)", + " Corio: (-38.08°, 144.38°)", + " Qingyuan: (23.70°, 113.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qingyuan: 6227.4 km from centroid", + " Hobart: 2010.7 km from centroid", + " Corio: 1425.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qingyuan", + "FINAL ANSWER: Qingyuan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.24667, + "lon": -38.13056, + "name": "Tabuleiro do Norte" + }, + { + "lat": -30.74179, + "lon": -59.64517, + "name": "La Paz" + }, + { + "lat": -12.76722, + "lon": -40.21167, + "name": "Iaçu" + }, + { + "lat": -19.30861, + "lon": -47.52528, + "name": "Santa Juliana" + }, + { + "lat": 40.9126, + "lon": -73.83708, + "name": "Mount Vernon" + } + ], + "question": "Which location is the geographic outlier among: Tabuleiro do Norte, La Paz, Iaçu, Santa Juliana, Mount Vernon?", + "ground_truth": { + "answer": "Mount Vernon", + "outlier_distance_km": 5618.3, + "second_furthest_km": 2929.5, + "clarity_ratio": 1.92, + "median_distance_km": 1613.3, + "distances_to_centroid": { + "Tabuleiro do Norte": 1521.2, + "La Paz": 2929.5, + "Iaçu": 1517.1, + "Santa Juliana": 1613.3, + "Mount Vernon": 5618.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tabuleiro do Norte: (-5.25°, -38.13°)", + " La Paz: (-30.74°, -59.65°)", + " Iaçu: (-12.77°, -40.21°)", + " Santa Juliana: (-19.31°, -47.53°)", + " Mount Vernon: (40.91°, -73.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Vernon: 5618.3 km from centroid", + " La Paz: 2929.5 km from centroid", + " Santa Juliana: 1613.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Vernon", + "FINAL ANSWER: Mount Vernon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.88782, + "lon": 30.28708, + "name": "Nkowakowa" + }, + { + "lat": 5.53532, + "lon": -0.39827, + "name": "Amanfrom" + }, + { + "lat": -24.88333, + "lon": 28.28333, + "name": "Bela Bela" + }, + { + "lat": 31.15823, + "lon": 31.936, + "name": "Al Manzalah" + }, + { + "lat": 11.54798, + "lon": 107.80772, + "name": "Bảo Lộc" + } + ], + "question": "Which location is the geographic outlier among: Nkowakowa, Amanfrom, Bela Bela, Al Manzalah, Bảo Lộc?", + "ground_truth": { + "answer": "Bảo Lộc", + "outlier_distance_km": 7640.2, + "second_furthest_km": 4482.8, + "clarity_ratio": 1.7, + "median_distance_km": 3568.7, + "distances_to_centroid": { + "Nkowakowa": 2828.2, + "Amanfrom": 4482.8, + "Bela Bela": 3011.4, + "Al Manzalah": 3568.7, + "Bảo Lộc": 7640.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nkowakowa: (-23.89°, 30.29°)", + " Amanfrom: (5.54°, -0.40°)", + " Bela Bela: (-24.88°, 28.28°)", + " Al Manzalah: (31.16°, 31.94°)", + " Bảo Lộc: (11.55°, 107.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bảo Lộc: 7640.2 km from centroid", + " Amanfrom: 4482.8 km from centroid", + " Al Manzalah: 3568.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bảo Lộc", + "FINAL ANSWER: Bảo Lộc" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.66472, + "lon": 76.84379, + "name": "Chhabra" + }, + { + "lat": 23.02302, + "lon": 73.07113, + "name": "Kapadvanj" + }, + { + "lat": 25.98546, + "lon": 84.17233, + "name": "Maniar" + }, + { + "lat": 10.65193, + "lon": 76.9778, + "name": "Ūttukuli" + }, + { + "lat": 51.10009, + "lon": 6.15484, + "name": "Wassenberg" + } + ], + "question": "Which location is the geographic outlier among: Chhabra, Kapadvanj, Maniar, Ūttukuli, Wassenberg?", + "ground_truth": { + "answer": "Wassenberg", + "outlier_distance_km": 5445.0, + "second_furthest_km": 2312.3, + "clarity_ratio": 2.35, + "median_distance_km": 2063.4, + "distances_to_centroid": { + "Chhabra": 1366.6, + "Kapadvanj": 1069.3, + "Maniar": 2063.4, + "Ūttukuli": 2312.3, + "Wassenberg": 5445.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chhabra: (24.66°, 76.84°)", + " Kapadvanj: (23.02°, 73.07°)", + " Maniar: (25.99°, 84.17°)", + " Ūttukuli: (10.65°, 76.98°)", + " Wassenberg: (51.10°, 6.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wassenberg: 5445.0 km from centroid", + " Ūttukuli: 2312.3 km from centroid", + " Maniar: 2063.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wassenberg", + "FINAL ANSWER: Wassenberg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.73099, + "lon": 11.28716, + "name": "Cento" + }, + { + "lat": 50.57953, + "lon": 13.00627, + "name": "Annaberg-Buchholz" + }, + { + "lat": 53.60639, + "lon": 10.11972, + "name": "Farmsen-Berne" + }, + { + "lat": 48.95, + "lon": 2.38333, + "name": "Stains" + }, + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + } + ], + "question": "Which location is the geographic outlier among: Cento, Annaberg-Buchholz, Farmsen-Berne, Stains, Doreen?", + "ground_truth": { + "answer": "Doreen", + "outlier_distance_km": 13640.1, + "second_furthest_km": 3391.3, + "clarity_ratio": 4.02, + "median_distance_km": 3178.1, + "distances_to_centroid": { + "Cento": 2585.9, + "Annaberg-Buchholz": 2814.8, + "Farmsen-Berne": 3178.1, + "Stains": 3391.3, + "Doreen": 13640.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cento: (44.73°, 11.29°)", + " Annaberg-Buchholz: (50.58°, 13.01°)", + " Farmsen-Berne: (53.61°, 10.12°)", + " Stains: (48.95°, 2.38°)", + " Doreen: (-37.60°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doreen: 13640.1 km from centroid", + " Stains: 3391.3 km from centroid", + " Farmsen-Berne: 3178.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doreen", + "FINAL ANSWER: Doreen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.66667, + "lon": 109.03333, + "name": "Shagang" + }, + { + "lat": 19.90873, + "lon": 109.68717, + "name": "Lingao" + }, + { + "lat": 21.33954, + "lon": 70.74966, + "name": "Vīsāvadar" + }, + { + "lat": 43.6475, + "lon": 111.97667, + "name": "Erenhot" + }, + { + "lat": 47.15538, + "lon": -122.43401, + "name": "Parkland" + } + ], + "question": "Which location is the geographic outlier among: Shagang, Lingao, Vīsāvadar, Erenhot, Parkland?", + "ground_truth": { + "answer": "Parkland", + "outlier_distance_km": 11351.3, + "second_furthest_km": 5496.3, + "clarity_ratio": 2.07, + "median_distance_km": 5356.8, + "distances_to_centroid": { + "Shagang": 5356.8, + "Lingao": 5496.3, + "Vīsāvadar": 1820.0, + "Erenhot": 5076.1, + "Parkland": 11351.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shagang: (21.67°, 109.03°)", + " Lingao: (19.91°, 109.69°)", + " Vīsāvadar: (21.34°, 70.75°)", + " Erenhot: (43.65°, 111.98°)", + " Parkland: (47.16°, -122.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Parkland: 11351.3 km from centroid", + " Lingao: 5496.3 km from centroid", + " Shagang: 5356.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Parkland", + "FINAL ANSWER: Parkland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.6567, + "lon": 120.2641, + "name": "Waingapu" + }, + { + "lat": 39.55, + "lon": 141.16667, + "name": "Hizume" + }, + { + "lat": 18.73312, + "lon": 76.38616, + "name": "Ambājogāi" + }, + { + "lat": 13.63229, + "lon": 79.48568, + "name": "Tirupati NMA" + }, + { + "lat": -20.60361, + "lon": -41.18472, + "name": "Castelo" + } + ], + "question": "Which location is the geographic outlier among: Waingapu, Hizume, Ambājogāi, Tirupati NMA, Castelo?", + "ground_truth": { + "answer": "Castelo", + "outlier_distance_km": 13073.8, + "second_furthest_km": 7363.1, + "clarity_ratio": 1.78, + "median_distance_km": 5373.2, + "distances_to_centroid": { + "Waingapu": 5373.2, + "Hizume": 7363.1, + "Ambājogāi": 1163.4, + "Tirupati NMA": 750.8, + "Castelo": 13073.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waingapu: (-9.66°, 120.26°)", + " Hizume: (39.55°, 141.17°)", + " Ambājogāi: (18.73°, 76.39°)", + " Tirupati NMA: (13.63°, 79.49°)", + " Castelo: (-20.60°, -41.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castelo: 13073.8 km from centroid", + " Hizume: 7363.1 km from centroid", + " Waingapu: 5373.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castelo", + "FINAL ANSWER: Castelo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.7511, + "lon": 151.28886, + "name": "Dee Why" + }, + { + "lat": -33.91972, + "lon": 151.07592, + "name": "Lakemba" + }, + { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": 43.1112, + "lon": 132.35021, + "name": "Bol’shoy Kamen’" + } + ], + "question": "Which location is the geographic outlier among: Dee Why, Lakemba, Hamilton, Greystanes, Bol’shoy Kamen’?", + "ground_truth": { + "answer": "Bol’shoy Kamen’", + "outlier_distance_km": 7223.2, + "second_furthest_km": 3040.8, + "clarity_ratio": 2.38, + "median_distance_km": 1636.8, + "distances_to_centroid": { + "Dee Why": 1616.8, + "Lakemba": 1636.8, + "Hamilton": 3040.8, + "Greystanes": 1627.0, + "Bol’shoy Kamen’": 7223.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dee Why: (-33.75°, 151.29°)", + " Lakemba: (-33.92°, 151.08°)", + " Hamilton: (-37.78°, 175.28°)", + " Greystanes: (-33.82°, 150.95°)", + " Bol’shoy Kamen’: (43.11°, 132.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bol’shoy Kamen’: 7223.2 km from centroid", + " Hamilton: 3040.8 km from centroid", + " Lakemba: 1636.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bol’shoy Kamen’", + "FINAL ANSWER: Bol’shoy Kamen’" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -32.22099, + "lon": 116.009, + "name": "Byford" + }, + { + "lat": -37.83834, + "lon": 144.99149, + "name": "South Yarra" + }, + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": 31.3529, + "lon": 27.23725, + "name": "Marsá Maţrūḩ" + } + ], + "question": "Which location is the geographic outlier among: Mildura, Byford, South Yarra, Yarraville, Marsá Maţrūḩ?", + "ground_truth": { + "answer": "Marsá Maţrūḩ", + "outlier_distance_km": 11070.4, + "second_furthest_km": 3347.1, + "clarity_ratio": 3.31, + "median_distance_km": 3338.7, + "distances_to_centroid": { + "Mildura": 2962.1, + "Byford": 1124.7, + "South Yarra": 3347.1, + "Yarraville": 3338.7, + "Marsá Maţrūḩ": 11070.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mildura: (-34.19°, 142.16°)", + " Byford: (-32.22°, 116.01°)", + " South Yarra: (-37.84°, 144.99°)", + " Yarraville: (-37.82°, 144.90°)", + " Marsá Maţrūḩ: (31.35°, 27.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marsá Maţrūḩ: 11070.4 km from centroid", + " South Yarra: 3347.1 km from centroid", + " Yarraville: 3338.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marsá Maţrūḩ", + "FINAL ANSWER: Marsá Maţrūḩ" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.69748, + "lon": 133.88362, + "name": "Alice Springs" + }, + { + "lat": -33.32711, + "lon": 115.64137, + "name": "Bunbury" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": 43.82634, + "lon": 144.09638, + "name": "Motomachi" + } + ], + "question": "Which location is the geographic outlier among: Alice Springs, Bunbury, Camberwell, Armidale, Motomachi?", + "ground_truth": { + "answer": "Motomachi", + "outlier_distance_km": 6714.7, + "second_furthest_km": 2938.0, + "clarity_ratio": 2.29, + "median_distance_km": 2490.6, + "distances_to_centroid": { + "Alice Springs": 930.7, + "Bunbury": 2938.0, + "Camberwell": 2490.6, + "Armidale": 2097.2, + "Motomachi": 6714.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alice Springs: (-23.70°, 133.88°)", + " Bunbury: (-33.33°, 115.64°)", + " Camberwell: (-37.84°, 145.07°)", + " Armidale: (-30.50°, 151.67°)", + " Motomachi: (43.83°, 144.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Motomachi: 6714.7 km from centroid", + " Bunbury: 2938.0 km from centroid", + " Camberwell: 2490.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Motomachi", + "FINAL ANSWER: Motomachi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.54184, + "lon": 81.26566, + "name": "Aral" + }, + { + "lat": 14.73694, + "lon": 120.96083, + "name": "Meycauayan" + }, + { + "lat": 26.43278, + "lon": 78.44205, + "name": "Gohad" + }, + { + "lat": 19.41018, + "lon": 109.55024, + "name": "Nanfeng" + }, + { + "lat": 35.07681, + "lon": -80.66924, + "name": "Indian Trail" + } + ], + "question": "Which location is the geographic outlier among: Aral, Meycauayan, Gohad, Nanfeng, Indian Trail?", + "ground_truth": { + "answer": "Indian Trail", + "outlier_distance_km": 12048.1, + "second_furthest_km": 6231.2, + "clarity_ratio": 1.93, + "median_distance_km": 4912.9, + "distances_to_centroid": { + "Aral": 2310.1, + "Meycauayan": 6231.2, + "Gohad": 1641.6, + "Nanfeng": 4912.9, + "Indian Trail": 12048.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aral: (40.54°, 81.27°)", + " Meycauayan: (14.74°, 120.96°)", + " Gohad: (26.43°, 78.44°)", + " Nanfeng: (19.41°, 109.55°)", + " Indian Trail: (35.08°, -80.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Indian Trail: 12048.1 km from centroid", + " Meycauayan: 6231.2 km from centroid", + " Nanfeng: 4912.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Indian Trail", + "FINAL ANSWER: Indian Trail" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.18284, + "lon": -80.76536, + "name": "Niles" + }, + { + "lat": 30.52663, + "lon": -115.93137, + "name": "Lázaro Cárdenas" + }, + { + "lat": 40.63871, + "lon": -73.64013, + "name": "Oceanside" + }, + { + "lat": 55.16667, + "lon": -118.80271, + "name": "Grande Prairie" + }, + { + "lat": -15.79411, + "lon": -47.8825, + "name": "Plano Piloto" + } + ], + "question": "Which location is the geographic outlier among: Niles, Lázaro Cárdenas, Oceanside, Grande Prairie, Plano Piloto?", + "ground_truth": { + "answer": "Plano Piloto", + "outlier_distance_km": 6649.1, + "second_furthest_km": 3707.2, + "clarity_ratio": 1.79, + "median_distance_km": 2727.6, + "distances_to_centroid": { + "Niles": 1344.8, + "Lázaro Cárdenas": 2727.6, + "Oceanside": 1688.2, + "Grande Prairie": 3707.2, + "Plano Piloto": 6649.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Niles: (41.18°, -80.77°)", + " Lázaro Cárdenas: (30.53°, -115.93°)", + " Oceanside: (40.64°, -73.64°)", + " Grande Prairie: (55.17°, -118.80°)", + " Plano Piloto: (-15.79°, -47.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Plano Piloto: 6649.1 km from centroid", + " Grande Prairie: 3707.2 km from centroid", + " Lázaro Cárdenas: 2727.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Plano Piloto", + "FINAL ANSWER: Plano Piloto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.21808, + "lon": -98.37706, + "name": "Ébano" + }, + { + "lat": 30.52297, + "lon": -87.90333, + "name": "Fairhope" + }, + { + "lat": 39.07955, + "lon": -77.07303, + "name": "Aspen Hill" + }, + { + "lat": 33.88399, + "lon": -84.51438, + "name": "Smyrna" + }, + { + "lat": 20.9948, + "lon": 105.9465, + "name": "Vinhomes Ocean Park" + } + ], + "question": "Which location is the geographic outlier among: Ébano, Fairhope, Aspen Hill, Smyrna, Vinhomes Ocean Park?", + "ground_truth": { + "answer": "Vinhomes Ocean Park", + "outlier_distance_km": 13778.9, + "second_furthest_km": 5030.9, + "clarity_ratio": 2.74, + "median_distance_km": 3790.9, + "distances_to_centroid": { + "Ébano": 5030.9, + "Fairhope": 3790.9, + "Aspen Hill": 2836.5, + "Smyrna": 3440.7, + "Vinhomes Ocean Park": 13778.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ébano: (22.22°, -98.38°)", + " Fairhope: (30.52°, -87.90°)", + " Aspen Hill: (39.08°, -77.07°)", + " Smyrna: (33.88°, -84.51°)", + " Vinhomes Ocean Park: (20.99°, 105.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vinhomes Ocean Park: 13778.9 km from centroid", + " Ébano: 5030.9 km from centroid", + " Fairhope: 3790.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vinhomes Ocean Park", + "FINAL ANSWER: Vinhomes Ocean Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.67817, + "lon": -75.28466, + "name": "El Doncello" + }, + { + "lat": -3.95056, + "lon": -40.47333, + "name": "Cariré" + }, + { + "lat": -6.24444, + "lon": -38.91361, + "name": "Orós" + }, + { + "lat": -38.37694, + "lon": -60.27563, + "name": "Tres Arroyos" + }, + { + "lat": 13.6882, + "lon": 101.07156, + "name": "Chachoengsao" + } + ], + "question": "Which location is the geographic outlier among: El Doncello, Cariré, Orós, Tres Arroyos, Chachoengsao?", + "ground_truth": { + "answer": "Chachoengsao", + "outlier_distance_km": 13832.1, + "second_furthest_km": 5900.6, + "clarity_ratio": 2.34, + "median_distance_km": 5159.9, + "distances_to_centroid": { + "El Doncello": 5900.6, + "Cariré": 1982.0, + "Orós": 1783.7, + "Tres Arroyos": 5159.9, + "Chachoengsao": 13832.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " El Doncello: (1.68°, -75.28°)", + " Cariré: (-3.95°, -40.47°)", + " Orós: (-6.24°, -38.91°)", + " Tres Arroyos: (-38.38°, -60.28°)", + " Chachoengsao: (13.69°, 101.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chachoengsao: 13832.1 km from centroid", + " El Doncello: 5900.6 km from centroid", + " Tres Arroyos: 5159.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chachoengsao", + "FINAL ANSWER: Chachoengsao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.20833, + "lon": 113.91667, + "name": "Palangkaraya" + }, + { + "lat": 23.78152, + "lon": 91.28579, + "name": "Madhuban" + }, + { + "lat": 29.35376, + "lon": 105.89392, + "name": "Yongchuan" + }, + { + "lat": 21.08718, + "lon": 72.88153, + "name": "Sachīn" + }, + { + "lat": 21.81295, + "lon": -105.20844, + "name": "Santiago Ixcuintla" + } + ], + "question": "Which location is the geographic outlier among: Palangkaraya, Madhuban, Yongchuan, Sachīn, Santiago Ixcuintla?", + "ground_truth": { + "answer": "Santiago Ixcuintla", + "outlier_distance_km": 15050.4, + "second_furthest_km": 6769.1, + "clarity_ratio": 2.22, + "median_distance_km": 5185.7, + "distances_to_centroid": { + "Palangkaraya": 6769.1, + "Madhuban": 3714.1, + "Yongchuan": 5185.7, + "Sachīn": 1808.1, + "Santiago Ixcuintla": 15050.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palangkaraya: (-2.21°, 113.92°)", + " Madhuban: (23.78°, 91.29°)", + " Yongchuan: (29.35°, 105.89°)", + " Sachīn: (21.09°, 72.88°)", + " Santiago Ixcuintla: (21.81°, -105.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santiago Ixcuintla: 15050.4 km from centroid", + " Palangkaraya: 6769.1 km from centroid", + " Yongchuan: 5185.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santiago Ixcuintla", + "FINAL ANSWER: Santiago Ixcuintla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.01335, + "lon": -73.67352, + "name": "Vélez" + }, + { + "lat": -2.63639, + "lon": -54.93722, + "name": "Belterra" + }, + { + "lat": -22.98444, + "lon": -43.22315, + "name": "Leblon" + }, + { + "lat": -11.26833, + "lon": -37.43833, + "name": "Estância" + }, + { + "lat": 50.84048, + "lon": 10.95198, + "name": "Arnstadt" + } + ], + "question": "Which location is the geographic outlier among: Vélez, Belterra, Leblon, Estância, Arnstadt?", + "ground_truth": { + "answer": "Arnstadt", + "outlier_distance_km": 7007.3, + "second_furthest_km": 3773.3, + "clarity_ratio": 1.86, + "median_distance_km": 3024.5, + "distances_to_centroid": { + "Vélez": 3773.3, + "Belterra": 1850.4, + "Leblon": 3024.5, + "Estância": 1714.7, + "Arnstadt": 7007.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vélez: (6.01°, -73.67°)", + " Belterra: (-2.64°, -54.94°)", + " Leblon: (-22.98°, -43.22°)", + " Estância: (-11.27°, -37.44°)", + " Arnstadt: (50.84°, 10.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arnstadt: 7007.3 km from centroid", + " Vélez: 3773.3 km from centroid", + " Leblon: 3024.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arnstadt", + "FINAL ANSWER: Arnstadt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.65028, + "lon": -50.85056, + "name": "Reserva" + }, + { + "lat": 10.77107, + "lon": -73.00314, + "name": "San Juan del Cesar" + }, + { + "lat": -14.89528, + "lon": -41.96861, + "name": "Condeúba" + }, + { + "lat": 1.21456, + "lon": -77.27846, + "name": "Pasto" + }, + { + "lat": 18.04531, + "lon": 78.26078, + "name": "Medak" + } + ], + "question": "Which location is the geographic outlier among: Reserva, San Juan del Cesar, Condeúba, Pasto, Medak?", + "ground_truth": { + "answer": "Medak", + "outlier_distance_km": 12315.4, + "second_furthest_km": 4938.6, + "clarity_ratio": 2.49, + "median_distance_km": 4647.3, + "distances_to_centroid": { + "Reserva": 3175.5, + "San Juan del Cesar": 4647.3, + "Condeúba": 1750.1, + "Pasto": 4938.6, + "Medak": 12315.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reserva: (-24.65°, -50.85°)", + " San Juan del Cesar: (10.77°, -73.00°)", + " Condeúba: (-14.90°, -41.97°)", + " Pasto: (1.21°, -77.28°)", + " Medak: (18.05°, 78.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Medak: 12315.4 km from centroid", + " Pasto: 4938.6 km from centroid", + " San Juan del Cesar: 4647.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Medak", + "FINAL ANSWER: Medak" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.1962, + "lon": 5.58681, + "name": "Owo" + }, + { + "lat": 7.2, + "lon": 38.6, + "name": "Shashamane" + }, + { + "lat": -33.58601, + "lon": 26.88329, + "name": "Port Alfred" + }, + { + "lat": 26.96637, + "lon": 31.37953, + "name": "Şidfā" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + } + ], + "question": "Which location is the geographic outlier among: Owo, Shashamane, Port Alfred, Şidfā, Doncaster East?", + "ground_truth": { + "answer": "Doncaster East", + "outlier_distance_km": 10090.5, + "second_furthest_km": 5090.1, + "clarity_ratio": 1.98, + "median_distance_km": 4153.5, + "distances_to_centroid": { + "Owo": 5090.1, + "Shashamane": 1903.3, + "Port Alfred": 3854.3, + "Şidfā": 4153.5, + "Doncaster East": 10090.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Owo: (7.20°, 5.59°)", + " Shashamane: (7.20°, 38.60°)", + " Port Alfred: (-33.59°, 26.88°)", + " Şidfā: (26.97°, 31.38°)", + " Doncaster East: (-37.79°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doncaster East: 10090.5 km from centroid", + " Owo: 5090.1 km from centroid", + " Şidfā: 4153.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doncaster East", + "FINAL ANSWER: Doncaster East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + { + "lat": 33.53567, + "lon": 130.47861, + "name": "Ōnojō" + } + ], + "question": "Which location is the geographic outlier among: Seven Hills, Cairns, Elwood, Titirangi, Ōnojō?", + "ground_truth": { + "answer": "Ōnojō", + "outlier_distance_km": 6112.5, + "second_furthest_km": 3214.4, + "clarity_ratio": 1.9, + "median_distance_km": 2207.9, + "distances_to_centroid": { + "Seven Hills": 1717.8, + "Cairns": 414.9, + "Elwood": 2207.9, + "Titirangi": 3214.4, + "Ōnojō": 6112.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Seven Hills: (-33.78°, 150.93°)", + " Cairns: (-16.92°, 145.77°)", + " Elwood: (-37.88°, 144.98°)", + " Titirangi: (-36.94°, 174.66°)", + " Ōnojō: (33.54°, 130.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ōnojō: 6112.5 km from centroid", + " Titirangi: 3214.4 km from centroid", + " Elwood: 2207.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ōnojō", + "FINAL ANSWER: Ōnojō" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + }, + { + "lat": 26.67418, + "lon": 31.49686, + "name": "Juhaynah" + } + ], + "question": "Which location is the geographic outlier among: Cabramatta, Tamworth, Ballarat, Redbank Plains, Juhaynah?", + "ground_truth": { + "answer": "Juhaynah", + "outlier_distance_km": 11450.4, + "second_furthest_km": 2854.2, + "clarity_ratio": 4.01, + "median_distance_km": 2823.9, + "distances_to_centroid": { + "Cabramatta": 2854.2, + "Tamworth": 2738.0, + "Ballarat": 2543.2, + "Redbank Plains": 2823.9, + "Juhaynah": 11450.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cabramatta: (-33.90°, 150.93°)", + " Tamworth: (-31.09°, 150.93°)", + " Ballarat: (-37.57°, 143.85°)", + " Redbank Plains: (-27.65°, 152.86°)", + " Juhaynah: (26.67°, 31.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Juhaynah: 11450.4 km from centroid", + " Cabramatta: 2854.2 km from centroid", + " Redbank Plains: 2823.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Juhaynah", + "FINAL ANSWER: Juhaynah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.73453, + "lon": 105.38609, + "name": "Liufeng" + }, + { + "lat": 11.2529, + "lon": 75.89059, + "name": "Perumanna" + }, + { + "lat": 9.96583, + "lon": 98.63476, + "name": "Ranong" + }, + { + "lat": 22.4756, + "lon": 88.09898, + "name": "Uluberiya" + }, + { + "lat": -6.70111, + "lon": -79.90611, + "name": "Lambayeque" + } + ], + "question": "Which location is the geographic outlier among: Liufeng, Perumanna, Ranong, Uluberiya, Lambayeque?", + "ground_truth": { + "answer": "Lambayeque", + "outlier_distance_km": 15302.0, + "second_furthest_km": 5275.3, + "clarity_ratio": 2.9, + "median_distance_km": 4479.2, + "distances_to_centroid": { + "Liufeng": 5275.3, + "Perumanna": 2010.0, + "Ranong": 4479.2, + "Uluberiya": 3333.0, + "Lambayeque": 15302.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Liufeng: (34.73°, 105.39°)", + " Perumanna: (11.25°, 75.89°)", + " Ranong: (9.97°, 98.63°)", + " Uluberiya: (22.48°, 88.10°)", + " Lambayeque: (-6.70°, -79.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lambayeque: 15302.0 km from centroid", + " Liufeng: 5275.3 km from centroid", + " Ranong: 4479.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lambayeque", + "FINAL ANSWER: Lambayeque" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.5448, + "lon": -2.13984, + "name": "Chadderton" + }, + { + "lat": 51.53443, + "lon": 9.93228, + "name": "Göttingen" + }, + { + "lat": 41.37857, + "lon": 2.15937, + "name": "Sant Antoni" + }, + { + "lat": 52.525, + "lon": 5.71806, + "name": "Dronten" + }, + { + "lat": 45.29984, + "lon": -122.77371, + "name": "Wilsonville" + } + ], + "question": "Which location is the geographic outlier among: Chadderton, Göttingen, Sant Antoni, Dronten, Wilsonville?", + "ground_truth": { + "answer": "Wilsonville", + "outlier_distance_km": 7075.3, + "second_furthest_km": 2234.1, + "clarity_ratio": 3.17, + "median_distance_km": 2017.6, + "distances_to_centroid": { + "Chadderton": 1435.4, + "Göttingen": 2234.1, + "Sant Antoni": 2017.6, + "Dronten": 1942.5, + "Wilsonville": 7075.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chadderton: (53.54°, -2.14°)", + " Göttingen: (51.53°, 9.93°)", + " Sant Antoni: (41.38°, 2.16°)", + " Dronten: (52.52°, 5.72°)", + " Wilsonville: (45.30°, -122.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wilsonville: 7075.3 km from centroid", + " Göttingen: 2234.1 km from centroid", + " Sant Antoni: 2017.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wilsonville", + "FINAL ANSWER: Wilsonville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.24994, + "lon": -0.80975, + "name": "Crevillente" + }, + { + "lat": 51.99313, + "lon": 4.47865, + "name": "Berkel en Rodenrijs" + }, + { + "lat": 45.32163, + "lon": 8.41989, + "name": "Vercelli" + }, + { + "lat": 43.46556, + "lon": 12.2375, + "name": "Città di Castello" + }, + { + "lat": 37.68104, + "lon": -122.12441, + "name": "San Lorenzo" + } + ], + "question": "Which location is the geographic outlier among: Crevillente, Berkel en Rodenrijs, Vercelli, Città di Castello, San Lorenzo?", + "ground_truth": { + "answer": "San Lorenzo", + "outlier_distance_km": 8104.2, + "second_furthest_km": 2553.0, + "clarity_ratio": 3.17, + "median_distance_km": 2225.0, + "distances_to_centroid": { + "Crevillente": 1672.4, + "Berkel en Rodenrijs": 2027.5, + "Vercelli": 2225.0, + "Città di Castello": 2553.0, + "San Lorenzo": 8104.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Crevillente: (38.25°, -0.81°)", + " Berkel en Rodenrijs: (51.99°, 4.48°)", + " Vercelli: (45.32°, 8.42°)", + " Città di Castello: (43.47°, 12.24°)", + " San Lorenzo: (37.68°, -122.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Lorenzo: 8104.2 km from centroid", + " Città di Castello: 2553.0 km from centroid", + " Vercelli: 2225.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Lorenzo", + "FINAL ANSWER: San Lorenzo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.34559, + "lon": -88.84258, + "name": "Ottawa" + }, + { + "lat": 42.33143, + "lon": -83.04575, + "name": "Detroit" + }, + { + "lat": 17.53768, + "lon": -101.26798, + "name": "Petatlán" + }, + { + "lat": 43.0389, + "lon": -87.90647, + "name": "Milwaukee" + }, + { + "lat": -11.57139, + "lon": -77.26722, + "name": "Chancay" + } + ], + "question": "Which location is the geographic outlier among: Ottawa, Detroit, Petatlán, Milwaukee, Chancay?", + "ground_truth": { + "answer": "Chancay", + "outlier_distance_km": 4383.9, + "second_furthest_km": 1835.1, + "clarity_ratio": 2.39, + "median_distance_km": 1805.9, + "distances_to_centroid": { + "Ottawa": 1650.2, + "Detroit": 1805.9, + "Petatlán": 1720.3, + "Milwaukee": 1835.1, + "Chancay": 4383.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ottawa: (41.35°, -88.84°)", + " Detroit: (42.33°, -83.05°)", + " Petatlán: (17.54°, -101.27°)", + " Milwaukee: (43.04°, -87.91°)", + " Chancay: (-11.57°, -77.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chancay: 4383.9 km from centroid", + " Milwaukee: 1835.1 km from centroid", + " Detroit: 1805.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chancay", + "FINAL ANSWER: Chancay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.57316, + "lon": -44.97108, + "name": "Cruzeiro" + }, + { + "lat": -6.43306, + "lon": -43.98361, + "name": "Paraibano" + }, + { + "lat": -22.63417, + "lon": -54.82222, + "name": "Caarapó" + }, + { + "lat": -7.51556, + "lon": -34.90833, + "name": "Caaporã" + }, + { + "lat": 28.31457, + "lon": 74.28952, + "name": "Bhādāsar" + } + ], + "question": "Which location is the geographic outlier among: Cruzeiro, Paraibano, Caarapó, Caaporã, Bhādāsar?", + "ground_truth": { + "answer": "Bhādāsar", + "outlier_distance_km": 10836.9, + "second_furthest_km": 4071.9, + "clarity_ratio": 2.66, + "median_distance_km": 3162.3, + "distances_to_centroid": { + "Cruzeiro": 3162.3, + "Paraibano": 2553.5, + "Caarapó": 4071.9, + "Caaporã": 1556.0, + "Bhādāsar": 10836.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cruzeiro: (-22.57°, -44.97°)", + " Paraibano: (-6.43°, -43.98°)", + " Caarapó: (-22.63°, -54.82°)", + " Caaporã: (-7.52°, -34.91°)", + " Bhādāsar: (28.31°, 74.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhādāsar: 10836.9 km from centroid", + " Caarapó: 4071.9 km from centroid", + " Cruzeiro: 3162.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhādāsar", + "FINAL ANSWER: Bhādāsar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + }, + { + "lat": 35.60004, + "lon": 126.91699, + "name": "Jeongeup" + } + ], + "question": "Which location is the geographic outlier among: Glenroy, Whangarei, Bendigo, Hawthorn, Jeongeup?", + "ground_truth": { + "answer": "Jeongeup", + "outlier_distance_km": 6799.1, + "second_furthest_km": 3012.4, + "clarity_ratio": 2.26, + "median_distance_km": 1716.9, + "distances_to_centroid": { + "Glenroy": 1704.8, + "Whangarei": 3012.4, + "Bendigo": 1610.4, + "Hawthorn": 1716.9, + "Jeongeup": 6799.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenroy: (-37.70°, 144.93°)", + " Whangarei: (-35.73°, 174.32°)", + " Bendigo: (-36.76°, 144.28°)", + " Hawthorn: (-37.82°, 145.04°)", + " Jeongeup: (35.60°, 126.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jeongeup: 6799.1 km from centroid", + " Whangarei: 3012.4 km from centroid", + " Hawthorn: 1716.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jeongeup", + "FINAL ANSWER: Jeongeup" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.88333, + "lon": -43.10361, + "name": "Niterói" + }, + { + "lat": -19.51361, + "lon": -43.745, + "name": "Jaboticatubas" + }, + { + "lat": -10.12528, + "lon": -36.66194, + "name": "Igreja Nova" + }, + { + "lat": -15.84577, + "lon": -47.88369, + "name": "Lago Sul" + }, + { + "lat": 36.49444, + "lon": 119.79417, + "name": "Jiangzhuang" + } + ], + "question": "Which location is the geographic outlier among: Niterói, Jaboticatubas, Igreja Nova, Lago Sul, Jiangzhuang?", + "ground_truth": { + "answer": "Jiangzhuang", + "outlier_distance_km": 13955.8, + "second_furthest_km": 4223.9, + "clarity_ratio": 3.3, + "median_distance_km": 3960.3, + "distances_to_centroid": { + "Niterói": 3960.3, + "Jaboticatubas": 3894.7, + "Igreja Nova": 2927.5, + "Lago Sul": 4223.9, + "Jiangzhuang": 13955.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Niterói: (-22.88°, -43.10°)", + " Jaboticatubas: (-19.51°, -43.74°)", + " Igreja Nova: (-10.13°, -36.66°)", + " Lago Sul: (-15.85°, -47.88°)", + " Jiangzhuang: (36.49°, 119.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jiangzhuang: 13955.8 km from centroid", + " Lago Sul: 4223.9 km from centroid", + " Niterói: 3960.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jiangzhuang", + "FINAL ANSWER: Jiangzhuang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.6698, + "lon": -0.01657, + "name": "Tema" + }, + { + "lat": 10.95627, + "lon": 36.50456, + "name": "Chagni" + }, + { + "lat": -33.60047, + "lon": 22.19955, + "name": "Oudtshoorn" + }, + { + "lat": 30.85711, + "lon": 32.31183, + "name": "Al Qanţarah" + }, + { + "lat": 35.58486, + "lon": -80.81007, + "name": "Mooresville" + } + ], + "question": "Which location is the geographic outlier among: Tema, Chagni, Oudtshoorn, Al Qanţarah, Mooresville?", + "ground_truth": { + "answer": "Mooresville", + "outlier_distance_km": 8726.5, + "second_furthest_km": 5285.4, + "clarity_ratio": 1.65, + "median_distance_km": 3899.3, + "distances_to_centroid": { + "Tema": 521.3, + "Chagni": 3769.1, + "Oudtshoorn": 5285.4, + "Al Qanţarah": 3899.3, + "Mooresville": 8726.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tema: (5.67°, -0.02°)", + " Chagni: (10.96°, 36.50°)", + " Oudtshoorn: (-33.60°, 22.20°)", + " Al Qanţarah: (30.86°, 32.31°)", + " Mooresville: (35.58°, -80.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mooresville: 8726.5 km from centroid", + " Oudtshoorn: 5285.4 km from centroid", + " Al Qanţarah: 3899.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mooresville", + "FINAL ANSWER: Mooresville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.4693, + "lon": -72.94237, + "name": "Puerto Montt" + }, + { + "lat": -3.45361, + "lon": -44.78, + "name": "Arari" + }, + { + "lat": -36.61617, + "lon": -64.28991, + "name": "Santa Rosa" + }, + { + "lat": -15.03833, + "lon": -41.25972, + "name": "Belo Campo" + }, + { + "lat": 41.09822, + "lon": 120.74792, + "name": "Nanpiao" + } + ], + "question": "Which location is the geographic outlier among: Puerto Montt, Arari, Santa Rosa, Belo Campo, Nanpiao?", + "ground_truth": { + "answer": "Nanpiao", + "outlier_distance_km": 14976.7, + "second_furthest_km": 6099.2, + "clarity_ratio": 2.46, + "median_distance_km": 5213.8, + "distances_to_centroid": { + "Puerto Montt": 6099.2, + "Arari": 2806.9, + "Santa Rosa": 5213.8, + "Belo Campo": 2289.3, + "Nanpiao": 14976.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Puerto Montt: (-41.47°, -72.94°)", + " Arari: (-3.45°, -44.78°)", + " Santa Rosa: (-36.62°, -64.29°)", + " Belo Campo: (-15.04°, -41.26°)", + " Nanpiao: (41.10°, 120.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nanpiao: 14976.7 km from centroid", + " Puerto Montt: 6099.2 km from centroid", + " Santa Rosa: 5213.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nanpiao", + "FINAL ANSWER: Nanpiao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.15892, + "lon": -98.40824, + "name": "Huejotzingo" + }, + { + "lat": 42.35176, + "lon": -71.86341, + "name": "Holden" + }, + { + "lat": 38.5245, + "lon": -90.35734, + "name": "Concord" + }, + { + "lat": 42.06642, + "lon": -87.93729, + "name": "Mount Prospect" + }, + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + } + ], + "question": "Which location is the geographic outlier among: Huejotzingo, Holden, Concord, Mount Prospect, Masterton?", + "ground_truth": { + "answer": "Masterton", + "outlier_distance_km": 16347.5, + "second_furthest_km": 6639.0, + "clarity_ratio": 2.46, + "median_distance_km": 5679.8, + "distances_to_centroid": { + "Huejotzingo": 6639.0, + "Holden": 4259.7, + "Concord": 5679.8, + "Mount Prospect": 5521.2, + "Masterton": 16347.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huejotzingo: (19.16°, -98.41°)", + " Holden: (42.35°, -71.86°)", + " Concord: (38.52°, -90.36°)", + " Mount Prospect: (42.07°, -87.94°)", + " Masterton: (-40.96°, 175.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Masterton: 16347.5 km from centroid", + " Huejotzingo: 6639.0 km from centroid", + " Concord: 5679.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Masterton", + "FINAL ANSWER: Masterton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": -25.88278, + "lon": -48.57472, + "name": "Guaratuba" + } + ], + "question": "Which location is the geographic outlier among: Bexley, Greystanes, Tamworth, Forest Lake, Guaratuba?", + "ground_truth": { + "answer": "Guaratuba", + "outlier_distance_km": 13398.6, + "second_furthest_km": 4023.3, + "clarity_ratio": 3.33, + "median_distance_km": 3749.2, + "distances_to_centroid": { + "Bexley": 3726.3, + "Greystanes": 3711.9, + "Tamworth": 3749.2, + "Forest Lake": 4023.3, + "Guaratuba": 13398.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexley: (-33.95°, 151.12°)", + " Greystanes: (-33.82°, 150.95°)", + " Tamworth: (-31.09°, 150.93°)", + " Forest Lake: (-27.63°, 152.97°)", + " Guaratuba: (-25.88°, -48.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guaratuba: 13398.6 km from centroid", + " Forest Lake: 4023.3 km from centroid", + " Tamworth: 3749.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guaratuba", + "FINAL ANSWER: Guaratuba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.18528, + "lon": -43.22056, + "name": "Ibotirama" + }, + { + "lat": -22.70556, + "lon": -46.98583, + "name": "Jaguariúna" + }, + { + "lat": 2.39341, + "lon": -75.89232, + "name": "La Plata" + }, + { + "lat": -22.97889, + "lon": -49.87056, + "name": "Ourinhos" + }, + { + "lat": 33.99307, + "lon": -117.96868, + "name": "Hacienda Heights" + } + ], + "question": "Which location is the geographic outlier among: Ibotirama, Jaguariúna, La Plata, Ourinhos, Hacienda Heights?", + "ground_truth": { + "answer": "Hacienda Heights", + "outlier_distance_km": 6844.1, + "second_furthest_km": 2953.8, + "clarity_ratio": 2.32, + "median_distance_km": 2760.6, + "distances_to_centroid": { + "Ibotirama": 2735.4, + "Jaguariúna": 2953.8, + "La Plata": 1255.7, + "Ourinhos": 2760.6, + "Hacienda Heights": 6844.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ibotirama: (-12.19°, -43.22°)", + " Jaguariúna: (-22.71°, -46.99°)", + " La Plata: (2.39°, -75.89°)", + " Ourinhos: (-22.98°, -49.87°)", + " Hacienda Heights: (33.99°, -117.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hacienda Heights: 6844.1 km from centroid", + " Jaguariúna: 2953.8 km from centroid", + " Ourinhos: 2760.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hacienda Heights", + "FINAL ANSWER: Hacienda Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.699, + "lon": 27.47475, + "name": "Marikana" + }, + { + "lat": 31.55371, + "lon": 25.15793, + "name": "As Sallūm" + }, + { + "lat": -0.33024, + "lon": 35.94445, + "name": "Njoro" + }, + { + "lat": -33.73378, + "lon": 18.97523, + "name": "Paarl" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + } + ], + "question": "Which location is the geographic outlier among: Marikana, As Sallūm, Njoro, Paarl, Dunedin?", + "ground_truth": { + "answer": "Dunedin", + "outlier_distance_km": 10644.1, + "second_furthest_km": 6094.2, + "clarity_ratio": 1.75, + "median_distance_km": 4234.2, + "distances_to_centroid": { + "Marikana": 3165.6, + "As Sallūm": 6094.2, + "Njoro": 2695.7, + "Paarl": 4234.2, + "Dunedin": 10644.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marikana: (-25.70°, 27.47°)", + " As Sallūm: (31.55°, 25.16°)", + " Njoro: (-0.33°, 35.94°)", + " Paarl: (-33.73°, 18.98°)", + " Dunedin: (-45.87°, 170.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dunedin: 10644.1 km from centroid", + " As Sallūm: 6094.2 km from centroid", + " Paarl: 4234.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dunedin", + "FINAL ANSWER: Dunedin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.21081, + "lon": -101.13212, + "name": "Yuriria" + }, + { + "lat": 43.59447, + "lon": -83.88886, + "name": "Bay City" + }, + { + "lat": 40.02845, + "lon": -75.15157, + "name": "Logan" + }, + { + "lat": 38.76279, + "lon": -93.73605, + "name": "Warrensburg" + }, + { + "lat": -27.25204, + "lon": 152.99226, + "name": "Kallangur" + } + ], + "question": "Which location is the geographic outlier among: Yuriria, Bay City, Logan, Warrensburg, Kallangur?", + "ground_truth": { + "answer": "Kallangur", + "outlier_distance_km": 18610.8, + "second_furthest_km": 6262.0, + "clarity_ratio": 2.97, + "median_distance_km": 5316.9, + "distances_to_centroid": { + "Yuriria": 6262.0, + "Bay City": 4586.4, + "Logan": 3777.3, + "Warrensburg": 5316.9, + "Kallangur": 18610.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yuriria: (20.21°, -101.13°)", + " Bay City: (43.59°, -83.89°)", + " Logan: (40.03°, -75.15°)", + " Warrensburg: (38.76°, -93.74°)", + " Kallangur: (-27.25°, 152.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kallangur: 18610.8 km from centroid", + " Yuriria: 6262.0 km from centroid", + " Warrensburg: 5316.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kallangur", + "FINAL ANSWER: Kallangur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -43.30437, + "lon": 172.58356, + "name": "Rangiora" + }, + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -27.50578, + "lon": 153.10236, + "name": "Carindale" + }, + { + "lat": -37.78821, + "lon": 175.2902, + "name": "Hamilton East" + }, + { + "lat": 51.92917, + "lon": 4.57778, + "name": "Capelle aan den IJssel" + } + ], + "question": "Which location is the geographic outlier among: Rangiora, Rotorua, Carindale, Hamilton East, Capelle aan den IJssel?", + "ground_truth": { + "answer": "Capelle aan den IJssel", + "outlier_distance_km": 14468.5, + "second_furthest_km": 4394.1, + "clarity_ratio": 3.29, + "median_distance_km": 4327.2, + "distances_to_centroid": { + "Rangiora": 4327.2, + "Rotorua": 4394.1, + "Carindale": 1953.8, + "Hamilton East": 4302.4, + "Capelle aan den IJssel": 14468.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rangiora: (-43.30°, 172.58°)", + " Rotorua: (-38.14°, 176.25°)", + " Carindale: (-27.51°, 153.10°)", + " Hamilton East: (-37.79°, 175.29°)", + " Capelle aan den IJssel: (51.93°, 4.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Capelle aan den IJssel: 14468.5 km from centroid", + " Rotorua: 4394.1 km from centroid", + " Rangiora: 4327.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Capelle aan den IJssel", + "FINAL ANSWER: Capelle aan den IJssel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.40076, + "lon": 37.93399, + "name": "Sheraro" + }, + { + "lat": -25.7287, + "lon": 27.87, + "name": "Hartbeespoort" + }, + { + "lat": -32.17588, + "lon": 26.82437, + "name": "Whittlesea" + }, + { + "lat": 0.78775, + "lon": 34.71562, + "name": "Kimilili" + }, + { + "lat": -9.37139, + "lon": -36.24083, + "name": "Viçosa" + } + ], + "question": "Which location is the geographic outlier among: Sheraro, Hartbeespoort, Whittlesea, Kimilili, Viçosa?", + "ground_truth": { + "answer": "Viçosa", + "outlier_distance_km": 5959.5, + "second_furthest_km": 3512.7, + "clarity_ratio": 1.7, + "median_distance_km": 2575.6, + "distances_to_centroid": { + "Sheraro": 3512.7, + "Hartbeespoort": 1982.6, + "Whittlesea": 2575.6, + "Kimilili": 2209.5, + "Viçosa": 5959.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sheraro: (14.40°, 37.93°)", + " Hartbeespoort: (-25.73°, 27.87°)", + " Whittlesea: (-32.18°, 26.82°)", + " Kimilili: (0.79°, 34.72°)", + " Viçosa: (-9.37°, -36.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viçosa: 5959.5 km from centroid", + " Sheraro: 3512.7 km from centroid", + " Whittlesea: 2575.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viçosa", + "FINAL ANSWER: Viçosa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + }, + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": -33.86667, + "lon": 150.95, + "name": "Fairfield" + }, + { + "lat": -23.84852, + "lon": 151.25775, + "name": "Gladstone" + }, + { + "lat": 38.80345, + "lon": -76.9897, + "name": "Oxon Hill" + } + ], + "question": "Which location is the geographic outlier among: Griffith, Randwick, Fairfield, Gladstone, Oxon Hill?", + "ground_truth": { + "answer": "Oxon Hill", + "outlier_distance_km": 17633.3, + "second_furthest_km": 4980.9, + "clarity_ratio": 3.54, + "median_distance_km": 4952.8, + "distances_to_centroid": { + "Griffith": 4520.5, + "Randwick": 4980.9, + "Fairfield": 4952.8, + "Gladstone": 4896.2, + "Oxon Hill": 17633.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Griffith: (-34.29°, 146.05°)", + " Randwick: (-33.91°, 151.25°)", + " Fairfield: (-33.87°, 150.95°)", + " Gladstone: (-23.85°, 151.26°)", + " Oxon Hill: (38.80°, -76.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oxon Hill: 17633.3 km from centroid", + " Randwick: 4980.9 km from centroid", + " Fairfield: 4952.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oxon Hill", + "FINAL ANSWER: Oxon Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.79667, + "lon": -49.52889, + "name": "Formoso do Araguaia" + }, + { + "lat": -13.73538, + "lon": -39.14785, + "name": "Ituberá" + }, + { + "lat": -42.76848, + "lon": -65.03827, + "name": "Puerto Madryn" + }, + { + "lat": -27.94972, + "lon": -51.80667, + "name": "Sananduva" + }, + { + "lat": 37.123, + "lon": -120.26018, + "name": "Chowchilla" + } + ], + "question": "Which location is the geographic outlier among: Formoso do Araguaia, Ituberá, Puerto Madryn, Sananduva, Chowchilla?", + "ground_truth": { + "answer": "Chowchilla", + "outlier_distance_km": 7913.6, + "second_furthest_km": 3440.7, + "clarity_ratio": 2.3, + "median_distance_km": 2827.0, + "distances_to_centroid": { + "Formoso do Araguaia": 1700.7, + "Ituberá": 2827.0, + "Puerto Madryn": 3440.7, + "Sananduva": 2268.1, + "Chowchilla": 7913.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Formoso do Araguaia: (-11.80°, -49.53°)", + " Ituberá: (-13.74°, -39.15°)", + " Puerto Madryn: (-42.77°, -65.04°)", + " Sananduva: (-27.95°, -51.81°)", + " Chowchilla: (37.12°, -120.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chowchilla: 7913.6 km from centroid", + " Puerto Madryn: 3440.7 km from centroid", + " Ituberá: 2827.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chowchilla", + "FINAL ANSWER: Chowchilla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": 11.01667, + "lon": 75.86667, + "name": "Pariyāpuram" + } + ], + "question": "Which location is the geographic outlier among: Thomastown, Hobart, Cessnock, Liverpool, Pariyāpuram?", + "ground_truth": { + "answer": "Pariyāpuram", + "outlier_distance_km": 7580.1, + "second_furthest_km": 2107.6, + "clarity_ratio": 3.6, + "median_distance_km": 1770.2, + "distances_to_centroid": { + "Thomastown": 1544.4, + "Hobart": 2107.6, + "Cessnock": 1770.2, + "Liverpool": 1769.7, + "Pariyāpuram": 7580.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thomastown: (-37.68°, 145.02°)", + " Hobart: (-42.88°, 147.33°)", + " Cessnock: (-32.83°, 151.36°)", + " Liverpool: (-33.92°, 150.93°)", + " Pariyāpuram: (11.02°, 75.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pariyāpuram: 7580.1 km from centroid", + " Hobart: 2107.6 km from centroid", + " Cessnock: 1770.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pariyāpuram", + "FINAL ANSWER: Pariyāpuram" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.89357, + "lon": 141.576, + "name": "Eniwa" + }, + { + "lat": 38.10583, + "lon": 127.98944, + "name": "Yanggu" + }, + { + "lat": 16.29078, + "lon": 80.26233, + "name": "Phirangipuram" + }, + { + "lat": 36.68333, + "lon": 139.96667, + "name": "Ujiie" + }, + { + "lat": -25.44141, + "lon": 27.51114, + "name": "Hartbeestfontein-A" + } + ], + "question": "Which location is the geographic outlier among: Eniwa, Yanggu, Phirangipuram, Ujiie, Hartbeestfontein-A?", + "ground_truth": { + "answer": "Hartbeestfontein-A", + "outlier_distance_km": 9722.0, + "second_furthest_km": 4233.1, + "clarity_ratio": 2.3, + "median_distance_km": 3884.1, + "distances_to_centroid": { + "Eniwa": 4233.1, + "Yanggu": 2969.3, + "Phirangipuram": 2509.4, + "Ujiie": 3884.1, + "Hartbeestfontein-A": 9722.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eniwa: (42.89°, 141.58°)", + " Yanggu: (38.11°, 127.99°)", + " Phirangipuram: (16.29°, 80.26°)", + " Ujiie: (36.68°, 139.97°)", + " Hartbeestfontein-A: (-25.44°, 27.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hartbeestfontein-A: 9722.0 km from centroid", + " Eniwa: 4233.1 km from centroid", + " Ujiie: 3884.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hartbeestfontein-A", + "FINAL ANSWER: Hartbeestfontein-A" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.13325, + "lon": 10.02129, + "name": "Cremona" + }, + { + "lat": 51.37992, + "lon": -0.24445, + "name": "Worcester Park" + }, + { + "lat": 52.43367, + "lon": 8.61263, + "name": "Rahden" + }, + { + "lat": 43.25, + "lon": -5.76667, + "name": "Mieres" + }, + { + "lat": 30.12303, + "lon": 31.13571, + "name": "Awsīm" + } + ], + "question": "Which location is the geographic outlier among: Cremona, Worcester Park, Rahden, Mieres, Awsīm?", + "ground_truth": { + "answer": "Awsīm", + "outlier_distance_km": 2527.6, + "second_furthest_km": 1170.3, + "clarity_ratio": 2.16, + "median_distance_km": 1018.7, + "distances_to_centroid": { + "Cremona": 124.8, + "Worcester Park": 1018.7, + "Rahden": 886.2, + "Mieres": 1170.3, + "Awsīm": 2527.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cremona: (45.13°, 10.02°)", + " Worcester Park: (51.38°, -0.24°)", + " Rahden: (52.43°, 8.61°)", + " Mieres: (43.25°, -5.77°)", + " Awsīm: (30.12°, 31.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Awsīm: 2527.6 km from centroid", + " Mieres: 1170.3 km from centroid", + " Worcester Park: 1018.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Awsīm", + "FINAL ANSWER: Awsīm" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.035, + "lon": 140.85111, + "name": "Watari" + }, + { + "lat": 34.61667, + "lon": 116.95, + "name": "Zhangzhai" + }, + { + "lat": 34.33284, + "lon": 132.56967, + "name": "Kumano" + }, + { + "lat": 28.24737, + "lon": 75.07666, + "name": "Bissāu" + }, + { + "lat": 36.20005, + "lon": -86.51861, + "name": "Mount Juliet" + } + ], + "question": "Which location is the geographic outlier among: Watari, Zhangzhai, Kumano, Bissāu, Mount Juliet?", + "ground_truth": { + "answer": "Mount Juliet", + "outlier_distance_km": 11965.3, + "second_furthest_km": 5735.2, + "clarity_ratio": 2.09, + "median_distance_km": 5143.1, + "distances_to_centroid": { + "Watari": 5735.2, + "Zhangzhai": 3747.7, + "Kumano": 5143.1, + "Bissāu": 674.9, + "Mount Juliet": 11965.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Watari: (38.03°, 140.85°)", + " Zhangzhai: (34.62°, 116.95°)", + " Kumano: (34.33°, 132.57°)", + " Bissāu: (28.25°, 75.08°)", + " Mount Juliet: (36.20°, -86.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Juliet: 11965.3 km from centroid", + " Watari: 5735.2 km from centroid", + " Kumano: 5143.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Juliet", + "FINAL ANSWER: Mount Juliet" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.04214, + "lon": 31.44446, + "name": "Al Qāhirah al Jadīdah" + }, + { + "lat": 26.74906, + "lon": 33.93891, + "name": "Safaga" + }, + { + "lat": 29.33778, + "lon": 31.20556, + "name": "Al Wāsiţah" + }, + { + "lat": -33.57565, + "lon": 22.44391, + "name": "Dysselsdorp" + }, + { + "lat": 25.7126, + "lon": -80.25699, + "name": "Coconut Grove" + } + ], + "question": "Which location is the geographic outlier among: Al Qāhirah al Jadīdah, Safaga, Al Wāsiţah, Dysselsdorp, Coconut Grove?", + "ground_truth": { + "answer": "Coconut Grove", + "outlier_distance_km": 9066.6, + "second_furthest_km": 5691.4, + "clarity_ratio": 1.59, + "median_distance_km": 2973.2, + "distances_to_centroid": { + "Al Qāhirah al Jadīdah": 2896.9, + "Safaga": 2973.2, + "Al Wāsiţah": 2840.0, + "Dysselsdorp": 5691.4, + "Coconut Grove": 9066.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Qāhirah al Jadīdah: (30.04°, 31.44°)", + " Safaga: (26.75°, 33.94°)", + " Al Wāsiţah: (29.34°, 31.21°)", + " Dysselsdorp: (-33.58°, 22.44°)", + " Coconut Grove: (25.71°, -80.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coconut Grove: 9066.6 km from centroid", + " Dysselsdorp: 5691.4 km from centroid", + " Safaga: 2973.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coconut Grove", + "FINAL ANSWER: Coconut Grove" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.27194, + "lon": 123.17306, + "name": "Liaoyang" + }, + { + "lat": 41.81626, + "lon": 140.63472, + "name": "Hokuto" + }, + { + "lat": 17.60184, + "lon": 80.70509, + "name": "Pāloncha" + }, + { + "lat": 9.53921, + "lon": 78.09843, + "name": "Pālaiyampatti" + }, + { + "lat": 37.37301, + "lon": -5.74951, + "name": "Mairena del Alcor" + } + ], + "question": "Which location is the geographic outlier among: Liaoyang, Hokuto, Pāloncha, Pālaiyampatti, Mairena del Alcor?", + "ground_truth": { + "answer": "Mairena del Alcor", + "outlier_distance_km": 8001.5, + "second_furthest_km": 5250.1, + "clarity_ratio": 1.52, + "median_distance_km": 3798.2, + "distances_to_centroid": { + "Liaoyang": 3798.2, + "Hokuto": 5250.1, + "Pāloncha": 1352.7, + "Pālaiyampatti": 2288.6, + "Mairena del Alcor": 8001.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Liaoyang: (41.27°, 123.17°)", + " Hokuto: (41.82°, 140.63°)", + " Pāloncha: (17.60°, 80.71°)", + " Pālaiyampatti: (9.54°, 78.10°)", + " Mairena del Alcor: (37.37°, -5.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mairena del Alcor: 8001.5 km from centroid", + " Hokuto: 5250.1 km from centroid", + " Liaoyang: 3798.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mairena del Alcor", + "FINAL ANSWER: Mairena del Alcor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.95914, + "lon": -89.63012, + "name": "Wausau" + }, + { + "lat": 41.71087, + "lon": -87.75811, + "name": "Oak Lawn" + }, + { + "lat": 38.42102, + "lon": -121.42384, + "name": "Laguna" + }, + { + "lat": 45.44979, + "lon": -73.6015, + "name": "Ville-Émard" + }, + { + "lat": 16.2838, + "lon": 121.0896, + "name": "Dupax del Sur" + } + ], + "question": "Which location is the geographic outlier among: Wausau, Oak Lawn, Laguna, Ville-Émard, Dupax del Sur?", + "ground_truth": { + "answer": "Dupax del Sur", + "outlier_distance_km": 13981.3, + "second_furthest_km": 6079.4, + "clarity_ratio": 2.3, + "median_distance_km": 3366.2, + "distances_to_centroid": { + "Wausau": 3366.2, + "Oak Lawn": 3225.4, + "Laguna": 6079.4, + "Ville-Émard": 2133.6, + "Dupax del Sur": 13981.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wausau: (44.96°, -89.63°)", + " Oak Lawn: (41.71°, -87.76°)", + " Laguna: (38.42°, -121.42°)", + " Ville-Émard: (45.45°, -73.60°)", + " Dupax del Sur: (16.28°, 121.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dupax del Sur: 13981.3 km from centroid", + " Laguna: 6079.4 km from centroid", + " Wausau: 3366.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dupax del Sur", + "FINAL ANSWER: Dupax del Sur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -30.29626, + "lon": 153.11351, + "name": "Coffs Harbour" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -20.08722, + "lon": -45.29361, + "name": "Santo Antônio do Monte" + } + ], + "question": "Which location is the geographic outlier among: Broken Hill, Saint Kilda, Coffs Harbour, Caboolture, Santo Antônio do Monte?", + "ground_truth": { + "answer": "Santo Antônio do Monte", + "outlier_distance_km": 13876.2, + "second_furthest_km": 4244.6, + "clarity_ratio": 3.27, + "median_distance_km": 4185.3, + "distances_to_centroid": { + "Broken Hill": 3061.7, + "Saint Kilda": 3396.8, + "Coffs Harbour": 4185.3, + "Caboolture": 4244.6, + "Santo Antônio do Monte": 13876.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Broken Hill: (-31.97°, 141.45°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Coffs Harbour: (-30.30°, 153.11°)", + " Caboolture: (-27.08°, 152.95°)", + " Santo Antônio do Monte: (-20.09°, -45.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santo Antônio do Monte: 13876.2 km from centroid", + " Caboolture: 4244.6 km from centroid", + " Coffs Harbour: 4185.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santo Antônio do Monte", + "FINAL ANSWER: Santo Antônio do Monte" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.56871, + "lon": -103.4996, + "name": "Gómez Palacio" + }, + { + "lat": 40.88149, + "lon": -74.1132, + "name": "Garfield" + }, + { + "lat": 47.68149, + "lon": -122.20874, + "name": "Kirkland" + }, + { + "lat": 40.50118, + "lon": -79.83922, + "name": "Penn Hills" + }, + { + "lat": -0.27088, + "lon": 36.37917, + "name": "Ol Kalou" + } + ], + "question": "Which location is the geographic outlier among: Gómez Palacio, Garfield, Kirkland, Penn Hills, Ol Kalou?", + "ground_truth": { + "answer": "Ol Kalou", + "outlier_distance_km": 11453.9, + "second_furthest_km": 4861.6, + "clarity_ratio": 2.36, + "median_distance_km": 3450.2, + "distances_to_centroid": { + "Gómez Palacio": 3450.2, + "Garfield": 1216.0, + "Kirkland": 4861.6, + "Penn Hills": 1469.4, + "Ol Kalou": 11453.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gómez Palacio: (25.57°, -103.50°)", + " Garfield: (40.88°, -74.11°)", + " Kirkland: (47.68°, -122.21°)", + " Penn Hills: (40.50°, -79.84°)", + " Ol Kalou: (-0.27°, 36.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ol Kalou: 11453.9 km from centroid", + " Kirkland: 4861.6 km from centroid", + " Gómez Palacio: 3450.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ol Kalou", + "FINAL ANSWER: Ol Kalou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.52334, + "lon": -43.69486, + "name": "Ouro Branco" + }, + { + "lat": -23.44859, + "lon": -46.68839, + "name": "Brasilandia" + }, + { + "lat": -27.17806, + "lon": -51.50472, + "name": "Joaçaba" + }, + { + "lat": -4.71306, + "lon": -37.35528, + "name": "Icapuí" + }, + { + "lat": 52.88157, + "lon": -1.48681, + "name": "Sinfin" + } + ], + "question": "Which location is the geographic outlier among: Ouro Branco, Brasilandia, Joaçaba, Icapuí, Sinfin?", + "ground_truth": { + "answer": "Sinfin", + "outlier_distance_km": 7169.4, + "second_furthest_km": 2993.0, + "clarity_ratio": 2.4, + "median_distance_km": 2382.0, + "distances_to_centroid": { + "Ouro Branco": 1950.1, + "Brasilandia": 2382.0, + "Joaçaba": 2993.0, + "Icapuí": 134.6, + "Sinfin": 7169.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ouro Branco: (-20.52°, -43.69°)", + " Brasilandia: (-23.45°, -46.69°)", + " Joaçaba: (-27.18°, -51.50°)", + " Icapuí: (-4.71°, -37.36°)", + " Sinfin: (52.88°, -1.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sinfin: 7169.4 km from centroid", + " Joaçaba: 2993.0 km from centroid", + " Brasilandia: 2382.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sinfin", + "FINAL ANSWER: Sinfin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -33.95, + "lon": 151.13333, + "name": "Rockdale" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": 42.44732, + "lon": -71.2245, + "name": "Lexington" + } + ], + "question": "Which location is the geographic outlier among: Caulfield North, Rockdale, Bendigo, Coorparoo, Lexington?", + "ground_truth": { + "answer": "Lexington", + "outlier_distance_km": 17346.1, + "second_furthest_km": 5034.1, + "clarity_ratio": 3.45, + "median_distance_km": 4902.2, + "distances_to_centroid": { + "Caulfield North": 4458.5, + "Rockdale": 4902.2, + "Bendigo": 4359.8, + "Coorparoo": 5034.1, + "Lexington": 17346.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caulfield North: (-37.87°, 145.02°)", + " Rockdale: (-33.95°, 151.13°)", + " Bendigo: (-36.76°, 144.28°)", + " Coorparoo: (-27.49°, 153.06°)", + " Lexington: (42.45°, -71.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lexington: 17346.1 km from centroid", + " Coorparoo: 5034.1 km from centroid", + " Rockdale: 4902.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lexington", + "FINAL ANSWER: Lexington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": 38.74728, + "lon": -104.71439, + "name": "Security-Widefield" + } + ], + "question": "Which location is the geographic outlier among: Burwood, Cairns, Mooroolbark, Earlwood, Security-Widefield?", + "ground_truth": { + "answer": "Security-Widefield", + "outlier_distance_km": 16739.3, + "second_furthest_km": 5628.1, + "clarity_ratio": 2.97, + "median_distance_km": 5625.3, + "distances_to_centroid": { + "Burwood": 5625.3, + "Cairns": 5100.2, + "Mooroolbark": 5183.1, + "Earlwood": 5628.1, + "Security-Widefield": 16739.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Burwood: (-33.88°, 151.10°)", + " Cairns: (-16.92°, 145.77°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Earlwood: (-33.92°, 151.13°)", + " Security-Widefield: (38.75°, -104.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Security-Widefield: 16739.3 km from centroid", + " Earlwood: 5628.1 km from centroid", + " Burwood: 5625.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Security-Widefield", + "FINAL ANSWER: Security-Widefield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.00012, + "lon": 8.51672, + "name": "Kano" + }, + { + "lat": -28.23078, + "lon": 28.30707, + "name": "Bethlehem" + }, + { + "lat": -0.45275, + "lon": 39.64601, + "name": "Garissa" + }, + { + "lat": -28.872, + "lon": 27.87506, + "name": "Ficksburg" + }, + { + "lat": 29.71801, + "lon": -95.43383, + "name": "West University Place" + } + ], + "question": "Which location is the geographic outlier among: Kano, Bethlehem, Garissa, Ficksburg, West University Place?", + "ground_truth": { + "answer": "West University Place", + "outlier_distance_km": 10878.7, + "second_furthest_km": 4218.5, + "clarity_ratio": 2.58, + "median_distance_km": 3971.3, + "distances_to_centroid": { + "Kano": 1843.5, + "Bethlehem": 3957.0, + "Garissa": 4218.5, + "Ficksburg": 3971.3, + "West University Place": 10878.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kano: (12.00°, 8.52°)", + " Bethlehem: (-28.23°, 28.31°)", + " Garissa: (-0.45°, 39.65°)", + " Ficksburg: (-28.87°, 27.88°)", + " West University Place: (29.72°, -95.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West University Place: 10878.7 km from centroid", + " Garissa: 4218.5 km from centroid", + " Ficksburg: 3971.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West University Place", + "FINAL ANSWER: West University Place" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.8724, + "lon": 101.49484, + "name": "Jenjarum" + }, + { + "lat": 34.28994, + "lon": 105.27225, + "name": "Yongping" + }, + { + "lat": 10.99223, + "lon": 76.46418, + "name": "Mannārakkāt" + }, + { + "lat": 16.74799, + "lon": 77.4954, + "name": "Nārāyanpet" + }, + { + "lat": -15.54667, + "lon": -55.16889, + "name": "Campo Verde" + } + ], + "question": "Which location is the geographic outlier among: Jenjarum, Yongping, Mannārakkāt, Nārāyanpet, Campo Verde?", + "ground_truth": { + "answer": "Campo Verde", + "outlier_distance_km": 13097.4, + "second_furthest_km": 5239.1, + "clarity_ratio": 2.5, + "median_distance_km": 4526.0, + "distances_to_centroid": { + "Jenjarum": 4526.0, + "Yongping": 5239.1, + "Mannārakkāt": 1683.3, + "Nārāyanpet": 1929.3, + "Campo Verde": 13097.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jenjarum: (2.87°, 101.49°)", + " Yongping: (34.29°, 105.27°)", + " Mannārakkāt: (10.99°, 76.46°)", + " Nārāyanpet: (16.75°, 77.50°)", + " Campo Verde: (-15.55°, -55.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Campo Verde: 13097.4 km from centroid", + " Yongping: 5239.1 km from centroid", + " Jenjarum: 4526.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Campo Verde", + "FINAL ANSWER: Campo Verde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.3352, + "lon": 77.21361, + "name": "Pacode" + }, + { + "lat": 23.72536, + "lon": 85.51023, + "name": "Kuju" + }, + { + "lat": 9.86667, + "lon": 76.5, + "name": "Piravam" + }, + { + "lat": 33.78333, + "lon": 130.98333, + "name": "Kanda" + }, + { + "lat": -33.8178, + "lon": 151.00348, + "name": "Parramatta" + } + ], + "question": "Which location is the geographic outlier among: Pacode, Kuju, Piravam, Kanda, Parramatta?", + "ground_truth": { + "answer": "Parramatta", + "outlier_distance_km": 6803.6, + "second_furthest_km": 3933.8, + "clarity_ratio": 1.73, + "median_distance_km": 3049.4, + "distances_to_centroid": { + "Pacode": 2972.9, + "Kuju": 2624.1, + "Piravam": 3049.4, + "Kanda": 3933.8, + "Parramatta": 6803.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacode: (8.34°, 77.21°)", + " Kuju: (23.73°, 85.51°)", + " Piravam: (9.87°, 76.50°)", + " Kanda: (33.78°, 130.98°)", + " Parramatta: (-33.82°, 151.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Parramatta: 6803.6 km from centroid", + " Kanda: 3933.8 km from centroid", + " Piravam: 3049.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Parramatta", + "FINAL ANSWER: Parramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.49587, + "lon": -87.84866, + "name": "Frankfort" + }, + { + "lat": 30.36576, + "lon": -88.55613, + "name": "Pascagoula" + }, + { + "lat": 42.25565, + "lon": -71.1245, + "name": "Hyde Park" + }, + { + "lat": 40.09344, + "lon": -74.96795, + "name": "Parkwood Manor" + }, + { + "lat": 56.32867, + "lon": 44.00205, + "name": "Nizhniy Novgorod" + } + ], + "question": "Which location is the geographic outlier among: Frankfort, Pascagoula, Hyde Park, Parkwood Manor, Nizhniy Novgorod?", + "ground_truth": { + "answer": "Nizhniy Novgorod", + "outlier_distance_km": 6754.3, + "second_furthest_km": 3197.6, + "clarity_ratio": 2.11, + "median_distance_km": 2650.0, + "distances_to_centroid": { + "Frankfort": 2650.0, + "Pascagoula": 3197.6, + "Hyde Park": 1269.4, + "Parkwood Manor": 1626.5, + "Nizhniy Novgorod": 6754.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frankfort: (41.50°, -87.85°)", + " Pascagoula: (30.37°, -88.56°)", + " Hyde Park: (42.26°, -71.12°)", + " Parkwood Manor: (40.09°, -74.97°)", + " Nizhniy Novgorod: (56.33°, 44.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nizhniy Novgorod: 6754.3 km from centroid", + " Pascagoula: 3197.6 km from centroid", + " Frankfort: 2650.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nizhniy Novgorod", + "FINAL ANSWER: Nizhniy Novgorod" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + }, + { + "lat": -43.53333, + "lon": 172.63333, + "name": "Christchurch" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + }, + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + { + "lat": 10.9992, + "lon": 10.41062, + "name": "Darazo" + } + ], + "question": "Which location is the geographic outlier among: Wantirna South, Christchurch, Casula, Titirangi, Darazo?", + "ground_truth": { + "answer": "Darazo", + "outlier_distance_km": 13545.7, + "second_furthest_km": 4185.2, + "clarity_ratio": 3.24, + "median_distance_km": 4082.3, + "distances_to_centroid": { + "Wantirna South": 1716.4, + "Christchurch": 4082.3, + "Casula": 2014.7, + "Titirangi": 4185.2, + "Darazo": 13545.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wantirna South: (-37.88°, 145.22°)", + " Christchurch: (-43.53°, 172.63°)", + " Casula: (-33.95°, 150.90°)", + " Titirangi: (-36.94°, 174.66°)", + " Darazo: (11.00°, 10.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Darazo: 13545.7 km from centroid", + " Titirangi: 4185.2 km from centroid", + " Christchurch: 4082.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Darazo", + "FINAL ANSWER: Darazo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": -27.50578, + "lon": 153.10236, + "name": "Carindale" + }, + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + }, + { + "lat": -29.98972, + "lon": -52.37806, + "name": "Rio Pardo" + } + ], + "question": "Which location is the geographic outlier among: Ballajura, Carindale, Robina, Greensborough, Rio Pardo?", + "ground_truth": { + "answer": "Rio Pardo", + "outlier_distance_km": 12749.8, + "second_furthest_km": 4842.2, + "clarity_ratio": 2.63, + "median_distance_km": 4833.1, + "distances_to_centroid": { + "Ballajura": 1224.0, + "Carindale": 4833.1, + "Robina": 4842.2, + "Greensborough": 3899.9, + "Rio Pardo": 12749.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ballajura: (-31.84°, 115.90°)", + " Carindale: (-27.51°, 153.10°)", + " Robina: (-28.07°, 153.39°)", + " Greensborough: (-37.70°, 145.10°)", + " Rio Pardo: (-29.99°, -52.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rio Pardo: 12749.8 km from centroid", + " Robina: 4842.2 km from centroid", + " Carindale: 4833.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rio Pardo", + "FINAL ANSWER: Rio Pardo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + }, + { + "lat": 5.7989, + "lon": 100.37264, + "name": "Yan Besar" + } + ], + "question": "Which location is the geographic outlier among: Reservoir, Otahuhu, Perth, Mulgrave, Yan Besar?", + "ground_truth": { + "answer": "Yan Besar", + "outlier_distance_km": 5360.8, + "second_furthest_km": 3738.8, + "clarity_ratio": 1.43, + "median_distance_km": 2017.8, + "distances_to_centroid": { + "Reservoir": 1376.4, + "Otahuhu": 3738.8, + "Perth": 2017.8, + "Mulgrave": 1404.5, + "Yan Besar": 5360.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reservoir: (-37.72°, 145.00°)", + " Otahuhu: (-36.94°, 174.84°)", + " Perth: (-31.95°, 115.86°)", + " Mulgrave: (-37.93°, 145.18°)", + " Yan Besar: (5.80°, 100.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yan Besar: 5360.8 km from centroid", + " Otahuhu: 3738.8 km from centroid", + " Perth: 2017.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yan Besar", + "FINAL ANSWER: Yan Besar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": 3.93726, + "lon": 41.85688, + "name": "Mandera" + } + ], + "question": "Which location is the geographic outlier among: Elwood, Mooroolbark, Engadine, Frankston South, Mandera?", + "ground_truth": { + "answer": "Mandera", + "outlier_distance_km": 9616.8, + "second_furthest_km": 2468.8, + "clarity_ratio": 3.9, + "median_distance_km": 2079.1, + "distances_to_centroid": { + "Elwood": 2053.9, + "Mooroolbark": 2076.5, + "Engadine": 2468.8, + "Frankston South": 2079.1, + "Mandera": 9616.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Elwood: (-37.88°, 144.98°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Engadine: (-34.07°, 151.01°)", + " Frankston South: (-38.17°, 145.14°)", + " Mandera: (3.94°, 41.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mandera: 9616.8 km from centroid", + " Engadine: 2468.8 km from centroid", + " Frankston South: 2079.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mandera", + "FINAL ANSWER: Mandera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.24179, + "lon": 27.57422, + "name": "Koppies" + }, + { + "lat": 12.37299, + "lon": 14.2069, + "name": "Gamboru" + }, + { + "lat": -24.88333, + "lon": 28.28333, + "name": "Bela Bela" + }, + { + "lat": -26.002, + "lon": 29.034, + "name": "Phola" + }, + { + "lat": 41.81892, + "lon": -87.69894, + "name": "Brighton Park" + } + ], + "question": "Which location is the geographic outlier among: Koppies, Gamboru, Bela Bela, Phola, Brighton Park?", + "ground_truth": { + "answer": "Brighton Park", + "outlier_distance_km": 10360.5, + "second_furthest_km": 3696.5, + "clarity_ratio": 2.8, + "median_distance_km": 3662.8, + "distances_to_centroid": { + "Koppies": 3662.8, + "Gamboru": 2319.2, + "Bela Bela": 3563.6, + "Phola": 3696.5, + "Brighton Park": 10360.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Koppies: (-27.24°, 27.57°)", + " Gamboru: (12.37°, 14.21°)", + " Bela Bela: (-24.88°, 28.28°)", + " Phola: (-26.00°, 29.03°)", + " Brighton Park: (41.82°, -87.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brighton Park: 10360.5 km from centroid", + " Phola: 3696.5 km from centroid", + " Koppies: 3662.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brighton Park", + "FINAL ANSWER: Brighton Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.59383, + "lon": 6.21798, + "name": "Ogaminana" + }, + { + "lat": 7.79688, + "lon": 6.74048, + "name": "Lokoja" + }, + { + "lat": 25.73826, + "lon": 32.63684, + "name": "Aţ Ţārif" + }, + { + "lat": 6.25532, + "lon": 45.3853, + "name": "Lasoano" + }, + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + } + ], + "question": "Which location is the geographic outlier among: Ogaminana, Lokoja, Aţ Ţārif, Lasoano, Thomastown?", + "ground_truth": { + "answer": "Thomastown", + "outlier_distance_km": 10827.0, + "second_furthest_km": 4581.9, + "clarity_ratio": 2.36, + "median_distance_km": 4527.0, + "distances_to_centroid": { + "Ogaminana": 4581.9, + "Lokoja": 4527.0, + "Aţ Ţārif": 3071.1, + "Lasoano": 520.3, + "Thomastown": 10827.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ogaminana: (7.59°, 6.22°)", + " Lokoja: (7.80°, 6.74°)", + " Aţ Ţārif: (25.74°, 32.64°)", + " Lasoano: (6.26°, 45.39°)", + " Thomastown: (-37.68°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thomastown: 10827.0 km from centroid", + " Ogaminana: 4581.9 km from centroid", + " Lokoja: 4527.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thomastown", + "FINAL ANSWER: Thomastown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.71816, + "lon": -73.35429, + "name": "West Babylon" + }, + { + "lat": 37.65042, + "lon": -77.61249, + "name": "Short Pump" + }, + { + "lat": 42.24587, + "lon": -84.40135, + "name": "Jackson" + }, + { + "lat": 42.8078, + "lon": -87.92425, + "name": "Caledonia" + }, + { + "lat": 41.56667, + "lon": 2.01667, + "name": "Terrassa" + } + ], + "question": "Which location is the geographic outlier among: West Babylon, Short Pump, Jackson, Caledonia, Terrassa?", + "ground_truth": { + "answer": "Terrassa", + "outlier_distance_km": 5394.0, + "second_furthest_km": 1962.7, + "clarity_ratio": 2.75, + "median_distance_km": 1676.4, + "distances_to_centroid": { + "West Babylon": 765.5, + "Short Pump": 1206.3, + "Jackson": 1676.4, + "Caledonia": 1962.7, + "Terrassa": 5394.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Babylon: (40.72°, -73.35°)", + " Short Pump: (37.65°, -77.61°)", + " Jackson: (42.25°, -84.40°)", + " Caledonia: (42.81°, -87.92°)", + " Terrassa: (41.57°, 2.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Terrassa: 5394.0 km from centroid", + " Caledonia: 1962.7 km from centroid", + " Jackson: 1676.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Terrassa", + "FINAL ANSWER: Terrassa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + { + "lat": -33.7061, + "lon": 150.7094, + "name": "Cranebrook" + }, + { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + { + "lat": -2.08033, + "lon": 37.47202, + "name": "Emali" + } + ], + "question": "Which location is the geographic outlier among: Altona Meadows, Masterton, Cranebrook, Landsdale, Emali?", + "ground_truth": { + "answer": "Emali", + "outlier_distance_km": 9644.8, + "second_furthest_km": 4725.4, + "clarity_ratio": 2.04, + "median_distance_km": 2489.2, + "distances_to_centroid": { + "Altona Meadows": 2069.2, + "Masterton": 4725.4, + "Cranebrook": 2489.2, + "Landsdale": 908.8, + "Emali": 9644.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Altona Meadows: (-37.88°, 144.78°)", + " Masterton: (-40.96°, 175.66°)", + " Cranebrook: (-33.71°, 150.71°)", + " Landsdale: (-31.81°, 115.87°)", + " Emali: (-2.08°, 37.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Emali: 9644.8 km from centroid", + " Masterton: 4725.4 km from centroid", + " Cranebrook: 2489.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Emali", + "FINAL ANSWER: Emali" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.0962, + "lon": 34.27322, + "name": "Bondo" + }, + { + "lat": 25.75089, + "lon": 32.6776, + "name": "Az Zaynīyah Qiblī" + }, + { + "lat": -29.47795, + "lon": 30.23057, + "name": "Howick" + }, + { + "lat": -33.93462, + "lon": 18.86676, + "name": "Stellenbosch" + }, + { + "lat": -19.95194, + "lon": -44.34278, + "name": "Juatuba" + } + ], + "question": "Which location is the geographic outlier among: Bondo, Az Zaynīyah Qiblī, Howick, Stellenbosch, Juatuba?", + "ground_truth": { + "answer": "Juatuba", + "outlier_distance_km": 6320.5, + "second_furthest_km": 4597.4, + "clarity_ratio": 1.37, + "median_distance_km": 2585.0, + "distances_to_centroid": { + "Bondo": 2542.5, + "Az Zaynīyah Qiblī": 4597.4, + "Howick": 2585.0, + "Stellenbosch": 2532.0, + "Juatuba": 6320.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bondo: (-0.10°, 34.27°)", + " Az Zaynīyah Qiblī: (25.75°, 32.68°)", + " Howick: (-29.48°, 30.23°)", + " Stellenbosch: (-33.93°, 18.87°)", + " Juatuba: (-19.95°, -44.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Juatuba: 6320.5 km from centroid", + " Az Zaynīyah Qiblī: 4597.4 km from centroid", + " Howick: 2585.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Juatuba", + "FINAL ANSWER: Juatuba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.53333, + "lon": 110.7, + "name": "Mlonggo" + }, + { + "lat": 19.45591, + "lon": 72.81136, + "name": "Virār" + }, + { + "lat": 9.94578, + "lon": 78.09352, + "name": "Vilāngudi" + }, + { + "lat": 18.92862, + "lon": 79.45712, + "name": "Saknepalli" + }, + { + "lat": 21.33999, + "lon": -158.03039, + "name": "‘Ewa Gentry" + } + ], + "question": "Which location is the geographic outlier among: Mlonggo, Virār, Vilāngudi, Saknepalli, ‘Ewa Gentry?", + "ground_truth": { + "answer": "‘Ewa Gentry", + "outlier_distance_km": 15913.8, + "second_furthest_km": 8458.0, + "clarity_ratio": 1.88, + "median_distance_km": 4627.4, + "distances_to_centroid": { + "Mlonggo": 8458.0, + "Virār": 3935.0, + "Vilāngudi": 4529.3, + "Saknepalli": 4627.4, + "‘Ewa Gentry": 15913.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mlonggo: (-6.53°, 110.70°)", + " Virār: (19.46°, 72.81°)", + " Vilāngudi: (9.95°, 78.09°)", + " Saknepalli: (18.93°, 79.46°)", + " ‘Ewa Gentry: (21.34°, -158.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " ‘Ewa Gentry: 15913.8 km from centroid", + " Mlonggo: 8458.0 km from centroid", + " Saknepalli: 4627.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: ‘Ewa Gentry", + "FINAL ANSWER: ‘Ewa Gentry" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.64789, + "lon": -2.31683, + "name": "Ramsbottom" + }, + { + "lat": 55.99456, + "lon": 37.82897, + "name": "Pushkino" + }, + { + "lat": 57.84998, + "lon": 61.69414, + "name": "Alapayevsk" + }, + { + "lat": 49.46633, + "lon": 7.16814, + "name": "Sankt Wendel" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + } + ], + "question": "Which location is the geographic outlier among: Ramsbottom, Pushkino, Alapayevsk, Sankt Wendel, Camberwell?", + "ground_truth": { + "answer": "Camberwell", + "outlier_distance_km": 12747.2, + "second_furthest_km": 4449.0, + "clarity_ratio": 2.87, + "median_distance_km": 3747.1, + "distances_to_centroid": { + "Ramsbottom": 4449.0, + "Pushkino": 2421.1, + "Alapayevsk": 2599.9, + "Sankt Wendel": 3747.1, + "Camberwell": 12747.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ramsbottom: (53.65°, -2.32°)", + " Pushkino: (55.99°, 37.83°)", + " Alapayevsk: (57.85°, 61.69°)", + " Sankt Wendel: (49.47°, 7.17°)", + " Camberwell: (-37.84°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camberwell: 12747.2 km from centroid", + " Ramsbottom: 4449.0 km from centroid", + " Sankt Wendel: 3747.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camberwell", + "FINAL ANSWER: Camberwell" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.49828, + "lon": -73.97591, + "name": "Astrea" + }, + { + "lat": 3.62057, + "lon": -75.09415, + "name": "Natagaima" + }, + { + "lat": -2.04278, + "lon": -45.95917, + "name": "Maracaçumé" + }, + { + "lat": -14.66429, + "lon": -52.35859, + "name": "Nova Xavantina" + }, + { + "lat": 9.88333, + "lon": 36.61667, + "name": "Āyana" + } + ], + "question": "Which location is the geographic outlier among: Astrea, Natagaima, Maracaçumé, Nova Xavantina, Āyana?", + "ground_truth": { + "answer": "Āyana", + "outlier_distance_km": 8753.5, + "second_furthest_km": 3668.5, + "clarity_ratio": 2.39, + "median_distance_km": 3636.6, + "distances_to_centroid": { + "Astrea": 3636.6, + "Natagaima": 3668.5, + "Maracaçumé": 560.1, + "Nova Xavantina": 2096.8, + "Āyana": 8753.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Astrea: (9.50°, -73.98°)", + " Natagaima: (3.62°, -75.09°)", + " Maracaçumé: (-2.04°, -45.96°)", + " Nova Xavantina: (-14.66°, -52.36°)", + " Āyana: (9.88°, 36.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Āyana: 8753.5 km from centroid", + " Natagaima: 3668.5 km from centroid", + " Astrea: 3636.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Āyana", + "FINAL ANSWER: Āyana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.87672, + "lon": -89.58786, + "name": "Sikeston" + }, + { + "lat": 19.96268, + "lon": -97.21141, + "name": "Tlapacoyan" + }, + { + "lat": 45.44979, + "lon": -73.6015, + "name": "Ville-Émard" + }, + { + "lat": 40.72677, + "lon": -73.6343, + "name": "Garden City" + }, + { + "lat": -13.52728, + "lon": -71.9843, + "name": "Santiago" + } + ], + "question": "Which location is the geographic outlier among: Sikeston, Tlapacoyan, Ville-Émard, Garden City, Santiago?", + "ground_truth": { + "answer": "Santiago", + "outlier_distance_km": 4496.0, + "second_furthest_km": 2277.3, + "clarity_ratio": 1.97, + "median_distance_km": 1790.8, + "distances_to_centroid": { + "Sikeston": 1455.8, + "Tlapacoyan": 1765.4, + "Ville-Émard": 2277.3, + "Garden City": 1790.8, + "Santiago": 4496.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sikeston: (36.88°, -89.59°)", + " Tlapacoyan: (19.96°, -97.21°)", + " Ville-Émard: (45.45°, -73.60°)", + " Garden City: (40.73°, -73.63°)", + " Santiago: (-13.53°, -71.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santiago: 4496.0 km from centroid", + " Ville-Émard: 2277.3 km from centroid", + " Garden City: 1790.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santiago", + "FINAL ANSWER: Santiago" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.52856, + "lon": 74.26396, + "name": "Kopawor" + }, + { + "lat": 30.79953, + "lon": 76.02355, + "name": "Dorāha" + }, + { + "lat": 26.86396, + "lon": 82.14103, + "name": "Nawābganj" + }, + { + "lat": 9.17048, + "lon": 77.54107, + "name": "Sankarankovil" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + } + ], + "question": "Which location is the geographic outlier among: Kopawor, Dorāha, Nawābganj, Sankarankovil, Chatswood?", + "ground_truth": { + "answer": "Chatswood", + "outlier_distance_km": 8154.8, + "second_furthest_km": 2954.0, + "clarity_ratio": 2.76, + "median_distance_km": 2539.0, + "distances_to_centroid": { + "Kopawor": 2954.0, + "Dorāha": 2539.0, + "Nawābganj": 1818.1, + "Sankarankovil": 1672.1, + "Chatswood": 8154.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kopawor: (34.53°, 74.26°)", + " Dorāha: (30.80°, 76.02°)", + " Nawābganj: (26.86°, 82.14°)", + " Sankarankovil: (9.17°, 77.54°)", + " Chatswood: (-33.80°, 151.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chatswood: 8154.8 km from centroid", + " Kopawor: 2954.0 km from centroid", + " Dorāha: 2539.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chatswood", + "FINAL ANSWER: Chatswood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.83333, + "lon": 139.58333, + "name": "Shiki" + }, + { + "lat": 23.78516, + "lon": 85.9783, + "name": "Kāro" + }, + { + "lat": 32.06167, + "lon": 118.77778, + "name": "Nanjing" + }, + { + "lat": 20.61013, + "lon": 72.93428, + "name": "Valsād" + }, + { + "lat": -32.17588, + "lon": 26.82437, + "name": "Whittlesea" + } + ], + "question": "Which location is the geographic outlier among: Shiki, Kāro, Nanjing, Valsād, Whittlesea?", + "ground_truth": { + "answer": "Whittlesea", + "outlier_distance_km": 8496.2, + "second_furthest_km": 5462.0, + "clarity_ratio": 1.56, + "median_distance_km": 3507.5, + "distances_to_centroid": { + "Shiki": 5462.0, + "Kāro": 912.7, + "Nanjing": 3507.5, + "Valsād": 1751.7, + "Whittlesea": 8496.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shiki: (35.83°, 139.58°)", + " Kāro: (23.79°, 85.98°)", + " Nanjing: (32.06°, 118.78°)", + " Valsād: (20.61°, 72.93°)", + " Whittlesea: (-32.18°, 26.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whittlesea: 8496.2 km from centroid", + " Shiki: 5462.0 km from centroid", + " Nanjing: 3507.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whittlesea", + "FINAL ANSWER: Whittlesea" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.74055, + "lon": -74.75443, + "name": "Palmar de Varela" + }, + { + "lat": 1.25744, + "lon": -70.23551, + "name": "Mitú" + }, + { + "lat": -10.53944, + "lon": -37.41667, + "name": "Ribeirópolis" + }, + { + "lat": -15.29333, + "lon": -39.07528, + "name": "Una" + }, + { + "lat": 44.53889, + "lon": 10.81166, + "name": "Fiorano" + } + ], + "question": "Which location is the geographic outlier among: Palmar de Varela, Mitú, Ribeirópolis, Una, Fiorano?", + "ground_truth": { + "answer": "Fiorano", + "outlier_distance_km": 6656.5, + "second_furthest_km": 3622.1, + "clarity_ratio": 1.84, + "median_distance_km": 3164.1, + "distances_to_centroid": { + "Palmar de Varela": 3622.1, + "Mitú": 3164.1, + "Ribeirópolis": 1926.9, + "Una": 2407.1, + "Fiorano": 6656.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palmar de Varela: (10.74°, -74.75°)", + " Mitú: (1.26°, -70.24°)", + " Ribeirópolis: (-10.54°, -37.42°)", + " Una: (-15.29°, -39.08°)", + " Fiorano: (44.54°, 10.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fiorano: 6656.5 km from centroid", + " Palmar de Varela: 3622.1 km from centroid", + " Mitú: 3164.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fiorano", + "FINAL ANSWER: Fiorano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.94956, + "lon": 14.72837, + "name": "Gubin" + }, + { + "lat": 52.7, + "lon": -2.51667, + "name": "Wellington" + }, + { + "lat": 46.69263, + "lon": 38.27907, + "name": "Yeysk" + }, + { + "lat": 50.93333, + "lon": 6.95, + "name": "Köln" + }, + { + "lat": -14.16417, + "lon": -39.37361, + "name": "Ibirapitanga" + } + ], + "question": "Which location is the geographic outlier among: Gubin, Wellington, Yeysk, Köln, Ibirapitanga?", + "ground_truth": { + "answer": "Ibirapitanga", + "outlier_distance_km": 7299.3, + "second_furthest_km": 3001.6, + "clarity_ratio": 2.43, + "median_distance_km": 1813.9, + "distances_to_centroid": { + "Gubin": 1813.9, + "Wellington": 1742.5, + "Yeysk": 3001.6, + "Köln": 1503.4, + "Ibirapitanga": 7299.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gubin: (51.95°, 14.73°)", + " Wellington: (52.70°, -2.52°)", + " Yeysk: (46.69°, 38.28°)", + " Köln: (50.93°, 6.95°)", + " Ibirapitanga: (-14.16°, -39.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ibirapitanga: 7299.3 km from centroid", + " Yeysk: 3001.6 km from centroid", + " Gubin: 1813.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ibirapitanga", + "FINAL ANSWER: Ibirapitanga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.91482, + "lon": 144.75088, + "name": "Point Cook" + }, + { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": 14.10307, + "lon": 38.28289, + "name": "Inda Silasē" + } + ], + "question": "Which location is the geographic outlier among: Point Cook, Warwick, Wahroonga, Mount Martha, Inda Silasē?", + "ground_truth": { + "answer": "Inda Silasē", + "outlier_distance_km": 10459.2, + "second_furthest_km": 2600.1, + "clarity_ratio": 4.02, + "median_distance_km": 2589.6, + "distances_to_centroid": { + "Point Cook": 2275.7, + "Warwick": 2589.6, + "Wahroonga": 2600.1, + "Mount Martha": 2317.1, + "Inda Silasē": 10459.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Point Cook: (-37.91°, 144.75°)", + " Warwick: (-28.22°, 152.03°)", + " Wahroonga: (-33.72°, 151.12°)", + " Mount Martha: (-38.27°, 145.02°)", + " Inda Silasē: (14.10°, 38.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Inda Silasē: 10459.2 km from centroid", + " Wahroonga: 2600.1 km from centroid", + " Warwick: 2589.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Inda Silasē", + "FINAL ANSWER: Inda Silasē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + { + "lat": -36.84853, + "lon": 174.76349, + "name": "Auckland" + }, + { + "lat": -33.73333, + "lon": 150.93284, + "name": "Glenwood" + }, + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": 22.62104, + "lon": 73.11725, + "name": "Od" + } + ], + "question": "Which location is the geographic outlier among: Cambridge, Auckland, Glenwood, Epsom, Od?", + "ground_truth": { + "answer": "Od", + "outlier_distance_km": 9793.7, + "second_furthest_km": 2838.6, + "clarity_ratio": 3.45, + "median_distance_km": 2740.4, + "distances_to_centroid": { + "Cambridge": 2838.6, + "Auckland": 2738.1, + "Glenwood": 1027.5, + "Epsom": 2740.4, + "Od": 9793.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cambridge: (-37.88°, 175.44°)", + " Auckland: (-36.85°, 174.76°)", + " Glenwood: (-33.73°, 150.93°)", + " Epsom: (-36.89°, 174.77°)", + " Od: (22.62°, 73.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Od: 9793.7 km from centroid", + " Cambridge: 2838.6 km from centroid", + " Epsom: 2740.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Od", + "FINAL ANSWER: Od" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.89428, + "lon": -77.4311, + "name": "Chantilly" + }, + { + "lat": 20.43108, + "lon": -101.72261, + "name": "Pénjamo" + }, + { + "lat": 40.76704, + "lon": -72.99622, + "name": "East Patchogue" + }, + { + "lat": 32.58394, + "lon": -117.11308, + "name": "Imperial Beach" + }, + { + "lat": 6.99536, + "lon": 0.29306, + "name": "Kpandu" + } + ], + "question": "Which location is the geographic outlier among: Chantilly, Pénjamo, East Patchogue, Imperial Beach, Kpandu?", + "ground_truth": { + "answer": "Kpandu", + "outlier_distance_km": 8083.2, + "second_furthest_km": 4164.2, + "clarity_ratio": 1.94, + "median_distance_km": 2945.5, + "distances_to_centroid": { + "Chantilly": 1264.3, + "Pénjamo": 2945.5, + "East Patchogue": 1428.8, + "Imperial Beach": 4164.2, + "Kpandu": 8083.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chantilly: (38.89°, -77.43°)", + " Pénjamo: (20.43°, -101.72°)", + " East Patchogue: (40.77°, -73.00°)", + " Imperial Beach: (32.58°, -117.11°)", + " Kpandu: (7.00°, 0.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kpandu: 8083.2 km from centroid", + " Imperial Beach: 4164.2 km from centroid", + " Pénjamo: 2945.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kpandu", + "FINAL ANSWER: Kpandu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.25738, + "lon": 33.81291, + "name": "Hurghada" + }, + { + "lat": 10.85, + "lon": 36.88333, + "name": "Gimja Bēt Maryam" + }, + { + "lat": -23.94299, + "lon": 31.14107, + "name": "Phalaborwa" + }, + { + "lat": 5.70773, + "lon": 6.43402, + "name": "Kwale" + }, + { + "lat": -6.31694, + "lon": 106.66417, + "name": "Serpong" + } + ], + "question": "Which location is the geographic outlier among: Hurghada, Gimja Bēt Maryam, Phalaborwa, Kwale, Serpong?", + "ground_truth": { + "answer": "Serpong", + "outlier_distance_km": 7140.1, + "second_furthest_km": 4066.4, + "clarity_ratio": 1.76, + "median_distance_km": 3229.0, + "distances_to_centroid": { + "Hurghada": 2898.7, + "Gimja Bēt Maryam": 1128.0, + "Phalaborwa": 3229.0, + "Kwale": 4066.4, + "Serpong": 7140.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hurghada: (27.26°, 33.81°)", + " Gimja Bēt Maryam: (10.85°, 36.88°)", + " Phalaborwa: (-23.94°, 31.14°)", + " Kwale: (5.71°, 6.43°)", + " Serpong: (-6.32°, 106.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Serpong: 7140.1 km from centroid", + " Kwale: 4066.4 km from centroid", + " Phalaborwa: 3229.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Serpong", + "FINAL ANSWER: Serpong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -29.58028, + "lon": -51.08528, + "name": "Dois Irmãos" + }, + { + "lat": -21.27528, + "lon": -47.30417, + "name": "Cajuru" + }, + { + "lat": -12.05354, + "lon": -77.09802, + "name": "Carmen De La Legua Reynoso" + }, + { + "lat": -7.35833, + "lon": -35.89833, + "name": "Queimadas" + }, + { + "lat": 53.18139, + "lon": 44.04944, + "name": "Kamenka" + } + ], + "question": "Which location is the geographic outlier among: Dois Irmãos, Cajuru, Carmen De La Legua Reynoso, Queimadas, Kamenka?", + "ground_truth": { + "answer": "Kamenka", + "outlier_distance_km": 9487.1, + "second_furthest_km": 4895.4, + "clarity_ratio": 1.94, + "median_distance_km": 3451.3, + "distances_to_centroid": { + "Dois Irmãos": 3451.3, + "Cajuru": 2486.1, + "Carmen De La Legua Reynoso": 4895.4, + "Queimadas": 514.2, + "Kamenka": 9487.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dois Irmãos: (-29.58°, -51.09°)", + " Cajuru: (-21.28°, -47.30°)", + " Carmen De La Legua Reynoso: (-12.05°, -77.10°)", + " Queimadas: (-7.36°, -35.90°)", + " Kamenka: (53.18°, 44.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kamenka: 9487.1 km from centroid", + " Carmen De La Legua Reynoso: 4895.4 km from centroid", + " Dois Irmãos: 3451.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kamenka", + "FINAL ANSWER: Kamenka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.91, + "lon": 140.11667, + "name": "Yonezawa" + }, + { + "lat": 42.81944, + "lon": 141.65222, + "name": "Chitose" + }, + { + "lat": 18.67337, + "lon": 105.69232, + "name": "Vinh" + }, + { + "lat": 32.89139, + "lon": 108.50472, + "name": "Hanyin Chengguanzhen" + }, + { + "lat": 51.67086, + "lon": -0.02748, + "name": "Enfield Lock" + } + ], + "question": "Which location is the geographic outlier among: Yonezawa, Chitose, Vinh, Hanyin Chengguanzhen, Enfield Lock?", + "ground_truth": { + "answer": "Enfield Lock", + "outlier_distance_km": 7453.0, + "second_furthest_km": 3649.2, + "clarity_ratio": 2.04, + "median_distance_km": 3590.6, + "distances_to_centroid": { + "Yonezawa": 3590.6, + "Chitose": 3649.2, + "Vinh": 2112.6, + "Hanyin Chengguanzhen": 953.9, + "Enfield Lock": 7453.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yonezawa: (37.91°, 140.12°)", + " Chitose: (42.82°, 141.65°)", + " Vinh: (18.67°, 105.69°)", + " Hanyin Chengguanzhen: (32.89°, 108.50°)", + " Enfield Lock: (51.67°, -0.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Enfield Lock: 7453.0 km from centroid", + " Chitose: 3649.2 km from centroid", + " Yonezawa: 3590.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Enfield Lock", + "FINAL ANSWER: Enfield Lock" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.5275, + "lon": -40.30694, + "name": "Itaberaba" + }, + { + "lat": -24.78927, + "lon": -50.01225, + "name": "Castro" + }, + { + "lat": -17.13806, + "lon": -49.98806, + "name": "Indiara" + }, + { + "lat": -7.94083, + "lon": -34.87306, + "name": "Paulista" + }, + { + "lat": -0.50974, + "lon": 34.73067, + "name": "Oyugis" + } + ], + "question": "Which location is the geographic outlier among: Itaberaba, Castro, Indiara, Paulista, Oyugis?", + "ground_truth": { + "answer": "Oyugis", + "outlier_distance_km": 7050.0, + "second_furthest_km": 2672.3, + "clarity_ratio": 2.64, + "median_distance_km": 2405.8, + "distances_to_centroid": { + "Itaberaba": 1325.9, + "Castro": 2672.3, + "Indiara": 2405.8, + "Paulista": 903.7, + "Oyugis": 7050.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itaberaba: (-12.53°, -40.31°)", + " Castro: (-24.79°, -50.01°)", + " Indiara: (-17.14°, -49.99°)", + " Paulista: (-7.94°, -34.87°)", + " Oyugis: (-0.51°, 34.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oyugis: 7050.0 km from centroid", + " Castro: 2672.3 km from centroid", + " Indiara: 2405.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oyugis", + "FINAL ANSWER: Oyugis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.63126, + "lon": 74.6902, + "name": "Kundapura" + }, + { + "lat": 3.10628, + "lon": 101.66761, + "name": "Bukit Kerinchi" + }, + { + "lat": 28.62169, + "lon": 76.9923, + "name": "Nangli Sakrawat" + }, + { + "lat": 44.15399, + "lon": 142.37307, + "name": "Minamishibetsuchō" + }, + { + "lat": 9.18361, + "lon": -75.38167, + "name": "Sampués" + } + ], + "question": "Which location is the geographic outlier among: Kundapura, Bukit Kerinchi, Nangli Sakrawat, Minamishibetsuchō, Sampués?", + "ground_truth": { + "answer": "Sampués", + "outlier_distance_km": 14533.3, + "second_furthest_km": 7578.1, + "clarity_ratio": 1.92, + "median_distance_km": 4478.4, + "distances_to_centroid": { + "Kundapura": 1318.9, + "Bukit Kerinchi": 4478.4, + "Nangli Sakrawat": 1639.3, + "Minamishibetsuchō": 7578.1, + "Sampués": 14533.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kundapura: (13.63°, 74.69°)", + " Bukit Kerinchi: (3.11°, 101.67°)", + " Nangli Sakrawat: (28.62°, 76.99°)", + " Minamishibetsuchō: (44.15°, 142.37°)", + " Sampués: (9.18°, -75.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sampués: 14533.3 km from centroid", + " Minamishibetsuchō: 7578.1 km from centroid", + " Bukit Kerinchi: 4478.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sampués", + "FINAL ANSWER: Sampués" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.97417, + "lon": 5.82917, + "name": "Geleen" + }, + { + "lat": 63.74549, + "lon": 34.31614, + "name": "Segezha" + }, + { + "lat": 52.42377, + "lon": 9.43585, + "name": "Wunstorf" + }, + { + "lat": 45.07073, + "lon": 7.51465, + "name": "Rivoli" + }, + { + "lat": -33.95, + "lon": 151.13333, + "name": "Rockdale" + } + ], + "question": "Which location is the geographic outlier among: Geleen, Segezha, Wunstorf, Rivoli, Rockdale?", + "ground_truth": { + "answer": "Rockdale", + "outlier_distance_km": 13720.7, + "second_furthest_km": 3314.4, + "clarity_ratio": 4.14, + "median_distance_km": 3163.3, + "distances_to_centroid": { + "Geleen": 3314.4, + "Segezha": 3163.3, + "Wunstorf": 3137.0, + "Rivoli": 3048.7, + "Rockdale": 13720.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Geleen: (50.97°, 5.83°)", + " Segezha: (63.75°, 34.32°)", + " Wunstorf: (52.42°, 9.44°)", + " Rivoli: (45.07°, 7.51°)", + " Rockdale: (-33.95°, 151.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rockdale: 13720.7 km from centroid", + " Geleen: 3314.4 km from centroid", + " Segezha: 3163.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rockdale", + "FINAL ANSWER: Rockdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.90155, + "lon": 108.43367, + "name": "Xiongjia" + }, + { + "lat": 11.23052, + "lon": 75.85178, + "name": "Pantheeramkavu" + }, + { + "lat": -6.28862, + "lon": 106.71789, + "name": "South Tangerang" + }, + { + "lat": 18.64028, + "lon": 109.69944, + "name": "Baocheng" + }, + { + "lat": -36.74075, + "lon": -72.99528, + "name": "Penco" + } + ], + "question": "Which location is the geographic outlier among: Xiongjia, Pantheeramkavu, South Tangerang, Baocheng, Penco?", + "ground_truth": { + "answer": "Penco", + "outlier_distance_km": 14402.3, + "second_furthest_km": 5421.8, + "clarity_ratio": 2.66, + "median_distance_km": 5082.9, + "distances_to_centroid": { + "Xiongjia": 5421.8, + "Pantheeramkavu": 1421.3, + "South Tangerang": 4700.6, + "Baocheng": 5082.9, + "Penco": 14402.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Xiongjia: (30.90°, 108.43°)", + " Pantheeramkavu: (11.23°, 75.85°)", + " South Tangerang: (-6.29°, 106.72°)", + " Baocheng: (18.64°, 109.70°)", + " Penco: (-36.74°, -73.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Penco: 14402.3 km from centroid", + " Xiongjia: 5421.8 km from centroid", + " Baocheng: 5082.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Penco", + "FINAL ANSWER: Penco" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.53333, + "lon": 29.06667, + "name": "eMbalenhle" + }, + { + "lat": -23.88384, + "lon": 29.70557, + "name": "Mankweng" + }, + { + "lat": 11.74697, + "lon": 11.96083, + "name": "Damaturu" + }, + { + "lat": -25.48251, + "lon": 29.02763, + "name": "Verena" + }, + { + "lat": 6.42942, + "lon": 100.28174, + "name": "Kampung Hutan Arau" + } + ], + "question": "Which location is the geographic outlier among: eMbalenhle, Mankweng, Damaturu, Verena, Kampung Hutan Arau?", + "ground_truth": { + "answer": "Kampung Hutan Arau", + "outlier_distance_km": 6959.6, + "second_furthest_km": 4037.3, + "clarity_ratio": 1.72, + "median_distance_km": 2022.3, + "distances_to_centroid": { + "eMbalenhle": 2022.3, + "Mankweng": 1751.3, + "Damaturu": 4037.3, + "Verena": 1932.2, + "Kampung Hutan Arau": 6959.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " eMbalenhle: (-26.53°, 29.07°)", + " Mankweng: (-23.88°, 29.71°)", + " Damaturu: (11.75°, 11.96°)", + " Verena: (-25.48°, 29.03°)", + " Kampung Hutan Arau: (6.43°, 100.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kampung Hutan Arau: 6959.6 km from centroid", + " Damaturu: 4037.3 km from centroid", + " eMbalenhle: 2022.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kampung Hutan Arau", + "FINAL ANSWER: Kampung Hutan Arau" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.12944, + "lon": 127.1, + "name": "Yŏnmu" + }, + { + "lat": 30.86761, + "lon": 108.36969, + "name": "Tiancheng" + }, + { + "lat": 25.56078, + "lon": 81.49164, + "name": "Bharwāri" + }, + { + "lat": 39.49944, + "lon": 106.71167, + "name": "Wuda" + }, + { + "lat": -22.41139, + "lon": -47.56139, + "name": "Rio Claro" + } + ], + "question": "Which location is the geographic outlier among: Yŏnmu, Tiancheng, Bharwāri, Wuda, Rio Claro?", + "ground_truth": { + "answer": "Rio Claro", + "outlier_distance_km": 14161.1, + "second_furthest_km": 5219.7, + "clarity_ratio": 2.71, + "median_distance_km": 3559.6, + "distances_to_centroid": { + "Yŏnmu": 5219.7, + "Tiancheng": 3433.3, + "Bharwāri": 755.0, + "Wuda": 3559.6, + "Rio Claro": 14161.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yŏnmu: (36.13°, 127.10°)", + " Tiancheng: (30.87°, 108.37°)", + " Bharwāri: (25.56°, 81.49°)", + " Wuda: (39.50°, 106.71°)", + " Rio Claro: (-22.41°, -47.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rio Claro: 14161.1 km from centroid", + " Yŏnmu: 5219.7 km from centroid", + " Wuda: 3559.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rio Claro", + "FINAL ANSWER: Rio Claro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + }, + { + "lat": 19.88372, + "lon": -103.60073, + "name": "Sayula" + } + ], + "question": "Which location is the geographic outlier among: Glen Iris, Mooroolbark, Springvale, Cherrybrook, Sayula?", + "ground_truth": { + "answer": "Sayula", + "outlier_distance_km": 17854.1, + "second_furthest_km": 5283.2, + "clarity_ratio": 3.38, + "median_distance_km": 4753.7, + "distances_to_centroid": { + "Glen Iris": 4732.1, + "Mooroolbark": 4753.7, + "Springvale": 4740.1, + "Cherrybrook": 5283.2, + "Sayula": 17854.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Iris: (-37.87°, 145.07°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Springvale: (-37.95°, 145.15°)", + " Cherrybrook: (-33.72°, 151.05°)", + " Sayula: (19.88°, -103.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sayula: 17854.1 km from centroid", + " Cherrybrook: 5283.2 km from centroid", + " Mooroolbark: 4753.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sayula", + "FINAL ANSWER: Sayula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.71715, + "lon": -122.40433, + "name": "Visitacion Valley" + }, + { + "lat": 41.41698, + "lon": -87.36531, + "name": "Crown Point" + }, + { + "lat": 38.15979, + "lon": -85.58774, + "name": "Fern Creek" + }, + { + "lat": 35.01424, + "lon": -85.2519, + "name": "East Ridge" + }, + { + "lat": -34.49459, + "lon": -58.62729, + "name": "Don Torcuato" + } + ], + "question": "Which location is the geographic outlier among: Visitacion Valley, Crown Point, Fern Creek, East Ridge, Don Torcuato?", + "ground_truth": { + "answer": "Don Torcuato", + "outlier_distance_km": 7154.9, + "second_furthest_km": 3633.8, + "clarity_ratio": 1.97, + "median_distance_km": 1985.8, + "distances_to_centroid": { + "Visitacion Valley": 3633.8, + "Crown Point": 1985.8, + "Fern Creek": 1637.2, + "East Ridge": 1297.8, + "Don Torcuato": 7154.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Visitacion Valley: (37.72°, -122.40°)", + " Crown Point: (41.42°, -87.37°)", + " Fern Creek: (38.16°, -85.59°)", + " East Ridge: (35.01°, -85.25°)", + " Don Torcuato: (-34.49°, -58.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Don Torcuato: 7154.9 km from centroid", + " Visitacion Valley: 3633.8 km from centroid", + " Crown Point: 1985.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Don Torcuato", + "FINAL ANSWER: Don Torcuato" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91667, + "lon": 151.03333, + "name": "Bankstown" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -20.39028, + "lon": -40.49611, + "name": "Viana" + } + ], + "question": "Which location is the geographic outlier among: Bankstown, Saint Albans, Landsdale, Seven Hills, Viana?", + "ground_truth": { + "answer": "Viana", + "outlier_distance_km": 13137.1, + "second_furthest_km": 4330.7, + "clarity_ratio": 3.03, + "median_distance_km": 4324.1, + "distances_to_centroid": { + "Bankstown": 4330.7, + "Saint Albans": 3728.4, + "Landsdale": 1082.5, + "Seven Hills": 4324.1, + "Viana": 13137.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bankstown: (-33.92°, 151.03°)", + " Saint Albans: (-37.73°, 144.80°)", + " Landsdale: (-31.81°, 115.87°)", + " Seven Hills: (-33.78°, 150.93°)", + " Viana: (-20.39°, -40.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viana: 13137.1 km from centroid", + " Bankstown: 4330.7 km from centroid", + " Seven Hills: 4324.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viana", + "FINAL ANSWER: Viana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.20528, + "lon": 19.27498, + "name": "Jaworzno" + }, + { + "lat": 40.96836, + "lon": 17.11329, + "name": "Conversano" + }, + { + "lat": 48.22399, + "lon": 8.38583, + "name": "Schramberg" + }, + { + "lat": 57.10501, + "lon": 41.73565, + "name": "Rodniki" + }, + { + "lat": 27.86371, + "lon": 77.20432, + "name": "Pūnāhāna" + } + ], + "question": "Which location is the geographic outlier among: Jaworzno, Conversano, Schramberg, Rodniki, Pūnāhāna?", + "ground_truth": { + "answer": "Pūnāhāna", + "outlier_distance_km": 4339.1, + "second_furthest_km": 1891.1, + "clarity_ratio": 2.29, + "median_distance_km": 1495.7, + "distances_to_centroid": { + "Jaworzno": 1169.5, + "Conversano": 1342.1, + "Schramberg": 1891.1, + "Rodniki": 1495.7, + "Pūnāhāna": 4339.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jaworzno: (50.21°, 19.27°)", + " Conversano: (40.97°, 17.11°)", + " Schramberg: (48.22°, 8.39°)", + " Rodniki: (57.11°, 41.74°)", + " Pūnāhāna: (27.86°, 77.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pūnāhāna: 4339.1 km from centroid", + " Schramberg: 1891.1 km from centroid", + " Rodniki: 1495.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pūnāhāna", + "FINAL ANSWER: Pūnāhāna" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.40008, + "lon": -71.89908, + "name": "Sherbrooke" + }, + { + "lat": 41.05343, + "lon": -73.53873, + "name": "Stamford" + }, + { + "lat": 41.77809, + "lon": -87.66672, + "name": "West Englewood" + }, + { + "lat": 45.1608, + "lon": -93.23495, + "name": "Blaine" + }, + { + "lat": 52.73632, + "lon": 41.44102, + "name": "Tambov" + } + ], + "question": "Which location is the geographic outlier among: Sherbrooke, Stamford, West Englewood, Blaine, Tambov?", + "ground_truth": { + "answer": "Tambov", + "outlier_distance_km": 6653.1, + "second_furthest_km": 2816.7, + "clarity_ratio": 2.36, + "median_distance_km": 2489.2, + "distances_to_centroid": { + "Sherbrooke": 1165.1, + "Stamford": 1418.3, + "West Englewood": 2489.2, + "Blaine": 2816.7, + "Tambov": 6653.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sherbrooke: (45.40°, -71.90°)", + " Stamford: (41.05°, -73.54°)", + " West Englewood: (41.78°, -87.67°)", + " Blaine: (45.16°, -93.23°)", + " Tambov: (52.74°, 41.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tambov: 6653.1 km from centroid", + " Blaine: 2816.7 km from centroid", + " West Englewood: 2489.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tambov", + "FINAL ANSWER: Tambov" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.43722, + "lon": -68.52556, + "name": "Albardón" + }, + { + "lat": -11.79611, + "lon": -37.945, + "name": "Esplanada" + }, + { + "lat": -23.60926, + "lon": -46.62304, + "name": "Bosque Saúde" + }, + { + "lat": -2.90472, + "lon": -41.77667, + "name": "Parnaíba" + }, + { + "lat": 51.4878, + "lon": -2.50403, + "name": "Mangotsfield" + } + ], + "question": "Which location is the geographic outlier among: Albardón, Esplanada, Bosque Saúde, Parnaíba, Mangotsfield?", + "ground_truth": { + "answer": "Mangotsfield", + "outlier_distance_km": 7057.8, + "second_furthest_km": 4332.2, + "clarity_ratio": 1.63, + "median_distance_km": 2348.2, + "distances_to_centroid": { + "Albardón": 4332.2, + "Esplanada": 921.1, + "Bosque Saúde": 2348.2, + "Parnaíba": 268.7, + "Mangotsfield": 7057.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albardón: (-31.44°, -68.53°)", + " Esplanada: (-11.80°, -37.95°)", + " Bosque Saúde: (-23.61°, -46.62°)", + " Parnaíba: (-2.90°, -41.78°)", + " Mangotsfield: (51.49°, -2.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mangotsfield: 7057.8 km from centroid", + " Albardón: 4332.2 km from centroid", + " Bosque Saúde: 2348.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mangotsfield", + "FINAL ANSWER: Mangotsfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.64265, + "lon": -47.21738, + "name": "Santa Luzia" + }, + { + "lat": -5.08917, + "lon": -81.11444, + "name": "Paita" + }, + { + "lat": -27.41444, + "lon": -49.6025, + "name": "Ituporanga" + }, + { + "lat": -11.15895, + "lon": -75.99304, + "name": "Junín" + }, + { + "lat": 8.06667, + "lon": 38.46667, + "name": "Insēno" + } + ], + "question": "Which location is the geographic outlier among: Santa Luzia, Paita, Ituporanga, Junín, Insēno?", + "ground_truth": { + "answer": "Insēno", + "outlier_distance_km": 9224.6, + "second_furthest_km": 4214.3, + "clarity_ratio": 2.19, + "median_distance_km": 3612.9, + "distances_to_centroid": { + "Santa Luzia": 467.6, + "Paita": 4214.3, + "Ituporanga": 2196.1, + "Junín": 3612.9, + "Insēno": 9224.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Luzia: (-7.64°, -47.22°)", + " Paita: (-5.09°, -81.11°)", + " Ituporanga: (-27.41°, -49.60°)", + " Junín: (-11.16°, -75.99°)", + " Insēno: (8.07°, 38.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Insēno: 9224.6 km from centroid", + " Paita: 4214.3 km from centroid", + " Junín: 3612.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Insēno", + "FINAL ANSWER: Insēno" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.52487, + "lon": -77.55777, + "name": "Bon Air" + }, + { + "lat": 34.98898, + "lon": -90.01259, + "name": "Southaven" + }, + { + "lat": 19.44204, + "lon": -98.10325, + "name": "Tetla" + }, + { + "lat": 36.13981, + "lon": -96.10889, + "name": "Sand Springs" + }, + { + "lat": -18.22047, + "lon": -49.72993, + "name": "Bom Jesus de Goiás" + } + ], + "question": "Which location is the geographic outlier among: Bon Air, Southaven, Tetla, Sand Springs, Bom Jesus de Goiás?", + "ground_truth": { + "answer": "Bom Jesus de Goiás", + "outlier_distance_km": 5703.8, + "second_furthest_km": 2064.4, + "clarity_ratio": 2.76, + "median_distance_km": 1788.0, + "distances_to_centroid": { + "Bon Air": 1788.0, + "Southaven": 1630.1, + "Tetla": 1666.6, + "Sand Springs": 2064.4, + "Bom Jesus de Goiás": 5703.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bon Air: (37.52°, -77.56°)", + " Southaven: (34.99°, -90.01°)", + " Tetla: (19.44°, -98.10°)", + " Sand Springs: (36.14°, -96.11°)", + " Bom Jesus de Goiás: (-18.22°, -49.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bom Jesus de Goiás: 5703.8 km from centroid", + " Sand Springs: 2064.4 km from centroid", + " Bon Air: 1788.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bom Jesus de Goiás", + "FINAL ANSWER: Bom Jesus de Goiás" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.73156, + "lon": -1.6137, + "name": "Tafo" + }, + { + "lat": 31.21452, + "lon": 31.35798, + "name": "Bilqās" + }, + { + "lat": 2.80922, + "lon": 40.92885, + "name": "El Wak" + }, + { + "lat": 8.55083, + "lon": -0.51875, + "name": "Salaga" + }, + { + "lat": 35.23338, + "lon": -106.66447, + "name": "Rio Rancho" + } + ], + "question": "Which location is the geographic outlier among: Tafo, Bilqās, El Wak, Salaga, Rio Rancho?", + "ground_truth": { + "answer": "Rio Rancho", + "outlier_distance_km": 9748.5, + "second_furthest_km": 5492.6, + "clarity_ratio": 1.77, + "median_distance_km": 4208.1, + "distances_to_centroid": { + "Tafo": 1289.4, + "Bilqās": 4208.1, + "El Wak": 5492.6, + "Salaga": 1184.8, + "Rio Rancho": 9748.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tafo: (6.73°, -1.61°)", + " Bilqās: (31.21°, 31.36°)", + " El Wak: (2.81°, 40.93°)", + " Salaga: (8.55°, -0.52°)", + " Rio Rancho: (35.23°, -106.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rio Rancho: 9748.5 km from centroid", + " El Wak: 5492.6 km from centroid", + " Bilqās: 4208.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rio Rancho", + "FINAL ANSWER: Rio Rancho" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.94167, + "lon": -54.73833, + "name": "Alenquer" + }, + { + "lat": -22.70861, + "lon": -42.60972, + "name": "Rio Bonito" + }, + { + "lat": -4.3788, + "lon": -44.67112, + "name": "São Luís Gonzaga do Maranhão" + }, + { + "lat": -34.43859, + "lon": -71.07751, + "name": "San Vicente de Tagua Tagua" + }, + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + } + ], + "question": "Which location is the geographic outlier among: Alenquer, Rio Bonito, São Luís Gonzaga do Maranhão, San Vicente de Tagua Tagua, Mascot?", + "ground_truth": { + "answer": "Mascot", + "outlier_distance_km": 13827.0, + "second_furthest_km": 5966.9, + "clarity_ratio": 2.32, + "median_distance_km": 4999.7, + "distances_to_centroid": { + "Alenquer": 4999.7, + "Rio Bonito": 3151.2, + "São Luís Gonzaga do Maranhão": 3881.3, + "San Vicente de Tagua Tagua": 5966.9, + "Mascot": 13827.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alenquer: (-1.94°, -54.74°)", + " Rio Bonito: (-22.71°, -42.61°)", + " São Luís Gonzaga do Maranhão: (-4.38°, -44.67°)", + " San Vicente de Tagua Tagua: (-34.44°, -71.08°)", + " Mascot: (-33.93°, 151.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mascot: 13827.0 km from centroid", + " San Vicente de Tagua Tagua: 5966.9 km from centroid", + " Alenquer: 4999.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mascot", + "FINAL ANSWER: Mascot" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.85833, + "lon": -35.35389, + "name": "Macaíba" + }, + { + "lat": -3.30708, + "lon": -52.53863, + "name": "Brasil Novo" + }, + { + "lat": 7.90745, + "lon": -72.5049, + "name": "Cúcuta" + }, + { + "lat": -25.97972, + "lon": -52.56778, + "name": "Coronel Vivida" + }, + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + } + ], + "question": "Which location is the geographic outlier among: Macaíba, Brasil Novo, Cúcuta, Coronel Vivida, Hoppers Crossing?", + "ground_truth": { + "answer": "Hoppers Crossing", + "outlier_distance_km": 13921.0, + "second_furthest_km": 6903.6, + "clarity_ratio": 2.02, + "median_distance_km": 4407.3, + "distances_to_centroid": { + "Macaíba": 2508.2, + "Brasil Novo": 4407.3, + "Cúcuta": 6903.6, + "Coronel Vivida": 4305.8, + "Hoppers Crossing": 13921.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macaíba: (-5.86°, -35.35°)", + " Brasil Novo: (-3.31°, -52.54°)", + " Cúcuta: (7.91°, -72.50°)", + " Coronel Vivida: (-25.98°, -52.57°)", + " Hoppers Crossing: (-37.88°, 144.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hoppers Crossing: 13921.0 km from centroid", + " Cúcuta: 6903.6 km from centroid", + " Brasil Novo: 4407.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hoppers Crossing", + "FINAL ANSWER: Hoppers Crossing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.8922, + "lon": 10.64713, + "name": "Stockelsdorf" + }, + { + "lat": 38.40148, + "lon": -0.43623, + "name": "Sant Joan d'Alacant" + }, + { + "lat": 48.69406, + "lon": 9.16809, + "name": "Leinfelden-Echterdingen" + }, + { + "lat": 48.8765, + "lon": 2.18967, + "name": "Rueil-Malmaison" + }, + { + "lat": -3.35335, + "lon": 40.02095, + "name": "Watamu" + } + ], + "question": "Which location is the geographic outlier among: Stockelsdorf, Sant Joan d'Alacant, Leinfelden-Echterdingen, Rueil-Malmaison, Watamu?", + "ground_truth": { + "answer": "Watamu", + "outlier_distance_km": 5350.4, + "second_furthest_km": 1849.2, + "clarity_ratio": 2.89, + "median_distance_km": 1524.3, + "distances_to_centroid": { + "Stockelsdorf": 1849.2, + "Sant Joan d'Alacant": 1125.5, + "Leinfelden-Echterdingen": 1292.1, + "Rueil-Malmaison": 1524.3, + "Watamu": 5350.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stockelsdorf: (53.89°, 10.65°)", + " Sant Joan d'Alacant: (38.40°, -0.44°)", + " Leinfelden-Echterdingen: (48.69°, 9.17°)", + " Rueil-Malmaison: (48.88°, 2.19°)", + " Watamu: (-3.35°, 40.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Watamu: 5350.4 km from centroid", + " Stockelsdorf: 1849.2 km from centroid", + " Rueil-Malmaison: 1524.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Watamu", + "FINAL ANSWER: Watamu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.92584, + "lon": 18.42322, + "name": "Cape Town" + }, + { + "lat": 6.84684, + "lon": -1.39612, + "name": "Effiduase" + }, + { + "lat": -26.21197, + "lon": 28.25958, + "name": "Boksburg" + }, + { + "lat": 29.14816, + "lon": 31.12733, + "name": "Būsh" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + } + ], + "question": "Which location is the geographic outlier among: Cape Town, Effiduase, Boksburg, Būsh, Papakura?", + "ground_truth": { + "answer": "Papakura", + "outlier_distance_km": 12054.6, + "second_furthest_km": 6092.8, + "clarity_ratio": 1.98, + "median_distance_km": 5040.4, + "distances_to_centroid": { + "Cape Town": 4023.2, + "Effiduase": 6092.8, + "Boksburg": 2776.8, + "Būsh": 5040.4, + "Papakura": 12054.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cape Town: (-33.93°, 18.42°)", + " Effiduase: (6.85°, -1.40°)", + " Boksburg: (-26.21°, 28.26°)", + " Būsh: (29.15°, 31.13°)", + " Papakura: (-37.06°, 174.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Papakura: 12054.6 km from centroid", + " Effiduase: 6092.8 km from centroid", + " Būsh: 5040.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Papakura", + "FINAL ANSWER: Papakura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.33306, + "lon": 27.85, + "name": "Khowa" + }, + { + "lat": 7.71393, + "lon": 3.91665, + "name": "Fiditi" + }, + { + "lat": 6.17559, + "lon": 45.29866, + "name": "Fadhigaradle" + }, + { + "lat": 9.17031, + "lon": 35.83491, + "name": "Gimbi" + }, + { + "lat": -23.66389, + "lon": -46.53833, + "name": "Santo André" + } + ], + "question": "Which location is the geographic outlier among: Khowa, Fiditi, Fadhigaradle, Gimbi, Santo André?", + "ground_truth": { + "answer": "Santo André", + "outlier_distance_km": 6654.2, + "second_furthest_km": 3818.7, + "clarity_ratio": 1.74, + "median_distance_km": 3161.5, + "distances_to_centroid": { + "Khowa": 3161.5, + "Fiditi": 1880.2, + "Fadhigaradle": 3818.7, + "Gimbi": 3040.5, + "Santo André": 6654.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Khowa: (-31.33°, 27.85°)", + " Fiditi: (7.71°, 3.92°)", + " Fadhigaradle: (6.18°, 45.30°)", + " Gimbi: (9.17°, 35.83°)", + " Santo André: (-23.66°, -46.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santo André: 6654.2 km from centroid", + " Fadhigaradle: 3818.7 km from centroid", + " Khowa: 3161.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santo André", + "FINAL ANSWER: Santo André" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -37.75405, + "lon": 145.14864, + "name": "Templestowe" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + }, + { + "lat": -26.66331, + "lon": 28.59016, + "name": "Balfour" + } + ], + "question": "Which location is the geographic outlier among: Warwick, Caboolture, Templestowe, Cherrybrook, Balfour?", + "ground_truth": { + "answer": "Balfour", + "outlier_distance_km": 9173.6, + "second_furthest_km": 2652.3, + "clarity_ratio": 3.46, + "median_distance_km": 2534.4, + "distances_to_centroid": { + "Warwick": 2534.4, + "Caboolture": 2652.3, + "Templestowe": 1926.9, + "Cherrybrook": 2378.8, + "Balfour": 9173.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warwick: (-28.22°, 152.03°)", + " Caboolture: (-27.08°, 152.95°)", + " Templestowe: (-37.75°, 145.15°)", + " Cherrybrook: (-33.72°, 151.05°)", + " Balfour: (-26.66°, 28.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Balfour: 9173.6 km from centroid", + " Caboolture: 2652.3 km from centroid", + " Warwick: 2534.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Balfour", + "FINAL ANSWER: Balfour" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.58612, + "lon": -48.52335, + "name": "Trindade" + }, + { + "lat": -23.53194, + "lon": -46.44417, + "name": "Itaquera" + }, + { + "lat": -31.6501, + "lon": -63.91165, + "name": "Río Segundo" + }, + { + "lat": -4.82778, + "lon": -42.16861, + "name": "Campo Maior" + }, + { + "lat": 9.03333, + "lon": 38.4, + "name": "Ādīs ‘Alem" + } + ], + "question": "Which location is the geographic outlier among: Trindade, Itaquera, Río Segundo, Campo Maior, Ādīs ‘Alem?", + "ground_truth": { + "answer": "Ādīs ‘Alem", + "outlier_distance_km": 8278.3, + "second_furthest_km": 3634.0, + "clarity_ratio": 2.28, + "median_distance_km": 2111.5, + "distances_to_centroid": { + "Trindade": 2111.5, + "Itaquera": 1695.4, + "Río Segundo": 3634.0, + "Campo Maior": 1604.2, + "Ādīs ‘Alem": 8278.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Trindade: (-27.59°, -48.52°)", + " Itaquera: (-23.53°, -46.44°)", + " Río Segundo: (-31.65°, -63.91°)", + " Campo Maior: (-4.83°, -42.17°)", + " Ādīs ‘Alem: (9.03°, 38.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ādīs ‘Alem: 8278.3 km from centroid", + " Río Segundo: 3634.0 km from centroid", + " Trindade: 2111.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ādīs ‘Alem", + "FINAL ANSWER: Ādīs ‘Alem" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.02148, + "lon": 80.91808, + "name": "Avanigadda" + }, + { + "lat": 32.97944, + "lon": 114.02944, + "name": "Zhumadian" + }, + { + "lat": 9.1756, + "lon": 76.47129, + "name": "Kandalloor" + }, + { + "lat": 37.75266, + "lon": 128.87239, + "name": "Gangneung" + }, + { + "lat": 12.87695, + "lon": 10.45536, + "name": "Nguru" + } + ], + "question": "Which location is the geographic outlier among: Avanigadda, Zhumadian, Kandalloor, Gangneung, Nguru?", + "ground_truth": { + "answer": "Nguru", + "outlier_distance_km": 7613.5, + "second_furthest_km": 4790.5, + "clarity_ratio": 1.59, + "median_distance_km": 3369.5, + "distances_to_centroid": { + "Avanigadda": 651.2, + "Zhumadian": 3369.5, + "Kandalloor": 1525.4, + "Gangneung": 4790.5, + "Nguru": 7613.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Avanigadda: (16.02°, 80.92°)", + " Zhumadian: (32.98°, 114.03°)", + " Kandalloor: (9.18°, 76.47°)", + " Gangneung: (37.75°, 128.87°)", + " Nguru: (12.88°, 10.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nguru: 7613.5 km from centroid", + " Gangneung: 4790.5 km from centroid", + " Zhumadian: 3369.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nguru", + "FINAL ANSWER: Nguru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -29.739, + "lon": 30.949, + "name": "Ntuzuma" + }, + { + "lat": -33.60047, + "lon": 22.19955, + "name": "Oudtshoorn" + }, + { + "lat": -34.18307, + "lon": 22.14605, + "name": "Mossel Bay" + }, + { + "lat": 7.13333, + "lon": 37.95, + "name": "Shonē" + }, + { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + } + ], + "question": "Which location is the geographic outlier among: Ntuzuma, Oudtshoorn, Mossel Bay, Shonē, Manly?", + "ground_truth": { + "answer": "Manly", + "outlier_distance_km": 9217.2, + "second_furthest_km": 3906.7, + "clarity_ratio": 2.36, + "median_distance_km": 3138.3, + "distances_to_centroid": { + "Ntuzuma": 2233.4, + "Oudtshoorn": 3121.6, + "Mossel Bay": 3138.3, + "Shonē": 3906.7, + "Manly": 9217.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ntuzuma: (-29.74°, 30.95°)", + " Oudtshoorn: (-33.60°, 22.20°)", + " Mossel Bay: (-34.18°, 22.15°)", + " Shonē: (7.13°, 37.95°)", + " Manly: (-33.80°, 151.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manly: 9217.2 km from centroid", + " Shonē: 3906.7 km from centroid", + " Mossel Bay: 3138.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manly", + "FINAL ANSWER: Manly" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.80222, + "lon": 117.11167, + "name": "Xiazhen" + }, + { + "lat": 28.74667, + "lon": 77.19348, + "name": "Kamal Pur Majra Burari" + }, + { + "lat": 26.32539, + "lon": 89.44508, + "name": "Koch Bihār" + }, + { + "lat": 36.31409, + "lon": 140.58389, + "name": "Ōarai" + }, + { + "lat": 47.76316, + "lon": -3.3393, + "name": "Lanester" + } + ], + "question": "Which location is the geographic outlier among: Xiazhen, Kamal Pur Majra Burari, Koch Bihār, Ōarai, Lanester?", + "ground_truth": { + "answer": "Lanester", + "outlier_distance_km": 7061.2, + "second_furthest_km": 5029.5, + "clarity_ratio": 1.4, + "median_distance_km": 2991.6, + "distances_to_centroid": { + "Xiazhen": 2991.6, + "Kamal Pur Majra Burari": 943.0, + "Koch Bihār": 1066.4, + "Ōarai": 5029.5, + "Lanester": 7061.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Xiazhen: (34.80°, 117.11°)", + " Kamal Pur Majra Burari: (28.75°, 77.19°)", + " Koch Bihār: (26.33°, 89.45°)", + " Ōarai: (36.31°, 140.58°)", + " Lanester: (47.76°, -3.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lanester: 7061.2 km from centroid", + " Ōarai: 5029.5 km from centroid", + " Xiazhen: 2991.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lanester", + "FINAL ANSWER: Lanester" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.90852, + "lon": -47.94053, + "name": "Park Way" + }, + { + "lat": -23.30528, + "lon": -45.96583, + "name": "Jacareí" + }, + { + "lat": -13.37028, + "lon": -39.07306, + "name": "Valença" + }, + { + "lat": -2.55778, + "lon": -47.495, + "name": "Ipixuna do Pará" + }, + { + "lat": 7.13333, + "lon": 37.95, + "name": "Shonē" + } + ], + "question": "Which location is the geographic outlier among: Park Way, Jacareí, Valença, Ipixuna do Pará, Shonē?", + "ground_truth": { + "answer": "Shonē", + "outlier_distance_km": 7592.1, + "second_furthest_km": 2401.3, + "clarity_ratio": 3.16, + "median_distance_km": 2239.7, + "distances_to_centroid": { + "Park Way": 2219.8, + "Jacareí": 2401.3, + "Valença": 1225.2, + "Ipixuna do Pará": 2239.7, + "Shonē": 7592.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Park Way: (-15.91°, -47.94°)", + " Jacareí: (-23.31°, -45.97°)", + " Valença: (-13.37°, -39.07°)", + " Ipixuna do Pará: (-2.56°, -47.49°)", + " Shonē: (7.13°, 37.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shonē: 7592.1 km from centroid", + " Jacareí: 2401.3 km from centroid", + " Ipixuna do Pará: 2239.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shonē", + "FINAL ANSWER: Shonē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.223, + "lon": -111.97383, + "name": "Ogden" + }, + { + "lat": 38.04937, + "lon": -122.15858, + "name": "Benicia" + }, + { + "lat": 35.74788, + "lon": -95.36969, + "name": "Muskogee" + }, + { + "lat": 41.23756, + "lon": -80.81842, + "name": "Warren" + }, + { + "lat": 10.65, + "lon": 36.21667, + "name": "Dibate" + } + ], + "question": "Which location is the geographic outlier among: Ogden, Benicia, Muskogee, Warren, Dibate?", + "ground_truth": { + "answer": "Dibate", + "outlier_distance_km": 11244.3, + "second_furthest_km": 4259.2, + "clarity_ratio": 2.64, + "median_distance_km": 3372.1, + "distances_to_centroid": { + "Ogden": 3372.1, + "Benicia": 4259.2, + "Muskogee": 1896.4, + "Warren": 1021.3, + "Dibate": 11244.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ogden: (41.22°, -111.97°)", + " Benicia: (38.05°, -122.16°)", + " Muskogee: (35.75°, -95.37°)", + " Warren: (41.24°, -80.82°)", + " Dibate: (10.65°, 36.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dibate: 11244.3 km from centroid", + " Benicia: 4259.2 km from centroid", + " Ogden: 3372.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dibate", + "FINAL ANSWER: Dibate" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.57565, + "lon": 22.44391, + "name": "Dysselsdorp" + }, + { + "lat": -30.30225, + "lon": 27.08395, + "name": "Zastron" + }, + { + "lat": -24.88333, + "lon": 28.28333, + "name": "Bela Bela" + }, + { + "lat": 30.4428, + "lon": 30.96975, + "name": "Sirs al Layyānah" + }, + { + "lat": 41.65726, + "lon": -87.68005, + "name": "Blue Island" + } + ], + "question": "Which location is the geographic outlier among: Dysselsdorp, Zastron, Bela Bela, Sirs al Layyānah, Blue Island?", + "ground_truth": { + "answer": "Blue Island", + "outlier_distance_km": 10411.5, + "second_furthest_km": 4708.4, + "clarity_ratio": 2.21, + "median_distance_km": 3858.1, + "distances_to_centroid": { + "Dysselsdorp": 3858.1, + "Zastron": 3843.0, + "Bela Bela": 3517.9, + "Sirs al Layyānah": 4708.4, + "Blue Island": 10411.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dysselsdorp: (-33.58°, 22.44°)", + " Zastron: (-30.30°, 27.08°)", + " Bela Bela: (-24.88°, 28.28°)", + " Sirs al Layyānah: (30.44°, 30.97°)", + " Blue Island: (41.66°, -87.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blue Island: 10411.5 km from centroid", + " Sirs al Layyānah: 4708.4 km from centroid", + " Dysselsdorp: 3858.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blue Island", + "FINAL ANSWER: Blue Island" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.84852, + "lon": 151.25775, + "name": "Gladstone" + }, + { + "lat": -34.78254, + "lon": 138.61077, + "name": "Parafield Gardens" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + }, + { + "lat": -4.95611, + "lon": -37.13694, + "name": "Areia Branca" + } + ], + "question": "Which location is the geographic outlier among: Gladstone, Parafield Gardens, Southport, New Plymouth, Areia Branca?", + "ground_truth": { + "answer": "Areia Branca", + "outlier_distance_km": 15509.9, + "second_furthest_km": 5528.9, + "clarity_ratio": 2.81, + "median_distance_km": 3690.9, + "distances_to_centroid": { + "Gladstone": 3547.6, + "Parafield Gardens": 2360.7, + "Southport": 3690.9, + "New Plymouth": 5528.9, + "Areia Branca": 15509.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gladstone: (-23.85°, 151.26°)", + " Parafield Gardens: (-34.78°, 138.61°)", + " Southport: (-27.97°, 153.40°)", + " New Plymouth: (-39.07°, 174.08°)", + " Areia Branca: (-4.96°, -37.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Areia Branca: 15509.9 km from centroid", + " New Plymouth: 5528.9 km from centroid", + " Southport: 3690.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Areia Branca", + "FINAL ANSWER: Areia Branca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.45, + "lon": 3.33333, + "name": "Aliayabiagba" + }, + { + "lat": 30.56412, + "lon": 31.93386, + "name": "Al Qaşşāşīn" + }, + { + "lat": 7.06205, + "lon": 38.47635, + "name": "Awasa" + }, + { + "lat": 7.45, + "lon": 37.63333, + "name": "Gīmbīcho" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + } + ], + "question": "Which location is the geographic outlier among: Aliayabiagba, Al Qaşşāşīn, Awasa, Gīmbīcho, Australind?", + "ground_truth": { + "answer": "Australind", + "outlier_distance_km": 8421.6, + "second_furthest_km": 4670.5, + "clarity_ratio": 1.8, + "median_distance_km": 3310.7, + "distances_to_centroid": { + "Aliayabiagba": 4670.5, + "Al Qaşşāşīn": 3310.7, + "Awasa": 857.0, + "Gīmbīcho": 959.5, + "Australind": 8421.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aliayabiagba: (6.45°, 3.33°)", + " Al Qaşşāşīn: (30.56°, 31.93°)", + " Awasa: (7.06°, 38.48°)", + " Gīmbīcho: (7.45°, 37.63°)", + " Australind: (-33.28°, 115.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Australind: 8421.6 km from centroid", + " Aliayabiagba: 4670.5 km from centroid", + " Al Qaşşāşīn: 3310.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Australind", + "FINAL ANSWER: Australind" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + }, + { + "lat": -37.0393, + "lon": 174.92815, + "name": "Takanini" + }, + { + "lat": 51.15, + "lon": 7.0, + "name": "Ohligs" + } + ], + "question": "Which location is the geographic outlier among: Footscray, Balwyn North, Wantirna South, Takanini, Ohligs?", + "ground_truth": { + "answer": "Ohligs", + "outlier_distance_km": 13546.1, + "second_furthest_km": 5312.1, + "clarity_ratio": 2.55, + "median_distance_km": 2903.0, + "distances_to_centroid": { + "Footscray": 2875.4, + "Balwyn North": 2888.2, + "Wantirna South": 2903.0, + "Takanini": 5312.1, + "Ohligs": 13546.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Footscray: (-37.80°, 144.90°)", + " Balwyn North: (-37.79°, 145.09°)", + " Wantirna South: (-37.88°, 145.22°)", + " Takanini: (-37.04°, 174.93°)", + " Ohligs: (51.15°, 7.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ohligs: 13546.1 km from centroid", + " Takanini: 5312.1 km from centroid", + " Wantirna South: 2903.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ohligs", + "FINAL ANSWER: Ohligs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.64148, + "lon": 30.85012, + "name": "Dayr Mawās" + }, + { + "lat": 6.72556, + "lon": 11.25652, + "name": "Gembu" + }, + { + "lat": 27.04514, + "lon": 31.31845, + "name": "Abū Tīj" + }, + { + "lat": 7.06273, + "lon": -1.4001, + "name": "Mampong" + }, + { + "lat": 21.3403, + "lon": 78.01258, + "name": "Morsi" + } + ], + "question": "Which location is the geographic outlier among: Dayr Mawās, Gembu, Abū Tīj, Mampong, Morsi?", + "ground_truth": { + "answer": "Morsi", + "outlier_distance_km": 5022.3, + "second_furthest_km": 3610.9, + "clarity_ratio": 1.39, + "median_distance_km": 2386.0, + "distances_to_centroid": { + "Dayr Mawās": 1079.6, + "Gembu": 2386.0, + "Abū Tīj": 1018.8, + "Mampong": 3610.9, + "Morsi": 5022.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dayr Mawās: (27.64°, 30.85°)", + " Gembu: (6.73°, 11.26°)", + " Abū Tīj: (27.05°, 31.32°)", + " Mampong: (7.06°, -1.40°)", + " Morsi: (21.34°, 78.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morsi: 5022.3 km from centroid", + " Mampong: 3610.9 km from centroid", + " Gembu: 2386.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morsi", + "FINAL ANSWER: Morsi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.98169, + "lon": 36.58642, + "name": "Mai" + }, + { + "lat": -26.98023, + "lon": 26.67272, + "name": "Orkney" + }, + { + "lat": 31.01887, + "lon": 33.0098, + "name": "Bi’r al ‘Abd" + }, + { + "lat": 31.09311, + "lon": 30.31418, + "name": "Abū Ḩummuş" + }, + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + } + ], + "question": "Which location is the geographic outlier among: Mai, Orkney, Bi’r al ‘Abd, Abū Ḩummuş, Northcote?", + "ground_truth": { + "answer": "Northcote", + "outlier_distance_km": 10018.3, + "second_furthest_km": 4351.2, + "clarity_ratio": 2.3, + "median_distance_km": 4185.5, + "distances_to_centroid": { + "Mai": 1971.5, + "Orkney": 4151.5, + "Bi’r al ‘Abd": 4185.5, + "Abū Ḩummuş": 4351.2, + "Northcote": 10018.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mai: (-0.98°, 36.59°)", + " Orkney: (-26.98°, 26.67°)", + " Bi’r al ‘Abd: (31.02°, 33.01°)", + " Abū Ḩummuş: (31.09°, 30.31°)", + " Northcote: (-37.77°, 145.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Northcote: 10018.3 km from centroid", + " Abū Ḩummuş: 4351.2 km from centroid", + " Bi’r al ‘Abd: 4185.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Northcote", + "FINAL ANSWER: Northcote" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.90778, + "lon": -48.66194, + "name": "Itajaí" + }, + { + "lat": 5.61161, + "lon": -75.45624, + "name": "Aguadas" + }, + { + "lat": 9.14334, + "lon": -74.22384, + "name": "Guamal" + }, + { + "lat": -34.50316, + "lon": -58.70596, + "name": "Los Polvorines" + }, + { + "lat": 56.37328, + "lon": 38.58321, + "name": "Strunino" + } + ], + "question": "Which location is the geographic outlier among: Itajaí, Aguadas, Guamal, Los Polvorines, Strunino?", + "ground_truth": { + "answer": "Strunino", + "outlier_distance_km": 9352.6, + "second_furthest_km": 4345.2, + "clarity_ratio": 2.15, + "median_distance_km": 3547.0, + "distances_to_centroid": { + "Itajaí": 3252.1, + "Aguadas": 3547.0, + "Guamal": 3469.9, + "Los Polvorines": 4345.2, + "Strunino": 9352.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itajaí: (-26.91°, -48.66°)", + " Aguadas: (5.61°, -75.46°)", + " Guamal: (9.14°, -74.22°)", + " Los Polvorines: (-34.50°, -58.71°)", + " Strunino: (56.37°, 38.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Strunino: 9352.6 km from centroid", + " Los Polvorines: 4345.2 km from centroid", + " Aguadas: 3547.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Strunino", + "FINAL ANSWER: Strunino" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.93333, + "lon": 6.95, + "name": "Köln" + }, + { + "lat": 52.41667, + "lon": 12.55, + "name": "Brandenburg an der Havel" + }, + { + "lat": 59.76831, + "lon": 60.0062, + "name": "Karpinsk" + }, + { + "lat": 37.64442, + "lon": 14.86685, + "name": "Biancavilla" + }, + { + "lat": 12.91823, + "lon": 80.08245, + "name": "Perunkalattu" + } + ], + "question": "Which location is the geographic outlier among: Köln, Brandenburg an der Havel, Karpinsk, Biancavilla, Perunkalattu?", + "ground_truth": { + "answer": "Perunkalattu", + "outlier_distance_km": 5447.1, + "second_furthest_km": 2546.5, + "clarity_ratio": 2.14, + "median_distance_km": 2294.9, + "distances_to_centroid": { + "Köln": 2294.9, + "Brandenburg an der Havel": 1979.2, + "Karpinsk": 2546.5, + "Biancavilla": 1787.5, + "Perunkalattu": 5447.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Köln: (50.93°, 6.95°)", + " Brandenburg an der Havel: (52.42°, 12.55°)", + " Karpinsk: (59.77°, 60.01°)", + " Biancavilla: (37.64°, 14.87°)", + " Perunkalattu: (12.92°, 80.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perunkalattu: 5447.1 km from centroid", + " Karpinsk: 2546.5 km from centroid", + " Köln: 2294.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perunkalattu", + "FINAL ANSWER: Perunkalattu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.56086, + "lon": -46.64758, + "name": "Bela Vista" + }, + { + "lat": -6.22944, + "lon": -36.02278, + "name": "Santa Cruz" + }, + { + "lat": -6.72917, + "lon": -38.44889, + "name": "São João do Rio do Peixe" + }, + { + "lat": 3.3223, + "lon": -76.2348, + "name": "Florida" + }, + { + "lat": 50.93893, + "lon": 6.95752, + "name": "Altstadt Nord" + } + ], + "question": "Which location is the geographic outlier among: Bela Vista, Santa Cruz, São João do Rio do Peixe, Florida, Altstadt Nord?", + "ground_truth": { + "answer": "Altstadt Nord", + "outlier_distance_km": 6726.7, + "second_furthest_km": 4234.9, + "clarity_ratio": 1.59, + "median_distance_km": 3154.2, + "distances_to_centroid": { + "Bela Vista": 3154.2, + "Santa Cruz": 1111.0, + "São João do Rio do Peixe": 1143.5, + "Florida": 4234.9, + "Altstadt Nord": 6726.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bela Vista: (-23.56°, -46.65°)", + " Santa Cruz: (-6.23°, -36.02°)", + " São João do Rio do Peixe: (-6.73°, -38.45°)", + " Florida: (3.32°, -76.23°)", + " Altstadt Nord: (50.94°, 6.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Altstadt Nord: 6726.7 km from centroid", + " Florida: 4234.9 km from centroid", + " Bela Vista: 3154.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Altstadt Nord", + "FINAL ANSWER: Altstadt Nord" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.83241, + "lon": 9.31641, + "name": "Waiblingen" + }, + { + "lat": 48.60974, + "lon": 42.8569, + "name": "Surovikino" + }, + { + "lat": 45.74123, + "lon": 3.19643, + "name": "Cournon-d'Auvergne" + }, + { + "lat": 59.88333, + "lon": 29.9, + "name": "Peterhof" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + } + ], + "question": "Which location is the geographic outlier among: Waiblingen, Surovikino, Cournon-d'Auvergne, Peterhof, Truganina?", + "ground_truth": { + "answer": "Truganina", + "outlier_distance_km": 12875.2, + "second_furthest_km": 3885.1, + "clarity_ratio": 3.31, + "median_distance_km": 3498.2, + "distances_to_centroid": { + "Waiblingen": 3498.2, + "Surovikino": 1749.9, + "Cournon-d'Auvergne": 3885.1, + "Peterhof": 3208.8, + "Truganina": 12875.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waiblingen: (48.83°, 9.32°)", + " Surovikino: (48.61°, 42.86°)", + " Cournon-d'Auvergne: (45.74°, 3.20°)", + " Peterhof: (59.88°, 29.90°)", + " Truganina: (-37.82°, 144.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Truganina: 12875.2 km from centroid", + " Cournon-d'Auvergne: 3885.1 km from centroid", + " Waiblingen: 3498.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Truganina", + "FINAL ANSWER: Truganina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.32485, + "lon": 8.11368, + "name": "Abakaliki" + }, + { + "lat": 6.11982, + "lon": 1.19012, + "name": "Aflao" + }, + { + "lat": 29.81667, + "lon": 31.05, + "name": "6th of October City" + }, + { + "lat": 7.73375, + "lon": 8.52139, + "name": "Makurdi" + }, + { + "lat": 25.48694, + "lon": 119.19834, + "name": "Jiangkou" + } + ], + "question": "Which location is the geographic outlier among: Abakaliki, Aflao, 6th of October City, Makurdi, Jiangkou?", + "ground_truth": { + "answer": "Jiangkou", + "outlier_distance_km": 8859.8, + "second_furthest_km": 3676.2, + "clarity_ratio": 2.41, + "median_distance_km": 2948.3, + "distances_to_centroid": { + "Abakaliki": 2948.3, + "Aflao": 3676.2, + "6th of October City": 1657.7, + "Makurdi": 2852.1, + "Jiangkou": 8859.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abakaliki: (6.32°, 8.11°)", + " Aflao: (6.12°, 1.19°)", + " 6th of October City: (29.82°, 31.05°)", + " Makurdi: (7.73°, 8.52°)", + " Jiangkou: (25.49°, 119.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jiangkou: 8859.8 km from centroid", + " Aflao: 3676.2 km from centroid", + " Abakaliki: 2948.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jiangkou", + "FINAL ANSWER: Jiangkou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.58654, + "lon": -122.39168, + "name": "Redding" + }, + { + "lat": 33.6803, + "lon": -116.17389, + "name": "Coachella" + }, + { + "lat": 51.05011, + "lon": -114.08529, + "name": "Calgary" + }, + { + "lat": 35.97987, + "lon": -78.50972, + "name": "Wake Forest" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + } + ], + "question": "Which location is the geographic outlier among: Redding, Coachella, Calgary, Wake Forest, Australind?", + "ground_truth": { + "answer": "Australind", + "outlier_distance_km": 19153.8, + "second_furthest_km": 5659.1, + "clarity_ratio": 3.38, + "median_distance_km": 5152.7, + "distances_to_centroid": { + "Redding": 5659.1, + "Coachella": 5152.7, + "Calgary": 5130.8, + "Wake Forest": 1866.9, + "Australind": 19153.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Redding: (40.59°, -122.39°)", + " Coachella: (33.68°, -116.17°)", + " Calgary: (51.05°, -114.09°)", + " Wake Forest: (35.98°, -78.51°)", + " Australind: (-33.28°, 115.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Australind: 19153.8 km from centroid", + " Redding: 5659.1 km from centroid", + " Coachella: 5152.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Australind", + "FINAL ANSWER: Australind" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.41, + "lon": -39.03056, + "name": "Paracuru" + }, + { + "lat": -7.71361, + "lon": -66.97639, + "name": "Pauini" + }, + { + "lat": 4.93722, + "lon": -75.73778, + "name": "Marsella" + }, + { + "lat": -21.72028, + "lon": -51.01889, + "name": "Lucélia" + }, + { + "lat": 30.19327, + "lon": 31.13703, + "name": "Al Qanāţir al Khayrīyah" + } + ], + "question": "Which location is the geographic outlier among: Paracuru, Pauini, Marsella, Lucélia, Al Qanāţir al Khayrīyah?", + "ground_truth": { + "answer": "Al Qanāţir al Khayrīyah", + "outlier_distance_km": 8207.4, + "second_furthest_km": 3963.6, + "clarity_ratio": 2.07, + "median_distance_km": 3091.4, + "distances_to_centroid": { + "Paracuru": 453.5, + "Pauini": 3091.4, + "Marsella": 3963.6, + "Lucélia": 2725.4, + "Al Qanāţir al Khayrīyah": 8207.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paracuru: (-3.41°, -39.03°)", + " Pauini: (-7.71°, -66.98°)", + " Marsella: (4.94°, -75.74°)", + " Lucélia: (-21.72°, -51.02°)", + " Al Qanāţir al Khayrīyah: (30.19°, 31.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Qanāţir al Khayrīyah: 8207.4 km from centroid", + " Marsella: 3963.6 km from centroid", + " Pauini: 3091.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Qanāţir al Khayrīyah", + "FINAL ANSWER: Al Qanāţir al Khayrīyah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.2471, + "lon": 10.561, + "name": "Kari" + }, + { + "lat": -0.90711, + "lon": 34.52895, + "name": "Awendo" + }, + { + "lat": 13.95, + "lon": 40.66667, + "name": "Arerti" + }, + { + "lat": 12.00012, + "lon": 8.51672, + "name": "Kano" + }, + { + "lat": -7.95889, + "lon": -79.23917, + "name": "Santiago de Cao" + } + ], + "question": "Which location is the geographic outlier among: Kari, Awendo, Arerti, Kano, Santiago de Cao?", + "ground_truth": { + "answer": "Santiago de Cao", + "outlier_distance_km": 9245.7, + "second_furthest_km": 4221.9, + "clarity_ratio": 2.19, + "median_distance_km": 3575.6, + "distances_to_centroid": { + "Kari": 1036.7, + "Awendo": 3575.6, + "Arerti": 4221.9, + "Kano": 928.5, + "Santiago de Cao": 9245.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kari: (11.25°, 10.56°)", + " Awendo: (-0.91°, 34.53°)", + " Arerti: (13.95°, 40.67°)", + " Kano: (12.00°, 8.52°)", + " Santiago de Cao: (-7.96°, -79.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santiago de Cao: 9245.7 km from centroid", + " Arerti: 4221.9 km from centroid", + " Awendo: 3575.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santiago de Cao", + "FINAL ANSWER: Santiago de Cao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.04943, + "lon": -92.90798, + "name": "Marshalltown" + }, + { + "lat": 44.64969, + "lon": -93.24272, + "name": "Lakeville" + }, + { + "lat": 30.57881, + "lon": -97.85307, + "name": "Leander" + }, + { + "lat": 31.76072, + "lon": -93.08627, + "name": "Natchitoches" + }, + { + "lat": -26.96083, + "lon": -50.42694, + "name": "Santa Cecília" + } + ], + "question": "Which location is the geographic outlier among: Marshalltown, Lakeville, Leander, Natchitoches, Santa Cecília?", + "ground_truth": { + "answer": "Santa Cecília", + "outlier_distance_km": 6841.1, + "second_furthest_km": 2356.2, + "clarity_ratio": 2.9, + "median_distance_km": 2076.1, + "distances_to_centroid": { + "Marshalltown": 2076.1, + "Lakeville": 2356.2, + "Leander": 1396.3, + "Natchitoches": 1104.0, + "Santa Cecília": 6841.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marshalltown: (42.05°, -92.91°)", + " Lakeville: (44.65°, -93.24°)", + " Leander: (30.58°, -97.85°)", + " Natchitoches: (31.76°, -93.09°)", + " Santa Cecília: (-26.96°, -50.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Cecília: 6841.1 km from centroid", + " Lakeville: 2356.2 km from centroid", + " Marshalltown: 2076.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Cecília", + "FINAL ANSWER: Santa Cecília" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.80639, + "lon": 145.03086, + "name": "Kew" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -21.04278, + "lon": -49.37722, + "name": "Potirendaba" + } + ], + "question": "Which location is the geographic outlier among: Kew, Morayfield, Mosman, Engadine, Potirendaba?", + "ground_truth": { + "answer": "Potirendaba", + "outlier_distance_km": 13853.4, + "second_furthest_km": 4157.7, + "clarity_ratio": 3.33, + "median_distance_km": 3849.4, + "distances_to_centroid": { + "Kew": 3276.4, + "Morayfield": 4157.7, + "Mosman": 3849.4, + "Engadine": 3825.8, + "Potirendaba": 13853.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kew: (-37.81°, 145.03°)", + " Morayfield: (-27.11°, 152.95°)", + " Mosman: (-33.84°, 151.24°)", + " Engadine: (-34.07°, 151.01°)", + " Potirendaba: (-21.04°, -49.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Potirendaba: 13853.4 km from centroid", + " Morayfield: 4157.7 km from centroid", + " Mosman: 3849.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Potirendaba", + "FINAL ANSWER: Potirendaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.05, + "lon": 4.76667, + "name": "Oyan" + }, + { + "lat": -31.52356, + "lon": 27.6952, + "name": "Cala" + }, + { + "lat": 26.08657, + "lon": 32.42265, + "name": "Al Waqf" + }, + { + "lat": -24.5878, + "lon": 31.09467, + "name": "Acornhoek" + }, + { + "lat": 50.0088, + "lon": -119.39672, + "name": "Lake Country" + } + ], + "question": "Which location is the geographic outlier among: Oyan, Cala, Al Waqf, Acornhoek, Lake Country?", + "ground_truth": { + "answer": "Lake Country", + "outlier_distance_km": 11242.0, + "second_furthest_km": 5369.5, + "clarity_ratio": 2.09, + "median_distance_km": 5124.9, + "distances_to_centroid": { + "Oyan": 1078.1, + "Cala": 5369.5, + "Al Waqf": 4548.3, + "Acornhoek": 5124.9, + "Lake Country": 11242.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oyan: (8.05°, 4.77°)", + " Cala: (-31.52°, 27.70°)", + " Al Waqf: (26.09°, 32.42°)", + " Acornhoek: (-24.59°, 31.09°)", + " Lake Country: (50.01°, -119.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lake Country: 11242.0 km from centroid", + " Cala: 5369.5 km from centroid", + " Acornhoek: 5124.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lake Country", + "FINAL ANSWER: Lake Country" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -27.20338, + "lon": 152.95923, + "name": "Narangba" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + }, + { + "lat": -1.17641, + "lon": 36.7564, + "name": "Karuri" + } + ], + "question": "Which location is the geographic outlier among: Maroochydore, Saint Kilda, Narangba, Mornington, Karuri?", + "ground_truth": { + "answer": "Karuri", + "outlier_distance_km": 9930.9, + "second_furthest_km": 2637.3, + "clarity_ratio": 3.77, + "median_distance_km": 2618.9, + "distances_to_centroid": { + "Maroochydore": 2637.3, + "Saint Kilda": 2158.3, + "Narangba": 2618.9, + "Mornington": 2183.1, + "Karuri": 9930.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maroochydore: (-26.66°, 153.10°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Narangba: (-27.20°, 152.96°)", + " Mornington: (-38.22°, 145.04°)", + " Karuri: (-1.18°, 36.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karuri: 9930.9 km from centroid", + " Maroochydore: 2637.3 km from centroid", + " Narangba: 2618.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karuri", + "FINAL ANSWER: Karuri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.19152, + "lon": 40.01675, + "name": "Batī" + }, + { + "lat": -26.49155, + "lon": 29.22878, + "name": "Trichardt" + }, + { + "lat": 7.1962, + "lon": 5.58681, + "name": "Owo" + }, + { + "lat": 11.91667, + "lon": 37.7, + "name": "Werota" + }, + { + "lat": 19.28786, + "lon": -99.65324, + "name": "Toluca" + } + ], + "question": "Which location is the geographic outlier among: Batī, Trichardt, Owo, Werota, Toluca?", + "ground_truth": { + "answer": "Toluca", + "outlier_distance_km": 11113.2, + "second_furthest_km": 4493.9, + "clarity_ratio": 2.47, + "median_distance_km": 4184.1, + "distances_to_centroid": { + "Batī": 4184.1, + "Trichardt": 4493.9, + "Owo": 439.2, + "Werota": 3945.3, + "Toluca": 11113.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Batī: (11.19°, 40.02°)", + " Trichardt: (-26.49°, 29.23°)", + " Owo: (7.20°, 5.59°)", + " Werota: (11.92°, 37.70°)", + " Toluca: (19.29°, -99.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Toluca: 11113.2 km from centroid", + " Trichardt: 4493.9 km from centroid", + " Batī: 4184.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Toluca", + "FINAL ANSWER: Toluca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.96375, + "lon": 1.3511, + "name": "Felixstowe" + }, + { + "lat": 63.19309, + "lon": 75.43728, + "name": "Noyabrsk" + }, + { + "lat": 50.4973, + "lon": 12.13782, + "name": "Plauen" + }, + { + "lat": 55.54004, + "lon": 89.20062, + "name": "Sharypovo" + }, + { + "lat": -12.05354, + "lon": -77.09802, + "name": "Carmen De La Legua Reynoso" + } + ], + "question": "Which location is the geographic outlier among: Felixstowe, Noyabrsk, Plauen, Sharypovo, Carmen De La Legua Reynoso?", + "ground_truth": { + "answer": "Carmen De La Legua Reynoso", + "outlier_distance_km": 11498.6, + "second_furthest_km": 5058.5, + "clarity_ratio": 2.27, + "median_distance_km": 4237.3, + "distances_to_centroid": { + "Felixstowe": 1813.6, + "Noyabrsk": 4237.3, + "Plauen": 1145.4, + "Sharypovo": 5058.5, + "Carmen De La Legua Reynoso": 11498.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Felixstowe: (51.96°, 1.35°)", + " Noyabrsk: (63.19°, 75.44°)", + " Plauen: (50.50°, 12.14°)", + " Sharypovo: (55.54°, 89.20°)", + " Carmen De La Legua Reynoso: (-12.05°, -77.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carmen De La Legua Reynoso: 11498.6 km from centroid", + " Sharypovo: 5058.5 km from centroid", + " Noyabrsk: 4237.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carmen De La Legua Reynoso", + "FINAL ANSWER: Carmen De La Legua Reynoso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.60528, + "lon": 18.34717, + "name": "Reda" + }, + { + "lat": 49.71443, + "lon": 7.30776, + "name": "Idar-Oberstein" + }, + { + "lat": 51.36973, + "lon": 10.87011, + "name": "Sondershausen" + }, + { + "lat": 40.49631, + "lon": -3.71957, + "name": "Mirasierra" + }, + { + "lat": -0.52731, + "lon": 34.45714, + "name": "Homa Bay" + } + ], + "question": "Which location is the geographic outlier among: Reda, Idar-Oberstein, Sondershausen, Mirasierra, Homa Bay?", + "ground_truth": { + "answer": "Homa Bay", + "outlier_distance_km": 4902.0, + "second_furthest_km": 1759.3, + "clarity_ratio": 2.79, + "median_distance_km": 1472.2, + "distances_to_centroid": { + "Reda": 1759.3, + "Idar-Oberstein": 1272.8, + "Sondershausen": 1375.5, + "Mirasierra": 1472.2, + "Homa Bay": 4902.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reda: (54.61°, 18.35°)", + " Idar-Oberstein: (49.71°, 7.31°)", + " Sondershausen: (51.37°, 10.87°)", + " Mirasierra: (40.50°, -3.72°)", + " Homa Bay: (-0.53°, 34.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Homa Bay: 4902.0 km from centroid", + " Reda: 1759.3 km from centroid", + " Mirasierra: 1472.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Homa Bay", + "FINAL ANSWER: Homa Bay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.38121, + "lon": 139.39651, + "name": "Ebina" + }, + { + "lat": 31.08434, + "lon": 108.08664, + "name": "Nanya" + }, + { + "lat": 26.80229, + "lon": 84.50311, + "name": "Bettiah" + }, + { + "lat": 16.83636, + "lon": 82.02871, + "name": "Rāmachandrapuram" + }, + { + "lat": 40.65899, + "lon": -74.34737, + "name": "Westfield" + } + ], + "question": "Which location is the geographic outlier among: Ebina, Nanya, Bettiah, Rāmachandrapuram, Westfield?", + "ground_truth": { + "answer": "Westfield", + "outlier_distance_km": 11235.8, + "second_furthest_km": 6561.0, + "clarity_ratio": 1.71, + "median_distance_km": 3822.5, + "distances_to_centroid": { + "Ebina": 6561.0, + "Nanya": 3822.5, + "Bettiah": 1660.1, + "Rāmachandrapuram": 2059.7, + "Westfield": 11235.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ebina: (35.38°, 139.40°)", + " Nanya: (31.08°, 108.09°)", + " Bettiah: (26.80°, 84.50°)", + " Rāmachandrapuram: (16.84°, 82.03°)", + " Westfield: (40.66°, -74.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Westfield: 11235.8 km from centroid", + " Ebina: 6561.0 km from centroid", + " Nanya: 3822.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Westfield", + "FINAL ANSWER: Westfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.06667, + "lon": 135.98333, + "name": "Moriyama" + }, + { + "lat": 39.23417, + "lon": 106.34389, + "name": "Shitanjing" + }, + { + "lat": 29.29524, + "lon": 108.16132, + "name": "Hanjia" + }, + { + "lat": 25.85091, + "lon": 84.3778, + "name": "Reoti" + }, + { + "lat": -9.52614, + "lon": -77.52869, + "name": "Huaraz" + } + ], + "question": "Which location is the geographic outlier among: Moriyama, Shitanjing, Hanjia, Reoti, Huaraz?", + "ground_truth": { + "answer": "Huaraz", + "outlier_distance_km": 16356.5, + "second_furthest_km": 6256.8, + "clarity_ratio": 2.61, + "median_distance_km": 3681.0, + "distances_to_centroid": { + "Moriyama": 6256.8, + "Shitanjing": 3681.0, + "Hanjia": 3679.5, + "Reoti": 1317.8, + "Huaraz": 16356.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Moriyama: (35.07°, 135.98°)", + " Shitanjing: (39.23°, 106.34°)", + " Hanjia: (29.30°, 108.16°)", + " Reoti: (25.85°, 84.38°)", + " Huaraz: (-9.53°, -77.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huaraz: 16356.5 km from centroid", + " Moriyama: 6256.8 km from centroid", + " Shitanjing: 3681.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huaraz", + "FINAL ANSWER: Huaraz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": -37.0393, + "lon": 174.92815, + "name": "Takanini" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": -6.35944, + "lon": -39.29861, + "name": "Iguatu" + } + ], + "question": "Which location is the geographic outlier among: Forest Lake, Takanini, Melbourne, Dunedin, Iguatu?", + "ground_truth": { + "answer": "Iguatu", + "outlier_distance_km": 15358.9, + "second_furthest_km": 4968.4, + "clarity_ratio": 3.09, + "median_distance_km": 4552.4, + "distances_to_centroid": { + "Forest Lake": 3129.6, + "Takanini": 4968.4, + "Melbourne": 2336.3, + "Dunedin": 4552.4, + "Iguatu": 15358.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Forest Lake: (-27.63°, 152.97°)", + " Takanini: (-37.04°, 174.93°)", + " Melbourne: (-37.81°, 144.96°)", + " Dunedin: (-45.87°, 170.50°)", + " Iguatu: (-6.36°, -39.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Iguatu: 15358.9 km from centroid", + " Takanini: 4968.4 km from centroid", + " Dunedin: 4552.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Iguatu", + "FINAL ANSWER: Iguatu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.22542, + "lon": -0.64889, + "name": "Yegyi" + }, + { + "lat": 7.15181, + "lon": 0.47362, + "name": "Hohoe" + }, + { + "lat": 31.07287, + "lon": 31.49503, + "name": "Maḩallat Damanah" + }, + { + "lat": 7.06667, + "lon": 37.7, + "name": "Āreka" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + } + ], + "question": "Which location is the geographic outlier among: Yegyi, Hohoe, Maḩallat Damanah, Āreka, Saint Ives?", + "ground_truth": { + "answer": "Saint Ives", + "outlier_distance_km": 11832.9, + "second_furthest_km": 4960.7, + "clarity_ratio": 2.39, + "median_distance_km": 4832.4, + "distances_to_centroid": { + "Yegyi": 4960.7, + "Hohoe": 4832.4, + "Maḩallat Damanah": 3288.7, + "Āreka": 781.8, + "Saint Ives": 11832.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yegyi: (8.23°, -0.65°)", + " Hohoe: (7.15°, 0.47°)", + " Maḩallat Damanah: (31.07°, 31.50°)", + " Āreka: (7.07°, 37.70°)", + " Saint Ives: (-33.73°, 151.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Ives: 11832.9 km from centroid", + " Yegyi: 4960.7 km from centroid", + " Hohoe: 4832.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Ives", + "FINAL ANSWER: Saint Ives" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.17559, + "lon": 45.29866, + "name": "Fadhigaradle" + }, + { + "lat": 1.09667, + "lon": 36.69806, + "name": "Maralal" + }, + { + "lat": -26.31905, + "lon": 27.6486, + "name": "Westonaria" + }, + { + "lat": -25.9957, + "lon": 28.1971, + "name": "Ivory Park" + }, + { + "lat": 20.30734, + "lon": -89.41809, + "name": "Oxkutzkab" + } + ], + "question": "Which location is the geographic outlier among: Fadhigaradle, Maralal, Westonaria, Ivory Park, Oxkutzkab?", + "ground_truth": { + "answer": "Oxkutzkab", + "outlier_distance_km": 11146.0, + "second_furthest_km": 4142.5, + "clarity_ratio": 2.69, + "median_distance_km": 3074.9, + "distances_to_centroid": { + "Fadhigaradle": 4142.5, + "Maralal": 3074.9, + "Westonaria": 3048.3, + "Ivory Park": 3058.8, + "Oxkutzkab": 11146.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fadhigaradle: (6.18°, 45.30°)", + " Maralal: (1.10°, 36.70°)", + " Westonaria: (-26.32°, 27.65°)", + " Ivory Park: (-26.00°, 28.20°)", + " Oxkutzkab: (20.31°, -89.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oxkutzkab: 11146.0 km from centroid", + " Fadhigaradle: 4142.5 km from centroid", + " Maralal: 3074.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oxkutzkab", + "FINAL ANSWER: Oxkutzkab" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.456, + "lon": 36.35302, + "name": "Bedelē" + }, + { + "lat": 27.20583, + "lon": 31.19639, + "name": "An Nāşirīyah" + }, + { + "lat": 29.4075, + "lon": 31.2525, + "name": "Aţfīḩ" + }, + { + "lat": 9.8, + "lon": 38.73333, + "name": "Fichē" + }, + { + "lat": 4.86242, + "lon": -74.90977, + "name": "Lérida" + } + ], + "question": "Which location is the geographic outlier among: Bedelē, An Nāşirīyah, Aţfīḩ, Fichē, Lérida?", + "ground_truth": { + "answer": "Lérida", + "outlier_distance_km": 9585.7, + "second_furthest_km": 2919.3, + "clarity_ratio": 3.28, + "median_distance_km": 2717.5, + "distances_to_centroid": { + "Bedelē": 2717.5, + "An Nāşirīyah": 2296.3, + "Aţfīḩ": 2429.3, + "Fichē": 2919.3, + "Lérida": 9585.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bedelē: (8.46°, 36.35°)", + " An Nāşirīyah: (27.21°, 31.20°)", + " Aţfīḩ: (29.41°, 31.25°)", + " Fichē: (9.80°, 38.73°)", + " Lérida: (4.86°, -74.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lérida: 9585.7 km from centroid", + " Fichē: 2919.3 km from centroid", + " Bedelē: 2717.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lérida", + "FINAL ANSWER: Lérida" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.72577, + "lon": 93.14659, + "name": "Biswanath Chariali" + }, + { + "lat": 10.90141, + "lon": 79.17984, + "name": "Ayyampettāi" + }, + { + "lat": 33.41998, + "lon": 131.61837, + "name": "Kitsuki" + }, + { + "lat": -2.88333, + "lon": 108.26667, + "name": "Manggar" + }, + { + "lat": 27.89364, + "lon": -82.24037, + "name": "Bloomingdale" + } + ], + "question": "Which location is the geographic outlier among: Biswanath Chariali, Ayyampettāi, Kitsuki, Manggar, Bloomingdale?", + "ground_truth": { + "answer": "Bloomingdale", + "outlier_distance_km": 13760.9, + "second_furthest_km": 6623.5, + "clarity_ratio": 2.08, + "median_distance_km": 5232.2, + "distances_to_centroid": { + "Biswanath Chariali": 2895.9, + "Ayyampettāi": 1689.3, + "Kitsuki": 6623.5, + "Manggar": 5232.2, + "Bloomingdale": 13760.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Biswanath Chariali: (26.73°, 93.15°)", + " Ayyampettāi: (10.90°, 79.18°)", + " Kitsuki: (33.42°, 131.62°)", + " Manggar: (-2.88°, 108.27°)", + " Bloomingdale: (27.89°, -82.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bloomingdale: 13760.9 km from centroid", + " Kitsuki: 6623.5 km from centroid", + " Manggar: 5232.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bloomingdale", + "FINAL ANSWER: Bloomingdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.80972, + "lon": -63.69556, + "name": "Candeias do Jamari" + }, + { + "lat": -8.14583, + "lon": -36.37111, + "name": "Brejo da Madre de Deus" + }, + { + "lat": -30.51436, + "lon": -53.48496, + "name": "Caçapava do Sul" + }, + { + "lat": -19.22444, + "lon": -44.93528, + "name": "Pompéu" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + } + ], + "question": "Which location is the geographic outlier among: Candeias do Jamari, Brejo da Madre de Deus, Caçapava do Sul, Pompéu, Boronia?", + "ground_truth": { + "answer": "Boronia", + "outlier_distance_km": 13011.2, + "second_furthest_km": 5831.8, + "clarity_ratio": 2.23, + "median_distance_km": 4395.6, + "distances_to_centroid": { + "Candeias do Jamari": 5831.8, + "Brejo da Madre de Deus": 3104.7, + "Caçapava do Sul": 4395.6, + "Pompéu": 3580.1, + "Boronia": 13011.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Candeias do Jamari: (-8.81°, -63.70°)", + " Brejo da Madre de Deus: (-8.15°, -36.37°)", + " Caçapava do Sul: (-30.51°, -53.48°)", + " Pompéu: (-19.22°, -44.94°)", + " Boronia: (-37.87°, 145.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Boronia: 13011.2 km from centroid", + " Candeias do Jamari: 5831.8 km from centroid", + " Caçapava do Sul: 4395.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Boronia", + "FINAL ANSWER: Boronia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.5, + "lon": 120.843, + "name": "Aliaga" + }, + { + "lat": 11.91393, + "lon": 79.75568, + "name": "Villianur" + }, + { + "lat": 28.94472, + "lon": 106.71056, + "name": "Sanjiang" + }, + { + "lat": 13.58333, + "lon": 100.81667, + "name": "Bang Bo District" + }, + { + "lat": 51.65147, + "lon": -0.08497, + "name": "Enfield Town" + } + ], + "question": "Which location is the geographic outlier among: Aliaga, Villianur, Sanjiang, Bang Bo District, Enfield Town?", + "ground_truth": { + "answer": "Enfield Town", + "outlier_distance_km": 7353.4, + "second_furthest_km": 4202.6, + "clarity_ratio": 1.75, + "median_distance_km": 2542.4, + "distances_to_centroid": { + "Aliaga": 4202.6, + "Villianur": 1393.1, + "Sanjiang": 2542.4, + "Bang Bo District": 2342.1, + "Enfield Town": 7353.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aliaga: (15.50°, 120.84°)", + " Villianur: (11.91°, 79.76°)", + " Sanjiang: (28.94°, 106.71°)", + " Bang Bo District: (13.58°, 100.82°)", + " Enfield Town: (51.65°, -0.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Enfield Town: 7353.4 km from centroid", + " Aliaga: 4202.6 km from centroid", + " Sanjiang: 2542.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Enfield Town", + "FINAL ANSWER: Enfield Town" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + }, + { + "lat": -37.74496, + "lon": 144.80049, + "name": "St Albans" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": 29.61972, + "lon": 31.2575, + "name": "Al ‘Ayyāţ" + } + ], + "question": "Which location is the geographic outlier among: Saint Ives, Dandenong, St Albans, Greystanes, Al ‘Ayyāţ?", + "ground_truth": { + "answer": "Al ‘Ayyāţ", + "outlier_distance_km": 11543.5, + "second_furthest_km": 2857.1, + "clarity_ratio": 4.04, + "median_distance_km": 2841.7, + "distances_to_centroid": { + "Saint Ives": 2857.1, + "Dandenong": 2588.0, + "St Albans": 2544.0, + "Greystanes": 2841.7, + "Al ‘Ayyāţ": 11543.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Ives: (-33.73°, 151.16°)", + " Dandenong: (-37.98°, 145.20°)", + " St Albans: (-37.74°, 144.80°)", + " Greystanes: (-33.82°, 150.95°)", + " Al ‘Ayyāţ: (29.62°, 31.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al ‘Ayyāţ: 11543.5 km from centroid", + " Saint Ives: 2857.1 km from centroid", + " Greystanes: 2841.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al ‘Ayyāţ", + "FINAL ANSWER: Al ‘Ayyāţ" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.37808, + "lon": -74.88356, + "name": "Campo de la Cruz" + }, + { + "lat": -5.19889, + "lon": -35.46083, + "name": "Touros" + }, + { + "lat": -6.66028, + "lon": -69.87361, + "name": "Eirunepé" + }, + { + "lat": -8.1654, + "lon": -70.35486, + "name": "Feijó" + }, + { + "lat": 8.61565, + "lon": 6.4185, + "name": "Baro" + } + ], + "question": "Which location is the geographic outlier among: Campo de la Cruz, Touros, Eirunepé, Feijó, Baro?", + "ground_truth": { + "answer": "Baro", + "outlier_distance_km": 6197.4, + "second_furthest_km": 3112.2, + "clarity_ratio": 1.99, + "median_distance_km": 2543.9, + "distances_to_centroid": { + "Campo de la Cruz": 3112.2, + "Touros": 1585.0, + "Eirunepé": 2442.2, + "Feijó": 2543.9, + "Baro": 6197.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Campo de la Cruz: (10.38°, -74.88°)", + " Touros: (-5.20°, -35.46°)", + " Eirunepé: (-6.66°, -69.87°)", + " Feijó: (-8.17°, -70.35°)", + " Baro: (8.62°, 6.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baro: 6197.4 km from centroid", + " Campo de la Cruz: 3112.2 km from centroid", + " Feijó: 2543.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Baro", + "FINAL ANSWER: Baro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.35833, + "lon": -42.67639, + "name": "Demerval Lobão" + }, + { + "lat": -29.55028, + "lon": -55.13111, + "name": "São Francisco de Assis" + }, + { + "lat": 4.80938, + "lon": -74.098, + "name": "Cota" + }, + { + "lat": -5.89056, + "lon": -38.62194, + "name": "Jaguaribe" + }, + { + "lat": 0.05196, + "lon": 35.72734, + "name": "Eldama Ravine" + } + ], + "question": "Which location is the geographic outlier among: Demerval Lobão, São Francisco de Assis, Cota, Jaguaribe, Eldama Ravine?", + "ground_truth": { + "answer": "Eldama Ravine", + "outlier_distance_km": 7878.4, + "second_furthest_km": 4543.2, + "clarity_ratio": 1.73, + "median_distance_km": 3260.8, + "distances_to_centroid": { + "Demerval Lobão": 876.8, + "São Francisco de Assis": 3260.8, + "Cota": 4543.2, + "Jaguaribe": 429.5, + "Eldama Ravine": 7878.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Demerval Lobão: (-5.36°, -42.68°)", + " São Francisco de Assis: (-29.55°, -55.13°)", + " Cota: (4.81°, -74.10°)", + " Jaguaribe: (-5.89°, -38.62°)", + " Eldama Ravine: (0.05°, 35.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eldama Ravine: 7878.4 km from centroid", + " Cota: 4543.2 km from centroid", + " São Francisco de Assis: 3260.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eldama Ravine", + "FINAL ANSWER: Eldama Ravine" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -41.33333, + "lon": 173.18333, + "name": "Richmond" + }, + { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + { + "lat": 20.79729, + "lon": -103.47712, + "name": "San Francisco Tesistán" + } + ], + "question": "Which location is the geographic outlier among: Coogee, Rochedale South, Richmond, Kellyville, San Francisco Tesistán?", + "ground_truth": { + "answer": "San Francisco Tesistán", + "outlier_distance_km": 17070.9, + "second_furthest_km": 6550.9, + "clarity_ratio": 2.61, + "median_distance_km": 4829.8, + "distances_to_centroid": { + "Coogee": 4633.0, + "Rochedale South": 4829.8, + "Richmond": 6550.9, + "Kellyville": 4603.9, + "San Francisco Tesistán": 17070.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coogee: (-33.92°, 151.26°)", + " Rochedale South: (-27.60°, 153.12°)", + " Richmond: (-41.33°, 173.18°)", + " Kellyville: (-33.71°, 150.95°)", + " San Francisco Tesistán: (20.80°, -103.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Francisco Tesistán: 17070.9 km from centroid", + " Richmond: 6550.9 km from centroid", + " Rochedale South: 4829.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Francisco Tesistán", + "FINAL ANSWER: San Francisco Tesistán" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.34984, + "lon": 18.22606, + "name": "Kędzierzyn-Koźle" + }, + { + "lat": 49.7688, + "lon": 43.65417, + "name": "Frolovo" + }, + { + "lat": 55.91536, + "lon": -4.33279, + "name": "Bearsden" + }, + { + "lat": 53.13333, + "lon": 46.58333, + "name": "Zarechnyy" + }, + { + "lat": 19.51194, + "lon": -98.88293, + "name": "Texcoco de Mora" + } + ], + "question": "Which location is the geographic outlier among: Kędzierzyn-Koźle, Frolovo, Bearsden, Zarechnyy, Texcoco de Mora?", + "ground_truth": { + "answer": "Texcoco de Mora", + "outlier_distance_km": 9204.5, + "second_furthest_km": 3332.9, + "clarity_ratio": 2.76, + "median_distance_km": 3172.9, + "distances_to_centroid": { + "Kędzierzyn-Koźle": 1372.2, + "Frolovo": 3172.9, + "Bearsden": 1192.5, + "Zarechnyy": 3332.9, + "Texcoco de Mora": 9204.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kędzierzyn-Koźle: (50.35°, 18.23°)", + " Frolovo: (49.77°, 43.65°)", + " Bearsden: (55.92°, -4.33°)", + " Zarechnyy: (53.13°, 46.58°)", + " Texcoco de Mora: (19.51°, -98.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Texcoco de Mora: 9204.5 km from centroid", + " Zarechnyy: 3332.9 km from centroid", + " Frolovo: 3172.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Texcoco de Mora", + "FINAL ANSWER: Texcoco de Mora" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.90556, + "lon": -40.07611, + "name": "Jaguaré" + }, + { + "lat": -22.70556, + "lon": -46.98583, + "name": "Jaguariúna" + }, + { + "lat": -28.4602, + "lon": -62.83354, + "name": "Añatuya" + }, + { + "lat": -15.88378, + "lon": -48.01634, + "name": "Riacho Fundo" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + } + ], + "question": "Which location is the geographic outlier among: Jaguaré, Jaguariúna, Añatuya, Riacho Fundo, Cranbourne West?", + "ground_truth": { + "answer": "Cranbourne West", + "outlier_distance_km": 12578.3, + "second_furthest_km": 5174.4, + "clarity_ratio": 2.43, + "median_distance_km": 4018.4, + "distances_to_centroid": { + "Jaguaré": 3112.5, + "Jaguariúna": 3706.8, + "Añatuya": 5174.4, + "Riacho Fundo": 4018.4, + "Cranbourne West": 12578.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jaguaré: (-18.91°, -40.08°)", + " Jaguariúna: (-22.71°, -46.99°)", + " Añatuya: (-28.46°, -62.83°)", + " Riacho Fundo: (-15.88°, -48.02°)", + " Cranbourne West: (-38.10°, 145.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cranbourne West: 12578.3 km from centroid", + " Añatuya: 5174.4 km from centroid", + " Riacho Fundo: 4018.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cranbourne West", + "FINAL ANSWER: Cranbourne West" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.39341, + "lon": -75.89232, + "name": "La Plata" + }, + { + "lat": -34.67907, + "lon": -58.47263, + "name": "Villa Lugano" + }, + { + "lat": 11.23855, + "lon": -74.19427, + "name": "Santa Marta" + }, + { + "lat": -5.09417, + "lon": -42.83667, + "name": "Timon" + }, + { + "lat": 8.53417, + "lon": 37.96515, + "name": "Waliso" + } + ], + "question": "Which location is the geographic outlier among: La Plata, Villa Lugano, Santa Marta, Timon, Waliso?", + "ground_truth": { + "answer": "Waliso", + "outlier_distance_km": 9040.4, + "second_furthest_km": 3852.6, + "clarity_ratio": 2.35, + "median_distance_km": 3828.8, + "distances_to_centroid": { + "La Plata": 3748.7, + "Villa Lugano": 3828.8, + "Santa Marta": 3852.6, + "Timon": 175.7, + "Waliso": 9040.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Plata: (2.39°, -75.89°)", + " Villa Lugano: (-34.68°, -58.47°)", + " Santa Marta: (11.24°, -74.19°)", + " Timon: (-5.09°, -42.84°)", + " Waliso: (8.53°, 37.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Waliso: 9040.4 km from centroid", + " Santa Marta: 3852.6 km from centroid", + " Villa Lugano: 3828.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Waliso", + "FINAL ANSWER: Waliso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -27.22426, + "lon": 153.02075, + "name": "North Lakes" + }, + { + "lat": -33.88374, + "lon": 151.21282, + "name": "Surry Hills" + }, + { + "lat": 42.98342, + "lon": -79.24958, + "name": "Welland" + } + ], + "question": "Which location is the geographic outlier among: Maroochydore, Newcastle, North Lakes, Surry Hills, Welland?", + "ground_truth": { + "answer": "Welland", + "outlier_distance_km": 16923.6, + "second_furthest_km": 5013.4, + "clarity_ratio": 3.38, + "median_distance_km": 5010.8, + "distances_to_centroid": { + "Maroochydore": 5013.4, + "Newcastle": 4983.5, + "North Lakes": 5010.8, + "Surry Hills": 4954.4, + "Welland": 16923.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maroochydore: (-26.66°, 153.10°)", + " Newcastle: (-32.93°, 151.78°)", + " North Lakes: (-27.22°, 153.02°)", + " Surry Hills: (-33.88°, 151.21°)", + " Welland: (42.98°, -79.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Welland: 16923.6 km from centroid", + " Maroochydore: 5013.4 km from centroid", + " North Lakes: 5010.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Welland", + "FINAL ANSWER: Welland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.925, + "lon": 119.59306, + "name": "Xinhe" + }, + { + "lat": 16.0184, + "lon": 80.82958, + "name": "Repalle" + }, + { + "lat": 21.02626, + "lon": 83.81197, + "name": "Binika" + }, + { + "lat": 19.40844, + "lon": 73.26285, + "name": "Vasind" + }, + { + "lat": -41.13827, + "lon": 175.0502, + "name": "Upper Hutt" + } + ], + "question": "Which location is the geographic outlier among: Xinhe, Repalle, Binika, Vasind, Upper Hutt?", + "ground_truth": { + "answer": "Upper Hutt", + "outlier_distance_km": 9037.6, + "second_furthest_km": 3700.8, + "clarity_ratio": 2.44, + "median_distance_km": 3223.5, + "distances_to_centroid": { + "Xinhe": 3223.5, + "Repalle": 2845.4, + "Binika": 2694.1, + "Vasind": 3700.8, + "Upper Hutt": 9037.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Xinhe: (36.92°, 119.59°)", + " Repalle: (16.02°, 80.83°)", + " Binika: (21.03°, 83.81°)", + " Vasind: (19.41°, 73.26°)", + " Upper Hutt: (-41.14°, 175.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upper Hutt: 9037.6 km from centroid", + " Vasind: 3700.8 km from centroid", + " Xinhe: 3223.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upper Hutt", + "FINAL ANSWER: Upper Hutt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.6707, + "lon": -45.84749, + "name": "Alto Alegre do Pindaré" + }, + { + "lat": -25.94111, + "lon": -52.17556, + "name": "Mangueirinha" + }, + { + "lat": -12.06866, + "lon": -75.21027, + "name": "Huancayo" + }, + { + "lat": -2.99, + "lon": -65.10833, + "name": "Uarini" + }, + { + "lat": 36.59917, + "lon": -4.53505, + "name": "Arroyo de la Miel" + } + ], + "question": "Which location is the geographic outlier among: Alto Alegre do Pindaré, Mangueirinha, Huancayo, Uarini, Arroyo de la Miel?", + "ground_truth": { + "answer": "Arroyo de la Miel", + "outlier_distance_km": 6220.0, + "second_furthest_km": 3157.7, + "clarity_ratio": 1.97, + "median_distance_km": 2732.3, + "distances_to_centroid": { + "Alto Alegre do Pindaré": 379.6, + "Mangueirinha": 2732.3, + "Huancayo": 3157.7, + "Uarini": 1843.2, + "Arroyo de la Miel": 6220.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alto Alegre do Pindaré: (-3.67°, -45.85°)", + " Mangueirinha: (-25.94°, -52.18°)", + " Huancayo: (-12.07°, -75.21°)", + " Uarini: (-2.99°, -65.11°)", + " Arroyo de la Miel: (36.60°, -4.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arroyo de la Miel: 6220.0 km from centroid", + " Huancayo: 3157.7 km from centroid", + " Mangueirinha: 2732.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arroyo de la Miel", + "FINAL ANSWER: Arroyo de la Miel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": 12.42417, + "lon": 37.325, + "name": "K’ola Diba" + } + ], + "question": "Which location is the geographic outlier among: Port Macquarie, Rotorua, Gosnells, Pacific Pines, K’ola Diba?", + "ground_truth": { + "answer": "K’ola Diba", + "outlier_distance_km": 10536.8, + "second_furthest_km": 4902.8, + "clarity_ratio": 2.15, + "median_distance_km": 2684.4, + "distances_to_centroid": { + "Port Macquarie": 2684.4, + "Rotorua": 4902.8, + "Gosnells": 1457.5, + "Pacific Pines": 2662.9, + "K’ola Diba": 10536.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Port Macquarie: (-31.43°, 152.91°)", + " Rotorua: (-38.14°, 176.25°)", + " Gosnells: (-32.08°, 116.01°)", + " Pacific Pines: (-27.94°, 153.31°)", + " K’ola Diba: (12.42°, 37.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " K’ola Diba: 10536.8 km from centroid", + " Rotorua: 4902.8 km from centroid", + " Port Macquarie: 2684.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: K’ola Diba", + "FINAL ANSWER: K’ola Diba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.73271, + "lon": -59.10989, + "name": "Pirané" + }, + { + "lat": -20.41667, + "lon": -54.06667, + "name": "Campo Verde" + }, + { + "lat": -23.96306, + "lon": -46.39194, + "name": "São Vicente" + }, + { + "lat": -23.66877, + "lon": -46.78051, + "name": "Capao Redondo" + }, + { + "lat": 30.27563, + "lon": 75.24253, + "name": "Rampura Phul" + } + ], + "question": "Which location is the geographic outlier among: Pirané, Campo Verde, São Vicente, Capao Redondo, Rampura Phul?", + "ground_truth": { + "answer": "Rampura Phul", + "outlier_distance_km": 11804.2, + "second_furthest_km": 3730.6, + "clarity_ratio": 3.16, + "median_distance_km": 3084.3, + "distances_to_centroid": { + "Pirané": 3730.6, + "Campo Verde": 3084.3, + "São Vicente": 2465.1, + "Capao Redondo": 2486.0, + "Rampura Phul": 11804.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pirané: (-25.73°, -59.11°)", + " Campo Verde: (-20.42°, -54.07°)", + " São Vicente: (-23.96°, -46.39°)", + " Capao Redondo: (-23.67°, -46.78°)", + " Rampura Phul: (30.28°, 75.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rampura Phul: 11804.2 km from centroid", + " Pirané: 3730.6 km from centroid", + " Campo Verde: 3084.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rampura Phul", + "FINAL ANSWER: Rampura Phul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.77676, + "lon": -1.57566, + "name": "Durham" + }, + { + "lat": 42.26413, + "lon": -8.78463, + "name": "Cangas do Morrazo" + }, + { + "lat": 52.19656, + "lon": 21.17752, + "name": "Wawer" + }, + { + "lat": 52.33645, + "lon": 13.41316, + "name": "Blankenfelde-Mahlow" + }, + { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + } + ], + "question": "Which location is the geographic outlier among: Durham, Cangas do Morrazo, Wawer, Blankenfelde-Mahlow, Cronulla?", + "ground_truth": { + "answer": "Cronulla", + "outlier_distance_km": 14209.7, + "second_furthest_km": 3924.8, + "clarity_ratio": 3.62, + "median_distance_km": 3691.7, + "distances_to_centroid": { + "Durham": 3691.7, + "Cangas do Morrazo": 3924.8, + "Wawer": 2358.1, + "Blankenfelde-Mahlow": 2716.4, + "Cronulla": 14209.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Durham: (54.78°, -1.58°)", + " Cangas do Morrazo: (42.26°, -8.78°)", + " Wawer: (52.20°, 21.18°)", + " Blankenfelde-Mahlow: (52.34°, 13.41°)", + " Cronulla: (-34.06°, 151.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cronulla: 14209.7 km from centroid", + " Cangas do Morrazo: 3924.8 km from centroid", + " Durham: 3691.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cronulla", + "FINAL ANSWER: Cronulla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.87215, + "lon": -113.994, + "name": "Missoula" + }, + { + "lat": 38.974, + "lon": -76.849, + "name": "Seabrook" + }, + { + "lat": 17.02921, + "lon": -96.70094, + "name": "San Antonio de la Cal" + }, + { + "lat": 44.31062, + "lon": -69.77949, + "name": "Augusta" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + } + ], + "question": "Which location is the geographic outlier among: Missoula, Seabrook, San Antonio de la Cal, Augusta, Balwyn North?", + "ground_truth": { + "answer": "Balwyn North", + "outlier_distance_km": 18104.0, + "second_furthest_km": 6870.3, + "clarity_ratio": 2.64, + "median_distance_km": 5686.1, + "distances_to_centroid": { + "Missoula": 6870.3, + "Seabrook": 3773.9, + "San Antonio de la Cal": 5686.1, + "Augusta": 3532.3, + "Balwyn North": 18104.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Missoula: (46.87°, -113.99°)", + " Seabrook: (38.97°, -76.85°)", + " San Antonio de la Cal: (17.03°, -96.70°)", + " Augusta: (44.31°, -69.78°)", + " Balwyn North: (-37.79°, 145.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Balwyn North: 18104.0 km from centroid", + " Missoula: 6870.3 km from centroid", + " San Antonio de la Cal: 5686.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Balwyn North", + "FINAL ANSWER: Balwyn North" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -33.7061, + "lon": 150.7094, + "name": "Cranebrook" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -34.92873, + "lon": 138.60334, + "name": "Adelaide city centre" + }, + { + "lat": 12.03609, + "lon": 13.91815, + "name": "Dikwa" + } + ], + "question": "Which location is the geographic outlier among: Glen Iris, Cranebrook, Mount Martha, Adelaide city centre, Dikwa?", + "ground_truth": { + "answer": "Dikwa", + "outlier_distance_km": 12055.0, + "second_furthest_km": 3169.3, + "clarity_ratio": 3.8, + "median_distance_km": 2782.2, + "distances_to_centroid": { + "Glen Iris": 2771.3, + "Cranebrook": 3169.3, + "Mount Martha": 2782.2, + "Adelaide city centre": 2116.1, + "Dikwa": 12055.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Iris: (-37.87°, 145.07°)", + " Cranebrook: (-33.71°, 150.71°)", + " Mount Martha: (-38.27°, 145.02°)", + " Adelaide city centre: (-34.93°, 138.60°)", + " Dikwa: (12.04°, 13.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dikwa: 12055.0 km from centroid", + " Cranebrook: 3169.3 km from centroid", + " Mount Martha: 2782.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dikwa", + "FINAL ANSWER: Dikwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": 31.865, + "lon": 120.53889, + "name": "Zhangjiagang" + } + ], + "question": "Which location is the geographic outlier among: Auburn, Traralgon, Hervey Bay, Timaru, Zhangjiagang?", + "ground_truth": { + "answer": "Zhangjiagang", + "outlier_distance_km": 6682.0, + "second_furthest_km": 3252.5, + "clarity_ratio": 2.05, + "median_distance_km": 1812.8, + "distances_to_centroid": { + "Auburn": 1345.1, + "Traralgon": 1812.8, + "Hervey Bay": 575.7, + "Timaru": 3252.5, + "Zhangjiagang": 6682.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auburn: (-33.85°, 151.03°)", + " Traralgon: (-38.20°, 146.54°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Timaru: (-44.40°, 171.25°)", + " Zhangjiagang: (31.86°, 120.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhangjiagang: 6682.0 km from centroid", + " Timaru: 3252.5 km from centroid", + " Traralgon: 1812.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhangjiagang", + "FINAL ANSWER: Zhangjiagang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + }, + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": 13.33868, + "lon": 80.19487, + "name": "Ponneri" + } + ], + "question": "Which location is the geographic outlier among: Epsom, Cambridge, Thomastown, Doreen, Ponneri?", + "ground_truth": { + "answer": "Ponneri", + "outlier_distance_km": 8239.2, + "second_furthest_km": 3140.7, + "clarity_ratio": 2.62, + "median_distance_km": 3059.9, + "distances_to_centroid": { + "Epsom": 3059.9, + "Cambridge": 3140.7, + "Thomastown": 1153.0, + "Doreen": 1144.7, + "Ponneri": 8239.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epsom: (-36.89°, 174.77°)", + " Cambridge: (-37.88°, 175.44°)", + " Thomastown: (-37.68°, 145.02°)", + " Doreen: (-37.60°, 145.15°)", + " Ponneri: (13.34°, 80.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ponneri: 8239.2 km from centroid", + " Cambridge: 3140.7 km from centroid", + " Epsom: 3059.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ponneri", + "FINAL ANSWER: Ponneri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.49755, + "lon": -2.16889, + "name": "Kingswinford" + }, + { + "lat": 52.18435, + "lon": 20.83952, + "name": "Piastów" + }, + { + "lat": 48.89148, + "lon": 2.46451, + "name": "Noisy-le-Sec" + }, + { + "lat": 43.16345, + "lon": 46.00152, + "name": "Avtury" + }, + { + "lat": -39.36708, + "lon": -72.63087, + "name": "Loncoche" + } + ], + "question": "Which location is the geographic outlier among: Kingswinford, Piastów, Noisy-le-Sec, Avtury, Loncoche?", + "ground_truth": { + "answer": "Loncoche", + "outlier_distance_km": 10788.7, + "second_furthest_km": 4301.2, + "clarity_ratio": 2.51, + "median_distance_km": 2909.6, + "distances_to_centroid": { + "Kingswinford": 2339.3, + "Piastów": 2909.6, + "Noisy-le-Sec": 1959.7, + "Avtury": 4301.2, + "Loncoche": 10788.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kingswinford: (52.50°, -2.17°)", + " Piastów: (52.18°, 20.84°)", + " Noisy-le-Sec: (48.89°, 2.46°)", + " Avtury: (43.16°, 46.00°)", + " Loncoche: (-39.37°, -72.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Loncoche: 10788.7 km from centroid", + " Avtury: 4301.2 km from centroid", + " Piastów: 2909.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Loncoche", + "FINAL ANSWER: Loncoche" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.90418, + "lon": 99.80286, + "name": "Fubang" + }, + { + "lat": 13.72784, + "lon": 100.74609, + "name": "Latkrabang" + }, + { + "lat": 35.91222, + "lon": 116.31167, + "name": "Zhoucheng" + }, + { + "lat": 17.05675, + "lon": 82.17639, + "name": "Sāmalkot" + }, + { + "lat": -26.77528, + "lon": -51.015, + "name": "Caçador" + } + ], + "question": "Which location is the geographic outlier among: Fubang, Latkrabang, Zhoucheng, Sāmalkot, Caçador?", + "ground_truth": { + "answer": "Caçador", + "outlier_distance_km": 13655.7, + "second_furthest_km": 5332.6, + "clarity_ratio": 2.56, + "median_distance_km": 3390.0, + "distances_to_centroid": { + "Fubang": 3390.0, + "Latkrabang": 3372.2, + "Zhoucheng": 5332.6, + "Sāmalkot": 1440.3, + "Caçador": 13655.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fubang: (22.90°, 99.80°)", + " Latkrabang: (13.73°, 100.75°)", + " Zhoucheng: (35.91°, 116.31°)", + " Sāmalkot: (17.06°, 82.18°)", + " Caçador: (-26.78°, -51.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caçador: 13655.7 km from centroid", + " Zhoucheng: 5332.6 km from centroid", + " Fubang: 3390.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caçador", + "FINAL ANSWER: Caçador" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.78864, + "lon": 31.07938, + "name": "Mafemani" + }, + { + "lat": 0.0607, + "lon": 34.28806, + "name": "Siaya" + }, + { + "lat": 30.18479, + "lon": 31.10649, + "name": "Manshīyat al Qanāţir" + }, + { + "lat": 5.51737, + "lon": 5.75006, + "name": "Warri" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + } + ], + "question": "Which location is the geographic outlier among: Mafemani, Siaya, Manshīyat al Qanāţir, Warri, Bundoora?", + "ground_truth": { + "answer": "Bundoora", + "outlier_distance_km": 10134.7, + "second_furthest_km": 5000.7, + "clarity_ratio": 2.03, + "median_distance_km": 4407.9, + "distances_to_centroid": { + "Mafemani": 2918.9, + "Siaya": 1788.3, + "Manshīyat al Qanāţir": 4407.9, + "Warri": 5000.7, + "Bundoora": 10134.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mafemani: (-24.79°, 31.08°)", + " Siaya: (0.06°, 34.29°)", + " Manshīyat al Qanāţir: (30.18°, 31.11°)", + " Warri: (5.52°, 5.75°)", + " Bundoora: (-37.70°, 145.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bundoora: 10134.7 km from centroid", + " Warri: 5000.7 km from centroid", + " Manshīyat al Qanāţir: 4407.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bundoora", + "FINAL ANSWER: Bundoora" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.7, + "lon": 37.18333, + "name": "Karuri" + }, + { + "lat": 9.22556, + "lon": 42.33222, + "name": "Babīlē" + }, + { + "lat": -27.83273, + "lon": 25.90833, + "name": "Hoopstad" + }, + { + "lat": -1.10148, + "lon": 37.0132, + "name": "Juja" + }, + { + "lat": 27.91989, + "lon": -110.89888, + "name": "Heroica Guaymas" + } + ], + "question": "Which location is the geographic outlier among: Karuri, Babīlē, Hoopstad, Juja, Heroica Guaymas?", + "ground_truth": { + "answer": "Heroica Guaymas", + "outlier_distance_km": 12570.8, + "second_furthest_km": 4076.0, + "clarity_ratio": 3.08, + "median_distance_km": 3876.3, + "distances_to_centroid": { + "Karuri": 3441.6, + "Babīlē": 4076.0, + "Hoopstad": 3876.3, + "Juja": 3426.2, + "Heroica Guaymas": 12570.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Karuri: (-0.70°, 37.18°)", + " Babīlē: (9.23°, 42.33°)", + " Hoopstad: (-27.83°, 25.91°)", + " Juja: (-1.10°, 37.01°)", + " Heroica Guaymas: (27.92°, -110.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Heroica Guaymas: 12570.8 km from centroid", + " Babīlē: 4076.0 km from centroid", + " Hoopstad: 3876.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Heroica Guaymas", + "FINAL ANSWER: Heroica Guaymas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.38484, + "lon": -41.78324, + "name": "Macaé" + }, + { + "lat": -33.56839, + "lon": -70.80584, + "name": "Padre Hurtado" + }, + { + "lat": -20.04917, + "lon": -44.27389, + "name": "São Joaquim de Bicas" + }, + { + "lat": -23.73306, + "lon": -52.87333, + "name": "Tapejara" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + } + ], + "question": "Which location is the geographic outlier among: Macaé, Padre Hurtado, São Joaquim de Bicas, Tapejara, Mangere East?", + "ground_truth": { + "answer": "Mangere East", + "outlier_distance_km": 12862.1, + "second_furthest_km": 6062.0, + "clarity_ratio": 2.12, + "median_distance_km": 4596.5, + "distances_to_centroid": { + "Macaé": 3542.5, + "Padre Hurtado": 6062.0, + "São Joaquim de Bicas": 3867.7, + "Tapejara": 4596.5, + "Mangere East": 12862.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macaé: (-22.38°, -41.78°)", + " Padre Hurtado: (-33.57°, -70.81°)", + " São Joaquim de Bicas: (-20.05°, -44.27°)", + " Tapejara: (-23.73°, -52.87°)", + " Mangere East: (-36.97°, 174.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mangere East: 12862.1 km from centroid", + " Padre Hurtado: 6062.0 km from centroid", + " Tapejara: 4596.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mangere East", + "FINAL ANSWER: Mangere East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.2471, + "lon": 10.561, + "name": "Kari" + }, + { + "lat": -26.002, + "lon": 29.034, + "name": "Phola" + }, + { + "lat": -26.43138, + "lon": 28.47713, + "name": "Nigel" + }, + { + "lat": 25.61988, + "lon": 32.54305, + "name": "Armant" + }, + { + "lat": 33.68906, + "lon": -78.88669, + "name": "Myrtle Beach" + } + ], + "question": "Which location is the geographic outlier among: Kari, Phola, Nigel, Armant, Myrtle Beach?", + "ground_truth": { + "answer": "Myrtle Beach", + "outlier_distance_km": 9158.2, + "second_furthest_km": 4233.0, + "clarity_ratio": 2.16, + "median_distance_km": 4231.3, + "distances_to_centroid": { + "Kari": 1089.6, + "Phola": 4233.0, + "Nigel": 4231.3, + "Armant": 3877.7, + "Myrtle Beach": 9158.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kari: (11.25°, 10.56°)", + " Phola: (-26.00°, 29.03°)", + " Nigel: (-26.43°, 28.48°)", + " Armant: (25.62°, 32.54°)", + " Myrtle Beach: (33.69°, -78.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Myrtle Beach: 9158.2 km from centroid", + " Phola: 4233.0 km from centroid", + " Nigel: 4231.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Myrtle Beach", + "FINAL ANSWER: Myrtle Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.27088, + "lon": 36.37917, + "name": "Ol Kalou" + }, + { + "lat": -28.52423, + "lon": 28.81582, + "name": "Phuthaditjhaba" + }, + { + "lat": -33.80342, + "lon": 19.88537, + "name": "Robertson" + }, + { + "lat": 31.26531, + "lon": 32.3019, + "name": "Port Said" + }, + { + "lat": -22.57306, + "lon": -47.1725, + "name": "Artur Nogueira" + } + ], + "question": "Which location is the geographic outlier among: Ol Kalou, Phuthaditjhaba, Robertson, Port Said, Artur Nogueira?", + "ground_truth": { + "answer": "Artur Nogueira", + "outlier_distance_km": 6608.3, + "second_furthest_km": 5064.6, + "clarity_ratio": 1.3, + "median_distance_km": 2731.2, + "distances_to_centroid": { + "Ol Kalou": 2731.2, + "Phuthaditjhaba": 2501.6, + "Robertson": 2628.2, + "Port Said": 5064.6, + "Artur Nogueira": 6608.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ol Kalou: (-0.27°, 36.38°)", + " Phuthaditjhaba: (-28.52°, 28.82°)", + " Robertson: (-33.80°, 19.89°)", + " Port Said: (31.27°, 32.30°)", + " Artur Nogueira: (-22.57°, -47.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Artur Nogueira: 6608.3 km from centroid", + " Port Said: 5064.6 km from centroid", + " Ol Kalou: 2731.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Artur Nogueira", + "FINAL ANSWER: Artur Nogueira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.70806, + "lon": -48.41722, + "name": "Porto Nacional" + }, + { + "lat": -23.00583, + "lon": -46.83889, + "name": "Itatiba" + }, + { + "lat": -33.2863, + "lon": -70.87561, + "name": "Lampa" + }, + { + "lat": -11.02889, + "lon": -68.74139, + "name": "Epitaciolândia" + }, + { + "lat": 52.14021, + "lon": 8.48475, + "name": "Spenge" + } + ], + "question": "Which location is the geographic outlier among: Porto Nacional, Itatiba, Lampa, Epitaciolândia, Spenge?", + "ground_truth": { + "answer": "Spenge", + "outlier_distance_km": 8132.6, + "second_furthest_km": 4096.1, + "clarity_ratio": 1.99, + "median_distance_km": 2662.2, + "distances_to_centroid": { + "Porto Nacional": 705.4, + "Itatiba": 1989.5, + "Lampa": 4096.1, + "Epitaciolândia": 2662.2, + "Spenge": 8132.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porto Nacional: (-10.71°, -48.42°)", + " Itatiba: (-23.01°, -46.84°)", + " Lampa: (-33.29°, -70.88°)", + " Epitaciolândia: (-11.03°, -68.74°)", + " Spenge: (52.14°, 8.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Spenge: 8132.6 km from centroid", + " Lampa: 4096.1 km from centroid", + " Epitaciolândia: 2662.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Spenge", + "FINAL ANSWER: Spenge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.99583, + "lon": -102.22694, + "name": "La Orilla" + }, + { + "lat": 39.9936, + "lon": -105.08971, + "name": "Lafayette" + }, + { + "lat": 42.29171, + "lon": -85.58723, + "name": "Kalamazoo" + }, + { + "lat": 36.98356, + "lon": -121.98052, + "name": "Live Oak" + }, + { + "lat": 6.74, + "lon": 44.27806, + "name": "Kebri Dahar" + } + ], + "question": "Which location is the geographic outlier among: La Orilla, Lafayette, Kalamazoo, Live Oak, Kebri Dahar?", + "ground_truth": { + "answer": "Kebri Dahar", + "outlier_distance_km": 12335.7, + "second_furthest_km": 4512.4, + "clarity_ratio": 2.73, + "median_distance_km": 3099.2, + "distances_to_centroid": { + "La Orilla": 3099.2, + "Lafayette": 3081.7, + "Kalamazoo": 1820.1, + "Live Oak": 4512.4, + "Kebri Dahar": 12335.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Orilla: (18.00°, -102.23°)", + " Lafayette: (39.99°, -105.09°)", + " Kalamazoo: (42.29°, -85.59°)", + " Live Oak: (36.98°, -121.98°)", + " Kebri Dahar: (6.74°, 44.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kebri Dahar: 12335.7 km from centroid", + " Live Oak: 4512.4 km from centroid", + " La Orilla: 3099.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kebri Dahar", + "FINAL ANSWER: Kebri Dahar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.21555, + "lon": -88.03001, + "name": "Mequon" + }, + { + "lat": 40.09923, + "lon": -83.11408, + "name": "Dublin" + }, + { + "lat": 27.50641, + "lon": -99.50754, + "name": "Laredo" + }, + { + "lat": 35.70791, + "lon": -79.81364, + "name": "Asheboro" + }, + { + "lat": -22.7775, + "lon": -47.29583, + "name": "Nova Odessa" + } + ], + "question": "Which location is the geographic outlier among: Mequon, Dublin, Laredo, Asheboro, Nova Odessa?", + "ground_truth": { + "answer": "Nova Odessa", + "outlier_distance_km": 6327.7, + "second_furthest_km": 2194.1, + "clarity_ratio": 2.88, + "median_distance_km": 2013.3, + "distances_to_centroid": { + "Mequon": 2194.1, + "Dublin": 1738.7, + "Laredo": 2013.3, + "Asheboro": 1218.7, + "Nova Odessa": 6327.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mequon: (43.22°, -88.03°)", + " Dublin: (40.10°, -83.11°)", + " Laredo: (27.51°, -99.51°)", + " Asheboro: (35.71°, -79.81°)", + " Nova Odessa: (-22.78°, -47.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nova Odessa: 6327.7 km from centroid", + " Mequon: 2194.1 km from centroid", + " Laredo: 2013.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nova Odessa", + "FINAL ANSWER: Nova Odessa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + }, + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + { + "lat": 26.45756, + "lon": 80.77403, + "name": "Purwā" + } + ], + "question": "Which location is the geographic outlier among: Manly, Casula, Yarraville, Werribee, Purwā?", + "ground_truth": { + "answer": "Purwā", + "outlier_distance_km": 8005.6, + "second_furthest_km": 2000.6, + "clarity_ratio": 4.0, + "median_distance_km": 1979.0, + "distances_to_centroid": { + "Manly": 2000.6, + "Casula": 1979.0, + "Yarraville": 1883.4, + "Werribee": 1879.5, + "Purwā": 8005.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manly: (-33.80°, 151.29°)", + " Casula: (-33.95°, 150.90°)", + " Yarraville: (-37.82°, 144.90°)", + " Werribee: (-37.90°, 144.67°)", + " Purwā: (26.46°, 80.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Purwā: 8005.6 km from centroid", + " Manly: 2000.6 km from centroid", + " Casula: 1979.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Purwā", + "FINAL ANSWER: Purwā" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.67846, + "lon": 3.1493, + "name": "Croix" + }, + { + "lat": 28.50038, + "lon": -13.86272, + "name": "Puerto del Rosario" + }, + { + "lat": 44.93553, + "lon": 10.51898, + "name": "Viadana" + }, + { + "lat": 40.43533, + "lon": -3.6251, + "name": "Simancas" + }, + { + "lat": 45.56995, + "lon": -73.692, + "name": "Laval" + } + ], + "question": "Which location is the geographic outlier among: Croix, Puerto del Rosario, Viadana, Simancas, Laval?", + "ground_truth": { + "answer": "Laval", + "outlier_distance_km": 4583.6, + "second_furthest_km": 2115.0, + "clarity_ratio": 2.17, + "median_distance_km": 1717.3, + "distances_to_centroid": { + "Croix": 1717.3, + "Puerto del Rosario": 1511.0, + "Viadana": 2115.0, + "Simancas": 1008.0, + "Laval": 4583.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Croix: (50.68°, 3.15°)", + " Puerto del Rosario: (28.50°, -13.86°)", + " Viadana: (44.94°, 10.52°)", + " Simancas: (40.44°, -3.63°)", + " Laval: (45.57°, -73.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Laval: 4583.6 km from centroid", + " Viadana: 2115.0 km from centroid", + " Croix: 1717.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Laval", + "FINAL ANSWER: Laval" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.03333, + "lon": 145.3, + "name": "Narre Warren" + }, + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + { + "lat": -8.9475, + "lon": -37.42278, + "name": "Itaíba" + } + ], + "question": "Which location is the geographic outlier among: Narre Warren, Bexley, Granville, Ballarat, Itaíba?", + "ground_truth": { + "answer": "Itaíba", + "outlier_distance_km": 14471.3, + "second_furthest_km": 3791.4, + "clarity_ratio": 3.82, + "median_distance_km": 3782.6, + "distances_to_centroid": { + "Narre Warren": 3262.9, + "Bexley": 3791.4, + "Granville": 3782.6, + "Ballarat": 3131.7, + "Itaíba": 14471.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Narre Warren: (-38.03°, 145.30°)", + " Bexley: (-33.95°, 151.12°)", + " Granville: (-33.84°, 151.01°)", + " Ballarat: (-37.57°, 143.85°)", + " Itaíba: (-8.95°, -37.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itaíba: 14471.3 km from centroid", + " Bexley: 3791.4 km from centroid", + " Granville: 3782.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itaíba", + "FINAL ANSWER: Itaíba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.62821, + "lon": -46.45395, + "name": "Sao Rafael" + }, + { + "lat": 10.45912, + "lon": -74.8797, + "name": "Candelaria" + }, + { + "lat": -1.39028, + "lon": -48.87111, + "name": "Ponta de Pedras" + }, + { + "lat": -19.00472, + "lon": -57.60167, + "name": "Ladário" + }, + { + "lat": 25.75089, + "lon": 32.6776, + "name": "Az Zaynīyah Qiblī" + } + ], + "question": "Which location is the geographic outlier among: Sao Rafael, Candelaria, Ponta de Pedras, Ladário, Az Zaynīyah Qiblī?", + "ground_truth": { + "answer": "Az Zaynīyah Qiblī", + "outlier_distance_km": 8260.4, + "second_furthest_km": 4186.0, + "clarity_ratio": 1.97, + "median_distance_km": 2802.8, + "distances_to_centroid": { + "Sao Rafael": 2580.8, + "Candelaria": 4186.0, + "Ponta de Pedras": 1094.6, + "Ladário": 2802.8, + "Az Zaynīyah Qiblī": 8260.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sao Rafael: (-23.63°, -46.45°)", + " Candelaria: (10.46°, -74.88°)", + " Ponta de Pedras: (-1.39°, -48.87°)", + " Ladário: (-19.00°, -57.60°)", + " Az Zaynīyah Qiblī: (25.75°, 32.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Az Zaynīyah Qiblī: 8260.4 km from centroid", + " Candelaria: 4186.0 km from centroid", + " Ladário: 2802.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Az Zaynīyah Qiblī", + "FINAL ANSWER: Az Zaynīyah Qiblī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": 32.74596, + "lon": -96.99778, + "name": "Grand Prairie" + } + ], + "question": "Which location is the geographic outlier among: Busselton, Footscray, Maitland, Mount Martha, Grand Prairie?", + "ground_truth": { + "answer": "Grand Prairie", + "outlier_distance_km": 18524.3, + "second_furthest_km": 5931.9, + "clarity_ratio": 3.12, + "median_distance_km": 5337.1, + "distances_to_centroid": { + "Busselton": 2633.4, + "Footscray": 5323.4, + "Maitland": 5931.9, + "Mount Martha": 5337.1, + "Grand Prairie": 18524.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Busselton: (-33.65°, 115.35°)", + " Footscray: (-37.80°, 144.90°)", + " Maitland: (-32.73°, 151.56°)", + " Mount Martha: (-38.27°, 145.02°)", + " Grand Prairie: (32.75°, -97.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Grand Prairie: 18524.3 km from centroid", + " Maitland: 5931.9 km from centroid", + " Mount Martha: 5337.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Grand Prairie", + "FINAL ANSWER: Grand Prairie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.73933, + "lon": 78.59784, + "name": "Wardha" + }, + { + "lat": 30.10778, + "lon": 78.29255, + "name": "Rishīkesh" + }, + { + "lat": 28.38812, + "lon": 104.56339, + "name": "Wenjiang" + }, + { + "lat": 31.48621, + "lon": 131.2421, + "name": "Kushima" + }, + { + "lat": 22.89088, + "lon": -109.91238, + "name": "Cabo San Lucas" + } + ], + "question": "Which location is the geographic outlier among: Wardha, Rishīkesh, Wenjiang, Kushima, Cabo San Lucas?", + "ground_truth": { + "answer": "Cabo San Lucas", + "outlier_distance_km": 14309.6, + "second_furthest_km": 7133.0, + "clarity_ratio": 2.01, + "median_distance_km": 4704.6, + "distances_to_centroid": { + "Wardha": 2336.5, + "Rishīkesh": 2155.4, + "Wenjiang": 4704.6, + "Kushima": 7133.0, + "Cabo San Lucas": 14309.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wardha: (20.74°, 78.60°)", + " Rishīkesh: (30.11°, 78.29°)", + " Wenjiang: (28.39°, 104.56°)", + " Kushima: (31.49°, 131.24°)", + " Cabo San Lucas: (22.89°, -109.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cabo San Lucas: 14309.6 km from centroid", + " Kushima: 7133.0 km from centroid", + " Wenjiang: 4704.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cabo San Lucas", + "FINAL ANSWER: Cabo San Lucas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.59407, + "lon": 9.47302, + "name": "Hansestadt Stade" + }, + { + "lat": 39.4696, + "lon": 3.14831, + "name": "Felanitx" + }, + { + "lat": 42.92779, + "lon": 10.76451, + "name": "Follonica" + }, + { + "lat": 51.21006, + "lon": 16.1619, + "name": "Legnica" + }, + { + "lat": -26.26781, + "lon": 27.85849, + "name": "Soweto" + } + ], + "question": "Which location is the geographic outlier among: Hansestadt Stade, Felanitx, Follonica, Legnica, Soweto?", + "ground_truth": { + "answer": "Soweto", + "outlier_distance_km": 6676.1, + "second_furthest_km": 2401.7, + "clarity_ratio": 2.78, + "median_distance_km": 2126.6, + "distances_to_centroid": { + "Hansestadt Stade": 2401.7, + "Felanitx": 1232.8, + "Follonica": 1217.9, + "Legnica": 2126.6, + "Soweto": 6676.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hansestadt Stade: (53.59°, 9.47°)", + " Felanitx: (39.47°, 3.15°)", + " Follonica: (42.93°, 10.76°)", + " Legnica: (51.21°, 16.16°)", + " Soweto: (-26.27°, 27.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Soweto: 6676.1 km from centroid", + " Hansestadt Stade: 2401.7 km from centroid", + " Legnica: 2126.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Soweto", + "FINAL ANSWER: Soweto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.16031, + "lon": 10.79784, + "name": "Mantova" + }, + { + "lat": 45.65192, + "lon": 10.25681, + "name": "San Sebastiano" + }, + { + "lat": 41.35353, + "lon": -1.64318, + "name": "Calatayud" + }, + { + "lat": 51.59638, + "lon": 7.14387, + "name": "Herten" + }, + { + "lat": 30.53629, + "lon": 120.68638, + "name": "Haining" + } + ], + "question": "Which location is the geographic outlier among: Mantova, San Sebastiano, Calatayud, Herten, Haining?", + "ground_truth": { + "answer": "Haining", + "outlier_distance_km": 7851.7, + "second_furthest_km": 2555.8, + "clarity_ratio": 3.07, + "median_distance_km": 1932.9, + "distances_to_centroid": { + "Mantova": 1509.8, + "San Sebastiano": 1555.7, + "Calatayud": 2555.8, + "Herten": 1932.9, + "Haining": 7851.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mantova: (45.16°, 10.80°)", + " San Sebastiano: (45.65°, 10.26°)", + " Calatayud: (41.35°, -1.64°)", + " Herten: (51.60°, 7.14°)", + " Haining: (30.54°, 120.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Haining: 7851.7 km from centroid", + " Calatayud: 2555.8 km from centroid", + " Herten: 1932.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Haining", + "FINAL ANSWER: Haining" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -43.58333, + "lon": 172.38333, + "name": "Rolleston" + }, + { + "lat": 28.15585, + "lon": -82.62121, + "name": "Keystone" + } + ], + "question": "Which location is the geographic outlier among: Perth, Launceston, Highton, Rolleston, Keystone?", + "ground_truth": { + "answer": "Keystone", + "outlier_distance_km": 19647.9, + "second_furthest_km": 6764.4, + "clarity_ratio": 2.9, + "median_distance_km": 4705.3, + "distances_to_centroid": { + "Perth": 1759.7, + "Launceston": 4705.3, + "Highton": 4427.0, + "Rolleston": 6764.4, + "Keystone": 19647.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Perth: (-31.95°, 115.86°)", + " Launceston: (-41.44°, 147.13°)", + " Highton: (-38.17°, 144.31°)", + " Rolleston: (-43.58°, 172.38°)", + " Keystone: (28.16°, -82.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Keystone: 19647.9 km from centroid", + " Rolleston: 6764.4 km from centroid", + " Launceston: 4705.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Keystone", + "FINAL ANSWER: Keystone" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.87363, + "lon": 14.34085, + "name": "Volla" + }, + { + "lat": 52.69583, + "lon": 6.19444, + "name": "Meppel" + }, + { + "lat": 55.80966, + "lon": -4.16096, + "name": "Cambuslang" + }, + { + "lat": 45.59665, + "lon": 9.88688, + "name": "Palazzolo sull'Oglio" + }, + { + "lat": -33.86482, + "lon": 151.20773, + "name": "Sydney Central Business District" + } + ], + "question": "Which location is the geographic outlier among: Volla, Meppel, Cambuslang, Palazzolo sull'Oglio, Sydney Central Business District?", + "ground_truth": { + "answer": "Sydney Central Business District", + "outlier_distance_km": 14122.5, + "second_furthest_km": 4024.1, + "clarity_ratio": 3.51, + "median_distance_km": 3268.7, + "distances_to_centroid": { + "Volla": 2112.7, + "Meppel": 3268.7, + "Cambuslang": 4024.1, + "Palazzolo sull'Oglio": 2649.9, + "Sydney Central Business District": 14122.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Volla: (40.87°, 14.34°)", + " Meppel: (52.70°, 6.19°)", + " Cambuslang: (55.81°, -4.16°)", + " Palazzolo sull'Oglio: (45.60°, 9.89°)", + " Sydney Central Business District: (-33.86°, 151.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sydney Central Business District: 14122.5 km from centroid", + " Cambuslang: 4024.1 km from centroid", + " Meppel: 3268.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sydney Central Business District", + "FINAL ANSWER: Sydney Central Business District" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.30297, + "lon": -90.97205, + "name": "Prairieville" + }, + { + "lat": 40.3359, + "lon": -80.08339, + "name": "Upper Saint Clair" + }, + { + "lat": 40.68927, + "lon": -73.85791, + "name": "Woodhaven" + }, + { + "lat": 19.44204, + "lon": -98.10325, + "name": "Tetla" + }, + { + "lat": -33.73333, + "lon": 150.88333, + "name": "Quakers Hill" + } + ], + "question": "Which location is the geographic outlier among: Prairieville, Upper Saint Clair, Woodhaven, Tetla, Quakers Hill?", + "ground_truth": { + "answer": "Quakers Hill", + "outlier_distance_km": 18174.8, + "second_furthest_km": 6223.5, + "clarity_ratio": 2.92, + "median_distance_km": 5390.8, + "distances_to_centroid": { + "Prairieville": 5390.8, + "Upper Saint Clair": 4583.0, + "Woodhaven": 4106.5, + "Tetla": 6223.5, + "Quakers Hill": 18174.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Prairieville: (30.30°, -90.97°)", + " Upper Saint Clair: (40.34°, -80.08°)", + " Woodhaven: (40.69°, -73.86°)", + " Tetla: (19.44°, -98.10°)", + " Quakers Hill: (-33.73°, 150.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Quakers Hill: 18174.8 km from centroid", + " Tetla: 6223.5 km from centroid", + " Prairieville: 5390.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Quakers Hill", + "FINAL ANSWER: Quakers Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.55778, + "lon": -81.4534, + "name": "Pine Hills" + }, + { + "lat": 30.57881, + "lon": -97.85307, + "name": "Leander" + }, + { + "lat": 33.44872, + "lon": -86.78777, + "name": "Vestavia Hills" + }, + { + "lat": 20.50038, + "lon": -86.94272, + "name": "Cozumel" + }, + { + "lat": 10.99544, + "lon": 77.09904, + "name": "Kannampālaiyam" + } + ], + "question": "Which location is the geographic outlier among: Pine Hills, Leander, Vestavia Hills, Cozumel, Kannampālaiyam?", + "ground_truth": { + "answer": "Kannampālaiyam", + "outlier_distance_km": 13487.4, + "second_furthest_km": 4224.3, + "clarity_ratio": 3.19, + "median_distance_km": 3286.2, + "distances_to_centroid": { + "Pine Hills": 2637.0, + "Leander": 4224.3, + "Vestavia Hills": 3201.5, + "Cozumel": 3286.2, + "Kannampālaiyam": 13487.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pine Hills: (28.56°, -81.45°)", + " Leander: (30.58°, -97.85°)", + " Vestavia Hills: (33.45°, -86.79°)", + " Cozumel: (20.50°, -86.94°)", + " Kannampālaiyam: (11.00°, 77.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kannampālaiyam: 13487.4 km from centroid", + " Leander: 4224.3 km from centroid", + " Cozumel: 3286.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kannampālaiyam", + "FINAL ANSWER: Kannampālaiyam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.76259, + "lon": 85.97319, + "name": "Karanjiā" + }, + { + "lat": 22.99138, + "lon": 79.8755, + "name": "Bargi" + }, + { + "lat": 29.70226, + "lon": 105.72363, + "name": "Tangxiang" + }, + { + "lat": 16.0111, + "lon": 120.36, + "name": "Calasiao" + }, + { + "lat": 8.23773, + "lon": -73.35604, + "name": "Ocaña" + } + ], + "question": "Which location is the geographic outlier among: Karanjiā, Bargi, Tangxiang, Calasiao, Ocaña?", + "ground_truth": { + "answer": "Ocaña", + "outlier_distance_km": 14379.8, + "second_furthest_km": 5982.3, + "clarity_ratio": 2.4, + "median_distance_km": 4359.8, + "distances_to_centroid": { + "Karanjiā": 2323.3, + "Bargi": 1711.0, + "Tangxiang": 4359.8, + "Calasiao": 5982.3, + "Ocaña": 14379.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Karanjiā: (21.76°, 85.97°)", + " Bargi: (22.99°, 79.88°)", + " Tangxiang: (29.70°, 105.72°)", + " Calasiao: (16.01°, 120.36°)", + " Ocaña: (8.24°, -73.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ocaña: 14379.8 km from centroid", + " Calasiao: 5982.3 km from centroid", + " Tangxiang: 4359.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ocaña", + "FINAL ANSWER: Ocaña" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.10267, + "lon": 108.66565, + "name": "Basuo" + }, + { + "lat": 34.88083, + "lon": 105.27639, + "name": "Anyuan" + }, + { + "lat": 28.23995, + "lon": 78.43994, + "name": "Gunnaur" + }, + { + "lat": 22.38185, + "lon": 71.98664, + "name": "Dhandhuka" + }, + { + "lat": -23.59957, + "lon": -46.61599, + "name": "Ipiranga" + } + ], + "question": "Which location is the geographic outlier among: Basuo, Anyuan, Gunnaur, Dhandhuka, Ipiranga?", + "ground_truth": { + "answer": "Ipiranga", + "outlier_distance_km": 12734.5, + "second_furthest_km": 4778.6, + "clarity_ratio": 2.66, + "median_distance_km": 4628.6, + "distances_to_centroid": { + "Basuo": 4778.6, + "Anyuan": 4628.6, + "Gunnaur": 2031.3, + "Dhandhuka": 1120.3, + "Ipiranga": 12734.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Basuo: (19.10°, 108.67°)", + " Anyuan: (34.88°, 105.28°)", + " Gunnaur: (28.24°, 78.44°)", + " Dhandhuka: (22.38°, 71.99°)", + " Ipiranga: (-23.60°, -46.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ipiranga: 12734.5 km from centroid", + " Basuo: 4778.6 km from centroid", + " Anyuan: 4628.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ipiranga", + "FINAL ANSWER: Ipiranga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": 60.017, + "lon": 30.417, + "name": "Grazhdanka" + } + ], + "question": "Which location is the geographic outlier among: Rockingham, Lara, Helensvale, Wollongong, Grazhdanka?", + "ground_truth": { + "answer": "Grazhdanka", + "outlier_distance_km": 11322.3, + "second_furthest_km": 3888.8, + "clarity_ratio": 2.91, + "median_distance_km": 3844.3, + "distances_to_centroid": { + "Rockingham": 2000.8, + "Lara": 3617.7, + "Helensvale": 3844.3, + "Wollongong": 3888.8, + "Grazhdanka": 11322.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rockingham: (-32.28°, 115.73°)", + " Lara: (-38.02°, 144.41°)", + " Helensvale: (-27.92°, 153.33°)", + " Wollongong: (-34.42°, 150.89°)", + " Grazhdanka: (60.02°, 30.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Grazhdanka: 11322.3 km from centroid", + " Wollongong: 3888.8 km from centroid", + " Helensvale: 3844.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Grazhdanka", + "FINAL ANSWER: Grazhdanka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + }, + { + "lat": -37.80639, + "lon": 145.03086, + "name": "Kew" + }, + { + "lat": -2.13389, + "lon": -47.55889, + "name": "Aurora do Pará" + } + ], + "question": "Which location is the geographic outlier among: Robina, Timaru, Paraparaumu, Kew, Aurora do Pará?", + "ground_truth": { + "answer": "Aurora do Pará", + "outlier_distance_km": 16116.0, + "second_furthest_km": 5055.3, + "clarity_ratio": 3.19, + "median_distance_km": 4731.5, + "distances_to_centroid": { + "Robina": 3291.7, + "Timaru": 4731.5, + "Paraparaumu": 5055.3, + "Kew": 2474.6, + "Aurora do Pará": 16116.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Timaru: (-44.40°, 171.25°)", + " Paraparaumu: (-40.92°, 175.02°)", + " Kew: (-37.81°, 145.03°)", + " Aurora do Pará: (-2.13°, -47.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aurora do Pará: 16116.0 km from centroid", + " Paraparaumu: 5055.3 km from centroid", + " Timaru: 4731.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aurora do Pará", + "FINAL ANSWER: Aurora do Pará" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.82483, + "lon": 93.77592, + "name": "Chumukedima" + }, + { + "lat": 22.46787, + "lon": 88.14524, + "name": "Pujali" + }, + { + "lat": 25.5637, + "lon": 91.9064, + "name": "Nongthymmai" + }, + { + "lat": 30.52956, + "lon": 107.48102, + "name": "Huilong" + }, + { + "lat": 39.46569, + "lon": -0.46005, + "name": "Aldaia" + } + ], + "question": "Which location is the geographic outlier among: Chumukedima, Pujali, Nongthymmai, Huilong, Aldaia?", + "ground_truth": { + "answer": "Aldaia", + "outlier_distance_km": 6945.0, + "second_furthest_km": 3022.5, + "clarity_ratio": 2.3, + "median_distance_km": 1768.5, + "distances_to_centroid": { + "Chumukedima": 1768.5, + "Pujali": 1389.0, + "Nongthymmai": 1595.8, + "Huilong": 3022.5, + "Aldaia": 6945.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chumukedima: (25.82°, 93.78°)", + " Pujali: (22.47°, 88.15°)", + " Nongthymmai: (25.56°, 91.91°)", + " Huilong: (30.53°, 107.48°)", + " Aldaia: (39.47°, -0.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aldaia: 6945.0 km from centroid", + " Huilong: 3022.5 km from centroid", + " Chumukedima: 1768.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aldaia", + "FINAL ANSWER: Aldaia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.30482, + "lon": -8.50749, + "name": "Arteixo" + }, + { + "lat": 42.69764, + "lon": 2.89541, + "name": "Perpignan" + }, + { + "lat": 45.74742, + "lon": -0.63489, + "name": "Saintes" + }, + { + "lat": 49.04, + "lon": 3.95922, + "name": "Épernay" + }, + { + "lat": -30.94432, + "lon": -59.78832, + "name": "Santa Elena" + } + ], + "question": "Which location is the geographic outlier among: Arteixo, Perpignan, Saintes, Épernay, Santa Elena?", + "ground_truth": { + "answer": "Santa Elena", + "outlier_distance_km": 8422.0, + "second_furthest_km": 2531.7, + "clarity_ratio": 3.33, + "median_distance_km": 2031.6, + "distances_to_centroid": { + "Arteixo": 1522.8, + "Perpignan": 1964.7, + "Saintes": 2031.6, + "Épernay": 2531.7, + "Santa Elena": 8422.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arteixo: (43.30°, -8.51°)", + " Perpignan: (42.70°, 2.90°)", + " Saintes: (45.75°, -0.63°)", + " Épernay: (49.04°, 3.96°)", + " Santa Elena: (-30.94°, -59.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Elena: 8422.0 km from centroid", + " Épernay: 2531.7 km from centroid", + " Saintes: 2031.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Elena", + "FINAL ANSWER: Santa Elena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.41889, + "lon": -48.15222, + "name": "Tomé-Açu" + }, + { + "lat": -16.44972, + "lon": -39.06472, + "name": "Porto Seguro" + }, + { + "lat": -22.50972, + "lon": -47.77806, + "name": "Charqueada" + }, + { + "lat": -4.02694, + "lon": -38.305, + "name": "Pindoretama" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + } + ], + "question": "Which location is the geographic outlier among: Tomé-Açu, Porto Seguro, Charqueada, Pindoretama, Engadine?", + "ground_truth": { + "answer": "Engadine", + "outlier_distance_km": 13882.6, + "second_furthest_km": 5010.8, + "clarity_ratio": 2.77, + "median_distance_km": 4592.5, + "distances_to_centroid": { + "Tomé-Açu": 5010.8, + "Porto Seguro": 3691.9, + "Charqueada": 4592.5, + "Pindoretama": 3926.4, + "Engadine": 13882.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tomé-Açu: (-2.42°, -48.15°)", + " Porto Seguro: (-16.45°, -39.06°)", + " Charqueada: (-22.51°, -47.78°)", + " Pindoretama: (-4.03°, -38.30°)", + " Engadine: (-34.07°, 151.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Engadine: 13882.6 km from centroid", + " Tomé-Açu: 5010.8 km from centroid", + " Charqueada: 4592.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Engadine", + "FINAL ANSWER: Engadine" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.29389, + "lon": -47.92639, + "name": "Castanhal" + }, + { + "lat": -22.87278, + "lon": -42.34306, + "name": "Araruama" + }, + { + "lat": -9.50194, + "lon": -36.02278, + "name": "Atalaia" + }, + { + "lat": -12.05, + "lon": -38.76667, + "name": "Irará" + }, + { + "lat": 13.56083, + "lon": 38.97389, + "name": "Ābīy Ādī" + } + ], + "question": "Which location is the geographic outlier among: Castanhal, Araruama, Atalaia, Irará, Ābīy Ādī?", + "ground_truth": { + "answer": "Ābīy Ādī", + "outlier_distance_km": 7425.3, + "second_furthest_km": 2589.8, + "clarity_ratio": 2.87, + "median_distance_km": 2582.5, + "distances_to_centroid": { + "Castanhal": 2582.5, + "Araruama": 2589.8, + "Atalaia": 1237.8, + "Irará": 1612.3, + "Ābīy Ādī": 7425.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Castanhal: (-1.29°, -47.93°)", + " Araruama: (-22.87°, -42.34°)", + " Atalaia: (-9.50°, -36.02°)", + " Irará: (-12.05°, -38.77°)", + " Ābīy Ādī: (13.56°, 38.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ābīy Ādī: 7425.3 km from centroid", + " Araruama: 2589.8 km from centroid", + " Castanhal: 2582.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ābīy Ādī", + "FINAL ANSWER: Ābīy Ādī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.8327, + "lon": 5.7934, + "name": "Lindenholt" + }, + { + "lat": 52.13012, + "lon": 21.08148, + "name": "Kabaty" + }, + { + "lat": 64.5461, + "lon": 40.55183, + "name": "Arkhangel’sk" + }, + { + "lat": 51.48165, + "lon": 7.21648, + "name": "Bochum" + }, + { + "lat": 40.85843, + "lon": -74.16376, + "name": "Clifton" + } + ], + "question": "Which location is the geographic outlier among: Lindenholt, Kabaty, Arkhangel’sk, Bochum, Clifton?", + "ground_truth": { + "answer": "Clifton", + "outlier_distance_km": 5561.8, + "second_furthest_km": 2665.7, + "clarity_ratio": 2.09, + "median_distance_km": 1426.8, + "distances_to_centroid": { + "Lindenholt": 391.7, + "Kabaty": 1426.8, + "Arkhangel’sk": 2665.7, + "Bochum": 495.1, + "Clifton": 5561.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lindenholt: (51.83°, 5.79°)", + " Kabaty: (52.13°, 21.08°)", + " Arkhangel’sk: (64.55°, 40.55°)", + " Bochum: (51.48°, 7.22°)", + " Clifton: (40.86°, -74.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clifton: 5561.8 km from centroid", + " Arkhangel’sk: 2665.7 km from centroid", + " Kabaty: 1426.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clifton", + "FINAL ANSWER: Clifton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.90015, + "lon": -76.99587, + "name": "H Street NE" + }, + { + "lat": 48.46686, + "lon": -81.33312, + "name": "Timmins" + }, + { + "lat": 45.56667, + "lon": -73.66667, + "name": "Ahuntsic-Cartierville" + }, + { + "lat": 43.7068, + "lon": -79.31223, + "name": "O'Connor-Parkview" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + } + ], + "question": "Which location is the geographic outlier among: H Street NE, Timmins, Ahuntsic-Cartierville, O'Connor-Parkview, Townsville?", + "ground_truth": { + "answer": "Townsville", + "outlier_distance_km": 18657.3, + "second_furthest_km": 4447.7, + "clarity_ratio": 4.19, + "median_distance_km": 4247.7, + "distances_to_centroid": { + "H Street NE": 4051.1, + "Timmins": 4447.7, + "Ahuntsic-Cartierville": 3825.9, + "O'Connor-Parkview": 4247.7, + "Townsville": 18657.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " H Street NE: (38.90°, -77.00°)", + " Timmins: (48.47°, -81.33°)", + " Ahuntsic-Cartierville: (45.57°, -73.67°)", + " O'Connor-Parkview: (43.71°, -79.31°)", + " Townsville: (-19.27°, 146.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Townsville: 18657.3 km from centroid", + " Timmins: 4447.7 km from centroid", + " O'Connor-Parkview: 4247.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Townsville", + "FINAL ANSWER: Townsville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.58106, + "lon": -111.85077, + "name": "Sandy Hills" + }, + { + "lat": 41.8317, + "lon": -87.67366, + "name": "McKinley Park" + }, + { + "lat": 35.9987, + "lon": -96.11417, + "name": "Sapulpa" + }, + { + "lat": 32.487, + "lon": -114.78218, + "name": "San Luis" + }, + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + } + ], + "question": "Which location is the geographic outlier among: Sandy Hills, McKinley Park, Sapulpa, San Luis, Bexley?", + "ground_truth": { + "answer": "Bexley", + "outlier_distance_km": 17492.9, + "second_furthest_km": 6177.2, + "clarity_ratio": 2.83, + "median_distance_km": 5852.7, + "distances_to_centroid": { + "Sandy Hills": 5852.7, + "McKinley Park": 3889.7, + "Sapulpa": 4456.2, + "San Luis": 6177.2, + "Bexley": 17492.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sandy Hills: (40.58°, -111.85°)", + " McKinley Park: (41.83°, -87.67°)", + " Sapulpa: (36.00°, -96.11°)", + " San Luis: (32.49°, -114.78°)", + " Bexley: (-33.95°, 151.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bexley: 17492.9 km from centroid", + " San Luis: 6177.2 km from centroid", + " Sandy Hills: 5852.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bexley", + "FINAL ANSWER: Bexley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.56554, + "lon": 133.70284, + "name": "Yamashita" + }, + { + "lat": 10.99223, + "lon": 76.46418, + "name": "Mannārakkāt" + }, + { + "lat": 27.95999, + "lon": 116.33333, + "name": "Fuzhou" + }, + { + "lat": 36.31667, + "lon": 138.43333, + "name": "Komoro" + }, + { + "lat": -23.44361, + "lon": -51.87389, + "name": "Sarandi" + } + ], + "question": "Which location is the geographic outlier among: Yamashita, Mannārakkāt, Fuzhou, Komoro, Sarandi?", + "ground_truth": { + "answer": "Sarandi", + "outlier_distance_km": 15233.9, + "second_furthest_km": 5854.9, + "clarity_ratio": 2.6, + "median_distance_km": 5392.7, + "distances_to_centroid": { + "Yamashita": 5392.7, + "Mannārakkāt": 947.2, + "Fuzhou": 3654.3, + "Komoro": 5854.9, + "Sarandi": 15233.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yamashita: (33.57°, 133.70°)", + " Mannārakkāt: (10.99°, 76.46°)", + " Fuzhou: (27.96°, 116.33°)", + " Komoro: (36.32°, 138.43°)", + " Sarandi: (-23.44°, -51.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sarandi: 15233.9 km from centroid", + " Komoro: 5854.9 km from centroid", + " Yamashita: 5392.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sarandi", + "FINAL ANSWER: Sarandi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.67031, + "lon": 31.86288, + "name": "Kamaqhekeza" + }, + { + "lat": 8.61565, + "lon": 6.4185, + "name": "Baro" + }, + { + "lat": -26.08577, + "lon": 27.77515, + "name": "Krugersdorp" + }, + { + "lat": -24.78864, + "lon": 31.07938, + "name": "Mafemani" + }, + { + "lat": -14.61222, + "lon": -41.13556, + "name": "Anagé" + } + ], + "question": "Which location is the geographic outlier among: Kamaqhekeza, Baro, Krugersdorp, Mafemani, Anagé?", + "ground_truth": { + "answer": "Anagé", + "outlier_distance_km": 5594.6, + "second_furthest_km": 2842.8, + "clarity_ratio": 1.97, + "median_distance_km": 2369.1, + "distances_to_centroid": { + "Kamaqhekeza": 2369.1, + "Baro": 2842.8, + "Krugersdorp": 2017.5, + "Mafemani": 2260.6, + "Anagé": 5594.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kamaqhekeza: (-25.67°, 31.86°)", + " Baro: (8.62°, 6.42°)", + " Krugersdorp: (-26.09°, 27.78°)", + " Mafemani: (-24.79°, 31.08°)", + " Anagé: (-14.61°, -41.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Anagé: 5594.6 km from centroid", + " Baro: 2842.8 km from centroid", + " Kamaqhekeza: 2369.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Anagé", + "FINAL ANSWER: Anagé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.3547, + "lon": 38.67465, + "name": "Arsi Negele" + }, + { + "lat": -26.84493, + "lon": 26.76829, + "name": "Stilfontein" + }, + { + "lat": -25.7287, + "lon": 27.87, + "name": "Hartbeespoort" + }, + { + "lat": -25.11319, + "lon": 29.04454, + "name": "Siyabuswa" + }, + { + "lat": 41.80114, + "lon": -88.07479, + "name": "Lisle" + } + ], + "question": "Which location is the geographic outlier among: Arsi Negele, Stilfontein, Hartbeespoort, Siyabuswa, Lisle?", + "ground_truth": { + "answer": "Lisle", + "outlier_distance_km": 10838.4, + "second_furthest_km": 3817.0, + "clarity_ratio": 2.84, + "median_distance_km": 3200.3, + "distances_to_centroid": { + "Arsi Negele": 3817.0, + "Stilfontein": 3158.1, + "Hartbeespoort": 3154.0, + "Siyabuswa": 3200.3, + "Lisle": 10838.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arsi Negele: (7.35°, 38.67°)", + " Stilfontein: (-26.84°, 26.77°)", + " Hartbeespoort: (-25.73°, 27.87°)", + " Siyabuswa: (-25.11°, 29.04°)", + " Lisle: (41.80°, -88.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lisle: 10838.4 km from centroid", + " Arsi Negele: 3817.0 km from centroid", + " Siyabuswa: 3200.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lisle", + "FINAL ANSWER: Lisle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.99997, + "lon": 108.30463, + "name": "Changsha" + }, + { + "lat": 35.38333, + "lon": 136.26667, + "name": "Nagahama" + }, + { + "lat": 11.58528, + "lon": 122.75111, + "name": "Roxas City" + }, + { + "lat": 16.61667, + "lon": 74.40442, + "name": "Hupari" + }, + { + "lat": 19.36357, + "lon": -98.97707, + "name": "Los Reyes Acaquilpan" + } + ], + "question": "Which location is the geographic outlier among: Changsha, Nagahama, Roxas City, Hupari, Los Reyes Acaquilpan?", + "ground_truth": { + "answer": "Los Reyes Acaquilpan", + "outlier_distance_km": 15136.1, + "second_furthest_km": 6603.0, + "clarity_ratio": 2.29, + "median_distance_km": 5859.2, + "distances_to_centroid": { + "Changsha": 4024.4, + "Nagahama": 6603.0, + "Roxas City": 5859.2, + "Hupari": 919.9, + "Los Reyes Acaquilpan": 15136.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Changsha: (31.00°, 108.30°)", + " Nagahama: (35.38°, 136.27°)", + " Roxas City: (11.59°, 122.75°)", + " Hupari: (16.62°, 74.40°)", + " Los Reyes Acaquilpan: (19.36°, -98.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Los Reyes Acaquilpan: 15136.1 km from centroid", + " Nagahama: 6603.0 km from centroid", + " Roxas City: 5859.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Los Reyes Acaquilpan", + "FINAL ANSWER: Los Reyes Acaquilpan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.76481, + "lon": -79.45606, + "name": "Bathurst Manor" + }, + { + "lat": 36.87672, + "lon": -89.58786, + "name": "Sikeston" + }, + { + "lat": 43.23418, + "lon": -86.24839, + "name": "Muskegon" + }, + { + "lat": 43.64506, + "lon": -79.46787, + "name": "High Park-Swansea" + }, + { + "lat": -4.83389, + "lon": -37.78111, + "name": "Jaguaruana" + } + ], + "question": "Which location is the geographic outlier among: Bathurst Manor, Sikeston, Muskegon, High Park-Swansea, Jaguaruana?", + "ground_truth": { + "answer": "Jaguaruana", + "outlier_distance_km": 5682.1, + "second_furthest_km": 1570.4, + "clarity_ratio": 3.62, + "median_distance_km": 1458.5, + "distances_to_centroid": { + "Bathurst Manor": 1320.6, + "Sikeston": 1458.5, + "Muskegon": 1570.4, + "High Park-Swansea": 1308.5, + "Jaguaruana": 5682.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bathurst Manor: (43.76°, -79.46°)", + " Sikeston: (36.88°, -89.59°)", + " Muskegon: (43.23°, -86.25°)", + " High Park-Swansea: (43.65°, -79.47°)", + " Jaguaruana: (-4.83°, -37.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaguaruana: 5682.1 km from centroid", + " Muskegon: 1570.4 km from centroid", + " Sikeston: 1458.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaguaruana", + "FINAL ANSWER: Jaguaruana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.85862, + "lon": -1.57408, + "name": "Chester-le-Street" + }, + { + "lat": 53.55, + "lon": -2.3, + "name": "Whitefield" + }, + { + "lat": 49.00875, + "lon": 2.39819, + "name": "Villiers-le-Bel" + }, + { + "lat": 53.35753, + "lon": 10.21282, + "name": "Winsen" + }, + { + "lat": 4.53656, + "lon": -75.67263, + "name": "Armenia" + } + ], + "question": "Which location is the geographic outlier among: Chester-le-Street, Whitefield, Villiers-le-Bel, Winsen, Armenia?", + "ground_truth": { + "answer": "Armenia", + "outlier_distance_km": 7436.3, + "second_furthest_km": 2075.0, + "clarity_ratio": 3.58, + "median_distance_km": 1565.2, + "distances_to_centroid": { + "Chester-le-Street": 1565.2, + "Whitefield": 1422.1, + "Villiers-le-Bel": 1382.6, + "Winsen": 2075.0, + "Armenia": 7436.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chester-le-Street: (54.86°, -1.57°)", + " Whitefield: (53.55°, -2.30°)", + " Villiers-le-Bel: (49.01°, 2.40°)", + " Winsen: (53.36°, 10.21°)", + " Armenia: (4.54°, -75.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Armenia: 7436.3 km from centroid", + " Winsen: 2075.0 km from centroid", + " Chester-le-Street: 1565.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Armenia", + "FINAL ANSWER: Armenia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.96502, + "lon": -75.96541, + "name": "Salgar" + }, + { + "lat": -36.61756, + "lon": -72.95593, + "name": "Tomé" + }, + { + "lat": 5.0668, + "lon": -75.50684, + "name": "Manizales" + }, + { + "lat": -18.77861, + "lon": -46.4075, + "name": "Lagoa Formosa" + }, + { + "lat": 54.60638, + "lon": 53.71179, + "name": "Tuymazy" + } + ], + "question": "Which location is the geographic outlier among: Salgar, Tomé, Manizales, Lagoa Formosa, Tuymazy?", + "ground_truth": { + "answer": "Tuymazy", + "outlier_distance_km": 10280.1, + "second_furthest_km": 5273.1, + "clarity_ratio": 1.95, + "median_distance_km": 3634.7, + "distances_to_centroid": { + "Salgar": 3634.7, + "Tomé": 5273.1, + "Manizales": 3575.7, + "Lagoa Formosa": 2338.7, + "Tuymazy": 10280.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Salgar: (5.97°, -75.97°)", + " Tomé: (-36.62°, -72.96°)", + " Manizales: (5.07°, -75.51°)", + " Lagoa Formosa: (-18.78°, -46.41°)", + " Tuymazy: (54.61°, 53.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tuymazy: 10280.1 km from centroid", + " Tomé: 5273.1 km from centroid", + " Salgar: 3634.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tuymazy", + "FINAL ANSWER: Tuymazy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.60592, + "lon": 103.12081, + "name": "Prakhon Chai" + }, + { + "lat": 28.65195, + "lon": 77.23149, + "name": "Delhi" + }, + { + "lat": 9.94719, + "lon": 106.34225, + "name": "Thành phố Trà Vinh" + }, + { + "lat": 11.10483, + "lon": 75.93269, + "name": "Peruvallur" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + } + ], + "question": "Which location is the geographic outlier among: Prakhon Chai, Delhi, Thành phố Trà Vinh, Peruvallur, Lincoln?", + "ground_truth": { + "answer": "Lincoln", + "outlier_distance_km": 8387.0, + "second_furthest_km": 4092.3, + "clarity_ratio": 2.05, + "median_distance_km": 3521.2, + "distances_to_centroid": { + "Prakhon Chai": 1118.7, + "Delhi": 4092.3, + "Thành phố Trà Vinh": 510.4, + "Peruvallur": 3521.2, + "Lincoln": 8387.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Prakhon Chai: (14.61°, 103.12°)", + " Delhi: (28.65°, 77.23°)", + " Thành phố Trà Vinh: (9.95°, 106.34°)", + " Peruvallur: (11.10°, 75.93°)", + " Lincoln: (-36.86°, 174.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lincoln: 8387.0 km from centroid", + " Delhi: 4092.3 km from centroid", + " Peruvallur: 3521.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lincoln", + "FINAL ANSWER: Lincoln" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.01809, + "lon": -40.5373, + "name": "São Gabriel da Palha" + }, + { + "lat": -15.61532, + "lon": -43.59187, + "name": "Barreiro do Jaíba" + }, + { + "lat": -26.34067, + "lon": -60.43207, + "name": "Tres Isletas" + }, + { + "lat": -21.19361, + "lon": -48.16389, + "name": "Barrinha" + }, + { + "lat": 35.99971, + "lon": 139.62486, + "name": "Shinden" + } + ], + "question": "Which location is the geographic outlier among: São Gabriel da Palha, Barreiro do Jaíba, Tres Isletas, Barrinha, Shinden?", + "ground_truth": { + "answer": "Shinden", + "outlier_distance_km": 15785.1, + "second_furthest_km": 5566.3, + "clarity_ratio": 2.84, + "median_distance_km": 4228.7, + "distances_to_centroid": { + "São Gabriel da Palha": 3398.0, + "Barreiro do Jaíba": 3645.7, + "Tres Isletas": 5566.3, + "Barrinha": 4228.7, + "Shinden": 15785.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Gabriel da Palha: (-19.02°, -40.54°)", + " Barreiro do Jaíba: (-15.62°, -43.59°)", + " Tres Isletas: (-26.34°, -60.43°)", + " Barrinha: (-21.19°, -48.16°)", + " Shinden: (36.00°, 139.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shinden: 15785.1 km from centroid", + " Tres Isletas: 5566.3 km from centroid", + " Barrinha: 4228.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shinden", + "FINAL ANSWER: Shinden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.66401, + "lon": -4.56139, + "name": "Alhaurín de la Torre" + }, + { + "lat": 55.73423, + "lon": 37.82616, + "name": "Kuskovo" + }, + { + "lat": 49.2855, + "lon": 6.88723, + "name": "Püttlingen" + }, + { + "lat": 53.15145, + "lon": 16.73782, + "name": "Piła" + }, + { + "lat": 33.63566, + "lon": -96.60888, + "name": "Sherman" + } + ], + "question": "Which location is the geographic outlier among: Alhaurín de la Torre, Kuskovo, Püttlingen, Piła, Sherman?", + "ground_truth": { + "answer": "Sherman", + "outlier_distance_km": 7316.5, + "second_furthest_km": 3339.5, + "clarity_ratio": 2.19, + "median_distance_km": 1955.3, + "distances_to_centroid": { + "Alhaurín de la Torre": 1043.0, + "Kuskovo": 3339.5, + "Püttlingen": 1181.4, + "Piła": 1955.3, + "Sherman": 7316.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alhaurín de la Torre: (36.66°, -4.56°)", + " Kuskovo: (55.73°, 37.83°)", + " Püttlingen: (49.29°, 6.89°)", + " Piła: (53.15°, 16.74°)", + " Sherman: (33.64°, -96.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sherman: 7316.5 km from centroid", + " Kuskovo: 3339.5 km from centroid", + " Piła: 1955.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sherman", + "FINAL ANSWER: Sherman" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.21667, + "lon": 174.91667, + "name": "Lower Hutt" + }, + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + { + "lat": -33.76667, + "lon": 150.81667, + "name": "Mount Druitt" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": -20.87222, + "lon": -51.4875, + "name": "Castilho" + } + ], + "question": "Which location is the geographic outlier among: Lower Hutt, Mernda, Mount Druitt, Willetton, Castilho?", + "ground_truth": { + "answer": "Castilho", + "outlier_distance_km": 13595.4, + "second_furthest_km": 5929.9, + "clarity_ratio": 2.29, + "median_distance_km": 4031.1, + "distances_to_centroid": { + "Lower Hutt": 5929.9, + "Mernda": 3463.1, + "Mount Druitt": 4031.1, + "Willetton": 836.4, + "Castilho": 13595.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lower Hutt: (-41.22°, 174.92°)", + " Mernda: (-37.60°, 145.10°)", + " Mount Druitt: (-33.77°, 150.82°)", + " Willetton: (-32.05°, 115.89°)", + " Castilho: (-20.87°, -51.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castilho: 13595.4 km from centroid", + " Lower Hutt: 5929.9 km from centroid", + " Mount Druitt: 4031.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castilho", + "FINAL ANSWER: Castilho" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.54861, + "lon": -42.55694, + "name": "Peçanha" + }, + { + "lat": -10.12528, + "lon": -36.66194, + "name": "Igreja Nova" + }, + { + "lat": -10.97141, + "lon": -41.0796, + "name": "Ourolândia" + }, + { + "lat": -6.23122, + "lon": -42.68691, + "name": "Regeneração" + }, + { + "lat": 38.58046, + "lon": -121.53023, + "name": "West Sacramento" + } + ], + "question": "Which location is the geographic outlier among: Peçanha, Igreja Nova, Ourolândia, Regeneração, West Sacramento?", + "ground_truth": { + "answer": "West Sacramento", + "outlier_distance_km": 7939.1, + "second_furthest_km": 2461.4, + "clarity_ratio": 3.23, + "median_distance_km": 2435.6, + "distances_to_centroid": { + "Peçanha": 2461.4, + "Igreja Nova": 2435.6, + "Ourolândia": 2042.2, + "Regeneração": 1663.6, + "West Sacramento": 7939.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Peçanha: (-18.55°, -42.56°)", + " Igreja Nova: (-10.13°, -36.66°)", + " Ourolândia: (-10.97°, -41.08°)", + " Regeneração: (-6.23°, -42.69°)", + " West Sacramento: (38.58°, -121.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Sacramento: 7939.1 km from centroid", + " Peçanha: 2461.4 km from centroid", + " Igreja Nova: 2435.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Sacramento", + "FINAL ANSWER: West Sacramento" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.15511, + "lon": -74.82877, + "name": "Levittown" + }, + { + "lat": 19.31108, + "lon": -99.57197, + "name": "San Pedro Totoltepec" + }, + { + "lat": 17.10165, + "lon": -96.77686, + "name": "Santa María Atzompa" + }, + { + "lat": 19.29513, + "lon": -99.16206, + "name": "Tlalpan" + }, + { + "lat": 23.71667, + "lon": 86.4, + "name": "Jāmadoba" + } + ], + "question": "Which location is the geographic outlier among: Levittown, San Pedro Totoltepec, Santa María Atzompa, Tlalpan, Jāmadoba?", + "ground_truth": { + "answer": "Jāmadoba", + "outlier_distance_km": 13395.0, + "second_furthest_km": 4436.1, + "clarity_ratio": 3.02, + "median_distance_km": 4394.9, + "distances_to_centroid": { + "Levittown": 2470.5, + "San Pedro Totoltepec": 4436.1, + "Santa María Atzompa": 4219.0, + "Tlalpan": 4394.9, + "Jāmadoba": 13395.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Levittown: (40.16°, -74.83°)", + " San Pedro Totoltepec: (19.31°, -99.57°)", + " Santa María Atzompa: (17.10°, -96.78°)", + " Tlalpan: (19.30°, -99.16°)", + " Jāmadoba: (23.72°, 86.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jāmadoba: 13395.0 km from centroid", + " San Pedro Totoltepec: 4436.1 km from centroid", + " Tlalpan: 4394.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jāmadoba", + "FINAL ANSWER: Jāmadoba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.58847, + "lon": -96.95612, + "name": "Cedar Hill" + }, + { + "lat": 43.18007, + "lon": -73.74429, + "name": "Wilton" + }, + { + "lat": 46.54354, + "lon": -87.39542, + "name": "Marquette" + }, + { + "lat": 42.86947, + "lon": -85.64475, + "name": "Kentwood" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + } + ], + "question": "Which location is the geographic outlier among: Cedar Hill, Wilton, Marquette, Kentwood, Mount Eden?", + "ground_truth": { + "answer": "Mount Eden", + "outlier_distance_km": 17043.2, + "second_furthest_km": 6095.9, + "clarity_ratio": 2.8, + "median_distance_km": 5224.1, + "distances_to_centroid": { + "Cedar Hill": 6095.9, + "Wilton": 4097.5, + "Marquette": 5224.1, + "Kentwood": 5043.4, + "Mount Eden": 17043.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cedar Hill: (32.59°, -96.96°)", + " Wilton: (43.18°, -73.74°)", + " Marquette: (46.54°, -87.40°)", + " Kentwood: (42.87°, -85.64°)", + " Mount Eden: (-36.88°, 174.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Eden: 17043.2 km from centroid", + " Cedar Hill: 6095.9 km from centroid", + " Marquette: 5224.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Eden", + "FINAL ANSWER: Mount Eden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -37.81819, + "lon": 145.00176, + "name": "Richmond" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": 0.28422, + "lon": 34.75229, + "name": "Kakamega" + } + ], + "question": "Which location is the geographic outlier among: Bexley, Richmond, Officer, Campsie, Kakamega?", + "ground_truth": { + "answer": "Kakamega", + "outlier_distance_km": 10093.4, + "second_furthest_km": 2497.6, + "clarity_ratio": 4.04, + "median_distance_km": 2495.9, + "distances_to_centroid": { + "Bexley": 2497.6, + "Richmond": 2073.8, + "Officer": 2117.3, + "Campsie": 2495.9, + "Kakamega": 10093.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexley: (-33.95°, 151.12°)", + " Richmond: (-37.82°, 145.00°)", + " Officer: (-38.06°, 145.41°)", + " Campsie: (-33.91°, 151.10°)", + " Kakamega: (0.28°, 34.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kakamega: 10093.4 km from centroid", + " Bexley: 2497.6 km from centroid", + " Campsie: 2495.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kakamega", + "FINAL ANSWER: Kakamega" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.28682, + "lon": 19.10385, + "name": "Sosnowiec" + }, + { + "lat": 45.38193, + "lon": 9.1559, + "name": "Rozzano" + }, + { + "lat": 50.81795, + "lon": -0.37538, + "name": "Worthing" + }, + { + "lat": 38.1324, + "lon": 13.18274, + "name": "Carini" + }, + { + "lat": 7.75537, + "lon": -0.98085, + "name": "Atebubu" + } + ], + "question": "Which location is the geographic outlier among: Sosnowiec, Rozzano, Worthing, Carini, Atebubu?", + "ground_truth": { + "answer": "Atebubu", + "outlier_distance_km": 3533.1, + "second_furthest_km": 1577.8, + "clarity_ratio": 2.24, + "median_distance_km": 1522.3, + "distances_to_centroid": { + "Sosnowiec": 1577.8, + "Rozzano": 773.8, + "Worthing": 1522.3, + "Carini": 452.3, + "Atebubu": 3533.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sosnowiec: (50.29°, 19.10°)", + " Rozzano: (45.38°, 9.16°)", + " Worthing: (50.82°, -0.38°)", + " Carini: (38.13°, 13.18°)", + " Atebubu: (7.76°, -0.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Atebubu: 3533.1 km from centroid", + " Sosnowiec: 1577.8 km from centroid", + " Worthing: 1522.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Atebubu", + "FINAL ANSWER: Atebubu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.76866, + "lon": 31.50198, + "name": "Ţahţā" + }, + { + "lat": -34.05274, + "lon": 23.3716, + "name": "Plettenberg Bay" + }, + { + "lat": 9.03528, + "lon": 38.66083, + "name": "Burayu" + }, + { + "lat": 31.02795, + "lon": 30.71493, + "name": "Shubrākhīt" + }, + { + "lat": -37.8149, + "lon": 144.95052, + "name": "Docklands" + } + ], + "question": "Which location is the geographic outlier among: Ţahţā, Plettenberg Bay, Burayu, Shubrākhīt, Docklands?", + "ground_truth": { + "answer": "Docklands", + "outlier_distance_km": 10036.4, + "second_furthest_km": 4851.1, + "clarity_ratio": 2.07, + "median_distance_km": 4319.0, + "distances_to_centroid": { + "Ţahţā": 3906.9, + "Plettenberg Bay": 4851.1, + "Burayu": 2018.5, + "Shubrākhīt": 4319.0, + "Docklands": 10036.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ţahţā: (26.77°, 31.50°)", + " Plettenberg Bay: (-34.05°, 23.37°)", + " Burayu: (9.04°, 38.66°)", + " Shubrākhīt: (31.03°, 30.71°)", + " Docklands: (-37.81°, 144.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Docklands: 10036.4 km from centroid", + " Plettenberg Bay: 4851.1 km from centroid", + " Shubrākhīt: 4319.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Docklands", + "FINAL ANSWER: Docklands" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91972, + "lon": 151.07592, + "name": "Lakemba" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + }, + { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + }, + { + "lat": -35.28346, + "lon": 149.12807, + "name": "Canberra" + }, + { + "lat": 40.5769, + "lon": 16.75655, + "name": "Ginosa" + } + ], + "question": "Which location is the geographic outlier among: Lakemba, Ringwood, Morphett Vale, Canberra, Ginosa?", + "ground_truth": { + "answer": "Ginosa", + "outlier_distance_km": 12565.0, + "second_furthest_km": 3396.2, + "clarity_ratio": 3.7, + "median_distance_km": 3282.5, + "distances_to_centroid": { + "Lakemba": 3396.2, + "Ringwood": 3101.9, + "Morphett Vale": 2438.5, + "Canberra": 3282.5, + "Ginosa": 12565.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lakemba: (-33.92°, 151.08°)", + " Ringwood: (-37.82°, 145.23°)", + " Morphett Vale: (-35.13°, 138.52°)", + " Canberra: (-35.28°, 149.13°)", + " Ginosa: (40.58°, 16.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ginosa: 12565.0 km from centroid", + " Lakemba: 3396.2 km from centroid", + " Canberra: 3282.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ginosa", + "FINAL ANSWER: Ginosa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.07029, + "lon": -117.39588, + "name": "Bloomington" + }, + { + "lat": 43.86544, + "lon": -79.99322, + "name": "Caledon" + }, + { + "lat": 38.14535, + "lon": -85.8583, + "name": "Pleasure Ridge Park" + }, + { + "lat": 41.98475, + "lon": -88.07979, + "name": "Roselle" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + } + ], + "question": "Which location is the geographic outlier among: Bloomington, Caledon, Pleasure Ridge Park, Roselle, Manukau City?", + "ground_truth": { + "answer": "Manukau City", + "outlier_distance_km": 16474.2, + "second_furthest_km": 7486.4, + "clarity_ratio": 2.2, + "median_distance_km": 4877.4, + "distances_to_centroid": { + "Bloomington": 7486.4, + "Caledon": 4280.1, + "Pleasure Ridge Park": 4638.8, + "Roselle": 4877.4, + "Manukau City": 16474.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bloomington: (34.07°, -117.40°)", + " Caledon: (43.87°, -79.99°)", + " Pleasure Ridge Park: (38.15°, -85.86°)", + " Roselle: (41.98°, -88.08°)", + " Manukau City: (-36.99°, 174.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manukau City: 16474.2 km from centroid", + " Bloomington: 7486.4 km from centroid", + " Roselle: 4877.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manukau City", + "FINAL ANSWER: Manukau City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.61277, + "lon": -46.42667, + "name": "Iguatemi" + }, + { + "lat": -23.52508, + "lon": -46.63889, + "name": "Bom Retiro" + }, + { + "lat": -37.71893, + "lon": -72.24099, + "name": "Mulchén" + }, + { + "lat": -24.75722, + "lon": -51.76139, + "name": "Pitanga" + }, + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + } + ], + "question": "Which location is the geographic outlier among: Iguatemi, Bom Retiro, Mulchén, Pitanga, Adelaide?", + "ground_truth": { + "answer": "Adelaide", + "outlier_distance_km": 12421.4, + "second_furthest_km": 5265.6, + "clarity_ratio": 2.36, + "median_distance_km": 3594.6, + "distances_to_centroid": { + "Iguatemi": 3111.6, + "Bom Retiro": 3135.2, + "Mulchén": 5265.6, + "Pitanga": 3594.6, + "Adelaide": 12421.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Iguatemi: (-23.61°, -46.43°)", + " Bom Retiro: (-23.53°, -46.64°)", + " Mulchén: (-37.72°, -72.24°)", + " Pitanga: (-24.76°, -51.76°)", + " Adelaide: (-34.93°, 138.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adelaide: 12421.4 km from centroid", + " Mulchén: 5265.6 km from centroid", + " Pitanga: 3594.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adelaide", + "FINAL ANSWER: Adelaide" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.9373, + "lon": 37.12275, + "name": "Kenol" + }, + { + "lat": 9.40079, + "lon": -0.8393, + "name": "Tamale" + }, + { + "lat": 9.11972, + "lon": 4.8236, + "name": "Jebba" + }, + { + "lat": 5.95753, + "lon": 6.85305, + "name": "Ozubulu" + }, + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + } + ], + "question": "Which location is the geographic outlier among: Kenol, Tamale, Jebba, Ozubulu, Albany?", + "ground_truth": { + "answer": "Albany", + "outlier_distance_km": 9379.8, + "second_furthest_km": 3985.6, + "clarity_ratio": 2.35, + "median_distance_km": 3387.7, + "distances_to_centroid": { + "Kenol": 464.8, + "Tamale": 3985.6, + "Jebba": 3387.7, + "Ozubulu": 3062.9, + "Albany": 9379.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kenol: (-0.94°, 37.12°)", + " Tamale: (9.40°, -0.84°)", + " Jebba: (9.12°, 4.82°)", + " Ozubulu: (5.96°, 6.85°)", + " Albany: (-35.03°, 117.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Albany: 9379.8 km from centroid", + " Tamale: 3985.6 km from centroid", + " Jebba: 3387.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Albany", + "FINAL ANSWER: Albany" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.29811, + "lon": 124.67895, + "name": "Carigara" + }, + { + "lat": 19.55158, + "lon": 110.80279, + "name": "Wenchang" + }, + { + "lat": 10.10695, + "lon": 76.47366, + "name": "Perumbavoor" + }, + { + "lat": 13.3188, + "lon": 123.7385, + "name": "Malilipot" + }, + { + "lat": 43.06425, + "lon": 12.54612, + "name": "Bastia umbra" + } + ], + "question": "Which location is the geographic outlier among: Carigara, Wenchang, Perumbavoor, Malilipot, Bastia umbra?", + "ground_truth": { + "answer": "Bastia umbra", + "outlier_distance_km": 7515.0, + "second_furthest_km": 3856.0, + "clarity_ratio": 1.95, + "median_distance_km": 3693.8, + "distances_to_centroid": { + "Carigara": 3856.0, + "Wenchang": 2215.8, + "Perumbavoor": 1756.0, + "Malilipot": 3693.8, + "Bastia umbra": 7515.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carigara: (11.30°, 124.68°)", + " Wenchang: (19.55°, 110.80°)", + " Perumbavoor: (10.11°, 76.47°)", + " Malilipot: (13.32°, 123.74°)", + " Bastia umbra: (43.06°, 12.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bastia umbra: 7515.0 km from centroid", + " Carigara: 3856.0 km from centroid", + " Malilipot: 3693.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bastia umbra", + "FINAL ANSWER: Bastia umbra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.87796, + "lon": -77.00314, + "name": "Capitol Riverfront" + }, + { + "lat": 38.89511, + "lon": -77.21165, + "name": "Idylwood" + }, + { + "lat": 19.95232, + "lon": -102.30781, + "name": "Jacona de Plancarte" + }, + { + "lat": 41.70149, + "lon": -71.15505, + "name": "Fall River" + }, + { + "lat": -33.41665, + "lon": 149.5806, + "name": "Bathurst" + } + ], + "question": "Which location is the geographic outlier among: Capitol Riverfront, Idylwood, Jacona de Plancarte, Fall River, Bathurst?", + "ground_truth": { + "answer": "Bathurst", + "outlier_distance_km": 18563.6, + "second_furthest_km": 6888.7, + "clarity_ratio": 2.69, + "median_distance_km": 4410.8, + "distances_to_centroid": { + "Capitol Riverfront": 4392.9, + "Idylwood": 4410.8, + "Jacona de Plancarte": 6888.7, + "Fall River": 4024.5, + "Bathurst": 18563.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Capitol Riverfront: (38.88°, -77.00°)", + " Idylwood: (38.90°, -77.21°)", + " Jacona de Plancarte: (19.95°, -102.31°)", + " Fall River: (41.70°, -71.16°)", + " Bathurst: (-33.42°, 149.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bathurst: 18563.6 km from centroid", + " Jacona de Plancarte: 6888.7 km from centroid", + " Idylwood: 4410.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bathurst", + "FINAL ANSWER: Bathurst" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.69099, + "lon": 43.52638, + "name": "Kalach-na-Donu" + }, + { + "lat": 53.53381, + "lon": 33.73075, + "name": "Zhukovka" + }, + { + "lat": 53.97312, + "lon": 38.53502, + "name": "Kimovsk" + }, + { + "lat": 53.10766, + "lon": 8.46322, + "name": "Hude" + }, + { + "lat": -22.85222, + "lon": -43.77528, + "name": "Itaguaí" + } + ], + "question": "Which location is the geographic outlier among: Kalach-na-Donu, Zhukovka, Kimovsk, Hude, Itaguaí?", + "ground_truth": { + "answer": "Itaguaí", + "outlier_distance_km": 9159.6, + "second_furthest_km": 2545.7, + "clarity_ratio": 3.6, + "median_distance_km": 2525.1, + "distances_to_centroid": { + "Kalach-na-Donu": 2545.7, + "Zhukovka": 2257.7, + "Kimovsk": 2525.1, + "Hude": 1855.1, + "Itaguaí": 9159.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kalach-na-Donu: (48.69°, 43.53°)", + " Zhukovka: (53.53°, 33.73°)", + " Kimovsk: (53.97°, 38.54°)", + " Hude: (53.11°, 8.46°)", + " Itaguaí: (-22.85°, -43.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itaguaí: 9159.6 km from centroid", + " Kalach-na-Donu: 2545.7 km from centroid", + " Kimovsk: 2525.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itaguaí", + "FINAL ANSWER: Itaguaí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.83615, + "lon": -87.59001, + "name": "Henderson" + }, + { + "lat": 39.01673, + "lon": -84.60078, + "name": "Erlanger" + }, + { + "lat": 33.61309, + "lon": -112.3246, + "name": "El Mirage" + }, + { + "lat": 42.74698, + "lon": -84.40108, + "name": "Haslett" + }, + { + "lat": -37.90232, + "lon": 145.01734, + "name": "Brighton East" + } + ], + "question": "Which location is the geographic outlier among: Henderson, Erlanger, El Mirage, Haslett, Brighton East?", + "ground_truth": { + "answer": "Brighton East", + "outlier_distance_km": 18119.4, + "second_furthest_km": 6601.4, + "clarity_ratio": 2.74, + "median_distance_km": 4374.7, + "distances_to_centroid": { + "Henderson": 4374.7, + "Erlanger": 4145.5, + "El Mirage": 6601.4, + "Haslett": 4242.6, + "Brighton East": 18119.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Henderson: (37.84°, -87.59°)", + " Erlanger: (39.02°, -84.60°)", + " El Mirage: (33.61°, -112.32°)", + " Haslett: (42.75°, -84.40°)", + " Brighton East: (-37.90°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brighton East: 18119.4 km from centroid", + " El Mirage: 6601.4 km from centroid", + " Henderson: 4374.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brighton East", + "FINAL ANSWER: Brighton East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.50099, + "lon": -46.65744, + "name": "Casa Verde" + }, + { + "lat": -23.52278, + "lon": -46.18833, + "name": "Mogi das Cruzes" + }, + { + "lat": -29.25611, + "lon": -51.53361, + "name": "Garibaldi" + }, + { + "lat": -34.5651, + "lon": -58.69034, + "name": "Bella Vista" + }, + { + "lat": 35.76232, + "lon": 139.31952, + "name": "Hamura" + } + ], + "question": "Which location is the geographic outlier among: Casa Verde, Mogi das Cruzes, Garibaldi, Bella Vista, Hamura?", + "ground_truth": { + "answer": "Hamura", + "outlier_distance_km": 16406.9, + "second_furthest_km": 5066.6, + "clarity_ratio": 3.24, + "median_distance_km": 4272.0, + "distances_to_centroid": { + "Casa Verde": 3672.3, + "Mogi das Cruzes": 3625.4, + "Garibaldi": 4272.0, + "Bella Vista": 5066.6, + "Hamura": 16406.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Casa Verde: (-23.50°, -46.66°)", + " Mogi das Cruzes: (-23.52°, -46.19°)", + " Garibaldi: (-29.26°, -51.53°)", + " Bella Vista: (-34.57°, -58.69°)", + " Hamura: (35.76°, 139.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hamura: 16406.9 km from centroid", + " Bella Vista: 5066.6 km from centroid", + " Garibaldi: 4272.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hamura", + "FINAL ANSWER: Hamura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.60357, + "lon": 87.33197, + "name": "Osinniki" + }, + { + "lat": 41.80064, + "lon": 12.60158, + "name": "Ciampino" + }, + { + "lat": 56.9083, + "lon": 60.8019, + "name": "Beryozovsky" + }, + { + "lat": 44.87058, + "lon": 38.15759, + "name": "Abinsk" + }, + { + "lat": -41.27078, + "lon": 173.28404, + "name": "Nelson" + } + ], + "question": "Which location is the geographic outlier among: Osinniki, Ciampino, Beryozovsky, Abinsk, Nelson?", + "ground_truth": { + "answer": "Nelson", + "outlier_distance_km": 12913.3, + "second_furthest_km": 5531.7, + "clarity_ratio": 2.33, + "median_distance_km": 3485.2, + "distances_to_centroid": { + "Osinniki": 2699.0, + "Ciampino": 5531.7, + "Beryozovsky": 3048.1, + "Abinsk": 3485.2, + "Nelson": 12913.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Osinniki: (53.60°, 87.33°)", + " Ciampino: (41.80°, 12.60°)", + " Beryozovsky: (56.91°, 60.80°)", + " Abinsk: (44.87°, 38.16°)", + " Nelson: (-41.27°, 173.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nelson: 12913.3 km from centroid", + " Ciampino: 5531.7 km from centroid", + " Abinsk: 3485.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nelson", + "FINAL ANSWER: Nelson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.70791, + "lon": -79.81364, + "name": "Asheboro" + }, + { + "lat": 42.9551, + "lon": -81.62232, + "name": "Strathroy" + }, + { + "lat": 40.12067, + "lon": -75.11795, + "name": "Abington" + }, + { + "lat": 41.77593, + "lon": -72.52148, + "name": "Manchester" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + } + ], + "question": "Which location is the geographic outlier among: Asheboro, Strathroy, Abington, Manchester, Rochedale South?", + "ground_truth": { + "answer": "Rochedale South", + "outlier_distance_km": 19573.8, + "second_furthest_km": 4868.8, + "clarity_ratio": 4.02, + "median_distance_km": 4688.4, + "distances_to_centroid": { + "Asheboro": 4688.4, + "Strathroy": 4868.8, + "Abington": 4298.0, + "Manchester": 4110.5, + "Rochedale South": 19573.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Asheboro: (35.71°, -79.81°)", + " Strathroy: (42.96°, -81.62°)", + " Abington: (40.12°, -75.12°)", + " Manchester: (41.78°, -72.52°)", + " Rochedale South: (-27.60°, 153.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rochedale South: 19573.8 km from centroid", + " Strathroy: 4868.8 km from centroid", + " Asheboro: 4688.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rochedale South", + "FINAL ANSWER: Rochedale South" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.51599, + "lon": -93.73212, + "name": "Bossier City" + }, + { + "lat": 18.01932, + "lon": -102.21225, + "name": "Guacamayas" + }, + { + "lat": 48.95001, + "lon": -57.95202, + "name": "Corner Brook" + }, + { + "lat": 34.97044, + "lon": -78.94531, + "name": "Hope Mills" + }, + { + "lat": 9.59306, + "lon": 41.86611, + "name": "Dire Dawa" + } + ], + "question": "Which location is the geographic outlier among: Bossier City, Guacamayas, Corner Brook, Hope Mills, Dire Dawa?", + "ground_truth": { + "answer": "Dire Dawa", + "outlier_distance_km": 10457.9, + "second_furthest_km": 4621.0, + "clarity_ratio": 2.26, + "median_distance_km": 3408.3, + "distances_to_centroid": { + "Bossier City": 3408.3, + "Guacamayas": 4621.0, + "Corner Brook": 2239.6, + "Hope Mills": 2070.6, + "Dire Dawa": 10457.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bossier City: (32.52°, -93.73°)", + " Guacamayas: (18.02°, -102.21°)", + " Corner Brook: (48.95°, -57.95°)", + " Hope Mills: (34.97°, -78.95°)", + " Dire Dawa: (9.59°, 41.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dire Dawa: 10457.9 km from centroid", + " Guacamayas: 4621.0 km from centroid", + " Bossier City: 3408.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dire Dawa", + "FINAL ANSWER: Dire Dawa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.85868, + "lon": 10.97187, + "name": "Beli" + }, + { + "lat": -26.18848, + "lon": 28.32078, + "name": "Benoni" + }, + { + "lat": 8.22542, + "lon": -0.64889, + "name": "Yegyi" + }, + { + "lat": -26.37945, + "lon": 28.92112, + "name": "Lebohang" + }, + { + "lat": 35.68698, + "lon": -105.9378, + "name": "Santa Fe" + } + ], + "question": "Which location is the geographic outlier among: Beli, Benoni, Yegyi, Lebohang, Santa Fe?", + "ground_truth": { + "answer": "Santa Fe", + "outlier_distance_km": 10763.4, + "second_furthest_km": 4882.0, + "clarity_ratio": 2.2, + "median_distance_km": 4819.7, + "distances_to_centroid": { + "Beli": 2251.0, + "Benoni": 4819.7, + "Yegyi": 1214.7, + "Lebohang": 4882.0, + "Santa Fe": 10763.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beli: (7.86°, 10.97°)", + " Benoni: (-26.19°, 28.32°)", + " Yegyi: (8.23°, -0.65°)", + " Lebohang: (-26.38°, 28.92°)", + " Santa Fe: (35.69°, -105.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Fe: 10763.4 km from centroid", + " Lebohang: 4882.0 km from centroid", + " Benoni: 4819.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Fe", + "FINAL ANSWER: Santa Fe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.02822, + "lon": -1.24188, + "name": "Las Torres de Cotillas" + }, + { + "lat": 51.39944, + "lon": -0.07469, + "name": "South Norwood" + }, + { + "lat": 48.92426, + "lon": 2.2128, + "name": "Bezons" + }, + { + "lat": 45.54917, + "lon": 9.15964, + "name": "Cormano" + }, + { + "lat": -31.49313, + "lon": -68.53263, + "name": "Chimbas" + } + ], + "question": "Which location is the geographic outlier among: Las Torres de Cotillas, South Norwood, Bezons, Cormano, Chimbas?", + "ground_truth": { + "answer": "Chimbas", + "outlier_distance_km": 9132.0, + "second_furthest_km": 2515.3, + "clarity_ratio": 3.63, + "median_distance_km": 2465.0, + "distances_to_centroid": { + "Las Torres de Cotillas": 1274.0, + "South Norwood": 2515.3, + "Bezons": 2362.3, + "Cormano": 2465.0, + "Chimbas": 9132.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Las Torres de Cotillas: (38.03°, -1.24°)", + " South Norwood: (51.40°, -0.07°)", + " Bezons: (48.92°, 2.21°)", + " Cormano: (45.55°, 9.16°)", + " Chimbas: (-31.49°, -68.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chimbas: 9132.0 km from centroid", + " South Norwood: 2515.3 km from centroid", + " Cormano: 2465.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chimbas", + "FINAL ANSWER: Chimbas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.11, + "lon": -42.94444, + "name": "Canto do Buriti" + }, + { + "lat": -21.18694, + "lon": -43.97583, + "name": "Barroso" + }, + { + "lat": -21.82694, + "lon": -47.24861, + "name": "Santa Cruz das Palmeiras" + }, + { + "lat": -7.77833, + "lon": -39.94111, + "name": "Bodocó" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + } + ], + "question": "Which location is the geographic outlier among: Canto do Buriti, Barroso, Santa Cruz das Palmeiras, Bodocó, Officer?", + "ground_truth": { + "answer": "Officer", + "outlier_distance_km": 12951.6, + "second_furthest_km": 4315.9, + "clarity_ratio": 3.0, + "median_distance_km": 4198.3, + "distances_to_centroid": { + "Canto do Buriti": 4198.3, + "Barroso": 3983.3, + "Santa Cruz das Palmeiras": 4315.9, + "Bodocó": 3905.6, + "Officer": 12951.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canto do Buriti: (-8.11°, -42.94°)", + " Barroso: (-21.19°, -43.98°)", + " Santa Cruz das Palmeiras: (-21.83°, -47.25°)", + " Bodocó: (-7.78°, -39.94°)", + " Officer: (-38.06°, 145.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Officer: 12951.6 km from centroid", + " Santa Cruz das Palmeiras: 4315.9 km from centroid", + " Canto do Buriti: 4198.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Officer", + "FINAL ANSWER: Officer" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.17506, + "lon": 11.16458, + "name": "Garko" + }, + { + "lat": 31.24193, + "lon": 30.94504, + "name": "Ar Riyāḑ" + }, + { + "lat": 0.28422, + "lon": 34.75229, + "name": "Kakamega" + }, + { + "lat": 0.08213, + "lon": 34.72139, + "name": "Mbale" + }, + { + "lat": -38.5545, + "lon": -58.73961, + "name": "Necochea" + } + ], + "question": "Which location is the geographic outlier among: Garko, Ar Riyāḑ, Kakamega, Mbale, Necochea?", + "ground_truth": { + "answer": "Necochea", + "outlier_distance_km": 8270.6, + "second_furthest_km": 4021.8, + "clarity_ratio": 2.06, + "median_distance_km": 2689.3, + "distances_to_centroid": { + "Garko": 1061.7, + "Ar Riyāḑ": 4021.8, + "Kakamega": 2689.3, + "Mbale": 2686.3, + "Necochea": 8270.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Garko: (10.18°, 11.16°)", + " Ar Riyāḑ: (31.24°, 30.95°)", + " Kakamega: (0.28°, 34.75°)", + " Mbale: (0.08°, 34.72°)", + " Necochea: (-38.55°, -58.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Necochea: 8270.6 km from centroid", + " Ar Riyāḑ: 4021.8 km from centroid", + " Kakamega: 2689.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Necochea", + "FINAL ANSWER: Necochea" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -40.35636, + "lon": 175.61113, + "name": "Palmerston North" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + }, + { + "lat": 25.74167, + "lon": -100.30222, + "name": "San Nicolás de los Garza" + } + ], + "question": "Which location is the geographic outlier among: Boronia, Wheelers Hill, Palmerston North, Wantirna South, San Nicolás de los Garza?", + "ground_truth": { + "answer": "San Nicolás de los Garza", + "outlier_distance_km": 17763.3, + "second_furthest_km": 6843.8, + "clarity_ratio": 2.6, + "median_distance_km": 4251.6, + "distances_to_centroid": { + "Boronia": 4251.6, + "Wheelers Hill": 4243.3, + "Palmerston North": 6843.8, + "Wantirna South": 4246.0, + "San Nicolás de los Garza": 17763.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boronia: (-37.87°, 145.28°)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Palmerston North: (-40.36°, 175.61°)", + " Wantirna South: (-37.88°, 145.22°)", + " San Nicolás de los Garza: (25.74°, -100.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Nicolás de los Garza: 17763.3 km from centroid", + " Palmerston North: 6843.8 km from centroid", + " Boronia: 4251.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Nicolás de los Garza", + "FINAL ANSWER: San Nicolás de los Garza" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.16308, + "lon": -1.15222, + "name": "La Rochelle" + }, + { + "lat": 61.71982, + "lon": 75.36827, + "name": "Pokachi" + }, + { + "lat": 52.61667, + "lon": -2.35, + "name": "Ryton" + }, + { + "lat": 48.26, + "lon": 11.43402, + "name": "Dachau" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + } + ], + "question": "Which location is the geographic outlier among: La Rochelle, Pokachi, Ryton, Dachau, Armidale?", + "ground_truth": { + "answer": "Armidale", + "outlier_distance_km": 13147.7, + "second_furthest_km": 4260.9, + "clarity_ratio": 3.09, + "median_distance_km": 4142.6, + "distances_to_centroid": { + "La Rochelle": 4142.6, + "Pokachi": 3510.2, + "Ryton": 4260.9, + "Dachau": 3219.6, + "Armidale": 13147.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Rochelle: (46.16°, -1.15°)", + " Pokachi: (61.72°, 75.37°)", + " Ryton: (52.62°, -2.35°)", + " Dachau: (48.26°, 11.43°)", + " Armidale: (-30.50°, 151.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Armidale: 13147.7 km from centroid", + " Ryton: 4260.9 km from centroid", + " La Rochelle: 4142.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Armidale", + "FINAL ANSWER: Armidale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 57.5888, + "lon": 34.56854, + "name": "Vyshniy Volochëk" + }, + { + "lat": 38.3964, + "lon": -0.5255, + "name": "San Vicent del Raspeig" + }, + { + "lat": 53.86828, + "lon": 8.69902, + "name": "Cuxhaven" + }, + { + "lat": 54.72531, + "lon": 39.51305, + "name": "Rybnoye" + }, + { + "lat": -12.77944, + "lon": -39.17, + "name": "Conceição do Almeida" + } + ], + "question": "Which location is the geographic outlier among: Vyshniy Volochëk, San Vicent del Raspeig, Cuxhaven, Rybnoye, Conceição do Almeida?", + "ground_truth": { + "answer": "Conceição do Almeida", + "outlier_distance_km": 7548.1, + "second_furthest_km": 2942.5, + "clarity_ratio": 2.57, + "median_distance_km": 2846.6, + "distances_to_centroid": { + "Vyshniy Volochëk": 2846.6, + "San Vicent del Raspeig": 796.6, + "Cuxhaven": 1724.5, + "Rybnoye": 2942.5, + "Conceição do Almeida": 7548.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vyshniy Volochëk: (57.59°, 34.57°)", + " San Vicent del Raspeig: (38.40°, -0.53°)", + " Cuxhaven: (53.87°, 8.70°)", + " Rybnoye: (54.73°, 39.51°)", + " Conceição do Almeida: (-12.78°, -39.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Conceição do Almeida: 7548.1 km from centroid", + " Rybnoye: 2942.5 km from centroid", + " Vyshniy Volochëk: 2846.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Conceição do Almeida", + "FINAL ANSWER: Conceição do Almeida" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.19354, + "lon": -99.46585, + "name": "Capulhuac de Mirafuentes" + }, + { + "lat": 19.29167, + "lon": -98.46806, + "name": "San Rafael Tlanalapan" + }, + { + "lat": 49.15, + "lon": -123.13333, + "name": "Broadmoor" + }, + { + "lat": 36.18674, + "lon": -94.12881, + "name": "Springdale" + }, + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + } + ], + "question": "Which location is the geographic outlier among: Capulhuac de Mirafuentes, San Rafael Tlanalapan, Broadmoor, Springdale, Surfers Paradise?", + "ground_truth": { + "answer": "Surfers Paradise", + "outlier_distance_km": 17217.0, + "second_furthest_km": 7021.7, + "clarity_ratio": 2.45, + "median_distance_km": 4931.9, + "distances_to_centroid": { + "Capulhuac de Mirafuentes": 4931.9, + "San Rafael Tlanalapan": 4826.7, + "Broadmoor": 7021.7, + "Springdale": 4484.2, + "Surfers Paradise": 17217.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Capulhuac de Mirafuentes: (19.19°, -99.47°)", + " San Rafael Tlanalapan: (19.29°, -98.47°)", + " Broadmoor: (49.15°, -123.13°)", + " Springdale: (36.19°, -94.13°)", + " Surfers Paradise: (-28.00°, 153.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Surfers Paradise: 17217.0 km from centroid", + " Broadmoor: 7021.7 km from centroid", + " Capulhuac de Mirafuentes: 4931.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Surfers Paradise", + "FINAL ANSWER: Surfers Paradise" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.55242, + "lon": -46.65735, + "name": "Consolação" + }, + { + "lat": -25.77889, + "lon": -49.32611, + "name": "Mandirituba" + }, + { + "lat": -30.00018, + "lon": -51.07632, + "name": "Alvorada" + }, + { + "lat": -9.00972, + "lon": -36.05833, + "name": "São José da Laje" + }, + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + } + ], + "question": "Which location is the geographic outlier among: Consolação, Mandirituba, Alvorada, São José da Laje, Kingsford?", + "ground_truth": { + "answer": "Kingsford", + "outlier_distance_km": 13105.8, + "second_furthest_km": 4434.9, + "clarity_ratio": 2.96, + "median_distance_km": 4307.3, + "distances_to_centroid": { + "Consolação": 4078.2, + "Mandirituba": 4307.3, + "Alvorada": 4434.9, + "São José da Laje": 3583.5, + "Kingsford": 13105.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Consolação: (-23.55°, -46.66°)", + " Mandirituba: (-25.78°, -49.33°)", + " Alvorada: (-30.00°, -51.08°)", + " São José da Laje: (-9.01°, -36.06°)", + " Kingsford: (-33.92°, 151.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kingsford: 13105.8 km from centroid", + " Alvorada: 4434.9 km from centroid", + " Mandirituba: 4307.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kingsford", + "FINAL ANSWER: Kingsford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.31833, + "lon": -35.56111, + "name": "São Luís do Quitunde" + }, + { + "lat": -17.01037, + "lon": -46.00851, + "name": "Brasilândia de Minas" + }, + { + "lat": -23.65055, + "lon": -46.64591, + "name": "Jabaquara" + }, + { + "lat": 8.65972, + "lon": -75.12809, + "name": "San Marcos" + }, + { + "lat": 41.3417, + "lon": -72.13597, + "name": "Waterford" + } + ], + "question": "Which location is the geographic outlier among: São Luís do Quitunde, Brasilândia de Minas, Jabaquara, San Marcos, Waterford?", + "ground_truth": { + "answer": "Waterford", + "outlier_distance_km": 4906.0, + "second_furthest_km": 2784.0, + "clarity_ratio": 1.76, + "median_distance_km": 2418.6, + "distances_to_centroid": { + "São Luís do Quitunde": 2398.1, + "Brasilândia de Minas": 2137.8, + "Jabaquara": 2784.0, + "San Marcos": 2418.6, + "Waterford": 4906.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Luís do Quitunde: (-9.32°, -35.56°)", + " Brasilândia de Minas: (-17.01°, -46.01°)", + " Jabaquara: (-23.65°, -46.65°)", + " San Marcos: (8.66°, -75.13°)", + " Waterford: (41.34°, -72.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Waterford: 4906.0 km from centroid", + " Jabaquara: 2784.0 km from centroid", + " San Marcos: 2418.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Waterford", + "FINAL ANSWER: Waterford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.32745, + "lon": -119.64568, + "name": "Hanford" + }, + { + "lat": 33.16262, + "lon": -96.93751, + "name": "Little Elm" + }, + { + "lat": 37.72493, + "lon": -122.15608, + "name": "San Leandro" + }, + { + "lat": 36.09719, + "lon": -115.14666, + "name": "Paradise" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + } + ], + "question": "Which location is the geographic outlier among: Hanford, Little Elm, San Leandro, Paradise, Launceston?", + "ground_truth": { + "answer": "Launceston", + "outlier_distance_km": 16457.5, + "second_furthest_km": 6107.0, + "clarity_ratio": 2.69, + "median_distance_km": 5882.6, + "distances_to_centroid": { + "Hanford": 5882.6, + "Little Elm": 3785.3, + "San Leandro": 6107.0, + "Paradise": 5478.4, + "Launceston": 16457.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hanford: (36.33°, -119.65°)", + " Little Elm: (33.16°, -96.94°)", + " San Leandro: (37.72°, -122.16°)", + " Paradise: (36.10°, -115.15°)", + " Launceston: (-41.44°, 147.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Launceston: 16457.5 km from centroid", + " San Leandro: 6107.0 km from centroid", + " Hanford: 5882.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Launceston", + "FINAL ANSWER: Launceston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.56757, + "lon": 11.52987, + "name": "San Giovanni Valdarno" + }, + { + "lat": 56.65317, + "lon": 66.30048, + "name": "Yalutorovsk" + }, + { + "lat": 53.35, + "lon": -3.01667, + "name": "Bebington" + }, + { + "lat": 55.3195, + "lon": 52.06942, + "name": "Zainsk" + }, + { + "lat": -30.18111, + "lon": -50.20556, + "name": "Cidreira" + } + ], + "question": "Which location is the geographic outlier among: San Giovanni Valdarno, Yalutorovsk, Bebington, Zainsk, Cidreira?", + "ground_truth": { + "answer": "Cidreira", + "outlier_distance_km": 10027.7, + "second_furthest_km": 4418.8, + "clarity_ratio": 2.27, + "median_distance_km": 3528.9, + "distances_to_centroid": { + "San Giovanni Valdarno": 928.9, + "Yalutorovsk": 4418.8, + "Bebington": 2423.7, + "Zainsk": 3528.9, + "Cidreira": 10027.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Giovanni Valdarno: (43.57°, 11.53°)", + " Yalutorovsk: (56.65°, 66.30°)", + " Bebington: (53.35°, -3.02°)", + " Zainsk: (55.32°, 52.07°)", + " Cidreira: (-30.18°, -50.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cidreira: 10027.7 km from centroid", + " Yalutorovsk: 4418.8 km from centroid", + " Zainsk: 3528.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cidreira", + "FINAL ANSWER: Cidreira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.81082, + "lon": -81.87786, + "name": "Leesburg" + }, + { + "lat": 25.96231, + "lon": -80.17671, + "name": "Ives Estates" + }, + { + "lat": 41.70149, + "lon": -71.15505, + "name": "Fall River" + }, + { + "lat": 19.64177, + "lon": -99.3068, + "name": "Nicolás Romero" + }, + { + "lat": 6.17146, + "lon": 7.00525, + "name": "Enugu-Ukwu" + } + ], + "question": "Which location is the geographic outlier among: Leesburg, Ives Estates, Fall River, Nicolás Romero, Enugu-Ukwu?", + "ground_truth": { + "answer": "Enugu-Ukwu", + "outlier_distance_km": 7915.2, + "second_furthest_km": 3556.6, + "clarity_ratio": 2.23, + "median_distance_km": 1997.3, + "distances_to_centroid": { + "Leesburg": 1734.4, + "Ives Estates": 1524.9, + "Fall River": 1997.3, + "Nicolás Romero": 3556.6, + "Enugu-Ukwu": 7915.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Leesburg: (28.81°, -81.88°)", + " Ives Estates: (25.96°, -80.18°)", + " Fall River: (41.70°, -71.16°)", + " Nicolás Romero: (19.64°, -99.31°)", + " Enugu-Ukwu: (6.17°, 7.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Enugu-Ukwu: 7915.2 km from centroid", + " Nicolás Romero: 3556.6 km from centroid", + " Fall River: 1997.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Enugu-Ukwu", + "FINAL ANSWER: Enugu-Ukwu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.75333, + "lon": -37.33972, + "name": "Tupanatinga" + }, + { + "lat": -23.54333, + "lon": -46.41083, + "name": "Guaianases" + }, + { + "lat": 10.59181, + "lon": -74.18983, + "name": "Aracataca" + }, + { + "lat": -11.74611, + "lon": -44.91, + "name": "Riachão das Neves" + }, + { + "lat": 41.0706, + "lon": -85.01441, + "name": "New Haven" + } + ], + "question": "Which location is the geographic outlier among: Tupanatinga, Guaianases, Aracataca, Riachão das Neves, New Haven?", + "ground_truth": { + "answer": "New Haven", + "outlier_distance_km": 5188.5, + "second_furthest_km": 3037.6, + "clarity_ratio": 1.71, + "median_distance_km": 2516.7, + "distances_to_centroid": { + "Tupanatinga": 2516.7, + "Guaianases": 3037.6, + "Aracataca": 2094.1, + "Riachão das Neves": 2033.5, + "New Haven": 5188.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tupanatinga: (-8.75°, -37.34°)", + " Guaianases: (-23.54°, -46.41°)", + " Aracataca: (10.59°, -74.19°)", + " Riachão das Neves: (-11.75°, -44.91°)", + " New Haven: (41.07°, -85.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " New Haven: 5188.5 km from centroid", + " Guaianases: 3037.6 km from centroid", + " Tupanatinga: 2516.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: New Haven", + "FINAL ANSWER: New Haven" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + }, + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + }, + { + "lat": -33.36889, + "lon": 19.31095, + "name": "Ceres" + } + ], + "question": "Which location is the geographic outlier among: Brisbane, Elwood, Maitland, Manukau City, Ceres?", + "ground_truth": { + "answer": "Ceres", + "outlier_distance_km": 9536.9, + "second_furthest_km": 4159.4, + "clarity_ratio": 2.29, + "median_distance_km": 2418.2, + "distances_to_centroid": { + "Brisbane": 2418.2, + "Elwood": 1534.1, + "Maitland": 2120.0, + "Manukau City": 4159.4, + "Ceres": 9536.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brisbane: (-27.47°, 153.03°)", + " Elwood: (-37.88°, 144.98°)", + " Maitland: (-32.73°, 151.56°)", + " Manukau City: (-36.99°, 174.88°)", + " Ceres: (-33.37°, 19.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ceres: 9536.9 km from centroid", + " Manukau City: 4159.4 km from centroid", + " Brisbane: 2418.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ceres", + "FINAL ANSWER: Ceres" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.79068, + "lon": 150.6693, + "name": "Glenmore Park" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -33.7061, + "lon": 150.7094, + "name": "Cranebrook" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -23.425, + "lon": -49.72083, + "name": "Carlópolis" + } + ], + "question": "Which location is the geographic outlier among: Glenmore Park, Townsville, Cranebrook, Perth, Carlópolis?", + "ground_truth": { + "answer": "Carlópolis", + "outlier_distance_km": 13544.3, + "second_furthest_km": 4557.7, + "clarity_ratio": 2.97, + "median_distance_km": 4554.5, + "distances_to_centroid": { + "Glenmore Park": 4549.8, + "Townsville": 4557.7, + "Cranebrook": 4554.5, + "Perth": 1308.1, + "Carlópolis": 13544.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenmore Park: (-33.79°, 150.67°)", + " Townsville: (-19.27°, 146.81°)", + " Cranebrook: (-33.71°, 150.71°)", + " Perth: (-31.95°, 115.86°)", + " Carlópolis: (-23.43°, -49.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carlópolis: 13544.3 km from centroid", + " Townsville: 4557.7 km from centroid", + " Cranebrook: 4554.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carlópolis", + "FINAL ANSWER: Carlópolis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.05584, + "lon": 145.90375, + "name": "Burnie" + }, + { + "lat": -38.38176, + "lon": 142.48799, + "name": "Warrnambool" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + { + "lat": 41.85059, + "lon": -87.882, + "name": "Westchester" + } + ], + "question": "Which location is the geographic outlier among: Burnie, Warrnambool, Mangere East, Yagoona, Westchester?", + "ground_truth": { + "answer": "Westchester", + "outlier_distance_km": 17458.9, + "second_furthest_km": 6806.1, + "clarity_ratio": 2.57, + "median_distance_km": 4659.1, + "distances_to_centroid": { + "Burnie": 4363.4, + "Warrnambool": 3997.4, + "Mangere East": 6806.1, + "Yagoona": 4659.1, + "Westchester": 17458.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Burnie: (-41.06°, 145.90°)", + " Warrnambool: (-38.38°, 142.49°)", + " Mangere East: (-36.97°, 174.82°)", + " Yagoona: (-33.90°, 151.02°)", + " Westchester: (41.85°, -87.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Westchester: 17458.9 km from centroid", + " Mangere East: 6806.1 km from centroid", + " Yagoona: 4659.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Westchester", + "FINAL ANSWER: Westchester" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + }, + { + "lat": 22.12745, + "lon": 75.61101, + "name": "Kasrāwad" + } + ], + "question": "Which location is the geographic outlier among: Auburn, Warragul, Surfers Paradise, Mornington, Kasrāwad?", + "ground_truth": { + "answer": "Kasrāwad", + "outlier_distance_km": 8099.3, + "second_furthest_km": 2019.7, + "clarity_ratio": 4.01, + "median_distance_km": 2000.0, + "distances_to_centroid": { + "Auburn": 2019.7, + "Warragul": 2000.0, + "Surfers Paradise": 1996.8, + "Mornington": 1959.4, + "Kasrāwad": 8099.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auburn: (-33.85°, 151.03°)", + " Warragul: (-38.16°, 145.93°)", + " Surfers Paradise: (-28.00°, 153.43°)", + " Mornington: (-38.22°, 145.04°)", + " Kasrāwad: (22.13°, 75.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kasrāwad: 8099.3 km from centroid", + " Auburn: 2019.7 km from centroid", + " Warragul: 2000.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kasrāwad", + "FINAL ANSWER: Kasrāwad" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.43548, + "lon": 13.54825, + "name": "Adlershof" + }, + { + "lat": 41.53809, + "lon": 1.87025, + "name": "Esparreguera" + }, + { + "lat": 48.53157, + "lon": 2.62829, + "name": "Le Mée-sur-Seine" + }, + { + "lat": 51.3751, + "lon": -2.36172, + "name": "Bath" + }, + { + "lat": 12.95479, + "lon": 36.15549, + "name": "Metemma" + } + ], + "question": "Which location is the geographic outlier among: Adlershof, Esparreguera, Le Mée-sur-Seine, Bath, Metemma?", + "ground_truth": { + "answer": "Metemma", + "outlier_distance_km": 4027.9, + "second_furthest_km": 1476.4, + "clarity_ratio": 2.73, + "median_distance_km": 1253.9, + "distances_to_centroid": { + "Adlershof": 1253.9, + "Esparreguera": 708.2, + "Le Mée-sur-Seine": 1001.7, + "Bath": 1476.4, + "Metemma": 4027.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adlershof: (52.44°, 13.55°)", + " Esparreguera: (41.54°, 1.87°)", + " Le Mée-sur-Seine: (48.53°, 2.63°)", + " Bath: (51.38°, -2.36°)", + " Metemma: (12.95°, 36.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Metemma: 4027.9 km from centroid", + " Bath: 1476.4 km from centroid", + " Adlershof: 1253.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Metemma", + "FINAL ANSWER: Metemma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -22.29194, + "lon": -51.90639, + "name": "Mirante do Paranapanema" + } + ], + "question": "Which location is the geographic outlier among: Tarneit, Cranbourne East, Adelaide, Wahroonga, Mirante do Paranapanema?", + "ground_truth": { + "answer": "Mirante do Paranapanema", + "outlier_distance_km": 13379.8, + "second_furthest_km": 4187.1, + "clarity_ratio": 3.2, + "median_distance_km": 3597.7, + "distances_to_centroid": { + "Tarneit": 3544.0, + "Cranbourne East": 3597.7, + "Adelaide": 3031.9, + "Wahroonga": 4187.1, + "Mirante do Paranapanema": 13379.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tarneit: (-37.84°, 144.66°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Adelaide: (-34.93°, 138.60°)", + " Wahroonga: (-33.72°, 151.12°)", + " Mirante do Paranapanema: (-22.29°, -51.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mirante do Paranapanema: 13379.8 km from centroid", + " Wahroonga: 4187.1 km from centroid", + " Cranbourne East: 3597.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mirante do Paranapanema", + "FINAL ANSWER: Mirante do Paranapanema" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.41919, + "lon": 45.85251, + "name": "Raqo" + }, + { + "lat": 4.86641, + "lon": -2.24181, + "name": "Esim" + }, + { + "lat": 7.37756, + "lon": 3.90591, + "name": "Ibadan" + }, + { + "lat": -28.70025, + "lon": 26.4581, + "name": "Winnie Mandela" + }, + { + "lat": -27.50578, + "lon": 153.10236, + "name": "Carindale" + } + ], + "question": "Which location is the geographic outlier among: Raqo, Esim, Ibadan, Winnie Mandela, Carindale?", + "ground_truth": { + "answer": "Carindale", + "outlier_distance_km": 11334.7, + "second_furthest_km": 5463.4, + "clarity_ratio": 2.07, + "median_distance_km": 4891.1, + "distances_to_centroid": { + "Raqo": 1549.5, + "Esim": 5463.4, + "Ibadan": 4891.1, + "Winnie Mandela": 3082.6, + "Carindale": 11334.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Raqo: (6.42°, 45.85°)", + " Esim: (4.87°, -2.24°)", + " Ibadan: (7.38°, 3.91°)", + " Winnie Mandela: (-28.70°, 26.46°)", + " Carindale: (-27.51°, 153.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carindale: 11334.7 km from centroid", + " Esim: 5463.4 km from centroid", + " Ibadan: 4891.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carindale", + "FINAL ANSWER: Carindale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.54437, + "lon": 44.59592, + "name": "Staryy Malgobek" + }, + { + "lat": 45.73764, + "lon": 7.31722, + "name": "Aosta" + }, + { + "lat": 45.58058, + "lon": 39.65741, + "name": "Vyselki" + }, + { + "lat": 39.96495, + "lon": -0.26041, + "name": "Onda" + }, + { + "lat": 31.41281, + "lon": 108.31465, + "name": "Zishui" + } + ], + "question": "Which location is the geographic outlier among: Staryy Malgobek, Aosta, Vyselki, Onda, Zishui?", + "ground_truth": { + "answer": "Zishui", + "outlier_distance_km": 6066.0, + "second_furthest_km": 3365.0, + "clarity_ratio": 1.8, + "median_distance_km": 2658.1, + "distances_to_centroid": { + "Staryy Malgobek": 460.7, + "Aosta": 2658.1, + "Vyselki": 482.2, + "Onda": 3365.0, + "Zishui": 6066.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Staryy Malgobek: (43.54°, 44.60°)", + " Aosta: (45.74°, 7.32°)", + " Vyselki: (45.58°, 39.66°)", + " Onda: (39.96°, -0.26°)", + " Zishui: (31.41°, 108.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zishui: 6066.0 km from centroid", + " Onda: 3365.0 km from centroid", + " Aosta: 2658.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zishui", + "FINAL ANSWER: Zishui" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.78588, + "lon": -71.53222, + "name": "Quintero" + }, + { + "lat": -1.75972, + "lon": -46.545, + "name": "Cachoeira do Piriá" + }, + { + "lat": -34.47775, + "lon": -58.70652, + "name": "Ingeniero Pablo Nogués" + }, + { + "lat": -13.18889, + "lon": -60.81222, + "name": "Cerejeiras" + }, + { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + } + ], + "question": "Which location is the geographic outlier among: Quintero, Cachoeira do Piriá, Ingeniero Pablo Nogués, Cerejeiras, Manly?", + "ground_truth": { + "answer": "Manly", + "outlier_distance_km": 13562.2, + "second_furthest_km": 5376.4, + "clarity_ratio": 2.52, + "median_distance_km": 4714.6, + "distances_to_centroid": { + "Quintero": 5376.4, + "Cachoeira do Piriá": 3955.4, + "Ingeniero Pablo Nogués": 4194.7, + "Cerejeiras": 4714.6, + "Manly": 13562.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Quintero: (-32.79°, -71.53°)", + " Cachoeira do Piriá: (-1.76°, -46.55°)", + " Ingeniero Pablo Nogués: (-34.48°, -58.71°)", + " Cerejeiras: (-13.19°, -60.81°)", + " Manly: (-33.80°, 151.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manly: 13562.2 km from centroid", + " Quintero: 5376.4 km from centroid", + " Cerejeiras: 4714.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manly", + "FINAL ANSWER: Manly" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.99409, + "lon": -90.24174, + "name": "Kenner" + }, + { + "lat": 38.9556, + "lon": -90.18678, + "name": "Godfrey" + }, + { + "lat": 25.8576, + "lon": -80.27811, + "name": "Hialeah" + }, + { + "lat": 19.36906, + "lon": -98.94935, + "name": "Magdalena Atlicpac" + }, + { + "lat": 38.09242, + "lon": -1.7985, + "name": "Cehegín" + } + ], + "question": "Which location is the geographic outlier among: Kenner, Godfrey, Hialeah, Magdalena Atlicpac, Cehegín?", + "ground_truth": { + "answer": "Cehegín", + "outlier_distance_km": 6379.0, + "second_furthest_km": 2947.3, + "clarity_ratio": 2.16, + "median_distance_km": 1884.4, + "distances_to_centroid": { + "Kenner": 1723.7, + "Godfrey": 1884.4, + "Hialeah": 934.6, + "Magdalena Atlicpac": 2947.3, + "Cehegín": 6379.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kenner: (29.99°, -90.24°)", + " Godfrey: (38.96°, -90.19°)", + " Hialeah: (25.86°, -80.28°)", + " Magdalena Atlicpac: (19.37°, -98.95°)", + " Cehegín: (38.09°, -1.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cehegín: 6379.0 km from centroid", + " Magdalena Atlicpac: 2947.3 km from centroid", + " Godfrey: 1884.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cehegín", + "FINAL ANSWER: Cehegín" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.71611, + "lon": -43.55528, + "name": "Queimados" + }, + { + "lat": -3.54306, + "lon": -43.91583, + "name": "Vargem Grande" + }, + { + "lat": -3.60722, + "lon": -38.96833, + "name": "São Gonçalo do Amarante" + }, + { + "lat": -20.02472, + "lon": -48.94056, + "name": "Frutal" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + } + ], + "question": "Which location is the geographic outlier among: Queimados, Vargem Grande, São Gonçalo do Amarante, Frutal, Cheltenham?", + "ground_truth": { + "answer": "Cheltenham", + "outlier_distance_km": 13141.5, + "second_furthest_km": 4509.4, + "clarity_ratio": 2.91, + "median_distance_km": 4408.5, + "distances_to_centroid": { + "Queimados": 3944.8, + "Vargem Grande": 4408.5, + "São Gonçalo do Amarante": 3906.5, + "Frutal": 4509.4, + "Cheltenham": 13141.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Queimados: (-22.72°, -43.56°)", + " Vargem Grande: (-3.54°, -43.92°)", + " São Gonçalo do Amarante: (-3.61°, -38.97°)", + " Frutal: (-20.02°, -48.94°)", + " Cheltenham: (-37.97°, 145.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cheltenham: 13141.5 km from centroid", + " Frutal: 4509.4 km from centroid", + " Vargem Grande: 4408.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cheltenham", + "FINAL ANSWER: Cheltenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.43167, + "lon": -54.05111, + "name": "Paranatinga" + }, + { + "lat": -19.70027, + "lon": -43.9602, + "name": "São José da Lapa" + }, + { + "lat": 5.26667, + "lon": -73.91667, + "name": "La Mesa" + }, + { + "lat": -6.75459, + "lon": -35.66449, + "name": "Solânea" + }, + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + } + ], + "question": "Which location is the geographic outlier among: Paranatinga, São José da Lapa, La Mesa, Solânea, Upper Coomera?", + "ground_truth": { + "answer": "Upper Coomera", + "outlier_distance_km": 15190.8, + "second_furthest_km": 7246.1, + "clarity_ratio": 2.1, + "median_distance_km": 4665.8, + "distances_to_centroid": { + "Paranatinga": 4665.8, + "São José da Lapa": 3612.4, + "La Mesa": 7246.1, + "Solânea": 2795.7, + "Upper Coomera": 15190.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paranatinga: (-14.43°, -54.05°)", + " São José da Lapa: (-19.70°, -43.96°)", + " La Mesa: (5.27°, -73.92°)", + " Solânea: (-6.75°, -35.66°)", + " Upper Coomera: (-27.88°, 153.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upper Coomera: 15190.8 km from centroid", + " La Mesa: 7246.1 km from centroid", + " Paranatinga: 4665.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upper Coomera", + "FINAL ANSWER: Upper Coomera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.15388, + "lon": 18.66031, + "name": "Moorreesburg" + }, + { + "lat": 27.06309, + "lon": 31.34425, + "name": "As Sāḩil" + }, + { + "lat": 9.03333, + "lon": 38.15, + "name": "Gīnch’ī" + }, + { + "lat": -26.67313, + "lon": 27.92615, + "name": "Vereeniging" + }, + { + "lat": -38.68333, + "lon": 176.08333, + "name": "Taupo" + } + ], + "question": "Which location is the geographic outlier among: Moorreesburg, As Sāḩil, Gīnch’ī, Vereeniging, Taupo?", + "ground_truth": { + "answer": "Taupo", + "outlier_distance_km": 11411.6, + "second_furthest_km": 5280.5, + "clarity_ratio": 2.16, + "median_distance_km": 4638.5, + "distances_to_centroid": { + "Moorreesburg": 4638.5, + "As Sāḩil": 5280.5, + "Gīnch’ī": 3278.1, + "Vereeniging": 3550.2, + "Taupo": 11411.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Moorreesburg: (-33.15°, 18.66°)", + " As Sāḩil: (27.06°, 31.34°)", + " Gīnch’ī: (9.03°, 38.15°)", + " Vereeniging: (-26.67°, 27.93°)", + " Taupo: (-38.68°, 176.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taupo: 11411.6 km from centroid", + " As Sāḩil: 5280.5 km from centroid", + " Moorreesburg: 4638.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taupo", + "FINAL ANSWER: Taupo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.99116, + "lon": 145.17385, + "name": "Keysborough" + }, + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + { + "lat": 30.24506, + "lon": 75.84488, + "name": "Sangrūr" + } + ], + "question": "Which location is the geographic outlier among: Keysborough, Greenvale, Springfield Lakes, Lalor, Sangrūr?", + "ground_truth": { + "answer": "Sangrūr", + "outlier_distance_km": 8418.2, + "second_furthest_km": 2124.1, + "clarity_ratio": 3.96, + "median_distance_km": 2120.9, + "distances_to_centroid": { + "Keysborough": 2124.1, + "Greenvale": 2076.1, + "Springfield Lakes": 2120.9, + "Lalor": 2087.1, + "Sangrūr": 8418.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Keysborough: (-37.99°, 145.17°)", + " Greenvale: (-37.63°, 144.87°)", + " Springfield Lakes: (-27.67°, 152.92°)", + " Lalor: (-37.67°, 145.02°)", + " Sangrūr: (30.25°, 75.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sangrūr: 8418.2 km from centroid", + " Keysborough: 2124.1 km from centroid", + " Springfield Lakes: 2120.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sangrūr", + "FINAL ANSWER: Sangrūr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + }, + { + "lat": -36.12179, + "lon": 146.88809, + "name": "Wodonga" + }, + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + { + "lat": 46.07844, + "lon": -64.68735, + "name": "Dieppe" + } + ], + "question": "Which location is the geographic outlier among: Lidcombe, Glenferrie, Wodonga, Kingsford, Dieppe?", + "ground_truth": { + "answer": "Dieppe", + "outlier_distance_km": 16897.2, + "second_furthest_km": 4755.6, + "clarity_ratio": 3.55, + "median_distance_km": 4737.5, + "distances_to_centroid": { + "Lidcombe": 4737.5, + "Glenferrie": 4310.5, + "Wodonga": 4415.4, + "Kingsford": 4755.6, + "Dieppe": 16897.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lidcombe: (-33.86°, 151.04°)", + " Glenferrie: (-37.83°, 145.05°)", + " Wodonga: (-36.12°, 146.89°)", + " Kingsford: (-33.92°, 151.23°)", + " Dieppe: (46.08°, -64.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dieppe: 16897.2 km from centroid", + " Kingsford: 4755.6 km from centroid", + " Lidcombe: 4737.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dieppe", + "FINAL ANSWER: Dieppe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.48333, + "lon": 136.63333, + "name": "Tamaru" + }, + { + "lat": 34.80472, + "lon": 105.57778, + "name": "Qianhu" + }, + { + "lat": 36.62528, + "lon": 119.71333, + "name": "Cuijiaji" + }, + { + "lat": 23.19073, + "lon": 82.35314, + "name": "Chirmiri" + }, + { + "lat": -8.66361, + "lon": -36.00583, + "name": "Panelas" + } + ], + "question": "Which location is the geographic outlier among: Tamaru, Qianhu, Cuijiaji, Chirmiri, Panelas?", + "ground_truth": { + "answer": "Panelas", + "outlier_distance_km": 13200.4, + "second_furthest_km": 5390.4, + "clarity_ratio": 2.45, + "median_distance_km": 3878.2, + "distances_to_centroid": { + "Tamaru": 5390.4, + "Qianhu": 2595.5, + "Cuijiaji": 3878.2, + "Chirmiri": 122.6, + "Panelas": 13200.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tamaru: (34.48°, 136.63°)", + " Qianhu: (34.80°, 105.58°)", + " Cuijiaji: (36.63°, 119.71°)", + " Chirmiri: (23.19°, 82.35°)", + " Panelas: (-8.66°, -36.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Panelas: 13200.4 km from centroid", + " Tamaru: 5390.4 km from centroid", + " Cuijiaji: 3878.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Panelas", + "FINAL ANSWER: Panelas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -16.33333, + "lon": -55.93333, + "name": "Lucas" + }, + { + "lat": 6.08236, + "lon": -75.33509, + "name": "Carmen de Viboral" + }, + { + "lat": -10.82294, + "lon": -42.72815, + "name": "Xique-Xique" + }, + { + "lat": -30.11972, + "lon": -51.96222, + "name": "Butiá" + }, + { + "lat": -37.91482, + "lon": 144.75088, + "name": "Point Cook" + } + ], + "question": "Which location is the geographic outlier among: Lucas, Carmen de Viboral, Xique-Xique, Butiá, Point Cook?", + "ground_truth": { + "answer": "Point Cook", + "outlier_distance_km": 13506.8, + "second_furthest_km": 7006.6, + "clarity_ratio": 1.93, + "median_distance_km": 4214.4, + "distances_to_centroid": { + "Lucas": 4214.4, + "Carmen de Viboral": 7006.6, + "Xique-Xique": 2954.3, + "Butiá": 3858.6, + "Point Cook": 13506.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lucas: (-16.33°, -55.93°)", + " Carmen de Viboral: (6.08°, -75.34°)", + " Xique-Xique: (-10.82°, -42.73°)", + " Butiá: (-30.12°, -51.96°)", + " Point Cook: (-37.91°, 144.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Point Cook: 13506.8 km from centroid", + " Carmen de Viboral: 7006.6 km from centroid", + " Lucas: 4214.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Point Cook", + "FINAL ANSWER: Point Cook" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + }, + { + "lat": 29.66301, + "lon": -95.23549, + "name": "South Houston" + } + ], + "question": "Which location is the geographic outlier among: Hobart, Wellington, Eastwood, New Plymouth, South Houston?", + "ground_truth": { + "answer": "South Houston", + "outlier_distance_km": 17450.5, + "second_furthest_km": 6087.3, + "clarity_ratio": 2.87, + "median_distance_km": 6051.0, + "distances_to_centroid": { + "Hobart": 3865.4, + "Wellington": 6087.3, + "Eastwood": 4011.5, + "New Plymouth": 6051.0, + "South Houston": 17450.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hobart: (-42.88°, 147.33°)", + " Wellington: (-41.29°, 174.78°)", + " Eastwood: (-33.79°, 151.08°)", + " New Plymouth: (-39.07°, 174.08°)", + " South Houston: (29.66°, -95.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " South Houston: 17450.5 km from centroid", + " Wellington: 6087.3 km from centroid", + " New Plymouth: 6051.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: South Houston", + "FINAL ANSWER: South Houston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.1626, + "lon": -71.04116, + "name": "Randolph" + }, + { + "lat": 45.53341, + "lon": -73.34916, + "name": "Saint-Bruno-de-Montarville" + }, + { + "lat": 41.95781, + "lon": -87.76506, + "name": "Portage Park" + }, + { + "lat": 41.14676, + "lon": -73.49484, + "name": "New Canaan" + }, + { + "lat": 41.72063, + "lon": 12.6723, + "name": "Ariccia" + } + ], + "question": "Which location is the geographic outlier among: Randolph, Saint-Bruno-de-Montarville, Portage Park, New Canaan, Ariccia?", + "ground_truth": { + "answer": "Ariccia", + "outlier_distance_km": 5695.2, + "second_furthest_km": 2390.5, + "clarity_ratio": 2.38, + "median_distance_km": 1242.1, + "distances_to_centroid": { + "Randolph": 1022.8, + "Saint-Bruno-de-Montarville": 1224.8, + "Portage Park": 2390.5, + "New Canaan": 1242.1, + "Ariccia": 5695.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Randolph: (42.16°, -71.04°)", + " Saint-Bruno-de-Montarville: (45.53°, -73.35°)", + " Portage Park: (41.96°, -87.77°)", + " New Canaan: (41.15°, -73.49°)", + " Ariccia: (41.72°, 12.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ariccia: 5695.2 km from centroid", + " Portage Park: 2390.5 km from centroid", + " New Canaan: 1242.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ariccia", + "FINAL ANSWER: Ariccia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.24202, + "lon": -71.53813, + "name": "East Concord" + }, + { + "lat": 41.80086, + "lon": -87.93701, + "name": "Hinsdale" + }, + { + "lat": 38.96667, + "lon": -94.6169, + "name": "Leawood" + }, + { + "lat": 40.91534, + "lon": -81.10593, + "name": "Alliance" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + } + ], + "question": "Which location is the geographic outlier among: East Concord, Hinsdale, Leawood, Alliance, Griffith?", + "ground_truth": { + "answer": "Griffith", + "outlier_distance_km": 19034.2, + "second_furthest_km": 5421.2, + "clarity_ratio": 3.51, + "median_distance_km": 4861.0, + "distances_to_centroid": { + "East Concord": 3585.7, + "Hinsdale": 4861.0, + "Leawood": 5421.2, + "Alliance": 4283.4, + "Griffith": 19034.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " East Concord: (43.24°, -71.54°)", + " Hinsdale: (41.80°, -87.94°)", + " Leawood: (38.97°, -94.62°)", + " Alliance: (40.92°, -81.11°)", + " Griffith: (-34.29°, 146.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Griffith: 19034.2 km from centroid", + " Leawood: 5421.2 km from centroid", + " Hinsdale: 4861.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Griffith", + "FINAL ANSWER: Griffith" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.5073, + "lon": 77.08145, + "name": "Kulathummal" + }, + { + "lat": 34.66667, + "lon": 116.58333, + "name": "Sunlou" + }, + { + "lat": 12.80569, + "lon": 74.86058, + "name": "Ullal" + }, + { + "lat": 30.01704, + "lon": 107.32576, + "name": "Baijia" + }, + { + "lat": -37.76722, + "lon": 144.76657, + "name": "Deer Park" + } + ], + "question": "Which location is the geographic outlier among: Kulathummal, Sunlou, Ullal, Baijia, Deer Park?", + "ground_truth": { + "answer": "Deer Park", + "outlier_distance_km": 6754.4, + "second_furthest_km": 3209.1, + "clarity_ratio": 2.1, + "median_distance_km": 3057.2, + "distances_to_centroid": { + "Kulathummal": 2971.2, + "Sunlou": 3057.2, + "Ullal": 3209.1, + "Baijia": 2289.4, + "Deer Park": 6754.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kulathummal: (8.51°, 77.08°)", + " Sunlou: (34.67°, 116.58°)", + " Ullal: (12.81°, 74.86°)", + " Baijia: (30.02°, 107.33°)", + " Deer Park: (-37.77°, 144.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Deer Park: 6754.4 km from centroid", + " Ullal: 3209.1 km from centroid", + " Sunlou: 3057.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Deer Park", + "FINAL ANSWER: Deer Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.91738, + "lon": 3.1631, + "name": "Palafrugell" + }, + { + "lat": 56.84659, + "lon": 62.71211, + "name": "Kamyshlov" + }, + { + "lat": 52.13129, + "lon": 11.63189, + "name": "Magdeburg" + }, + { + "lat": 52.25917, + "lon": 5.60694, + "name": "Putten" + }, + { + "lat": -32.77477, + "lon": 26.63376, + "name": "Fort Beaufort" + } + ], + "question": "Which location is the geographic outlier among: Palafrugell, Kamyshlov, Magdeburg, Putten, Fort Beaufort?", + "ground_truth": { + "answer": "Fort Beaufort", + "outlier_distance_km": 7449.6, + "second_furthest_km": 3968.6, + "clarity_ratio": 1.88, + "median_distance_km": 2405.2, + "distances_to_centroid": { + "Palafrugell": 1857.1, + "Kamyshlov": 3968.6, + "Magdeburg": 2170.3, + "Putten": 2405.2, + "Fort Beaufort": 7449.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palafrugell: (41.92°, 3.16°)", + " Kamyshlov: (56.85°, 62.71°)", + " Magdeburg: (52.13°, 11.63°)", + " Putten: (52.26°, 5.61°)", + " Fort Beaufort: (-32.77°, 26.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fort Beaufort: 7449.6 km from centroid", + " Kamyshlov: 3968.6 km from centroid", + " Putten: 2405.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fort Beaufort", + "FINAL ANSWER: Fort Beaufort" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.865, + "lon": 120.53889, + "name": "Zhangjiagang" + }, + { + "lat": -7.068, + "lon": 107.794, + "name": "Paseh" + }, + { + "lat": -6.73361, + "lon": 108.26278, + "name": "Jatiwangi" + }, + { + "lat": 34.61667, + "lon": 136.08333, + "name": "Nabari" + }, + { + "lat": 32.68589, + "lon": -117.18309, + "name": "Coronado" + } + ], + "question": "Which location is the geographic outlier among: Zhangjiagang, Paseh, Jatiwangi, Nabari, Coronado?", + "ground_truth": { + "answer": "Coronado", + "outlier_distance_km": 14412.4, + "second_furthest_km": 6675.7, + "clarity_ratio": 2.16, + "median_distance_km": 5218.2, + "distances_to_centroid": { + "Zhangjiagang": 5218.2, + "Paseh": 4844.7, + "Jatiwangi": 4867.1, + "Nabari": 6675.7, + "Coronado": 14412.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhangjiagang: (31.86°, 120.54°)", + " Paseh: (-7.07°, 107.79°)", + " Jatiwangi: (-6.73°, 108.26°)", + " Nabari: (34.62°, 136.08°)", + " Coronado: (32.69°, -117.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coronado: 14412.4 km from centroid", + " Nabari: 6675.7 km from centroid", + " Zhangjiagang: 5218.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coronado", + "FINAL ANSWER: Coronado" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.64643, + "lon": 106.43043, + "name": "Ligang" + }, + { + "lat": 29.83774, + "lon": 91.72889, + "name": "Maizhokunggar" + }, + { + "lat": 35.86667, + "lon": 140.01667, + "name": "Abiko" + }, + { + "lat": 27.96282, + "lon": 79.73827, + "name": "Tilhar" + }, + { + "lat": -37.8318, + "lon": 140.77919, + "name": "Mount Gambier" + } + ], + "question": "Which location is the geographic outlier among: Ligang, Maizhokunggar, Abiko, Tilhar, Mount Gambier?", + "ground_truth": { + "answer": "Mount Gambier", + "outlier_distance_km": 7000.5, + "second_furthest_km": 3405.3, + "clarity_ratio": 2.06, + "median_distance_km": 3349.4, + "distances_to_centroid": { + "Ligang": 2255.1, + "Maizhokunggar": 2358.1, + "Abiko": 3349.4, + "Tilhar": 3405.3, + "Mount Gambier": 7000.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ligang: (38.65°, 106.43°)", + " Maizhokunggar: (29.84°, 91.73°)", + " Abiko: (35.87°, 140.02°)", + " Tilhar: (27.96°, 79.74°)", + " Mount Gambier: (-37.83°, 140.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Gambier: 7000.5 km from centroid", + " Tilhar: 3405.3 km from centroid", + " Abiko: 3349.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Gambier", + "FINAL ANSWER: Mount Gambier" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.14268, + "lon": -88.15101, + "name": "Tizimín" + }, + { + "lat": 27.80058, + "lon": -97.39638, + "name": "Corpus Christi" + }, + { + "lat": 39.15817, + "lon": -75.52437, + "name": "Dover" + }, + { + "lat": 28.05002, + "lon": -82.49287, + "name": "Carrollwood" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + } + ], + "question": "Which location is the geographic outlier among: Tizimín, Corpus Christi, Dover, Carrollwood, Mornington?", + "ground_truth": { + "answer": "Mornington", + "outlier_distance_km": 17456.0, + "second_furthest_km": 6060.0, + "clarity_ratio": 2.88, + "median_distance_km": 5131.0, + "distances_to_centroid": { + "Tizimín": 5131.0, + "Corpus Christi": 6060.0, + "Dover": 4355.2, + "Carrollwood": 4602.5, + "Mornington": 17456.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tizimín: (21.14°, -88.15°)", + " Corpus Christi: (27.80°, -97.40°)", + " Dover: (39.16°, -75.52°)", + " Carrollwood: (28.05°, -82.49°)", + " Mornington: (-38.22°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mornington: 17456.0 km from centroid", + " Corpus Christi: 6060.0 km from centroid", + " Tizimín: 5131.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mornington", + "FINAL ANSWER: Mornington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.98154, + "lon": -81.23621, + "name": "Lexington" + }, + { + "lat": 36.30078, + "lon": -119.78291, + "name": "Lemoore" + }, + { + "lat": 37.74786, + "lon": -84.29465, + "name": "Richmond" + }, + { + "lat": 34.02893, + "lon": -84.19858, + "name": "Johns Creek" + }, + { + "lat": 28.28635, + "lon": 117.20656, + "name": "Huayuan" + } + ], + "question": "Which location is the geographic outlier among: Lexington, Lemoore, Richmond, Johns Creek, Huayuan?", + "ground_truth": { + "answer": "Huayuan", + "outlier_distance_km": 12961.0, + "second_furthest_km": 6163.7, + "clarity_ratio": 2.1, + "median_distance_km": 3093.9, + "distances_to_centroid": { + "Lexington": 2825.3, + "Lemoore": 6163.7, + "Richmond": 3057.7, + "Johns Creek": 3093.9, + "Huayuan": 12961.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lexington: (33.98°, -81.24°)", + " Lemoore: (36.30°, -119.78°)", + " Richmond: (37.75°, -84.29°)", + " Johns Creek: (34.03°, -84.20°)", + " Huayuan: (28.29°, 117.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huayuan: 12961.0 km from centroid", + " Lemoore: 6163.7 km from centroid", + " Johns Creek: 3093.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huayuan", + "FINAL ANSWER: Huayuan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + }, + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": 40.76843, + "lon": -73.52513, + "name": "Hicksville" + } + ], + "question": "Which location is the geographic outlier among: Mandurah, Mascot, Wellington, Mount Isa, Hicksville?", + "ground_truth": { + "answer": "Hicksville", + "outlier_distance_km": 17389.1, + "second_furthest_km": 7348.1, + "clarity_ratio": 2.37, + "median_distance_km": 5240.6, + "distances_to_centroid": { + "Mandurah": 2190.8, + "Mascot": 5240.6, + "Wellington": 7348.1, + "Mount Isa": 3995.2, + "Hicksville": 17389.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mandurah: (-32.53°, 115.72°)", + " Mascot: (-33.93°, 151.19°)", + " Wellington: (-41.29°, 174.78°)", + " Mount Isa: (-20.73°, 139.50°)", + " Hicksville: (40.77°, -73.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hicksville: 17389.1 km from centroid", + " Wellington: 7348.1 km from centroid", + " Mascot: 5240.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hicksville", + "FINAL ANSWER: Hicksville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -37.75819, + "lon": 145.00583, + "name": "Thornbury" + }, + { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + { + "lat": -26.25, + "lon": 28.4, + "name": "Springs" + } + ], + "question": "Which location is the geographic outlier among: Maryborough, Ellenbrook, Thornbury, Wyndham Vale, Springs?", + "ground_truth": { + "answer": "Springs", + "outlier_distance_km": 8414.7, + "second_furthest_km": 3503.9, + "clarity_ratio": 2.4, + "median_distance_km": 2599.8, + "distances_to_centroid": { + "Maryborough": 3503.9, + "Ellenbrook": 129.9, + "Thornbury": 2599.8, + "Wyndham Vale": 2568.1, + "Springs": 8414.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maryborough: (-25.54°, 152.70°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Thornbury: (-37.76°, 145.01°)", + " Wyndham Vale: (-37.89°, 144.62°)", + " Springs: (-26.25°, 28.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Springs: 8414.7 km from centroid", + " Maryborough: 3503.9 km from centroid", + " Thornbury: 2599.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Springs", + "FINAL ANSWER: Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.35573, + "lon": 31.68484, + "name": "Kafr Sa‘d" + }, + { + "lat": -25.11319, + "lon": 29.04454, + "name": "Siyabuswa" + }, + { + "lat": 30.06667, + "lon": 31.3, + "name": "Madīnat an Naşr" + }, + { + "lat": -25.40892, + "lon": 28.287, + "name": "Hammanskraal" + }, + { + "lat": 42.49698, + "lon": -82.88881, + "name": "Saint Clair Shores" + } + ], + "question": "Which location is the geographic outlier among: Kafr Sa‘d, Siyabuswa, Madīnat an Naşr, Hammanskraal, Saint Clair Shores?", + "ground_truth": { + "answer": "Saint Clair Shores", + "outlier_distance_km": 9238.3, + "second_furthest_km": 4615.2, + "clarity_ratio": 2.0, + "median_distance_km": 4602.1, + "distances_to_centroid": { + "Kafr Sa‘d": 3388.7, + "Siyabuswa": 4615.2, + "Madīnat an Naşr": 3273.4, + "Hammanskraal": 4602.1, + "Saint Clair Shores": 9238.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kafr Sa‘d: (31.36°, 31.68°)", + " Siyabuswa: (-25.11°, 29.04°)", + " Madīnat an Naşr: (30.07°, 31.30°)", + " Hammanskraal: (-25.41°, 28.29°)", + " Saint Clair Shores: (42.50°, -82.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Clair Shores: 9238.3 km from centroid", + " Siyabuswa: 4615.2 km from centroid", + " Hammanskraal: 4602.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Clair Shores", + "FINAL ANSWER: Saint Clair Shores" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.16852, + "lon": 9.87134, + "name": "Sondrio" + }, + { + "lat": 55.9825, + "lon": 37.18139, + "name": "Zelenograd" + }, + { + "lat": 38.61372, + "lon": -0.1269, + "name": "la Nucia" + }, + { + "lat": 41.37452, + "lon": 2.16326, + "name": "Poble Sec" + }, + { + "lat": 7.34813, + "lon": 37.95063, + "name": "Damboya" + } + ], + "question": "Which location is the geographic outlier among: Sondrio, Zelenograd, la Nucia, Poble Sec, Damboya?", + "ground_truth": { + "answer": "Damboya", + "outlier_distance_km": 3976.8, + "second_furthest_km": 2490.4, + "clarity_ratio": 1.6, + "median_distance_km": 1530.8, + "distances_to_centroid": { + "Sondrio": 1109.4, + "Zelenograd": 2490.4, + "la Nucia": 1530.8, + "Poble Sec": 1359.4, + "Damboya": 3976.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sondrio: (46.17°, 9.87°)", + " Zelenograd: (55.98°, 37.18°)", + " la Nucia: (38.61°, -0.13°)", + " Poble Sec: (41.37°, 2.16°)", + " Damboya: (7.35°, 37.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Damboya: 3976.8 km from centroid", + " Zelenograd: 2490.4 km from centroid", + " la Nucia: 1530.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Damboya", + "FINAL ANSWER: Damboya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -29.20932, + "lon": 26.83898, + "name": "Thaba Nchu" + }, + { + "lat": -0.90711, + "lon": 34.52895, + "name": "Awendo" + }, + { + "lat": -23.90449, + "lon": 29.46885, + "name": "Polokwane" + }, + { + "lat": 5.55221, + "lon": -0.33912, + "name": "Mandela" + }, + { + "lat": 24.57578, + "lon": 77.73123, + "name": "Ashoknagar" + } + ], + "question": "Which location is the geographic outlier among: Thaba Nchu, Awendo, Polokwane, Mandela, Ashoknagar?", + "ground_truth": { + "answer": "Ashoknagar", + "outlier_distance_km": 5776.8, + "second_furthest_km": 3944.7, + "clarity_ratio": 1.46, + "median_distance_km": 2809.5, + "distances_to_centroid": { + "Thaba Nchu": 2809.5, + "Awendo": 441.5, + "Polokwane": 2173.3, + "Mandela": 3944.7, + "Ashoknagar": 5776.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thaba Nchu: (-29.21°, 26.84°)", + " Awendo: (-0.91°, 34.53°)", + " Polokwane: (-23.90°, 29.47°)", + " Mandela: (5.55°, -0.34°)", + " Ashoknagar: (24.58°, 77.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ashoknagar: 5776.8 km from centroid", + " Mandela: 3944.7 km from centroid", + " Thaba Nchu: 2809.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ashoknagar", + "FINAL ANSWER: Ashoknagar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.43333, + "lon": 136.68333, + "name": "Kitagata" + }, + { + "lat": 22.26138, + "lon": 100.0829, + "name": "Huimin" + }, + { + "lat": 34.50896, + "lon": 135.7929, + "name": "Kashihara-shi" + }, + { + "lat": 23.42564, + "lon": 72.65739, + "name": "Mānsa" + }, + { + "lat": -33.79728, + "lon": 150.7847, + "name": "St Clair" + } + ], + "question": "Which location is the geographic outlier among: Kitagata, Huimin, Kashihara-shi, Mānsa, St Clair?", + "ground_truth": { + "answer": "St Clair", + "outlier_distance_km": 6505.0, + "second_furthest_km": 4908.8, + "clarity_ratio": 1.33, + "median_distance_km": 2738.6, + "distances_to_centroid": { + "Kitagata": 2738.6, + "Huimin": 2108.4, + "Kashihara-shi": 2608.3, + "Mānsa": 4908.8, + "St Clair": 6505.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kitagata: (35.43°, 136.68°)", + " Huimin: (22.26°, 100.08°)", + " Kashihara-shi: (34.51°, 135.79°)", + " Mānsa: (23.43°, 72.66°)", + " St Clair: (-33.80°, 150.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " St Clair: 6505.0 km from centroid", + " Mānsa: 4908.8 km from centroid", + " Kitagata: 2738.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: St Clair", + "FINAL ANSWER: St Clair" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.74197, + "lon": -122.4863, + "name": "Parkside" + }, + { + "lat": 28.69889, + "lon": -81.30812, + "name": "Winter Springs" + }, + { + "lat": 26.15952, + "lon": -97.99084, + "name": "Weslaco" + }, + { + "lat": 20.12776, + "lon": -88.92282, + "name": "Peto" + }, + { + "lat": 45.45346, + "lon": 41.97244, + "name": "Donskoye" + } + ], + "question": "Which location is the geographic outlier among: Parkside, Winter Springs, Weslaco, Peto, Donskoye?", + "ground_truth": { + "answer": "Donskoye", + "outlier_distance_km": 9030.2, + "second_furthest_km": 4806.2, + "clarity_ratio": 1.88, + "median_distance_km": 2807.7, + "distances_to_centroid": { + "Parkside": 4806.2, + "Winter Springs": 1157.7, + "Weslaco": 2807.7, + "Peto": 2300.0, + "Donskoye": 9030.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Parkside: (37.74°, -122.49°)", + " Winter Springs: (28.70°, -81.31°)", + " Weslaco: (26.16°, -97.99°)", + " Peto: (20.13°, -88.92°)", + " Donskoye: (45.45°, 41.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Donskoye: 9030.2 km from centroid", + " Parkside: 4806.2 km from centroid", + " Weslaco: 2807.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Donskoye", + "FINAL ANSWER: Donskoye" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.515, + "lon": -48.04472, + "name": "Bujaru" + }, + { + "lat": -27.42039, + "lon": -59.03731, + "name": "Fontana" + }, + { + "lat": -20.25694, + "lon": -47.47667, + "name": "Pedregulho" + }, + { + "lat": -16.525, + "lon": -50.37222, + "name": "São Luís de Montes Belos" + }, + { + "lat": 27.96585, + "lon": -82.8001, + "name": "Clearwater" + } + ], + "question": "Which location is the geographic outlier among: Bujaru, Fontana, Pedregulho, São Luís de Montes Belos, Clearwater?", + "ground_truth": { + "answer": "Clearwater", + "outlier_distance_km": 4791.5, + "second_furthest_km": 2215.0, + "clarity_ratio": 2.16, + "median_distance_km": 1780.9, + "distances_to_centroid": { + "Bujaru": 1248.4, + "Fontana": 2215.0, + "Pedregulho": 1780.9, + "São Luís de Montes Belos": 1266.1, + "Clearwater": 4791.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bujaru: (-1.51°, -48.04°)", + " Fontana: (-27.42°, -59.04°)", + " Pedregulho: (-20.26°, -47.48°)", + " São Luís de Montes Belos: (-16.52°, -50.37°)", + " Clearwater: (27.97°, -82.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clearwater: 4791.5 km from centroid", + " Fontana: 2215.0 km from centroid", + " Pedregulho: 1780.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clearwater", + "FINAL ANSWER: Clearwater" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.25612, + "lon": 72.17928, + "name": "Deesa" + }, + { + "lat": 14.67784, + "lon": 77.60813, + "name": "Anantapur" + }, + { + "lat": 36.91218, + "lon": 119.5566, + "name": "Buzhuang" + }, + { + "lat": 34.53472, + "lon": 135.70925, + "name": "Kashiba" + }, + { + "lat": -11.84722, + "lon": -40.79139, + "name": "Tapiramutá" + } + ], + "question": "Which location is the geographic outlier among: Deesa, Anantapur, Buzhuang, Kashiba, Tapiramutá?", + "ground_truth": { + "answer": "Tapiramutá", + "outlier_distance_km": 12901.3, + "second_furthest_km": 6335.6, + "clarity_ratio": 2.04, + "median_distance_km": 4898.3, + "distances_to_centroid": { + "Deesa": 510.6, + "Anantapur": 753.4, + "Buzhuang": 4898.3, + "Kashiba": 6335.6, + "Tapiramutá": 12901.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deesa: (24.26°, 72.18°)", + " Anantapur: (14.68°, 77.61°)", + " Buzhuang: (36.91°, 119.56°)", + " Kashiba: (34.53°, 135.71°)", + " Tapiramutá: (-11.85°, -40.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tapiramutá: 12901.3 km from centroid", + " Kashiba: 6335.6 km from centroid", + " Buzhuang: 4898.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tapiramutá", + "FINAL ANSWER: Tapiramutá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.99417, + "lon": 4.20972, + "name": "Naaldwijk" + }, + { + "lat": 40.3818, + "lon": -3.77109, + "name": "Las Águilas" + }, + { + "lat": 41.44163, + "lon": 2.17727, + "name": "Nou Barris" + }, + { + "lat": 41.08156, + "lon": 14.25342, + "name": "Santa Maria Capua Vetere" + }, + { + "lat": 6.85783, + "lon": 7.39577, + "name": "Nsukka" + } + ], + "question": "Which location is the geographic outlier among: Naaldwijk, Las Águilas, Nou Barris, Santa Maria Capua Vetere, Nsukka?", + "ground_truth": { + "answer": "Nsukka", + "outlier_distance_km": 3289.7, + "second_furthest_km": 1740.1, + "clarity_ratio": 1.89, + "median_distance_km": 969.6, + "distances_to_centroid": { + "Naaldwijk": 1740.1, + "Las Águilas": 874.7, + "Nou Barris": 611.5, + "Santa Maria Capua Vetere": 969.6, + "Nsukka": 3289.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Naaldwijk: (51.99°, 4.21°)", + " Las Águilas: (40.38°, -3.77°)", + " Nou Barris: (41.44°, 2.18°)", + " Santa Maria Capua Vetere: (41.08°, 14.25°)", + " Nsukka: (6.86°, 7.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nsukka: 3289.7 km from centroid", + " Naaldwijk: 1740.1 km from centroid", + " Santa Maria Capua Vetere: 969.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nsukka", + "FINAL ANSWER: Nsukka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.9803, + "lon": 11.32903, + "name": "Weimar" + }, + { + "lat": 41.41209, + "lon": 2.14394, + "name": "Vallcarca" + }, + { + "lat": 53.96796, + "lon": 38.33151, + "name": "Donskoy" + }, + { + "lat": 48.88075, + "lon": 2.35513, + "name": "Saint-Vincent de Paul" + }, + { + "lat": -13.07556, + "lon": -76.38528, + "name": "San Vicente de Cañete" + } + ], + "question": "Which location is the geographic outlier among: Weimar, Vallcarca, Donskoy, Saint-Vincent de Paul, San Vicente de Cañete?", + "ground_truth": { + "answer": "San Vicente de Cañete", + "outlier_distance_km": 9314.3, + "second_furthest_km": 3796.4, + "clarity_ratio": 2.45, + "median_distance_km": 2046.2, + "distances_to_centroid": { + "Weimar": 2046.2, + "Vallcarca": 794.2, + "Donskoy": 3796.4, + "Saint-Vincent de Paul": 1490.1, + "San Vicente de Cañete": 9314.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Weimar: (50.98°, 11.33°)", + " Vallcarca: (41.41°, 2.14°)", + " Donskoy: (53.97°, 38.33°)", + " Saint-Vincent de Paul: (48.88°, 2.36°)", + " San Vicente de Cañete: (-13.08°, -76.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Vicente de Cañete: 9314.3 km from centroid", + " Donskoy: 3796.4 km from centroid", + " Weimar: 2046.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Vicente de Cañete", + "FINAL ANSWER: San Vicente de Cañete" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.81568, + "lon": 2.38487, + "name": "Ivry-sur-Seine" + }, + { + "lat": 41.21667, + "lon": 1.53333, + "name": "El Vendrell" + }, + { + "lat": 51.80924, + "lon": 8.42841, + "name": "Rietberg" + }, + { + "lat": 42.35055, + "lon": 13.39954, + "name": "L'Aquila" + }, + { + "lat": 34.09001, + "lon": -117.89034, + "name": "Covina" + } + ], + "question": "Which location is the geographic outlier among: Ivry-sur-Seine, El Vendrell, Rietberg, L'Aquila, Covina?", + "ground_truth": { + "answer": "Covina", + "outlier_distance_km": 8143.4, + "second_furthest_km": 2576.4, + "clarity_ratio": 3.16, + "median_distance_km": 2187.3, + "distances_to_centroid": { + "Ivry-sur-Seine": 1694.0, + "El Vendrell": 1656.3, + "Rietberg": 2187.3, + "L'Aquila": 2576.4, + "Covina": 8143.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ivry-sur-Seine: (48.82°, 2.38°)", + " El Vendrell: (41.22°, 1.53°)", + " Rietberg: (51.81°, 8.43°)", + " L'Aquila: (42.35°, 13.40°)", + " Covina: (34.09°, -117.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Covina: 8143.4 km from centroid", + " L'Aquila: 2576.4 km from centroid", + " Rietberg: 2187.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Covina", + "FINAL ANSWER: Covina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.76333, + "lon": -52.11556, + "name": "Presidente Epitácio" + }, + { + "lat": -28.21344, + "lon": -49.16383, + "name": "São José" + }, + { + "lat": -7.90278, + "lon": -35.98833, + "name": "Vertentes" + }, + { + "lat": -23.53872, + "lon": -46.68093, + "name": "Perdizes" + }, + { + "lat": 29.28581, + "lon": -81.05589, + "name": "Ormond Beach" + } + ], + "question": "Which location is the geographic outlier among: Presidente Epitácio, São José, Vertentes, Perdizes, Ormond Beach?", + "ground_truth": { + "answer": "Ormond Beach", + "outlier_distance_km": 5343.0, + "second_furthest_km": 2017.9, + "clarity_ratio": 2.65, + "median_distance_km": 1888.2, + "distances_to_centroid": { + "Presidente Epitácio": 1264.1, + "São José": 2017.9, + "Vertentes": 1888.2, + "Perdizes": 1604.7, + "Ormond Beach": 5343.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Presidente Epitácio: (-21.76°, -52.12°)", + " São José: (-28.21°, -49.16°)", + " Vertentes: (-7.90°, -35.99°)", + " Perdizes: (-23.54°, -46.68°)", + " Ormond Beach: (29.29°, -81.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ormond Beach: 5343.0 km from centroid", + " São José: 2017.9 km from centroid", + " Vertentes: 1888.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ormond Beach", + "FINAL ANSWER: Ormond Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.88733, + "lon": -102.20636, + "name": "Tangancícuaro de Arista" + }, + { + "lat": 40.67677, + "lon": -73.84375, + "name": "Ozone Park" + }, + { + "lat": 40.83242, + "lon": -115.76312, + "name": "Elko" + }, + { + "lat": 20.62263, + "lon": -103.24168, + "name": "Tonalá" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + } + ], + "question": "Which location is the geographic outlier among: Tangancícuaro de Arista, Ozone Park, Elko, Tonalá, Shepparton?", + "ground_truth": { + "answer": "Shepparton", + "outlier_distance_km": 17396.2, + "second_furthest_km": 6755.3, + "clarity_ratio": 2.58, + "median_distance_km": 5598.5, + "distances_to_centroid": { + "Tangancícuaro de Arista": 5499.1, + "Ozone Park": 3479.8, + "Elko": 6755.3, + "Tonalá": 5598.5, + "Shepparton": 17396.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tangancícuaro de Arista: (19.89°, -102.21°)", + " Ozone Park: (40.68°, -73.84°)", + " Elko: (40.83°, -115.76°)", + " Tonalá: (20.62°, -103.24°)", + " Shepparton: (-36.38°, 145.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shepparton: 17396.2 km from centroid", + " Elko: 6755.3 km from centroid", + " Tonalá: 5598.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shepparton", + "FINAL ANSWER: Shepparton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 60.72383, + "lon": 114.93447, + "name": "Lensk" + }, + { + "lat": 43.96182, + "lon": 12.73631, + "name": "Cattolica" + }, + { + "lat": 44.6333, + "lon": 41.9444, + "name": "Nevinnomyssk" + }, + { + "lat": 40.75337, + "lon": 14.45251, + "name": "Torre Annunziata" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + } + ], + "question": "Which location is the geographic outlier among: Lensk, Cattolica, Nevinnomyssk, Torre Annunziata, Sunshine West?", + "ground_truth": { + "answer": "Sunshine West", + "outlier_distance_km": 11167.7, + "second_furthest_km": 4906.5, + "clarity_ratio": 2.28, + "median_distance_km": 4841.1, + "distances_to_centroid": { + "Lensk": 4906.5, + "Cattolica": 4841.1, + "Nevinnomyssk": 2610.2, + "Torre Annunziata": 4709.9, + "Sunshine West": 11167.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lensk: (60.72°, 114.93°)", + " Cattolica: (43.96°, 12.74°)", + " Nevinnomyssk: (44.63°, 41.94°)", + " Torre Annunziata: (40.75°, 14.45°)", + " Sunshine West: (-37.79°, 144.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunshine West: 11167.7 km from centroid", + " Lensk: 4906.5 km from centroid", + " Cattolica: 4841.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunshine West", + "FINAL ANSWER: Sunshine West" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.2463, + "lon": -73.31752, + "name": "Arauco" + }, + { + "lat": -16.17028, + "lon": -42.29028, + "name": "Salinas" + }, + { + "lat": -6.79111, + "lon": -50.46694, + "name": "Água Azul do Norte" + }, + { + "lat": 4.81367, + "lon": -74.35453, + "name": "Facatativá" + }, + { + "lat": 26.90806, + "lon": 75.19137, + "name": "Sāmbhar" + } + ], + "question": "Which location is the geographic outlier among: Arauco, Salinas, Água Azul do Norte, Facatativá, Sāmbhar?", + "ground_truth": { + "answer": "Sāmbhar", + "outlier_distance_km": 12100.5, + "second_furthest_km": 5377.2, + "clarity_ratio": 2.25, + "median_distance_km": 4733.0, + "distances_to_centroid": { + "Arauco": 5377.2, + "Salinas": 1539.9, + "Água Azul do Norte": 1929.2, + "Facatativá": 4733.0, + "Sāmbhar": 12100.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arauco: (-37.25°, -73.32°)", + " Salinas: (-16.17°, -42.29°)", + " Água Azul do Norte: (-6.79°, -50.47°)", + " Facatativá: (4.81°, -74.35°)", + " Sāmbhar: (26.91°, 75.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sāmbhar: 12100.5 km from centroid", + " Arauco: 5377.2 km from centroid", + " Facatativá: 4733.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sāmbhar", + "FINAL ANSWER: Sāmbhar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.88939, + "lon": -111.88077, + "name": "Bountiful" + }, + { + "lat": 18.98856, + "lon": -97.44643, + "name": "Ciudad Serdán" + }, + { + "lat": 47.44846, + "lon": -122.29217, + "name": "SeaTac" + }, + { + "lat": 44.02471, + "lon": -88.54261, + "name": "Oshkosh" + }, + { + "lat": 10.73828, + "lon": 77.53223, + "name": "Dharapuram" + } + ], + "question": "Which location is the geographic outlier among: Bountiful, Ciudad Serdán, SeaTac, Oshkosh, Dharapuram?", + "ground_truth": { + "answer": "Dharapuram", + "outlier_distance_km": 14013.6, + "second_furthest_km": 4772.1, + "clarity_ratio": 2.94, + "median_distance_km": 3938.3, + "distances_to_centroid": { + "Bountiful": 3938.3, + "Ciudad Serdán": 3244.4, + "SeaTac": 4772.1, + "Oshkosh": 2163.6, + "Dharapuram": 14013.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bountiful: (40.89°, -111.88°)", + " Ciudad Serdán: (18.99°, -97.45°)", + " SeaTac: (47.45°, -122.29°)", + " Oshkosh: (44.02°, -88.54°)", + " Dharapuram: (10.74°, 77.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dharapuram: 14013.6 km from centroid", + " SeaTac: 4772.1 km from centroid", + " Bountiful: 3938.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dharapuram", + "FINAL ANSWER: Dharapuram" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.6, + "lon": 37.46667, + "name": "Gonder" + }, + { + "lat": -0.4841, + "lon": 37.12662, + "name": "Karatina" + }, + { + "lat": 9.03333, + "lon": 38.4, + "name": "Ādīs ��Alem" + }, + { + "lat": 12.74482, + "lon": 4.52514, + "name": "Argungu" + }, + { + "lat": 7.97917, + "lon": -75.4202, + "name": "Montelíbano" + } + ], + "question": "Which location is the geographic outlier among: Gonder, Karatina, Ādīs ‘Alem, Argungu, Montelíbano?", + "ground_truth": { + "answer": "Montelíbano", + "outlier_distance_km": 9206.8, + "second_furthest_km": 3330.1, + "clarity_ratio": 2.76, + "median_distance_km": 3295.2, + "distances_to_centroid": { + "Gonder": 3208.6, + "Karatina": 3330.1, + "Ādīs ‘Alem": 3295.2, + "Argungu": 646.0, + "Montelíbano": 9206.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gonder: (12.60°, 37.47°)", + " Karatina: (-0.48°, 37.13°)", + " Ādīs ‘Alem: (9.03°, 38.40°)", + " Argungu: (12.74°, 4.53°)", + " Montelíbano: (7.98°, -75.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Montelíbano: 9206.8 km from centroid", + " Karatina: 3330.1 km from centroid", + " Ādīs ‘Alem: 3295.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Montelíbano", + "FINAL ANSWER: Montelíbano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.56033, + "lon": -45.13155, + "name": "Lago da Pedra" + }, + { + "lat": -20.84889, + "lon": -41.11278, + "name": "Cachoeiro de Itapemirim" + }, + { + "lat": -34.16327, + "lon": -58.95919, + "name": "Campana" + }, + { + "lat": -8.66361, + "lon": -36.32, + "name": "Lajedo" + }, + { + "lat": -27.66606, + "lon": 28.13132, + "name": "Mamafubedu" + } + ], + "question": "Which location is the geographic outlier among: Lago da Pedra, Cachoeiro de Itapemirim, Campana, Lajedo, Mamafubedu?", + "ground_truth": { + "answer": "Mamafubedu", + "outlier_distance_km": 6020.5, + "second_furthest_km": 3249.5, + "clarity_ratio": 1.85, + "median_distance_km": 2258.4, + "distances_to_centroid": { + "Lago da Pedra": 2258.4, + "Cachoeiro de Itapemirim": 1105.6, + "Campana": 3249.5, + "Lajedo": 1318.0, + "Mamafubedu": 6020.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lago da Pedra: (-4.56°, -45.13°)", + " Cachoeiro de Itapemirim: (-20.85°, -41.11°)", + " Campana: (-34.16°, -58.96°)", + " Lajedo: (-8.66°, -36.32°)", + " Mamafubedu: (-27.67°, 28.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mamafubedu: 6020.5 km from centroid", + " Campana: 3249.5 km from centroid", + " Lago da Pedra: 2258.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mamafubedu", + "FINAL ANSWER: Mamafubedu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.56222, + "lon": -38.50889, + "name": "Conceição" + }, + { + "lat": -6.03389, + "lon": -37.02028, + "name": "Jucurutu" + }, + { + "lat": -29.76028, + "lon": -51.14722, + "name": "São Leopoldo" + }, + { + "lat": -6.10917, + "lon": -38.20444, + "name": "Pau dos Ferros" + }, + { + "lat": 27.30193, + "lon": 105.28627, + "name": "Bijie" + } + ], + "question": "Which location is the geographic outlier among: Conceição, Jucurutu, São Leopoldo, Pau dos Ferros, Bijie?", + "ground_truth": { + "answer": "Bijie", + "outlier_distance_km": 12913.6, + "second_furthest_km": 4988.3, + "clarity_ratio": 2.59, + "median_distance_km": 2960.3, + "distances_to_centroid": { + "Conceição": 2960.3, + "Jucurutu": 2784.9, + "São Leopoldo": 4988.3, + "Pau dos Ferros": 2916.1, + "Bijie": 12913.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Conceição: (-7.56°, -38.51°)", + " Jucurutu: (-6.03°, -37.02°)", + " São Leopoldo: (-29.76°, -51.15°)", + " Pau dos Ferros: (-6.11°, -38.20°)", + " Bijie: (27.30°, 105.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bijie: 12913.6 km from centroid", + " São Leopoldo: 4988.3 km from centroid", + " Conceição: 2960.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bijie", + "FINAL ANSWER: Bijie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.21411, + "lon": 86.12492, + "name": "Anandpur" + }, + { + "lat": 8.20549, + "lon": 77.34439, + "name": "Nallavila" + }, + { + "lat": 20.0054, + "lon": 79.30273, + "name": "Durgāpur" + }, + { + "lat": 21.70656, + "lon": 109.47502, + "name": "Zhakou" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + } + ], + "question": "Which location is the geographic outlier among: Anandpur, Nallavila, Durgāpur, Zhakou, Saint Ives?", + "ground_truth": { + "answer": "Saint Ives", + "outlier_distance_km": 7016.3, + "second_furthest_km": 2691.3, + "clarity_ratio": 2.61, + "median_distance_km": 2571.6, + "distances_to_centroid": { + "Anandpur": 2185.4, + "Nallavila": 2571.6, + "Durgāpur": 2691.3, + "Zhakou": 1841.8, + "Saint Ives": 7016.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Anandpur: (21.21°, 86.12°)", + " Nallavila: (8.21°, 77.34°)", + " Durgāpur: (20.01°, 79.30°)", + " Zhakou: (21.71°, 109.48°)", + " Saint Ives: (-33.73°, 151.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Ives: 7016.3 km from centroid", + " Durgāpur: 2691.3 km from centroid", + " Nallavila: 2571.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Ives", + "FINAL ANSWER: Saint Ives" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.71065, + "lon": -72.20813, + "name": "Willimantic" + }, + { + "lat": 43.91452, + "lon": -69.96533, + "name": "Brunswick" + }, + { + "lat": 48.42122, + "lon": -122.33405, + "name": "Mount Vernon" + }, + { + "lat": 49.21359, + "lon": -123.12979, + "name": "Marpole" + }, + { + "lat": -38.11342, + "lon": 145.28326, + "name": "Cranbourne" + } + ], + "question": "Which location is the geographic outlier among: Willimantic, Brunswick, Mount Vernon, Marpole, Cranbourne?", + "ground_truth": { + "answer": "Cranbourne", + "outlier_distance_km": 18392.2, + "second_furthest_km": 6534.6, + "clarity_ratio": 2.81, + "median_distance_km": 6491.7, + "distances_to_centroid": { + "Willimantic": 2559.4, + "Brunswick": 2522.5, + "Mount Vernon": 6491.7, + "Marpole": 6534.6, + "Cranbourne": 18392.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Willimantic: (41.71°, -72.21°)", + " Brunswick: (43.91°, -69.97°)", + " Mount Vernon: (48.42°, -122.33°)", + " Marpole: (49.21°, -123.13°)", + " Cranbourne: (-38.11°, 145.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cranbourne: 18392.2 km from centroid", + " Marpole: 6534.6 km from centroid", + " Mount Vernon: 6491.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cranbourne", + "FINAL ANSWER: Cranbourne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -38.68333, + "lon": 176.08333, + "name": "Taupo" + }, + { + "lat": 16.62473, + "lon": -93.09894, + "name": "Suchiapa" + } + ], + "question": "Which location is the geographic outlier among: Caboolture, Perth, Rockingham, Taupo, Suchiapa?", + "ground_truth": { + "answer": "Suchiapa", + "outlier_distance_km": 19050.6, + "second_furthest_km": 7838.0, + "clarity_ratio": 2.43, + "median_distance_km": 5962.2, + "distances_to_centroid": { + "Caboolture": 5962.2, + "Perth": 2431.1, + "Rockingham": 2431.8, + "Taupo": 7838.0, + "Suchiapa": 19050.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caboolture: (-27.08°, 152.95°)", + " Perth: (-31.95°, 115.86°)", + " Rockingham: (-32.28°, 115.73°)", + " Taupo: (-38.68°, 176.08°)", + " Suchiapa: (16.62°, -93.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Suchiapa: 19050.6 km from centroid", + " Taupo: 7838.0 km from centroid", + " Caboolture: 5962.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Suchiapa", + "FINAL ANSWER: Suchiapa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.22119, + "lon": -122.68965, + "name": "Pitt Meadows" + }, + { + "lat": 37.59855, + "lon": -122.38719, + "name": "Millbrae" + }, + { + "lat": 39.92678, + "lon": -75.15712, + "name": "Wharton" + }, + { + "lat": 21.192, + "lon": -97.74088, + "name": "Cerro Azul" + }, + { + "lat": 28.46824, + "lon": -16.25462, + "name": "Santa Cruz de Tenerife" + } + ], + "question": "Which location is the geographic outlier among: Pitt Meadows, Millbrae, Wharton, Cerro Azul, Santa Cruz de Tenerife?", + "ground_truth": { + "answer": "Santa Cruz de Tenerife", + "outlier_distance_km": 6569.8, + "second_furthest_km": 3290.3, + "clarity_ratio": 2.0, + "median_distance_km": 3170.8, + "distances_to_centroid": { + "Pitt Meadows": 3290.3, + "Millbrae": 3170.8, + "Wharton": 1150.7, + "Cerro Azul": 1892.6, + "Santa Cruz de Tenerife": 6569.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pitt Meadows: (49.22°, -122.69°)", + " Millbrae: (37.60°, -122.39°)", + " Wharton: (39.93°, -75.16°)", + " Cerro Azul: (21.19°, -97.74°)", + " Santa Cruz de Tenerife: (28.47°, -16.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Cruz de Tenerife: 6569.8 km from centroid", + " Pitt Meadows: 3290.3 km from centroid", + " Millbrae: 3170.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Cruz de Tenerife", + "FINAL ANSWER: Santa Cruz de Tenerife" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.4245, + "lon": 100.689, + "name": "Yunnanyi" + }, + { + "lat": 30.08333, + "lon": 114.95, + "name": "Daye" + }, + { + "lat": -7.3817, + "lon": 108.2082, + "name": "Kawalu" + }, + { + "lat": 0.79065, + "lon": 127.38424, + "name": "Ternate" + }, + { + "lat": 50.92149, + "lon": 6.36267, + "name": "Jülich" + } + ], + "question": "Which location is the geographic outlier among: Yunnanyi, Daye, Kawalu, Ternate, Jülich?", + "ground_truth": { + "answer": "Jülich", + "outlier_distance_km": 7965.1, + "second_furthest_km": 4445.1, + "clarity_ratio": 1.79, + "median_distance_km": 3547.3, + "distances_to_centroid": { + "Yunnanyi": 1118.8, + "Daye": 2607.8, + "Kawalu": 3547.3, + "Ternate": 4445.1, + "Jülich": 7965.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yunnanyi: (25.42°, 100.69°)", + " Daye: (30.08°, 114.95°)", + " Kawalu: (-7.38°, 108.21°)", + " Ternate: (0.79°, 127.38°)", + " Jülich: (50.92°, 6.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jülich: 7965.1 km from centroid", + " Ternate: 4445.1 km from centroid", + " Kawalu: 3547.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jülich", + "FINAL ANSWER: Jülich" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.69303, + "lon": -83.41181, + "name": "Waterford" + }, + { + "lat": 19.95232, + "lon": -102.30781, + "name": "Jacona de Plancarte" + }, + { + "lat": 39.08289, + "lon": -77.26498, + "name": "North Potomac" + }, + { + "lat": 21.17429, + "lon": -86.84656, + "name": "Cancún" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + } + ], + "question": "Which location is the geographic outlier among: Waterford, Jacona de Plancarte, North Potomac, Cancún, New Plymouth?", + "ground_truth": { + "answer": "New Plymouth", + "outlier_distance_km": 16251.5, + "second_furthest_km": 7049.4, + "clarity_ratio": 2.31, + "median_distance_km": 5435.5, + "distances_to_centroid": { + "Waterford": 5380.2, + "Jacona de Plancarte": 7049.4, + "North Potomac": 4764.1, + "Cancún": 5435.5, + "New Plymouth": 16251.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waterford: (42.69°, -83.41°)", + " Jacona de Plancarte: (19.95°, -102.31°)", + " North Potomac: (39.08°, -77.26°)", + " Cancún: (21.17°, -86.85°)", + " New Plymouth: (-39.07°, 174.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " New Plymouth: 16251.5 km from centroid", + " Jacona de Plancarte: 7049.4 km from centroid", + " Cancún: 5435.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: New Plymouth", + "FINAL ANSWER: New Plymouth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.36667, + "lon": 1.75, + "name": "Romorantin-Lanthenay" + }, + { + "lat": 53.32498, + "lon": -3.83148, + "name": "Llandudno" + }, + { + "lat": 51.84967, + "lon": 8.30017, + "name": "Rheda-Wiedenbrück" + }, + { + "lat": 47.62604, + "lon": 6.14251, + "name": "Vesoul" + }, + { + "lat": 5.86006, + "lon": -0.6635, + "name": "Asamankese" + } + ], + "question": "Which location is the geographic outlier among: Romorantin-Lanthenay, Llandudno, Rheda-Wiedenbrück, Vesoul, Asamankese?", + "ground_truth": { + "answer": "Asamankese", + "outlier_distance_km": 3941.5, + "second_furthest_km": 1424.5, + "clarity_ratio": 2.77, + "median_distance_km": 1267.3, + "distances_to_centroid": { + "Romorantin-Lanthenay": 686.7, + "Llandudno": 1424.5, + "Rheda-Wiedenbrück": 1267.3, + "Vesoul": 774.9, + "Asamankese": 3941.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Romorantin-Lanthenay: (47.37°, 1.75°)", + " Llandudno: (53.32°, -3.83°)", + " Rheda-Wiedenbrück: (51.85°, 8.30°)", + " Vesoul: (47.63°, 6.14°)", + " Asamankese: (5.86°, -0.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Asamankese: 3941.5 km from centroid", + " Llandudno: 1424.5 km from centroid", + " Rheda-Wiedenbrück: 1267.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Asamankese", + "FINAL ANSWER: Asamankese" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.75003, + "lon": -87.80422, + "name": "Bridgeview" + }, + { + "lat": 40.69538, + "lon": -73.99375, + "name": "Brooklyn Heights" + }, + { + "lat": 40.54929, + "lon": -74.21019, + "name": "Rossville" + }, + { + "lat": 30.29469, + "lon": -81.39314, + "name": "Jacksonville Beach" + }, + { + "lat": 31.61166, + "lon": 25.92539, + "name": "Sīdī Barānī" + } + ], + "question": "Which location is the geographic outlier among: Bridgeview, Brooklyn Heights, Rossville, Jacksonville Beach, Sīdī Barānī?", + "ground_truth": { + "answer": "Sīdī Barānī", + "outlier_distance_km": 7497.9, + "second_furthest_km": 2578.3, + "clarity_ratio": 2.91, + "median_distance_km": 2256.9, + "distances_to_centroid": { + "Bridgeview": 2578.3, + "Brooklyn Heights": 1418.8, + "Rossville": 1433.5, + "Jacksonville Beach": 2256.9, + "Sīdī Barānī": 7497.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bridgeview: (41.75°, -87.80°)", + " Brooklyn Heights: (40.70°, -73.99°)", + " Rossville: (40.55°, -74.21°)", + " Jacksonville Beach: (30.29°, -81.39°)", + " Sīdī Barānī: (31.61°, 25.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sīdī Barānī: 7497.9 km from centroid", + " Bridgeview: 2578.3 km from centroid", + " Jacksonville Beach: 2256.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sīdī Barānī", + "FINAL ANSWER: Sīdī Barānī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + { + "lat": -37.66667, + "lon": 145.06667, + "name": "Mill Park" + }, + { + "lat": 28.96912, + "lon": 76.29495, + "name": "Maham" + } + ], + "question": "Which location is the geographic outlier among: Chatswood, Mandurah, Werribee, Mill Park, Maham?", + "ground_truth": { + "answer": "Maham", + "outlier_distance_km": 7864.5, + "second_furthest_km": 2703.9, + "clarity_ratio": 2.91, + "median_distance_km": 2434.6, + "distances_to_centroid": { + "Chatswood": 2703.9, + "Mandurah": 1537.3, + "Werribee": 2423.6, + "Mill Park": 2434.6, + "Maham": 7864.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chatswood: (-33.80°, 151.18°)", + " Mandurah: (-32.53°, 115.72°)", + " Werribee: (-37.90°, 144.67°)", + " Mill Park: (-37.67°, 145.07°)", + " Maham: (28.97°, 76.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maham: 7864.5 km from centroid", + " Chatswood: 2703.9 km from centroid", + " Mill Park: 2434.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maham", + "FINAL ANSWER: Maham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.86083, + "lon": 5.76667, + "name": "Beuningen" + }, + { + "lat": 50.58333, + "lon": 3.06667, + "name": "Faches-Thumesnil" + }, + { + "lat": 48.9193, + "lon": 2.54305, + "name": "Livry-Gargan" + }, + { + "lat": 39.98567, + "lon": -0.04935, + "name": "Castelló de la Plana" + }, + { + "lat": 6.59651, + "lon": 3.34205, + "name": "Ikeja" + } + ], + "question": "Which location is the geographic outlier among: Beuningen, Faches-Thumesnil, Livry-Gargan, Castelló de la Plana, Ikeja?", + "ground_truth": { + "answer": "Ikeja", + "outlier_distance_km": 3668.8, + "second_furthest_km": 1381.9, + "clarity_ratio": 2.65, + "median_distance_km": 1222.5, + "distances_to_centroid": { + "Beuningen": 1381.9, + "Faches-Thumesnil": 1222.5, + "Livry-Gargan": 1037.9, + "Castelló de la Plana": 258.7, + "Ikeja": 3668.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beuningen: (51.86°, 5.77°)", + " Faches-Thumesnil: (50.58°, 3.07°)", + " Livry-Gargan: (48.92°, 2.54°)", + " Castelló de la Plana: (39.99°, -0.05°)", + " Ikeja: (6.60°, 3.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ikeja: 3668.8 km from centroid", + " Beuningen: 1381.9 km from centroid", + " Faches-Thumesnil: 1222.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ikeja", + "FINAL ANSWER: Ikeja" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.15, + "lon": 32.71667, + "name": "Al Başalīyah Baḩrī" + }, + { + "lat": 12.56841, + "lon": 6.06225, + "name": "Talata Mafara" + }, + { + "lat": 10.98133, + "lon": 8.05749, + "name": "Soba" + }, + { + "lat": 5.48363, + "lon": 7.03325, + "name": "Owerri" + }, + { + "lat": 17.3381, + "lon": 77.90441, + "name": "Vikārābād" + } + ], + "question": "Which location is the geographic outlier among: Al Başalīyah Baḩrī, Talata Mafara, Soba, Owerri, Vikārābād?", + "ground_truth": { + "answer": "Vikārābād", + "outlier_distance_km": 5509.5, + "second_furthest_km": 2330.4, + "clarity_ratio": 2.36, + "median_distance_km": 2202.4, + "distances_to_centroid": { + "Al Başalīyah Baḩrī": 1376.9, + "Talata Mafara": 2202.4, + "Soba": 2018.6, + "Owerri": 2330.4, + "Vikārābād": 5509.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Başalīyah Baḩrī: (25.15°, 32.72°)", + " Talata Mafara: (12.57°, 6.06°)", + " Soba: (10.98°, 8.06°)", + " Owerri: (5.48°, 7.03°)", + " Vikārābād: (17.34°, 77.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vikārābād: 5509.5 km from centroid", + " Owerri: 2330.4 km from centroid", + " Talata Mafara: 2202.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vikārābād", + "FINAL ANSWER: Vikārābād" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": -27.19354, + "lon": 153.02631, + "name": "Deception Bay" + }, + { + "lat": 40.67019, + "lon": -73.74659, + "name": "Laurelton" + } + ], + "question": "Which location is the geographic outlier among: Maitland, Mooroolbark, Eastwood, Deception Bay, Laurelton?", + "ground_truth": { + "answer": "Laurelton", + "outlier_distance_km": 17511.6, + "second_furthest_km": 4954.3, + "clarity_ratio": 3.53, + "median_distance_km": 4861.7, + "distances_to_centroid": { + "Maitland": 4861.7, + "Mooroolbark": 4434.7, + "Eastwood": 4835.3, + "Deception Bay": 4954.3, + "Laurelton": 17511.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maitland: (-32.73°, 151.56°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Eastwood: (-33.79°, 151.08°)", + " Deception Bay: (-27.19°, 153.03°)", + " Laurelton: (40.67°, -73.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Laurelton: 17511.6 km from centroid", + " Deception Bay: 4954.3 km from centroid", + " Maitland: 4861.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Laurelton", + "FINAL ANSWER: Laurelton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.42291, + "lon": 136.76039, + "name": "Gifu" + }, + { + "lat": 13.9624, + "lon": 121.5265, + "name": "Sariaya" + }, + { + "lat": 12.50429, + "lon": 79.60556, + "name": "Vandavāsi" + }, + { + "lat": 11.6388, + "lon": 124.8417, + "name": "Zumarraga" + }, + { + "lat": 52.10714, + "lon": 19.94525, + "name": "Łowicz" + } + ], + "question": "Which location is the geographic outlier among: Gifu, Sariaya, Vandavāsi, Zumarraga, Łowicz?", + "ground_truth": { + "answer": "Łowicz", + "outlier_distance_km": 6933.1, + "second_furthest_km": 3998.6, + "clarity_ratio": 1.73, + "median_distance_km": 3331.2, + "distances_to_centroid": { + "Gifu": 3998.6, + "Sariaya": 2890.8, + "Vandavāsi": 2264.0, + "Zumarraga": 3331.2, + "Łowicz": 6933.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gifu: (35.42°, 136.76°)", + " Sariaya: (13.96°, 121.53°)", + " Vandavāsi: (12.50°, 79.61°)", + " Zumarraga: (11.64°, 124.84°)", + " Łowicz: (52.11°, 19.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Łowicz: 6933.1 km from centroid", + " Gifu: 3998.6 km from centroid", + " Zumarraga: 3331.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Łowicz", + "FINAL ANSWER: Łowicz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.81667, + "lon": 140.5, + "name": "Date" + }, + { + "lat": 22.4382, + "lon": 88.43205, + "name": "Rajpur Sonarpur" + }, + { + "lat": 11.13849, + "lon": 79.07556, + "name": "Ariyalūr" + }, + { + "lat": 35.85295, + "lon": 139.41212, + "name": "Sayama" + }, + { + "lat": -23.55108, + "lon": -46.53829, + "name": "Carrao" + } + ], + "question": "Which location is the geographic outlier among: Date, Rajpur Sonarpur, Ariyalūr, Sayama, Carrao?", + "ground_truth": { + "answer": "Carrao", + "outlier_distance_km": 14431.3, + "second_furthest_km": 6288.6, + "clarity_ratio": 2.29, + "median_distance_km": 6176.7, + "distances_to_centroid": { + "Date": 6288.6, + "Rajpur Sonarpur": 1071.7, + "Ariyalūr": 634.0, + "Sayama": 6176.7, + "Carrao": 14431.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Date: (37.82°, 140.50°)", + " Rajpur Sonarpur: (22.44°, 88.43°)", + " Ariyalūr: (11.14°, 79.08°)", + " Sayama: (35.85°, 139.41°)", + " Carrao: (-23.55°, -46.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carrao: 14431.3 km from centroid", + " Date: 6288.6 km from centroid", + " Sayama: 6176.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carrao", + "FINAL ANSWER: Carrao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.99116, + "lon": 145.17385, + "name": "Keysborough" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + }, + { + "lat": -37.62581, + "lon": 144.92555, + "name": "Roxburgh Park" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -25.34604, + "lon": 28.83431, + "name": "Somaroboro" + } + ], + "question": "Which location is the geographic outlier among: Keysborough, Manukau City, Roxburgh Park, Logan City, Somaroboro?", + "ground_truth": { + "answer": "Somaroboro", + "outlier_distance_km": 9399.4, + "second_furthest_km": 4124.3, + "clarity_ratio": 2.28, + "median_distance_km": 2350.2, + "distances_to_centroid": { + "Keysborough": 1525.2, + "Manukau City": 4124.3, + "Roxburgh Park": 1493.3, + "Logan City": 2350.2, + "Somaroboro": 9399.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Keysborough: (-37.99°, 145.17°)", + " Manukau City: (-36.99°, 174.88°)", + " Roxburgh Park: (-37.63°, 144.93°)", + " Logan City: (-27.64°, 153.11°)", + " Somaroboro: (-25.35°, 28.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Somaroboro: 9399.4 km from centroid", + " Manukau City: 4124.3 km from centroid", + " Logan City: 2350.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Somaroboro", + "FINAL ANSWER: Somaroboro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.31667, + "lon": 173.23333, + "name": "Stoke" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -38.65333, + "lon": 178.00417, + "name": "Gisborne" + }, + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": 34.34322, + "lon": 134.88911, + "name": "Sumoto" + } + ], + "question": "Which location is the geographic outlier among: Stoke, Melbourne, Gisborne, Elwood, Sumoto?", + "ground_truth": { + "answer": "Sumoto", + "outlier_distance_km": 6861.2, + "second_furthest_km": 2676.4, + "clarity_ratio": 2.56, + "median_distance_km": 2525.5, + "distances_to_centroid": { + "Stoke": 2525.5, + "Melbourne": 1792.7, + "Gisborne": 2676.4, + "Elwood": 1797.9, + "Sumoto": 6861.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stoke: (-41.32°, 173.23°)", + " Melbourne: (-37.81°, 144.96°)", + " Gisborne: (-38.65°, 178.00°)", + " Elwood: (-37.88°, 144.98°)", + " Sumoto: (34.34°, 134.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sumoto: 6861.2 km from centroid", + " Gisborne: 2676.4 km from centroid", + " Stoke: 2525.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sumoto", + "FINAL ANSWER: Sumoto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.89258, + "lon": 7.93534, + "name": "Afikpo" + }, + { + "lat": 5.18194, + "lon": 7.71481, + "name": "Ikot Ekpene" + }, + { + "lat": 5.78333, + "lon": 36.56667, + "name": "Bako" + }, + { + "lat": 7.57127, + "lon": -1.7087, + "name": "Nkoranza" + }, + { + "lat": 67.93972, + "lon": 32.87389, + "name": "Monchegorsk" + } + ], + "question": "Which location is the geographic outlier among: Afikpo, Ikot Ekpene, Bako, Nkoranza, Monchegorsk?", + "ground_truth": { + "answer": "Monchegorsk", + "outlier_distance_km": 5618.0, + "second_furthest_km": 2577.4, + "clarity_ratio": 2.18, + "median_distance_km": 2328.3, + "distances_to_centroid": { + "Afikpo": 1689.8, + "Ikot Ekpene": 1769.4, + "Bako": 2577.4, + "Nkoranza": 2328.3, + "Monchegorsk": 5618.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Afikpo: (5.89°, 7.94°)", + " Ikot Ekpene: (5.18°, 7.71°)", + " Bako: (5.78��, 36.57°)", + " Nkoranza: (7.57°, -1.71°)", + " Monchegorsk: (67.94°, 32.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Monchegorsk: 5618.0 km from centroid", + " Bako: 2577.4 km from centroid", + " Nkoranza: 2328.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Monchegorsk", + "FINAL ANSWER: Monchegorsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 57.64947, + "lon": -3.31843, + "name": "Elgin" + }, + { + "lat": 48.02708, + "lon": 40.12305, + "name": "Zverevo" + }, + { + "lat": 51.46072, + "lon": -0.21814, + "name": "Putney" + }, + { + "lat": 55.67719, + "lon": 37.89322, + "name": "Lyubertsy" + }, + { + "lat": -9.53222, + "lon": -36.985, + "name": "Major Isidoro" + } + ], + "question": "Which location is the geographic outlier among: Elgin, Zverevo, Putney, Lyubertsy, Major Isidoro?", + "ground_truth": { + "answer": "Major Isidoro", + "outlier_distance_km": 7204.8, + "second_furthest_km": 2768.8, + "clarity_ratio": 2.6, + "median_distance_km": 2697.6, + "distances_to_centroid": { + "Elgin": 2040.9, + "Zverevo": 2697.6, + "Putney": 1339.1, + "Lyubertsy": 2768.8, + "Major Isidoro": 7204.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Elgin: (57.65°, -3.32°)", + " Zverevo: (48.03°, 40.12°)", + " Putney: (51.46°, -0.22°)", + " Lyubertsy: (55.68°, 37.89°)", + " Major Isidoro: (-9.53°, -36.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Major Isidoro: 7204.8 km from centroid", + " Lyubertsy: 2768.8 km from centroid", + " Zverevo: 2697.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Major Isidoro", + "FINAL ANSWER: Major Isidoro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.4475, + "lon": 125.8046, + "name": "Magugpo Poblacion" + }, + { + "lat": 25.06567, + "lon": 84.97247, + "name": "Makhdumpur" + }, + { + "lat": 28.16992, + "lon": 105.43452, + "name": "Xuyong" + }, + { + "lat": 38.70882, + "lon": 141.15578, + "name": "Tome" + }, + { + "lat": -22.21389, + "lon": -49.94583, + "name": "Marília" + } + ], + "question": "Which location is the geographic outlier among: Magugpo Poblacion, Makhdumpur, Xuyong, Tome, Marília?", + "ground_truth": { + "answer": "Marília", + "outlier_distance_km": 14868.9, + "second_furthest_km": 6325.7, + "clarity_ratio": 2.35, + "median_distance_km": 4901.9, + "distances_to_centroid": { + "Magugpo Poblacion": 4901.9, + "Makhdumpur": 1130.8, + "Xuyong": 2840.6, + "Tome": 6325.7, + "Marília": 14868.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Magugpo Poblacion: (7.45°, 125.80°)", + " Makhdumpur: (25.07°, 84.97°)", + " Xuyong: (28.17°, 105.43°)", + " Tome: (38.71°, 141.16°)", + " Marília: (-22.21°, -49.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marília: 14868.9 km from centroid", + " Tome: 6325.7 km from centroid", + " Magugpo Poblacion: 4901.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marília", + "FINAL ANSWER: Marília" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.69864, + "lon": -88.0684, + "name": "Bolingbrook" + }, + { + "lat": 41.59649, + "lon": -72.8776, + "name": "Southington" + }, + { + "lat": 34.63813, + "lon": -99.33398, + "name": "Altus" + }, + { + "lat": 45.43123, + "lon": -122.77149, + "name": "Tigard" + }, + { + "lat": 36.11667, + "lon": 139.96667, + "name": "Ishige" + } + ], + "question": "Which location is the geographic outlier among: Bolingbrook, Southington, Altus, Tigard, Ishige?", + "ground_truth": { + "answer": "Ishige", + "outlier_distance_km": 11517.3, + "second_furthest_km": 5876.3, + "clarity_ratio": 1.96, + "median_distance_km": 4465.8, + "distances_to_centroid": { + "Bolingbrook": 3297.9, + "Southington": 2045.7, + "Altus": 4465.8, + "Tigard": 5876.3, + "Ishige": 11517.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bolingbrook: (41.70°, -88.07°)", + " Southington: (41.60°, -72.88°)", + " Altus: (34.64°, -99.33°)", + " Tigard: (45.43°, -122.77°)", + " Ishige: (36.12°, 139.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ishige: 11517.3 km from centroid", + " Tigard: 5876.3 km from centroid", + " Altus: 4465.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ishige", + "FINAL ANSWER: Ishige" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.55838, + "lon": -3.06999, + "name": "Formby" + }, + { + "lat": 45.52027, + "lon": 11.33446, + "name": "Arzignano" + }, + { + "lat": 39.8581, + "lon": -4.02263, + "name": "Toledo" + }, + { + "lat": 47.7742, + "lon": 7.35175, + "name": "Illzach" + }, + { + "lat": 24.81978, + "lon": 118.57415, + "name": "Jinjiang" + } + ], + "question": "Which location is the geographic outlier among: Formby, Arzignano, Toledo, Illzach, Jinjiang?", + "ground_truth": { + "answer": "Jinjiang", + "outlier_distance_km": 8379.4, + "second_furthest_km": 2520.6, + "clarity_ratio": 3.32, + "median_distance_km": 2477.9, + "distances_to_centroid": { + "Formby": 2477.9, + "Arzignano": 1228.4, + "Toledo": 2520.6, + "Illzach": 1583.7, + "Jinjiang": 8379.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Formby: (53.56°, -3.07°)", + " Arzignano: (45.52°, 11.33°)", + " Toledo: (39.86°, -4.02°)", + " Illzach: (47.77°, 7.35°)", + " Jinjiang: (24.82°, 118.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jinjiang: 8379.4 km from centroid", + " Toledo: 2520.6 km from centroid", + " Formby: 2477.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jinjiang", + "FINAL ANSWER: Jinjiang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.90034, + "lon": 151.05563, + "name": "Greenacre" + }, + { + "lat": -38.16667, + "lon": 145.16667, + "name": "Langwarrin" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": 51.39822, + "lon": -0.19837, + "name": "Morden" + } + ], + "question": "Which location is the geographic outlier among: Greenacre, Langwarrin, Palmerston, Ashfield, Morden?", + "ground_truth": { + "answer": "Morden", + "outlier_distance_km": 12949.9, + "second_furthest_km": 4238.7, + "clarity_ratio": 3.06, + "median_distance_km": 4233.6, + "distances_to_centroid": { + "Greenacre": 4233.6, + "Langwarrin": 4006.8, + "Palmerston": 1667.1, + "Ashfield": 4238.7, + "Morden": 12949.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Greenacre: (-33.90°, 151.06°)", + " Langwarrin: (-38.17°, 145.17°)", + " Palmerston: (-12.49°, 130.98°)", + " Ashfield: (-33.89°, 151.12°)", + " Morden: (51.40°, -0.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morden: 12949.9 km from centroid", + " Ashfield: 4238.7 km from centroid", + " Greenacre: 4233.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morden", + "FINAL ANSWER: Morden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.84034, + "lon": -1.46427, + "name": "Houghton-Le-Spring" + }, + { + "lat": 53.48097, + "lon": -2.24555, + "name": "Manchester City Centre" + }, + { + "lat": 59.88333, + "lon": 29.9, + "name": "Peterhof" + }, + { + "lat": 40.45975, + "lon": -3.6975, + "name": "Tetuán de las Victorias" + }, + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + } + ], + "question": "Which location is the geographic outlier among: Houghton-Le-Spring, Manchester City Centre, Peterhof, Tetuán de las Victorias, Taylors Hill?", + "ground_truth": { + "answer": "Taylors Hill", + "outlier_distance_km": 13961.1, + "second_furthest_km": 3534.4, + "clarity_ratio": 3.95, + "median_distance_km": 3517.9, + "distances_to_centroid": { + "Houghton-Le-Spring": 3534.4, + "Manchester City Centre": 3517.9, + "Peterhof": 2868.5, + "Tetuán de las Victorias": 3332.1, + "Taylors Hill": 13961.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Houghton-Le-Spring: (54.84°, -1.46°)", + " Manchester City Centre: (53.48°, -2.25°)", + " Peterhof: (59.88°, 29.90°)", + " Tetuán de las Victorias: (40.46°, -3.70°)", + " Taylors Hill: (-37.71°, 144.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taylors Hill: 13961.1 km from centroid", + " Houghton-Le-Spring: 3534.4 km from centroid", + " Manchester City Centre: 3517.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taylors Hill", + "FINAL ANSWER: Taylors Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.39563, + "lon": 43.8381, + "name": "Arzamas" + }, + { + "lat": 49.24762, + "lon": 11.09111, + "name": "Roth" + }, + { + "lat": 43.66352, + "lon": 7.1479, + "name": "Cagnes-sur-Mer" + }, + { + "lat": 57.87597, + "lon": 35.00702, + "name": "Udomlya" + }, + { + "lat": -12.11331, + "lon": -77.03274, + "name": "Miraflores" + } + ], + "question": "Which location is the geographic outlier among: Arzamas, Roth, Cagnes-sur-Mer, Udomlya, Miraflores?", + "ground_truth": { + "answer": "Miraflores", + "outlier_distance_km": 10089.8, + "second_furthest_km": 3464.7, + "clarity_ratio": 2.91, + "median_distance_km": 3071.8, + "distances_to_centroid": { + "Arzamas": 3464.7, + "Roth": 1289.5, + "Cagnes-sur-Mer": 599.6, + "Udomlya": 3071.8, + "Miraflores": 10089.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arzamas: (55.40°, 43.84°)", + " Roth: (49.25°, 11.09°)", + " Cagnes-sur-Mer: (43.66°, 7.15°)", + " Udomlya: (57.88°, 35.01°)", + " Miraflores: (-12.11°, -77.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Miraflores: 10089.8 km from centroid", + " Arzamas: 3464.7 km from centroid", + " Udomlya: 3071.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Miraflores", + "FINAL ANSWER: Miraflores" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.975, + "lon": -48.95972, + "name": "Igarapé Miri" + }, + { + "lat": -12.35306, + "lon": -38.37889, + "name": "Catu" + }, + { + "lat": -18.47552, + "lon": -70.30058, + "name": "Arica" + }, + { + "lat": -22.8075, + "lon": -43.41389, + "name": "Nilópolis" + }, + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + } + ], + "question": "Which location is the geographic outlier among: Igarapé Miri, Catu, Arica, Nilópolis, Busselton?", + "ground_truth": { + "answer": "Busselton", + "outlier_distance_km": 12389.8, + "second_furthest_km": 5595.7, + "clarity_ratio": 2.21, + "median_distance_km": 3894.7, + "distances_to_centroid": { + "Igarapé Miri": 3894.7, + "Catu": 2358.6, + "Arica": 5595.7, + "Nilópolis": 2790.1, + "Busselton": 12389.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Igarapé Miri: (-1.98°, -48.96°)", + " Catu: (-12.35°, -38.38°)", + " Arica: (-18.48°, -70.30°)", + " Nilópolis: (-22.81°, -43.41°)", + " Busselton: (-33.65°, 115.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Busselton: 12389.8 km from centroid", + " Arica: 5595.7 km from centroid", + " Igarapé Miri: 3894.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Busselton", + "FINAL ANSWER: Busselton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.555, + "lon": 5.91111, + "name": "Kampen" + }, + { + "lat": 40.9, + "lon": 14.26667, + "name": "Secondigliano" + }, + { + "lat": 44.86694, + "lon": 10.06039, + "name": "Fidenza" + }, + { + "lat": 55.76412, + "lon": -4.17669, + "name": "East Kilbride" + }, + { + "lat": -7.42639, + "lon": 111.02222, + "name": "Sragen" + } + ], + "question": "Which location is the geographic outlier among: Kampen, Secondigliano, Fidenza, East Kilbride, Sragen?", + "ground_truth": { + "answer": "Sragen", + "outlier_distance_km": 9947.5, + "second_furthest_km": 3120.9, + "clarity_ratio": 3.19, + "median_distance_km": 2376.1, + "distances_to_centroid": { + "Kampen": 2376.1, + "Secondigliano": 1200.4, + "Fidenza": 1673.3, + "East Kilbride": 3120.9, + "Sragen": 9947.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kampen: (52.55°, 5.91°)", + " Secondigliano: (40.90°, 14.27°)", + " Fidenza: (44.87°, 10.06°)", + " East Kilbride: (55.76°, -4.18°)", + " Sragen: (-7.43°, 111.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sragen: 9947.5 km from centroid", + " East Kilbride: 3120.9 km from centroid", + " Kampen: 2376.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sragen", + "FINAL ANSWER: Sragen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.40206, + "lon": -75.03934, + "name": "Millville" + }, + { + "lat": 39.16261, + "lon": -76.62469, + "name": "Glen Burnie" + }, + { + "lat": 40.67019, + "lon": -73.74659, + "name": "Laurelton" + }, + { + "lat": 19.62923, + "lon": -99.10689, + "name": "Coacalco" + }, + { + "lat": -8.62306, + "lon": -37.15583, + "name": "Buíque" + } + ], + "question": "Which location is the geographic outlier among: Millville, Glen Burnie, Laurelton, Coacalco, Buíque?", + "ground_truth": { + "answer": "Buíque", + "outlier_distance_km": 5413.6, + "second_furthest_km": 2829.0, + "clarity_ratio": 1.91, + "median_distance_km": 1631.1, + "distances_to_centroid": { + "Millville": 1506.1, + "Glen Burnie": 1512.1, + "Laurelton": 1631.1, + "Coacalco": 2829.0, + "Buíque": 5413.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Millville: (39.40°, -75.04°)", + " Glen Burnie: (39.16°, -76.62°)", + " Laurelton: (40.67°, -73.75°)", + " Coacalco: (19.63°, -99.11°)", + " Buíque: (-8.62°, -37.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Buíque: 5413.6 km from centroid", + " Coacalco: 2829.0 km from centroid", + " Laurelton: 1631.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Buíque", + "FINAL ANSWER: Buíque" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.59306, + "lon": -49.41028, + "name": "Araucária" + }, + { + "lat": -34.74947, + "lon": -58.70158, + "name": "Pontevedra" + }, + { + "lat": -29.94218, + "lon": -50.99278, + "name": "Gravataí" + }, + { + "lat": -23.70675, + "lon": -46.64982, + "name": "Pedreira" + }, + { + "lat": 28.35039, + "lon": -14.1076, + "name": "Pájara" + } + ], + "question": "Which location is the geographic outlier among: Araucária, Pontevedra, Gravataí, Pedreira, Pájara?", + "ground_truth": { + "answer": "Pájara", + "outlier_distance_km": 5991.1, + "second_furthest_km": 2444.7, + "clarity_ratio": 2.45, + "median_distance_km": 1593.4, + "distances_to_centroid": { + "Araucária": 1096.4, + "Pontevedra": 2444.7, + "Gravataí": 1593.4, + "Pedreira": 782.8, + "Pájara": 5991.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Araucária: (-25.59°, -49.41°)", + " Pontevedra: (-34.75°, -58.70°)", + " Gravataí: (-29.94°, -50.99°)", + " Pedreira: (-23.71°, -46.65°)", + " Pájara: (28.35°, -14.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pájara: 5991.1 km from centroid", + " Pontevedra: 2444.7 km from centroid", + " Gravataí: 1593.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pájara", + "FINAL ANSWER: Pájara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.65028, + "lon": -50.85056, + "name": "Reserva" + }, + { + "lat": -10.43778, + "lon": -39.33278, + "name": "Monte Santo" + }, + { + "lat": -20.02472, + "lon": -48.94056, + "name": "Frutal" + }, + { + "lat": -7.66778, + "lon": -35.10167, + "name": "Itaquitinga" + }, + { + "lat": 22.83474, + "lon": -105.77766, + "name": "Escuinapa de Hidalgo" + } + ], + "question": "Which location is the geographic outlier among: Reserva, Monte Santo, Frutal, Itaquitinga, Escuinapa de Hidalgo?", + "ground_truth": { + "answer": "Escuinapa de Hidalgo", + "outlier_distance_km": 6407.7, + "second_furthest_km": 2302.2, + "clarity_ratio": 2.78, + "median_distance_km": 1931.7, + "distances_to_centroid": { + "Reserva": 1931.7, + "Monte Santo": 1849.3, + "Frutal": 1539.0, + "Itaquitinga": 2302.2, + "Escuinapa de Hidalgo": 6407.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reserva: (-24.65°, -50.85°)", + " Monte Santo: (-10.44°, -39.33°)", + " Frutal: (-20.02°, -48.94°)", + " Itaquitinga: (-7.67°, -35.10°)", + " Escuinapa de Hidalgo: (22.83°, -105.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Escuinapa de Hidalgo: 6407.7 km from centroid", + " Itaquitinga: 2302.2 km from centroid", + " Reserva: 1931.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Escuinapa de Hidalgo", + "FINAL ANSWER: Escuinapa de Hidalgo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.76889, + "lon": 37.62389, + "name": "Amba Giorgis" + }, + { + "lat": 10.82379, + "lon": 10.77221, + "name": "Dukku" + }, + { + "lat": 30.71877, + "lon": 31.56299, + "name": "Al Ibrāhīmīyah" + }, + { + "lat": -25.67031, + "lon": 31.86288, + "name": "Kamaqhekeza" + }, + { + "lat": 40.18361, + "lon": 140.78722, + "name": "Hanawa" + } + ], + "question": "Which location is the geographic outlier among: Amba Giorgis, Dukku, Al Ibrāhīmīyah, Kamaqhekeza, Hanawa?", + "ground_truth": { + "answer": "Hanawa", + "outlier_distance_km": 9047.7, + "second_furthest_km": 4828.1, + "clarity_ratio": 1.87, + "median_distance_km": 4326.3, + "distances_to_centroid": { + "Amba Giorgis": 1400.1, + "Dukku": 4326.3, + "Al Ibrāhīmīyah": 2704.5, + "Kamaqhekeza": 4828.1, + "Hanawa": 9047.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Amba Giorgis: (12.77°, 37.62°)", + " Dukku: (10.82°, 10.77°)", + " Al Ibrāhīmīyah: (30.72°, 31.56°)", + " Kamaqhekeza: (-25.67°, 31.86°)", + " Hanawa: (40.18°, 140.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hanawa: 9047.7 km from centroid", + " Kamaqhekeza: 4828.1 km from centroid", + " Dukku: 4326.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hanawa", + "FINAL ANSWER: Hanawa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.74614, + "lon": 31.12964, + "name": "As Sanţah" + }, + { + "lat": 31.09311, + "lon": 30.31418, + "name": "Abū Ḩummuş" + }, + { + "lat": -29.8579, + "lon": 31.0292, + "name": "Durban" + }, + { + "lat": 10.52641, + "lon": 7.43879, + "name": "Kaduna" + }, + { + "lat": 33.24528, + "lon": 131.69165, + "name": "Tsurusaki" + } + ], + "question": "Which location is the geographic outlier among: As Sanţah, Abū Ḩummuş, Durban, Kaduna, Tsurusaki?", + "ground_truth": { + "answer": "Tsurusaki", + "outlier_distance_km": 8669.8, + "second_furthest_km": 5266.4, + "clarity_ratio": 1.65, + "median_distance_km": 4241.2, + "distances_to_centroid": { + "As Sanţah": 2324.1, + "Abū Ḩummuş": 2406.7, + "Durban": 5266.4, + "Kaduna": 4241.2, + "Tsurusaki": 8669.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " As Sanţah: (30.75°, 31.13°)", + " Abū Ḩummuş: (31.09°, 30.31°)", + " Durban: (-29.86°, 31.03°)", + " Kaduna: (10.53°, 7.44°)", + " Tsurusaki: (33.25°, 131.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tsurusaki: 8669.8 km from centroid", + " Durban: 5266.4 km from centroid", + " Kaduna: 4241.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tsurusaki", + "FINAL ANSWER: Tsurusaki" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.43411, + "lon": -99.20024, + "name": "Miguel Hidalgo" + }, + { + "lat": 42.32002, + "lon": -89.05816, + "name": "Loves Park" + }, + { + "lat": 26.92978, + "lon": -82.04537, + "name": "Punta Gorda" + }, + { + "lat": 41.60054, + "lon": -93.60911, + "name": "Des Moines" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + } + ], + "question": "Which location is the geographic outlier among: Miguel Hidalgo, Loves Park, Punta Gorda, Des Moines, Lalor?", + "ground_truth": { + "answer": "Lalor", + "outlier_distance_km": 17721.1, + "second_furthest_km": 5802.2, + "clarity_ratio": 3.05, + "median_distance_km": 5344.4, + "distances_to_centroid": { + "Miguel Hidalgo": 5802.2, + "Loves Park": 5002.7, + "Punta Gorda": 4018.1, + "Des Moines": 5344.4, + "Lalor": 17721.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miguel Hidalgo: (19.43°, -99.20°)", + " Loves Park: (42.32°, -89.06°)", + " Punta Gorda: (26.93°, -82.05°)", + " Des Moines: (41.60°, -93.61°)", + " Lalor: (-37.67°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lalor: 17721.1 km from centroid", + " Miguel Hidalgo: 5802.2 km from centroid", + " Des Moines: 5344.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lalor", + "FINAL ANSWER: Lalor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.33645, + "lon": 6.55381, + "name": "Krefeld" + }, + { + "lat": 53.55, + "lon": 9.93333, + "name": "Altona" + }, + { + "lat": 40.34077, + "lon": -3.68843, + "name": "San Cristobal" + }, + { + "lat": 57.45795, + "lon": 40.57169, + "name": "Nerekhta" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + } + ], + "question": "Which location is the geographic outlier among: Krefeld, Altona, San Cristobal, Nerekhta, Saint Albans?", + "ground_truth": { + "answer": "Saint Albans", + "outlier_distance_km": 13393.3, + "second_furthest_km": 3909.3, + "clarity_ratio": 3.43, + "median_distance_km": 3358.6, + "distances_to_centroid": { + "Krefeld": 3358.6, + "Altona": 3274.0, + "San Cristobal": 3909.3, + "Nerekhta": 2721.6, + "Saint Albans": 13393.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Krefeld: (51.34°, 6.55°)", + " Altona: (53.55°, 9.93°)", + " San Cristobal: (40.34°, -3.69°)", + " Nerekhta: (57.46°, 40.57°)", + " Saint Albans: (-37.73°, 144.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Albans: 13393.3 km from centroid", + " San Cristobal: 3909.3 km from centroid", + " Krefeld: 3358.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Albans", + "FINAL ANSWER: Saint Albans" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.47402, + "lon": 1.93062, + "name": "Martorell" + }, + { + "lat": 55.7, + "lon": 37.5, + "name": "Ramenki" + }, + { + "lat": 44.59445, + "lon": 11.04979, + "name": "Castelfranco Emilia" + }, + { + "lat": 51.5, + "lon": 7.63333, + "name": "Holzwickede" + }, + { + "lat": -0.21209, + "lon": 36.27248, + "name": "Upper Gilgil" + } + ], + "question": "Which location is the geographic outlier among: Martorell, Ramenki, Castelfranco Emilia, Holzwickede, Upper Gilgil?", + "ground_truth": { + "answer": "Upper Gilgil", + "outlier_distance_km": 4668.3, + "second_furthest_km": 2349.0, + "clarity_ratio": 1.99, + "median_distance_km": 1679.1, + "distances_to_centroid": { + "Martorell": 1474.7, + "Ramenki": 2349.0, + "Castelfranco Emilia": 929.8, + "Holzwickede": 1679.1, + "Upper Gilgil": 4668.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Martorell: (41.47°, 1.93°)", + " Ramenki: (55.70°, 37.50°)", + " Castelfranco Emilia: (44.59°, 11.05°)", + " Holzwickede: (51.50°, 7.63°)", + " Upper Gilgil: (-0.21°, 36.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upper Gilgil: 4668.3 km from centroid", + " Ramenki: 2349.0 km from centroid", + " Holzwickede: 1679.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upper Gilgil", + "FINAL ANSWER: Upper Gilgil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.25222, + "lon": -45.70333, + "name": "Santa Rita do Sapucaí" + }, + { + "lat": 7.06528, + "lon": -73.85472, + "name": "Barrancabermeja" + }, + { + "lat": -31.395, + "lon": -52.67556, + "name": "Canguçu" + }, + { + "lat": -8.51417, + "lon": -39.31, + "name": "Cabrobó" + }, + { + "lat": 9.46374, + "lon": 12.03062, + "name": "Numan" + } + ], + "question": "Which location is the geographic outlier among: Santa Rita do Sapucaí, Barrancabermeja, Canguçu, Cabrobó, Numan?", + "ground_truth": { + "answer": "Numan", + "outlier_distance_km": 6109.2, + "second_furthest_km": 4170.6, + "clarity_ratio": 1.46, + "median_distance_km": 2806.1, + "distances_to_centroid": { + "Santa Rita do Sapucaí": 1585.5, + "Barrancabermeja": 4170.6, + "Canguçu": 2806.1, + "Cabrobó": 94.2, + "Numan": 6109.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Rita do Sapucaí: (-22.25°, -45.70°)", + " Barrancabermeja: (7.07°, -73.85°)", + " Canguçu: (-31.39°, -52.68°)", + " Cabrobó: (-8.51°, -39.31°)", + " Numan: (9.46°, 12.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Numan: 6109.2 km from centroid", + " Barrancabermeja: 4170.6 km from centroid", + " Canguçu: 2806.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Numan", + "FINAL ANSWER: Numan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.72445, + "lon": 38.20908, + "name": "Elektrougli" + }, + { + "lat": 55.76667, + "lon": -4.03333, + "name": "Hamilton" + }, + { + "lat": 51.40089, + "lon": 16.20149, + "name": "Lubin" + }, + { + "lat": 45.75499, + "lon": 4.78812, + "name": "Tassin-la-Demi-Lune" + }, + { + "lat": 32.2504, + "lon": -101.47874, + "name": "Big Spring" + } + ], + "question": "Which location is the geographic outlier among: Elektrougli, Hamilton, Lubin, Tassin-la-Demi-Lune, Big Spring?", + "ground_truth": { + "answer": "Big Spring", + "outlier_distance_km": 7552.6, + "second_furthest_km": 3289.3, + "clarity_ratio": 2.3, + "median_distance_km": 1852.8, + "distances_to_centroid": { + "Elektrougli": 3289.3, + "Hamilton": 915.9, + "Lubin": 1852.8, + "Tassin-la-Demi-Lune": 1098.0, + "Big Spring": 7552.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Elektrougli: (55.72°, 38.21°)", + " Hamilton: (55.77°, -4.03°)", + " Lubin: (51.40°, 16.20°)", + " Tassin-la-Demi-Lune: (45.75°, 4.79°)", + " Big Spring: (32.25°, -101.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Big Spring: 7552.6 km from centroid", + " Elektrougli: 3289.3 km from centroid", + " Lubin: 1852.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Big Spring", + "FINAL ANSWER: Big Spring" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.41667, + "lon": -2.11667, + "name": "Bredbury" + }, + { + "lat": 41.61674, + "lon": 0.62218, + "name": "Lleida" + }, + { + "lat": 39.34474, + "lon": 16.23802, + "name": "Quattromiglia" + }, + { + "lat": 41.36, + "lon": 2.13986, + "name": "la Marina de Port" + }, + { + "lat": 36.85293, + "lon": -75.97799, + "name": "Virginia Beach" + } + ], + "question": "Which location is the geographic outlier among: Bredbury, Lleida, Quattromiglia, la Marina de Port, Virginia Beach?", + "ground_truth": { + "answer": "Virginia Beach", + "outlier_distance_km": 5394.8, + "second_furthest_km": 2372.2, + "clarity_ratio": 2.27, + "median_distance_km": 1407.9, + "distances_to_centroid": { + "Bredbury": 1407.9, + "Lleida": 1030.9, + "Quattromiglia": 2372.2, + "la Marina de Port": 1160.4, + "Virginia Beach": 5394.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bredbury: (53.42°, -2.12°)", + " Lleida: (41.62°, 0.62°)", + " Quattromiglia: (39.34°, 16.24°)", + " la Marina de Port: (41.36°, 2.14°)", + " Virginia Beach: (36.85°, -75.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Virginia Beach: 5394.8 km from centroid", + " Quattromiglia: 2372.2 km from centroid", + " Bredbury: 1407.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Virginia Beach", + "FINAL ANSWER: Virginia Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.2, + "lon": 35.45, + "name": "Tēpī" + }, + { + "lat": 9.08297, + "lon": 3.85196, + "name": "Kisi" + }, + { + "lat": 30.94384, + "lon": 31.52926, + "name": "Timayy al Imdīd" + }, + { + "lat": 13.15498, + "lon": 10.63468, + "name": "Kumagunnam" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + } + ], + "question": "Which location is the geographic outlier among: Tēpī, Kisi, Timayy al Imdīd, Kumagunnam, Townsville?", + "ground_truth": { + "answer": "Townsville", + "outlier_distance_km": 11472.3, + "second_furthest_km": 4593.8, + "clarity_ratio": 2.5, + "median_distance_km": 3862.1, + "distances_to_centroid": { + "Tēpī": 1130.1, + "Kisi": 4593.8, + "Timayy al Imdīd": 2920.9, + "Kumagunnam": 3862.1, + "Townsville": 11472.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tēpī: (7.20°, 35.45°)", + " Kisi: (9.08°, 3.85°)", + " Timayy al Imdīd: (30.94°, 31.53°)", + " Kumagunnam: (13.15°, 10.63°)", + " Townsville: (-19.27°, 146.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Townsville: 11472.3 km from centroid", + " Kisi: 4593.8 km from centroid", + " Kumagunnam: 3862.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Townsville", + "FINAL ANSWER: Townsville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.954, + "lon": 7.00481, + "name": "Gescher" + }, + { + "lat": 48.78889, + "lon": 2.27078, + "name": "Le Plessis-Robinson" + }, + { + "lat": 43.2907, + "lon": 5.4384, + "name": "Marseille 11" + }, + { + "lat": 41.72063, + "lon": 12.6723, + "name": "Ariccia" + }, + { + "lat": 42.40843, + "lon": -71.05366, + "name": "Everett" + } + ], + "question": "Which location is the geographic outlier among: Gescher, Le Plessis-Robinson, Marseille 11, Ariccia, Everett?", + "ground_truth": { + "answer": "Everett", + "outlier_distance_km": 4868.6, + "second_furthest_km": 1769.7, + "clarity_ratio": 2.75, + "median_distance_km": 1346.0, + "distances_to_centroid": { + "Gescher": 1346.0, + "Le Plessis-Robinson": 901.2, + "Marseille 11": 1152.8, + "Ariccia": 1769.7, + "Everett": 4868.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gescher: (51.95°, 7.00°)", + " Le Plessis-Robinson: (48.79°, 2.27°)", + " Marseille 11: (43.29°, 5.44°)", + " Ariccia: (41.72°, 12.67°)", + " Everett: (42.41°, -71.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Everett: 4868.6 km from centroid", + " Ariccia: 1769.7 km from centroid", + " Gescher: 1346.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Everett", + "FINAL ANSWER: Everett" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.65105, + "lon": 7.82089, + "name": "Schopfheim" + }, + { + "lat": 51.97417, + "lon": 5.34167, + "name": "Wijk bij Duurstede" + }, + { + "lat": 52.29583, + "lon": 5.1625, + "name": "Naarden" + }, + { + "lat": 51.80174, + "lon": -0.20691, + "name": "Welwyn Garden City" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + } + ], + "question": "Which location is the geographic outlier among: Schopfheim, Wijk bij Duurstede, Naarden, Welwyn Garden City, Broken Hill?", + "ground_truth": { + "answer": "Broken Hill", + "outlier_distance_km": 13588.6, + "second_furthest_km": 3208.7, + "clarity_ratio": 4.23, + "median_distance_km": 2912.5, + "distances_to_centroid": { + "Schopfheim": 2487.7, + "Wijk bij Duurstede": 2883.0, + "Naarden": 2912.5, + "Welwyn Garden City": 3208.7, + "Broken Hill": 13588.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Schopfheim: (47.65°, 7.82°)", + " Wijk bij Duurstede: (51.97°, 5.34°)", + " Naarden: (52.30°, 5.16°)", + " Welwyn Garden City: (51.80°, -0.21°)", + " Broken Hill: (-31.97°, 141.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Broken Hill: 13588.6 km from centroid", + " Welwyn Garden City: 3208.7 km from centroid", + " Naarden: 2912.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Broken Hill", + "FINAL ANSWER: Broken Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.26722, + "lon": -43.16194, + "name": "Palmas de Monte Alto" + }, + { + "lat": -28.93575, + "lon": -49.49538, + "name": "Araranguá" + }, + { + "lat": -32.85704, + "lon": -61.15114, + "name": "Carcarañá" + }, + { + "lat": -7.43861, + "lon": -34.91444, + "name": "Alhandra" + }, + { + "lat": 18.62926, + "lon": -100.897, + "name": "Huetamo de Núñez" + } + ], + "question": "Which location is the geographic outlier among: Palmas de Monte Alto, Araranguá, Carcarañá, Alhandra, Huetamo de Núñez?", + "ground_truth": { + "answer": "Huetamo de Núñez", + "outlier_distance_km": 5876.5, + "second_furthest_km": 2590.6, + "clarity_ratio": 2.27, + "median_distance_km": 2235.1, + "distances_to_centroid": { + "Palmas de Monte Alto": 1601.5, + "Araranguá": 1977.1, + "Carcarañá": 2235.1, + "Alhandra": 2590.6, + "Huetamo de Núñez": 5876.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palmas de Monte Alto: (-14.27°, -43.16°)", + " Araranguá: (-28.94°, -49.50°)", + " Carcarañá: (-32.86°, -61.15°)", + " Alhandra: (-7.44°, -34.91°)", + " Huetamo de Núñez: (18.63°, -100.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huetamo de Núñez: 5876.5 km from centroid", + " Alhandra: 2590.6 km from centroid", + " Carcarañá: 2235.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huetamo de Núñez", + "FINAL ANSWER: Huetamo de Núñez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.83834, + "lon": 144.99149, + "name": "South Yarra" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -37.91482, + "lon": 144.75088, + "name": "Point Cook" + }, + { + "lat": -19.88, + "lon": -43.66972, + "name": "Caeté" + } + ], + "question": "Which location is the geographic outlier among: South Yarra, Chatswood, Rochedale South, Point Cook, Caeté?", + "ground_truth": { + "answer": "Caeté", + "outlier_distance_km": 13661.8, + "second_furthest_km": 4161.4, + "clarity_ratio": 3.28, + "median_distance_km": 3834.5, + "distances_to_centroid": { + "South Yarra": 3254.1, + "Chatswood": 3834.5, + "Rochedale South": 4161.4, + "Point Cook": 3233.3, + "Caeté": 13661.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " South Yarra: (-37.84°, 144.99°)", + " Chatswood: (-33.80°, 151.18°)", + " Rochedale South: (-27.60°, 153.12°)", + " Point Cook: (-37.91°, 144.75°)", + " Caeté: (-19.88°, -43.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caeté: 13661.8 km from centroid", + " Rochedale South: 4161.4 km from centroid", + " Chatswood: 3834.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caeté", + "FINAL ANSWER: Caeté" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -46.4, + "lon": 168.35, + "name": "Invercargill" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -19.53791, + "lon": -49.48813, + "name": "Campina Verde" + } + ], + "question": "Which location is the geographic outlier among: Invercargill, Morayfield, Liverpool, North Melbourne, Campina Verde?", + "ground_truth": { + "answer": "Campina Verde", + "outlier_distance_km": 13906.0, + "second_furthest_km": 4818.5, + "clarity_ratio": 2.89, + "median_distance_km": 3827.0, + "distances_to_centroid": { + "Invercargill": 4818.5, + "Morayfield": 3827.0, + "Liverpool": 3451.8, + "North Melbourne": 2884.1, + "Campina Verde": 13906.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Invercargill: (-46.40°, 168.35°)", + " Morayfield: (-27.11°, 152.95°)", + " Liverpool: (-33.92°, 150.93°)", + " North Melbourne: (-37.80°, 144.95°)", + " Campina Verde: (-19.54°, -49.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Campina Verde: 13906.0 km from centroid", + " Invercargill: 4818.5 km from centroid", + " Morayfield: 3827.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Campina Verde", + "FINAL ANSWER: Campina Verde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": -33.73333, + "lon": 151.0, + "name": "Castle Hill" + }, + { + "lat": -27.56056, + "lon": 151.95386, + "name": "Toowoomba" + }, + { + "lat": 28.18779, + "lon": -82.73955, + "name": "Holiday" + } + ], + "question": "Which location is the geographic outlier among: Doreen, Ballajura, Castle Hill, Toowoomba, Holiday?", + "ground_truth": { + "answer": "Holiday", + "outlier_distance_km": 19155.2, + "second_furthest_km": 5665.4, + "clarity_ratio": 3.38, + "median_distance_km": 5548.5, + "distances_to_centroid": { + "Doreen": 5053.1, + "Ballajura": 2324.0, + "Castle Hill": 5548.5, + "Toowoomba": 5665.4, + "Holiday": 19155.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doreen: (-37.60°, 145.15°)", + " Ballajura: (-31.84°, 115.90°)", + " Castle Hill: (-33.73°, 151.00°)", + " Toowoomba: (-27.56°, 151.95°)", + " Holiday: (28.19°, -82.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Holiday: 19155.2 km from centroid", + " Toowoomba: 5665.4 km from centroid", + " Castle Hill: 5548.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Holiday", + "FINAL ANSWER: Holiday" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.27954, + "lon": -72.59843, + "name": "Madison" + }, + { + "lat": 50.01634, + "lon": -125.24459, + "name": "Campbell River" + }, + { + "lat": 36.30477, + "lon": -86.62, + "name": "Hendersonville" + }, + { + "lat": 33.77483, + "lon": -84.29631, + "name": "Decatur" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + } + ], + "question": "Which location is the geographic outlier among: Madison, Campbell River, Hendersonville, Decatur, Hawthorn?", + "ground_truth": { + "answer": "Hawthorn", + "outlier_distance_km": 18288.7, + "second_furthest_km": 7269.5, + "clarity_ratio": 2.52, + "median_distance_km": 4177.4, + "distances_to_centroid": { + "Madison": 3161.4, + "Campbell River": 7269.5, + "Hendersonville": 4177.4, + "Decatur": 3941.7, + "Hawthorn": 18288.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Madison: (41.28°, -72.60°)", + " Campbell River: (50.02°, -125.24°)", + " Hendersonville: (36.30°, -86.62°)", + " Decatur: (33.77°, -84.30°)", + " Hawthorn: (-37.82°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hawthorn: 18288.7 km from centroid", + " Campbell River: 7269.5 km from centroid", + " Hendersonville: 4177.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hawthorn", + "FINAL ANSWER: Hawthorn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -33.80383, + "lon": 150.98768, + "name": "Westmead" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + { + "lat": 21.735, + "lon": 81.94711, + "name": "Bhātāpāra" + } + ], + "question": "Which location is the geographic outlier among: Armidale, Westmead, Pacific Pines, Tuggeranong Administrative District, Bhātāpāra?", + "ground_truth": { + "answer": "Bhātāpāra", + "outlier_distance_km": 7679.2, + "second_furthest_km": 1948.5, + "clarity_ratio": 3.94, + "median_distance_km": 1936.7, + "distances_to_centroid": { + "Armidale": 1761.4, + "Westmead": 1936.7, + "Pacific Pines": 1774.2, + "Tuggeranong Administrative District": 1948.5, + "Bhātāpāra": 7679.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Armidale: (-30.50°, 151.67°)", + " Westmead: (-33.80°, 150.99°)", + " Pacific Pines: (-27.94°, 153.31°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + " Bhātāpāra: (21.73°, 81.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhātāpāra: 7679.2 km from centroid", + " Tuggeranong Administrative District: 1948.5 km from centroid", + " Westmead: 1936.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhātāpāra", + "FINAL ANSWER: Bhātāpāra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.19025, + "lon": 132.50846, + "name": "Ōdachō-ōda" + }, + { + "lat": 32.50124, + "lon": 80.09758, + "name": "Gar" + }, + { + "lat": 8.68447, + "lon": 76.76755, + "name": "Vakkam" + }, + { + "lat": 8.94917, + "lon": 125.54361, + "name": "Butuan" + }, + { + "lat": -27.58472, + "lon": -50.36111, + "name": "Correia Pinto" + } + ], + "question": "Which location is the geographic outlier among: Ōdachō-ōda, Gar, Vakkam, Butuan, Correia Pinto?", + "ground_truth": { + "answer": "Correia Pinto", + "outlier_distance_km": 13864.7, + "second_furthest_km": 6519.2, + "clarity_ratio": 2.13, + "median_distance_km": 5758.8, + "distances_to_centroid": { + "Ōdachō-ōda": 6519.2, + "Gar": 2442.9, + "Vakkam": 528.7, + "Butuan": 5758.8, + "Correia Pinto": 13864.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ōdachō-ōda: (35.19°, 132.51°)", + " Gar: (32.50°, 80.10°)", + " Vakkam: (8.68°, 76.77°)", + " Butuan: (8.95°, 125.54°)", + " Correia Pinto: (-27.58°, -50.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Correia Pinto: 13864.7 km from centroid", + " Ōdachō-ōda: 6519.2 km from centroid", + " Butuan: 5758.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Correia Pinto", + "FINAL ANSWER: Correia Pinto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + { + "lat": -33.91667, + "lon": 151.03333, + "name": "Bankstown" + }, + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + }, + { + "lat": -37.95855, + "lon": 176.98545, + "name": "Whakatane" + }, + { + "lat": -11.73028, + "lon": -40.55528, + "name": "Piritiba" + } + ], + "question": "Which location is the geographic outlier among: Werribee, Bankstown, Te Atatu South, Whakatane, Piritiba?", + "ground_truth": { + "answer": "Piritiba", + "outlier_distance_km": 14818.1, + "second_furthest_km": 5051.5, + "clarity_ratio": 2.93, + "median_distance_km": 4868.1, + "distances_to_centroid": { + "Werribee": 2231.5, + "Bankstown": 2775.6, + "Te Atatu South": 4868.1, + "Whakatane": 5051.5, + "Piritiba": 14818.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Werribee: (-37.90°, 144.67°)", + " Bankstown: (-33.92°, 151.03°)", + " Te Atatu South: (-36.86°, 174.65°)", + " Whakatane: (-37.96°, 176.99°)", + " Piritiba: (-11.73°, -40.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piritiba: 14818.1 km from centroid", + " Whakatane: 5051.5 km from centroid", + " Te Atatu South: 4868.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piritiba", + "FINAL ANSWER: Piritiba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -37.0393, + "lon": 174.92815, + "name": "Takanini" + }, + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -32.035, + "lon": -52.09861, + "name": "Rio Grande" + } + ], + "question": "Which location is the geographic outlier among: Mandurah, Takanini, Kensington, Auburn, Rio Grande?", + "ground_truth": { + "answer": "Rio Grande", + "outlier_distance_km": 12400.4, + "second_furthest_km": 5930.3, + "clarity_ratio": 2.09, + "median_distance_km": 3944.2, + "distances_to_centroid": { + "Mandurah": 719.0, + "Takanini": 5930.3, + "Kensington": 3944.2, + "Auburn": 3928.8, + "Rio Grande": 12400.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mandurah: (-32.53°, 115.72°)", + " Takanini: (-37.04°, 174.93°)", + " Kensington: (-33.92°, 151.22°)", + " Auburn: (-33.85°, 151.03°)", + " Rio Grande: (-32.03°, -52.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rio Grande: 12400.4 km from centroid", + " Takanini: 5930.3 km from centroid", + " Kensington: 3944.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rio Grande", + "FINAL ANSWER: Rio Grande" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.15843, + "lon": -71.14477, + "name": "Canton" + }, + { + "lat": 33.58011, + "lon": -85.07661, + "name": "Carrollton" + }, + { + "lat": 40.91677, + "lon": -74.17181, + "name": "Paterson" + }, + { + "lat": 32.566, + "lon": -116.63187, + "name": "Tecate" + }, + { + "lat": 34.4833, + "lon": 136.84186, + "name": "Toba" + } + ], + "question": "Which location is the geographic outlier among: Canton, Carrollton, Paterson, Tecate, Toba?", + "ground_truth": { + "answer": "Toba", + "outlier_distance_km": 12094.5, + "second_furthest_km": 6661.5, + "clarity_ratio": 1.82, + "median_distance_km": 3895.6, + "distances_to_centroid": { + "Canton": 2557.4, + "Carrollton": 3895.6, + "Paterson": 2805.9, + "Tecate": 6661.5, + "Toba": 12094.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canton: (42.16°, -71.14°)", + " Carrollton: (33.58°, -85.08°)", + " Paterson: (40.92°, -74.17°)", + " Tecate: (32.57°, -116.63°)", + " Toba: (34.48°, 136.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Toba: 12094.5 km from centroid", + " Tecate: 6661.5 km from centroid", + " Carrollton: 3895.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Toba", + "FINAL ANSWER: Toba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.09345, + "lon": 21.25725, + "name": "Riversdale" + }, + { + "lat": 6.6584, + "lon": 8.79923, + "name": "Ogoja" + }, + { + "lat": -29.26737, + "lon": 26.72595, + "name": "Botshabelo" + }, + { + "lat": 14.07294, + "lon": 36.56828, + "name": "May Cadera" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + } + ], + "question": "Which location is the geographic outlier among: Riversdale, Ogoja, Botshabelo, May Cadera, Otahuhu?", + "ground_truth": { + "answer": "Otahuhu", + "outlier_distance_km": 11508.6, + "second_furthest_km": 5536.9, + "clarity_ratio": 2.08, + "median_distance_km": 3825.8, + "distances_to_centroid": { + "Riversdale": 3812.3, + "Ogoja": 5536.9, + "Botshabelo": 3124.8, + "May Cadera": 3825.8, + "Otahuhu": 11508.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Riversdale: (-34.09°, 21.26°)", + " Ogoja: (6.66°, 8.80°)", + " Botshabelo: (-29.27°, 26.73°)", + " May Cadera: (14.07°, 36.57°)", + " Otahuhu: (-36.94°, 174.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Otahuhu: 11508.6 km from centroid", + " Ogoja: 5536.9 km from centroid", + " May Cadera: 3825.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Otahuhu", + "FINAL ANSWER: Otahuhu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.64563, + "lon": -84.77217, + "name": "Danville" + }, + { + "lat": 39.92678, + "lon": -75.15712, + "name": "Wharton" + }, + { + "lat": 22.62795, + "lon": -101.71417, + "name": "Salinas de Hidalgo" + }, + { + "lat": 39.99345, + "lon": -75.10017, + "name": "Port Richmond" + }, + { + "lat": 7.26667, + "lon": 9.98333, + "name": "Takum" + } + ], + "question": "Which location is the geographic outlier among: Danville, Wharton, Salinas de Hidalgo, Port Richmond, Takum?", + "ground_truth": { + "answer": "Takum", + "outlier_distance_km": 8193.8, + "second_furthest_km": 3696.0, + "clarity_ratio": 2.22, + "median_distance_km": 2009.3, + "distances_to_centroid": { + "Danville": 2009.3, + "Wharton": 1464.1, + "Salinas de Hidalgo": 3696.0, + "Port Richmond": 1466.6, + "Takum": 8193.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Danville: (37.65°, -84.77°)", + " Wharton: (39.93°, -75.16°)", + " Salinas de Hidalgo: (22.63°, -101.71°)", + " Port Richmond: (39.99°, -75.10°)", + " Takum: (7.27°, 9.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Takum: 8193.8 km from centroid", + " Salinas de Hidalgo: 3696.0 km from centroid", + " Danville: 2009.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Takum", + "FINAL ANSWER: Takum" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.47937, + "lon": -112.07823, + "name": "Encanto" + }, + { + "lat": 40.79455, + "lon": -73.81847, + "name": "Whitestone" + }, + { + "lat": 41.27954, + "lon": -72.8151, + "name": "Branford" + }, + { + "lat": 40.85843, + "lon": -74.16376, + "name": "Clifton" + }, + { + "lat": -37.87709, + "lon": 145.12939, + "name": "Mount Waverley" + } + ], + "question": "Which location is the geographic outlier among: Encanto, Whitestone, Branford, Clifton, Mount Waverley?", + "ground_truth": { + "answer": "Mount Waverley", + "outlier_distance_km": 18419.0, + "second_furthest_km": 7207.3, + "clarity_ratio": 2.56, + "median_distance_km": 3894.9, + "distances_to_centroid": { + "Encanto": 7207.3, + "Whitestone": 3865.1, + "Branford": 3803.1, + "Clifton": 3894.9, + "Mount Waverley": 18419.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Encanto: (33.48°, -112.08°)", + " Whitestone: (40.79°, -73.82°)", + " Branford: (41.28°, -72.82°)", + " Clifton: (40.86°, -74.16°)", + " Mount Waverley: (-37.88°, 145.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Waverley: 18419.0 km from centroid", + " Encanto: 7207.3 km from centroid", + " Clifton: 3894.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Waverley", + "FINAL ANSWER: Mount Waverley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.24424, + "lon": 21.08545, + "name": "Praga Południe" + }, + { + "lat": 48.716, + "lon": 9.5236, + "name": "Ebersbach an der Fils" + }, + { + "lat": 27.99243, + "lon": -15.41915, + "name": "Telde" + }, + { + "lat": 61.09979, + "lon": 72.60349, + "name": "Nefteyugansk" + }, + { + "lat": -4.83222, + "lon": -40.32056, + "name": "Tamboril" + } + ], + "question": "Which location is the geographic outlier among: Praga Południe, Ebersbach an der Fils, Telde, Nefteyugansk, Tamboril?", + "ground_truth": { + "answer": "Tamboril", + "outlier_distance_km": 6944.7, + "second_furthest_km": 5050.7, + "clarity_ratio": 1.37, + "median_distance_km": 2533.6, + "distances_to_centroid": { + "Praga Południe": 1917.5, + "Ebersbach an der Fils": 1297.9, + "Telde": 2533.6, + "Nefteyugansk": 5050.7, + "Tamboril": 6944.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Praga Południe: (52.24°, 21.09°)", + " Ebersbach an der Fils: (48.72°, 9.52°)", + " Telde: (27.99°, -15.42°)", + " Nefteyugansk: (61.10°, 72.60°)", + " Tamboril: (-4.83°, -40.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tamboril: 6944.7 km from centroid", + " Nefteyugansk: 5050.7 km from centroid", + " Telde: 2533.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tamboril", + "FINAL ANSWER: Tamboril" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.75714, + "lon": -108.8242, + "name": "Juan José Ríos" + }, + { + "lat": 22.62795, + "lon": -101.71417, + "name": "Salinas de Hidalgo" + }, + { + "lat": 40.40816, + "lon": -74.35432, + "name": "South Old Bridge" + }, + { + "lat": 25.66705, + "lon": -80.30811, + "name": "Pinecrest" + }, + { + "lat": -20.67182, + "lon": -40.50196, + "name": "Guarapari" + } + ], + "question": "Which location is the geographic outlier among: Juan José Ríos, Salinas de Hidalgo, South Old Bridge, Pinecrest, Guarapari?", + "ground_truth": { + "answer": "Guarapari", + "outlier_distance_km": 6230.3, + "second_furthest_km": 2946.8, + "clarity_ratio": 2.11, + "median_distance_km": 2493.2, + "distances_to_centroid": { + "Juan José Ríos": 2946.8, + "Salinas de Hidalgo": 2180.9, + "South Old Bridge": 2493.2, + "Pinecrest": 773.0, + "Guarapari": 6230.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Juan José Ríos: (25.76°, -108.82°)", + " Salinas de Hidalgo: (22.63°, -101.71°)", + " South Old Bridge: (40.41°, -74.35°)", + " Pinecrest: (25.67°, -80.31°)", + " Guarapari: (-20.67°, -40.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guarapari: 6230.3 km from centroid", + " Juan José Ríos: 2946.8 km from centroid", + " South Old Bridge: 2493.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guarapari", + "FINAL ANSWER: Guarapari" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.71056, + "lon": -40.40056, + "name": "Nova Venécia" + }, + { + "lat": -4.54167, + "lon": -40.71889, + "name": "Ipueiras" + }, + { + "lat": -25.83219, + "lon": -48.53966, + "name": "Matinhos" + }, + { + "lat": -22.96611, + "lon": -42.02778, + "name": "Arraial do Cabo" + }, + { + "lat": 33.19081, + "lon": 130.13804, + "name": "Higashigō" + } + ], + "question": "Which location is the geographic outlier among: Nova Venécia, Ipueiras, Matinhos, Arraial do Cabo, Higashigō?", + "ground_truth": { + "answer": "Higashigō", + "outlier_distance_km": 14899.0, + "second_furthest_km": 4702.1, + "clarity_ratio": 3.17, + "median_distance_km": 3975.2, + "distances_to_centroid": { + "Nova Venécia": 3672.1, + "Ipueiras": 3599.8, + "Matinhos": 4702.1, + "Arraial do Cabo": 3975.2, + "Higashigō": 14899.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nova Venécia: (-18.71°, -40.40°)", + " Ipueiras: (-4.54°, -40.72°)", + " Matinhos: (-25.83°, -48.54°)", + " Arraial do Cabo: (-22.97°, -42.03°)", + " Higashigō: (33.19°, 130.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Higashigō: 14899.0 km from centroid", + " Matinhos: 4702.1 km from centroid", + " Arraial do Cabo: 3975.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Higashigō", + "FINAL ANSWER: Higashigō" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + }, + { + "lat": 36.10945, + "lon": 129.34517, + "name": "Heunghae" + } + ], + "question": "Which location is the geographic outlier among: Mandurah, Corio, Palmerston, Brisbane, Heunghae?", + "ground_truth": { + "answer": "Heunghae", + "outlier_distance_km": 5698.8, + "second_furthest_km": 2749.2, + "clarity_ratio": 2.07, + "median_distance_km": 2742.9, + "distances_to_centroid": { + "Mandurah": 2742.9, + "Corio": 2749.2, + "Palmerston": 481.7, + "Brisbane": 2354.8, + "Heunghae": 5698.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mandurah: (-32.53°, 115.72°)", + " Corio: (-38.08°, 144.38°)", + " Palmerston: (-12.49°, 130.98°)", + " Brisbane: (-27.47°, 153.03°)", + " Heunghae: (36.11°, 129.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Heunghae: 5698.8 km from centroid", + " Corio: 2749.2 km from centroid", + " Mandurah: 2742.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Heunghae", + "FINAL ANSWER: Heunghae" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.39889, + "lon": -35.06389, + "name": "Ipojuca" + }, + { + "lat": -6.05675, + "lon": -77.16651, + "name": "Rioja" + }, + { + "lat": -9.89667, + "lon": -39.02639, + "name": "Canudos" + }, + { + "lat": -34.61082, + "lon": -58.481, + "name": "Villa Santa Rita" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + } + ], + "question": "Which location is the geographic outlier among: Ipojuca, Rioja, Canudos, Villa Santa Rita, Yagoona?", + "ground_truth": { + "answer": "Yagoona", + "outlier_distance_km": 13900.5, + "second_furthest_km": 7206.3, + "clarity_ratio": 1.93, + "median_distance_km": 4926.8, + "distances_to_centroid": { + "Ipojuca": 2759.3, + "Rioja": 7206.3, + "Canudos": 3090.0, + "Villa Santa Rita": 4926.8, + "Yagoona": 13900.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ipojuca: (-8.40°, -35.06°)", + " Rioja: (-6.06°, -77.17°)", + " Canudos: (-9.90°, -39.03°)", + " Villa Santa Rita: (-34.61°, -58.48°)", + " Yagoona: (-33.90°, 151.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yagoona: 13900.5 km from centroid", + " Rioja: 7206.3 km from centroid", + " Villa Santa Rita: 4926.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yagoona", + "FINAL ANSWER: Yagoona" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.39603, + "lon": -88.88531, + "name": "Biloxi" + }, + { + "lat": 20.05523, + "lon": -97.05214, + "name": "Villa Independencia" + }, + { + "lat": 33.94724, + "lon": -118.08535, + "name": "Santa Fe Springs" + }, + { + "lat": 43.63552, + "lon": -79.50113, + "name": "Stonegate-Queensway" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + } + ], + "question": "Which location is the geographic outlier among: Biloxi, Villa Independencia, Santa Fe Springs, Stonegate-Queensway, Helensvale?", + "ground_truth": { + "answer": "Helensvale", + "outlier_distance_km": 17863.7, + "second_furthest_km": 7165.5, + "clarity_ratio": 2.49, + "median_distance_km": 5306.9, + "distances_to_centroid": { + "Biloxi": 4434.2, + "Villa Independencia": 5306.9, + "Santa Fe Springs": 7165.5, + "Stonegate-Queensway": 4061.8, + "Helensvale": 17863.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Biloxi: (30.40°, -88.89°)", + " Villa Independencia: (20.06°, -97.05°)", + " Santa Fe Springs: (33.95°, -118.09°)", + " Stonegate-Queensway: (43.64°, -79.50°)", + " Helensvale: (-27.92°, 153.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Helensvale: 17863.7 km from centroid", + " Santa Fe Springs: 7165.5 km from centroid", + " Villa Independencia: 5306.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Helensvale", + "FINAL ANSWER: Helensvale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.05056, + "lon": -49.62278, + "name": "Presidente Getúlio" + }, + { + "lat": -10.43778, + "lon": -39.33278, + "name": "Monte Santo" + }, + { + "lat": -18.22047, + "lon": -49.72993, + "name": "Bom Jesus de Goiás" + }, + { + "lat": 2.95395, + "lon": -76.69644, + "name": "Suárez" + }, + { + "lat": 41.92111, + "lon": -71.435, + "name": "Lincoln" + } + ], + "question": "Which location is the geographic outlier among: Presidente Getúlio, Monte Santo, Bom Jesus de Goiás, Suárez, Lincoln?", + "ground_truth": { + "answer": "Lincoln", + "outlier_distance_km": 5103.4, + "second_furthest_km": 2887.3, + "clarity_ratio": 1.77, + "median_distance_km": 2223.1, + "distances_to_centroid": { + "Presidente Getúlio": 2887.3, + "Monte Santo": 2193.1, + "Bom Jesus de Goiás": 1969.6, + "Suárez": 2223.1, + "Lincoln": 5103.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Presidente Getúlio: (-27.05°, -49.62°)", + " Monte Santo: (-10.44°, -39.33°)", + " Bom Jesus de Goiás: (-18.22°, -49.73°)", + " Suárez: (2.95°, -76.70°)", + " Lincoln: (41.92°, -71.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lincoln: 5103.4 km from centroid", + " Presidente Getúlio: 2887.3 km from centroid", + " Suárez: 2223.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lincoln", + "FINAL ANSWER: Lincoln" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.57952, + "lon": 105.74238, + "name": "Tianshui" + }, + { + "lat": 28.1722, + "lon": 78.06376, + "name": "Pahāsu" + }, + { + "lat": 11.50526, + "lon": 77.23826, + "name": "Sathyamangalam" + }, + { + "lat": 23.02302, + "lon": 73.07113, + "name": "Kapadvanj" + }, + { + "lat": 36.46154, + "lon": -77.65415, + "name": "Roanoke Rapids" + } + ], + "question": "Which location is the geographic outlier among: Tianshui, Pahāsu, Sathyamangalam, Kapadvanj, Roanoke Rapids?", + "ground_truth": { + "answer": "Roanoke Rapids", + "outlier_distance_km": 11186.4, + "second_furthest_km": 5218.2, + "clarity_ratio": 2.14, + "median_distance_km": 3198.3, + "distances_to_centroid": { + "Tianshui": 5218.2, + "Pahāsu": 2640.9, + "Sathyamangalam": 3198.3, + "Kapadvanj": 2232.6, + "Roanoke Rapids": 11186.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tianshui: (34.58°, 105.74°)", + " Pahāsu: (28.17°, 78.06°)", + " Sathyamangalam: (11.51°, 77.24°)", + " Kapadvanj: (23.02°, 73.07°)", + " Roanoke Rapids: (36.46°, -77.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Roanoke Rapids: 11186.4 km from centroid", + " Tianshui: 5218.2 km from centroid", + " Sathyamangalam: 3198.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Roanoke Rapids", + "FINAL ANSWER: Roanoke Rapids" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.25628, + "lon": -78.04471, + "name": "Leland" + }, + { + "lat": 41.72449, + "lon": -81.24566, + "name": "Painesville" + }, + { + "lat": 19.40061, + "lon": -99.01483, + "name": "Ciudad Nezahualcoyotl" + }, + { + "lat": 40.65995, + "lon": -111.99633, + "name": "Kearns" + }, + { + "lat": 27.66368, + "lon": 80.47371, + "name": "Maholi" + } + ], + "question": "Which location is the geographic outlier among: Leland, Painesville, Ciudad Nezahualcoyotl, Kearns, Maholi?", + "ground_truth": { + "answer": "Maholi", + "outlier_distance_km": 11991.0, + "second_furthest_km": 4820.4, + "clarity_ratio": 2.49, + "median_distance_km": 4328.3, + "distances_to_centroid": { + "Leland": 1866.4, + "Painesville": 2280.4, + "Ciudad Nezahualcoyotl": 4328.3, + "Kearns": 4820.4, + "Maholi": 11991.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Leland: (34.26°, -78.04°)", + " Painesville: (41.72°, -81.25°)", + " Ciudad Nezahualcoyotl: (19.40°, -99.01°)", + " Kearns: (40.66°, -112.00°)", + " Maholi: (27.66°, 80.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maholi: 11991.0 km from centroid", + " Kearns: 4820.4 km from centroid", + " Ciudad Nezahualcoyotl: 4328.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maholi", + "FINAL ANSWER: Maholi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": 45.03442, + "lon": 41.9642, + "name": "Stavropol’" + } + ], + "question": "Which location is the geographic outlier among: Reservoir, North Melbourne, Lara, Tamworth, Stavropol’?", + "ground_truth": { + "answer": "Stavropol’", + "outlier_distance_km": 11067.9, + "second_furthest_km": 2833.2, + "clarity_ratio": 3.91, + "median_distance_km": 2737.3, + "distances_to_centroid": { + "Reservoir": 2735.0, + "North Melbourne": 2737.3, + "Lara": 2718.8, + "Tamworth": 2833.2, + "Stavropol’": 11067.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reservoir: (-37.72°, 145.00°)", + " North Melbourne: (-37.80°, 144.95°)", + " Lara: (-38.02°, 144.41°)", + " Tamworth: (-31.09°, 150.93°)", + " Stavropol’: (45.03°, 41.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stavropol’: 11067.9 km from centroid", + " Tamworth: 2833.2 km from centroid", + " North Melbourne: 2737.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stavropol’", + "FINAL ANSWER: Stavropol’" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.3727, + "lon": -99.1564, + "name": "Benito Juárez" + }, + { + "lat": 32.93457, + "lon": -97.25168, + "name": "Keller" + }, + { + "lat": 33.44734, + "lon": -84.14686, + "name": "McDonough" + }, + { + "lat": 37.22764, + "lon": -80.01282, + "name": "Cave Spring" + }, + { + "lat": 32.80589, + "lon": 130.69181, + "name": "Kumamoto" + } + ], + "question": "Which location is the geographic outlier among: Benito Juárez, Keller, McDonough, Cave Spring, Kumamoto?", + "ground_truth": { + "answer": "Kumamoto", + "outlier_distance_km": 12894.0, + "second_furthest_km": 5453.9, + "clarity_ratio": 2.36, + "median_distance_km": 4788.5, + "distances_to_centroid": { + "Benito Juárez": 5453.9, + "Keller": 4788.5, + "McDonough": 3576.6, + "Cave Spring": 3184.6, + "Kumamoto": 12894.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Benito Juárez: (19.37°, -99.16°)", + " Keller: (32.93°, -97.25°)", + " McDonough: (33.45°, -84.15°)", + " Cave Spring: (37.23°, -80.01°)", + " Kumamoto: (32.81°, 130.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kumamoto: 12894.0 km from centroid", + " Benito Juárez: 5453.9 km from centroid", + " Keller: 4788.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kumamoto", + "FINAL ANSWER: Kumamoto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.82923, + "lon": 8.83572, + "name": "Reinheim" + }, + { + "lat": 49.25672, + "lon": 2.48477, + "name": "Creil" + }, + { + "lat": 50.34802, + "lon": 18.93282, + "name": "Bytom" + }, + { + "lat": 53.14214, + "lon": 17.60181, + "name": "Nakło nad Notecią" + }, + { + "lat": -37.96667, + "lon": 145.16667, + "name": "Noble Park" + } + ], + "question": "Which location is the geographic outlier among: Reinheim, Creil, Bytom, Nakło nad Notecią, Noble Park?", + "ground_truth": { + "answer": "Noble Park", + "outlier_distance_km": 13513.9, + "second_furthest_km": 3482.0, + "clarity_ratio": 3.88, + "median_distance_km": 3081.1, + "distances_to_centroid": { + "Reinheim": 3081.1, + "Creil": 3482.0, + "Bytom": 2519.1, + "Nakło nad Notecią": 2800.7, + "Noble Park": 13513.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reinheim: (49.83°, 8.84°)", + " Creil: (49.26°, 2.48°)", + " Bytom: (50.35°, 18.93°)", + " Nakło nad Notecią: (53.14°, 17.60°)", + " Noble Park: (-37.97°, 145.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Noble Park: 13513.9 km from centroid", + " Creil: 3482.0 km from centroid", + " Reinheim: 3081.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Noble Park", + "FINAL ANSWER: Noble Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.15534, + "lon": 12.75638, + "name": "Damboa" + }, + { + "lat": 10.40319, + "lon": 5.4708, + "name": "Kontagora" + }, + { + "lat": 30.08843, + "lon": 31.28351, + "name": "Ḩadā’iq al Qubbah" + }, + { + "lat": -26.41663, + "lon": 29.08668, + "name": "Kinross" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + } + ], + "question": "Which location is the geographic outlier among: Damboa, Kontagora, Ḩadā’iq al Qubbah, Kinross, Karori?", + "ground_truth": { + "answer": "Karori", + "outlier_distance_km": 12514.3, + "second_furthest_km": 5227.1, + "clarity_ratio": 2.39, + "median_distance_km": 4487.7, + "distances_to_centroid": { + "Damboa": 4487.7, + "Kontagora": 5227.1, + "Ḩadā’iq al Qubbah": 4237.5, + "Kinross": 3456.4, + "Karori": 12514.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Damboa: (11.16°, 12.76°)", + " Kontagora: (10.40°, 5.47°)", + " Ḩadā’iq al Qubbah: (30.09°, 31.28°)", + " Kinross: (-26.42°, 29.09°)", + " Karori: (-41.28°, 174.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karori: 12514.3 km from centroid", + " Kontagora: 5227.1 km from centroid", + " Damboa: 4487.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karori", + "FINAL ANSWER: Karori" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.26083, + "lon": -50.64278, + "name": "Guararapes" + }, + { + "lat": -35.5952, + "lon": -71.72924, + "name": "San Javier" + }, + { + "lat": -5.89222, + "lon": -42.63611, + "name": "Água Branca" + }, + { + "lat": -6.98111, + "lon": -34.83389, + "name": "Cabedelo" + }, + { + "lat": 34.09751, + "lon": -117.64839, + "name": "Upland" + } + ], + "question": "Which location is the geographic outlier among: Guararapes, San Javier, Água Branca, Cabedelo, Upland?", + "ground_truth": { + "answer": "Upland", + "outlier_distance_km": 7304.3, + "second_furthest_km": 3275.0, + "clarity_ratio": 2.23, + "median_distance_km": 3162.7, + "distances_to_centroid": { + "Guararapes": 2092.5, + "San Javier": 3275.0, + "Água Branca": 2308.7, + "Cabedelo": 3162.7, + "Upland": 7304.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guararapes: (-21.26°, -50.64°)", + " San Javier: (-35.60°, -71.73°)", + " Água Branca: (-5.89°, -42.64°)", + " Cabedelo: (-6.98°, -34.83°)", + " Upland: (34.10°, -117.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upland: 7304.3 km from centroid", + " San Javier: 3275.0 km from centroid", + " Cabedelo: 3162.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upland", + "FINAL ANSWER: Upland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.22426, + "lon": 153.02075, + "name": "North Lakes" + }, + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -37.62581, + "lon": 144.92555, + "name": "Roxburgh Park" + }, + { + "lat": -33.73333, + "lon": 151.0, + "name": "Castle Hill" + }, + { + "lat": 9.04439, + "lon": 6.57089, + "name": "Lapai" + } + ], + "question": "Which location is the geographic outlier among: North Lakes, Epsom, Roxburgh Park, Castle Hill, Lapai?", + "ground_truth": { + "answer": "Lapai", + "outlier_distance_km": 13392.6, + "second_furthest_km": 4760.7, + "clarity_ratio": 2.81, + "median_distance_km": 2692.3, + "distances_to_centroid": { + "North Lakes": 2692.3, + "Epsom": 4760.7, + "Roxburgh Park": 2247.6, + "Castle Hill": 2581.6, + "Lapai": 13392.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Lakes: (-27.22°, 153.02°)", + " Epsom: (-36.89°, 174.77°)", + " Roxburgh Park: (-37.63°, 144.93°)", + " Castle Hill: (-33.73°, 151.00°)", + " Lapai: (9.04°, 6.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lapai: 13392.6 km from centroid", + " Epsom: 4760.7 km from centroid", + " North Lakes: 2692.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lapai", + "FINAL ANSWER: Lapai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": -37.83961, + "lon": 144.94228, + "name": "Port Melbourne" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": 41.69982, + "lon": -72.15702, + "name": "Windham" + } + ], + "question": "Which location is the geographic outlier among: Pascoe Vale, Epping, Port Melbourne, Caroline Springs, Windham?", + "ground_truth": { + "answer": "Windham", + "outlier_distance_km": 17729.9, + "second_furthest_km": 4506.4, + "clarity_ratio": 3.93, + "median_distance_km": 4502.3, + "distances_to_centroid": { + "Pascoe Vale": 4499.4, + "Epping": 4506.4, + "Port Melbourne": 4502.3, + "Caroline Springs": 4482.5, + "Windham": 17729.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pascoe Vale: (-37.73°, 144.93°)", + " Epping: (-37.65°, 145.03°)", + " Port Melbourne: (-37.84°, 144.94°)", + " Caroline Springs: (-37.74°, 144.74°)", + " Windham: (41.70°, -72.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Windham: 17729.9 km from centroid", + " Epping: 4506.4 km from centroid", + " Port Melbourne: 4502.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Windham", + "FINAL ANSWER: Windham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.65084, + "lon": -48.11119, + "name": "Araguatins" + }, + { + "lat": -26.89889, + "lon": -48.65417, + "name": "Navegantes" + }, + { + "lat": 6.96321, + "lon": -75.41738, + "name": "Yarumal" + }, + { + "lat": -16.02028, + "lon": -49.81028, + "name": "Itaberaí" + }, + { + "lat": 30.9128, + "lon": 30.29019, + "name": "Ḩawsh ‘Īsá" + } + ], + "question": "Which location is the geographic outlier among: Araguatins, Navegantes, Yarumal, Itaberaí, Ḩawsh ‘Īsá?", + "ground_truth": { + "answer": "Ḩawsh ‘Īsá", + "outlier_distance_km": 8111.5, + "second_furthest_km": 4237.2, + "clarity_ratio": 1.91, + "median_distance_km": 2964.7, + "distances_to_centroid": { + "Araguatins": 1152.0, + "Navegantes": 2964.7, + "Yarumal": 4237.2, + "Itaberaí": 1990.0, + "Ḩawsh ‘Īsá": 8111.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Araguatins: (-5.65°, -48.11°)", + " Navegantes: (-26.90°, -48.65°)", + " Yarumal: (6.96°, -75.42°)", + " Itaberaí: (-16.02°, -49.81°)", + " Ḩawsh ‘Īsá: (30.91°, 30.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ḩawsh ‘Īsá: 8111.5 km from centroid", + " Yarumal: 4237.2 km from centroid", + " Navegantes: 2964.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ḩawsh ‘Īsá", + "FINAL ANSWER: Ḩawsh ‘Īsá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.73865, + "lon": 4.91303, + "name": "Bron" + }, + { + "lat": 54.66079, + "lon": -5.66802, + "name": "Bangor" + }, + { + "lat": 53.82146, + "lon": 83.57063, + "name": "Tal’menka" + }, + { + "lat": 52.52956, + "lon": -2.06773, + "name": "Tipton" + }, + { + "lat": 34.25765, + "lon": 134.71535, + "name": "Fukura" + } + ], + "question": "Which location is the geographic outlier among: Bron, Bangor, Tal’menka, Tipton, Fukura?", + "ground_truth": { + "answer": "Fukura", + "outlier_distance_km": 7357.6, + "second_furthest_km": 3383.4, + "clarity_ratio": 2.17, + "median_distance_km": 3185.5, + "distances_to_centroid": { + "Bron": 2879.9, + "Bangor": 3383.4, + "Tal’menka": 2858.5, + "Tipton": 3185.5, + "Fukura": 7357.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bron: (45.74°, 4.91°)", + " Bangor: (54.66°, -5.67°)", + " Tal’menka: (53.82°, 83.57°)", + " Tipton: (52.53°, -2.07°)", + " Fukura: (34.26°, 134.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fukura: 7357.6 km from centroid", + " Bangor: 3383.4 km from centroid", + " Tipton: 3185.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fukura", + "FINAL ANSWER: Fukura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.96806, + "lon": 120.95472, + "name": "Pantubig" + }, + { + "lat": 14.64953, + "lon": 120.96788, + "name": "Caloocan City" + }, + { + "lat": 22.75278, + "lon": 88.34222, + "name": "Shrīrāmpur" + }, + { + "lat": 20.31379, + "lon": 77.34178, + "name": "Mangrūl Pīr" + }, + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + } + ], + "question": "Which location is the geographic outlier among: Pantubig, Caloocan City, Shrīrāmpur, Mangrūl Pīr, Mildura?", + "ground_truth": { + "answer": "Mildura", + "outlier_distance_km": 5760.5, + "second_furthest_km": 3777.2, + "clarity_ratio": 1.53, + "median_distance_km": 2852.3, + "distances_to_centroid": { + "Pantubig": 1445.5, + "Caloocan City": 1427.8, + "Shrīrāmpur": 2852.3, + "Mangrūl Pīr": 3777.2, + "Mildura": 5760.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pantubig: (14.97°, 120.95°)", + " Caloocan City: (14.65°, 120.97°)", + " Shrīrāmpur: (22.75°, 88.34°)", + " Mangrūl Pīr: (20.31°, 77.34°)", + " Mildura: (-34.19°, 142.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mildura: 5760.5 km from centroid", + " Mangrūl Pīr: 3777.2 km from centroid", + " Shrīrāmpur: 2852.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mildura", + "FINAL ANSWER: Mildura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.33643, + "lon": -82.53065, + "name": "Sarasota" + }, + { + "lat": 37.4032, + "lon": -79.17808, + "name": "West Lynchburg" + }, + { + "lat": 34.89859, + "lon": -117.02282, + "name": "Barstow" + }, + { + "lat": 32.94124, + "lon": -97.13418, + "name": "Southlake" + }, + { + "lat": 51.2504, + "lon": 6.97536, + "name": "Mettmann" + } + ], + "question": "Which location is the geographic outlier among: Sarasota, West Lynchburg, Barstow, Southlake, Mettmann?", + "ground_truth": { + "answer": "Mettmann", + "outlier_distance_km": 6317.3, + "second_furthest_km": 3870.8, + "clarity_ratio": 1.63, + "median_distance_km": 2167.5, + "distances_to_centroid": { + "Sarasota": 1332.7, + "West Lynchburg": 484.2, + "Barstow": 3870.8, + "Southlake": 2167.5, + "Mettmann": 6317.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sarasota: (27.34°, -82.53°)", + " West Lynchburg: (37.40°, -79.18°)", + " Barstow: (34.90°, -117.02°)", + " Southlake: (32.94°, -97.13°)", + " Mettmann: (51.25°, 6.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mettmann: 6317.3 km from centroid", + " Barstow: 3870.8 km from centroid", + " Southlake: 2167.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mettmann", + "FINAL ANSWER: Mettmann" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.94384, + "lon": 31.52926, + "name": "Timayy al Imdīd" + }, + { + "lat": -28.78301, + "lon": 32.03768, + "name": "Richards Bay" + }, + { + "lat": 7.81667, + "lon": 4.91667, + "name": "Oke Mesi" + }, + { + "lat": 7.93333, + "lon": 38.71667, + "name": "Ziway" + }, + { + "lat": 40.66676, + "lon": -75.49991, + "name": "Whitehall Township" + } + ], + "question": "Which location is the geographic outlier among: Timayy al Imdīd, Richards Bay, Oke Mesi, Ziway, Whitehall Township?", + "ground_truth": { + "answer": "Whitehall Township", + "outlier_distance_km": 8478.3, + "second_furthest_km": 5282.2, + "clarity_ratio": 1.61, + "median_distance_km": 3570.1, + "distances_to_centroid": { + "Timayy al Imdīd": 3357.1, + "Richards Bay": 5282.2, + "Oke Mesi": 460.7, + "Ziway": 3570.1, + "Whitehall Township": 8478.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Timayy al Imdīd: (30.94°, 31.53°)", + " Richards Bay: (-28.78°, 32.04°)", + " Oke Mesi: (7.82°, 4.92°)", + " Ziway: (7.93°, 38.72°)", + " Whitehall Township: (40.67°, -75.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whitehall Township: 8478.3 km from centroid", + " Richards Bay: 5282.2 km from centroid", + " Ziway: 3570.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whitehall Township", + "FINAL ANSWER: Whitehall Township" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.40278, + "lon": 118.91806, + "name": "Honghe" + }, + { + "lat": 8.65417, + "lon": 124.75556, + "name": "Jasaan" + }, + { + "lat": 13.07, + "lon": 80.24083, + "name": "Chetput" + }, + { + "lat": 14.6488, + "lon": 121.0509, + "name": "Quezon City" + }, + { + "lat": 41.95781, + "lon": -87.76506, + "name": "Portage Park" + } + ], + "question": "Which location is the geographic outlier among: Honghe, Jasaan, Chetput, Quezon City, Portage Park?", + "ground_truth": { + "answer": "Portage Park", + "outlier_distance_km": 12487.6, + "second_furthest_km": 5887.6, + "clarity_ratio": 2.12, + "median_distance_km": 5279.1, + "distances_to_centroid": { + "Honghe": 4772.4, + "Jasaan": 5887.6, + "Chetput": 1438.5, + "Quezon City": 5279.1, + "Portage Park": 12487.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Honghe: (36.40°, 118.92°)", + " Jasaan: (8.65°, 124.76°)", + " Chetput: (13.07°, 80.24°)", + " Quezon City: (14.65°, 121.05°)", + " Portage Park: (41.96°, -87.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Portage Park: 12487.6 km from centroid", + " Jasaan: 5887.6 km from centroid", + " Quezon City: 5279.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Portage Park", + "FINAL ANSWER: Portage Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -41.05584, + "lon": 145.90375, + "name": "Burnie" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": 50.84688, + "lon": 12.46473, + "name": "Meerane" + } + ], + "question": "Which location is the geographic outlier among: Banora Point, Burnie, Footscray, Officer, Meerane?", + "ground_truth": { + "answer": "Meerane", + "outlier_distance_km": 12875.1, + "second_furthest_km": 3517.5, + "clarity_ratio": 3.66, + "median_distance_km": 3454.5, + "distances_to_centroid": { + "Banora Point": 3517.5, + "Burnie": 3454.5, + "Footscray": 3170.0, + "Officer": 3223.2, + "Meerane": 12875.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banora Point: (-28.21°, 153.54°)", + " Burnie: (-41.06°, 145.90°)", + " Footscray: (-37.80°, 144.90°)", + " Officer: (-38.06°, 145.41°)", + " Meerane: (50.85°, 12.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Meerane: 12875.1 km from centroid", + " Banora Point: 3517.5 km from centroid", + " Burnie: 3454.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Meerane", + "FINAL ANSWER: Meerane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.31401, + "lon": 26.82223, + "name": "Ventersdorp" + }, + { + "lat": 5.30383, + "lon": -1.98956, + "name": "Tarkwa" + }, + { + "lat": 11.73333, + "lon": 38.46667, + "name": "Nefas Mewch’a" + }, + { + "lat": 7.45, + "lon": 37.63333, + "name": "Gīmbīcho" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + } + ], + "question": "Which location is the geographic outlier among: Ventersdorp, Tarkwa, Nefas Mewch’a, Gīmbīcho, Port Macquarie?", + "ground_truth": { + "answer": "Port Macquarie", + "outlier_distance_km": 10760.1, + "second_furthest_km": 6004.2, + "clarity_ratio": 1.79, + "median_distance_km": 3348.2, + "distances_to_centroid": { + "Ventersdorp": 3348.2, + "Tarkwa": 6004.2, + "Nefas Mewch’a": 2455.7, + "Gīmbīcho": 2140.3, + "Port Macquarie": 10760.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ventersdorp: (-26.31°, 26.82°)", + " Tarkwa: (5.30°, -1.99°)", + " Nefas Mewch’a: (11.73°, 38.47°)", + " Gīmbīcho: (7.45°, 37.63°)", + " Port Macquarie: (-31.43°, 152.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Macquarie: 10760.1 km from centroid", + " Tarkwa: 6004.2 km from centroid", + " Ventersdorp: 3348.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Macquarie", + "FINAL ANSWER: Port Macquarie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.32058, + "lon": 42.17402, + "name": "Vyksa" + }, + { + "lat": 53.39693, + "lon": 8.13621, + "name": "Varel" + }, + { + "lat": 51.52609, + "lon": -0.01665, + "name": "Bow" + }, + { + "lat": 49.10465, + "lon": 6.70402, + "name": "Saint-Avold" + }, + { + "lat": 35.78611, + "lon": 139.66118, + "name": "Takashimadaira" + } + ], + "question": "Which location is the geographic outlier among: Vyksa, Varel, Bow, Saint-Avold, Takashimadaira?", + "ground_truth": { + "answer": "Takashimadaira", + "outlier_distance_km": 7755.8, + "second_furthest_km": 2775.9, + "clarity_ratio": 2.79, + "median_distance_km": 2358.5, + "distances_to_centroid": { + "Vyksa": 726.0, + "Varel": 2207.7, + "Bow": 2775.9, + "Saint-Avold": 2358.5, + "Takashimadaira": 7755.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vyksa: (55.32°, 42.17°)", + " Varel: (53.40°, 8.14°)", + " Bow: (51.53°, -0.02°)", + " Saint-Avold: (49.10°, 6.70°)", + " Takashimadaira: (35.79°, 139.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Takashimadaira: 7755.8 km from centroid", + " Bow: 2775.9 km from centroid", + " Saint-Avold: 2358.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Takashimadaira", + "FINAL ANSWER: Takashimadaira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -43.53333, + "lon": 172.63333, + "name": "Christchurch" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + }, + { + "lat": 53.44769, + "lon": 56.03873, + "name": "Ishimbay" + } + ], + "question": "Which location is the geographic outlier among: Christchurch, Melbourne City Centre, Strathfield, Mount Eden, Ishimbay?", + "ground_truth": { + "answer": "Ishimbay", + "outlier_distance_km": 11363.6, + "second_furthest_km": 4029.6, + "clarity_ratio": 2.82, + "median_distance_km": 3878.1, + "distances_to_centroid": { + "Christchurch": 4029.6, + "Melbourne City Centre": 2069.6, + "Strathfield": 1922.3, + "Mount Eden": 3878.1, + "Ishimbay": 11363.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Christchurch: (-43.53°, 172.63°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Strathfield: (-33.88°, 151.08°)", + " Mount Eden: (-36.88°, 174.76°)", + " Ishimbay: (53.45°, 56.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ishimbay: 11363.6 km from centroid", + " Christchurch: 4029.6 km from centroid", + " Mount Eden: 3878.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ishimbay", + "FINAL ANSWER: Ishimbay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.89783, + "lon": 37.5868, + "name": "Lianozovo" + }, + { + "lat": 50.79899, + "lon": -1.09125, + "name": "Portsmouth" + }, + { + "lat": 51.41655, + "lon": 21.96939, + "name": "Puławy" + }, + { + "lat": 50.78628, + "lon": 3.12611, + "name": "Halluin" + }, + { + "lat": 41.70011, + "lon": -70.29947, + "name": "Barnstable" + } + ], + "question": "Which location is the geographic outlier among: Lianozovo, Portsmouth, Puławy, Halluin, Barnstable?", + "ground_truth": { + "answer": "Barnstable", + "outlier_distance_km": 5195.6, + "second_furthest_km": 2669.3, + "clarity_ratio": 1.95, + "median_distance_km": 1666.4, + "distances_to_centroid": { + "Lianozovo": 2669.3, + "Portsmouth": 88.4, + "Puławy": 1666.4, + "Halluin": 352.4, + "Barnstable": 5195.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lianozovo: (55.90°, 37.59°)", + " Portsmouth: (50.80°, -1.09°)", + " Puławy: (51.42°, 21.97°)", + " Halluin: (50.79°, 3.13°)", + " Barnstable: (41.70°, -70.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barnstable: 5195.6 km from centroid", + " Lianozovo: 2669.3 km from centroid", + " Puławy: 1666.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barnstable", + "FINAL ANSWER: Barnstable" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.10726, + "lon": 101.60671, + "name": "Petaling Jaya" + }, + { + "lat": 12.02999, + "lon": 75.28193, + "name": "Ezhome" + }, + { + "lat": 11.10933, + "lon": 77.182, + "name": "Karumattampatti" + }, + { + "lat": -7.91346, + "lon": 113.82145, + "name": "Bondowoso" + }, + { + "lat": 21.25993, + "lon": -98.78935, + "name": "Tamazunchale" + } + ], + "question": "Which location is the geographic outlier among: Petaling Jaya, Ezhome, Karumattampatti, Bondowoso, Tamazunchale?", + "ground_truth": { + "answer": "Tamazunchale", + "outlier_distance_km": 15602.9, + "second_furthest_km": 6879.2, + "clarity_ratio": 2.27, + "median_distance_km": 5312.9, + "distances_to_centroid": { + "Petaling Jaya": 5312.9, + "Ezhome": 2393.4, + "Karumattampatti": 2585.5, + "Bondowoso": 6879.2, + "Tamazunchale": 15602.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Petaling Jaya: (3.11°, 101.61°)", + " Ezhome: (12.03°, 75.28°)", + " Karumattampatti: (11.11°, 77.18°)", + " Bondowoso: (-7.91°, 113.82°)", + " Tamazunchale: (21.26°, -98.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tamazunchale: 15602.9 km from centroid", + " Bondowoso: 6879.2 km from centroid", + " Petaling Jaya: 5312.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tamazunchale", + "FINAL ANSWER: Tamazunchale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + }, + { + "lat": 50.62388, + "lon": 7.02942, + "name": "Meckenheim" + } + ], + "question": "Which location is the geographic outlier among: Hawthorn South, Miranda, North Melbourne, Moonee Ponds, Meckenheim?", + "ground_truth": { + "answer": "Meckenheim", + "outlier_distance_km": 13171.0, + "second_furthest_km": 3595.0, + "clarity_ratio": 3.66, + "median_distance_km": 3277.1, + "distances_to_centroid": { + "Hawthorn South": 3277.1, + "Miranda": 3595.0, + "North Melbourne": 3268.2, + "Moonee Ponds": 3264.3, + "Meckenheim": 13171.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hawthorn South: (-37.83°, 145.04°)", + " Miranda: (-34.04°, 151.10°)", + " North Melbourne: (-37.80°, 144.95°)", + " Moonee Ponds: (-37.77°, 144.92°)", + " Meckenheim: (50.62°, 7.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Meckenheim: 13171.0 km from centroid", + " Miranda: 3595.0 km from centroid", + " Hawthorn South: 3277.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Meckenheim", + "FINAL ANSWER: Meckenheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.78864, + "lon": -89.69622, + "name": "Sterling" + }, + { + "lat": 40.48979, + "lon": -81.44567, + "name": "New Philadelphia" + }, + { + "lat": 45.17191, + "lon": -93.87469, + "name": "Buffalo" + }, + { + "lat": 18.17678, + "lon": -93.06376, + "name": "Jalpa de Méndez" + }, + { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + } + ], + "question": "Which location is the geographic outlier among: Sterling, New Philadelphia, Buffalo, Jalpa de Méndez, Rockhampton?", + "ground_truth": { + "answer": "Rockhampton", + "outlier_distance_km": 18787.8, + "second_furthest_km": 5356.0, + "clarity_ratio": 3.51, + "median_distance_km": 5195.9, + "distances_to_centroid": { + "Sterling": 4809.1, + "New Philadelphia": 4103.7, + "Buffalo": 5195.9, + "Jalpa de Méndez": 5356.0, + "Rockhampton": 18787.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sterling: (41.79°, -89.70°)", + " New Philadelphia: (40.49°, -81.45°)", + " Buffalo: (45.17°, -93.87°)", + " Jalpa de Méndez: (18.18°, -93.06°)", + " Rockhampton: (-23.38°, 150.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rockhampton: 18787.8 km from centroid", + " Jalpa de Méndez: 5356.0 km from centroid", + " Buffalo: 5195.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rockhampton", + "FINAL ANSWER: Rockhampton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.78438, + "lon": -4.10007, + "name": "High Blantyre" + }, + { + "lat": 55.36352, + "lon": 37.52984, + "name": "Klimovsk" + }, + { + "lat": 49.4925, + "lon": 9.77361, + "name": "Bad Mergentheim" + }, + { + "lat": 40.85734, + "lon": 14.2228, + "name": "Arenella" + }, + { + "lat": -36.88012, + "lon": 174.61975, + "name": "Henderson" + } + ], + "question": "Which location is the geographic outlier among: High Blantyre, Klimovsk, Bad Mergentheim, Arenella, Henderson?", + "ground_truth": { + "answer": "Henderson", + "outlier_distance_km": 15329.3, + "second_furthest_km": 4608.2, + "clarity_ratio": 3.33, + "median_distance_km": 3525.4, + "distances_to_centroid": { + "High Blantyre": 4608.2, + "Klimovsk": 2589.0, + "Bad Mergentheim": 3525.4, + "Arenella": 2976.1, + "Henderson": 15329.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " High Blantyre: (55.78°, -4.10°)", + " Klimovsk: (55.36°, 37.53°)", + " Bad Mergentheim: (49.49°, 9.77°)", + " Arenella: (40.86°, 14.22°)", + " Henderson: (-36.88°, 174.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Henderson: 15329.3 km from centroid", + " High Blantyre: 4608.2 km from centroid", + " Bad Mergentheim: 3525.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Henderson", + "FINAL ANSWER: Henderson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.4984, + "lon": -3.7314, + "name": "Fuencarral-El Pardo" + }, + { + "lat": 48.98826, + "lon": 2.3434, + "name": "Montmorency" + }, + { + "lat": 51.45984, + "lon": 12.63338, + "name": "Eilenburg" + }, + { + "lat": 40.60861, + "lon": 14.98209, + "name": "Battipaglia" + }, + { + "lat": 21.99631, + "lon": -99.01093, + "name": "Ciudad Valles" + } + ], + "question": "Which location is the geographic outlier among: Fuencarral-El Pardo, Montmorency, Eilenburg, Battipaglia, Ciudad Valles?", + "ground_truth": { + "answer": "Ciudad Valles", + "outlier_distance_km": 7984.6, + "second_furthest_km": 2479.8, + "clarity_ratio": 3.22, + "median_distance_km": 2393.4, + "distances_to_centroid": { + "Fuencarral-El Pardo": 913.6, + "Montmorency": 1613.6, + "Eilenburg": 2393.4, + "Battipaglia": 2479.8, + "Ciudad Valles": 7984.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fuencarral-El Pardo: (40.50°, -3.73°)", + " Montmorency: (48.99°, 2.34°)", + " Eilenburg: (51.46°, 12.63°)", + " Battipaglia: (40.61°, 14.98°)", + " Ciudad Valles: (22.00°, -99.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciudad Valles: 7984.6 km from centroid", + " Battipaglia: 2479.8 km from centroid", + " Eilenburg: 2393.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciudad Valles", + "FINAL ANSWER: Ciudad Valles" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.342, + "lon": 31.58, + "name": "Ncotshane" + }, + { + "lat": 31.03408, + "lon": 30.46823, + "name": "Damanhur" + }, + { + "lat": -25.91849, + "lon": 28.19881, + "name": "Midstream" + }, + { + "lat": 8.45, + "lon": 39.28333, + "name": "Wenjī" + }, + { + "lat": 10.88606, + "lon": -72.8487, + "name": "Fonseca" + } + ], + "question": "Which location is the geographic outlier among: Ncotshane, Damanhur, Midstream, Wenjī, Fonseca?", + "ground_truth": { + "answer": "Fonseca", + "outlier_distance_km": 9384.9, + "second_furthest_km": 4054.0, + "clarity_ratio": 2.31, + "median_distance_km": 3677.2, + "distances_to_centroid": { + "Ncotshane": 3677.2, + "Damanhur": 4054.0, + "Midstream": 3347.5, + "Wenjī": 3255.5, + "Fonseca": 9384.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ncotshane: (-27.34°, 31.58°)", + " Damanhur: (31.03°, 30.47°)", + " Midstream: (-25.92°, 28.20°)", + " Wenjī: (8.45°, 39.28°)", + " Fonseca: (10.89°, -72.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fonseca: 9384.9 km from centroid", + " Damanhur: 4054.0 km from centroid", + " Ncotshane: 3677.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fonseca", + "FINAL ANSWER: Fonseca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.81009, + "lon": -48.03077, + "name": "Vicente Pires" + }, + { + "lat": -30.42498, + "lon": -64.35274, + "name": "Deán Funes" + }, + { + "lat": -26.17722, + "lon": -50.39, + "name": "Canoinhas" + }, + { + "lat": -23.74417, + "lon": -46.39833, + "name": "Rio Grande da Serra" + }, + { + "lat": 40.32605, + "lon": -3.51089, + "name": "Rivas-Vaciamadrid" + } + ], + "question": "Which location is the geographic outlier among: Vicente Pires, Deán Funes, Canoinhas, Rio Grande da Serra, Rivas-Vaciamadrid?", + "ground_truth": { + "answer": "Rivas-Vaciamadrid", + "outlier_distance_km": 6992.8, + "second_furthest_km": 3106.6, + "clarity_ratio": 2.25, + "median_distance_km": 1861.5, + "distances_to_centroid": { + "Vicente Pires": 787.0, + "Deán Funes": 3106.6, + "Canoinhas": 1861.5, + "Rio Grande da Serra": 1457.1, + "Rivas-Vaciamadrid": 6992.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vicente Pires: (-15.81°, -48.03°)", + " Deán Funes: (-30.42°, -64.35°)", + " Canoinhas: (-26.18°, -50.39°)", + " Rio Grande da Serra: (-23.74°, -46.40°)", + " Rivas-Vaciamadrid: (40.33°, -3.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rivas-Vaciamadrid: 6992.8 km from centroid", + " Deán Funes: 3106.6 km from centroid", + " Canoinhas: 1861.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rivas-Vaciamadrid", + "FINAL ANSWER: Rivas-Vaciamadrid" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.11599, + "lon": -0.50044, + "name": "Kempston" + }, + { + "lat": 56.1218, + "lon": 93.33814, + "name": "Sosnovoborsk" + }, + { + "lat": 51.52517, + "lon": 14.00164, + "name": "Senftenberg" + }, + { + "lat": 51.41363, + "lon": -0.75054, + "name": "Bracknell" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + } + ], + "question": "Which location is the geographic outlier among: Kempston, Sosnovoborsk, Senftenberg, Bracknell, Corio?", + "ground_truth": { + "answer": "Corio", + "outlier_distance_km": 12621.4, + "second_furthest_km": 4426.7, + "clarity_ratio": 2.85, + "median_distance_km": 4416.6, + "distances_to_centroid": { + "Kempston": 4416.6, + "Sosnovoborsk": 4037.5, + "Senftenberg": 3430.4, + "Bracknell": 4426.7, + "Corio": 12621.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kempston: (52.12°, -0.50°)", + " Sosnovoborsk: (56.12°, 93.34°)", + " Senftenberg: (51.53°, 14.00°)", + " Bracknell: (51.41°, -0.75°)", + " Corio: (-38.08°, 144.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Corio: 12621.4 km from centroid", + " Bracknell: 4426.7 km from centroid", + " Kempston: 4416.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Corio", + "FINAL ANSWER: Corio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.03238, + "lon": 23.11652, + "name": "Biała Podlaska" + }, + { + "lat": 51.90425, + "lon": 10.42766, + "name": "Goslar" + }, + { + "lat": 40.42629, + "lon": -3.63546, + "name": "Pueblo Nuevo" + }, + { + "lat": 41.61674, + "lon": 0.62218, + "name": "Lleida" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + } + ], + "question": "Which location is the geographic outlier among: Biała Podlaska, Goslar, Pueblo Nuevo, Lleida, Glenferrie?", + "ground_truth": { + "answer": "Glenferrie", + "outlier_distance_km": 13621.4, + "second_furthest_km": 3693.2, + "clarity_ratio": 3.69, + "median_distance_km": 3362.3, + "distances_to_centroid": { + "Biała Podlaska": 2679.7, + "Goslar": 3201.8, + "Pueblo Nuevo": 3693.2, + "Lleida": 3362.3, + "Glenferrie": 13621.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Biała Podlaska: (52.03°, 23.12°)", + " Goslar: (51.90°, 10.43°)", + " Pueblo Nuevo: (40.43°, -3.64°)", + " Lleida: (41.62°, 0.62°)", + " Glenferrie: (-37.83°, 145.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glenferrie: 13621.4 km from centroid", + " Pueblo Nuevo: 3693.2 km from centroid", + " Lleida: 3362.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glenferrie", + "FINAL ANSWER: Glenferrie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.68417, + "lon": -79.29936, + "name": "East End-Danforth" + }, + { + "lat": 44.27804, + "lon": -88.27205, + "name": "Kaukauna" + }, + { + "lat": 47.76232, + "lon": -122.2054, + "name": "Bothell" + }, + { + "lat": 19.34745, + "lon": -90.72039, + "name": "Champotón" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + } + ], + "question": "Which location is the geographic outlier among: East End-Danforth, Kaukauna, Bothell, Champotón, Caboolture?", + "ground_truth": { + "answer": "Caboolture", + "outlier_distance_km": 18169.8, + "second_furthest_km": 6966.7, + "clarity_ratio": 2.61, + "median_distance_km": 4675.3, + "distances_to_centroid": { + "East End-Danforth": 3648.9, + "Kaukauna": 4351.5, + "Bothell": 6966.7, + "Champotón": 4675.3, + "Caboolture": 18169.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " East End-Danforth: (43.68°, -79.30°)", + " Kaukauna: (44.28°, -88.27°)", + " Bothell: (47.76°, -122.21°)", + " Champotón: (19.35°, -90.72°)", + " Caboolture: (-27.08°, 152.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caboolture: 18169.8 km from centroid", + " Bothell: 6966.7 km from centroid", + " Champotón: 4675.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caboolture", + "FINAL ANSWER: Caboolture" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73333, + "lon": 150.88333, + "name": "Quakers Hill" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -28.00029, + "lon": 153.43088, + "name": "Gold Coast" + }, + { + "lat": 37.30216, + "lon": -120.48297, + "name": "Merced" + } + ], + "question": "Which location is the geographic outlier among: Quakers Hill, Dandenong North, Ashburton, Gold Coast, Merced?", + "ground_truth": { + "answer": "Merced", + "outlier_distance_km": 15730.8, + "second_furthest_km": 6936.0, + "clarity_ratio": 2.27, + "median_distance_km": 5396.1, + "distances_to_centroid": { + "Quakers Hill": 5139.0, + "Dandenong North": 4680.1, + "Ashburton": 6936.0, + "Gold Coast": 5396.1, + "Merced": 15730.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Quakers Hill: (-33.73°, 150.88°)", + " Dandenong North: (-37.97°, 145.21°)", + " Ashburton: (-43.90°, 171.73°)", + " Gold Coast: (-28.00°, 153.43°)", + " Merced: (37.30°, -120.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Merced: 15730.8 km from centroid", + " Ashburton: 6936.0 km from centroid", + " Gold Coast: 5396.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Merced", + "FINAL ANSWER: Merced" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.65649, + "lon": 4.92235, + "name": "Efon-Alaaye" + }, + { + "lat": 3.52661, + "lon": 39.0561, + "name": "Moyale" + }, + { + "lat": 9.96278, + "lon": 42.49278, + "name": "Ārabī" + }, + { + "lat": 9.03333, + "lon": 38.4, + "name": "Ādīs ‘Alem" + }, + { + "lat": 25.8576, + "lon": -80.27811, + "name": "Hialeah" + } + ], + "question": "Which location is the geographic outlier among: Efon-Alaaye, Moyale, Ārabī, Ādīs ‘Alem, Hialeah?", + "ground_truth": { + "answer": "Hialeah", + "outlier_distance_km": 9387.7, + "second_furthest_km": 3670.4, + "clarity_ratio": 2.56, + "median_distance_km": 3428.3, + "distances_to_centroid": { + "Efon-Alaaye": 589.9, + "Moyale": 3428.3, + "Ārabī": 3670.4, + "Ādīs ‘Alem": 3234.9, + "Hialeah": 9387.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Efon-Alaaye: (7.66°, 4.92°)", + " Moyale: (3.53°, 39.06°)", + " Ārabī: (9.96°, 42.49°)", + " Ādīs ‘Alem: (9.03°, 38.40°)", + " Hialeah: (25.86°, -80.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hialeah: 9387.7 km from centroid", + " Ārabī: 3670.4 km from centroid", + " Moyale: 3428.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hialeah", + "FINAL ANSWER: Hialeah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.10521, + "lon": 1.83547, + "name": "Abbeville" + }, + { + "lat": 36.75793, + "lon": -3.95233, + "name": "Torrox" + }, + { + "lat": 41.38879, + "lon": 2.15899, + "name": "Barcelona" + }, + { + "lat": 47.29964, + "lon": -1.55239, + "name": "La Chapelle-sur-Erdre" + }, + { + "lat": 8.09008, + "lon": 77.53841, + "name": "Kanniyākumāri" + } + ], + "question": "Which location is the geographic outlier among: Abbeville, Torrox, Barcelona, La Chapelle-sur-Erdre, Kanniyākumāri?", + "ground_truth": { + "answer": "Kanniyākumāri", + "outlier_distance_km": 7015.1, + "second_furthest_km": 1832.1, + "clarity_ratio": 3.83, + "median_distance_km": 1809.3, + "distances_to_centroid": { + "Abbeville": 1832.1, + "Torrox": 1704.2, + "Barcelona": 1238.2, + "La Chapelle-sur-Erdre": 1809.3, + "Kanniyākumāri": 7015.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abbeville: (50.11°, 1.84°)", + " Torrox: (36.76°, -3.95°)", + " Barcelona: (41.39°, 2.16°)", + " La Chapelle-sur-Erdre: (47.30°, -1.55°)", + " Kanniyākumāri: (8.09°, 77.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kanniyākumāri: 7015.1 km from centroid", + " Abbeville: 1832.1 km from centroid", + " La Chapelle-sur-Erdre: 1809.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kanniyākumāri", + "FINAL ANSWER: Kanniyākumāri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.48862, + "lon": 27.49387, + "name": "Fochville" + }, + { + "lat": -32.93324, + "lon": 27.77656, + "name": "Mdantsane" + }, + { + "lat": 8.45, + "lon": 39.28333, + "name": "Wenjī" + }, + { + "lat": -32.33083, + "lon": 28.14981, + "name": "Butterworth" + }, + { + "lat": 42.3501, + "lon": -71.15644, + "name": "Brighton" + } + ], + "question": "Which location is the geographic outlier among: Fochville, Mdantsane, Wenjī, Butterworth, Brighton?", + "ground_truth": { + "answer": "Brighton", + "outlier_distance_km": 9927.4, + "second_furthest_km": 3705.4, + "clarity_ratio": 2.68, + "median_distance_km": 3286.3, + "distances_to_centroid": { + "Fochville": 2725.4, + "Mdantsane": 3286.3, + "Wenjī": 3705.4, + "Butterworth": 3254.6, + "Brighton": 9927.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fochville: (-26.49°, 27.49°)", + " Mdantsane: (-32.93°, 27.78°)", + " Wenjī: (8.45°, 39.28°)", + " Butterworth: (-32.33°, 28.15°)", + " Brighton: (42.35°, -71.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brighton: 9927.4 km from centroid", + " Wenjī: 3705.4 km from centroid", + " Mdantsane: 3286.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brighton", + "FINAL ANSWER: Brighton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.85, + "lon": 36.88333, + "name": "Gimja Bēt Maryam" + }, + { + "lat": 0.52036, + "lon": 35.26993, + "name": "Eldoret" + }, + { + "lat": 0.87178, + "lon": 35.12213, + "name": "Moi‘s Bridge" + }, + { + "lat": 29.95, + "lon": 31.2, + "name": "Abū an Numrus" + }, + { + "lat": -8.87556, + "lon": -36.36667, + "name": "São João" + } + ], + "question": "Which location is the geographic outlier among: Gimja Bēt Maryam, Eldoret, Moi‘s Bridge, Abū an Numrus, São João?", + "ground_truth": { + "answer": "São João", + "outlier_distance_km": 6526.4, + "second_furthest_km": 2824.0, + "clarity_ratio": 2.31, + "median_distance_km": 1867.5, + "distances_to_centroid": { + "Gimja Bēt Maryam": 1867.5, + "Eldoret": 1783.0, + "Moi‘s Bridge": 1752.9, + "Abū an Numrus": 2824.0, + "São João": 6526.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gimja Bēt Maryam: (10.85°, 36.88°)", + " Eldoret: (0.52°, 35.27°)", + " Moi‘s Bridge: (0.87°, 35.12°)", + " Abū an Numrus: (29.95°, 31.20°)", + " São João: (-8.88°, -36.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São João: 6526.4 km from centroid", + " Abū an Numrus: 2824.0 km from centroid", + " Gimja Bēt Maryam: 1867.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São João", + "FINAL ANSWER: São João" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.90569, + "lon": 79.31897, + "name": "Arcot" + }, + { + "lat": 34.80472, + "lon": 105.57778, + "name": "Qianhu" + }, + { + "lat": 29.28222, + "lon": 106.89806, + "name": "Shilong" + }, + { + "lat": 12.75975, + "lon": 75.20169, + "name": "Puttūr" + }, + { + "lat": 45.5152, + "lon": -73.46818, + "name": "Longueuil" + } + ], + "question": "Which location is the geographic outlier among: Arcot, Qianhu, Shilong, Puttūr, Longueuil?", + "ground_truth": { + "answer": "Longueuil", + "outlier_distance_km": 10610.4, + "second_furthest_km": 4697.3, + "clarity_ratio": 2.26, + "median_distance_km": 4512.1, + "distances_to_centroid": { + "Arcot": 2660.1, + "Qianhu": 4512.1, + "Shilong": 4697.3, + "Puttūr": 2340.2, + "Longueuil": 10610.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arcot: (12.91°, 79.32°)", + " Qianhu: (34.80°, 105.58°)", + " Shilong: (29.28°, 106.90°)", + " Puttūr: (12.76°, 75.20°)", + " Longueuil: (45.52°, -73.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Longueuil: 10610.4 km from centroid", + " Shilong: 4697.3 km from centroid", + " Qianhu: 4512.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Longueuil", + "FINAL ANSWER: Longueuil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.41866, + "lon": 30.77861, + "name": "Maţāy" + }, + { + "lat": 8.61565, + "lon": 6.4185, + "name": "Baro" + }, + { + "lat": -28.23078, + "lon": 28.30707, + "name": "Bethlehem" + }, + { + "lat": 7.1127, + "lon": 5.1159, + "name": "Idanre" + }, + { + "lat": 36.66833, + "lon": 116.99722, + "name": "Jinan" + } + ], + "question": "Which location is the geographic outlier among: Maţāy, Baro, Bethlehem, Idanre, Jinan?", + "ground_truth": { + "answer": "Jinan", + "outlier_distance_km": 8377.5, + "second_furthest_km": 4421.1, + "clarity_ratio": 1.89, + "median_distance_km": 3579.4, + "distances_to_centroid": { + "Maţāy": 2111.1, + "Baro": 3415.8, + "Bethlehem": 4421.1, + "Idanre": 3579.4, + "Jinan": 8377.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maţāy: (28.42°, 30.78°)", + " Baro: (8.62°, 6.42°)", + " Bethlehem: (-28.23°, 28.31°)", + " Idanre: (7.11°, 5.12°)", + " Jinan: (36.67°, 117.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jinan: 8377.5 km from centroid", + " Bethlehem: 4421.1 km from centroid", + " Idanre: 3579.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jinan", + "FINAL ANSWER: Jinan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.85029, + "lon": 36.89277, + "name": "Ginja Bet" + }, + { + "lat": 31.20176, + "lon": 29.91582, + "name": "Alexandria" + }, + { + "lat": 29.84144, + "lon": 31.30084, + "name": "Ḩalwān" + }, + { + "lat": 6.50153, + "lon": 3.35808, + "name": "Surulere" + }, + { + "lat": 42.49747, + "lon": -94.16802, + "name": "Fort Dodge" + } + ], + "question": "Which location is the geographic outlier among: Ginja Bet, Alexandria, Ḩalwān, Surulere, Fort Dodge?", + "ground_truth": { + "answer": "Fort Dodge", + "outlier_distance_km": 8654.8, + "second_furthest_km": 4023.4, + "clarity_ratio": 2.15, + "median_distance_km": 3013.6, + "distances_to_centroid": { + "Ginja Bet": 4023.4, + "Alexandria": 2899.4, + "Ḩalwān": 3013.6, + "Surulere": 1976.0, + "Fort Dodge": 8654.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ginja Bet: (10.85°, 36.89°)", + " Alexandria: (31.20°, 29.92°)", + " Ḩalwān: (29.84°, 31.30°)", + " Surulere: (6.50°, 3.36°)", + " Fort Dodge: (42.50°, -94.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fort Dodge: 8654.8 km from centroid", + " Ginja Bet: 4023.4 km from centroid", + " Ḩalwān: 3013.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fort Dodge", + "FINAL ANSWER: Fort Dodge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.0088, + "lon": -119.39672, + "name": "Lake Country" + }, + { + "lat": 34.82984, + "lon": -82.60152, + "name": "Easley" + }, + { + "lat": 18.10721, + "lon": -95.87904, + "name": "Loma Bonita" + }, + { + "lat": 44.94441, + "lon": -93.09327, + "name": "Saint Paul" + }, + { + "lat": -6.72917, + "lon": -38.44889, + "name": "São João do Rio do Peixe" + } + ], + "question": "Which location is the geographic outlier among: Lake Country, Easley, Loma Bonita, Saint Paul, São João do Rio do Peixe?", + "ground_truth": { + "answer": "São João do Rio do Peixe", + "outlier_distance_km": 6400.3, + "second_furthest_km": 3717.8, + "clarity_ratio": 1.72, + "median_distance_km": 1964.6, + "distances_to_centroid": { + "Lake Country": 3717.8, + "Easley": 796.7, + "Loma Bonita": 1518.9, + "Saint Paul": 1964.6, + "São João do Rio do Peixe": 6400.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lake Country: (50.01°, -119.40°)", + " Easley: (34.83°, -82.60°)", + " Loma Bonita: (18.11°, -95.88°)", + " Saint Paul: (44.94°, -93.09°)", + " São João do Rio do Peixe: (-6.73°, -38.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São João do Rio do Peixe: 6400.3 km from centroid", + " Lake Country: 3717.8 km from centroid", + " Saint Paul: 1964.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São João do Rio do Peixe", + "FINAL ANSWER: São João do Rio do Peixe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.31636, + "lon": -123.06934, + "name": "North Vancouver" + }, + { + "lat": 32.75957, + "lon": -97.45835, + "name": "White Settlement" + }, + { + "lat": 19.53159, + "lon": -98.87464, + "name": "Tulantongo" + }, + { + "lat": 43.68947, + "lon": -79.3314, + "name": "Danforth East York" + }, + { + "lat": 50.88365, + "lon": 5.98154, + "name": "Heerlen" + } + ], + "question": "Which location is the geographic outlier among: North Vancouver, White Settlement, Tulantongo, Danforth East York, Heerlen?", + "ground_truth": { + "answer": "Heerlen", + "outlier_distance_km": 6393.6, + "second_furthest_km": 3657.8, + "clarity_ratio": 1.75, + "median_distance_km": 2931.5, + "distances_to_centroid": { + "North Vancouver": 3657.8, + "White Settlement": 1842.5, + "Tulantongo": 2931.5, + "Danforth East York": 499.4, + "Heerlen": 6393.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Vancouver: (49.32°, -123.07°)", + " White Settlement: (32.76°, -97.46°)", + " Tulantongo: (19.53°, -98.87°)", + " Danforth East York: (43.69°, -79.33°)", + " Heerlen: (50.88°, 5.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Heerlen: 6393.6 km from centroid", + " North Vancouver: 3657.8 km from centroid", + " Tulantongo: 2931.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Heerlen", + "FINAL ANSWER: Heerlen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": -32.23013, + "lon": 115.78128, + "name": "Kwinana" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": 43.11682, + "lon": -79.19958, + "name": "Thorold" + } + ], + "question": "Which location is the geographic outlier among: Mount Isa, Kwinana, Caboolture, Dunedin, Thorold?", + "ground_truth": { + "answer": "Thorold", + "outlier_distance_km": 17060.8, + "second_furthest_km": 7201.8, + "clarity_ratio": 2.37, + "median_distance_km": 5559.4, + "distances_to_centroid": { + "Mount Isa": 4186.9, + "Kwinana": 2364.7, + "Caboolture": 5559.4, + "Dunedin": 7201.8, + "Thorold": 17060.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mount Isa: (-20.73°, 139.50°)", + " Kwinana: (-32.23°, 115.78°)", + " Caboolture: (-27.08°, 152.95°)", + " Dunedin: (-45.87°, 170.50°)", + " Thorold: (43.12°, -79.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thorold: 17060.8 km from centroid", + " Dunedin: 7201.8 km from centroid", + " Caboolture: 5559.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thorold", + "FINAL ANSWER: Thorold" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.98154, + "lon": -81.23621, + "name": "Lexington" + }, + { + "lat": 28.6, + "lon": -81.33924, + "name": "Winter Park" + }, + { + "lat": 38.95171, + "lon": -92.33407, + "name": "Columbia" + }, + { + "lat": 42.21947, + "lon": -87.97952, + "name": "Vernon Hills" + }, + { + "lat": -26.96501, + "lon": 30.43571, + "name": "Driefontein" + } + ], + "question": "Which location is the geographic outlier among: Lexington, Winter Park, Columbia, Vernon Hills, Driefontein?", + "ground_truth": { + "answer": "Driefontein", + "outlier_distance_km": 11430.8, + "second_furthest_km": 3304.0, + "clarity_ratio": 3.46, + "median_distance_km": 3151.5, + "distances_to_centroid": { + "Lexington": 2171.4, + "Winter Park": 1969.6, + "Columbia": 3304.0, + "Vernon Hills": 3151.5, + "Driefontein": 11430.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lexington: (33.98°, -81.24°)", + " Winter Park: (28.60°, -81.34°)", + " Columbia: (38.95°, -92.33°)", + " Vernon Hills: (42.22°, -87.98°)", + " Driefontein: (-26.97°, 30.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Driefontein: 11430.8 km from centroid", + " Columbia: 3304.0 km from centroid", + " Vernon Hills: 3151.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Driefontein", + "FINAL ANSWER: Driefontein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.51302, + "lon": 105.95341, + "name": "Banqiao" + }, + { + "lat": 27.45493, + "lon": 112.16943, + "name": "Yongfeng" + }, + { + "lat": 31.66667, + "lon": 130.38333, + "name": "Umeki" + }, + { + "lat": 34.31667, + "lon": 118.51667, + "name": "Gaoliu" + }, + { + "lat": 51.68033, + "lon": 7.82089, + "name": "Hamm" + } + ], + "question": "Which location is the geographic outlier among: Banqiao, Yongfeng, Umeki, Gaoliu, Hamm?", + "ground_truth": { + "answer": "Hamm", + "outlier_distance_km": 6857.9, + "second_furthest_km": 3294.3, + "clarity_ratio": 2.08, + "median_distance_km": 2150.8, + "distances_to_centroid": { + "Banqiao": 1194.8, + "Yongfeng": 1831.3, + "Umeki": 3294.3, + "Gaoliu": 2150.8, + "Hamm": 6857.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banqiao: (29.51°, 105.95°)", + " Yongfeng: (27.45°, 112.17°)", + " Umeki: (31.67°, 130.38°)", + " Gaoliu: (34.32°, 118.52°)", + " Hamm: (51.68°, 7.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hamm: 6857.9 km from centroid", + " Umeki: 3294.3 km from centroid", + " Gaoliu: 2150.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hamm", + "FINAL ANSWER: Hamm" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.87342, + "lon": 7.95407, + "name": "Kachia" + }, + { + "lat": 7.81667, + "lon": 4.91667, + "name": "Oke Mesi" + }, + { + "lat": 14.12109, + "lon": 38.72337, + "name": "Aksum" + }, + { + "lat": 30.71877, + "lon": 31.56299, + "name": "Al Ibrāhīmīyah" + }, + { + "lat": 38.99167, + "lon": -94.63357, + "name": "Prairie Village" + } + ], + "question": "Which location is the geographic outlier among: Kachia, Oke Mesi, Aksum, Al Ibrāhīmīyah, Prairie Village?", + "ground_truth": { + "answer": "Prairie Village", + "outlier_distance_km": 8798.7, + "second_furthest_km": 4399.5, + "clarity_ratio": 2.0, + "median_distance_km": 3573.2, + "distances_to_centroid": { + "Kachia": 1597.4, + "Oke Mesi": 1590.7, + "Aksum": 4399.5, + "Al Ibrāhīmīyah": 3573.2, + "Prairie Village": 8798.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kachia: (9.87°, 7.95°)", + " Oke Mesi: (7.82°, 4.92°)", + " Aksum: (14.12°, 38.72°)", + " Al Ibrāhīmīyah: (30.72°, 31.56°)", + " Prairie Village: (38.99°, -94.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Prairie Village: 8798.7 km from centroid", + " Aksum: 4399.5 km from centroid", + " Al Ibrāhīmīyah: 3573.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Prairie Village", + "FINAL ANSWER: Prairie Village" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.61591, + "lon": 120.31663, + "name": "San Fernando" + }, + { + "lat": 36.62528, + "lon": 119.71333, + "name": "Cuijiaji" + }, + { + "lat": 13.2233, + "lon": 120.596, + "name": "Mamburao" + }, + { + "lat": 30.73294, + "lon": 108.27419, + "name": "Zhushan" + }, + { + "lat": 28.31214, + "lon": 30.71007, + "name": "Samālūţ" + } + ], + "question": "Which location is the geographic outlier among: San Fernando, Cuijiaji, Mamburao, Zhushan, Samālūţ?", + "ground_truth": { + "answer": "Samālūţ", + "outlier_distance_km": 6787.7, + "second_furthest_km": 2536.0, + "clarity_ratio": 2.68, + "median_distance_km": 2315.9, + "distances_to_centroid": { + "San Fernando": 2315.9, + "Cuijiaji": 2275.1, + "Mamburao": 2536.0, + "Zhushan": 1031.6, + "Samālūţ": 6787.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Fernando: (16.62°, 120.32°)", + " Cuijiaji: (36.63°, 119.71°)", + " Mamburao: (13.22°, 120.60°)", + " Zhushan: (30.73°, 108.27°)", + " Samālūţ: (28.31°, 30.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Samālūţ: 6787.7 km from centroid", + " Mamburao: 2536.0 km from centroid", + " San Fernando: 2315.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Samālūţ", + "FINAL ANSWER: Samālūţ" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": -9.16972, + "lon": -36.67972, + "name": "Bom Conselho" + } + ], + "question": "Which location is the geographic outlier among: Mount Isa, Orange, Warragul, Earlwood, Bom Conselho?", + "ground_truth": { + "answer": "Bom Conselho", + "outlier_distance_km": 14603.9, + "second_furthest_km": 4006.0, + "clarity_ratio": 3.65, + "median_distance_km": 3818.8, + "distances_to_centroid": { + "Mount Isa": 3092.8, + "Orange": 3818.8, + "Warragul": 3576.3, + "Earlwood": 4006.0, + "Bom Conselho": 14603.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mount Isa: (-20.73°, 139.50°)", + " Orange: (-33.28°, 149.10°)", + " Warragul: (-38.16°, 145.93°)", + " Earlwood: (-33.92°, 151.13°)", + " Bom Conselho: (-9.17°, -36.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bom Conselho: 14603.9 km from centroid", + " Earlwood: 4006.0 km from centroid", + " Orange: 3818.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bom Conselho", + "FINAL ANSWER: Bom Conselho" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.21167, + "lon": 5.2875, + "name": "Baarn" + }, + { + "lat": 53.47424, + "lon": 9.88289, + "name": "Hausbruch" + }, + { + "lat": 51.64674, + "lon": -0.16103, + "name": "East Barnet" + }, + { + "lat": 48.77275, + "lon": 5.16108, + "name": "Bar-le-Duc" + }, + { + "lat": -5.70729, + "lon": -78.80785, + "name": "Jaén" + } + ], + "question": "Which location is the geographic outlier among: Baarn, Hausbruch, East Barnet, Bar-le-Duc, Jaén?", + "ground_truth": { + "answer": "Jaén", + "outlier_distance_km": 8512.8, + "second_furthest_km": 2203.4, + "clarity_ratio": 3.86, + "median_distance_km": 1871.9, + "distances_to_centroid": { + "Baarn": 1871.9, + "Hausbruch": 2203.4, + "East Barnet": 1563.2, + "Bar-le-Duc": 1647.2, + "Jaén": 8512.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baarn: (52.21°, 5.29°)", + " Hausbruch: (53.47°, 9.88°)", + " East Barnet: (51.65°, -0.16°)", + " Bar-le-Duc: (48.77°, 5.16°)", + " Jaén: (-5.71°, -78.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaén: 8512.8 km from centroid", + " Hausbruch: 2203.4 km from centroid", + " Baarn: 1871.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaén", + "FINAL ANSWER: Jaén" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.91342, + "lon": 19.00479, + "name": "Czechowice-Dziedzice" + }, + { + "lat": 54.25354, + "lon": 20.80819, + "name": "Bartoszyce" + }, + { + "lat": 55.79479, + "lon": 37.94794, + "name": "Balashikha" + }, + { + "lat": 40.31991, + "lon": 9.32568, + "name": "Nuoro" + }, + { + "lat": 34.77453, + "lon": -96.67834, + "name": "Ada" + } + ], + "question": "Which location is the geographic outlier among: Czechowice-Dziedzice, Bartoszyce, Balashikha, Nuoro, Ada?", + "ground_truth": { + "answer": "Ada", + "outlier_distance_km": 7587.9, + "second_furthest_km": 2885.6, + "clarity_ratio": 2.63, + "median_distance_km": 1783.0, + "distances_to_centroid": { + "Czechowice-Dziedzice": 1570.6, + "Bartoszyce": 1783.0, + "Balashikha": 2885.6, + "Nuoro": 1169.1, + "Ada": 7587.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Czechowice-Dziedzice: (49.91°, 19.00°)", + " Bartoszyce: (54.25°, 20.81°)", + " Balashikha: (55.79°, 37.95°)", + " Nuoro: (40.32°, 9.33°)", + " Ada: (34.77°, -96.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ada: 7587.9 km from centroid", + " Balashikha: 2885.6 km from centroid", + " Bartoszyce: 1783.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ada", + "FINAL ANSWER: Ada" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.02867, + "lon": 100.40691, + "name": "Tokai" + }, + { + "lat": 24.36667, + "lon": 92.16667, + "name": "Dharmanagar" + }, + { + "lat": 21.22899, + "lon": 79.2398, + "name": "Kanhān" + }, + { + "lat": 42.94769, + "lon": 89.17886, + "name": "Turpan" + }, + { + "lat": 32.5007, + "lon": -94.74049, + "name": "Longview" + } + ], + "question": "Which location is the geographic outlier among: Tokai, Dharmanagar, Kanhān, Turpan, Longview?", + "ground_truth": { + "answer": "Longview", + "outlier_distance_km": 12736.5, + "second_furthest_km": 5450.2, + "clarity_ratio": 2.34, + "median_distance_km": 3913.1, + "distances_to_centroid": { + "Tokai": 5450.2, + "Dharmanagar": 3913.1, + "Kanhān": 2689.8, + "Turpan": 3795.1, + "Longview": 12736.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tokai: (6.03°, 100.41°)", + " Dharmanagar: (24.37°, 92.17°)", + " Kanhān: (21.23°, 79.24°)", + " Turpan: (42.95°, 89.18°)", + " Longview: (32.50°, -94.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Longview: 12736.5 km from centroid", + " Tokai: 5450.2 km from centroid", + " Dharmanagar: 3913.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Longview", + "FINAL ANSWER: Longview" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + }, + { + "lat": -30.98153, + "lon": -64.09424, + "name": "Jesús María" + } + ], + "question": "Which location is the geographic outlier among: Titirangi, Earlwood, Rockingham, Hurstville, Jesús María?", + "ground_truth": { + "answer": "Jesús María", + "outlier_distance_km": 12752.7, + "second_furthest_km": 6129.9, + "clarity_ratio": 2.08, + "median_distance_km": 4163.2, + "distances_to_centroid": { + "Titirangi": 6129.9, + "Earlwood": 4163.2, + "Rockingham": 947.0, + "Hurstville": 4160.0, + "Jesús María": 12752.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Titirangi: (-36.94°, 174.66°)", + " Earlwood: (-33.92°, 151.13°)", + " Rockingham: (-32.28°, 115.73°)", + " Hurstville: (-33.97°, 151.10°)", + " Jesús María: (-30.98°, -64.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jesús María: 12752.7 km from centroid", + " Titirangi: 6129.9 km from centroid", + " Earlwood: 4163.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jesús María", + "FINAL ANSWER: Jesús María" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.78088, + "lon": -90.42179, + "name": "Farmington" + }, + { + "lat": 39.57538, + "lon": -76.99581, + "name": "Westminster" + }, + { + "lat": 31.12406, + "lon": -97.90308, + "name": "Copperas Cove" + }, + { + "lat": 36.98038, + "lon": -76.42975, + "name": "Newport News" + }, + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + } + ], + "question": "Which location is the geographic outlier among: Farmington, Westminster, Copperas Cove, Newport News, Pascoe Vale?", + "ground_truth": { + "answer": "Pascoe Vale", + "outlier_distance_km": 18168.4, + "second_furthest_km": 5864.8, + "clarity_ratio": 3.1, + "median_distance_km": 5182.1, + "distances_to_centroid": { + "Farmington": 5182.1, + "Westminster": 4081.3, + "Copperas Cove": 5864.8, + "Newport News": 3950.9, + "Pascoe Vale": 18168.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Farmington: (37.78°, -90.42°)", + " Westminster: (39.58°, -77.00°)", + " Copperas Cove: (31.12°, -97.90°)", + " Newport News: (36.98°, -76.43°)", + " Pascoe Vale: (-37.73°, 144.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pascoe Vale: 18168.4 km from centroid", + " Copperas Cove: 5864.8 km from centroid", + " Farmington: 5182.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pascoe Vale", + "FINAL ANSWER: Pascoe Vale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.05056, + "lon": -49.62278, + "name": "Presidente Getúlio" + }, + { + "lat": -11.25222, + "lon": -74.63861, + "name": "Satipo" + }, + { + "lat": -17.70306, + "lon": -40.76639, + "name": "Carlos Chagas" + }, + { + "lat": -23.60389, + "lon": -46.91917, + "name": "Cotia" + }, + { + "lat": 8.35362, + "lon": 77.1859, + "name": "Palugal" + } + ], + "question": "Which location is the geographic outlier among: Presidente Getúlio, Satipo, Carlos Chagas, Cotia, Palugal?", + "ground_truth": { + "answer": "Palugal", + "outlier_distance_km": 11749.3, + "second_furthest_km": 5174.0, + "clarity_ratio": 2.27, + "median_distance_km": 2747.3, + "distances_to_centroid": { + "Presidente Getúlio": 2747.3, + "Satipo": 5174.0, + "Carlos Chagas": 1525.3, + "Cotia": 2339.7, + "Palugal": 11749.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Presidente Getúlio: (-27.05°, -49.62°)", + " Satipo: (-11.25°, -74.64°)", + " Carlos Chagas: (-17.70°, -40.77°)", + " Cotia: (-23.60°, -46.92°)", + " Palugal: (8.35°, 77.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Palugal: 11749.3 km from centroid", + " Satipo: 5174.0 km from centroid", + " Presidente Getúlio: 2747.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Palugal", + "FINAL ANSWER: Palugal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 59.77234, + "lon": 30.13455, + "name": "Gorelovo" + }, + { + "lat": 45.74123, + "lon": 3.19643, + "name": "Cournon-d'Auvergne" + }, + { + "lat": 39.56964, + "lon": 3.20955, + "name": "Manacor" + }, + { + "lat": 51.57558, + "lon": 8.10619, + "name": "Soest" + }, + { + "lat": 3.3285, + "lon": 99.1625, + "name": "Tebingtinggi" + } + ], + "question": "Which location is the geographic outlier among: Gorelovo, Cournon-d'Auvergne, Manacor, Soest, Tebingtinggi?", + "ground_truth": { + "answer": "Tebingtinggi", + "outlier_distance_km": 8107.3, + "second_furthest_km": 2200.9, + "clarity_ratio": 3.68, + "median_distance_km": 2176.5, + "distances_to_centroid": { + "Gorelovo": 2200.9, + "Cournon-d'Auvergne": 2168.4, + "Manacor": 2176.5, + "Soest": 2042.5, + "Tebingtinggi": 8107.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gorelovo: (59.77°, 30.13°)", + " Cournon-d'Auvergne: (45.74°, 3.20°)", + " Manacor: (39.57°, 3.21°)", + " Soest: (51.58°, 8.11°)", + " Tebingtinggi: (3.33°, 99.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tebingtinggi: 8107.3 km from centroid", + " Gorelovo: 2200.9 km from centroid", + " Manacor: 2176.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tebingtinggi", + "FINAL ANSWER: Tebingtinggi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.44417, + "lon": -46.91778, + "name": "Santana de Parnaíba" + }, + { + "lat": 7.125, + "lon": -73.11895, + "name": "Bucaramanga" + }, + { + "lat": -27.58504, + "lon": -56.68707, + "name": "Ituzaingó" + }, + { + "lat": -20.48361, + "lon": -55.80694, + "name": "Anastácio" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + } + ], + "question": "Which location is the geographic outlier among: Santana de Parnaíba, Bucaramanga, Ituzaingó, Anastácio, Doncaster East?", + "ground_truth": { + "answer": "Doncaster East", + "outlier_distance_km": 13290.8, + "second_furthest_km": 6807.4, + "clarity_ratio": 1.95, + "median_distance_km": 4044.1, + "distances_to_centroid": { + "Santana de Parnaíba": 3049.8, + "Bucaramanga": 6807.4, + "Ituzaingó": 4044.1, + "Anastácio": 3983.8, + "Doncaster East": 13290.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santana de Parnaíba: (-23.44°, -46.92°)", + " Bucaramanga: (7.12°, -73.12°)", + " Ituzaingó: (-27.59°, -56.69°)", + " Anastácio: (-20.48°, -55.81°)", + " Doncaster East: (-37.79°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doncaster East: 13290.8 km from centroid", + " Bucaramanga: 6807.4 km from centroid", + " Ituzaingó: 4044.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doncaster East", + "FINAL ANSWER: Doncaster East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.8282, + "lon": 174.62019, + "name": "Massey East" + }, + { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + }, + { + "lat": -28.00029, + "lon": 153.43088, + "name": "Gold Coast" + }, + { + "lat": -38.11342, + "lon": 145.28326, + "name": "Cranbourne" + }, + { + "lat": 40.45572, + "lon": -3.63509, + "name": "Piovera" + } + ], + "question": "Which location is the geographic outlier among: Massey East, Whanganui, Gold Coast, Cranbourne, Piovera?", + "ground_truth": { + "answer": "Piovera", + "outlier_distance_km": 15032.0, + "second_furthest_km": 4861.7, + "clarity_ratio": 3.09, + "median_distance_km": 4759.1, + "distances_to_centroid": { + "Massey East": 4759.1, + "Whanganui": 4861.7, + "Gold Coast": 2613.3, + "Cranbourne": 2511.7, + "Piovera": 15032.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Massey East: (-36.83°, 174.62°)", + " Whanganui: (-39.93°, 175.05°)", + " Gold Coast: (-28.00°, 153.43°)", + " Cranbourne: (-38.11°, 145.28°)", + " Piovera: (40.46°, -3.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piovera: 15032.0 km from centroid", + " Whanganui: 4861.7 km from centroid", + " Massey East: 4759.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piovera", + "FINAL ANSWER: Piovera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.22436, + "lon": -79.42476, + "name": "Chepén" + }, + { + "lat": -38.95078, + "lon": -68.0592, + "name": "Neuquén" + }, + { + "lat": -8.28773, + "lon": -35.02925, + "name": "Cabo de Santo Agostinho" + }, + { + "lat": -18.08639, + "lon": -39.55083, + "name": "Mucuri" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + } + ], + "question": "Which location is the geographic outlier among: Chepén, Neuquén, Cabo de Santo Agostinho, Mucuri, Karori?", + "ground_truth": { + "answer": "Karori", + "outlier_distance_km": 12879.8, + "second_furthest_km": 7646.8, + "clarity_ratio": 1.68, + "median_distance_km": 5771.7, + "distances_to_centroid": { + "Chepén": 7646.8, + "Neuquén": 5771.7, + "Cabo de Santo Agostinho": 3167.8, + "Mucuri": 3172.3, + "Karori": 12879.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chepén: (-7.22°, -79.42°)", + " Neuquén: (-38.95°, -68.06°)", + " Cabo de Santo Agostinho: (-8.29°, -35.03°)", + " Mucuri: (-18.09°, -39.55°)", + " Karori: (-41.28°, 174.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karori: 12879.8 km from centroid", + " Chepén: 7646.8 km from centroid", + " Neuquén: 5771.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karori", + "FINAL ANSWER: Karori" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.76884, + "lon": -119.24705, + "name": "Delano" + }, + { + "lat": 39.4667, + "lon": -87.41391, + "name": "Terre Haute" + }, + { + "lat": 33.96358, + "lon": -117.56418, + "name": "Eastvale" + }, + { + "lat": 44.47588, + "lon": -73.21207, + "name": "Burlington" + }, + { + "lat": 0.46005, + "lon": 34.11169, + "name": "Busia" + } + ], + "question": "Which location is the geographic outlier among: Delano, Terre Haute, Eastvale, Burlington, Busia?", + "ground_truth": { + "answer": "Busia", + "outlier_distance_km": 11576.2, + "second_furthest_km": 4323.7, + "clarity_ratio": 2.68, + "median_distance_km": 4196.6, + "distances_to_centroid": { + "Delano": 4323.7, + "Terre Haute": 1646.0, + "Eastvale": 4196.6, + "Burlington": 1518.4, + "Busia": 11576.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Delano: (35.77°, -119.25°)", + " Terre Haute: (39.47°, -87.41°)", + " Eastvale: (33.96°, -117.56°)", + " Burlington: (44.48°, -73.21°)", + " Busia: (0.46°, 34.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Busia: 11576.2 km from centroid", + " Delano: 4323.7 km from centroid", + " Eastvale: 4196.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Busia", + "FINAL ANSWER: Busia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.6826, + "lon": 39.0676, + "name": "Pridonskoy" + }, + { + "lat": 44.85614, + "lon": -0.53355, + "name": "Cenon" + }, + { + "lat": 48.76872, + "lon": 2.53474, + "name": "Sucy-en-Brie" + }, + { + "lat": 48.93196, + "lon": 9.2024, + "name": "Freiberg am Neckar" + }, + { + "lat": -25.32729, + "lon": 28.94224, + "name": "Kwaggafontein" + } + ], + "question": "Which location is the geographic outlier among: Pridonskoy, Cenon, Sucy-en-Brie, Freiberg am Neckar, Kwaggafontein?", + "ground_truth": { + "answer": "Kwaggafontein", + "outlier_distance_km": 6716.9, + "second_furthest_km": 2726.2, + "clarity_ratio": 2.46, + "median_distance_km": 1997.0, + "distances_to_centroid": { + "Pridonskoy": 2726.2, + "Cenon": 1864.6, + "Sucy-en-Brie": 1997.0, + "Freiberg am Neckar": 1771.7, + "Kwaggafontein": 6716.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pridonskoy: (51.68°, 39.07°)", + " Cenon: (44.86°, -0.53°)", + " Sucy-en-Brie: (48.77°, 2.53°)", + " Freiberg am Neckar: (48.93°, 9.20°)", + " Kwaggafontein: (-25.33°, 28.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kwaggafontein: 6716.9 km from centroid", + " Pridonskoy: 2726.2 km from centroid", + " Sucy-en-Brie: 1997.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kwaggafontein", + "FINAL ANSWER: Kwaggafontein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -38.38176, + "lon": 142.48799, + "name": "Warrnambool" + }, + { + "lat": -33.73333, + "lon": 150.93284, + "name": "Glenwood" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": 22.49396, + "lon": -105.36369, + "name": "Acaponeta" + } + ], + "question": "Which location is the geographic outlier among: Porirua, Warrnambool, Glenwood, Morayfield, Acaponeta?", + "ground_truth": { + "answer": "Acaponeta", + "outlier_distance_km": 17097.4, + "second_furthest_km": 6817.4, + "clarity_ratio": 2.51, + "median_distance_km": 4986.0, + "distances_to_centroid": { + "Porirua": 6817.4, + "Warrnambool": 4055.4, + "Glenwood": 4752.2, + "Morayfield": 4986.0, + "Acaponeta": 17097.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porirua: (-41.13°, 174.85°)", + " Warrnambool: (-38.38°, 142.49°)", + " Glenwood: (-33.73°, 150.93°)", + " Morayfield: (-27.11°, 152.95°)", + " Acaponeta: (22.49°, -105.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Acaponeta: 17097.4 km from centroid", + " Porirua: 6817.4 km from centroid", + " Morayfield: 4986.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Acaponeta", + "FINAL ANSWER: Acaponeta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.7875, + "lon": 39.54222, + "name": "Maych’ew" + }, + { + "lat": 25.90107, + "lon": 32.72392, + "name": "Naqādah" + }, + { + "lat": 11.73292, + "lon": 41.082, + "name": "Dubti" + }, + { + "lat": 14.18722, + "lon": 39.56389, + "name": "Idaga Hamus" + }, + { + "lat": 48.86667, + "lon": 2.71667, + "name": "Lagny-sur-Marne" + } + ], + "question": "Which location is the geographic outlier among: Maych’ew, Naqādah, Dubti, Idaga Hamus, Lagny-sur-Marne?", + "ground_truth": { + "answer": "Lagny-sur-Marne", + "outlier_distance_km": 3833.2, + "second_furthest_km": 1612.3, + "clarity_ratio": 2.38, + "median_distance_km": 1416.2, + "distances_to_centroid": { + "Maych’ew": 1416.2, + "Naqādah": 391.5, + "Dubti": 1612.3, + "Idaga Hamus": 1298.1, + "Lagny-sur-Marne": 3833.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maych’ew: (12.79°, 39.54°)", + " Naqādah: (25.90°, 32.72°)", + " Dubti: (11.73°, 41.08°)", + " Idaga Hamus: (14.19°, 39.56°)", + " Lagny-sur-Marne: (48.87°, 2.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lagny-sur-Marne: 3833.2 km from centroid", + " Dubti: 1612.3 km from centroid", + " Maych’ew: 1416.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lagny-sur-Marne", + "FINAL ANSWER: Lagny-sur-Marne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.09755, + "lon": 31.30312, + "name": "Nabarūh" + }, + { + "lat": 5.65, + "lon": 37.36667, + "name": "Gīdolē" + }, + { + "lat": -26.81358, + "lon": 27.81695, + "name": "Sasolburg" + }, + { + "lat": 6.38706, + "lon": -0.37738, + "name": "Begoro" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + } + ], + "question": "Which location is the geographic outlier among: Nabarūh, Gīdolē, Sasolburg, Begoro, Miranda?", + "ground_truth": { + "answer": "Miranda", + "outlier_distance_km": 10854.4, + "second_furthest_km": 5639.9, + "clarity_ratio": 1.92, + "median_distance_km": 4305.0, + "distances_to_centroid": { + "Nabarūh": 4305.0, + "Gīdolē": 1686.2, + "Sasolburg": 3462.0, + "Begoro": 5639.9, + "Miranda": 10854.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nabarūh: (31.10°, 31.30°)", + " Gīdolē: (5.65°, 37.37°)", + " Sasolburg: (-26.81°, 27.82°)", + " Begoro: (6.39°, -0.38°)", + " Miranda: (-34.04°, 151.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Miranda: 10854.4 km from centroid", + " Begoro: 5639.9 km from centroid", + " Nabarūh: 4305.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Miranda", + "FINAL ANSWER: Miranda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.17139, + "lon": 36.83556, + "name": "Kiambu" + }, + { + "lat": -33.4608, + "lon": 18.72714, + "name": "Malmesbury" + }, + { + "lat": -26.26786, + "lon": 28.12225, + "name": "Alberton" + }, + { + "lat": -26.002, + "lon": 29.034, + "name": "Phola" + }, + { + "lat": 36.88, + "lon": 118.7375, + "name": "Shouguang" + } + ], + "question": "Which location is the geographic outlier among: Kiambu, Malmesbury, Alberton, Phola, Shouguang?", + "ground_truth": { + "answer": "Shouguang", + "outlier_distance_km": 9155.6, + "second_furthest_km": 3836.4, + "clarity_ratio": 2.39, + "median_distance_km": 2630.7, + "distances_to_centroid": { + "Kiambu": 1434.4, + "Malmesbury": 3836.4, + "Alberton": 2630.7, + "Phola": 2542.4, + "Shouguang": 9155.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kiambu: (-1.17°, 36.84°)", + " Malmesbury: (-33.46°, 18.73°)", + " Alberton: (-26.27°, 28.12°)", + " Phola: (-26.00°, 29.03°)", + " Shouguang: (36.88°, 118.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shouguang: 9155.6 km from centroid", + " Malmesbury: 3836.4 km from centroid", + " Alberton: 2630.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shouguang", + "FINAL ANSWER: Shouguang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.81601, + "lon": -65.21051, + "name": "San Miguel de Tucumán" + }, + { + "lat": -23.52272, + "lon": -46.835, + "name": "Carapicuíba" + }, + { + "lat": -2.62833, + "lon": -56.73583, + "name": "Parintins" + }, + { + "lat": -5.61278, + "lon": -38.76694, + "name": "Jaguaretama" + }, + { + "lat": 12.35275, + "lon": 121.06761, + "name": "San Jose" + } + ], + "question": "Which location is the geographic outlier among: San Miguel de Tucumán, Carapicuíba, Parintins, Jaguaretama, San Jose?", + "ground_truth": { + "answer": "San Jose", + "outlier_distance_km": 15458.5, + "second_furthest_km": 5390.8, + "clarity_ratio": 2.87, + "median_distance_km": 4420.2, + "distances_to_centroid": { + "San Miguel de Tucumán": 5390.8, + "Carapicuíba": 3516.7, + "Parintins": 4420.2, + "Jaguaretama": 2401.0, + "San Jose": 15458.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Miguel de Tucumán: (-26.82°, -65.21°)", + " Carapicuíba: (-23.52°, -46.84°)", + " Parintins: (-2.63°, -56.74°)", + " Jaguaretama: (-5.61°, -38.77°)", + " San Jose: (12.35°, 121.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Jose: 15458.5 km from centroid", + " San Miguel de Tucumán: 5390.8 km from centroid", + " Parintins: 4420.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Jose", + "FINAL ANSWER: San Jose" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96667, + "lon": 145.16667, + "name": "Noble Park" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + { + "lat": -36.8382, + "lon": 174.61019, + "name": "Massey" + }, + { + "lat": 41.04376, + "lon": 16.88491, + "name": "Valenzano" + } + ], + "question": "Which location is the geographic outlier among: Noble Park, Seaford, Yagoona, Massey, Valenzano?", + "ground_truth": { + "answer": "Valenzano", + "outlier_distance_km": 13152.4, + "second_furthest_km": 4929.1, + "clarity_ratio": 2.67, + "median_distance_km": 2786.3, + "distances_to_centroid": { + "Noble Park": 2584.6, + "Seaford": 2592.2, + "Yagoona": 2786.3, + "Massey": 4929.1, + "Valenzano": 13152.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Noble Park: (-37.97°, 145.17°)", + " Seaford: (-38.10°, 145.13°)", + " Yagoona: (-33.90°, 151.02°)", + " Massey: (-36.84°, 174.61°)", + " Valenzano: (41.04°, 16.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Valenzano: 13152.4 km from centroid", + " Massey: 4929.1 km from centroid", + " Yagoona: 2786.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Valenzano", + "FINAL ANSWER: Valenzano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.13139, + "lon": 106.37972, + "name": "Kresek" + }, + { + "lat": 21.6318, + "lon": 85.59686, + "name": "Keonjhargarh" + }, + { + "lat": 3.6746, + "lon": 100.9867, + "name": "Sungai Besar" + }, + { + "lat": 35.21667, + "lon": 136.83333, + "name": "Kiyosu" + }, + { + "lat": -20.08722, + "lon": -45.29361, + "name": "Santo Antônio do Monte" + } + ], + "question": "Which location is the geographic outlier among: Kresek, Keonjhargarh, Sungai Besar, Kiyosu, Santo Antônio do Monte?", + "ground_truth": { + "answer": "Santo Antônio do Monte", + "outlier_distance_km": 13625.4, + "second_furthest_km": 6852.1, + "clarity_ratio": 1.99, + "median_distance_km": 3575.6, + "distances_to_centroid": { + "Kresek": 3575.6, + "Keonjhargarh": 1889.5, + "Sungai Besar": 2689.9, + "Kiyosu": 6852.1, + "Santo Antônio do Monte": 13625.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kresek: (-6.13°, 106.38°)", + " Keonjhargarh: (21.63°, 85.60°)", + " Sungai Besar: (3.67°, 100.99°)", + " Kiyosu: (35.22°, 136.83°)", + " Santo Antônio do Monte: (-20.09°, -45.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santo Antônio do Monte: 13625.4 km from centroid", + " Kiyosu: 6852.1 km from centroid", + " Kresek: 3575.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santo Antônio do Monte", + "FINAL ANSWER: Santo Antônio do Monte" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.6558, + "lon": 37.37454, + "name": "Kinoi" + }, + { + "lat": 29.2376, + "lon": 30.78944, + "name": "Iţsā" + }, + { + "lat": -24.78864, + "lon": 31.07938, + "name": "Mafemani" + }, + { + "lat": -0.7, + "lon": 37.18333, + "name": "Karuri" + }, + { + "lat": 26.23786, + "lon": -80.12477, + "name": "Pompano Beach" + } + ], + "question": "Which location is the geographic outlier among: Kinoi, Iţsā, Mafemani, Karuri, Pompano Beach?", + "ground_truth": { + "answer": "Pompano Beach", + "outlier_distance_km": 9866.9, + "second_furthest_km": 4008.4, + "clarity_ratio": 2.46, + "median_distance_km": 3328.4, + "distances_to_centroid": { + "Kinoi": 3012.1, + "Iţsā": 3328.4, + "Mafemani": 4008.4, + "Karuri": 2964.0, + "Pompano Beach": 9866.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kinoi: (-1.66°, 37.37°)", + " Iţsā: (29.24°, 30.79°)", + " Mafemani: (-24.79°, 31.08°)", + " Karuri: (-0.70°, 37.18°)", + " Pompano Beach: (26.24°, -80.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pompano Beach: 9866.9 km from centroid", + " Mafemani: 4008.4 km from centroid", + " Iţsā: 3328.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pompano Beach", + "FINAL ANSWER: Pompano Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + }, + { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + }, + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -7.35917, + "lon": -41.13778, + "name": "Jaicós" + } + ], + "question": "Which location is the geographic outlier among: Upper Coomera, Scarborough, Mornington, Hastings, Jaicós?", + "ground_truth": { + "answer": "Jaicós", + "outlier_distance_km": 14923.6, + "second_furthest_km": 6115.3, + "clarity_ratio": 2.44, + "median_distance_km": 4214.1, + "distances_to_centroid": { + "Upper Coomera": 4214.1, + "Scarborough": 642.8, + "Mornington": 3383.5, + "Hastings": 6115.3, + "Jaicós": 14923.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Upper Coomera: (-27.88°, 153.29°)", + " Scarborough: (-31.90°, 115.76°)", + " Mornington: (-38.22°, 145.04°)", + " Hastings: (-39.64°, 176.85°)", + " Jaicós: (-7.36°, -41.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaicós: 14923.6 km from centroid", + " Hastings: 6115.3 km from centroid", + " Upper Coomera: 4214.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaicós", + "FINAL ANSWER: Jaicós" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.90034, + "lon": 151.05563, + "name": "Greenacre" + }, + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + }, + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + { + "lat": -37.81667, + "lon": 145.2, + "name": "Mitcham" + }, + { + "lat": -10.6875, + "lon": -37.86167, + "name": "Paripiranga" + } + ], + "question": "Which location is the geographic outlier among: Greenacre, Thomastown, Traralgon, Mitcham, Paripiranga?", + "ground_truth": { + "answer": "Paripiranga", + "outlier_distance_km": 14194.3, + "second_furthest_km": 3821.8, + "clarity_ratio": 3.71, + "median_distance_km": 3387.7, + "distances_to_centroid": { + "Greenacre": 3821.8, + "Thomastown": 3252.8, + "Traralgon": 3387.7, + "Mitcham": 3269.3, + "Paripiranga": 14194.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Greenacre: (-33.90°, 151.06°)", + " Thomastown: (-37.68°, 145.02°)", + " Traralgon: (-38.20°, 146.54°)", + " Mitcham: (-37.82°, 145.20°)", + " Paripiranga: (-10.69°, -37.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paripiranga: 14194.3 km from centroid", + " Greenacre: 3821.8 km from centroid", + " Traralgon: 3387.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paripiranga", + "FINAL ANSWER: Paripiranga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.99997, + "lon": 78.64733, + "name": "Slavgorod" + }, + { + "lat": 58.47959, + "lon": 41.53587, + "name": "Buy" + }, + { + "lat": 52.51559, + "lon": 13.45482, + "name": "Friedrichshain" + }, + { + "lat": 55.07108, + "lon": 38.78399, + "name": "Kolomna" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + } + ], + "question": "Which location is the geographic outlier among: Slavgorod, Buy, Friedrichshain, Kolomna, Chatswood?", + "ground_truth": { + "answer": "Chatswood", + "outlier_distance_km": 11910.6, + "second_furthest_km": 4287.0, + "clarity_ratio": 2.78, + "median_distance_km": 2914.3, + "distances_to_centroid": { + "Slavgorod": 2075.6, + "Buy": 2914.3, + "Friedrichshain": 4287.0, + "Kolomna": 2800.5, + "Chatswood": 11910.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Slavgorod: (53.00°, 78.65°)", + " Buy: (58.48°, 41.54°)", + " Friedrichshain: (52.52°, 13.45°)", + " Kolomna: (55.07°, 38.78°)", + " Chatswood: (-33.80°, 151.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chatswood: 11910.6 km from centroid", + " Friedrichshain: 4287.0 km from centroid", + " Buy: 2914.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chatswood", + "FINAL ANSWER: Chatswood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.75389, + "lon": -42.88194, + "name": "Viçosa" + }, + { + "lat": -7.125, + "lon": -34.93222, + "name": "Bayeux" + }, + { + "lat": -34.51541, + "lon": -58.76813, + "name": "José C. Paz" + }, + { + "lat": -27.68806, + "lon": -48.77861, + "name": "Santo Amaro da Imperatriz" + }, + { + "lat": -7.6051, + "lon": 111.9035, + "name": "Nganjuk" + } + ], + "question": "Which location is the geographic outlier among: Viçosa, Bayeux, José C. Paz, Santo Amaro da Imperatriz, Nganjuk?", + "ground_truth": { + "answer": "Nganjuk", + "outlier_distance_km": 13436.7, + "second_furthest_km": 4629.9, + "clarity_ratio": 2.9, + "median_distance_km": 3576.6, + "distances_to_centroid": { + "Viçosa": 2942.3, + "Bayeux": 2583.9, + "José C. Paz": 4629.9, + "Santo Amaro da Imperatriz": 3576.6, + "Nganjuk": 13436.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viçosa: (-20.75°, -42.88°)", + " Bayeux: (-7.12°, -34.93°)", + " José C. Paz: (-34.52°, -58.77°)", + " Santo Amaro da Imperatriz: (-27.69°, -48.78°)", + " Nganjuk: (-7.61°, 111.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nganjuk: 13436.7 km from centroid", + " José C. Paz: 4629.9 km from centroid", + " Santo Amaro da Imperatriz: 3576.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nganjuk", + "FINAL ANSWER: Nganjuk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.66667, + "lon": -45.38, + "name": "Santa Inês" + }, + { + "lat": -9.805, + "lon": -37.68444, + "name": "Poço Redondo" + }, + { + "lat": -19.51889, + "lon": -41.01583, + "name": "Baixo Guandu" + }, + { + "lat": -4.28805, + "lon": -45.24611, + "name": "Vitorino Freire" + }, + { + "lat": 12.9343, + "lon": 78.7189, + "name": "Peranāmpattu" + } + ], + "question": "Which location is the geographic outlier among: Santa Inês, Poço Redondo, Baixo Guandu, Vitorino Freire, Peranāmpattu?", + "ground_truth": { + "answer": "Peranāmpattu", + "outlier_distance_km": 10868.1, + "second_furthest_km": 3025.3, + "clarity_ratio": 3.59, + "median_distance_km": 3007.0, + "distances_to_centroid": { + "Santa Inês": 3025.3, + "Poço Redondo": 2225.4, + "Baixo Guandu": 2967.0, + "Vitorino Freire": 3007.0, + "Peranāmpattu": 10868.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Inês: (-3.67°, -45.38°)", + " Poço Redondo: (-9.80°, -37.68°)", + " Baixo Guandu: (-19.52°, -41.02°)", + " Vitorino Freire: (-4.29°, -45.25°)", + " Peranāmpattu: (12.93°, 78.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Peranāmpattu: 10868.1 km from centroid", + " Santa Inês: 3025.3 km from centroid", + " Vitorino Freire: 3007.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Peranāmpattu", + "FINAL ANSWER: Peranāmpattu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.56002, + "lon": 9.71295, + "name": "Petersberg" + }, + { + "lat": 53.5, + "lon": -1.45, + "name": "Hoyland Nether" + }, + { + "lat": 53.44325, + "lon": -1.949, + "name": "Glossop" + }, + { + "lat": 41.69993, + "lon": 2.84565, + "name": "Lloret de Mar" + }, + { + "lat": 16.1026, + "lon": 80.78074, + "name": "Bhattiprolu" + } + ], + "question": "Which location is the geographic outlier among: Petersberg, Hoyland Nether, Glossop, Lloret de Mar, Bhattiprolu?", + "ground_truth": { + "answer": "Bhattiprolu", + "outlier_distance_km": 6595.5, + "second_furthest_km": 1863.1, + "clarity_ratio": 3.54, + "median_distance_km": 1837.9, + "distances_to_centroid": { + "Petersberg": 1043.6, + "Hoyland Nether": 1837.9, + "Glossop": 1863.1, + "Lloret de Mar": 1251.2, + "Bhattiprolu": 6595.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Petersberg: (50.56°, 9.71°)", + " Hoyland Nether: (53.50°, -1.45°)", + " Glossop: (53.44°, -1.95°)", + " Lloret de Mar: (41.70°, 2.85°)", + " Bhattiprolu: (16.10°, 80.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhattiprolu: 6595.5 km from centroid", + " Glossop: 1863.1 km from centroid", + " Hoyland Nether: 1837.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhattiprolu", + "FINAL ANSWER: Bhattiprolu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.53635, + "lon": 1.34428, + "name": "Cugnaux" + }, + { + "lat": 41.64662, + "lon": 2.74135, + "name": "Malgrat de Mar" + }, + { + "lat": 48.9482, + "lon": 2.19169, + "name": "Sartrouville" + }, + { + "lat": 48.16783, + "lon": 8.62719, + "name": "Rottweil" + }, + { + "lat": 31.02795, + "lon": 30.71493, + "name": "Shubrākhīt" + } + ], + "question": "Which location is the geographic outlier among: Cugnaux, Malgrat de Mar, Sartrouville, Rottweil, Shubrākhīt?", + "ground_truth": { + "answer": "Shubrākhīt", + "outlier_distance_km": 2305.6, + "second_furthest_km": 880.6, + "clarity_ratio": 2.62, + "median_distance_km": 638.8, + "distances_to_centroid": { + "Cugnaux": 638.8, + "Malgrat de Mar": 538.0, + "Sartrouville": 880.6, + "Rottweil": 613.1, + "Shubrākhīt": 2305.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cugnaux: (43.54°, 1.34°)", + " Malgrat de Mar: (41.65°, 2.74°)", + " Sartrouville: (48.95°, 2.19°)", + " Rottweil: (48.17°, 8.63°)", + " Shubrākhīt: (31.03°, 30.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shubrākhīt: 2305.6 km from centroid", + " Sartrouville: 880.6 km from centroid", + " Cugnaux: 638.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shubrākhīt", + "FINAL ANSWER: Shubrākhīt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.59703, + "lon": 6.6863, + "name": "Voerde" + }, + { + "lat": 53.9165, + "lon": 15.20027, + "name": "Gryfice" + }, + { + "lat": 50.89328, + "lon": 6.99481, + "name": "Rodenkirchen" + }, + { + "lat": 53.6052, + "lon": 10.03988, + "name": "Barmbek-Nord" + }, + { + "lat": 9.90917, + "lon": 78.16088, + "name": "Vandiyūr" + } + ], + "question": "Which location is the geographic outlier among: Voerde, Gryfice, Rodenkirchen, Barmbek-Nord, Vandiyūr?", + "ground_truth": { + "answer": "Vandiyūr", + "outlier_distance_km": 6458.9, + "second_furthest_km": 1504.0, + "clarity_ratio": 4.29, + "median_distance_km": 1449.7, + "distances_to_centroid": { + "Voerde": 1504.0, + "Gryfice": 1254.9, + "Rodenkirchen": 1449.7, + "Barmbek-Nord": 1446.0, + "Vandiyūr": 6458.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Voerde: (51.60°, 6.69°)", + " Gryfice: (53.92°, 15.20°)", + " Rodenkirchen: (50.89°, 6.99°)", + " Barmbek-Nord: (53.61°, 10.04°)", + " Vandiyūr: (9.91°, 78.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vandiyūr: 6458.9 km from centroid", + " Voerde: 1504.0 km from centroid", + " Rodenkirchen: 1449.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vandiyūr", + "FINAL ANSWER: Vandiyūr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 23.16485, + "lon": 81.92859, + "name": "Pasan" + }, + { + "lat": 16.83553, + "lon": 74.31338, + "name": "Wadgaon" + }, + { + "lat": 23.53878, + "lon": 86.6735, + "name": "Raghunathpur" + }, + { + "lat": 33.65526, + "lon": 105.65786, + "name": "Jifeng" + }, + { + "lat": 51.35045, + "lon": -1.1285, + "name": "Tadley" + } + ], + "question": "Which location is the geographic outlier among: Pasan, Wadgaon, Raghunathpur, Jifeng, Tadley?", + "ground_truth": { + "answer": "Tadley", + "outlier_distance_km": 6166.1, + "second_furthest_km": 3433.0, + "clarity_ratio": 1.8, + "median_distance_km": 1838.3, + "distances_to_centroid": { + "Pasan": 1435.1, + "Wadgaon": 1513.4, + "Raghunathpur": 1838.3, + "Jifeng": 3433.0, + "Tadley": 6166.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pasan: (23.16°, 81.93°)", + " Wadgaon: (16.84°, 74.31°)", + " Raghunathpur: (23.54°, 86.67°)", + " Jifeng: (33.66°, 105.66°)", + " Tadley: (51.35°, -1.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tadley: 6166.1 km from centroid", + " Jifeng: 3433.0 km from centroid", + " Raghunathpur: 1838.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tadley", + "FINAL ANSWER: Tadley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.43139, + "lon": -61.14639, + "name": "Pacaraima" + }, + { + "lat": -33.73257, + "lon": -70.74281, + "name": "Buin" + }, + { + "lat": -5.35, + "lon": -40.38333, + "name": "Várzea Alegre" + }, + { + "lat": 8.09263, + "lon": -76.72822, + "name": "Turbo" + }, + { + "lat": -32.88076, + "lon": 27.39377, + "name": "Qonce" + } + ], + "question": "Which location is the geographic outlier among: Pacaraima, Buin, Várzea Alegre, Turbo, Qonce?", + "ground_truth": { + "answer": "Qonce", + "outlier_distance_km": 7595.2, + "second_furthest_km": 4215.9, + "clarity_ratio": 1.8, + "median_distance_km": 3616.2, + "distances_to_centroid": { + "Pacaraima": 2598.9, + "Buin": 3616.2, + "Várzea Alegre": 846.0, + "Turbo": 4215.9, + "Qonce": 7595.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacaraima: (4.43°, -61.15°)", + " Buin: (-33.73°, -70.74°)", + " Várzea Alegre: (-5.35°, -40.38°)", + " Turbo: (8.09°, -76.73°)", + " Qonce: (-32.88°, 27.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qonce: 7595.2 km from centroid", + " Turbo: 4215.9 km from centroid", + " Buin: 3616.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qonce", + "FINAL ANSWER: Qonce" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.86736, + "lon": 130.35689, + "name": "Hunchun" + }, + { + "lat": 36.09047, + "lon": 140.21047, + "name": "Tsuchiura" + }, + { + "lat": 15.88214, + "lon": 108.12092, + "name": "Đại Lộc" + }, + { + "lat": 23.84306, + "lon": 73.71466, + "name": "Dūngarpur" + }, + { + "lat": -41.27078, + "lon": 173.28404, + "name": "Nelson" + } + ], + "question": "Which location is the geographic outlier among: Hunchun, Tsuchiura, Đại Lộc, Dūngarpur, Nelson?", + "ground_truth": { + "answer": "Nelson", + "outlier_distance_km": 8018.1, + "second_furthest_km": 5435.9, + "clarity_ratio": 1.48, + "median_distance_km": 3085.4, + "distances_to_centroid": { + "Hunchun": 3085.4, + "Tsuchiura": 2735.7, + "Đại Lộc": 1821.8, + "Dūngarpur": 5435.9, + "Nelson": 8018.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hunchun: (42.87°, 130.36°)", + " Tsuchiura: (36.09°, 140.21°)", + " Đại Lộc: (15.88°, 108.12°)", + " Dūngarpur: (23.84°, 73.71°)", + " Nelson: (-41.27°, 173.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nelson: 8018.1 km from centroid", + " Dūngarpur: 5435.9 km from centroid", + " Hunchun: 3085.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nelson", + "FINAL ANSWER: Nelson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + }, + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + }, + { + "lat": -7.04222, + "lon": -39.28361, + "name": "Caririaçu" + } + ], + "question": "Which location is the geographic outlier among: Ballajura, Hamilton, Tauranga, Griffith, Caririaçu?", + "ground_truth": { + "answer": "Caririaçu", + "outlier_distance_km": 15078.4, + "second_furthest_km": 5643.1, + "clarity_ratio": 2.67, + "median_distance_km": 5564.8, + "distances_to_centroid": { + "Ballajura": 256.3, + "Hamilton": 5564.8, + "Tauranga": 5643.1, + "Griffith": 2975.9, + "Caririaçu": 15078.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ballajura: (-31.84°, 115.90°)", + " Hamilton: (-37.78°, 175.28°)", + " Tauranga: (-37.69°, 176.17°)", + " Griffith: (-34.29°, 146.05°)", + " Caririaçu: (-7.04°, -39.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caririaçu: 15078.4 km from centroid", + " Tauranga: 5643.1 km from centroid", + " Hamilton: 5564.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caririaçu", + "FINAL ANSWER: Caririaçu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.35048, + "lon": 18.65556, + "name": "Środmieście" + }, + { + "lat": 53.18139, + "lon": 44.04944, + "name": "Kamenka" + }, + { + "lat": 41.41849, + "lon": 2.1677, + "name": "Horta-Guinardó" + }, + { + "lat": 40.39476, + "lon": -3.69907, + "name": "Chopera" + }, + { + "lat": 35.29235, + "lon": -81.53565, + "name": "Shelby" + } + ], + "question": "Which location is the geographic outlier among: Środmieście, Kamenka, Horta-Guinardó, Chopera, Shelby?", + "ground_truth": { + "answer": "Shelby", + "outlier_distance_km": 6422.7, + "second_furthest_km": 3551.8, + "clarity_ratio": 1.81, + "median_distance_km": 1930.0, + "distances_to_centroid": { + "Środmieście": 1930.0, + "Kamenka": 3551.8, + "Horta-Guinardó": 638.7, + "Chopera": 504.9, + "Shelby": 6422.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Środmieście: (54.35°, 18.66°)", + " Kamenka: (53.18°, 44.05°)", + " Horta-Guinardó: (41.42°, 2.17°)", + " Chopera: (40.39°, -3.70°)", + " Shelby: (35.29°, -81.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shelby: 6422.7 km from centroid", + " Kamenka: 3551.8 km from centroid", + " Środmieście: 1930.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shelby", + "FINAL ANSWER: Shelby" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.255, + "lon": -57.51972, + "name": "Juara" + }, + { + "lat": -3.63222, + "lon": -44.55583, + "name": "Matões do Norte" + }, + { + "lat": -17.73111, + "lon": -49.09944, + "name": "Morrinhos" + }, + { + "lat": 9.16095, + "lon": -75.04811, + "name": "Galeras" + }, + { + "lat": 38.14501, + "lon": 114.56556, + "name": "Zhengding" + } + ], + "question": "Which location is the geographic outlier among: Juara, Matões do Norte, Morrinhos, Galeras, Zhengding?", + "ground_truth": { + "answer": "Zhengding", + "outlier_distance_km": 13655.4, + "second_furthest_km": 5864.6, + "clarity_ratio": 2.33, + "median_distance_km": 4199.7, + "distances_to_centroid": { + "Juara": 4199.7, + "Matões do Norte": 2575.6, + "Morrinhos": 3727.2, + "Galeras": 5864.6, + "Zhengding": 13655.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Juara: (-11.26°, -57.52°)", + " Matões do Norte: (-3.63°, -44.56°)", + " Morrinhos: (-17.73°, -49.10°)", + " Galeras: (9.16°, -75.05°)", + " Zhengding: (38.15°, 114.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhengding: 13655.4 km from centroid", + " Galeras: 5864.6 km from centroid", + " Juara: 4199.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhengding", + "FINAL ANSWER: Zhengding" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.86437, + "lon": 21.30507, + "name": "Mrągowo" + }, + { + "lat": 37.33791, + "lon": -5.83951, + "name": "Alcalá de Guadaira" + }, + { + "lat": 53.0, + "lon": -1.13333, + "name": "Arnold" + }, + { + "lat": 51.13434, + "lon": 6.63857, + "name": "Neubrück" + }, + { + "lat": -11.08944, + "lon": -43.14167, + "name": "Barra" + } + ], + "question": "Which location is the geographic outlier among: Mrągowo, Alcalá de Guadaira, Arnold, Neubrück, Barra?", + "ground_truth": { + "answer": "Barra", + "outlier_distance_km": 6690.5, + "second_furthest_km": 2732.8, + "clarity_ratio": 2.45, + "median_distance_km": 1814.1, + "distances_to_centroid": { + "Mrągowo": 2732.8, + "Alcalá de Guadaira": 136.0, + "Arnold": 1814.1, + "Neubrück": 1814.1, + "Barra": 6690.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mrągowo: (53.86°, 21.31°)", + " Alcalá de Guadaira: (37.34°, -5.84°)", + " Arnold: (53.00°, -1.13°)", + " Neubrück: (51.13°, 6.64°)", + " Barra: (-11.09°, -43.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barra: 6690.5 km from centroid", + " Mrągowo: 2732.8 km from centroid", + " Arnold: 1814.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barra", + "FINAL ANSWER: Barra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.35139, + "lon": 127.94528, + "name": "Wŏnju" + }, + { + "lat": 26.47703, + "lon": 90.55815, + "name": "Bongaigaon" + }, + { + "lat": 23.4067, + "lon": 88.36861, + "name": "Navadwīp" + }, + { + "lat": 34.18868, + "lon": 117.91265, + "name": "Balu" + }, + { + "lat": 55.75533, + "lon": 38.09578, + "name": "Zarya" + } + ], + "question": "Which location is the geographic outlier among: Wŏnju, Bongaigaon, Navadwīp, Balu, Zarya?", + "ground_truth": { + "answer": "Zarya", + "outlier_distance_km": 4646.2, + "second_furthest_km": 3154.5, + "clarity_ratio": 1.47, + "median_distance_km": 2310.9, + "distances_to_centroid": { + "Wŏnju": 3154.5, + "Bongaigaon": 1014.5, + "Navadwīp": 1397.8, + "Balu": 2310.9, + "Zarya": 4646.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wŏnju: (37.35°, 127.95°)", + " Bongaigaon: (26.48°, 90.56°)", + " Navadwīp: (23.41°, 88.37°)", + " Balu: (34.19°, 117.91°)", + " Zarya: (55.76°, 38.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zarya: 4646.2 km from centroid", + " Wŏnju: 3154.5 km from centroid", + " Balu: 2310.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zarya", + "FINAL ANSWER: Zarya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.19966, + "lon": 83.90938, + "name": "Baliguda" + }, + { + "lat": 36.90123, + "lon": 137.44955, + "name": "Kurobe-shi" + }, + { + "lat": 28.77549, + "lon": 108.54646, + "name": "Dingshi" + }, + { + "lat": 26.05509, + "lon": 86.14557, + "name": "Benipur" + }, + { + "lat": -27.05056, + "lon": -49.62278, + "name": "Presidente Getúlio" + } + ], + "question": "Which location is the geographic outlier among: Baliguda, Kurobe-shi, Dingshi, Benipur, Presidente Getúlio?", + "ground_truth": { + "answer": "Presidente Getúlio", + "outlier_distance_km": 14072.0, + "second_furthest_km": 6608.1, + "clarity_ratio": 2.13, + "median_distance_km": 3825.6, + "distances_to_centroid": { + "Baliguda": 1175.3, + "Kurobe-shi": 6608.1, + "Dingshi": 3825.6, + "Benipur": 1668.1, + "Presidente Getúlio": 14072.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baliguda: (20.20°, 83.91°)", + " Kurobe-shi: (36.90°, 137.45°)", + " Dingshi: (28.78°, 108.55°)", + " Benipur: (26.06°, 86.15°)", + " Presidente Getúlio: (-27.05°, -49.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Presidente Getúlio: 14072.0 km from centroid", + " Kurobe-shi: 6608.1 km from centroid", + " Dingshi: 3825.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Presidente Getúlio", + "FINAL ANSWER: Presidente Getúlio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.16667, + "lon": 145.16667, + "name": "Langwarrin" + }, + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -38.14458, + "lon": 145.12291, + "name": "Frankston" + }, + { + "lat": 36.00667, + "lon": 106.28083, + "name": "Guyuan" + } + ], + "question": "Which location is the geographic outlier among: Langwarrin, Calamvale, Maryborough, Frankston, Guyuan?", + "ground_truth": { + "answer": "Guyuan", + "outlier_distance_km": 7066.1, + "second_furthest_km": 2212.7, + "clarity_ratio": 3.19, + "median_distance_km": 2209.4, + "distances_to_centroid": { + "Langwarrin": 2212.7, + "Calamvale": 1623.1, + "Maryborough": 1471.7, + "Frankston": 2209.4, + "Guyuan": 7066.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Langwarrin: (-38.17°, 145.17°)", + " Calamvale: (-27.62°, 153.05°)", + " Maryborough: (-25.54°, 152.70°)", + " Frankston: (-38.14°, 145.12°)", + " Guyuan: (36.01°, 106.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guyuan: 7066.1 km from centroid", + " Langwarrin: 2212.7 km from centroid", + " Frankston: 2209.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guyuan", + "FINAL ANSWER: Guyuan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.89359, + "lon": 145.05534, + "name": "Carnegie" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + }, + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -17.70306, + "lon": -40.76639, + "name": "Carlos Chagas" + } + ], + "question": "Which location is the geographic outlier among: Carnegie, Sunnybank Hills, Glenferrie, Mildura, Carlos Chagas?", + "ground_truth": { + "answer": "Carlos Chagas", + "outlier_distance_km": 13700.3, + "second_furthest_km": 4268.7, + "clarity_ratio": 3.21, + "median_distance_km": 3377.5, + "distances_to_centroid": { + "Carnegie": 3377.5, + "Sunnybank Hills": 4268.7, + "Glenferrie": 3376.8, + "Mildura": 3120.1, + "Carlos Chagas": 13700.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carnegie: (-37.89°, 145.06°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Glenferrie: (-37.83°, 145.05°)", + " Mildura: (-34.19°, 142.16°)", + " Carlos Chagas: (-17.70°, -40.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carlos Chagas: 13700.3 km from centroid", + " Sunnybank Hills: 4268.7 km from centroid", + " Carnegie: 3377.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carlos Chagas", + "FINAL ANSWER: Carlos Chagas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.59983, + "lon": -0.33711, + "name": "Wealdstone" + }, + { + "lat": 37.46325, + "lon": -6.01113, + "name": "La Algaba" + }, + { + "lat": 47.86219, + "lon": 1.8991, + "name": "Olivet" + }, + { + "lat": 51.2823, + "lon": -0.07889, + "name": "Caterham" + }, + { + "lat": -23.46013, + "lon": -46.5749, + "name": "Jaçanã" + } + ], + "question": "Which location is the geographic outlier among: Wealdstone, La Algaba, Olivet, Caterham, Jaçanã?", + "ground_truth": { + "answer": "Jaçanã", + "outlier_distance_km": 7361.9, + "second_furthest_km": 2222.8, + "clarity_ratio": 3.31, + "median_distance_km": 2198.6, + "distances_to_centroid": { + "Wealdstone": 2222.8, + "La Algaba": 630.8, + "Olivet": 1944.8, + "Caterham": 2198.6, + "Jaçanã": 7361.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wealdstone: (51.60°, -0.34°)", + " La Algaba: (37.46°, -6.01°)", + " Olivet: (47.86°, 1.90°)", + " Caterham: (51.28°, -0.08°)", + " Jaçanã: (-23.46°, -46.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaçanã: 7361.9 km from centroid", + " Wealdstone: 2222.8 km from centroid", + " Caterham: 2198.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaçanã", + "FINAL ANSWER: Jaçanã" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.83222, + "lon": -46.89361, + "name": "Vargem Grande do Sul" + }, + { + "lat": -5.03806, + "lon": -42.46, + "name": "Altos" + }, + { + "lat": 10.96854, + "lon": -74.78132, + "name": "Barranquilla" + }, + { + "lat": -24.08204, + "lon": -54.24622, + "name": "Guaíra" + }, + { + "lat": 30.40644, + "lon": 108.3502, + "name": "Linxi" + } + ], + "question": "Which location is the geographic outlier among: Vargem Grande do Sul, Altos, Barranquilla, Guaíra, Linxi?", + "ground_truth": { + "answer": "Linxi", + "outlier_distance_km": 13911.1, + "second_furthest_km": 6009.1, + "clarity_ratio": 2.31, + "median_distance_km": 4252.3, + "distances_to_centroid": { + "Vargem Grande do Sul": 3485.6, + "Altos": 2296.2, + "Barranquilla": 6009.1, + "Guaíra": 4252.3, + "Linxi": 13911.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vargem Grande do Sul: (-21.83°, -46.89°)", + " Altos: (-5.04°, -42.46°)", + " Barranquilla: (10.97°, -74.78°)", + " Guaíra: (-24.08°, -54.25°)", + " Linxi: (30.41°, 108.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Linxi: 13911.1 km from centroid", + " Barranquilla: 6009.1 km from centroid", + " Guaíra: 4252.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Linxi", + "FINAL ANSWER: Linxi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87709, + "lon": 145.12939, + "name": "Mount Waverley" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": 16.3888, + "lon": 75.10873, + "name": "Mahālingpur" + } + ], + "question": "Which location is the geographic outlier among: Mount Waverley, Balwyn North, The Gap, Reservoir, Mahālingpur?", + "ground_truth": { + "answer": "Mahālingpur", + "outlier_distance_km": 7741.2, + "second_furthest_km": 2041.9, + "clarity_ratio": 3.79, + "median_distance_km": 1864.0, + "distances_to_centroid": { + "Mount Waverley": 1864.0, + "Balwyn North": 1854.8, + "The Gap": 2041.9, + "Reservoir": 1843.2, + "Mahālingpur": 7741.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mount Waverley: (-37.88°, 145.13°)", + " Balwyn North: (-37.79°, 145.09°)", + " The Gap: (-27.44°, 152.94°)", + " Reservoir: (-37.72°, 145.00°)", + " Mahālingpur: (16.39°, 75.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mahālingpur: 7741.2 km from centroid", + " The Gap: 2041.9 km from centroid", + " Mount Waverley: 1864.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mahālingpur", + "FINAL ANSWER: Mahālingpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.51707, + "lon": 100.4265, + "name": "Kepala Batas" + }, + { + "lat": 31.21093, + "lon": 109.32154, + "name": "Dashu" + }, + { + "lat": 27.83333, + "lon": 114.4, + "name": "Yichun" + }, + { + "lat": 18.74486, + "lon": 99.11953, + "name": "San Kamphaeng" + }, + { + "lat": 6.33732, + "lon": -75.55795, + "name": "Bello" + } + ], + "question": "Which location is the geographic outlier among: Kepala Batas, Dashu, Yichun, San Kamphaeng, Bello?", + "ground_truth": { + "answer": "Bello", + "outlier_distance_km": 15330.0, + "second_furthest_km": 4698.8, + "clarity_ratio": 3.26, + "median_distance_km": 4257.7, + "distances_to_centroid": { + "Kepala Batas": 3626.3, + "Dashu": 4257.7, + "Yichun": 4698.8, + "San Kamphaeng": 3119.7, + "Bello": 15330.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kepala Batas: (5.52°, 100.43°)", + " Dashu: (31.21°, 109.32°)", + " Yichun: (27.83°, 114.40°)", + " San Kamphaeng: (18.74°, 99.12°)", + " Bello: (6.34°, -75.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bello: 15330.0 km from centroid", + " Yichun: 4698.8 km from centroid", + " Dashu: 4257.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bello", + "FINAL ANSWER: Bello" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.4399, + "lon": -75.66498, + "name": "Vanier" + }, + { + "lat": 22.00554, + "lon": -98.77972, + "name": "Tamuín" + }, + { + "lat": 26.77534, + "lon": -80.0581, + "name": "Riviera Beach" + }, + { + "lat": 45.68338, + "lon": -73.43246, + "name": "Varennes" + }, + { + "lat": 31.4071, + "lon": 26.5832, + "name": "An-Najaylah" + } + ], + "question": "Which location is the geographic outlier among: Vanier, Tamuín, Riviera Beach, Varennes, An-Najaylah?", + "ground_truth": { + "answer": "An-Najaylah", + "outlier_distance_km": 7850.8, + "second_furthest_km": 3986.4, + "clarity_ratio": 1.97, + "median_distance_km": 2065.5, + "distances_to_centroid": { + "Vanier": 1802.9, + "Tamuín": 3986.4, + "Riviera Beach": 2065.5, + "Varennes": 1689.8, + "An-Najaylah": 7850.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vanier: (45.44°, -75.66°)", + " Tamuín: (22.01°, -98.78°)", + " Riviera Beach: (26.78°, -80.06°)", + " Varennes: (45.68°, -73.43°)", + " An-Najaylah: (31.41°, 26.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " An-Najaylah: 7850.8 km from centroid", + " Tamuín: 3986.4 km from centroid", + " Riviera Beach: 2065.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: An-Najaylah", + "FINAL ANSWER: An-Najaylah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.36667, + "lon": -38.33333, + "name": "Olindina" + }, + { + "lat": -22.50917, + "lon": -48.55778, + "name": "Igaraçu do Tietê" + }, + { + "lat": -3.79278, + "lon": -39.27028, + "name": "Pentecoste" + }, + { + "lat": -21.29917, + "lon": -46.8025, + "name": "Guaranésia" + }, + { + "lat": 6.44132, + "lon": 7.49883, + "name": "Enugu" + } + ], + "question": "Which location is the geographic outlier among: Olindina, Igaraçu do Tietê, Pentecoste, Guaranésia, Enugu?", + "ground_truth": { + "answer": "Enugu", + "outlier_distance_km": 4873.0, + "second_furthest_km": 2118.0, + "clarity_ratio": 2.3, + "median_distance_km": 1892.4, + "distances_to_centroid": { + "Olindina": 580.1, + "Igara��u do Tietê": 2118.0, + "Pentecoste": 1010.5, + "Guaranésia": 1892.4, + "Enugu": 4873.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Olindina: (-11.37°, -38.33°)", + " Igaraçu do Tietê: (-22.51°, -48.56°)", + " Pentecoste: (-3.79°, -39.27°)", + " Guaranésia: (-21.30°, -46.80°)", + " Enugu: (6.44°, 7.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Enugu: 4873.0 km from centroid", + " Igaraçu do Tietê: 2118.0 km from centroid", + " Guaranésia: 1892.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Enugu", + "FINAL ANSWER: Enugu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.83079, + "lon": 18.6486, + "name": "Durbanville" + }, + { + "lat": -33.96722, + "lon": 18.50214, + "name": "Athlone" + }, + { + "lat": 11.21566, + "lon": 38.36452, + "name": "Wegeda" + }, + { + "lat": 29.30995, + "lon": 30.8418, + "name": "Al Fayyum" + }, + { + "lat": 38.84028, + "lon": -97.61142, + "name": "Salina" + } + ], + "question": "Which location is the geographic outlier among: Durbanville, Athlone, Wegeda, Al Fayyum, Salina?", + "ground_truth": { + "answer": "Salina", + "outlier_distance_km": 10653.8, + "second_furthest_km": 4398.9, + "clarity_ratio": 2.42, + "median_distance_km": 4391.5, + "distances_to_centroid": { + "Durbanville": 4391.5, + "Athlone": 4398.9, + "Wegeda": 4157.4, + "Al Fayyum": 4296.3, + "Salina": 10653.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Durbanville: (-33.83°, 18.65°)", + " Athlone: (-33.97°, 18.50°)", + " Wegeda: (11.22°, 38.36°)", + " Al Fayyum: (29.31°, 30.84°)", + " Salina: (38.84°, -97.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Salina: 10653.8 km from centroid", + " Athlone: 4398.9 km from centroid", + " Durbanville: 4391.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Salina", + "FINAL ANSWER: Salina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.01887, + "lon": 33.0098, + "name": "Bi’r al ‘Abd" + }, + { + "lat": 31.39951, + "lon": 30.41718, + "name": "Rosetta" + }, + { + "lat": 28.49456, + "lon": 30.80526, + "name": "Banī Mazār" + }, + { + "lat": 6.90306, + "lon": -1.65199, + "name": "Ahwiaa" + }, + { + "lat": 28.38556, + "lon": -81.36646, + "name": "Meadow Woods" + } + ], + "question": "Which location is the geographic outlier among: Bi’r al ‘Abd, Rosetta, Banī Mazār, Ahwiaa, Meadow Woods?", + "ground_truth": { + "answer": "Meadow Woods", + "outlier_distance_km": 8124.4, + "second_furthest_km": 3074.3, + "clarity_ratio": 2.64, + "median_distance_km": 2849.5, + "distances_to_centroid": { + "Bi’r al ‘Abd": 3074.3, + "Rosetta": 2833.0, + "Banī Mazār": 2849.5, + "Ahwiaa": 2080.6, + "Meadow Woods": 8124.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bi’r al ‘Abd: (31.02°, 33.01°)", + " Rosetta: (31.40°, 30.42°)", + " Banī Mazār: (28.49°, 30.81°)", + " Ahwiaa: (6.90°, -1.65°)", + " Meadow Woods: (28.39°, -81.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Meadow Woods: 8124.4 km from centroid", + " Bi’r al ‘Abd: 3074.3 km from centroid", + " Banī Mazār: 2849.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Meadow Woods", + "FINAL ANSWER: Meadow Woods" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.934, + "lon": -76.89664, + "name": "Landover" + }, + { + "lat": 38.93067, + "lon": -77.04081, + "name": "Mount Pleasant" + }, + { + "lat": 35.48736, + "lon": -80.62173, + "name": "Kannapolis" + }, + { + "lat": 46.87497, + "lon": -96.90036, + "name": "West Fargo" + }, + { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + } + ], + "question": "Which location is the geographic outlier among: Landover, Mount Pleasant, Kannapolis, West Fargo, Whanganui?", + "ground_truth": { + "answer": "Whanganui", + "outlier_distance_km": 16987.7, + "second_furthest_km": 6257.4, + "clarity_ratio": 2.71, + "median_distance_km": 4876.3, + "distances_to_centroid": { + "Landover": 4575.3, + "Mount Pleasant": 4587.6, + "Kannapolis": 4876.3, + "West Fargo": 6257.4, + "Whanganui": 16987.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Landover: (38.93°, -76.90°)", + " Mount Pleasant: (38.93°, -77.04°)", + " Kannapolis: (35.49°, -80.62°)", + " West Fargo: (46.87°, -96.90°)", + " Whanganui: (-39.93°, 175.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whanganui: 16987.7 km from centroid", + " West Fargo: 6257.4 km from centroid", + " Kannapolis: 4876.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whanganui", + "FINAL ANSWER: Whanganui" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.41869, + "lon": -81.4173, + "name": "Immokalee" + }, + { + "lat": 32.47986, + "lon": -86.36192, + "name": "Millbrook" + }, + { + "lat": 41.66199, + "lon": -86.15862, + "name": "Mishawaka" + }, + { + "lat": 29.99409, + "lon": -90.24174, + "name": "Kenner" + }, + { + "lat": -16.02511, + "lon": -48.07121, + "name": "Gama" + } + ], + "question": "Which location is the geographic outlier among: Immokalee, Millbrook, Mishawaka, Kenner, Gama?", + "ground_truth": { + "answer": "Gama", + "outlier_distance_km": 5446.1, + "second_furthest_km": 2205.5, + "clarity_ratio": 2.47, + "median_distance_km": 1412.5, + "distances_to_centroid": { + "Immokalee": 492.4, + "Millbrook": 1318.1, + "Mishawaka": 2205.5, + "Kenner": 1412.5, + "Gama": 5446.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Immokalee: (26.42°, -81.42°)", + " Millbrook: (32.48°, -86.36°)", + " Mishawaka: (41.66°, -86.16°)", + " Kenner: (29.99°, -90.24°)", + " Gama: (-16.03°, -48.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gama: 5446.1 km from centroid", + " Mishawaka: 2205.5 km from centroid", + " Kenner: 1412.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gama", + "FINAL ANSWER: Gama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.79139, + "lon": -79.22167, + "name": "Chocope" + }, + { + "lat": -0.75, + "lon": -48.02, + "name": "São Caetano de Odivelas" + }, + { + "lat": -9.62167, + "lon": -42.08139, + "name": "Remanso" + }, + { + "lat": -12.06982, + "lon": -77.04495, + "name": "Jesus Maria" + }, + { + "lat": 30.91018, + "lon": 30.17438, + "name": "Abū al Maţāmīr" + } + ], + "question": "Which location is the geographic outlier among: Chocope, São Caetano de Odivelas, Remanso, Jesus Maria, Abū al Maţāmīr?", + "ground_truth": { + "answer": "Abū al Maţāmīr", + "outlier_distance_km": 8423.1, + "second_furthest_km": 4084.9, + "clarity_ratio": 2.06, + "median_distance_km": 3969.9, + "distances_to_centroid": { + "Chocope": 4084.9, + "São Caetano de Odivelas": 540.7, + "Remanso": 1092.5, + "Jesus Maria": 3969.9, + "Abū al Maţāmīr": 8423.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chocope: (-7.79°, -79.22°)", + " São Caetano de Odivelas: (-0.75°, -48.02°)", + " Remanso: (-9.62°, -42.08°)", + " Jesus Maria: (-12.07°, -77.04°)", + " Abū al Maţāmīr: (30.91°, 30.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Abū al Maţāmīr: 8423.1 km from centroid", + " Chocope: 4084.9 km from centroid", + " Jesus Maria: 3969.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Abū al Maţāmīr", + "FINAL ANSWER: Abū al Maţāmīr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.12056, + "lon": -60.37972, + "name": "Novo Aripuanã" + }, + { + "lat": -23.66333, + "lon": -52.605, + "name": "Cianorte" + }, + { + "lat": -6.55573, + "lon": -47.44149, + "name": "Estreito" + }, + { + "lat": -41.96051, + "lon": -71.53336, + "name": "El Bolsón" + }, + { + "lat": 25.40138, + "lon": 88.52978, + "name": "Gangārāmpur" + } + ], + "question": "Which location is the geographic outlier among: Novo Aripuanã, Cianorte, Estreito, El Bolsón, Gangārāmpur?", + "ground_truth": { + "answer": "Gangārāmpur", + "outlier_distance_km": 13223.8, + "second_furthest_km": 5442.9, + "clarity_ratio": 2.43, + "median_distance_km": 3538.5, + "distances_to_centroid": { + "Novo Aripuanã": 3538.5, + "Cianorte": 2933.2, + "Estreito": 2105.6, + "El Bolsón": 5442.9, + "Gangārāmpur": 13223.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Novo Aripuanã: (-5.12°, -60.38°)", + " Cianorte: (-23.66°, -52.60°)", + " Estreito: (-6.56°, -47.44°)", + " El Bolsón: (-41.96°, -71.53°)", + " Gangārāmpur: (25.40°, 88.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gangārāmpur: 13223.8 km from centroid", + " El Bolsón: 5442.9 km from centroid", + " Novo Aripuanã: 3538.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gangārāmpur", + "FINAL ANSWER: Gangārāmpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 59.13333, + "lon": 37.9, + "name": "Cherepovets" + }, + { + "lat": 43.60527, + "lon": 2.24088, + "name": "Castres" + }, + { + "lat": 48.68333, + "lon": 2.13333, + "name": "Gif-sur-Yvette" + }, + { + "lat": 36.71715, + "lon": -4.27583, + "name": "Rincón de la Victoria" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + } + ], + "question": "Which location is the geographic outlier among: Cherepovets, Castres, Gif-sur-Yvette, Rincón de la Victoria, Mandurah?", + "ground_truth": { + "answer": "Mandurah", + "outlier_distance_km": 11386.3, + "second_furthest_km": 3271.9, + "clarity_ratio": 3.48, + "median_distance_km": 3160.8, + "distances_to_centroid": { + "Cherepovets": 3160.8, + "Castres": 2855.5, + "Gif-sur-Yvette": 3093.9, + "Rincón de la Victoria": 3271.9, + "Mandurah": 11386.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cherepovets: (59.13°, 37.90°)", + " Castres: (43.61°, 2.24°)", + " Gif-sur-Yvette: (48.68°, 2.13°)", + " Rincón de la Victoria: (36.72°, -4.28°)", + " Mandurah: (-32.53°, 115.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mandurah: 11386.3 km from centroid", + " Rincón de la Victoria: 3271.9 km from centroid", + " Cherepovets: 3160.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mandurah", + "FINAL ANSWER: Mandurah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.42167, + "lon": 5.55972, + "name": "Geldrop" + }, + { + "lat": 39.85316, + "lon": 3.12138, + "name": "Alcúdia" + }, + { + "lat": 44.40478, + "lon": 8.94439, + "name": "Genoa" + }, + { + "lat": 52.39635, + "lon": 9.59727, + "name": "Seelze" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + } + ], + "question": "Which location is the geographic outlier among: Geldrop, Alcúdia, Genoa, Seelze, Saint Ives?", + "ground_truth": { + "answer": "Saint Ives", + "outlier_distance_km": 14044.1, + "second_furthest_km": 3360.4, + "clarity_ratio": 4.18, + "median_distance_km": 3194.3, + "distances_to_centroid": { + "Geldrop": 3360.4, + "Alcúdia": 3096.5, + "Genoa": 2774.2, + "Seelze": 3194.3, + "Saint Ives": 14044.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Geldrop: (51.42°, 5.56°)", + " Alcúdia: (39.85°, 3.12°)", + " Genoa: (44.40°, 8.94°)", + " Seelze: (52.40°, 9.60°)", + " Saint Ives: (-33.73°, 151.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Ives: 14044.1 km from centroid", + " Geldrop: 3360.4 km from centroid", + " Seelze: 3194.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Ives", + "FINAL ANSWER: Saint Ives" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.94617, + "lon": -75.44275, + "name": "Sahagún" + }, + { + "lat": -12.76556, + "lon": -39.42833, + "name": "Castro Alves" + }, + { + "lat": -16.39899, + "lon": -71.53747, + "name": "Arequipa" + }, + { + "lat": -19.41361, + "lon": -42.41944, + "name": "Ipaba" + }, + { + "lat": 41.77639, + "lon": 126.03194, + "name": "Erdaojiang" + } + ], + "question": "Which location is the geographic outlier among: Sahagún, Castro Alves, Arequipa, Ipaba, Erdaojiang?", + "ground_truth": { + "answer": "Erdaojiang", + "outlier_distance_km": 14248.0, + "second_furthest_km": 6148.2, + "clarity_ratio": 2.32, + "median_distance_km": 5892.9, + "distances_to_centroid": { + "Sahagún": 6148.2, + "Castro Alves": 2546.3, + "Arequipa": 5892.9, + "Ipaba": 3248.3, + "Erdaojiang": 14248.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sahagún: (8.95°, -75.44°)", + " Castro Alves: (-12.77°, -39.43°)", + " Arequipa: (-16.40°, -71.54°)", + " Ipaba: (-19.41°, -42.42°)", + " Erdaojiang: (41.78°, 126.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Erdaojiang: 14248.0 km from centroid", + " Sahagún: 6148.2 km from centroid", + " Arequipa: 5892.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Erdaojiang", + "FINAL ANSWER: Erdaojiang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.67194, + "lon": -53.80889, + "name": "Capanema" + }, + { + "lat": -23.26917, + "lon": -51.04806, + "name": "Ibiporã" + }, + { + "lat": -27.91421, + "lon": -55.75355, + "name": "Apóstoles" + }, + { + "lat": 8.4115, + "lon": -75.58508, + "name": "Planeta Rica" + }, + { + "lat": 51.15, + "lon": 7.0, + "name": "Ohligs" + } + ], + "question": "Which location is the geographic outlier among: Capanema, Ibiporã, Apóstoles, Planeta Rica, Ohligs?", + "ground_truth": { + "answer": "Ohligs", + "outlier_distance_km": 7856.6, + "second_furthest_km": 3552.7, + "clarity_ratio": 2.21, + "median_distance_km": 2915.4, + "distances_to_centroid": { + "Capanema": 2612.5, + "Ibiporã": 2272.9, + "Apóstoles": 2915.4, + "Planeta Rica": 3552.7, + "Ohligs": 7856.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Capanema: (-25.67°, -53.81°)", + " Ibiporã: (-23.27°, -51.05°)", + " Apóstoles: (-27.91°, -55.75°)", + " Planeta Rica: (8.41°, -75.59°)", + " Ohligs: (51.15°, 7.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ohligs: 7856.6 km from centroid", + " Planeta Rica: 3552.7 km from centroid", + " Apóstoles: 2915.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ohligs", + "FINAL ANSWER: Ohligs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.65083, + "lon": -42.39167, + "name": "Silva Jardim" + }, + { + "lat": -4.21079, + "lon": -69.93944, + "name": "Leticia" + }, + { + "lat": -15.85072, + "lon": -48.96087, + "name": "Pirenópolis" + }, + { + "lat": -16.06583, + "lon": -47.97861, + "name": "Valparaíso de Goiás" + }, + { + "lat": 31.3529, + "lon": 27.23725, + "name": "Marsá Maţrūḩ" + } + ], + "question": "Which location is the geographic outlier among: Silva Jardim, Leticia, Pirenópolis, Valparaíso de Goiás, Marsá Maţrūḩ?", + "ground_truth": { + "answer": "Marsá Maţrūḩ", + "outlier_distance_km": 7880.8, + "second_furthest_km": 3717.6, + "clarity_ratio": 2.12, + "median_distance_km": 2014.0, + "distances_to_centroid": { + "Silva Jardim": 2014.0, + "Leticia": 3717.6, + "Pirenópolis": 1790.1, + "Valparaíso de Goiás": 1725.3, + "Marsá Maţrūḩ": 7880.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Silva Jardim: (-22.65°, -42.39°)", + " Leticia: (-4.21°, -69.94°)", + " Pirenópolis: (-15.85°, -48.96°)", + " Valparaíso de Goiás: (-16.07°, -47.98°)", + " Marsá Maţrūḩ: (31.35°, 27.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marsá Maţrūḩ: 7880.8 km from centroid", + " Leticia: 3717.6 km from centroid", + " Silva Jardim: 2014.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marsá Maţrūḩ", + "FINAL ANSWER: Marsá Maţrūḩ" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.5266, + "lon": 121.1536, + "name": "Angono" + }, + { + "lat": 14.92295, + "lon": 75.26221, + "name": "Bankāpur" + }, + { + "lat": 27.89055, + "lon": 78.74621, + "name": "Soron" + }, + { + "lat": 12.97194, + "lon": 77.59369, + "name": "Bengaluru" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + } + ], + "question": "Which location is the geographic outlier among: Angono, Bankāpur, Soron, Bengaluru, Camberwell?", + "ground_truth": { + "answer": "Camberwell", + "outlier_distance_km": 6814.0, + "second_furthest_km": 3236.2, + "clarity_ratio": 2.11, + "median_distance_km": 2812.7, + "distances_to_centroid": { + "Angono": 2521.2, + "Bankāpur": 2812.7, + "Soron": 3236.2, + "Bengaluru": 2511.6, + "Camberwell": 6814.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Angono: (14.53°, 121.15°)", + " Bankāpur: (14.92°, 75.26°)", + " Soron: (27.89°, 78.75°)", + " Bengaluru: (12.97°, 77.59°)", + " Camberwell: (-37.84°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camberwell: 6814.0 km from centroid", + " Soron: 3236.2 km from centroid", + " Bankāpur: 2812.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camberwell", + "FINAL ANSWER: Camberwell" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.06837, + "lon": 7.62503, + "name": "Pozzo Strada" + }, + { + "lat": 41.4202, + "lon": 2.19632, + "name": "Sant Martí de Provençals" + }, + { + "lat": 51.95838, + "lon": 4.47124, + "name": "Schiebroek" + }, + { + "lat": 45.64933, + "lon": 9.60617, + "name": "Dalmine" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + } + ], + "question": "Which location is the geographic outlier among: Pozzo Strada, Sant Martí de Provençals, Schiebroek, Dalmine, Helensvale?", + "ground_truth": { + "answer": "Helensvale", + "outlier_distance_km": 14076.9, + "second_furthest_km": 3409.8, + "clarity_ratio": 4.13, + "median_distance_km": 3163.0, + "distances_to_centroid": { + "Pozzo Strada": 2856.0, + "Sant Martí de Provençals": 3163.0, + "Schiebroek": 3409.8, + "Dalmine": 2742.7, + "Helensvale": 14076.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pozzo Strada: (45.07°, 7.63°)", + " Sant Martí de Provençals: (41.42°, 2.20°)", + " Schiebroek: (51.96°, 4.47°)", + " Dalmine: (45.65°, 9.61°)", + " Helensvale: (-27.92°, 153.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Helensvale: 14076.9 km from centroid", + " Schiebroek: 3409.8 km from centroid", + " Sant Martí de Provençals: 3163.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Helensvale", + "FINAL ANSWER: Helensvale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.54983, + "lon": 9.34044, + "name": "Carugate" + }, + { + "lat": 52.44653, + "lon": 13.5066, + "name": "Johannisthal" + }, + { + "lat": 40.8356, + "lon": 14.50487, + "name": "San Giuseppe Vesuviano" + }, + { + "lat": 57.2145, + "lon": 41.92555, + "name": "Vichuga" + }, + { + "lat": -21.19361, + "lon": -48.16389, + "name": "Barrinha" + } + ], + "question": "Which location is the geographic outlier among: Carugate, Johannisthal, San Giuseppe Vesuviano, Vichuga, Barrinha?", + "ground_truth": { + "answer": "Barrinha", + "outlier_distance_km": 8478.6, + "second_furthest_km": 3628.1, + "clarity_ratio": 2.34, + "median_distance_km": 2027.0, + "distances_to_centroid": { + "Carugate": 1205.5, + "Johannisthal": 2027.0, + "San Giuseppe Vesuviano": 975.6, + "Vichuga": 3628.1, + "Barrinha": 8478.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carugate: (45.55°, 9.34°)", + " Johannisthal: (52.45°, 13.51°)", + " San Giuseppe Vesuviano: (40.84°, 14.50°)", + " Vichuga: (57.21°, 41.93°)", + " Barrinha: (-21.19°, -48.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barrinha: 8478.6 km from centroid", + " Vichuga: 3628.1 km from centroid", + " Johannisthal: 2027.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barrinha", + "FINAL ANSWER: Barrinha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.85798, + "lon": -99.56768, + "name": "Linares" + }, + { + "lat": 43.68364, + "lon": -79.55422, + "name": "Willowridge-Martingrove-Richview" + }, + { + "lat": 41.18389, + "lon": -96.03113, + "name": "La Vista" + }, + { + "lat": 29.36857, + "lon": -94.97131, + "name": "La Marque" + }, + { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + } + ], + "question": "Which location is the geographic outlier among: Linares, Willowridge-Martingrove-Richview, La Vista, La Marque, Cronulla?", + "ground_truth": { + "answer": "Cronulla", + "outlier_distance_km": 17951.3, + "second_furthest_km": 5688.8, + "clarity_ratio": 3.16, + "median_distance_km": 5361.5, + "distances_to_centroid": { + "Linares": 5688.8, + "Willowridge-Martingrove-Richview": 4148.1, + "La Vista": 5361.5, + "La Marque": 5192.5, + "Cronulla": 17951.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Linares: (24.86°, -99.57°)", + " Willowridge-Martingrove-Richview: (43.68°, -79.55°)", + " La Vista: (41.18°, -96.03°)", + " La Marque: (29.37°, -94.97°)", + " Cronulla: (-34.06°, 151.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cronulla: 17951.3 km from centroid", + " Linares: 5688.8 km from centroid", + " La Vista: 5361.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cronulla", + "FINAL ANSWER: Cronulla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.2, + "lon": 38.6, + "name": "Shashamane" + }, + { + "lat": 26.12242, + "lon": 32.46749, + "name": "Dishnā" + }, + { + "lat": 6.70608, + "lon": 37.76966, + "name": "Tebela" + }, + { + "lat": 14.12109, + "lon": 38.72337, + "name": "Aksum" + }, + { + "lat": 40.83255, + "lon": 14.22677, + "name": "Chiaia" + } + ], + "question": "Which location is the geographic outlier among: Shashamane, Dishnā, Tebela, Aksum, Chiaia?", + "ground_truth": { + "answer": "Chiaia", + "outlier_distance_km": 2978.0, + "second_furthest_km": 1486.7, + "clarity_ratio": 2.0, + "median_distance_km": 1475.0, + "distances_to_centroid": { + "Shashamane": 1475.0, + "Dishnā": 792.5, + "Tebela": 1486.7, + "Aksum": 868.3, + "Chiaia": 2978.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shashamane: (7.20°, 38.60°)", + " Dishnā: (26.12°, 32.47°)", + " Tebela: (6.71°, 37.77°)", + " Aksum: (14.12°, 38.72°)", + " Chiaia: (40.83°, 14.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chiaia: 2978.0 km from centroid", + " Tebela: 1486.7 km from centroid", + " Shashamane: 1475.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chiaia", + "FINAL ANSWER: Chiaia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -38.14458, + "lon": 145.12291, + "name": "Frankston" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + }, + { + "lat": 45.04616, + "lon": 38.79491, + "name": "Yelizavetinskaya" + } + ], + "question": "Which location is the geographic outlier among: Robina, Frankston, Punchbowl, Mangere East, Yelizavetinskaya?", + "ground_truth": { + "answer": "Yelizavetinskaya", + "outlier_distance_km": 11739.1, + "second_furthest_km": 4588.6, + "clarity_ratio": 2.56, + "median_distance_km": 2512.4, + "distances_to_centroid": { + "Robina": 2372.0, + "Frankston": 2505.9, + "Punchbowl": 2512.4, + "Mangere East": 4588.6, + "Yelizavetinskaya": 11739.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Frankston: (-38.14°, 145.12°)", + " Punchbowl: (-33.93°, 151.05°)", + " Mangere East: (-36.97°, 174.82°)", + " Yelizavetinskaya: (45.05°, 38.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yelizavetinskaya: 11739.1 km from centroid", + " Mangere East: 4588.6 km from centroid", + " Punchbowl: 2512.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yelizavetinskaya", + "FINAL ANSWER: Yelizavetinskaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.75427, + "lon": -79.42475, + "name": "Lansing-Westgate" + }, + { + "lat": 33.92044, + "lon": -80.34147, + "name": "Sumter" + }, + { + "lat": 20.58806, + "lon": -100.38806, + "name": "Santiago de Querétaro" + }, + { + "lat": 36.96134, + "lon": -120.06072, + "name": "Madera" + }, + { + "lat": 10.99342, + "lon": 75.93504, + "name": "Tennala" + } + ], + "question": "Which location is the geographic outlier among: Lansing-Westgate, Sumter, Santiago de Querétaro, Madera, Tennala?", + "ground_truth": { + "answer": "Tennala", + "outlier_distance_km": 13574.9, + "second_furthest_km": 5493.8, + "clarity_ratio": 2.47, + "median_distance_km": 4080.8, + "distances_to_centroid": { + "Lansing-Westgate": 2304.5, + "Sumter": 1914.2, + "Santiago de Querétaro": 4080.8, + "Madera": 5493.8, + "Tennala": 13574.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lansing-Westgate: (43.75°, -79.42°)", + " Sumter: (33.92°, -80.34°)", + " Santiago de Querétaro: (20.59°, -100.39°)", + " Madera: (36.96°, -120.06°)", + " Tennala: (10.99°, 75.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tennala: 13574.9 km from centroid", + " Madera: 5493.8 km from centroid", + " Santiago de Querétaro: 4080.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tennala", + "FINAL ANSWER: Tennala" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -37.97695, + "lon": 145.25866, + "name": "Endeavour Hills" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + }, + { + "lat": 52.16667, + "lon": 8.61667, + "name": "Hiddenhausen" + } + ], + "question": "Which location is the geographic outlier among: Sunnybank Hills, Endeavour Hills, Lincoln, New Plymouth, Hiddenhausen?", + "ground_truth": { + "answer": "Hiddenhausen", + "outlier_distance_km": 13764.4, + "second_furthest_km": 4754.7, + "clarity_ratio": 2.89, + "median_distance_km": 4733.1, + "distances_to_centroid": { + "Sunnybank Hills": 2490.4, + "Endeavour Hills": 2624.5, + "Lincoln": 4733.1, + "New Plymouth": 4754.7, + "Hiddenhausen": 13764.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Endeavour Hills: (-37.98°, 145.26°)", + " Lincoln: (-36.86°, 174.62°)", + " New Plymouth: (-39.07°, 174.08°)", + " Hiddenhausen: (52.17°, 8.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hiddenhausen: 13764.4 km from centroid", + " New Plymouth: 4754.7 km from centroid", + " Lincoln: 4733.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hiddenhausen", + "FINAL ANSWER: Hiddenhausen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.9936, + "lon": -105.08971, + "name": "Lafayette" + }, + { + "lat": 33.50094, + "lon": -86.75221, + "name": "Mountain Brook" + }, + { + "lat": 40.70621, + "lon": -73.30623, + "name": "West Islip" + }, + { + "lat": 38.68789, + "lon": -77.29776, + "name": "Lake Ridge" + }, + { + "lat": 13.7523, + "lon": 100.54335, + "name": "Makkasan" + } + ], + "question": "Which location is the geographic outlier among: Lafayette, Mountain Brook, West Islip, Lake Ridge, Makkasan?", + "ground_truth": { + "answer": "Makkasan", + "outlier_distance_km": 13829.0, + "second_furthest_km": 5027.4, + "clarity_ratio": 2.75, + "median_distance_km": 3540.7, + "distances_to_centroid": { + "Lafayette": 5027.4, + "Mountain Brook": 3540.7, + "West Islip": 2350.3, + "Lake Ridge": 2656.6, + "Makkasan": 13829.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lafayette: (39.99°, -105.09°)", + " Mountain Brook: (33.50°, -86.75°)", + " West Islip: (40.71°, -73.31°)", + " Lake Ridge: (38.69°, -77.30°)", + " Makkasan: (13.75°, 100.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Makkasan: 13829.0 km from centroid", + " Lafayette: 5027.4 km from centroid", + " Mountain Brook: 3540.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Makkasan", + "FINAL ANSWER: Makkasan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.50958, + "lon": 85.30504, + "name": "Fatwa" + }, + { + "lat": 35.09466, + "lon": 136.60062, + "name": "Tōin" + }, + { + "lat": 12.26416, + "lon": 79.06745, + "name": "Vengikkal" + }, + { + "lat": 22.90418, + "lon": 99.80286, + "name": "Fubang" + }, + { + "lat": -12.06866, + "lon": -75.21027, + "name": "Huancayo" + } + ], + "question": "Which location is the geographic outlier among: Fatwa, Tōin, Vengikkal, Fubang, Huancayo?", + "ground_truth": { + "answer": "Huancayo", + "outlier_distance_km": 15717.4, + "second_furthest_km": 7285.4, + "clarity_ratio": 2.16, + "median_distance_km": 3684.0, + "distances_to_centroid": { + "Fatwa": 2306.2, + "Tōin": 7285.4, + "Vengikkal": 1581.9, + "Fubang": 3684.0, + "Huancayo": 15717.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fatwa: (25.51°, 85.31°)", + " Tōin: (35.09°, 136.60°)", + " Vengikkal: (12.26°, 79.07°)", + " Fubang: (22.90°, 99.80°)", + " Huancayo: (-12.07°, -75.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huancayo: 15717.4 km from centroid", + " Tōin: 7285.4 km from centroid", + " Fubang: 3684.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huancayo", + "FINAL ANSWER: Huancayo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.54015, + "lon": -46.48581, + "name": "Artur Alvim" + }, + { + "lat": -8.88202, + "lon": -36.50216, + "name": "Garanhuns" + }, + { + "lat": -34.57365, + "lon": -58.44924, + "name": "Colegiales" + }, + { + "lat": -32.88946, + "lon": -68.84582, + "name": "Mendoza" + }, + { + "lat": 14.865, + "lon": 120.95722, + "name": "Pandi" + } + ], + "question": "Which location is the geographic outlier among: Artur Alvim, Garanhuns, Colegiales, Mendoza, Pandi?", + "ground_truth": { + "answer": "Pandi", + "outlier_distance_km": 15613.7, + "second_furthest_km": 5378.1, + "clarity_ratio": 2.9, + "median_distance_km": 4468.6, + "distances_to_centroid": { + "Artur Alvim": 3066.6, + "Garanhuns": 2210.2, + "Colegiales": 4468.6, + "Mendoza": 5378.1, + "Pandi": 15613.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Artur Alvim: (-23.54°, -46.49°)", + " Garanhuns: (-8.88°, -36.50°)", + " Colegiales: (-34.57°, -58.45°)", + " Mendoza: (-32.89°, -68.85°)", + " Pandi: (14.87°, 120.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pandi: 15613.7 km from centroid", + " Mendoza: 5378.1 km from centroid", + " Colegiales: 4468.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pandi", + "FINAL ANSWER: Pandi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.08829, + "lon": 16.64866, + "name": "Kościan" + }, + { + "lat": 42.54664, + "lon": -6.59619, + "name": "Ponferrada" + }, + { + "lat": 45.38956, + "lon": 4.2886, + "name": "Firminy" + }, + { + "lat": 53.45801, + "lon": -2.20104, + "name": "Longsight" + }, + { + "lat": 29.23552, + "lon": 77.01273, + "name": "Samālkha" + } + ], + "question": "Which location is the geographic outlier among: Kościan, Ponferrada, Firminy, Longsight, Samālkha?", + "ground_truth": { + "answer": "Samālkha", + "outlier_distance_km": 5404.9, + "second_furthest_km": 1973.8, + "clarity_ratio": 2.74, + "median_distance_km": 1756.2, + "distances_to_centroid": { + "Kościan": 843.4, + "Ponferrada": 1973.8, + "Firminy": 1068.2, + "Longsight": 1756.2, + "Samālkha": 5404.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kościan: (52.09°, 16.65°)", + " Ponferrada: (42.55°, -6.60°)", + " Firminy: (45.39°, 4.29°)", + " Longsight: (53.46°, -2.20°)", + " Samālkha: (29.24°, 77.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Samālkha: 5404.9 km from centroid", + " Ponferrada: 1973.8 km from centroid", + " Longsight: 1756.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Samālkha", + "FINAL ANSWER: Samālkha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.77944, + "lon": -39.17, + "name": "Conceição do Almeida" + }, + { + "lat": -12.31667, + "lon": -38.76667, + "name": "Conceição do Jacuípe" + }, + { + "lat": -11.80361, + "lon": -61.80333, + "name": "Rolim de Moura" + }, + { + "lat": -7.09829, + "lon": -49.9435, + "name": "Xinguara" + }, + { + "lat": 21.55, + "lon": 107.96667, + "name": "Dongxing" + } + ], + "question": "Which location is the geographic outlier among: Conceição do Almeida, Conceição do Jacuípe, Rolim de Moura, Xinguara, Dongxing?", + "ground_truth": { + "answer": "Dongxing", + "outlier_distance_km": 13728.6, + "second_furthest_km": 5063.2, + "clarity_ratio": 2.71, + "median_distance_km": 3727.5, + "distances_to_centroid": { + "Conceição do Almeida": 2670.8, + "Conceição do Jacuípe": 2613.4, + "Rolim de Moura": 5063.2, + "Xinguara": 3727.5, + "Dongxing": 13728.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Conceição do Almeida: (-12.78°, -39.17°)", + " Conceição do Jacuípe: (-12.32°, -38.77°)", + " Rolim de Moura: (-11.80°, -61.80°)", + " Xinguara: (-7.10°, -49.94°)", + " Dongxing: (21.55°, 107.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dongxing: 13728.6 km from centroid", + " Rolim de Moura: 5063.2 km from centroid", + " Xinguara: 3727.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dongxing", + "FINAL ANSWER: Dongxing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.41552, + "lon": -107.91166, + "name": "Nuevo Casas Grandes" + }, + { + "lat": 43.22862, + "lon": -88.11037, + "name": "Germantown" + }, + { + "lat": 44.60868, + "lon": -79.42068, + "name": "Orillia" + }, + { + "lat": 40.53078, + "lon": -112.29828, + "name": "Tooele" + }, + { + "lat": -2.27808, + "lon": 37.81867, + "name": "Makindu" + } + ], + "question": "Which location is the geographic outlier among: Nuevo Casas Grandes, Germantown, Orillia, Tooele, Makindu?", + "ground_truth": { + "answer": "Makindu", + "outlier_distance_km": 11826.8, + "second_furthest_km": 3906.2, + "clarity_ratio": 3.03, + "median_distance_km": 3603.6, + "distances_to_centroid": { + "Nuevo Casas Grandes": 3603.6, + "Germantown": 2073.3, + "Orillia": 1692.6, + "Tooele": 3906.2, + "Makindu": 11826.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nuevo Casas Grandes: (30.42°, -107.91°)", + " Germantown: (43.23°, -88.11°)", + " Orillia: (44.61°, -79.42°)", + " Tooele: (40.53°, -112.30°)", + " Makindu: (-2.28°, 37.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Makindu: 11826.8 km from centroid", + " Tooele: 3906.2 km from centroid", + " Nuevo Casas Grandes: 3603.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Makindu", + "FINAL ANSWER: Makindu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88012, + "lon": 174.61975, + "name": "Henderson" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + }, + { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": 31.18065, + "lon": 31.86497, + "name": "Al Jammālīyah" + } + ], + "question": "Which location is the geographic outlier among: Henderson, Papakura, Hurstville, Sunnybank Hills, Al Jammālīyah?", + "ground_truth": { + "answer": "Al Jammālīyah", + "outlier_distance_km": 12592.7, + "second_furthest_km": 4060.9, + "clarity_ratio": 3.1, + "median_distance_km": 4027.8, + "distances_to_centroid": { + "Henderson": 4027.8, + "Papakura": 4060.9, + "Hurstville": 2002.5, + "Sunnybank Hills": 1779.2, + "Al Jammālīyah": 12592.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Henderson: (-36.88°, 174.62°)", + " Papakura: (-37.06°, 174.94°)", + " Hurstville: (-33.97°, 151.10°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Al Jammālīyah: (31.18°, 31.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Jammālīyah: 12592.7 km from centroid", + " Papakura: 4060.9 km from centroid", + " Henderson: 4027.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Jammālīyah", + "FINAL ANSWER: Al Jammālīyah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -21.13056, + "lon": -42.36639, + "name": "Muriaé" + } + ], + "question": "Which location is the geographic outlier among: Busselton, South Morang, Blenheim, Bundoora, Muriaé?", + "ground_truth": { + "answer": "Muriaé", + "outlier_distance_km": 13069.6, + "second_furthest_km": 5746.8, + "clarity_ratio": 2.27, + "median_distance_km": 3387.5, + "distances_to_centroid": { + "Busselton": 734.5, + "South Morang": 3387.5, + "Blenheim": 5746.8, + "Bundoora": 3383.5, + "Muriaé": 13069.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Busselton: (-33.65°, 115.35°)", + " South Morang: (-37.65°, 145.10°)", + " Blenheim: (-41.52°, 173.95°)", + " Bundoora: (-37.70°, 145.06°)", + " Muriaé: (-21.13°, -42.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Muriaé: 13069.6 km from centroid", + " Blenheim: 5746.8 km from centroid", + " South Morang: 3387.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Muriaé", + "FINAL ANSWER: Muriaé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.09198, + "lon": -70.19792, + "name": "Tocopilla" + }, + { + "lat": -6.51056, + "lon": -36.34694, + "name": "Picuí" + }, + { + "lat": -23.56338, + "lon": -46.63228, + "name": "Liberdade" + }, + { + "lat": -20.91806, + "lon": -49.44528, + "name": "Bady Bassitt" + }, + { + "lat": 53.11254, + "lon": 6.0989, + "name": "Drachten" + } + ], + "question": "Which location is the geographic outlier among: Tocopilla, Picuí, Liberdade, Bady Bassitt, Drachten?", + "ground_truth": { + "answer": "Drachten", + "outlier_distance_km": 7629.2, + "second_furthest_km": 3889.2, + "clarity_ratio": 1.96, + "median_distance_km": 2313.8, + "distances_to_centroid": { + "Tocopilla": 3889.2, + "Picuí": 430.7, + "Liberdade": 2313.8, + "Bady Bassitt": 2177.9, + "Drachten": 7629.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tocopilla: (-22.09°, -70.20°)", + " Picuí: (-6.51°, -36.35°)", + " Liberdade: (-23.56°, -46.63°)", + " Bady Bassitt: (-20.92°, -49.45°)", + " Drachten: (53.11°, 6.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Drachten: 7629.2 km from centroid", + " Tocopilla: 3889.2 km from centroid", + " Liberdade: 2313.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Drachten", + "FINAL ANSWER: Drachten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.3417, + "lon": -72.13597, + "name": "Waterford" + }, + { + "lat": 40.88593, + "lon": -74.04347, + "name": "Hackensack" + }, + { + "lat": 43.82602, + "lon": -111.78969, + "name": "Rexburg" + }, + { + "lat": 42.32226, + "lon": -83.17631, + "name": "Dearborn" + }, + { + "lat": -23.84852, + "lon": 151.25775, + "name": "Gladstone" + } + ], + "question": "Which location is the geographic outlier among: Waterford, Hackensack, Rexburg, Dearborn, Gladstone?", + "ground_truth": { + "answer": "Gladstone", + "outlier_distance_km": 18937.5, + "second_furthest_km": 6592.0, + "clarity_ratio": 2.87, + "median_distance_km": 4291.9, + "distances_to_centroid": { + "Waterford": 3372.3, + "Hackensack": 3518.1, + "Rexburg": 6592.0, + "Dearborn": 4291.9, + "Gladstone": 18937.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waterford: (41.34°, -72.14°)", + " Hackensack: (40.89°, -74.04°)", + " Rexburg: (43.83°, -111.79°)", + " Dearborn: (42.32°, -83.18°)", + " Gladstone: (-23.85°, 151.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gladstone: 18937.5 km from centroid", + " Rexburg: 6592.0 km from centroid", + " Dearborn: 4291.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gladstone", + "FINAL ANSWER: Gladstone" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.91756, + "lon": -82.07842, + "name": "Punta Gorda Isles" + }, + { + "lat": 40.74899, + "lon": -74.26126, + "name": "South Orange" + }, + { + "lat": 42.59726, + "lon": -82.87798, + "name": "Mount Clemens" + }, + { + "lat": 45.44979, + "lon": -73.6015, + "name": "Ville-Émard" + }, + { + "lat": 35.53638, + "lon": 135.19934, + "name": "Miyazu" + } + ], + "question": "Which location is the geographic outlier among: Punta Gorda Isles, South Orange, Mount Clemens, Ville-Émard, Miyazu?", + "ground_truth": { + "answer": "Miyazu", + "outlier_distance_km": 11755.0, + "second_furthest_km": 4489.7, + "clarity_ratio": 2.62, + "median_distance_km": 3985.1, + "distances_to_centroid": { + "Punta Gorda Isles": 4489.7, + "South Orange": 3308.3, + "Mount Clemens": 3985.1, + "Ville-Émard": 3221.4, + "Miyazu": 11755.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Punta Gorda Isles: (26.92°, -82.08°)", + " South Orange: (40.75°, -74.26°)", + " Mount Clemens: (42.60°, -82.88°)", + " Ville-Émard: (45.45°, -73.60°)", + " Miyazu: (35.54°, 135.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Miyazu: 11755.0 km from centroid", + " Punta Gorda Isles: 4489.7 km from centroid", + " Mount Clemens: 3985.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Miyazu", + "FINAL ANSWER: Miyazu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.85023, + "lon": 0.47095, + "name": "Bexhill-on-Sea" + }, + { + "lat": 40.90959, + "lon": 14.26519, + "name": "Arzano" + }, + { + "lat": 50.71429, + "lon": -1.98458, + "name": "Poole" + }, + { + "lat": 51.34103, + "lon": 9.8554, + "name": "Witzenhausen" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + } + ], + "question": "Which location is the geographic outlier among: Bexhill-on-Sea, Arzano, Poole, Witzenhausen, Wollongong city centre?", + "ground_truth": { + "answer": "Wollongong city centre", + "outlier_distance_km": 14169.2, + "second_furthest_km": 3654.5, + "clarity_ratio": 3.88, + "median_distance_km": 3500.5, + "distances_to_centroid": { + "Bexhill-on-Sea": 3500.5, + "Arzano": 2079.3, + "Poole": 3654.5, + "Witzenhausen": 2963.4, + "Wollongong city centre": 14169.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexhill-on-Sea: (50.85°, 0.47°)", + " Arzano: (40.91°, 14.27°)", + " Poole: (50.71°, -1.98°)", + " Witzenhausen: (51.34°, 9.86°)", + " Wollongong city centre: (-34.43°, 150.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wollongong city centre: 14169.2 km from centroid", + " Poole: 3654.5 km from centroid", + " Bexhill-on-Sea: 3500.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wollongong city centre", + "FINAL ANSWER: Wollongong city centre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.38558, + "lon": -1.35617, + "name": "Ejura" + }, + { + "lat": -26.08577, + "lon": 27.77515, + "name": "Krugersdorp" + }, + { + "lat": 31.27133, + "lon": 30.78617, + "name": "Sīdī Sālim" + }, + { + "lat": -27.78324, + "lon": 24.68768, + "name": "Pampierstad" + }, + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + } + ], + "question": "Which location is the geographic outlier among: Ejura, Krugersdorp, Sīdī Sālim, Pampierstad, Hastings?", + "ground_truth": { + "answer": "Hastings", + "outlier_distance_km": 12037.9, + "second_furthest_km": 6220.4, + "clarity_ratio": 1.94, + "median_distance_km": 5201.8, + "distances_to_centroid": { + "Ejura": 6220.4, + "Krugersdorp": 3025.6, + "Sīdī Sālim": 5201.8, + "Pampierstad": 3384.7, + "Hastings": 12037.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ejura: (7.39°, -1.36°)", + " Krugersdorp: (-26.09°, 27.78°)", + " Sīdī Sālim: (31.27°, 30.79°)", + " Pampierstad: (-27.78°, 24.69°)", + " Hastings: (-39.64°, 176.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hastings: 12037.9 km from centroid", + " Ejura: 6220.4 km from centroid", + " Sīdī Sālim: 5201.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hastings", + "FINAL ANSWER: Hastings" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.0725, + "lon": 114.04611, + "name": "Kuangshi" + }, + { + "lat": 13.03565, + "lon": 80.15821, + "name": "Porur" + }, + { + "lat": 30.84349, + "lon": 108.36642, + "name": "Zhoujiaba" + }, + { + "lat": 14.94659, + "lon": 120.08673, + "name": "San Antonio" + }, + { + "lat": -29.55028, + "lon": -55.13111, + "name": "São Francisco de Assis" + } + ], + "question": "Which location is the geographic outlier among: Kuangshi, Porur, Zhoujiaba, San Antonio, São Francisco de Assis?", + "ground_truth": { + "answer": "São Francisco de Assis", + "outlier_distance_km": 14457.9, + "second_furthest_km": 5014.8, + "clarity_ratio": 2.88, + "median_distance_km": 4836.4, + "distances_to_centroid": { + "Kuangshi": 4836.4, + "Porur": 721.7, + "Zhoujiaba": 4051.3, + "San Antonio": 5014.8, + "São Francisco de Assis": 14457.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kuangshi: (38.07°, 114.05°)", + " Porur: (13.04°, 80.16°)", + " Zhoujiaba: (30.84°, 108.37°)", + " San Antonio: (14.95°, 120.09°)", + " São Francisco de Assis: (-29.55°, -55.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Francisco de Assis: 14457.9 km from centroid", + " San Antonio: 5014.8 km from centroid", + " Kuangshi: 4836.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Francisco de Assis", + "FINAL ANSWER: São Francisco de Assis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.82889, + "lon": -56.08222, + "name": "Nova Mutum" + }, + { + "lat": -27.81611, + "lon": -50.32611, + "name": "Lages" + }, + { + "lat": -23.5275, + "lon": -46.9025, + "name": "Jandira" + }, + { + "lat": -10.6, + "lon": -38.38333, + "name": "Cícero Dantas" + }, + { + "lat": 53.50098, + "lon": 8.48965, + "name": "Nordenham" + } + ], + "question": "Which location is the geographic outlier among: Nova Mutum, Lages, Jandira, Cícero Dantas, Nordenham?", + "ground_truth": { + "answer": "Nordenham", + "outlier_distance_km": 7689.0, + "second_furthest_km": 2974.4, + "clarity_ratio": 2.59, + "median_distance_km": 2389.6, + "distances_to_centroid": { + "Nova Mutum": 2372.7, + "Lages": 2974.4, + "Jandira": 2389.6, + "Cícero Dantas": 709.8, + "Nordenham": 7689.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nova Mutum: (-13.83°, -56.08°)", + " Lages: (-27.82°, -50.33°)", + " Jandira: (-23.53°, -46.90°)", + " Cícero Dantas: (-10.60°, -38.38°)", + " Nordenham: (53.50°, 8.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nordenham: 7689.0 km from centroid", + " Lages: 2974.4 km from centroid", + " Jandira: 2389.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nordenham", + "FINAL ANSWER: Nordenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.99472, + "lon": 119.3975, + "name": "Zhucheng" + }, + { + "lat": 14.1463, + "lon": 121.4729, + "name": "Majayjay" + }, + { + "lat": 25.45598, + "lon": 85.5329, + "name": "Bakhtiarpur" + }, + { + "lat": 11.84326, + "lon": 75.54368, + "name": "Mangattidam" + }, + { + "lat": -0.15667, + "lon": -50.38667, + "name": "Afuá" + } + ], + "question": "Which location is the geographic outlier among: Zhucheng, Majayjay, Bakhtiarpur, Mangattidam, Afuá?", + "ground_truth": { + "answer": "Afuá", + "outlier_distance_km": 13254.2, + "second_furthest_km": 5470.7, + "clarity_ratio": 2.42, + "median_distance_km": 5228.0, + "distances_to_centroid": { + "Zhucheng": 5228.0, + "Majayjay": 5470.7, + "Bakhtiarpur": 1806.8, + "Mangattidam": 840.3, + "Afuá": 13254.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhucheng: (35.99°, 119.40°)", + " Majayjay: (14.15°, 121.47°)", + " Bakhtiarpur: (25.46°, 85.53°)", + " Mangattidam: (11.84°, 75.54°)", + " Afuá: (-0.16°, -50.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Afuá: 13254.2 km from centroid", + " Majayjay: 5470.7 km from centroid", + " Zhucheng: 5228.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Afuá", + "FINAL ANSWER: Afuá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.33639, + "lon": -49.90639, + "name": "Itaiópolis" + }, + { + "lat": -6.23169, + "lon": -77.86903, + "name": "Chachapoyas" + }, + { + "lat": -1.29389, + "lon": -47.92639, + "name": "Castanhal" + }, + { + "lat": -34.98279, + "lon": -71.23943, + "name": "Curicó" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + } + ], + "question": "Which location is the geographic outlier among: Itaiópolis, Chachapoyas, Castanhal, Curicó, Morayfield?", + "ground_truth": { + "answer": "Morayfield", + "outlier_distance_km": 14790.5, + "second_furthest_km": 6536.7, + "clarity_ratio": 2.26, + "median_distance_km": 5413.9, + "distances_to_centroid": { + "Itaiópolis": 3278.2, + "Chachapoyas": 6536.7, + "Castanhal": 3744.4, + "Curicó": 5413.9, + "Morayfield": 14790.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itaiópolis: (-26.34°, -49.91°)", + " Chachapoyas: (-6.23°, -77.87°)", + " Castanhal: (-1.29°, -47.93°)", + " Curicó: (-34.98°, -71.24°)", + " Morayfield: (-27.11°, 152.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morayfield: 14790.5 km from centroid", + " Chachapoyas: 6536.7 km from centroid", + " Curicó: 5413.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morayfield", + "FINAL ANSWER: Morayfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.09917, + "lon": -98.25417, + "name": "Sanctorum" + }, + { + "lat": 41.71087, + "lon": -87.75811, + "name": "Oak Lawn" + }, + { + "lat": 26.25175, + "lon": -80.17894, + "name": "Coconut Creek" + }, + { + "lat": 35.91402, + "lon": -81.53898, + "name": "Lenoir" + }, + { + "lat": 52.50575, + "lon": 13.50812, + "name": "Friedrichsfelde" + } + ], + "question": "Which location is the geographic outlier among: Sanctorum, Oak Lawn, Coconut Creek, Lenoir, Friedrichsfelde?", + "ground_truth": { + "answer": "Friedrichsfelde", + "outlier_distance_km": 6376.0, + "second_furthest_km": 3559.1, + "clarity_ratio": 1.79, + "median_distance_km": 1958.8, + "distances_to_centroid": { + "Sanctorum": 3559.1, + "Oak Lawn": 1958.8, + "Coconut Creek": 1607.8, + "Lenoir": 1332.0, + "Friedrichsfelde": 6376.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sanctorum: (19.10°, -98.25°)", + " Oak Lawn: (41.71°, -87.76°)", + " Coconut Creek: (26.25°, -80.18°)", + " Lenoir: (35.91°, -81.54°)", + " Friedrichsfelde: (52.51°, 13.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Friedrichsfelde: 6376.0 km from centroid", + " Sanctorum: 3559.1 km from centroid", + " Oak Lawn: 1958.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Friedrichsfelde", + "FINAL ANSWER: Friedrichsfelde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": 7.71393, + "lon": 3.91665, + "name": "Fiditi" + } + ], + "question": "Which location is the geographic outlier among: Sunnybank Hills, Sunshine West, Palm Beach, Auburn, Fiditi?", + "ground_truth": { + "answer": "Fiditi", + "outlier_distance_km": 13128.0, + "second_furthest_km": 3242.3, + "clarity_ratio": 4.05, + "median_distance_km": 3201.4, + "distances_to_centroid": { + "Sunnybank Hills": 3201.4, + "Sunshine West": 2713.3, + "Palm Beach": 3242.3, + "Auburn": 3087.8, + "Fiditi": 13128.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Sunshine West: (-37.79°, 144.82°)", + " Palm Beach: (-28.12°, 153.47°)", + " Auburn: (-33.85°, 151.03°)", + " Fiditi: (7.71°, 3.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fiditi: 13128.0 km from centroid", + " Palm Beach: 3242.3 km from centroid", + " Sunnybank Hills: 3201.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fiditi", + "FINAL ANSWER: Fiditi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.79392, + "lon": -71.35191, + "name": "L'Ancienne-Lorette" + }, + { + "lat": 40.02789, + "lon": -74.86905, + "name": "Willingboro" + }, + { + "lat": 31.15013, + "lon": -81.49147, + "name": "Brunswick" + }, + { + "lat": 25.5783, + "lon": -80.3377, + "name": "Cutler Bay" + }, + { + "lat": 43.66228, + "lon": -7.59344, + "name": "Viveiro" + } + ], + "question": "Which location is the geographic outlier among: L'Ancienne-Lorette, Willingboro, Brunswick, Cutler Bay, Viveiro?", + "ground_truth": { + "answer": "Viveiro", + "outlier_distance_km": 4654.6, + "second_furthest_km": 2091.9, + "clarity_ratio": 2.23, + "median_distance_km": 1822.2, + "distances_to_centroid": { + "L'Ancienne-Lorette": 1239.9, + "Willingboro": 1057.2, + "Brunswick": 1822.2, + "Cutler Bay": 2091.9, + "Viveiro": 4654.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " L'Ancienne-Lorette: (46.79°, -71.35°)", + " Willingboro: (40.03°, -74.87°)", + " Brunswick: (31.15°, -81.49°)", + " Cutler Bay: (25.58°, -80.34°)", + " Viveiro: (43.66°, -7.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viveiro: 4654.6 km from centroid", + " Cutler Bay: 2091.9 km from centroid", + " Brunswick: 1822.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viveiro", + "FINAL ANSWER: Viveiro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.09179, + "lon": -97.04668, + "name": "Highland Village" + }, + { + "lat": 16.68393, + "lon": -93.71814, + "name": "Cintalapa de Figueroa" + }, + { + "lat": 20.58806, + "lon": -100.38806, + "name": "Santiago de Querétaro" + }, + { + "lat": 41.65394, + "lon": -81.45039, + "name": "Eastlake" + }, + { + "lat": 35.77952, + "lon": 139.53014, + "name": "Kiyose" + } + ], + "question": "Which location is the geographic outlier among: Highland Village, Cintalapa de Figueroa, Santiago de Querétaro, Eastlake, Kiyose?", + "ground_truth": { + "answer": "Kiyose", + "outlier_distance_km": 12721.3, + "second_furthest_km": 5460.0, + "clarity_ratio": 2.33, + "median_distance_km": 4988.6, + "distances_to_centroid": { + "Highland Village": 4760.8, + "Cintalapa de Figueroa": 4988.6, + "Santiago de Querétaro": 5460.0, + "Eastlake": 3395.2, + "Kiyose": 12721.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Highland Village: (33.09°, -97.05°)", + " Cintalapa de Figueroa: (16.68°, -93.72°)", + " Santiago de Querétaro: (20.59°, -100.39°)", + " Eastlake: (41.65°, -81.45°)", + " Kiyose: (35.78°, 139.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kiyose: 12721.3 km from centroid", + " Santiago de Querétaro: 5460.0 km from centroid", + " Cintalapa de Figueroa: 4988.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kiyose", + "FINAL ANSWER: Kiyose" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -37.6, + "lon": 144.95, + "name": "Craigieburn" + }, + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + }, + { + "lat": 36.24624, + "lon": 139.07204, + "name": "Fujioka" + } + ], + "question": "Which location is the geographic outlier among: Hobart, Craigieburn, Bexley, Cherrybrook, Fujioka?", + "ground_truth": { + "answer": "Fujioka", + "outlier_distance_km": 6568.2, + "second_furthest_km": 2280.0, + "clarity_ratio": 2.88, + "median_distance_km": 1700.6, + "distances_to_centroid": { + "Hobart": 2280.0, + "Craigieburn": 1700.6, + "Bexley": 1356.8, + "Cherrybrook": 1330.7, + "Fujioka": 6568.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hobart: (-42.88°, 147.33°)", + " Craigieburn: (-37.60°, 144.95°)", + " Bexley: (-33.95°, 151.12°)", + " Cherrybrook: (-33.72°, 151.05°)", + " Fujioka: (36.25°, 139.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fujioka: 6568.2 km from centroid", + " Hobart: 2280.0 km from centroid", + " Craigieburn: 1700.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fujioka", + "FINAL ANSWER: Fujioka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.11758, + "lon": 16.48421, + "name": "Ruvo di Puglia" + }, + { + "lat": 52.62264, + "lon": 10.08047, + "name": "Celle" + }, + { + "lat": 59.992, + "lon": 29.77616, + "name": "Kronstadt" + }, + { + "lat": 50.80904, + "lon": 8.77069, + "name": "Marburg an der Lahn" + }, + { + "lat": 11.71733, + "lon": 75.6419, + "name": "Chekkiād" + } + ], + "question": "Which location is the geographic outlier among: Ruvo di Puglia, Celle, Kronstadt, Marburg an der Lahn, Chekkiād?", + "ground_truth": { + "answer": "Chekkiād", + "outlier_distance_km": 5738.5, + "second_furthest_km": 1864.7, + "clarity_ratio": 3.08, + "median_distance_km": 1694.3, + "distances_to_centroid": { + "Ruvo di Puglia": 989.2, + "Celle": 1694.3, + "Kronstadt": 1864.7, + "Marburg an der Lahn": 1684.8, + "Chekkiād": 5738.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ruvo di Puglia: (41.12°, 16.48°)", + " Celle: (52.62°, 10.08°)", + " Kronstadt: (59.99°, 29.78°)", + " Marburg an der Lahn: (50.81°, 8.77°)", + " Chekkiād: (11.72°, 75.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chekkiād: 5738.5 km from centroid", + " Kronstadt: 1864.7 km from centroid", + " Celle: 1694.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chekkiād", + "FINAL ANSWER: Chekkiād" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.76194, + "lon": -40.26778, + "name": "Trindade" + }, + { + "lat": -27.48132, + "lon": -58.93925, + "name": "Barranqueras" + }, + { + "lat": -21.29917, + "lon": -46.8025, + "name": "Guaranésia" + }, + { + "lat": 3.43054, + "lon": -76.5199, + "name": "Cali" + }, + { + "lat": 0.39337, + "lon": 34.30399, + "name": "Lugulu" + } + ], + "question": "Which location is the geographic outlier among: Trindade, Barranqueras, Guaranésia, Cali, Lugulu?", + "ground_truth": { + "answer": "Lugulu", + "outlier_distance_km": 8043.8, + "second_furthest_km": 4575.1, + "clarity_ratio": 1.76, + "median_distance_km": 2915.9, + "distances_to_centroid": { + "Trindade": 422.6, + "Barranqueras": 2915.9, + "Guaranésia": 1544.5, + "Cali": 4575.1, + "Lugulu": 8043.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Trindade: (-7.76°, -40.27°)", + " Barranqueras: (-27.48°, -58.94°)", + " Guaranésia: (-21.30°, -46.80°)", + " Cali: (3.43°, -76.52°)", + " Lugulu: (0.39°, 34.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lugulu: 8043.8 km from centroid", + " Cali: 4575.1 km from centroid", + " Barranqueras: 2915.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lugulu", + "FINAL ANSWER: Lugulu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.10387, + "lon": 20.6337, + "name": "Grodzisk Mazowiecki" + }, + { + "lat": 53.55, + "lon": 10.13333, + "name": "Billstedt" + }, + { + "lat": 53.16532, + "lon": 8.68873, + "name": "Burglesum" + }, + { + "lat": 52.44653, + "lon": 13.5066, + "name": "Johannisthal" + }, + { + "lat": 31.81679, + "lon": 75.6531, + "name": "Dasūya" + } + ], + "question": "Which location is the geographic outlier among: Grodzisk Mazowiecki, Billstedt, Burglesum, Johannisthal, Dasūya?", + "ground_truth": { + "answer": "Dasūya", + "outlier_distance_km": 4535.0, + "second_furthest_km": 1293.4, + "clarity_ratio": 3.51, + "median_distance_km": 1215.8, + "distances_to_centroid": { + "Grodzisk Mazowiecki": 529.6, + "Billstedt": 1215.8, + "Burglesum": 1293.4, + "Johannisthal": 961.1, + "Dasūya": 4535.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Grodzisk Mazowiecki: (52.10°, 20.63°)", + " Billstedt: (53.55°, 10.13°)", + " Burglesum: (53.17°, 8.69°)", + " Johannisthal: (52.45°, 13.51°)", + " Dasūya: (31.82°, 75.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dasūya: 4535.0 km from centroid", + " Burglesum: 1293.4 km from centroid", + " Billstedt: 1215.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dasūya", + "FINAL ANSWER: Dasūya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.78664, + "lon": 20.12106, + "name": "Montagu" + }, + { + "lat": -25.48251, + "lon": 29.02763, + "name": "Verena" + }, + { + "lat": -27.24179, + "lon": 27.57422, + "name": "Koppies" + }, + { + "lat": 8.89367, + "lon": 11.3596, + "name": "Jalingo" + }, + { + "lat": -23.4717, + "lon": -46.57923, + "name": "Vila Galvão" + } + ], + "question": "Which location is the geographic outlier among: Montagu, Verena, Koppies, Jalingo, Vila Galvão?", + "ground_truth": { + "answer": "Vila Galvão", + "outlier_distance_km": 5642.2, + "second_furthest_km": 3254.3, + "clarity_ratio": 1.73, + "median_distance_km": 2200.3, + "distances_to_centroid": { + "Montagu": 1906.7, + "Verena": 2200.3, + "Koppies": 2108.5, + "Jalingo": 3254.3, + "Vila Galvão": 5642.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Montagu: (-33.79°, 20.12°)", + " Verena: (-25.48°, 29.03°)", + " Koppies: (-27.24°, 27.57°)", + " Jalingo: (8.89°, 11.36°)", + " Vila Galvão: (-23.47°, -46.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vila Galvão: 5642.2 km from centroid", + " Jalingo: 3254.3 km from centroid", + " Verena: 2200.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vila Galvão", + "FINAL ANSWER: Vila Galvão" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.30011, + "lon": -114.03528, + "name": "Airdrie" + }, + { + "lat": 42.05009, + "lon": -82.59981, + "name": "Leamington" + }, + { + "lat": 19.33002, + "lon": -99.32721, + "name": "San Lorenzo Acopilco" + }, + { + "lat": 38.97167, + "lon": -95.23525, + "name": "Lawrence" + }, + { + "lat": 51.88083, + "lon": 5.28889, + "name": "Geldermalsen" + } + ], + "question": "Which location is the geographic outlier among: Airdrie, Leamington, San Lorenzo Acopilco, Lawrence, Geldermalsen?", + "ground_truth": { + "answer": "Geldermalsen", + "outlier_distance_km": 6109.2, + "second_furthest_km": 3174.1, + "clarity_ratio": 1.92, + "median_distance_km": 3040.8, + "distances_to_centroid": { + "Airdrie": 3040.8, + "Leamington": 476.0, + "San Lorenzo Acopilco": 3174.1, + "Lawrence": 1550.7, + "Geldermalsen": 6109.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Airdrie: (51.30°, -114.04°)", + " Leamington: (42.05°, -82.60°)", + " San Lorenzo Acopilco: (19.33°, -99.33°)", + " Lawrence: (38.97°, -95.24°)", + " Geldermalsen: (51.88°, 5.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Geldermalsen: 6109.2 km from centroid", + " San Lorenzo Acopilco: 3174.1 km from centroid", + " Airdrie: 3040.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Geldermalsen", + "FINAL ANSWER: Geldermalsen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.6713, + "lon": 31.58801, + "name": "Hihyā" + }, + { + "lat": 8.22542, + "lon": -0.64889, + "name": "Yegyi" + }, + { + "lat": 31.31146, + "lon": 31.14766, + "name": "Al Ḩāmūl" + }, + { + "lat": 30.00944, + "lon": 31.20861, + "name": "Giza" + }, + { + "lat": 33.29622, + "lon": -86.8436, + "name": "Helena" + } + ], + "question": "Which location is the geographic outlier among: Hihyā, Yegyi, Al Ḩāmūl, Giza, Helena?", + "ground_truth": { + "answer": "Helena", + "outlier_distance_km": 8259.1, + "second_furthest_km": 2979.1, + "clarity_ratio": 2.77, + "median_distance_km": 2942.2, + "distances_to_centroid": { + "Hihyā": 2979.1, + "Yegyi": 2064.7, + "Al Ḩāmūl": 2939.1, + "Giza": 2942.2, + "Helena": 8259.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hihyā: (30.67°, 31.59°)", + " Yegyi: (8.23°, -0.65°)", + " Al Ḩāmūl: (31.31°, 31.15°)", + " Giza: (30.01��, 31.21°)", + " Helena: (33.30°, -86.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Helena: 8259.1 km from centroid", + " Hihyā: 2979.1 km from centroid", + " Giza: 2942.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Helena", + "FINAL ANSWER: Helena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.39337, + "lon": 34.30399, + "name": "Lugulu" + }, + { + "lat": -25.86301, + "lon": 26.89756, + "name": "Koster" + }, + { + "lat": 6.34656, + "lon": 45.47811, + "name": "El Bahay" + }, + { + "lat": -30.31002, + "lon": 30.66275, + "name": "eMuziwezinto" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + } + ], + "question": "Which location is the geographic outlier among: Lugulu, Koster, El Bahay, eMuziwezinto, Maitland?", + "ground_truth": { + "answer": "Maitland", + "outlier_distance_km": 9370.6, + "second_furthest_km": 3360.0, + "clarity_ratio": 2.79, + "median_distance_km": 3182.7, + "distances_to_centroid": { + "Lugulu": 3182.7, + "Koster": 3360.0, + "El Bahay": 2871.9, + "eMuziwezinto": 3156.0, + "Maitland": 9370.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lugulu: (0.39°, 34.30°)", + " Koster: (-25.86°, 26.90°)", + " El Bahay: (6.35°, 45.48°)", + " eMuziwezinto: (-30.31°, 30.66°)", + " Maitland: (-32.73°, 151.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maitland: 9370.6 km from centroid", + " Koster: 3360.0 km from centroid", + " Lugulu: 3182.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maitland", + "FINAL ANSWER: Maitland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.17291, + "lon": -92.33392, + "name": "Yajalón" + }, + { + "lat": 33.76446, + "lon": -117.79394, + "name": "North Tustin" + }, + { + "lat": 34.22843, + "lon": -92.0032, + "name": "Pine Bluff" + }, + { + "lat": 35.05257, + "lon": -97.93643, + "name": "Chickasha" + }, + { + "lat": -15.93444, + "lon": -50.14028, + "name": "Goiás" + } + ], + "question": "Which location is the geographic outlier among: Yajalón, North Tustin, Pine Bluff, Chickasha, Goiás?", + "ground_truth": { + "answer": "Goiás", + "outlier_distance_km": 5974.5, + "second_furthest_km": 3080.4, + "clarity_ratio": 1.94, + "median_distance_km": 1757.0, + "distances_to_centroid": { + "Yajalón": 475.2, + "North Tustin": 3080.4, + "Pine Bluff": 1499.3, + "Chickasha": 1757.0, + "Goiás": 5974.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yajalón: (17.17°, -92.33°)", + " North Tustin: (33.76°, -117.79°)", + " Pine Bluff: (34.23°, -92.00°)", + " Chickasha: (35.05°, -97.94°)", + " Goiás: (-15.93°, -50.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Goiás: 5974.5 km from centroid", + " North Tustin: 3080.4 km from centroid", + " Chickasha: 1757.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Goiás", + "FINAL ANSWER: Goiás" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.68333, + "lon": -54.64278, + "name": "Mojuí dos Campos" + }, + { + "lat": -11.52472, + "lon": -61.01278, + "name": "Espigão dOeste" + }, + { + "lat": -20.25333, + "lon": -43.80139, + "name": "Itabirito" + }, + { + "lat": -23.87444, + "lon": -53.90167, + "name": "Altônia" + }, + { + "lat": -26.31401, + "lon": 26.82223, + "name": "Ventersdorp" + } + ], + "question": "Which location is the geographic outlier among: Mojuí dos Campos, Espigão dOeste, Itabirito, Altônia, Ventersdorp?", + "ground_truth": { + "answer": "Ventersdorp", + "outlier_distance_km": 6647.7, + "second_furthest_km": 2622.6, + "clarity_ratio": 2.53, + "median_distance_km": 2469.1, + "distances_to_centroid": { + "Mojuí dos Campos": 2469.1, + "Espigão dOeste": 2622.6, + "Itabirito": 777.7, + "Altônia": 1892.0, + "Ventersdorp": 6647.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mojuí dos Campos: (-2.68°, -54.64°)", + " Espigão dOeste: (-11.52°, -61.01°)", + " Itabirito: (-20.25°, -43.80°)", + " Altônia: (-23.87°, -53.90°)", + " Ventersdorp: (-26.31°, 26.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ventersdorp: 6647.7 km from centroid", + " Espigão dOeste: 2622.6 km from centroid", + " Mojuí dos Campos: 2469.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ventersdorp", + "FINAL ANSWER: Ventersdorp" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.07936, + "lon": 7.01344, + "name": "Ahaus" + }, + { + "lat": 41.65541, + "lon": -4.72353, + "name": "Valladolid" + }, + { + "lat": 43.71795, + "lon": 10.94758, + "name": "Empoli" + }, + { + "lat": 48.07086, + "lon": 1.33783, + "name": "Châteaudun" + }, + { + "lat": 33.22375, + "lon": 132.56001, + "name": "Uwajima" + } + ], + "question": "Which location is the geographic outlier among: Ahaus, Valladolid, Empoli, Châteaudun, Uwajima?", + "ground_truth": { + "answer": "Uwajima", + "outlier_distance_km": 8453.0, + "second_furthest_km": 2780.5, + "clarity_ratio": 3.04, + "median_distance_km": 2212.5, + "distances_to_centroid": { + "Ahaus": 1898.8, + "Valladolid": 2780.5, + "Empoli": 1481.6, + "Châteaudun": 2212.5, + "Uwajima": 8453.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ahaus: (52.08°, 7.01°)", + " Valladolid: (41.66°, -4.72°)", + " Empoli: (43.72°, 10.95°)", + " Châteaudun: (48.07°, 1.34°)", + " Uwajima: (33.22°, 132.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uwajima: 8453.0 km from centroid", + " Valladolid: 2780.5 km from centroid", + " Châteaudun: 2212.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uwajima", + "FINAL ANSWER: Uwajima" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.84493, + "lon": 26.76829, + "name": "Stilfontein" + }, + { + "lat": 8.05, + "lon": 4.76667, + "name": "Oyan" + }, + { + "lat": 5.86006, + "lon": -0.6635, + "name": "Asamankese" + }, + { + "lat": 5.82917, + "lon": 7.35056, + "name": "Okigwe" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + } + ], + "question": "Which location is the geographic outlier among: Stilfontein, Oyan, Asamankese, Okigwe, Cranbourne West?", + "ground_truth": { + "answer": "Cranbourne West", + "outlier_distance_km": 10970.4, + "second_furthest_km": 4460.1, + "clarity_ratio": 2.46, + "median_distance_km": 4015.3, + "distances_to_centroid": { + "Stilfontein": 2238.5, + "Oyan": 4015.3, + "Asamankese": 4460.1, + "Okigwe": 3648.8, + "Cranbourne West": 10970.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stilfontein: (-26.84°, 26.77°)", + " Oyan: (8.05°, 4.77°)", + " Asamankese: (5.86°, -0.66°)", + " Okigwe: (5.83°, 7.35°)", + " Cranbourne West: (-38.10°, 145.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cranbourne West: 10970.4 km from centroid", + " Asamankese: 4460.1 km from centroid", + " Oyan: 4015.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cranbourne West", + "FINAL ANSWER: Cranbourne West" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.44879, + "lon": -81.78317, + "name": "Statesboro" + }, + { + "lat": 43.50092, + "lon": -70.44283, + "name": "Saco" + }, + { + "lat": 40.84982, + "lon": -73.91986, + "name": "Morris Heights" + }, + { + "lat": 31.12406, + "lon": -97.90308, + "name": "Copperas Cove" + }, + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + } + ], + "question": "Which location is the geographic outlier among: Statesboro, Saco, Morris Heights, Copperas Cove, Coogee?", + "ground_truth": { + "answer": "Coogee", + "outlier_distance_km": 18654.7, + "second_furthest_km": 6264.1, + "clarity_ratio": 2.98, + "median_distance_km": 4735.6, + "distances_to_centroid": { + "Statesboro": 4735.6, + "Saco": 4008.3, + "Morris Heights": 4177.5, + "Copperas Cove": 6264.1, + "Coogee": 18654.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Statesboro: (32.45°, -81.78°)", + " Saco: (43.50°, -70.44°)", + " Morris Heights: (40.85°, -73.92°)", + " Copperas Cove: (31.12°, -97.90°)", + " Coogee: (-33.92°, 151.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coogee: 18654.7 km from centroid", + " Copperas Cove: 6264.1 km from centroid", + " Statesboro: 4735.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coogee", + "FINAL ANSWER: Coogee" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.73081, + "lon": 81.20578, + "name": "Balod" + }, + { + "lat": 23.48054, + "lon": 111.28848, + "name": "Wuzhou" + }, + { + "lat": 13.884, + "lon": 122.2604, + "name": "Lopez" + }, + { + "lat": 24.40583, + "lon": 109.60861, + "name": "Luorong" + }, + { + "lat": 12.76889, + "lon": 37.62389, + "name": "Amba Giorgis" + } + ], + "question": "Which location is the geographic outlier among: Balod, Wuzhou, Lopez, Luorong, Amba Giorgis?", + "ground_truth": { + "answer": "Amba Giorgis", + "outlier_distance_km": 5876.9, + "second_furthest_km": 3231.6, + "clarity_ratio": 1.82, + "median_distance_km": 2016.6, + "distances_to_centroid": { + "Balod": 1184.7, + "Wuzhou": 2016.6, + "Lopez": 3231.6, + "Luorong": 1873.0, + "Amba Giorgis": 5876.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Balod: (20.73°, 81.21°)", + " Wuzhou: (23.48°, 111.29°)", + " Lopez: (13.88°, 122.26°)", + " Luorong: (24.41°, 109.61°)", + " Amba Giorgis: (12.77°, 37.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amba Giorgis: 5876.9 km from centroid", + " Lopez: 3231.6 km from centroid", + " Wuzhou: 2016.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amba Giorgis", + "FINAL ANSWER: Amba Giorgis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": 42.31474, + "lon": -88.4487, + "name": "Woodstock" + } + ], + "question": "Which location is the geographic outlier among: Wheelers Hill, Sunshine West, Karori, Coorparoo, Woodstock?", + "ground_truth": { + "answer": "Woodstock", + "outlier_distance_km": 17236.8, + "second_furthest_km": 6787.7, + "clarity_ratio": 2.54, + "median_distance_km": 4830.5, + "distances_to_centroid": { + "Wheelers Hill": 4240.6, + "Sunshine West": 4206.3, + "Karori": 6787.7, + "Coorparoo": 4830.5, + "Woodstock": 17236.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Sunshine West: (-37.79°, 144.82°)", + " Karori: (-41.28°, 174.74°)", + " Coorparoo: (-27.49°, 153.06°)", + " Woodstock: (42.31°, -88.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Woodstock: 17236.8 km from centroid", + " Karori: 6787.7 km from centroid", + " Coorparoo: 4830.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Woodstock", + "FINAL ANSWER: Woodstock" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.77121, + "lon": -79.42756, + "name": "Willowdale West" + }, + { + "lat": 40.09344, + "lon": -74.96795, + "name": "Parkwood Manor" + }, + { + "lat": 20.91154, + "lon": -97.67554, + "name": "Álamo" + }, + { + "lat": 38.74761, + "lon": -77.08303, + "name": "Hybla Valley" + }, + { + "lat": -33.90741, + "lon": 151.15546, + "name": "Marrickville" + } + ], + "question": "Which location is the geographic outlier among: Willowdale West, Parkwood Manor, Álamo, Hybla Valley, Marrickville?", + "ground_truth": { + "answer": "Marrickville", + "outlier_distance_km": 18527.4, + "second_furthest_km": 6380.2, + "clarity_ratio": 2.9, + "median_distance_km": 4685.3, + "distances_to_centroid": { + "Willowdale West": 4685.3, + "Parkwood Manor": 4214.1, + "Álamo": 6380.2, + "Hybla Valley": 4351.2, + "Marrickville": 18527.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Willowdale West: (43.77°, -79.43°)", + " Parkwood Manor: (40.09°, -74.97°)", + " Álamo: (20.91°, -97.68°)", + " Hybla Valley: (38.75°, -77.08°)", + " Marrickville: (-33.91°, 151.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marrickville: 18527.4 km from centroid", + " Álamo: 6380.2 km from centroid", + " Willowdale West: 4685.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marrickville", + "FINAL ANSWER: Marrickville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.72306, + "lon": -44.13556, + "name": "Rio Claro" + }, + { + "lat": -14.02139, + "lon": -41.24806, + "name": "Tanhaçu" + }, + { + "lat": -3.74167, + "lon": -43.36028, + "name": "Chapadinha" + }, + { + "lat": -19.225, + "lon": -40.85139, + "name": "Pancas" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + } + ], + "question": "Which location is the geographic outlier among: Rio Claro, Tanhaçu, Chapadinha, Pancas, Broken Hill?", + "ground_truth": { + "answer": "Broken Hill", + "outlier_distance_km": 13413.2, + "second_furthest_km": 4411.8, + "clarity_ratio": 3.04, + "median_distance_km": 4028.4, + "distances_to_centroid": { + "Rio Claro": 4028.4, + "Tanhaçu": 3827.9, + "Chapadinha": 4411.8, + "Pancas": 3703.1, + "Broken Hill": 13413.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rio Claro: (-22.72°, -44.14°)", + " Tanhaçu: (-14.02°, -41.25°)", + " Chapadinha: (-3.74°, -43.36°)", + " Pancas: (-19.23°, -40.85°)", + " Broken Hill: (-31.97°, 141.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Broken Hill: 13413.2 km from centroid", + " Chapadinha: 4411.8 km from centroid", + " Rio Claro: 4028.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Broken Hill", + "FINAL ANSWER: Broken Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.06306, + "lon": -60.10261, + "name": "Arrecifes" + }, + { + "lat": -10.1497, + "lon": -67.73741, + "name": "Senador Guiomard" + }, + { + "lat": -6.76694, + "lon": -43.0225, + "name": "Floriano" + }, + { + "lat": -23.57381, + "lon": -46.51561, + "name": "Aricanduva" + }, + { + "lat": 21.8156, + "lon": 80.18845, + "name": "Bālāghāt" + } + ], + "question": "Which location is the geographic outlier among: Arrecifes, Senador Guiomard, Floriano, Aricanduva, Bālāghāt?", + "ground_truth": { + "answer": "Bālāghāt", + "outlier_distance_km": 12247.6, + "second_furthest_km": 4405.3, + "clarity_ratio": 2.78, + "median_distance_km": 4224.0, + "distances_to_centroid": { + "Arrecifes": 4224.0, + "Senador Guiomard": 4405.3, + "Floriano": 1763.6, + "Aricanduva": 2486.9, + "Bālāghāt": 12247.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arrecifes: (-34.06°, -60.10°)", + " Senador Guiomard: (-10.15°, -67.74°)", + " Floriano: (-6.77°, -43.02°)", + " Aricanduva: (-23.57°, -46.52°)", + " Bālāghāt: (21.82°, 80.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bālāghāt: 12247.6 km from centroid", + " Senador Guiomard: 4405.3 km from centroid", + " Arrecifes: 4224.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bālāghāt", + "FINAL ANSWER: Bālāghāt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.66583, + "lon": -35.73528, + "name": "Maceió" + }, + { + "lat": -34.65118, + "lon": -58.62205, + "name": "Morón" + }, + { + "lat": -4.45194, + "lon": -37.79722, + "name": "Fortim" + }, + { + "lat": -27.58612, + "lon": -48.52335, + "name": "Trindade" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + } + ], + "question": "Which location is the geographic outlier among: Maceió, Morón, Fortim, Trindade, Napier?", + "ground_truth": { + "answer": "Napier", + "outlier_distance_km": 13043.2, + "second_furthest_km": 5698.6, + "clarity_ratio": 2.29, + "median_distance_km": 4795.4, + "distances_to_centroid": { + "Maceió": 4007.4, + "Morón": 5698.6, + "Fortim": 4486.5, + "Trindade": 4795.4, + "Napier": 13043.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maceió: (-9.67°, -35.74°)", + " Morón: (-34.65°, -58.62°)", + " Fortim: (-4.45°, -37.80°)", + " Trindade: (-27.59°, -48.52°)", + " Napier: (-39.49°, 176.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Napier: 13043.2 km from centroid", + " Morón: 5698.6 km from centroid", + " Trindade: 4795.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Napier", + "FINAL ANSWER: Napier" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + { + "lat": -26.65682, + "lon": 153.07955, + "name": "Sunshine Coast" + }, + { + "lat": -34.60251, + "lon": 138.74902, + "name": "Gawler" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": 51.28951, + "lon": 13.5335, + "name": "Großenhain" + } + ], + "question": "Which location is the geographic outlier among: Traralgon, Sunshine Coast, Gawler, Cheltenham, Großenhain?", + "ground_truth": { + "answer": "Großenhain", + "outlier_distance_km": 12589.8, + "second_furthest_km": 3616.9, + "clarity_ratio": 3.48, + "median_distance_km": 3521.9, + "distances_to_centroid": { + "Traralgon": 3521.9, + "Sunshine Coast": 3616.9, + "Gawler": 2724.9, + "Cheltenham": 3400.1, + "Großenhain": 12589.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Traralgon: (-38.20°, 146.54°)", + " Sunshine Coast: (-26.66°, 153.08°)", + " Gawler: (-34.60°, 138.75°)", + " Cheltenham: (-37.97°, 145.05°)", + " Großenhain: (51.29°, 13.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Großenhain: 12589.8 km from centroid", + " Sunshine Coast: 3616.9 km from centroid", + " Traralgon: 3521.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Großenhain", + "FINAL ANSWER: Großenhain" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + }, + { + "lat": -36.84853, + "lon": 174.76349, + "name": "Auckland" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": 3.17301, + "lon": -76.26275, + "name": "Corinto" + } + ], + "question": "Which location is the geographic outlier among: Melbourne, Busselton, Auckland, Boronia, Corinto?", + "ground_truth": { + "answer": "Corinto", + "outlier_distance_km": 17170.7, + "second_furthest_km": 6807.8, + "clarity_ratio": 2.52, + "median_distance_km": 4220.3, + "distances_to_centroid": { + "Melbourne": 4192.1, + "Busselton": 1490.7, + "Auckland": 6807.8, + "Boronia": 4220.3, + "Corinto": 17170.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Melbourne: (-37.81°, 144.96°)", + " Busselton: (-33.65°, 115.35°)", + " Auckland: (-36.85°, 174.76°)", + " Boronia: (-37.87°, 145.28°)", + " Corinto: (3.17°, -76.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Corinto: 17170.7 km from centroid", + " Auckland: 6807.8 km from centroid", + " Boronia: 4220.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Corinto", + "FINAL ANSWER: Corinto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.8969, + "lon": -60.01909, + "name": "Chivilcoy" + }, + { + "lat": 8.55666, + "lon": -74.26355, + "name": "Tiquisio" + }, + { + "lat": -9.47833, + "lon": -35.85333, + "name": "Rio Largo" + }, + { + "lat": -21.04333, + "lon": -40.82444, + "name": "Marataizes" + }, + { + "lat": 38.55185, + "lon": -121.36467, + "name": "Rosemont" + } + ], + "question": "Which location is the geographic outlier among: Chivilcoy, Tiquisio, Rio Largo, Marataizes, Rosemont?", + "ground_truth": { + "answer": "Rosemont", + "outlier_distance_km": 7323.4, + "second_furthest_km": 3536.2, + "clarity_ratio": 2.07, + "median_distance_km": 3440.8, + "distances_to_centroid": { + "Chivilcoy": 3536.2, + "Tiquisio": 1610.5, + "Rio Largo": 3440.8, + "Marataizes": 3379.0, + "Rosemont": 7323.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chivilcoy: (-34.90°, -60.02°)", + " Tiquisio: (8.56°, -74.26°)", + " Rio Largo: (-9.48°, -35.85°)", + " Marataizes: (-21.04°, -40.82°)", + " Rosemont: (38.55°, -121.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rosemont: 7323.4 km from centroid", + " Chivilcoy: 3536.2 km from centroid", + " Rio Largo: 3440.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rosemont", + "FINAL ANSWER: Rosemont" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + }, + { + "lat": -37.74496, + "lon": 144.80049, + "name": "St Albans" + }, + { + "lat": -33.86482, + "lon": 151.20773, + "name": "Sydney Central Business District" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": 41.00997, + "lon": 17.00558, + "name": "Rutigliano" + } + ], + "question": "Which location is the geographic outlier among: Lilydale, St Albans, Sydney Central Business District, Otahuhu, Rutigliano?", + "ground_truth": { + "answer": "Rutigliano", + "outlier_distance_km": 13142.2, + "second_furthest_km": 4949.5, + "clarity_ratio": 2.66, + "median_distance_km": 2799.9, + "distances_to_centroid": { + "Lilydale": 2584.0, + "St Albans": 2547.3, + "Sydney Central Business District": 2799.9, + "Otahuhu": 4949.5, + "Rutigliano": 13142.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lilydale: (-37.75°, 145.35°)", + " St Albans: (-37.74°, 144.80°)", + " Sydney Central Business District: (-33.86°, 151.21°)", + " Otahuhu: (-36.94°, 174.84°)", + " Rutigliano: (41.01°, 17.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rutigliano: 13142.2 km from centroid", + " Otahuhu: 4949.5 km from centroid", + " Sydney Central Business District: 2799.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rutigliano", + "FINAL ANSWER: Rutigliano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.9216, + "lon": 1.07772, + "name": "Dieppe" + }, + { + "lat": 52.92656, + "lon": 78.57508, + "name": "Yarovoye" + }, + { + "lat": 51.31903, + "lon": -0.55893, + "name": "Woking" + }, + { + "lat": 43.33904, + "lon": -1.78938, + "name": "Irun" + }, + { + "lat": 11.2471, + "lon": 10.561, + "name": "Kari" + } + ], + "question": "Which location is the geographic outlier among: Dieppe, Yarovoye, Woking, Irun, Kari?", + "ground_truth": { + "answer": "Yarovoye", + "outlier_distance_km": 4611.1, + "second_furthest_km": 3459.9, + "clarity_ratio": 1.33, + "median_distance_km": 1740.0, + "distances_to_centroid": { + "Dieppe": 1562.4, + "Yarovoye": 4611.1, + "Woking": 1740.0, + "Irun": 1592.4, + "Kari": 3459.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dieppe: (49.92°, 1.08°)", + " Yarovoye: (52.93°, 78.58°)", + " Woking: (51.32°, -0.56°)", + " Irun: (43.34°, -1.79°)", + " Kari: (11.25°, 10.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yarovoye: 4611.1 km from centroid", + " Kari: 3459.9 km from centroid", + " Woking: 1740.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yarovoye", + "FINAL ANSWER: Yarovoye" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.21386, + "lon": 49.61838, + "name": "Dimitrovgrad" + }, + { + "lat": 52.03634, + "lon": 4.32501, + "name": "Rijswijk" + }, + { + "lat": 52.39886, + "lon": 13.06566, + "name": "Potsdam" + }, + { + "lat": 48.91936, + "lon": 2.27485, + "name": "Bois-Colombes" + }, + { + "lat": 26.58509, + "lon": 101.71276, + "name": "Panzhihua" + } + ], + "question": "Which location is the geographic outlier among: Dimitrovgrad, Rijswijk, Potsdam, Bois-Colombes, Panzhihua?", + "ground_truth": { + "answer": "Panzhihua", + "outlier_distance_km": 6217.6, + "second_furthest_km": 2374.7, + "clarity_ratio": 2.62, + "median_distance_km": 2219.1, + "distances_to_centroid": { + "Dimitrovgrad": 1359.8, + "Rijswijk": 2219.1, + "Potsdam": 1636.1, + "Bois-Colombes": 2374.7, + "Panzhihua": 6217.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dimitrovgrad: (54.21°, 49.62°)", + " Rijswijk: (52.04°, 4.33°)", + " Potsdam: (52.40°, 13.07°)", + " Bois-Colombes: (48.92°, 2.27°)", + " Panzhihua: (26.59°, 101.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Panzhihua: 6217.6 km from centroid", + " Bois-Colombes: 2374.7 km from centroid", + " Rijswijk: 2219.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Panzhihua", + "FINAL ANSWER: Panzhihua" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73333, + "lon": 150.93284, + "name": "Glenwood" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": 2.33468, + "lon": 37.99086, + "name": "Marsabit" + } + ], + "question": "Which location is the geographic outlier among: Glenwood, Mount Martha, Pacific Pines, Doreen, Marsabit?", + "ground_truth": { + "answer": "Marsabit", + "outlier_distance_km": 9976.1, + "second_furthest_km": 2643.4, + "clarity_ratio": 3.77, + "median_distance_km": 2453.6, + "distances_to_centroid": { + "Glenwood": 2453.6, + "Mount Martha": 2130.8, + "Pacific Pines": 2643.4, + "Doreen": 2104.5, + "Marsabit": 9976.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenwood: (-33.73°, 150.93°)", + " Mount Martha: (-38.27°, 145.02°)", + " Pacific Pines: (-27.94°, 153.31°)", + " Doreen: (-37.60°, 145.15°)", + " Marsabit: (2.33°, 37.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marsabit: 9976.1 km from centroid", + " Pacific Pines: 2643.4 km from centroid", + " Glenwood: 2453.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marsabit", + "FINAL ANSWER: Marsabit" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.15847, + "lon": -43.29321, + "name": "Paraíba do Sul" + }, + { + "lat": -29.19167, + "lon": -54.86722, + "name": "Santiago" + }, + { + "lat": 4.91857, + "lon": -74.02799, + "name": "Cajicá" + }, + { + "lat": -6.80306, + "lon": -35.08056, + "name": "Rio Tinto" + }, + { + "lat": 18.91614, + "lon": -103.87713, + "name": "Tecomán" + } + ], + "question": "Which location is the geographic outlier among: Paraíba do Sul, Santiago, Cajicá, Rio Tinto, Tecomán?", + "ground_truth": { + "answer": "Tecomán", + "outlier_distance_km": 5389.1, + "second_furthest_km": 2997.0, + "clarity_ratio": 1.8, + "median_distance_km": 2648.7, + "distances_to_centroid": { + "Paraíba do Sul": 2648.7, + "Santiago": 2600.0, + "Cajicá": 1852.3, + "Rio Tinto": 2997.0, + "Tecomán": 5389.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paraíba do Sul: (-22.16°, -43.29°)", + " Santiago: (-29.19°, -54.87°)", + " Cajicá: (4.92°, -74.03°)", + " Rio Tinto: (-6.80°, -35.08°)", + " Tecomán: (18.92°, -103.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tecomán: 5389.1 km from centroid", + " Rio Tinto: 2997.0 km from centroid", + " Paraíba do Sul: 2648.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tecomán", + "FINAL ANSWER: Tecomán" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.83193, + "lon": 11.19924, + "name": "Sesto Fiorentino" + }, + { + "lat": 45.8088, + "lon": 9.22609, + "name": "Erba" + }, + { + "lat": 45.77255, + "lon": 4.80326, + "name": "Lyon 09" + }, + { + "lat": 49.91985, + "lon": 9.07596, + "name": "Großostheim" + }, + { + "lat": 29.77415, + "lon": 106.3688, + "name": "Xiema" + } + ], + "question": "Which location is the geographic outlier among: Sesto Fiorentino, Erba, Lyon 09, Großostheim, Xiema?", + "ground_truth": { + "answer": "Xiema", + "outlier_distance_km": 6903.2, + "second_furthest_km": 1871.8, + "clarity_ratio": 3.69, + "median_distance_km": 1642.3, + "distances_to_centroid": { + "Sesto Fiorentino": 1368.2, + "Erba": 1529.6, + "Lyon 09": 1871.8, + "Großostheim": 1642.3, + "Xiema": 6903.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sesto Fiorentino: (43.83°, 11.20°)", + " Erba: (45.81°, 9.23°)", + " Lyon 09: (45.77°, 4.80°)", + " Großostheim: (49.92°, 9.08°)", + " Xiema: (29.77°, 106.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xiema: 6903.2 km from centroid", + " Lyon 09: 1871.8 km from centroid", + " Großostheim: 1642.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xiema", + "FINAL ANSWER: Xiema" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.6653, + "lon": 120.6406, + "name": "Ramos" + }, + { + "lat": 11.16105, + "lon": 77.37398, + "name": "Nerupperichchal" + }, + { + "lat": 17.92851, + "lon": 103.95519, + "name": "Seka" + }, + { + "lat": 34.5735, + "lon": 133.23513, + "name": "Fuchūchō" + }, + { + "lat": -30.29831, + "lon": 29.93772, + "name": "Clydesdale" + } + ], + "question": "Which location is the geographic outlier among: Ramos, Nerupperichchal, Seka, Fuchūchō, Clydesdale?", + "ground_truth": { + "answer": "Clydesdale", + "outlier_distance_km": 8072.2, + "second_furthest_km": 4920.3, + "clarity_ratio": 1.64, + "median_distance_km": 3062.0, + "distances_to_centroid": { + "Ramos": 3062.0, + "Nerupperichchal": 1718.0, + "Seka": 1484.6, + "Fuchūchō": 4920.3, + "Clydesdale": 8072.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ramos: (15.67°, 120.64°)", + " Nerupperichchal: (11.16°, 77.37°)", + " Seka: (17.93°, 103.96°)", + " Fuchūchō: (34.57°, 133.24°)", + " Clydesdale: (-30.30°, 29.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clydesdale: 8072.2 km from centroid", + " Fuchūchō: 4920.3 km from centroid", + " Ramos: 3062.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clydesdale", + "FINAL ANSWER: Clydesdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.82307, + "lon": 77.98381, + "name": "Tirumangalam" + }, + { + "lat": 3.02938, + "lon": 101.74714, + "name": "Kampung Baru Balakong" + }, + { + "lat": 11.16669, + "lon": 77.33502, + "name": "Chettipālaiyam" + }, + { + "lat": 33.14916, + "lon": 75.54746, + "name": "Doda" + }, + { + "lat": -27.02611, + "lon": -50.92139, + "name": "Fraiburgo" + } + ], + "question": "Which location is the geographic outlier among: Tirumangalam, Kampung Baru Balakong, Chettipālaiyam, Doda, Fraiburgo?", + "ground_truth": { + "answer": "Fraiburgo", + "outlier_distance_km": 12019.4, + "second_furthest_km": 5043.0, + "clarity_ratio": 2.38, + "median_distance_km": 3610.3, + "distances_to_centroid": { + "Tirumangalam": 2420.2, + "Kampung Baru Balakong": 5043.0, + "Chettipālaiyam": 2377.0, + "Doda": 3610.3, + "Fraiburgo": 12019.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tirumangalam: (9.82°, 77.98°)", + " Kampung Baru Balakong: (3.03°, 101.75°)", + " Chettipālaiyam: (11.17°, 77.34°)", + " Doda: (33.15°, 75.55°)", + " Fraiburgo: (-27.03°, -50.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fraiburgo: 12019.4 km from centroid", + " Kampung Baru Balakong: 5043.0 km from centroid", + " Doda: 3610.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fraiburgo", + "FINAL ANSWER: Fraiburgo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 59.70056, + "lon": 30.78472, + "name": "Nikol’skoye" + }, + { + "lat": 52.77917, + "lon": 6.90694, + "name": "Emmen" + }, + { + "lat": 47.1069, + "lon": 39.41486, + "name": "Azov" + }, + { + "lat": 53.55173, + "lon": 9.88632, + "name": "Othmarschen" + }, + { + "lat": 26.538, + "lon": 99.91715, + "name": "Jinhua" + } + ], + "question": "Which location is the geographic outlier among: Nikol’skoye, Emmen, Azov, Othmarschen, Jinhua?", + "ground_truth": { + "answer": "Jinhua", + "outlier_distance_km": 5842.8, + "second_furthest_km": 2209.9, + "clarity_ratio": 2.64, + "median_distance_km": 2018.3, + "distances_to_centroid": { + "Nikol’skoye": 1376.4, + "Emmen": 2209.9, + "Azov": 178.3, + "Othmarschen": 2018.3, + "Jinhua": 5842.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nikol’skoye: (59.70°, 30.78°)", + " Emmen: (52.78°, 6.91°)", + " Azov: (47.11°, 39.41°)", + " Othmarschen: (53.55°, 9.89°)", + " Jinhua: (26.54°, 99.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jinhua: 5842.8 km from centroid", + " Emmen: 2209.9 km from centroid", + " Othmarschen: 2018.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jinhua", + "FINAL ANSWER: Jinhua" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -27.87083, + "lon": -54.48139, + "name": "Santa Rosa" + } + ], + "question": "Which location is the geographic outlier among: Clayton, Cheltenham, Scarborough, Palmerston, Santa Rosa?", + "ground_truth": { + "answer": "Santa Rosa", + "outlier_distance_km": 12915.6, + "second_furthest_km": 4536.5, + "clarity_ratio": 2.85, + "median_distance_km": 4530.2, + "distances_to_centroid": { + "Clayton": 4536.5, + "Cheltenham": 4530.2, + "Scarborough": 1856.7, + "Palmerston": 4032.0, + "Santa Rosa": 12915.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Clayton: (-37.92°, 145.12°)", + " Cheltenham: (-37.97°, 145.05°)", + " Scarborough: (-31.90°, 115.76°)", + " Palmerston: (-12.49°, 130.98°)", + " Santa Rosa: (-27.87°, -54.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Rosa: 12915.6 km from centroid", + " Clayton: 4536.5 km from centroid", + " Cheltenham: 4530.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Rosa", + "FINAL ANSWER: Santa Rosa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.78329, + "lon": -79.35364, + "name": "Don Valley Village" + }, + { + "lat": 48.0974, + "lon": -77.79737, + "name": "Val-d'Or" + }, + { + "lat": 38.80033, + "lon": -90.62651, + "name": "Saint Peters" + }, + { + "lat": 40.30428, + "lon": -74.10042, + "name": "Tinton Falls" + }, + { + "lat": -4.62778, + "lon": -43.47056, + "name": "Aldeias Altas" + } + ], + "question": "Which location is the geographic outlier among: Don Valley Village, Val-d'Or, Saint Peters, Tinton Falls, Aldeias Altas?", + "ground_truth": { + "answer": "Aldeias Altas", + "outlier_distance_km": 5240.6, + "second_furthest_km": 1695.2, + "clarity_ratio": 3.09, + "median_distance_km": 1690.7, + "distances_to_centroid": { + "Don Valley Village": 1289.4, + "Val-d'Or": 1695.2, + "Saint Peters": 1690.7, + "Tinton Falls": 787.4, + "Aldeias Altas": 5240.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Don Valley Village: (43.78°, -79.35°)", + " Val-d'Or: (48.10°, -77.80°)", + " Saint Peters: (38.80°, -90.63°)", + " Tinton Falls: (40.30°, -74.10°)", + " Aldeias Altas: (-4.63°, -43.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aldeias Altas: 5240.6 km from centroid", + " Val-d'Or: 1695.2 km from centroid", + " Saint Peters: 1690.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aldeias Altas", + "FINAL ANSWER: Aldeias Altas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.0353, + "lon": -82.38926, + "name": "Temple Terrace" + }, + { + "lat": 49.27997, + "lon": -123.10556, + "name": "Chinatown" + }, + { + "lat": 39.92054, + "lon": -105.08665, + "name": "Broomfield" + }, + { + "lat": 45.67965, + "lon": -111.03856, + "name": "Bozeman" + }, + { + "lat": 52.52956, + "lon": -2.06773, + "name": "Tipton" + } + ], + "question": "Which location is the geographic outlier among: Temple Terrace, Chinatown, Broomfield, Bozeman, Tipton?", + "ground_truth": { + "answer": "Tipton", + "outlier_distance_km": 5916.8, + "second_furthest_km": 2998.4, + "clarity_ratio": 1.97, + "median_distance_km": 2100.2, + "distances_to_centroid": { + "Temple Terrace": 1687.1, + "Chinatown": 2998.4, + "Broomfield": 1726.2, + "Bozeman": 2100.2, + "Tipton": 5916.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Temple Terrace: (28.04°, -82.39°)", + " Chinatown: (49.28°, -123.11°)", + " Broomfield: (39.92°, -105.09°)", + " Bozeman: (45.68°, -111.04°)", + " Tipton: (52.53°, -2.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tipton: 5916.8 km from centroid", + " Chinatown: 2998.4 km from centroid", + " Bozeman: 2100.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tipton", + "FINAL ANSWER: Tipton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -27.25204, + "lon": 152.99226, + "name": "Kallangur" + }, + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + { + "lat": -33.76667, + "lon": 150.81667, + "name": "Mount Druitt" + }, + { + "lat": 51.46593, + "lon": -0.10652, + "name": "Brixton" + } + ], + "question": "Which location is the geographic outlier among: Maryborough, Kallangur, Coogee, Mount Druitt, Brixton?", + "ground_truth": { + "answer": "Brixton", + "outlier_distance_km": 13372.7, + "second_furthest_km": 3735.6, + "clarity_ratio": 3.58, + "median_distance_km": 3692.0, + "distances_to_centroid": { + "Maryborough": 3503.5, + "Kallangur": 3586.7, + "Coogee": 3735.6, + "Mount Druitt": 3692.0, + "Brixton": 13372.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maryborough: (-25.54°, 152.70°)", + " Kallangur: (-27.25°, 152.99°)", + " Coogee: (-33.92°, 151.26°)", + " Mount Druitt: (-33.77°, 150.82°)", + " Brixton: (51.47°, -0.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brixton: 13372.7 km from centroid", + " Coogee: 3735.6 km from centroid", + " Mount Druitt: 3692.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brixton", + "FINAL ANSWER: Brixton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.96775, + "lon": 7.98848, + "name": "Kreuztal" + }, + { + "lat": 56.9083, + "lon": 60.8019, + "name": "Beryozovsky" + }, + { + "lat": 52.09237, + "lon": -1.94887, + "name": "Evesham" + }, + { + "lat": 55.10993, + "lon": 36.61238, + "name": "Obninsk" + }, + { + "lat": -26.25, + "lon": 29.26, + "name": "Kriel" + } + ], + "question": "Which location is the geographic outlier among: Kreuztal, Beryozovsky, Evesham, Obninsk, Kriel?", + "ground_truth": { + "answer": "Kriel", + "outlier_distance_km": 7123.9, + "second_furthest_km": 3287.2, + "clarity_ratio": 2.17, + "median_distance_km": 2722.5, + "distances_to_centroid": { + "Kreuztal": 2069.7, + "Beryozovsky": 3287.2, + "Evesham": 2722.5, + "Obninsk": 2072.3, + "Kriel": 7123.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kreuztal: (50.97°, 7.99°)", + " Beryozovsky: (56.91°, 60.80°)", + " Evesham: (52.09°, -1.95°)", + " Obninsk: (55.11°, 36.61°)", + " Kriel: (-26.25°, 29.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kriel: 7123.9 km from centroid", + " Beryozovsky: 3287.2 km from centroid", + " Evesham: 2722.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kriel", + "FINAL ANSWER: Kriel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -37.75, + "lon": 145.01667, + "name": "Preston" + }, + { + "lat": -33.51889, + "lon": -53.36806, + "name": "Santa Vitória do Palmar" + } + ], + "question": "Which location is the geographic outlier among: Glen Waverley, Maroochydore, Karori, Preston, Santa Vitória do Palmar?", + "ground_truth": { + "answer": "Santa Vitória do Palmar", + "outlier_distance_km": 12218.2, + "second_furthest_km": 5315.6, + "clarity_ratio": 2.3, + "median_distance_km": 3920.4, + "distances_to_centroid": { + "Glen Waverley": 2874.4, + "Maroochydore": 3920.4, + "Karori": 5315.6, + "Preston": 2862.6, + "Santa Vitória do Palmar": 12218.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Waverley: (-37.88°, 145.16°)", + " Maroochydore: (-26.66°, 153.10°)", + " Karori: (-41.28°, 174.74°)", + " Preston: (-37.75°, 145.02°)", + " Santa Vitória do Palmar: (-33.52°, -53.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Vitória do Palmar: 12218.2 km from centroid", + " Karori: 5315.6 km from centroid", + " Maroochydore: 3920.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Vitória do Palmar", + "FINAL ANSWER: Santa Vitória do Palmar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": 50.39138, + "lon": 116.53355, + "name": "Borzya" + } + ], + "question": "Which location is the geographic outlier among: Robina, Eastwood, Morphett Vale, Rockingham, Borzya?", + "ground_truth": { + "answer": "Borzya", + "outlier_distance_km": 7577.1, + "second_furthest_km": 2677.3, + "clarity_ratio": 2.83, + "median_distance_km": 2567.7, + "distances_to_centroid": { + "Robina": 2329.0, + "Eastwood": 2567.7, + "Morphett Vale": 2179.9, + "Rockingham": 2677.3, + "Borzya": 7577.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Eastwood: (-33.79°, 151.08°)", + " Morphett Vale: (-35.13°, 138.52°)", + " Rockingham: (-32.28°, 115.73°)", + " Borzya: (50.39°, 116.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Borzya: 7577.1 km from centroid", + " Rockingham: 2677.3 km from centroid", + " Eastwood: 2567.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Borzya", + "FINAL ANSWER: Borzya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.37299, + "lon": 14.2069, + "name": "Gamboru" + }, + { + "lat": 31.55371, + "lon": 25.15793, + "name": "As Sallūm" + }, + { + "lat": 9.18059, + "lon": 7.17939, + "name": "Suleja" + }, + { + "lat": 8.45, + "lon": 39.28333, + "name": "Wenjī" + }, + { + "lat": 3.58234, + "lon": -76.49146, + "name": "Yumbo" + } + ], + "question": "Which location is the geographic outlier among: Gamboru, As Sallūm, Suleja, Wenjī, Yumbo?", + "ground_truth": { + "answer": "Yumbo", + "outlier_distance_km": 8657.7, + "second_furthest_km": 4115.4, + "clarity_ratio": 2.1, + "median_distance_km": 3146.2, + "distances_to_centroid": { + "Gamboru": 1340.4, + "As Sallūm": 3146.2, + "Suleja": 720.3, + "Wenjī": 4115.4, + "Yumbo": 8657.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gamboru: (12.37°, 14.21°)", + " As Sallūm: (31.55°, 25.16°)", + " Suleja: (9.18°, 7.18°)", + " Wenjī: (8.45°, 39.28°)", + " Yumbo: (3.58°, -76.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yumbo: 8657.7 km from centroid", + " Wenjī: 4115.4 km from centroid", + " As Sallūm: 3146.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yumbo", + "FINAL ANSWER: Yumbo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.97583, + "lon": 108.48306, + "name": "Kuningan" + }, + { + "lat": 35.99472, + "lon": 119.3975, + "name": "Zhucheng" + }, + { + "lat": 22.70722, + "lon": 110.34917, + "name": "Beiliu" + }, + { + "lat": 19.11393, + "lon": 84.68721, + "name": "Ichchāpuram" + }, + { + "lat": 7.32275, + "lon": 9.00108, + "name": "Gboko" + } + ], + "question": "Which location is the geographic outlier among: Kuningan, Zhucheng, Beiliu, Ichchāpuram, Gboko?", + "ground_truth": { + "answer": "Gboko", + "outlier_distance_km": 8443.8, + "second_furthest_km": 3973.7, + "clarity_ratio": 2.12, + "median_distance_km": 3499.1, + "distances_to_centroid": { + "Kuningan": 3499.1, + "Zhucheng": 3973.7, + "Beiliu": 2633.1, + "Ichchāpuram": 426.9, + "Gboko": 8443.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kuningan: (-6.98°, 108.48°)", + " Zhucheng: (35.99°, 119.40°)", + " Beiliu: (22.71°, 110.35°)", + " Ichchāpuram: (19.11°, 84.69°)", + " Gboko: (7.32°, 9.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gboko: 8443.8 km from centroid", + " Zhucheng: 3973.7 km from centroid", + " Kuningan: 3499.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gboko", + "FINAL ANSWER: Gboko" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -38.14458, + "lon": 145.12291, + "name": "Frankston" + }, + { + "lat": 6.13833, + "lon": -75.26417, + "name": "Santuario" + } + ], + "question": "Which location is the geographic outlier among: Wollongong city centre, Taylors Hill, Truganina, Frankston, Santuario?", + "ground_truth": { + "answer": "Santuario", + "outlier_distance_km": 17524.5, + "second_furthest_km": 4639.1, + "clarity_ratio": 3.78, + "median_distance_km": 4109.4, + "distances_to_centroid": { + "Wollongong city centre": 4639.1, + "Taylors Hill": 4075.4, + "Truganina": 4075.4, + "Frankston": 4109.4, + "Santuario": 17524.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Taylors Hill: (-37.71°, 144.75°)", + " Truganina: (-37.82°, 144.75°)", + " Frankston: (-38.14°, 145.12°)", + " Santuario: (6.14°, -75.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santuario: 17524.5 km from centroid", + " Wollongong city centre: 4639.1 km from centroid", + " Frankston: 4109.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santuario", + "FINAL ANSWER: Santuario" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.00092, + "lon": -49.5068, + "name": "Breu Branco" + }, + { + "lat": -31.6501, + "lon": -63.91165, + "name": "Río Segundo" + }, + { + "lat": -23.10417, + "lon": -55.22583, + "name": "Amambai" + }, + { + "lat": -17.83917, + "lon": -40.35389, + "name": "Nanuque" + }, + { + "lat": 42.13615, + "lon": -0.4087, + "name": "Huesca" + } + ], + "question": "Which location is the geographic outlier among: Breu Branco, Río Segundo, Amambai, Nanuque, Huesca?", + "ground_truth": { + "answer": "Huesca", + "outlier_distance_km": 6882.3, + "second_furthest_km": 3578.3, + "clarity_ratio": 1.92, + "median_distance_km": 2299.3, + "distances_to_centroid": { + "Breu Branco": 903.1, + "Río Segundo": 3578.3, + "Amambai": 2299.3, + "Nanuque": 1228.5, + "Huesca": 6882.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Breu Branco: (-4.00°, -49.51°)", + " Río Segundo: (-31.65°, -63.91°)", + " Amambai: (-23.10°, -55.23°)", + " Nanuque: (-17.84°, -40.35°)", + " Huesca: (42.14°, -0.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huesca: 6882.3 km from centroid", + " Río Segundo: 3578.3 km from centroid", + " Amambai: 2299.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huesca", + "FINAL ANSWER: Huesca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.50194, + "lon": -36.02278, + "name": "Atalaia" + }, + { + "lat": -7.67167, + "lon": -36.88, + "name": "Sumé" + }, + { + "lat": -11.95972, + "lon": -40.16806, + "name": "Baixa Grande" + }, + { + "lat": -15.56833, + "lon": -40.42306, + "name": "Macarani" + }, + { + "lat": 30.56412, + "lon": 31.93386, + "name": "Al Qaşşāşīn" + } + ], + "question": "Which location is the geographic outlier among: Atalaia, Sumé, Baixa Grande, Macarani, Al Qaşşāşīn?", + "ground_truth": { + "answer": "Al Qaşşāşīn", + "outlier_distance_km": 7014.0, + "second_furthest_km": 2262.7, + "clarity_ratio": 3.1, + "median_distance_km": 2020.2, + "distances_to_centroid": { + "Atalaia": 1491.6, + "Sumé": 1491.8, + "Baixa Grande": 2020.2, + "Macarani": 2262.7, + "Al Qaşşāşīn": 7014.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Atalaia: (-9.50°, -36.02°)", + " Sumé: (-7.67°, -36.88°)", + " Baixa Grande: (-11.96°, -40.17°)", + " Macarani: (-15.57°, -40.42°)", + " Al Qaşşāşīn: (30.56°, 31.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Qaşşāşīn: 7014.0 km from centroid", + " Macarani: 2262.7 km from centroid", + " Baixa Grande: 2020.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Qaşşāşīn", + "FINAL ANSWER: Al Qaşşāşīn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.13333, + "lon": 39.23333, + "name": "Īteya" + }, + { + "lat": -25.43321, + "lon": 31.95478, + "name": "Komatipoort" + }, + { + "lat": 10.55, + "lon": 37.48333, + "name": "Dembech’a" + }, + { + "lat": -1.4275, + "lon": 36.6865, + "name": "Kiserian" + }, + { + "lat": -3.12873, + "lon": -58.15501, + "name": "Urucurituba" + } + ], + "question": "Which location is the geographic outlier among: Īteya, Komatipoort, Dembech’a, Kiserian, Urucurituba?", + "ground_truth": { + "answer": "Urucurituba", + "outlier_distance_km": 8395.4, + "second_furthest_km": 3009.0, + "clarity_ratio": 2.79, + "median_distance_km": 2678.8, + "distances_to_centroid": { + "Īteya": 2678.8, + "Komatipoort": 3009.0, + "Dembech’a": 2636.1, + "Kiserian": 2140.9, + "Urucurituba": 8395.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Īteya: (8.13°, 39.23°)", + " Komatipoort: (-25.43°, 31.95°)", + " Dembech’a: (10.55°, 37.48°)", + " Kiserian: (-1.43°, 36.69°)", + " Urucurituba: (-3.13°, -58.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Urucurituba: 8395.4 km from centroid", + " Komatipoort: 3009.0 km from centroid", + " Īteya: 2678.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Urucurituba", + "FINAL ANSWER: Urucurituba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.03103, + "lon": 31.11109, + "name": "Kirdāsah" + }, + { + "lat": 11.91667, + "lon": 37.7, + "name": "Werota" + }, + { + "lat": -30.99766, + "lon": 26.32862, + "name": "Burgersdorp" + }, + { + "lat": 6.16667, + "lon": 38.2, + "name": "Yirga Ch’efē" + }, + { + "lat": 33.49567, + "lon": -88.42726, + "name": "Columbus" + } + ], + "question": "Which location is the geographic outlier among: Kirdāsah, Werota, Burgersdorp, Yirga Ch’efē, Columbus?", + "ground_truth": { + "answer": "Columbus", + "outlier_distance_km": 10064.1, + "second_furthest_km": 4932.7, + "clarity_ratio": 2.04, + "median_distance_km": 3244.6, + "distances_to_centroid": { + "Kirdāsah": 3187.1, + "Werota": 3139.3, + "Burgersdorp": 4932.7, + "Yirga Ch’efē": 3244.6, + "Columbus": 10064.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kirdāsah: (30.03°, 31.11°)", + " Werota: (11.92°, 37.70°)", + " Burgersdorp: (-31.00°, 26.33°)", + " Yirga Ch’efē: (6.17°, 38.20°)", + " Columbus: (33.50°, -88.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Columbus: 10064.1 km from centroid", + " Burgersdorp: 4932.7 km from centroid", + " Yirga Ch’efē: 3244.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Columbus", + "FINAL ANSWER: Columbus" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -38.11342, + "lon": 145.28326, + "name": "Cranbourne" + }, + { + "lat": -37.83834, + "lon": 144.99149, + "name": "South Yarra" + }, + { + "lat": -0.77071, + "lon": -47.45176, + "name": "Maracanã" + } + ], + "question": "Which location is the geographic outlier among: Wollongong city centre, Ellenbrook, Cranbourne, South Yarra, Maracanã?", + "ground_truth": { + "answer": "Maracanã", + "outlier_distance_km": 15403.3, + "second_furthest_km": 4641.9, + "clarity_ratio": 3.32, + "median_distance_km": 4123.7, + "distances_to_centroid": { + "Wollongong city centre": 4641.9, + "Ellenbrook": 1393.4, + "Cranbourne": 4123.7, + "South Yarra": 4097.3, + "Maracanã": 15403.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Cranbourne: (-38.11°, 145.28°)", + " South Yarra: (-37.84°, 144.99°)", + " Maracanã: (-0.77°, -47.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maracanã: 15403.3 km from centroid", + " Wollongong city centre: 4641.9 km from centroid", + " Cranbourne: 4123.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maracanã", + "FINAL ANSWER: Maracanã" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -1.28333, + "lon": 36.81667, + "name": "Nairobi" + } + ], + "question": "Which location is the geographic outlier among: Glen Waverley, Carrum Downs, Palmerston, Reservoir, Nairobi?", + "ground_truth": { + "answer": "Nairobi", + "outlier_distance_km": 9325.0, + "second_furthest_km": 2697.4, + "clarity_ratio": 3.46, + "median_distance_km": 2686.8, + "distances_to_centroid": { + "Glen Waverley": 2686.8, + "Carrum Downs": 2697.4, + "Palmerston": 1808.3, + "Reservoir": 2666.3, + "Nairobi": 9325.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Waverley: (-37.88°, 145.16°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Palmerston: (-12.49°, 130.98°)", + " Reservoir: (-37.72°, 145.00°)", + " Nairobi: (-1.28°, 36.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nairobi: 9325.0 km from centroid", + " Carrum Downs: 2697.4 km from centroid", + " Glen Waverley: 2686.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nairobi", + "FINAL ANSWER: Nairobi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.08722, + "lon": -45.29361, + "name": "Santo Antônio do Monte" + }, + { + "lat": -23.49032, + "lon": -46.6387, + "name": "Santana" + }, + { + "lat": -6.78889, + "lon": -39.29583, + "name": "Várzea Alegre" + }, + { + "lat": 6.28535, + "lon": -75.33385, + "name": "San Vicente" + }, + { + "lat": -33.86785, + "lon": 151.20732, + "name": "Sydney" + } + ], + "question": "Which location is the geographic outlier among: Santo Antônio do Monte, Santana, Várzea Alegre, San Vicente, Sydney?", + "ground_truth": { + "answer": "Sydney", + "outlier_distance_km": 14203.9, + "second_furthest_km": 7480.5, + "clarity_ratio": 1.9, + "median_distance_km": 3818.6, + "distances_to_centroid": { + "Santo Antônio do Monte": 3650.4, + "Santana": 3818.6, + "Várzea Alegre": 3226.2, + "San Vicente": 7480.5, + "Sydney": 14203.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santo Antônio do Monte: (-20.09°, -45.29°)", + " Santana: (-23.49°, -46.64°)", + " Várzea Alegre: (-6.79°, -39.30°)", + " San Vicente: (6.29°, -75.33°)", + " Sydney: (-33.87°, 151.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sydney: 14203.9 km from centroid", + " San Vicente: 7480.5 km from centroid", + " Santana: 3818.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sydney", + "FINAL ANSWER: Sydney" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.02413, + "lon": 4.83887, + "name": "Beaune" + }, + { + "lat": 48.62423, + "lon": 9.82736, + "name": "Geislingen an der Steige" + }, + { + "lat": 55.42018, + "lon": 55.54212, + "name": "Birsk" + }, + { + "lat": 38.99042, + "lon": -0.51852, + "name": "Xàtiva" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + } + ], + "question": "Which location is the geographic outlier among: Beaune, Geislingen an der Steige, Birsk, Xàtiva, Dunedin?", + "ground_truth": { + "answer": "Dunedin", + "outlier_distance_km": 14716.1, + "second_furthest_km": 4564.7, + "clarity_ratio": 3.22, + "median_distance_km": 4223.5, + "distances_to_centroid": { + "Beaune": 4223.5, + "Geislingen an der Steige": 3916.9, + "Birsk": 3016.0, + "Xàtiva": 4564.7, + "Dunedin": 14716.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beaune: (47.02°, 4.84°)", + " Geislingen an der Steige: (48.62°, 9.83°)", + " Birsk: (55.42°, 55.54°)", + " Xàtiva: (38.99°, -0.52°)", + " Dunedin: (-45.87°, 170.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dunedin: 14716.1 km from centroid", + " Xàtiva: 4564.7 km from centroid", + " Beaune: 4223.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dunedin", + "FINAL ANSWER: Dunedin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.32389, + "lon": -50.61556, + "name": "Telêmaco Borba" + }, + { + "lat": -4.39143, + "lon": -59.58864, + "name": "Borba" + }, + { + "lat": -6.75639, + "lon": -43.02417, + "name": "Barão de Grajaú" + }, + { + "lat": -32.84043, + "lon": -70.95623, + "name": "Llaillay" + }, + { + "lat": 25.128, + "lon": 113.35041, + "name": "Lecheng" + } + ], + "question": "Which location is the geographic outlier among: Telêmaco Borba, Borba, Barão de Grajaú, Llaillay, Lecheng?", + "ground_truth": { + "answer": "Lecheng", + "outlier_distance_km": 14968.9, + "second_furthest_km": 5676.0, + "clarity_ratio": 2.64, + "median_distance_km": 4159.1, + "distances_to_centroid": { + "Telêmaco Borba": 3486.5, + "Borba": 4159.1, + "Barão de Grajaú": 2307.5, + "Llaillay": 5676.0, + "Lecheng": 14968.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Telêmaco Borba: (-24.32°, -50.62°)", + " Borba: (-4.39°, -59.59°)", + " Barão de Grajaú: (-6.76°, -43.02°)", + " Llaillay: (-32.84°, -70.96°)", + " Lecheng: (25.13°, 113.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lecheng: 14968.9 km from centroid", + " Llaillay: 5676.0 km from centroid", + " Borba: 4159.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lecheng", + "FINAL ANSWER: Lecheng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.07643, + "lon": 77.00449, + "name": "Srvanampatti" + }, + { + "lat": 12.62091, + "lon": 80.19331, + "name": "Mahabalipuram" + }, + { + "lat": 18.23454, + "lon": 75.69275, + "name": "Barshi" + }, + { + "lat": 38.03333, + "lon": 106.3, + "name": "Chongxing" + }, + { + "lat": 58.36848, + "lon": 45.51622, + "name": "Shar’ya" + } + ], + "question": "Which location is the geographic outlier among: Srvanampatti, Mahabalipuram, Barshi, Chongxing, Shar’ya?", + "ground_truth": { + "answer": "Shar’ya", + "outlier_distance_km": 4187.0, + "second_furthest_km": 2958.8, + "clarity_ratio": 1.42, + "median_distance_km": 1844.8, + "distances_to_centroid": { + "Srvanampatti": 1844.8, + "Mahabalipuram": 1706.8, + "Barshi": 1056.5, + "Chongxing": 2958.8, + "Shar’ya": 4187.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Srvanampatti: (11.08°, 77.00°)", + " Mahabalipuram: (12.62°, 80.19°)", + " Barshi: (18.23°, 75.69°)", + " Chongxing: (38.03°, 106.30°)", + " Shar’ya: (58.37°, 45.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shar’ya: 4187.0 km from centroid", + " Chongxing: 2958.8 km from centroid", + " Srvanampatti: 1844.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shar’ya", + "FINAL ANSWER: Shar’ya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.56848, + "lon": -1.3187, + "name": "Stockton-on-Tees" + }, + { + "lat": 52.6461, + "lon": 9.22086, + "name": "Nienburg" + }, + { + "lat": 52.6425, + "lon": 5.05972, + "name": "Hoorn" + }, + { + "lat": 52.08226, + "lon": 0.43891, + "name": "Haverhill" + }, + { + "lat": 7.49748, + "lon": 5.23041, + "name": "Ikere-Ekiti" + } + ], + "question": "Which location is the geographic outlier among: Stockton-on-Tees, Nienburg, Hoorn, Haverhill, Ikere-Ekiti?", + "ground_truth": { + "answer": "Ikere-Ekiti", + "outlier_distance_km": 4049.0, + "second_furthest_km": 1242.1, + "clarity_ratio": 3.26, + "median_distance_km": 1054.7, + "distances_to_centroid": { + "Stockton-on-Tees": 1242.1, + "Nienburg": 1054.7, + "Hoorn": 978.5, + "Haverhill": 943.2, + "Ikere-Ekiti": 4049.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stockton-on-Tees: (54.57°, -1.32°)", + " Nienburg: (52.65°, 9.22°)", + " Hoorn: (52.64°, 5.06°)", + " Haverhill: (52.08°, 0.44°)", + " Ikere-Ekiti: (7.50°, 5.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ikere-Ekiti: 4049.0 km from centroid", + " Stockton-on-Tees: 1242.1 km from centroid", + " Nienburg: 1054.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ikere-Ekiti", + "FINAL ANSWER: Ikere-Ekiti" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + }, + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + }, + { + "lat": -33.78269, + "lon": 151.04888, + "name": "Carlingford" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": 7.49748, + "lon": 5.23041, + "name": "Ikere-Ekiti" + } + ], + "question": "Which location is the geographic outlier among: Cessnock, Surfers Paradise, Carlingford, Townsville, Ikere-Ekiti?", + "ground_truth": { + "answer": "Ikere-Ekiti", + "outlier_distance_km": 13033.7, + "second_furthest_km": 3295.2, + "clarity_ratio": 3.96, + "median_distance_km": 3206.0, + "distances_to_centroid": { + "Cessnock": 3202.3, + "Surfers Paradise": 3295.2, + "Carlingford": 3206.0, + "Townsville": 2638.5, + "Ikere-Ekiti": 13033.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cessnock: (-32.83°, 151.36°)", + " Surfers Paradise: (-28.00°, 153.43°)", + " Carlingford: (-33.78°, 151.05°)", + " Townsville: (-19.27°, 146.81°)", + " Ikere-Ekiti: (7.50°, 5.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ikere-Ekiti: 13033.7 km from centroid", + " Surfers Paradise: 3295.2 km from centroid", + " Carlingford: 3206.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ikere-Ekiti", + "FINAL ANSWER: Ikere-Ekiti" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.85095, + "lon": 75.54224, + "name": "Depālpur" + }, + { + "lat": 8.33702, + "lon": 77.86776, + "name": "Tisaiyanvilai" + }, + { + "lat": 35.28361, + "lon": 139.66722, + "name": "Yokosuka" + }, + { + "lat": 7.16985, + "lon": 124.20836, + "name": "Dinaig" + }, + { + "lat": -15.80778, + "lon": -42.23306, + "name": "Taiobeiras" + } + ], + "question": "Which location is the geographic outlier among: Depālpur, Tisaiyanvilai, Yokosuka, Dinaig, Taiobeiras?", + "ground_truth": { + "answer": "Taiobeiras", + "outlier_distance_km": 13241.9, + "second_furthest_km": 6975.6, + "clarity_ratio": 1.9, + "median_distance_km": 5413.5, + "distances_to_centroid": { + "Depālpur": 1256.0, + "Tisaiyanvilai": 476.3, + "Yokosuka": 6975.6, + "Dinaig": 5413.5, + "Taiobeiras": 13241.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Depālpur: (22.85°, 75.54°)", + " Tisaiyanvilai: (8.34°, 77.87°)", + " Yokosuka: (35.28°, 139.67°)", + " Dinaig: (7.17°, 124.21°)", + " Taiobeiras: (-15.81°, -42.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taiobeiras: 13241.9 km from centroid", + " Yokosuka: 6975.6 km from centroid", + " Dinaig: 5413.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taiobeiras", + "FINAL ANSWER: Taiobeiras" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75, + "lon": 145.01667, + "name": "Preston" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": -37.80639, + "lon": 145.03086, + "name": "Kew" + }, + { + "lat": 49.62612, + "lon": -1.64349, + "name": "Octeville" + } + ], + "question": "Which location is the geographic outlier among: Preston, Thornlie, Timaru, Kew, Octeville?", + "ground_truth": { + "answer": "Octeville", + "outlier_distance_km": 13640.3, + "second_furthest_km": 5764.9, + "clarity_ratio": 2.37, + "median_distance_km": 3461.0, + "distances_to_centroid": { + "Preston": 3457.2, + "Thornlie": 1290.6, + "Timaru": 5764.9, + "Kew": 3461.0, + "Octeville": 13640.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Preston: (-37.75°, 145.02°)", + " Thornlie: (-32.06°, 115.95°)", + " Timaru: (-44.40°, 171.25°)", + " Kew: (-37.81°, 145.03°)", + " Octeville: (49.63°, -1.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Octeville: 13640.3 km from centroid", + " Timaru: 5764.9 km from centroid", + " Kew: 3461.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Octeville", + "FINAL ANSWER: Octeville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": 43.38285, + "lon": -3.22043, + "name": "Castro-Urdiales" + } + ], + "question": "Which location is the geographic outlier among: Blenheim, Casula, Carrum Downs, Saint Albans, Castro-Urdiales?", + "ground_truth": { + "answer": "Castro-Urdiales", + "outlier_distance_km": 14478.1, + "second_furthest_km": 5278.1, + "clarity_ratio": 2.74, + "median_distance_km": 3115.3, + "distances_to_centroid": { + "Blenheim": 5278.1, + "Casula": 3115.3, + "Carrum Downs": 2854.3, + "Saint Albans": 2804.6, + "Castro-Urdiales": 14478.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blenheim: (-41.52°, 173.95°)", + " Casula: (-33.95°, 150.90°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Saint Albans: (-37.73°, 144.80°)", + " Castro-Urdiales: (43.38°, -3.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castro-Urdiales: 14478.1 km from centroid", + " Blenheim: 5278.1 km from centroid", + " Casula: 3115.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castro-Urdiales", + "FINAL ANSWER: Castro-Urdiales" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + { + "lat": 39.03483, + "lon": -76.90747, + "name": "Beltsville" + } + ], + "question": "Which location is the geographic outlier among: Glen Waverley, Springfield Lakes, Australind, Wyndham Vale, Beltsville?", + "ground_truth": { + "answer": "Beltsville", + "outlier_distance_km": 17751.0, + "second_furthest_km": 5791.6, + "clarity_ratio": 3.06, + "median_distance_km": 5114.5, + "distances_to_centroid": { + "Glen Waverley": 5114.5, + "Springfield Lakes": 5791.6, + "Australind": 2456.4, + "Wyndham Vale": 5067.9, + "Beltsville": 17751.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Waverley: (-37.88°, 145.16°)", + " Springfield Lakes: (-27.67°, 152.92°)", + " Australind: (-33.28°, 115.72°)", + " Wyndham Vale: (-37.89°, 144.62°)", + " Beltsville: (39.03°, -76.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Beltsville: 17751.0 km from centroid", + " Springfield Lakes: 5791.6 km from centroid", + " Glen Waverley: 5114.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Beltsville", + "FINAL ANSWER: Beltsville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.21145, + "lon": 79.05665, + "name": "Wazīrganj" + }, + { + "lat": 21.61675, + "lon": 73.02759, + "name": "Anklesvar INA" + }, + { + "lat": 23.66505, + "lon": 85.30353, + "name": "Patrātu" + }, + { + "lat": 27.11716, + "lon": 114.97927, + "name": "Ji’an" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + } + ], + "question": "Which location is the geographic outlier among: Wazīrganj, Anklesvar INA, Patrātu, Ji’an, Napier?", + "ground_truth": { + "answer": "Napier", + "outlier_distance_km": 9304.1, + "second_furthest_km": 3636.3, + "clarity_ratio": 2.56, + "median_distance_km": 3300.1, + "distances_to_centroid": { + "Wazīrganj": 3300.1, + "Anklesvar INA": 3636.3, + "Patrātu": 2513.9, + "Ji’an": 1909.9, + "Napier": 9304.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wazīrganj: (28.21°, 79.06°)", + " Anklesvar INA: (21.62°, 73.03°)", + " Patrātu: (23.67°, 85.30°)", + " Ji’an: (27.12°, 114.98°)", + " Napier: (-39.49°, 176.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Napier: 9304.1 km from centroid", + " Anklesvar INA: 3636.3 km from centroid", + " Wazīrganj: 3300.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Napier", + "FINAL ANSWER: Napier" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + }, + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": 32.88096, + "lon": -97.15501, + "name": "Colleyville" + } + ], + "question": "Which location is the geographic outlier among: Strathfield, Doreen, Hastings, Saint Ives, Colleyville?", + "ground_truth": { + "answer": "Colleyville", + "outlier_distance_km": 17512.2, + "second_furthest_km": 6892.0, + "clarity_ratio": 2.54, + "median_distance_km": 4622.1, + "distances_to_centroid": { + "Strathfield": 4615.8, + "Doreen": 4144.2, + "Hastings": 6892.0, + "Saint Ives": 4622.1, + "Colleyville": 17512.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Strathfield: (-33.88°, 151.08°)", + " Doreen: (-37.60°, 145.15°)", + " Hastings: (-39.64°, 176.85°)", + " Saint Ives: (-33.73°, 151.16°)", + " Colleyville: (32.88°, -97.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Colleyville: 17512.2 km from centroid", + " Hastings: 6892.0 km from centroid", + " Saint Ives: 4622.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Colleyville", + "FINAL ANSWER: Colleyville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.44734, + "lon": -84.14686, + "name": "McDonough" + }, + { + "lat": 37.82159, + "lon": -121.99996, + "name": "Danville" + }, + { + "lat": 40.94454, + "lon": -74.07542, + "name": "Paramus" + }, + { + "lat": 20.88136, + "lon": -89.74728, + "name": "Umán" + }, + { + "lat": 55.86486, + "lon": 38.44853, + "name": "Noginsk" + } + ], + "question": "Which location is the geographic outlier among: McDonough, Danville, Paramus, Umán, Noginsk?", + "ground_truth": { + "answer": "Noginsk", + "outlier_distance_km": 7425.3, + "second_furthest_km": 4816.6, + "clarity_ratio": 1.54, + "median_distance_km": 2934.1, + "distances_to_centroid": { + "McDonough": 1680.5, + "Danville": 4816.6, + "Paramus": 754.0, + "Umán": 2934.1, + "Noginsk": 7425.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " McDonough: (33.45°, -84.15°)", + " Danville: (37.82°, -122.00°)", + " Paramus: (40.94°, -74.08°)", + " Umán: (20.88°, -89.75°)", + " Noginsk: (55.86°, 38.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Noginsk: 7425.3 km from centroid", + " Danville: 4816.6 km from centroid", + " Umán: 2934.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Noginsk", + "FINAL ANSWER: Noginsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + }, + { + "lat": -30.29626, + "lon": 153.11351, + "name": "Coffs Harbour" + }, + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + }, + { + "lat": -29.81292, + "lon": 30.63646, + "name": "Mpumalanga" + } + ], + "question": "Which location is the geographic outlier among: Umina Beach, Coffs Harbour, Mernda, West Pennant Hills, Mpumalanga?", + "ground_truth": { + "answer": "Mpumalanga", + "outlier_distance_km": 8726.8, + "second_furthest_km": 2554.4, + "clarity_ratio": 3.42, + "median_distance_km": 2326.3, + "distances_to_centroid": { + "Umina Beach": 2326.3, + "Coffs Harbour": 2554.4, + "Mernda": 1782.4, + "West Pennant Hills": 2299.5, + "Mpumalanga": 8726.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Umina Beach: (-33.52°, 151.31°)", + " Coffs Harbour: (-30.30°, 153.11°)", + " Mernda: (-37.60°, 145.10°)", + " West Pennant Hills: (-33.75°, 151.05°)", + " Mpumalanga: (-29.81°, 30.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mpumalanga: 8726.8 km from centroid", + " Coffs Harbour: 2554.4 km from centroid", + " Umina Beach: 2326.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mpumalanga", + "FINAL ANSWER: Mpumalanga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.5392, + "lon": 103.8092, + "name": "Johor Jaya" + }, + { + "lat": -8.6199, + "lon": 122.2111, + "name": "Maumere" + }, + { + "lat": 5.9258, + "lon": 116.06094, + "name": "Putatan" + }, + { + "lat": 31.18874, + "lon": 75.99495, + "name": "Banga" + }, + { + "lat": 31.30862, + "lon": -110.94217, + "name": "Nogales" + } + ], + "question": "Which location is the geographic outlier among: Johor Jaya, Maumere, Putatan, Banga, Nogales?", + "ground_truth": { + "answer": "Nogales", + "outlier_distance_km": 15101.6, + "second_furthest_km": 7106.9, + "clarity_ratio": 2.12, + "median_distance_km": 6030.4, + "distances_to_centroid": { + "Johor Jaya": 4819.7, + "Maumere": 7106.9, + "Putatan": 6030.4, + "Banga": 2580.4, + "Nogales": 15101.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Johor Jaya: (1.54°, 103.81°)", + " Maumere: (-8.62°, 122.21°)", + " Putatan: (5.93°, 116.06°)", + " Banga: (31.19°, 75.99°)", + " Nogales: (31.31°, -110.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nogales: 15101.6 km from centroid", + " Maumere: 7106.9 km from centroid", + " Putatan: 6030.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nogales", + "FINAL ANSWER: Nogales" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + { + "lat": 30.9616, + "lon": 31.24069, + "name": "Samannūd" + } + ], + "question": "Which location is the geographic outlier among: Wheelers Hill, Hornsby, Shepparton, Masterton, Samannūd?", + "ground_truth": { + "answer": "Samannūd", + "outlier_distance_km": 12094.5, + "second_furthest_km": 4665.5, + "clarity_ratio": 2.59, + "median_distance_km": 2363.0, + "distances_to_centroid": { + "Wheelers Hill": 2165.1, + "Hornsby": 2363.0, + "Shepparton": 2068.7, + "Masterton": 4665.5, + "Samannūd": 12094.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Hornsby: (-33.70°, 151.10°)", + " Shepparton: (-36.38°, 145.40°)", + " Masterton: (-40.96°, 175.66°)", + " Samannūd: (30.96°, 31.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Samannūd: 12094.5 km from centroid", + " Masterton: 4665.5 km from centroid", + " Hornsby: 2363.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Samannūd", + "FINAL ANSWER: Samannūd" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.78269, + "lon": 151.04888, + "name": "Carlingford" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -33.90034, + "lon": 151.05563, + "name": "Greenacre" + }, + { + "lat": 51.39462, + "lon": 8.57146, + "name": "Brilon" + } + ], + "question": "Which location is the geographic outlier among: Carlingford, Campsie, Port Macquarie, Greenacre, Brilon?", + "ground_truth": { + "answer": "Brilon", + "outlier_distance_km": 13101.1, + "second_furthest_km": 3462.1, + "clarity_ratio": 3.78, + "median_distance_km": 3424.8, + "distances_to_centroid": { + "Carlingford": 3413.7, + "Campsie": 3424.8, + "Port Macquarie": 3462.1, + "Greenacre": 3420.3, + "Brilon": 13101.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlingford: (-33.78°, 151.05°)", + " Campsie: (-33.91°, 151.10°)", + " Port Macquarie: (-31.43°, 152.91°)", + " Greenacre: (-33.90°, 151.06°)", + " Brilon: (51.39°, 8.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brilon: 13101.1 km from centroid", + " Port Macquarie: 3462.1 km from centroid", + " Campsie: 3424.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brilon", + "FINAL ANSWER: Brilon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.14621, + "lon": 140.31507, + "name": "Katsuura" + }, + { + "lat": 13.68333, + "lon": 79.35, + "name": "Tirumala" + }, + { + "lat": 16.78854, + "lon": 80.84593, + "name": "Nūzvīd" + }, + { + "lat": 38.15389, + "lon": 140.27361, + "name": "Kaminoyama" + }, + { + "lat": -25.43998, + "lon": -54.40161, + "name": "Santa Terezinha de Itaipu" + } + ], + "question": "Which location is the geographic outlier among: Katsuura, Tirumala, Nūzvīd, Kaminoyama, Santa Terezinha de Itaipu?", + "ground_truth": { + "answer": "Santa Terezinha de Itaipu", + "outlier_distance_km": 14895.7, + "second_furthest_km": 6593.5, + "clarity_ratio": 2.26, + "median_distance_km": 6580.0, + "distances_to_centroid": { + "Katsuura": 6580.0, + "Tirumala": 313.6, + "Nūzvīd": 401.0, + "Kaminoyama": 6593.5, + "Santa Terezinha de Itaipu": 14895.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Katsuura: (35.15°, 140.32°)", + " Tirumala: (13.68°, 79.35°)", + " Nūzvīd: (16.79°, 80.85°)", + " Kaminoyama: (38.15°, 140.27°)", + " Santa Terezinha de Itaipu: (-25.44°, -54.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Terezinha de Itaipu: 14895.7 km from centroid", + " Kaminoyama: 6593.5 km from centroid", + " Katsuura: 6580.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Terezinha de Itaipu", + "FINAL ANSWER: Santa Terezinha de Itaipu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.65105, + "lon": 7.82089, + "name": "Schopfheim" + }, + { + "lat": 51.11112, + "lon": 13.91199, + "name": "Radeberg" + }, + { + "lat": 45.9836, + "lon": 12.70038, + "name": "Cordenons" + }, + { + "lat": 40.28419, + "lon": -3.79415, + "name": "Fuenlabrada" + }, + { + "lat": 8.27338, + "lon": 5.83526, + "name": "Isanlu-Itedoijowa" + } + ], + "question": "Which location is the geographic outlier among: Schopfheim, Radeberg, Cordenons, Fuenlabrada, Isanlu-Itedoijowa?", + "ground_truth": { + "answer": "Isanlu-Itedoijowa", + "outlier_distance_km": 3382.1, + "second_furthest_km": 1477.8, + "clarity_ratio": 2.29, + "median_distance_km": 1000.6, + "distances_to_centroid": { + "Schopfheim": 1000.6, + "Radeberg": 1477.8, + "Cordenons": 927.1, + "Fuenlabrada": 968.1, + "Isanlu-Itedoijowa": 3382.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Schopfheim: (47.65°, 7.82°)", + " Radeberg: (51.11°, 13.91°)", + " Cordenons: (45.98°, 12.70°)", + " Fuenlabrada: (40.28°, -3.79°)", + " Isanlu-Itedoijowa: (8.27°, 5.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Isanlu-Itedoijowa: 3382.1 km from centroid", + " Radeberg: 1477.8 km from centroid", + " Schopfheim: 1000.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Isanlu-Itedoijowa", + "FINAL ANSWER: Isanlu-Itedoijowa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.33165, + "lon": 136.87042, + "name": "Kōnan" + }, + { + "lat": 21.09687, + "lon": 81.0289, + "name": "Rāj-Nāndgaon" + }, + { + "lat": 21.71974, + "lon": 73.01098, + "name": "Bholav" + }, + { + "lat": 18.86131, + "lon": 72.95257, + "name": "Chanaje" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + } + ], + "question": "Which location is the geographic outlier among: Kōnan, Rāj-Nāndgaon, Bholav, Chanaje, Glen Iris?", + "ground_truth": { + "answer": "Glen Iris", + "outlier_distance_km": 7128.4, + "second_furthest_km": 4388.9, + "clarity_ratio": 1.62, + "median_distance_km": 3247.8, + "distances_to_centroid": { + "Kōnan": 4388.9, + "Rāj-Nāndgaon": 2437.9, + "Bholav": 3247.8, + "Chanaje": 3184.6, + "Glen Iris": 7128.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kōnan: (35.33°, 136.87°)", + " Rāj-Nāndgaon: (21.10°, 81.03°)", + " Bholav: (21.72°, 73.01°)", + " Chanaje: (18.86°, 72.95°)", + " Glen Iris: (-37.87°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glen Iris: 7128.4 km from centroid", + " Kōnan: 4388.9 km from centroid", + " Bholav: 3247.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glen Iris", + "FINAL ANSWER: Glen Iris" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.11357, + "lon": -0.86245, + "name": "Bordon" + }, + { + "lat": 52.31939, + "lon": 9.65544, + "name": "Ronnenberg" + }, + { + "lat": 59.98499, + "lon": 30.34295, + "name": "Sampsonievskiy" + }, + { + "lat": 48.46695, + "lon": 8.41371, + "name": "Freudenstadt" + }, + { + "lat": 34.75, + "lon": 138.25, + "name": "Sumiyoshi" + } + ], + "question": "Which location is the geographic outlier among: Bordon, Ronnenberg, Sampsonievskiy, Freudenstadt, Sumiyoshi?", + "ground_truth": { + "answer": "Sumiyoshi", + "outlier_distance_km": 7869.6, + "second_furthest_km": 2682.2, + "clarity_ratio": 2.93, + "median_distance_km": 2090.8, + "distances_to_centroid": { + "Bordon": 2682.2, + "Ronnenberg": 1948.2, + "Sampsonievskiy": 1262.0, + "Freudenstadt": 2090.8, + "Sumiyoshi": 7869.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bordon: (51.11°, -0.86°)", + " Ronnenberg: (52.32°, 9.66°)", + " Sampsonievskiy: (59.98°, 30.34°)", + " Freudenstadt: (48.47°, 8.41°)", + " Sumiyoshi: (34.75°, 138.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sumiyoshi: 7869.6 km from centroid", + " Bordon: 2682.2 km from centroid", + " Freudenstadt: 2090.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sumiyoshi", + "FINAL ANSWER: Sumiyoshi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.50528, + "lon": -35.31833, + "name": "Timbaúba" + }, + { + "lat": -21.42917, + "lon": -45.94722, + "name": "Alfenas" + }, + { + "lat": -11.495, + "lon": -77.20778, + "name": "Huaral" + }, + { + "lat": -32.56611, + "lon": -53.37583, + "name": "Jaguarão" + }, + { + "lat": 44.02163, + "lon": -92.4699, + "name": "Rochester" + } + ], + "question": "Which location is the geographic outlier among: Timbaúba, Alfenas, Huaral, Jaguarão, Rochester?", + "ground_truth": { + "answer": "Rochester", + "outlier_distance_km": 6379.9, + "second_furthest_km": 3076.4, + "clarity_ratio": 2.07, + "median_distance_km": 2827.4, + "distances_to_centroid": { + "Timbaúba": 2827.4, + "Alfenas": 2366.7, + "Huaral": 1904.4, + "Jaguarão": 3076.4, + "Rochester": 6379.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Timbaúba: (-7.51°, -35.32°)", + " Alfenas: (-21.43°, -45.95°)", + " Huaral: (-11.49°, -77.21°)", + " Jaguarão: (-32.57°, -53.38°)", + " Rochester: (44.02°, -92.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rochester: 6379.9 km from centroid", + " Jaguarão: 3076.4 km from centroid", + " Timbaúba: 2827.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rochester", + "FINAL ANSWER: Rochester" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.4668, + "lon": 8.99016, + "name": "Eberbach" + }, + { + "lat": 48.78363, + "lon": 9.21032, + "name": "Stuttgart-Ost" + }, + { + "lat": 48.76476, + "lon": 2.3503, + "name": "Chevilly-Larue" + }, + { + "lat": 37.20764, + "lon": -3.63493, + "name": "Maracena" + }, + { + "lat": -19.32556, + "lon": -41.25528, + "name": "Resplendor" + } + ], + "question": "Which location is the geographic outlier among: Eberbach, Stuttgart-Ost, Chevilly-Larue, Maracena, Resplendor?", + "ground_truth": { + "answer": "Resplendor", + "outlier_distance_km": 6982.9, + "second_furthest_km": 2161.2, + "clarity_ratio": 3.23, + "median_distance_km": 2111.2, + "distances_to_centroid": { + "Eberbach": 2161.2, + "Stuttgart-Ost": 2111.2, + "Chevilly-Larue": 1855.1, + "Maracena": 483.3, + "Resplendor": 6982.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eberbach: (49.47°, 8.99°)", + " Stuttgart-Ost: (48.78°, 9.21°)", + " Chevilly-Larue: (48.76°, 2.35°)", + " Maracena: (37.21°, -3.63°)", + " Resplendor: (-19.33°, -41.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Resplendor: 6982.9 km from centroid", + " Eberbach: 2161.2 km from centroid", + " Stuttgart-Ost: 2111.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Resplendor", + "FINAL ANSWER: Resplendor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.26667, + "lon": 36.83333, + "name": "Dangila" + }, + { + "lat": 6.92471, + "lon": 37.65263, + "name": "Gununo" + }, + { + "lat": -25.40892, + "lon": 28.287, + "name": "Hammanskraal" + }, + { + "lat": -32.77477, + "lon": 26.63376, + "name": "Fort Beaufort" + }, + { + "lat": -18.50667, + "lon": -54.76, + "name": "Coxim" + } + ], + "question": "Which location is the geographic outlier among: Dangila, Gununo, Hammanskraal, Fort Beaufort, Coxim?", + "ground_truth": { + "answer": "Coxim", + "outlier_distance_km": 7478.0, + "second_furthest_km": 3517.7, + "clarity_ratio": 2.13, + "median_distance_km": 3256.6, + "distances_to_centroid": { + "Dangila": 3517.7, + "Gununo": 3256.6, + "Hammanskraal": 2071.9, + "Fort Beaufort": 2630.1, + "Coxim": 7478.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dangila: (11.27°, 36.83°)", + " Gununo: (6.92°, 37.65°)", + " Hammanskraal: (-25.41°, 28.29°)", + " Fort Beaufort: (-32.77°, 26.63°)", + " Coxim: (-18.51°, -54.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coxim: 7478.0 km from centroid", + " Dangila: 3517.7 km from centroid", + " Gununo: 3256.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coxim", + "FINAL ANSWER: Coxim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -23.84852, + "lon": 151.25775, + "name": "Gladstone" + }, + { + "lat": -43.30437, + "lon": 172.58356, + "name": "Rangiora" + }, + { + "lat": 53.52189, + "lon": -1.39698, + "name": "Wombwell" + } + ], + "question": "Which location is the geographic outlier among: Blenheim, Gosnells, Gladstone, Rangiora, Wombwell?", + "ground_truth": { + "answer": "Wombwell", + "outlier_distance_km": 13773.0, + "second_furthest_km": 5552.4, + "clarity_ratio": 2.48, + "median_distance_km": 5491.8, + "distances_to_centroid": { + "Blenheim": 5552.4, + "Gosnells": 1752.7, + "Gladstone": 3071.8, + "Rangiora": 5491.8, + "Wombwell": 13773.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blenheim: (-41.52°, 173.95°)", + " Gosnells: (-32.08°, 116.01°)", + " Gladstone: (-23.85°, 151.26°)", + " Rangiora: (-43.30°, 172.58°)", + " Wombwell: (53.52°, -1.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wombwell: 13773.0 km from centroid", + " Blenheim: 5552.4 km from centroid", + " Rangiora: 5491.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wombwell", + "FINAL ANSWER: Wombwell" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.8, + "lon": 38.4, + "name": "Gebre Guracha" + }, + { + "lat": 8.91667, + "lon": 38.61667, + "name": "Sebeta" + }, + { + "lat": 0.89284, + "lon": 34.92468, + "name": "Kiminini" + }, + { + "lat": 10.21187, + "lon": 11.3871, + "name": "Deba" + }, + { + "lat": 36.8, + "lon": 139.93333, + "name": "Yaita" + } + ], + "question": "Which location is the geographic outlier among: Gebre Guracha, Sebeta, Kiminini, Deba, Yaita?", + "ground_truth": { + "answer": "Yaita", + "outlier_distance_km": 8886.8, + "second_furthest_km": 4500.5, + "clarity_ratio": 1.97, + "median_distance_km": 2391.8, + "distances_to_centroid": { + "Gebre Guracha": 1600.9, + "Sebeta": 1607.4, + "Kiminini": 2391.8, + "Deba": 4500.5, + "Yaita": 8886.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gebre Guracha: (9.80°, 38.40°)", + " Sebeta: (8.92°, 38.62°)", + " Kiminini: (0.89°, 34.92°)", + " Deba: (10.21°, 11.39°)", + " Yaita: (36.80°, 139.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yaita: 8886.8 km from centroid", + " Deba: 4500.5 km from centroid", + " Kiminini: 2391.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yaita", + "FINAL ANSWER: Yaita" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.68393, + "lon": -112.13488, + "name": "Deer Valley" + }, + { + "lat": 42.25754, + "lon": -83.21104, + "name": "Allen Park" + }, + { + "lat": 42.76537, + "lon": -71.46757, + "name": "Nashua" + }, + { + "lat": 20.99165, + "lon": -101.28434, + "name": "Marfil" + }, + { + "lat": 10.85029, + "lon": 36.89277, + "name": "Ginja Bet" + } + ], + "question": "Which location is the geographic outlier among: Deer Valley, Allen Park, Nashua, Marfil, Ginja Bet?", + "ground_truth": { + "answer": "Ginja Bet", + "outlier_distance_km": 10636.9, + "second_furthest_km": 4315.6, + "clarity_ratio": 2.46, + "median_distance_km": 3642.7, + "distances_to_centroid": { + "Deer Valley": 4315.6, + "Allen Park": 2028.7, + "Nashua": 1482.1, + "Marfil": 3642.7, + "Ginja Bet": 10636.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deer Valley: (33.68°, -112.13°)", + " Allen Park: (42.26°, -83.21°)", + " Nashua: (42.77°, -71.47°)", + " Marfil: (20.99°, -101.28°)", + " Ginja Bet: (10.85°, 36.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ginja Bet: 10636.9 km from centroid", + " Deer Valley: 4315.6 km from centroid", + " Marfil: 3642.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ginja Bet", + "FINAL ANSWER: Ginja Bet" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.21167, + "lon": -63.82861, + "name": "Buritis" + }, + { + "lat": -27.04346, + "lon": -55.22698, + "name": "Jardín América" + }, + { + "lat": -23.44077, + "lon": -46.73774, + "name": "Jaraguá" + }, + { + "lat": 2.64644, + "lon": -75.97269, + "name": "Belalcázar" + }, + { + "lat": 34.1, + "lon": 131.4, + "name": "Ogōri-shimogō" + } + ], + "question": "Which location is the geographic outlier among: Buritis, Jardín América, Jaraguá, Belalcázar, Ogōri-shimogō?", + "ground_truth": { + "answer": "Ogōri-shimogō", + "outlier_distance_km": 15759.8, + "second_furthest_km": 6044.8, + "clarity_ratio": 2.61, + "median_distance_km": 4638.9, + "distances_to_centroid": { + "Buritis": 4638.9, + "Jardín América": 4297.1, + "Jaraguá": 3360.6, + "Belalcázar": 6044.8, + "Ogōri-shimogō": 15759.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Buritis: (-10.21°, -63.83°)", + " Jardín América: (-27.04°, -55.23°)", + " Jaraguá: (-23.44°, -46.74°)", + " Belalcázar: (2.65°, -75.97°)", + " Ogōri-shimogō: (34.10°, 131.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ogōri-shimogō: 15759.8 km from centroid", + " Belalcázar: 6044.8 km from centroid", + " Buritis: 4638.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ogōri-shimogō", + "FINAL ANSWER: Ogōri-shimogō" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.88732, + "lon": 116.82364, + "name": "Kudat" + }, + { + "lat": 35.7091, + "lon": 139.41891, + "name": "Tachikawa" + }, + { + "lat": 28.10077, + "lon": 104.56063, + "name": "Xunsi" + }, + { + "lat": 33.77037, + "lon": 132.78977, + "name": "Haramachi" + }, + { + "lat": -37.88461, + "lon": 145.29539, + "name": "Ferntree Gully" + } + ], + "question": "Which location is the geographic outlier among: Kudat, Tachikawa, Xunsi, Haramachi, Ferntree Gully?", + "ground_truth": { + "answer": "Ferntree Gully", + "outlier_distance_km": 5979.4, + "second_furthest_km": 2911.6, + "clarity_ratio": 2.05, + "median_distance_km": 2749.0, + "distances_to_centroid": { + "Kudat": 1395.4, + "Tachikawa": 2749.0, + "Xunsi": 2911.6, + "Haramachi": 2330.1, + "Ferntree Gully": 5979.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kudat: (6.89°, 116.82°)", + " Tachikawa: (35.71°, 139.42°)", + " Xunsi: (28.10°, 104.56°)", + " Haramachi: (33.77°, 132.79°)", + " Ferntree Gully: (-37.88°, 145.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ferntree Gully: 5979.4 km from centroid", + " Xunsi: 2911.6 km from centroid", + " Tachikawa: 2749.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ferntree Gully", + "FINAL ANSWER: Ferntree Gully" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.56838, + "lon": 41.43869, + "name": "Asaita" + }, + { + "lat": 8.27338, + "lon": 5.83526, + "name": "Isanlu-Itedoijowa" + }, + { + "lat": 30.9128, + "lon": 30.29019, + "name": "Ḩawsh ‘Īsá" + }, + { + "lat": 6.45, + "lon": 3.33333, + "name": "Aliayabiagba" + }, + { + "lat": 40.01499, + "lon": -105.27055, + "name": "Boulder" + } + ], + "question": "Which location is the geographic outlier among: Asaita, Isanlu-Itedoijowa, Ḩawsh ‘Īsá, Aliayabiagba, Boulder?", + "ground_truth": { + "answer": "Boulder", + "outlier_distance_km": 9473.5, + "second_furthest_km": 5024.1, + "clarity_ratio": 1.89, + "median_distance_km": 3742.3, + "distances_to_centroid": { + "Asaita": 5024.1, + "Isanlu-Itedoijowa": 1695.4, + "Ḩawsh ‘Īsá": 3742.3, + "Aliayabiagba": 1695.5, + "Boulder": 9473.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Asaita: (11.57°, 41.44°)", + " Isanlu-Itedoijowa: (8.27°, 5.84°)", + " Ḩawsh ‘Īsá: (30.91°, 30.29°)", + " Aliayabiagba: (6.45°, 3.33°)", + " Boulder: (40.01°, -105.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Boulder: 9473.5 km from centroid", + " Asaita: 5024.1 km from centroid", + " Ḩawsh ‘Īsá: 3742.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Boulder", + "FINAL ANSWER: Boulder" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.02111, + "lon": 117.64694, + "name": "Tanggu" + }, + { + "lat": 22.85095, + "lon": 75.54224, + "name": "Depālpur" + }, + { + "lat": 34.209, + "lon": 74.34285, + "name": "Bāramūla" + }, + { + "lat": 36.00667, + "lon": 106.28083, + "name": "Guyuan" + }, + { + "lat": -9.4075, + "lon": -36.07361, + "name": "Capela" + } + ], + "question": "Which location is the geographic outlier among: Tanggu, Depālpur, Bāramūla, Guyuan, Capela?", + "ground_truth": { + "answer": "Capela", + "outlier_distance_km": 11810.5, + "second_furthest_km": 4934.0, + "clarity_ratio": 2.39, + "median_distance_km": 3902.6, + "distances_to_centroid": { + "Tanggu": 4934.0, + "Depālpur": 835.1, + "Bāramūla": 1260.3, + "Guyuan": 3902.6, + "Capela": 11810.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tanggu: (39.02°, 117.65°)", + " Depālpur: (22.85°, 75.54°)", + " Bāramūla: (34.21°, 74.34°)", + " Guyuan: (36.01°, 106.28°)", + " Capela: (-9.41°, -36.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Capela: 11810.5 km from centroid", + " Tanggu: 4934.0 km from centroid", + " Guyuan: 3902.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Capela", + "FINAL ANSWER: Capela" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.56884, + "lon": -97.96473, + "name": "Seguin" + }, + { + "lat": 40.62122, + "lon": -73.93486, + "name": "Flatlands" + }, + { + "lat": 39.75961, + "lon": -121.62192, + "name": "Paradise" + }, + { + "lat": 26.77534, + "lon": -80.0581, + "name": "Riviera Beach" + }, + { + "lat": -23.69748, + "lon": 133.88362, + "name": "Alice Springs" + } + ], + "question": "Which location is the geographic outlier among: Seguin, Flatlands, Paradise, Riviera Beach, Alice Springs?", + "ground_truth": { + "answer": "Alice Springs", + "outlier_distance_km": 19792.7, + "second_furthest_km": 7067.8, + "clarity_ratio": 2.8, + "median_distance_km": 5018.0, + "distances_to_centroid": { + "Seguin": 5018.0, + "Flatlands": 3152.2, + "Paradise": 7067.8, + "Riviera Beach": 3269.2, + "Alice Springs": 19792.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Seguin: (29.57°, -97.96°)", + " Flatlands: (40.62°, -73.93°)", + " Paradise: (39.76°, -121.62°)", + " Riviera Beach: (26.78°, -80.06°)", + " Alice Springs: (-23.70°, 133.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alice Springs: 19792.7 km from centroid", + " Paradise: 7067.8 km from centroid", + " Seguin: 5018.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alice Springs", + "FINAL ANSWER: Alice Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.93422, + "lon": -1.71454, + "name": "Sekondi" + }, + { + "lat": 26.5622, + "lon": 31.74566, + "name": "Akhmīm" + }, + { + "lat": 6.60656, + "lon": 3.30235, + "name": "Alimosho" + }, + { + "lat": -29.32816, + "lon": 31.28954, + "name": "KwaDukuza" + }, + { + "lat": 46.87215, + "lon": -113.994, + "name": "Missoula" + } + ], + "question": "Which location is the geographic outlier among: Sekondi, Akhmīm, Alimosho, KwaDukuza, Missoula?", + "ground_truth": { + "answer": "Missoula", + "outlier_distance_km": 10152.6, + "second_furthest_km": 6301.5, + "clarity_ratio": 1.61, + "median_distance_km": 4677.3, + "distances_to_centroid": { + "Sekondi": 1131.7, + "Akhmīm": 4677.3, + "Alimosho": 1532.1, + "KwaDukuza": 6301.5, + "Missoula": 10152.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sekondi: (4.93°, -1.71°)", + " Akhmīm: (26.56°, 31.75°)", + " Alimosho: (6.61°, 3.30°)", + " KwaDukuza: (-29.33°, 31.29°)", + " Missoula: (46.87°, -113.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Missoula: 10152.6 km from centroid", + " KwaDukuza: 6301.5 km from centroid", + " Akhmīm: 4677.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Missoula", + "FINAL ANSWER: Missoula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.38333, + "lon": 110.75, + "name": "Simunjan" + }, + { + "lat": 8.12027, + "lon": 77.38904, + "name": "Dharmapuram" + }, + { + "lat": 34.8045, + "lon": 135.76681, + "name": "Kyōtanabe" + }, + { + "lat": 28.24737, + "lon": 75.07666, + "name": "Bissāu" + }, + { + "lat": -4.23246, + "lon": -44.78164, + "name": "Bacabal" + } + ], + "question": "Which location is the geographic outlier among: Simunjan, Dharmapuram, Kyōtanabe, Bissāu, Bacabal?", + "ground_truth": { + "answer": "Bacabal", + "outlier_distance_km": 12885.2, + "second_furthest_km": 6868.9, + "clarity_ratio": 1.88, + "median_distance_km": 4596.5, + "distances_to_centroid": { + "Simunjan": 4596.5, + "Dharmapuram": 943.9, + "Kyōtanabe": 6868.9, + "Bissāu": 1679.7, + "Bacabal": 12885.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Simunjan: (1.38°, 110.75°)", + " Dharmapuram: (8.12°, 77.39°)", + " Kyōtanabe: (34.80°, 135.77°)", + " Bissāu: (28.25°, 75.08°)", + " Bacabal: (-4.23°, -44.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bacabal: 12885.2 km from centroid", + " Kyōtanabe: 6868.9 km from centroid", + " Simunjan: 4596.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bacabal", + "FINAL ANSWER: Bacabal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.09316, + "lon": 4.83528, + "name": "Ondo" + }, + { + "lat": 6.92471, + "lon": 37.65263, + "name": "Gununo" + }, + { + "lat": 30.93055, + "lon": 31.69864, + "name": "Awlād Şaqr" + }, + { + "lat": 6.09408, + "lon": -0.25913, + "name": "Koforidua" + }, + { + "lat": 41.79194, + "lon": 120.77917, + "name": "Beipiao" + } + ], + "question": "Which location is the geographic outlier among: Ondo, Gununo, Awlād Şaqr, Koforidua, Beipiao?", + "ground_truth": { + "answer": "Beipiao", + "outlier_distance_km": 7982.4, + "second_furthest_km": 4465.5, + "clarity_ratio": 1.79, + "median_distance_km": 3902.2, + "distances_to_centroid": { + "Ondo": 3902.2, + "Gununo": 1302.0, + "Awlād Şaqr": 1556.1, + "Koforidua": 4465.5, + "Beipiao": 7982.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ondo: (7.09°, 4.84°)", + " Gununo: (6.92°, 37.65°)", + " Awlād Şaqr: (30.93°, 31.70°)", + " Koforidua: (6.09°, -0.26°)", + " Beipiao: (41.79°, 120.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Beipiao: 7982.4 km from centroid", + " Koforidua: 4465.5 km from centroid", + " Ondo: 3902.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Beipiao", + "FINAL ANSWER: Beipiao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.41537, + "lon": -71.15644, + "name": "Arlington" + }, + { + "lat": 21.47831, + "lon": -101.21566, + "name": "San Felipe" + }, + { + "lat": 33.96168, + "lon": -118.35313, + "name": "Inglewood" + }, + { + "lat": 45.35699, + "lon": -71.99676, + "name": "Rock Forest" + }, + { + "lat": -26.76566, + "lon": 26.42024, + "name": "Hartbeesfontein" + } + ], + "question": "Which location is the geographic outlier among: Arlington, San Felipe, Inglewood, Rock Forest, Hartbeesfontein?", + "ground_truth": { + "answer": "Hartbeesfontein", + "outlier_distance_km": 11490.7, + "second_furthest_km": 5073.3, + "clarity_ratio": 2.26, + "median_distance_km": 3489.1, + "distances_to_centroid": { + "Arlington": 2157.0, + "San Felipe": 3489.1, + "Inglewood": 5073.3, + "Rock Forest": 2490.9, + "Hartbeesfontein": 11490.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arlington: (42.42°, -71.16°)", + " San Felipe: (21.48°, -101.22°)", + " Inglewood: (33.96°, -118.35°)", + " Rock Forest: (45.36°, -72.00°)", + " Hartbeesfontein: (-26.77°, 26.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hartbeesfontein: 11490.7 km from centroid", + " Inglewood: 5073.3 km from centroid", + " San Felipe: 3489.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hartbeesfontein", + "FINAL ANSWER: Hartbeesfontein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.7836, + "lon": -1.4854, + "name": "Witney" + }, + { + "lat": 53.35801, + "lon": -2.16539, + "name": "Bramhall" + }, + { + "lat": 48.9735, + "lon": 2.28729, + "name": "Saint-Gratien" + }, + { + "lat": 51.19166, + "lon": 20.40607, + "name": "Końskie" + }, + { + "lat": -19.63006, + "lon": -43.9009, + "name": "Lagoa Santa" + } + ], + "question": "Which location is the geographic outlier among: Witney, Bramhall, Saint-Gratien, Końskie, Lagoa Santa?", + "ground_truth": { + "answer": "Lagoa Santa", + "outlier_distance_km": 7515.1, + "second_furthest_km": 2535.6, + "clarity_ratio": 2.96, + "median_distance_km": 1816.8, + "distances_to_centroid": { + "Witney": 1651.6, + "Bramhall": 1816.8, + "Saint-Gratien": 1440.8, + "Końskie": 2535.6, + "Lagoa Santa": 7515.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Witney: (51.78°, -1.49°)", + " Bramhall: (53.36°, -2.17°)", + " Saint-Gratien: (48.97°, 2.29°)", + " Końskie: (51.19°, 20.41°)", + " Lagoa Santa: (-19.63°, -43.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lagoa Santa: 7515.1 km from centroid", + " Końskie: 2535.6 km from centroid", + " Bramhall: 1816.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lagoa Santa", + "FINAL ANSWER: Lagoa Santa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.8748, + "lon": 134.36191, + "name": "Kamigōri" + }, + { + "lat": 8.95003, + "lon": 76.59861, + "name": "Karuva" + }, + { + "lat": 34.01515, + "lon": 74.91895, + "name": "Pāmpur" + }, + { + "lat": 28.65195, + "lon": 77.23149, + "name": "Delhi" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + } + ], + "question": "Which location is the geographic outlier among: Kamigōri, Karuva, Pāmpur, Delhi, Tuggeranong Administrative District?", + "ground_truth": { + "answer": "Tuggeranong Administrative District", + "outlier_distance_km": 7384.6, + "second_furthest_km": 3933.4, + "clarity_ratio": 1.88, + "median_distance_km": 3534.9, + "distances_to_centroid": { + "Kamigōri": 3933.4, + "Karuva": 2872.7, + "Pāmpur": 3534.9, + "Delhi": 3052.0, + "Tuggeranong Administrative District": 7384.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kamigōri: (34.87°, 134.36°)", + " Karuva: (8.95°, 76.60°)", + " Pāmpur: (34.02°, 74.92°)", + " Delhi: (28.65°, 77.23°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tuggeranong Administrative District: 7384.6 km from centroid", + " Kamigōri: 3933.4 km from centroid", + " Pāmpur: 3534.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tuggeranong Administrative District", + "FINAL ANSWER: Tuggeranong Administrative District" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.5225, + "lon": -99.89167, + "name": "Tequisquiapan" + }, + { + "lat": 40.82149, + "lon": -73.98764, + "name": "Cliffside Park" + }, + { + "lat": 19.82189, + "lon": -101.78928, + "name": "Zacapu" + }, + { + "lat": 40.78121, + "lon": -73.24623, + "name": "Brentwood" + }, + { + "lat": 5.75279, + "lon": 45.64603, + "name": "Kahandhale" + } + ], + "question": "Which location is the geographic outlier among: Tequisquiapan, Cliffside Park, Zacapu, Brentwood, Kahandhale?", + "ground_truth": { + "answer": "Kahandhale", + "outlier_distance_km": 11347.3, + "second_furthest_km": 4251.4, + "clarity_ratio": 2.67, + "median_distance_km": 4039.5, + "distances_to_centroid": { + "Tequisquiapan": 4039.5, + "Cliffside Park": 2098.6, + "Zacapu": 4251.4, + "Brentwood": 2055.7, + "Kahandhale": 11347.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tequisquiapan: (20.52°, -99.89°)", + " Cliffside Park: (40.82°, -73.99°)", + " Zacapu: (19.82°, -101.79°)", + " Brentwood: (40.78°, -73.25°)", + " Kahandhale: (5.75°, 45.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kahandhale: 11347.3 km from centroid", + " Zacapu: 4251.4 km from centroid", + " Tequisquiapan: 4039.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kahandhale", + "FINAL ANSWER: Kahandhale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -32.22099, + "lon": 116.009, + "name": "Byford" + }, + { + "lat": -41.27078, + "lon": 173.28404, + "name": "Nelson" + }, + { + "lat": -25.66756, + "lon": 27.24208, + "name": "Rustenburg" + } + ], + "question": "Which location is the geographic outlier among: Eight Mile Plains, Blacktown, Byford, Nelson, Rustenburg?", + "ground_truth": { + "answer": "Rustenburg", + "outlier_distance_km": 9119.9, + "second_furthest_km": 4440.5, + "clarity_ratio": 2.05, + "median_distance_km": 2832.0, + "distances_to_centroid": { + "Eight Mile Plains": 2832.0, + "Blacktown": 2501.5, + "Byford": 762.5, + "Nelson": 4440.5, + "Rustenburg": 9119.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Blacktown: (-33.77°, 150.92°)", + " Byford: (-32.22°, 116.01°)", + " Nelson: (-41.27°, 173.28°)", + " Rustenburg: (-25.67°, 27.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rustenburg: 9119.9 km from centroid", + " Nelson: 4440.5 km from centroid", + " Eight Mile Plains: 2832.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rustenburg", + "FINAL ANSWER: Rustenburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.39841, + "lon": 9.99155, + "name": "Ulm" + }, + { + "lat": 52.774, + "lon": -1.55744, + "name": "Swadlincote" + }, + { + "lat": 44.1391, + "lon": 12.24315, + "name": "Cesena" + }, + { + "lat": 52.85435, + "lon": 11.1525, + "name": "Salzwedel" + }, + { + "lat": -25.509, + "lon": 28.064, + "name": "Mabopane" + } + ], + "question": "Which location is the geographic outlier among: Ulm, Swadlincote, Cesena, Salzwedel, Mabopane?", + "ground_truth": { + "answer": "Mabopane", + "outlier_distance_km": 6888.2, + "second_furthest_km": 2293.6, + "clarity_ratio": 3.0, + "median_distance_km": 2038.5, + "distances_to_centroid": { + "Ulm": 1550.7, + "Swadlincote": 2293.6, + "Cesena": 1068.6, + "Salzwedel": 2038.5, + "Mabopane": 6888.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ulm: (48.40°, 9.99°)", + " Swadlincote: (52.77°, -1.56°)", + " Cesena: (44.14°, 12.24°)", + " Salzwedel: (52.85°, 11.15°)", + " Mabopane: (-25.51°, 28.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mabopane: 6888.2 km from centroid", + " Swadlincote: 2293.6 km from centroid", + " Salzwedel: 2038.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mabopane", + "FINAL ANSWER: Mabopane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.92849, + "lon": 8.89212, + "name": "Jos" + }, + { + "lat": 11.09596, + "lon": 11.33261, + "name": "Nafada" + }, + { + "lat": 3.11988, + "lon": 35.59642, + "name": "Lodwar" + }, + { + "lat": -27.00805, + "lon": 27.3646, + "name": "Vredefort" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + } + ], + "question": "Which location is the geographic outlier among: Jos, Nafada, Lodwar, Vredefort, Lara?", + "ground_truth": { + "answer": "Lara", + "outlier_distance_km": 10216.9, + "second_furthest_km": 4527.3, + "clarity_ratio": 2.26, + "median_distance_km": 4346.9, + "distances_to_centroid": { + "Jos": 4527.3, + "Nafada": 4346.9, + "Lodwar": 1670.0, + "Vredefort": 2835.5, + "Lara": 10216.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jos: (9.93°, 8.89°)", + " Nafada: (11.10°, 11.33°)", + " Lodwar: (3.12°, 35.60°)", + " Vredefort: (-27.01°, 27.36°)", + " Lara: (-38.02°, 144.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lara: 10216.9 km from centroid", + " Jos: 4527.3 km from centroid", + " Nafada: 4346.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lara", + "FINAL ANSWER: Lara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.61917, + "lon": -43.22694, + "name": "Itabira" + }, + { + "lat": -22.50917, + "lon": -48.55778, + "name": "Igaraçu do Tietê" + }, + { + "lat": -31.6515, + "lon": -68.28216, + "name": "Caucete" + }, + { + "lat": 4.9218, + "lon": -75.06232, + "name": "Líbano" + }, + { + "lat": -2.0561, + "lon": 101.3913, + "name": "Sungai Penuh" + } + ], + "question": "Which location is the geographic outlier among: Itabira, Igaraçu do Tietê, Caucete, Líbano, Sungai Penuh?", + "ground_truth": { + "answer": "Sungai Penuh", + "outlier_distance_km": 14024.6, + "second_furthest_km": 5735.9, + "clarity_ratio": 2.45, + "median_distance_km": 4639.5, + "distances_to_centroid": { + "Itabira": 1853.3, + "Igaraçu do Tietê": 2477.3, + "Caucete": 4639.5, + "Líbano": 5735.9, + "Sungai Penuh": 14024.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itabira: (-19.62°, -43.23°)", + " Igaraçu do Tietê: (-22.51°, -48.56°)", + " Caucete: (-31.65°, -68.28°)", + " Líbano: (4.92°, -75.06°)", + " Sungai Penuh: (-2.06°, 101.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sungai Penuh: 14024.6 km from centroid", + " Líbano: 5735.9 km from centroid", + " Caucete: 4639.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sungai Penuh", + "FINAL ANSWER: Sungai Penuh" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.54139, + "lon": 110.51083, + "name": "Salaqi" + }, + { + "lat": 27.83333, + "lon": 113.15, + "name": "Zhuzhou" + }, + { + "lat": 20.0054, + "lon": 79.30273, + "name": "Durgāpur" + }, + { + "lat": 27.70283, + "lon": 81.9343, + "name": "Bhinga" + }, + { + "lat": -35.28346, + "lon": 149.12807, + "name": "Canberra" + } + ], + "question": "Which location is the geographic outlier among: Salaqi, Zhuzhou, Durgāpur, Bhinga, Canberra?", + "ground_truth": { + "answer": "Canberra", + "outlier_distance_km": 7253.5, + "second_furthest_km": 2934.9, + "clarity_ratio": 2.47, + "median_distance_km": 2860.2, + "distances_to_centroid": { + "Salaqi": 2734.6, + "Zhuzhou": 1452.8, + "Durgāpur": 2934.9, + "Bhinga": 2860.2, + "Canberra": 7253.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Salaqi: (40.54°, 110.51°)", + " Zhuzhou: (27.83°, 113.15°)", + " Durgāpur: (20.01°, 79.30°)", + " Bhinga: (27.70°, 81.93°)", + " Canberra: (-35.28°, 149.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Canberra: 7253.5 km from centroid", + " Durgāpur: 2934.9 km from centroid", + " Bhinga: 2860.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Canberra", + "FINAL ANSWER: Canberra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.6151, + "lon": -80.31061, + "name": "Cutler" + }, + { + "lat": 31.95758, + "lon": -110.95565, + "name": "Sahuarita" + }, + { + "lat": 38.78394, + "lon": -90.48123, + "name": "Saint Charles" + }, + { + "lat": 19.35638, + "lon": -99.65724, + "name": "San Pablo Autopan" + }, + { + "lat": 45.21439, + "lon": 39.6884, + "name": "Ust’-Labinsk" + } + ], + "question": "Which location is the geographic outlier among: Cutler, Sahuarita, Saint Charles, San Pablo Autopan, Ust’-Labinsk?", + "ground_truth": { + "answer": "Ust’-Labinsk", + "outlier_distance_km": 8766.9, + "second_furthest_km": 3988.1, + "clarity_ratio": 2.2, + "median_distance_km": 3427.8, + "distances_to_centroid": { + "Cutler": 1373.7, + "Sahuarita": 3988.1, + "Saint Charles": 2127.9, + "San Pablo Autopan": 3427.8, + "Ust’-Labinsk": 8766.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cutler: (25.62°, -80.31°)", + " Sahuarita: (31.96°, -110.96°)", + " Saint Charles: (38.78°, -90.48°)", + " San Pablo Autopan: (19.36°, -99.66°)", + " Ust’-Labinsk: (45.21°, 39.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ust’-Labinsk: 8766.9 km from centroid", + " Sahuarita: 3988.1 km from centroid", + " San Pablo Autopan: 3427.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ust’-Labinsk", + "FINAL ANSWER: Ust’-Labinsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.515, + "lon": -41.005, + "name": "Afrânio" + }, + { + "lat": -12.15833, + "lon": -39.73722, + "name": "Ipirá" + }, + { + "lat": -23.49472, + "lon": -46.47389, + "name": "Ermelino Matarazzo" + }, + { + "lat": -9.58833, + "lon": -67.5325, + "name": "Porto Acre" + }, + { + "lat": 40.39162, + "lon": -111.85077, + "name": "Lehi" + } + ], + "question": "Which location is the geographic outlier among: Afrânio, Ipirá, Ermelino Matarazzo, Porto Acre, Lehi?", + "ground_truth": { + "answer": "Lehi", + "outlier_distance_km": 7009.5, + "second_furthest_km": 2812.8, + "clarity_ratio": 2.49, + "median_distance_km": 2600.2, + "distances_to_centroid": { + "Afrânio": 2339.1, + "Ipirá": 2600.2, + "Ermelino Matarazzo": 2812.8, + "Porto Acre": 1030.8, + "Lehi": 7009.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Afrânio: (-8.52°, -41.01°)", + " Ipirá: (-12.16°, -39.74°)", + " Ermelino Matarazzo: (-23.49°, -46.47°)", + " Porto Acre: (-9.59°, -67.53°)", + " Lehi: (40.39°, -111.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lehi: 7009.5 km from centroid", + " Ermelino Matarazzo: 2812.8 km from centroid", + " Ipirá: 2600.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lehi", + "FINAL ANSWER: Lehi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.58295, + "lon": 117.09503, + "name": "Loa Janan" + }, + { + "lat": 19.15516, + "lon": 73.26553, + "name": "Badlapur" + }, + { + "lat": 36.53333, + "lon": 136.61667, + "name": "Nonoichi" + }, + { + "lat": 23.24212, + "lon": 111.5284, + "name": "Ducheng" + }, + { + "lat": 30.28604, + "lon": -97.73889, + "name": "University of Texas" + } + ], + "question": "Which location is the geographic outlier among: Loa Janan, Badlapur, Nonoichi, Ducheng, University of Texas?", + "ground_truth": { + "answer": "University of Texas", + "outlier_distance_km": 14038.2, + "second_furthest_km": 6713.0, + "clarity_ratio": 2.09, + "median_distance_km": 5856.9, + "distances_to_centroid": { + "Loa Janan": 5856.9, + "Badlapur": 604.5, + "Nonoichi": 6713.0, + "Ducheng": 4443.1, + "University of Texas": 14038.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Loa Janan: (-0.58°, 117.10°)", + " Badlapur: (19.16°, 73.27°)", + " Nonoichi: (36.53°, 136.62°)", + " Ducheng: (23.24°, 111.53°)", + " University of Texas: (30.29°, -97.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " University of Texas: 14038.2 km from centroid", + " Nonoichi: 6713.0 km from centroid", + " Loa Janan: 5856.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: University of Texas", + "FINAL ANSWER: University of Texas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.12268, + "lon": 106.53435, + "name": "Xiaomian" + }, + { + "lat": 18.0554, + "lon": 120.56489, + "name": "Batac City" + }, + { + "lat": 35.80472, + "lon": 139.60194, + "name": "Asaka" + }, + { + "lat": 26.19698, + "lon": 127.72591, + "name": "Kanegusuku" + }, + { + "lat": -22.29583, + "lon": -44.93472, + "name": "Itanhandu" + } + ], + "question": "Which location is the geographic outlier among: Xiaomian, Batac City, Asaka, Kanegusuku, Itanhandu?", + "ground_truth": { + "answer": "Itanhandu", + "outlier_distance_km": 15281.5, + "second_furthest_km": 5272.2, + "clarity_ratio": 2.9, + "median_distance_km": 4003.7, + "distances_to_centroid": { + "Xiaomian": 2187.9, + "Batac City": 3243.1, + "Asaka": 5272.2, + "Kanegusuku": 4003.7, + "Itanhandu": 15281.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Xiaomian: (30.12°, 106.53°)", + " Batac City: (18.06°, 120.56°)", + " Asaka: (35.80°, 139.60°)", + " Kanegusuku: (26.20°, 127.73°)", + " Itanhandu: (-22.30°, -44.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itanhandu: 15281.5 km from centroid", + " Asaka: 5272.2 km from centroid", + " Kanegusuku: 4003.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itanhandu", + "FINAL ANSWER: Itanhandu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.25297, + "lon": 13.7597, + "name": "Porto Sant'Elpidio" + }, + { + "lat": 51.2372, + "lon": -2.6266, + "name": "Mendip" + }, + { + "lat": 50.20228, + "lon": 10.07784, + "name": "Bad Kissingen" + }, + { + "lat": 48.92578, + "lon": 2.44533, + "name": "Drancy" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + } + ], + "question": "Which location is the geographic outlier among: Porto Sant'Elpidio, Mendip, Bad Kissingen, Drancy, Saint Ives?", + "ground_truth": { + "answer": "Saint Ives", + "outlier_distance_km": 14151.2, + "second_furthest_km": 3726.3, + "clarity_ratio": 3.8, + "median_distance_km": 3295.3, + "distances_to_centroid": { + "Porto Sant'Elpidio": 2239.1, + "Mendip": 3726.3, + "Bad Kissingen": 2881.9, + "Drancy": 3295.3, + "Saint Ives": 14151.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porto Sant'Elpidio: (43.25°, 13.76°)", + " Mendip: (51.24°, -2.63°)", + " Bad Kissingen: (50.20°, 10.08°)", + " Drancy: (48.93°, 2.45°)", + " Saint Ives: (-33.73°, 151.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Ives: 14151.2 km from centroid", + " Mendip: 3726.3 km from centroid", + " Drancy: 3295.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Ives", + "FINAL ANSWER: Saint Ives" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.97854, + "lon": -90.16396, + "name": "Metairie Terrace" + }, + { + "lat": 40.48979, + "lon": -81.44567, + "name": "New Philadelphia" + }, + { + "lat": 20.55257, + "lon": -100.41511, + "name": "San José de los Olvera" + }, + { + "lat": 29.94296, + "lon": -89.96537, + "name": "Chalmette" + }, + { + "lat": 6.41919, + "lon": 45.85251, + "name": "Raqo" + } + ], + "question": "Which location is the geographic outlier among: Metairie Terrace, New Philadelphia, San José de los Olvera, Chalmette, Raqo?", + "ground_truth": { + "answer": "Raqo", + "outlier_distance_km": 11585.6, + "second_furthest_km": 3832.8, + "clarity_ratio": 3.02, + "median_distance_km": 2691.6, + "distances_to_centroid": { + "Metairie Terrace": 2691.6, + "New Philadelphia": 2372.7, + "San José de los Olvera": 3832.8, + "Chalmette": 2672.2, + "Raqo": 11585.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Metairie Terrace: (29.98°, -90.16°)", + " New Philadelphia: (40.49°, -81.45°)", + " San José de los Olvera: (20.55°, -100.42°)", + " Chalmette: (29.94°, -89.97°)", + " Raqo: (6.42°, 45.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Raqo: 11585.6 km from centroid", + " San José de los Olvera: 3832.8 km from centroid", + " Metairie Terrace: 2691.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Raqo", + "FINAL ANSWER: Raqo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.8432, + "lon": 121.6623, + "name": "Ende" + }, + { + "lat": 10.77494, + "lon": 106.68628, + "name": "Quận Ba" + }, + { + "lat": 32.28034, + "lon": 119.16999, + "name": "Zhenzhou" + }, + { + "lat": 23.01279, + "lon": 104.45081, + "name": "Mabai" + }, + { + "lat": 48.2, + "lon": 11.33333, + "name": "Olching" + } + ], + "question": "Which location is the geographic outlier among: Ende, Quận Ba, Zhenzhou, Mabai, Olching?", + "ground_truth": { + "answer": "Olching", + "outlier_distance_km": 7647.9, + "second_furthest_km": 4594.5, + "clarity_ratio": 1.66, + "median_distance_km": 2902.1, + "distances_to_centroid": { + "Ende": 4594.5, + "Quận Ba": 1885.5, + "Zhenzhou": 2902.1, + "Mabai": 1233.5, + "Olching": 7647.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ende: (-8.84°, 121.66°)", + " Quận Ba: (10.77°, 106.69°)", + " Zhenzhou: (32.28°, 119.17°)", + " Mabai: (23.01°, 104.45°)", + " Olching: (48.20°, 11.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Olching: 7647.9 km from centroid", + " Ende: 4594.5 km from centroid", + " Zhenzhou: 2902.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Olching", + "FINAL ANSWER: Olching" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.8542, + "lon": 14.33038, + "name": "Ponticelli" + }, + { + "lat": 45.71262, + "lon": 11.35671, + "name": "Schio" + }, + { + "lat": 51.61794, + "lon": -0.11012, + "name": "Palmers Green" + }, + { + "lat": 51.845, + "lon": 4.32917, + "name": "Spijkenisse" + }, + { + "lat": 38.16007, + "lon": -85.65968, + "name": "Newburg" + } + ], + "question": "Which location is the geographic outlier among: Ponticelli, Schio, Palmers Green, Spijkenisse, Newburg?", + "ground_truth": { + "answer": "Newburg", + "outlier_distance_km": 5998.4, + "second_furthest_km": 2121.4, + "clarity_ratio": 2.83, + "median_distance_km": 1742.9, + "distances_to_centroid": { + "Ponticelli": 2121.4, + "Schio": 1742.9, + "Palmers Green": 1047.1, + "Spijkenisse": 1324.5, + "Newburg": 5998.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ponticelli: (40.85°, 14.33°)", + " Schio: (45.71°, 11.36°)", + " Palmers Green: (51.62°, -0.11°)", + " Spijkenisse: (51.84°, 4.33°)", + " Newburg: (38.16°, -85.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Newburg: 5998.4 km from centroid", + " Ponticelli: 2121.4 km from centroid", + " Schio: 1742.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Newburg", + "FINAL ANSWER: Newburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.41899, + "lon": -75.68992, + "name": "Tarma" + }, + { + "lat": -9.91333, + "lon": -63.04083, + "name": "Ariquemes" + }, + { + "lat": -4.16694, + "lon": -40.7475, + "name": "Guaraciaba do Norte" + }, + { + "lat": -15.5, + "lon": -70.13333, + "name": "Juliaca" + }, + { + "lat": 44.42137, + "lon": 11.91094, + "name": "Lugo" + } + ], + "question": "Which location is the geographic outlier among: Tarma, Ariquemes, Guaraciaba do Norte, Juliaca, Lugo?", + "ground_truth": { + "answer": "Lugo", + "outlier_distance_km": 7583.6, + "second_furthest_km": 3388.8, + "clarity_ratio": 2.24, + "median_distance_km": 3066.0, + "distances_to_centroid": { + "Tarma": 3388.8, + "Ariquemes": 2081.2, + "Guaraciaba do Norte": 927.7, + "Juliaca": 3066.0, + "Lugo": 7583.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tarma: (-11.42°, -75.69°)", + " Ariquemes: (-9.91°, -63.04°)", + " Guaraciaba do Norte: (-4.17°, -40.75°)", + " Juliaca: (-15.50°, -70.13°)", + " Lugo: (44.42°, 11.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lugo: 7583.6 km from centroid", + " Tarma: 3388.8 km from centroid", + " Juliaca: 3066.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lugo", + "FINAL ANSWER: Lugo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.61559, + "lon": -87.52949, + "name": "Calumet City" + }, + { + "lat": 43.70775, + "lon": -79.34998, + "name": "Thorncliffe Park" + }, + { + "lat": 41.85059, + "lon": -87.79367, + "name": "Berwyn" + }, + { + "lat": 38.79289, + "lon": -77.49749, + "name": "Sudley" + }, + { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + } + ], + "question": "Which location is the geographic outlier among: Calumet City, Thorncliffe Park, Berwyn, Sudley, Moonee Ponds?", + "ground_truth": { + "answer": "Moonee Ponds", + "outlier_distance_km": 18648.3, + "second_furthest_km": 4911.5, + "clarity_ratio": 3.8, + "median_distance_km": 4887.4, + "distances_to_centroid": { + "Calumet City": 4887.4, + "Thorncliffe Park": 4266.1, + "Berwyn": 4911.5, + "Sudley": 4003.1, + "Moonee Ponds": 18648.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Calumet City: (41.62°, -87.53°)", + " Thorncliffe Park: (43.71°, -79.35°)", + " Berwyn: (41.85°, -87.79°)", + " Sudley: (38.79°, -77.50°)", + " Moonee Ponds: (-37.77°, 144.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Moonee Ponds: 18648.3 km from centroid", + " Berwyn: 4911.5 km from centroid", + " Calumet City: 4887.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Moonee Ponds", + "FINAL ANSWER: Moonee Ponds" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.15038, + "lon": 6.83042, + "name": "Nkpor" + }, + { + "lat": 30.12303, + "lon": 31.13571, + "name": "Awsīm" + }, + { + "lat": 6.01798, + "lon": 7.02027, + "name": "Igbo-Ukwu" + }, + { + "lat": 5.35328, + "lon": 5.50826, + "name": "Burutu" + }, + { + "lat": -43.30437, + "lon": 172.58356, + "name": "Rangiora" + } + ], + "question": "Which location is the geographic outlier among: Nkpor, Awsīm, Igbo-Ukwu, Burutu, Rangiora?", + "ground_truth": { + "answer": "Rangiora", + "outlier_distance_km": 13038.9, + "second_furthest_km": 4369.3, + "clarity_ratio": 2.98, + "median_distance_km": 4232.8, + "distances_to_centroid": { + "Nkpor": 4232.8, + "Awsīm": 3551.3, + "Igbo-Ukwu": 4210.3, + "Burutu": 4369.3, + "Rangiora": 13038.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nkpor: (6.15°, 6.83°)", + " Awsīm: (30.12°, 31.14°)", + " Igbo-Ukwu: (6.02°, 7.02°)", + " Burutu: (5.35°, 5.51°)", + " Rangiora: (-43.30°, 172.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rangiora: 13038.9 km from centroid", + " Burutu: 4369.3 km from centroid", + " Nkpor: 4232.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rangiora", + "FINAL ANSWER: Rangiora" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.56056, + "lon": 151.95386, + "name": "Toowoomba" + }, + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": -28.44917, + "lon": -52.2, + "name": "Marau" + } + ], + "question": "Which location is the geographic outlier among: Toowoomba, Malvern East, Sunnybank Hills, Dunedin, Marau?", + "ground_truth": { + "answer": "Marau", + "outlier_distance_km": 12970.4, + "second_furthest_km": 4944.7, + "clarity_ratio": 2.62, + "median_distance_km": 3804.7, + "distances_to_centroid": { + "Toowoomba": 3704.5, + "Malvern East": 2861.9, + "Sunnybank Hills": 3804.7, + "Dunedin": 4944.7, + "Marau": 12970.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Toowoomba: (-27.56°, 151.95°)", + " Malvern East: (-37.87°, 145.04°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Dunedin: (-45.87°, 170.50°)", + " Marau: (-28.45°, -52.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marau: 12970.4 km from centroid", + " Dunedin: 4944.7 km from centroid", + " Sunnybank Hills: 3804.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marau", + "FINAL ANSWER: Marau" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.56333, + "lon": 34.93583, + "name": "Nyamira" + }, + { + "lat": 9.98333, + "lon": 39.98333, + "name": "Abomsa" + }, + { + "lat": 29.4075, + "lon": 31.2525, + "name": "Aţfīḩ" + }, + { + "lat": -25.77507, + "lon": 29.46482, + "name": "Middelburg" + }, + { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + } + ], + "question": "Which location is the geographic outlier among: Nyamira, Abomsa, Aţfīḩ, Middelburg, Scarborough?", + "ground_truth": { + "answer": "Scarborough", + "outlier_distance_km": 7481.0, + "second_furthest_km": 4210.0, + "clarity_ratio": 1.78, + "median_distance_km": 3304.3, + "distances_to_centroid": { + "Nyamira": 1741.6, + "Abomsa": 1907.6, + "Aţfīḩ": 4210.0, + "Middelburg": 3304.3, + "Scarborough": 7481.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nyamira: (-0.56°, 34.94°)", + " Abomsa: (9.98°, 39.98°)", + " Aţfīḩ: (29.41°, 31.25°)", + " Middelburg: (-25.78°, 29.46°)", + " Scarborough: (-31.90°, 115.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Scarborough: 7481.0 km from centroid", + " Aţfīḩ: 4210.0 km from centroid", + " Middelburg: 3304.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Scarborough", + "FINAL ANSWER: Scarborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.51461, + "lon": 9.28772, + "name": "Vimodrone" + }, + { + "lat": 53.52285, + "lon": -1.13116, + "name": "Doncaster" + }, + { + "lat": 58.45073, + "lon": 92.17243, + "name": "Yeniseysk" + }, + { + "lat": 51.53782, + "lon": 0.71433, + "name": "Southend-on-Sea" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + } + ], + "question": "Which location is the geographic outlier among: Vimodrone, Doncaster, Yeniseysk, Southend-on-Sea, Redbank Plains?", + "ground_truth": { + "answer": "Redbank Plains", + "outlier_distance_km": 12797.0, + "second_furthest_km": 4394.3, + "clarity_ratio": 2.91, + "median_distance_km": 4254.7, + "distances_to_centroid": { + "Vimodrone": 3591.6, + "Doncaster": 4394.3, + "Yeniseysk": 3874.9, + "Southend-on-Sea": 4254.7, + "Redbank Plains": 12797.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vimodrone: (45.51°, 9.29°)", + " Doncaster: (53.52°, -1.13°)", + " Yeniseysk: (58.45°, 92.17°)", + " Southend-on-Sea: (51.54°, 0.71°)", + " Redbank Plains: (-27.65°, 152.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Redbank Plains: 12797.0 km from centroid", + " Doncaster: 4394.3 km from centroid", + " Southend-on-Sea: 4254.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Redbank Plains", + "FINAL ANSWER: Redbank Plains" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.59754, + "lon": -112.27182, + "name": "Sun City" + }, + { + "lat": 19.18666, + "lon": -102.8493, + "name": "Tepalcatepec" + }, + { + "lat": 44.30011, + "lon": -79.64964, + "name": "Innisfil" + }, + { + "lat": 34.30778, + "lon": -118.44925, + "name": "Sylmar" + }, + { + "lat": 43.14322, + "lon": -2.96204, + "name": "Laudio / Llodio" + } + ], + "question": "Which location is the geographic outlier among: Sun City, Tepalcatepec, Innisfil, Sylmar, Laudio / Llodio?", + "ground_truth": { + "answer": "Laudio / Llodio", + "outlier_distance_km": 6727.5, + "second_furthest_km": 3206.6, + "clarity_ratio": 2.1, + "median_distance_km": 2663.3, + "distances_to_centroid": { + "Sun City": 2663.3, + "Tepalcatepec": 2603.5, + "Innisfil": 1088.4, + "Sylmar": 3206.6, + "Laudio / Llodio": 6727.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sun City: (33.60°, -112.27°)", + " Tepalcatepec: (19.19°, -102.85°)", + " Innisfil: (44.30°, -79.65°)", + " Sylmar: (34.31°, -118.45°)", + " Laudio / Llodio: (43.14°, -2.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Laudio / Llodio: 6727.5 km from centroid", + " Sylmar: 3206.6 km from centroid", + " Sun City: 2663.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Laudio / Llodio", + "FINAL ANSWER: Laudio / Llodio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.94889, + "lon": -102.70222, + "name": "Víctor Rosales" + }, + { + "lat": 41.42973, + "lon": -97.36838, + "name": "Columbus" + }, + { + "lat": 35.07681, + "lon": -80.66924, + "name": "Indian Trail" + }, + { + "lat": 41.9217, + "lon": -87.64783, + "name": "Lincoln Park" + }, + { + "lat": 34.76143, + "lon": 135.51567, + "name": "Suita" + } + ], + "question": "Which location is the geographic outlier among: Víctor Rosales, Columbus, Indian Trail, Lincoln Park, Suita?", + "ground_truth": { + "answer": "Suita", + "outlier_distance_km": 12229.6, + "second_furthest_km": 5548.4, + "clarity_ratio": 2.2, + "median_distance_km": 4420.1, + "distances_to_centroid": { + "Víctor Rosales": 5548.4, + "Columbus": 4420.1, + "Indian Trail": 3084.3, + "Lincoln Park": 3611.5, + "Suita": 12229.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Víctor Rosales: (22.95°, -102.70°)", + " Columbus: (41.43°, -97.37°)", + " Indian Trail: (35.08°, -80.67°)", + " Lincoln Park: (41.92°, -87.65°)", + " Suita: (34.76°, 135.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Suita: 12229.6 km from centroid", + " Víctor Rosales: 5548.4 km from centroid", + " Columbus: 4420.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Suita", + "FINAL ANSWER: Suita" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.86417, + "lon": -55.5025, + "name": "Sinop" + }, + { + "lat": -20.96278, + "lon": -42.04083, + "name": "Porciúncula" + }, + { + "lat": -12.05605, + "lon": -77.05295, + "name": "Breña" + }, + { + "lat": -29.95917, + "lon": -51.72222, + "name": "São Jerônimo" + }, + { + "lat": 51.65877, + "lon": 6.45297, + "name": "Xanten" + } + ], + "question": "Which location is the geographic outlier among: Sinop, Porciúncula, Breña, São Jerônimo, Xanten?", + "ground_truth": { + "answer": "Xanten", + "outlier_distance_km": 7861.5, + "second_furthest_km": 3728.0, + "clarity_ratio": 2.11, + "median_distance_km": 2931.0, + "distances_to_centroid": { + "Sinop": 1501.1, + "Porciúncula": 1827.3, + "Breña": 3728.0, + "São Jerônimo": 2931.0, + "Xanten": 7861.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sinop: (-11.86°, -55.50°)", + " Porciúncula: (-20.96°, -42.04°)", + " Breña: (-12.06°, -77.05°)", + " São Jerônimo: (-29.96°, -51.72°)", + " Xanten: (51.66°, 6.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xanten: 7861.5 km from centroid", + " Breña: 3728.0 km from centroid", + " São Jerônimo: 2931.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xanten", + "FINAL ANSWER: Xanten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.80645, + "lon": -65.41999, + "name": "Salta" + }, + { + "lat": -17.16639, + "lon": -40.33, + "name": "Itanhém" + }, + { + "lat": -11.51893, + "lon": -75.89935, + "name": "La Oroya" + }, + { + "lat": -22.70861, + "lon": -42.60972, + "name": "Rio Bonito" + }, + { + "lat": -26.45794, + "lon": 29.46553, + "name": "Bethal" + } + ], + "question": "Which location is the geographic outlier among: Salta, Itanhém, La Oroya, Rio Bonito, Bethal?", + "ground_truth": { + "answer": "Bethal", + "outlier_distance_km": 6929.4, + "second_furthest_km": 4063.0, + "clarity_ratio": 1.71, + "median_distance_km": 2751.8, + "distances_to_centroid": { + "Salta": 2751.8, + "Itanhém": 401.1, + "La Oroya": 4063.0, + "Rio Bonito": 448.3, + "Bethal": 6929.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Salta: (-24.81°, -65.42°)", + " Itanhém: (-17.17°, -40.33°)", + " La Oroya: (-11.52°, -75.90°)", + " Rio Bonito: (-22.71°, -42.61°)", + " Bethal: (-26.46°, 29.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bethal: 6929.4 km from centroid", + " La Oroya: 4063.0 km from centroid", + " Salta: 2751.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bethal", + "FINAL ANSWER: Bethal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.81509, + "lon": -92.22432, + "name": "Sherwood" + }, + { + "lat": 34.03612, + "lon": -117.99118, + "name": "Avocado Heights" + }, + { + "lat": 30.67436, + "lon": -96.36996, + "name": "Bryan" + }, + { + "lat": 34.59593, + "lon": -92.48905, + "name": "Bryant" + }, + { + "lat": -33.88374, + "lon": 151.21282, + "name": "Surry Hills" + } + ], + "question": "Which location is the geographic outlier among: Sherwood, Avocado Heights, Bryan, Bryant, Surry Hills?", + "ground_truth": { + "answer": "Surry Hills", + "outlier_distance_km": 17453.1, + "second_furthest_km": 6830.9, + "clarity_ratio": 2.56, + "median_distance_km": 4812.6, + "distances_to_centroid": { + "Sherwood": 4478.3, + "Avocado Heights": 6830.9, + "Bryan": 4812.6, + "Bryant": 4498.0, + "Surry Hills": 17453.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sherwood: (34.82°, -92.22°)", + " Avocado Heights: (34.04°, -117.99°)", + " Bryan: (30.67°, -96.37°)", + " Bryant: (34.60°, -92.49°)", + " Surry Hills: (-33.88°, 151.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Surry Hills: 17453.1 km from centroid", + " Avocado Heights: 6830.9 km from centroid", + " Bryan: 4812.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Surry Hills", + "FINAL ANSWER: Surry Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.06775, + "lon": 105.26485, + "name": "Luotang" + }, + { + "lat": 10.79366, + "lon": 78.76898, + "name": "Tiruverumbūr" + }, + { + "lat": 35.27389, + "lon": 119.37028, + "name": "Taoluo" + }, + { + "lat": 36.78361, + "lon": 127.00417, + "name": "Asan" + }, + { + "lat": 28.98888, + "lon": -80.90228, + "name": "Edgewater" + } + ], + "question": "Which location is the geographic outlier among: Luotang, Tiruverumbūr, Taoluo, Asan, Edgewater?", + "ground_truth": { + "answer": "Edgewater", + "outlier_distance_km": 12861.6, + "second_furthest_km": 5324.3, + "clarity_ratio": 2.42, + "median_distance_km": 4662.8, + "distances_to_centroid": { + "Luotang": 3384.3, + "Tiruverumbūr": 2222.5, + "Taoluo": 4662.8, + "Asan": 5324.3, + "Edgewater": 12861.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Luotang: (33.07°, 105.26°)", + " Tiruverumbūr: (10.79°, 78.77°)", + " Taoluo: (35.27°, 119.37°)", + " Asan: (36.78°, 127.00°)", + " Edgewater: (28.99°, -80.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Edgewater: 12861.6 km from centroid", + " Asan: 5324.3 km from centroid", + " Taoluo: 4662.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Edgewater", + "FINAL ANSWER: Edgewater" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.60157, + "lon": -98.46152, + "name": "Izúcar de Matamoros" + }, + { + "lat": 47.03426, + "lon": -122.82319, + "name": "Lacey" + }, + { + "lat": 23.1749, + "lon": -102.86785, + "name": "Fresnillo" + }, + { + "lat": 49.23839, + "lon": -122.86676, + "name": "Maillardville" + }, + { + "lat": -13.53806, + "lon": -39.09861, + "name": "Taperoá" + } + ], + "question": "Which location is the geographic outlier among: Izúcar de Matamoros, Lacey, Fresnillo, Maillardville, Taperoá?", + "ground_truth": { + "answer": "Taperoá", + "outlier_distance_km": 7612.8, + "second_furthest_km": 3500.5, + "clarity_ratio": 2.17, + "median_distance_km": 3340.8, + "distances_to_centroid": { + "Izúcar de Matamoros": 712.2, + "Lacey": 3340.8, + "Fresnillo": 604.4, + "Maillardville": 3500.5, + "Taperoá": 7612.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Izúcar de Matamoros: (18.60°, -98.46°)", + " Lacey: (47.03°, -122.82°)", + " Fresnillo: (23.17°, -102.87°)", + " Maillardville: (49.24°, -122.87°)", + " Taperoá: (-13.54°, -39.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taperoá: 7612.8 km from centroid", + " Maillardville: 3500.5 km from centroid", + " Lacey: 3340.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taperoá", + "FINAL ANSWER: Taperoá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + }, + { + "lat": 1.25881, + "lon": 35.09569, + "name": "Makutano" + } + ], + "question": "Which location is the geographic outlier among: Banora Point, Hobart, Caulfield North, Mascot, Makutano?", + "ground_truth": { + "answer": "Makutano", + "outlier_distance_km": 10205.1, + "second_furthest_km": 2648.4, + "clarity_ratio": 3.85, + "median_distance_km": 2474.7, + "distances_to_centroid": { + "Banora Point": 2648.4, + "Hobart": 2474.7, + "Caulfield North": 2025.2, + "Mascot": 2430.7, + "Makutano": 10205.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banora Point: (-28.21°, 153.54°)", + " Hobart: (-42.88°, 147.33°)", + " Caulfield North: (-37.87°, 145.02°)", + " Mascot: (-33.93°, 151.19°)", + " Makutano: (1.26°, 35.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Makutano: 10205.1 km from centroid", + " Banora Point: 2648.4 km from centroid", + " Hobart: 2474.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Makutano", + "FINAL ANSWER: Makutano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.72173, + "lon": 25.58804, + "name": "Somerset East" + }, + { + "lat": 6.60084, + "lon": 0.4713, + "name": "Ho" + }, + { + "lat": -27.78324, + "lon": 24.68768, + "name": "Pampierstad" + }, + { + "lat": 8.45, + "lon": 39.28333, + "name": "Wenjī" + }, + { + "lat": 39.60678, + "lon": -75.83327, + "name": "Elkton" + } + ], + "question": "Which location is the geographic outlier among: Somerset East, Ho, Pampierstad, Wenjī, Elkton?", + "ground_truth": { + "answer": "Elkton", + "outlier_distance_km": 9123.7, + "second_furthest_km": 4238.6, + "clarity_ratio": 2.15, + "median_distance_km": 4178.3, + "distances_to_centroid": { + "Somerset East": 4238.6, + "Ho": 903.1, + "Pampierstad": 3763.8, + "Wenjī": 4178.3, + "Elkton": 9123.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Somerset East: (-32.72°, 25.59°)", + " Ho: (6.60°, 0.47°)", + " Pampierstad: (-27.78°, 24.69°)", + " Wenjī: (8.45°, 39.28°)", + " Elkton: (39.61°, -75.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Elkton: 9123.7 km from centroid", + " Somerset East: 4238.6 km from centroid", + " Wenjī: 4178.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Elkton", + "FINAL ANSWER: Elkton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 63.56904, + "lon": 53.69141, + "name": "Ukhta" + }, + { + "lat": 45.76106, + "lon": 4.82677, + "name": "Lyon 05" + }, + { + "lat": 51.5388, + "lon": 7.22572, + "name": "Herne" + }, + { + "lat": 41.27733, + "lon": 16.41011, + "name": "Trani" + }, + { + "lat": 34.97159, + "lon": 138.94643, + "name": "Izu" + } + ], + "question": "Which location is the geographic outlier among: Ukhta, Lyon 05, Herne, Trani, Izu?", + "ground_truth": { + "answer": "Izu", + "outlier_distance_km": 7549.0, + "second_furthest_km": 2983.5, + "clarity_ratio": 2.53, + "median_distance_km": 2681.8, + "distances_to_centroid": { + "Ukhta": 1887.1, + "Lyon 05": 2983.5, + "Herne": 2681.8, + "Trani": 2300.3, + "Izu": 7549.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ukhta: (63.57°, 53.69°)", + " Lyon 05: (45.76°, 4.83°)", + " Herne: (51.54°, 7.23°)", + " Trani: (41.28°, 16.41°)", + " Izu: (34.97°, 138.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Izu: 7549.0 km from centroid", + " Lyon 05: 2983.5 km from centroid", + " Herne: 2681.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Izu", + "FINAL ANSWER: Izu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.70083, + "lon": 122.99111, + "name": "Zhuanghe" + }, + { + "lat": 11.1683, + "lon": 123.7223, + "name": "Bantayan" + }, + { + "lat": 34.85, + "lon": 136.45, + "name": "Kameyama" + }, + { + "lat": 47.23489, + "lon": 127.10769, + "name": "Suiling" + }, + { + "lat": 40.65205, + "lon": -73.95903, + "name": "Flatbush" + } + ], + "question": "Which location is the geographic outlier among: Zhuanghe, Bantayan, Kameyama, Suiling, Flatbush?", + "ground_truth": { + "answer": "Flatbush", + "outlier_distance_km": 11416.3, + "second_furthest_km": 4518.5, + "clarity_ratio": 2.53, + "median_distance_km": 4444.9, + "distances_to_centroid": { + "Zhuanghe": 3190.5, + "Bantayan": 4518.5, + "Kameyama": 4444.9, + "Suiling": 3575.1, + "Flatbush": 11416.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhuanghe: (39.70°, 122.99°)", + " Bantayan: (11.17°, 123.72°)", + " Kameyama: (34.85°, 136.45°)", + " Suiling: (47.23°, 127.11°)", + " Flatbush: (40.65°, -73.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Flatbush: 11416.3 km from centroid", + " Bantayan: 4518.5 km from centroid", + " Kameyama: 4444.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Flatbush", + "FINAL ANSWER: Flatbush" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.34564, + "lon": -98.86034, + "name": "San Francisco Acuautla" + }, + { + "lat": 41.88142, + "lon": -87.88312, + "name": "Bellwood" + }, + { + "lat": 41.60232, + "lon": -72.98677, + "name": "Wolcott" + }, + { + "lat": 33.976, + "lon": -118.06909, + "name": "West Whittier-Los Nietos" + }, + { + "lat": -26.81358, + "lon": 27.81695, + "name": "Sasolburg" + } + ], + "question": "Which location is the geographic outlier among: San Francisco Acuautla, Bellwood, Wolcott, West Whittier-Los Nietos, Sasolburg?", + "ground_truth": { + "answer": "Sasolburg", + "outlier_distance_km": 11825.3, + "second_furthest_km": 4858.0, + "clarity_ratio": 2.43, + "median_distance_km": 3012.9, + "distances_to_centroid": { + "San Francisco Acuautla": 3012.9, + "Bellwood": 2769.1, + "Wolcott": 2197.7, + "West Whittier-Los Nietos": 4858.0, + "Sasolburg": 11825.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Francisco Acuautla: (19.35°, -98.86°)", + " Bellwood: (41.88°, -87.88°)", + " Wolcott: (41.60°, -72.99°)", + " West Whittier-Los Nietos: (33.98°, -118.07°)", + " Sasolburg: (-26.81°, 27.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sasolburg: 11825.3 km from centroid", + " West Whittier-Los Nietos: 4858.0 km from centroid", + " San Francisco Acuautla: 3012.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sasolburg", + "FINAL ANSWER: Sasolburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.33083, + "lon": 28.14981, + "name": "Butterworth" + }, + { + "lat": 11.10389, + "lon": 5.25556, + "name": "Rijau" + }, + { + "lat": -29.01269, + "lon": 29.86619, + "name": "Estcourt" + }, + { + "lat": -27.1974, + "lon": 25.98311, + "name": "Wolmaransstad" + }, + { + "lat": 54.41166, + "lon": 18.5984, + "name": "Przymorze Wielkie" + } + ], + "question": "Which location is the geographic outlier among: Butterworth, Rijau, Estcourt, Wolmaransstad, Przymorze Wielkie?", + "ground_truth": { + "answer": "Przymorze Wielkie", + "outlier_distance_km": 6568.2, + "second_furthest_km": 3158.1, + "clarity_ratio": 2.08, + "median_distance_km": 2851.4, + "distances_to_centroid": { + "Butterworth": 3158.1, + "Rijau": 2512.1, + "Estcourt": 2851.4, + "Wolmaransstad": 2555.4, + "Przymorze Wielkie": 6568.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Butterworth: (-32.33°, 28.15°)", + " Rijau: (11.10°, 5.26°)", + " Estcourt: (-29.01°, 29.87°)", + " Wolmaransstad: (-27.20°, 25.98°)", + " Przymorze Wielkie: (54.41°, 18.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Przymorze Wielkie: 6568.2 km from centroid", + " Butterworth: 3158.1 km from centroid", + " Estcourt: 2851.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Przymorze Wielkie", + "FINAL ANSWER: Przymorze Wielkie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + { + "lat": -22.15214, + "lon": -42.92335, + "name": "São José do Vale do Rio Preto" + } + ], + "question": "Which location is the geographic outlier among: Greenvale, Rockingham, Ashfield, Lalor, São José do Vale do Rio Preto?", + "ground_truth": { + "answer": "São José do Vale do Rio Preto", + "outlier_distance_km": 12908.3, + "second_furthest_km": 4453.7, + "clarity_ratio": 2.9, + "median_distance_km": 3846.1, + "distances_to_centroid": { + "Greenvale": 3833.3, + "Rockingham": 1216.3, + "Ashfield": 4453.7, + "Lalor": 3846.1, + "São José do Vale do Rio Preto": 12908.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Greenvale: (-37.63°, 144.87°)", + " Rockingham: (-32.28°, 115.73°)", + " Ashfield: (-33.89°, 151.12°)", + " Lalor: (-37.67°, 145.02°)", + " São José do Vale do Rio Preto: (-22.15°, -42.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São José do Vale do Rio Preto: 12908.3 km from centroid", + " Ashfield: 4453.7 km from centroid", + " Lalor: 3846.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São José do Vale do Rio Preto", + "FINAL ANSWER: São José do Vale do Rio Preto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.93333, + "lon": 100.88333, + "name": "Pattaya" + }, + { + "lat": 8.16667, + "lon": 124.21667, + "name": "Mantampay" + }, + { + "lat": 32.68222, + "lon": 112.08194, + "name": "Dengzhou" + }, + { + "lat": 35.76417, + "lon": 116.79139, + "name": "Ningyang" + }, + { + "lat": -10.7375, + "lon": -37.08167, + "name": "Maruim" + } + ], + "question": "Which location is the geographic outlier among: Pattaya, Mantampay, Dengzhou, Ningyang, Maruim?", + "ground_truth": { + "answer": "Maruim", + "outlier_distance_km": 13566.0, + "second_furthest_km": 4514.1, + "clarity_ratio": 3.01, + "median_distance_km": 3985.7, + "distances_to_centroid": { + "Pattaya": 1911.1, + "Mantampay": 4514.1, + "Dengzhou": 3447.0, + "Ningyang": 3985.7, + "Maruim": 13566.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pattaya: (12.93°, 100.88°)", + " Mantampay: (8.17°, 124.22°)", + " Dengzhou: (32.68°, 112.08°)", + " Ningyang: (35.76°, 116.79°)", + " Maruim: (-10.74°, -37.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maruim: 13566.0 km from centroid", + " Mantampay: 4514.1 km from centroid", + " Ningyang: 3985.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maruim", + "FINAL ANSWER: Maruim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.51472, + "lon": -51.43361, + "name": "Junqueirópolis" + }, + { + "lat": -3.44611, + "lon": -52.88889, + "name": "Medicilândia" + }, + { + "lat": -35.84667, + "lon": -71.59308, + "name": "Linares" + }, + { + "lat": -22.63333, + "lon": -47.05, + "name": "Terra Preta" + }, + { + "lat": 25.76343, + "lon": -80.37311, + "name": "Sweetwater" + } + ], + "question": "Which location is the geographic outlier among: Junqueirópolis, Medicilândia, Linares, Terra Preta, Sweetwater?", + "ground_truth": { + "answer": "Sweetwater", + "outlier_distance_km": 4663.8, + "second_furthest_km": 2918.1, + "clarity_ratio": 1.6, + "median_distance_km": 1899.6, + "distances_to_centroid": { + "Junqueirópolis": 1482.2, + "Medicilândia": 1242.3, + "Linares": 2918.1, + "Terra Preta": 1899.6, + "Sweetwater": 4663.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Junqueirópolis: (-21.51°, -51.43°)", + " Medicilândia: (-3.45°, -52.89°)", + " Linares: (-35.85°, -71.59°)", + " Terra Preta: (-22.63°, -47.05°)", + " Sweetwater: (25.76°, -80.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sweetwater: 4663.8 km from centroid", + " Linares: 2918.1 km from centroid", + " Terra Preta: 1899.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sweetwater", + "FINAL ANSWER: Sweetwater" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.89359, + "lon": 145.05534, + "name": "Carnegie" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + { + "lat": -10.6875, + "lon": -37.86167, + "name": "Paripiranga" + } + ], + "question": "Which location is the geographic outlier among: Carnegie, Ashburton, Clayton, Cambridge, Paripiranga?", + "ground_truth": { + "answer": "Paripiranga", + "outlier_distance_km": 14551.8, + "second_furthest_km": 4959.6, + "clarity_ratio": 2.93, + "median_distance_km": 4557.1, + "distances_to_centroid": { + "Carnegie": 2310.7, + "Ashburton": 4557.1, + "Clayton": 2316.2, + "Cambridge": 4959.6, + "Paripiranga": 14551.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carnegie: (-37.89°, 145.06°)", + " Ashburton: (-43.90°, 171.73°)", + " Clayton: (-37.92°, 145.12°)", + " Cambridge: (-37.88°, 175.44°)", + " Paripiranga: (-10.69°, -37.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paripiranga: 14551.8 km from centroid", + " Cambridge: 4959.6 km from centroid", + " Ashburton: 4557.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paripiranga", + "FINAL ANSWER: Paripiranga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.72059, + "lon": -87.70172, + "name": "Evergreen Park" + }, + { + "lat": 29.36857, + "lon": -94.97131, + "name": "La Marque" + }, + { + "lat": 41.44987, + "lon": -72.81892, + "name": "Wallingford Center" + }, + { + "lat": 39.50956, + "lon": -76.16412, + "name": "Aberdeen" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + } + ], + "question": "Which location is the geographic outlier among: Evergreen Park, La Marque, Wallingford Center, Aberdeen, Wollongong city centre?", + "ground_truth": { + "answer": "Wollongong city centre", + "outlier_distance_km": 18623.4, + "second_furthest_km": 5832.2, + "clarity_ratio": 3.19, + "median_distance_km": 5145.6, + "distances_to_centroid": { + "Evergreen Park": 5145.6, + "La Marque": 5832.2, + "Wallingford Center": 3932.5, + "Aberdeen": 4144.8, + "Wollongong city centre": 18623.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Evergreen Park: (41.72°, -87.70°)", + " La Marque: (29.37°, -94.97°)", + " Wallingford Center: (41.45°, -72.82°)", + " Aberdeen: (39.51°, -76.16°)", + " Wollongong city centre: (-34.43°, 150.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wollongong city centre: 18623.4 km from centroid", + " La Marque: 5832.2 km from centroid", + " Evergreen Park: 5145.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wollongong city centre", + "FINAL ANSWER: Wollongong city centre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + }, + { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + }, + { + "lat": 40.8601, + "lon": -73.9093, + "name": "University Heights" + } + ], + "question": "Which location is the geographic outlier among: Wangaratta, Hawthorn, Moonee Ponds, Levin, University Heights?", + "ground_truth": { + "answer": "University Heights", + "outlier_distance_km": 17951.7, + "second_furthest_km": 6572.8, + "clarity_ratio": 2.73, + "median_distance_km": 4036.4, + "distances_to_centroid": { + "Wangaratta": 4036.4, + "Hawthorn": 3963.0, + "Moonee Ponds": 3951.3, + "Levin": 6572.8, + "University Heights": 17951.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wangaratta: (-36.36°, 146.32°)", + " Hawthorn: (-37.82°, 145.04°)", + " Moonee Ponds: (-37.77°, 144.92°)", + " Levin: (-40.63°, 175.28°)", + " University Heights: (40.86°, -73.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " University Heights: 17951.7 km from centroid", + " Levin: 6572.8 km from centroid", + " Wangaratta: 4036.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: University Heights", + "FINAL ANSWER: University Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.4668, + "lon": 8.99016, + "name": "Eberbach" + }, + { + "lat": 43.30482, + "lon": -8.50749, + "name": "Arteixo" + }, + { + "lat": 54.84763, + "lon": 38.18214, + "name": "Kashira" + }, + { + "lat": 48.22336, + "lon": 10.10347, + "name": "Illertissen" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + } + ], + "question": "Which location is the geographic outlier among: Eberbach, Arteixo, Kashira, Illertissen, Ashburton?", + "ground_truth": { + "answer": "Ashburton", + "outlier_distance_km": 15223.6, + "second_furthest_km": 4811.0, + "clarity_ratio": 3.16, + "median_distance_km": 3617.6, + "distances_to_centroid": { + "Eberbach": 3617.6, + "Arteixo": 4811.0, + "Kashira": 2760.1, + "Illertissen": 3489.5, + "Ashburton": 15223.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eberbach: (49.47°, 8.99°)", + " Arteixo: (43.30°, -8.51°)", + " Kashira: (54.85°, 38.18°)", + " Illertissen: (48.22°, 10.10°)", + " Ashburton: (-43.90°, 171.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ashburton: 15223.6 km from centroid", + " Arteixo: 4811.0 km from centroid", + " Eberbach: 3617.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ashburton", + "FINAL ANSWER: Ashburton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -46.4, + "lon": 168.35, + "name": "Invercargill" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + { + "lat": 51.22097, + "lon": 18.56964, + "name": "Wieluń" + } + ], + "question": "Which location is the geographic outlier among: Invercargill, Liverpool, Lincoln, Mosman, Wieluń?", + "ground_truth": { + "answer": "Wieluń", + "outlier_distance_km": 13396.2, + "second_furthest_km": 4461.0, + "clarity_ratio": 3.0, + "median_distance_km": 4366.5, + "distances_to_centroid": { + "Invercargill": 4366.5, + "Liverpool": 2371.7, + "Lincoln": 4461.0, + "Mosman": 2389.9, + "Wieluń": 13396.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Invercargill: (-46.40°, 168.35°)", + " Liverpool: (-33.92°, 150.93°)", + " Lincoln: (-36.86°, 174.62°)", + " Mosman: (-33.84°, 151.24°)", + " Wieluń: (51.22°, 18.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wieluń: 13396.2 km from centroid", + " Lincoln: 4461.0 km from centroid", + " Invercargill: 4366.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wieluń", + "FINAL ANSWER: Wieluń" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.65055, + "lon": -46.64591, + "name": "Jabaquara" + }, + { + "lat": -6.33833, + "lon": -47.39917, + "name": "Porto Franco" + }, + { + "lat": -6.64472, + "lon": -51.995, + "name": "São Félix do Xingu" + }, + { + "lat": -9.66583, + "lon": -35.73528, + "name": "Maceió" + }, + { + "lat": 47.67323, + "lon": -117.23937, + "name": "Spokane Valley" + } + ], + "question": "Which location is the geographic outlier among: Jabaquara, Porto Franco, São Félix do Xingu, Maceió, Spokane Valley?", + "ground_truth": { + "answer": "Spokane Valley", + "outlier_distance_km": 7620.5, + "second_furthest_km": 3015.9, + "clarity_ratio": 2.53, + "median_distance_km": 2883.9, + "distances_to_centroid": { + "Jabaquara": 3015.9, + "Porto Franco": 1560.6, + "São Félix do Xingu": 1158.7, + "Maceió": 2883.9, + "Spokane Valley": 7620.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jabaquara: (-23.65°, -46.65°)", + " Porto Franco: (-6.34°, -47.40°)", + " São Félix do Xingu: (-6.64°, -51.99°)", + " Maceió: (-9.67°, -35.74°)", + " Spokane Valley: (47.67°, -117.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Spokane Valley: 7620.5 km from centroid", + " Jabaquara: 3015.9 km from centroid", + " Maceió: 2883.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Spokane Valley", + "FINAL ANSWER: Spokane Valley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.79688, + "lon": 6.74048, + "name": "Lokoja" + }, + { + "lat": -26.26781, + "lon": 27.85849, + "name": "Soweto" + }, + { + "lat": 7.53333, + "lon": 39.25, + "name": "Bek’ojī" + }, + { + "lat": 10.7, + "lon": 37.26667, + "name": "Finote Selam" + }, + { + "lat": 33.6103, + "lon": -114.59635, + "name": "Blythe" + } + ], + "question": "Which location is the geographic outlier among: Lokoja, Soweto, Bek’ojī, Finote Selam, Blythe?", + "ground_truth": { + "answer": "Blythe", + "outlier_distance_km": 11754.6, + "second_furthest_km": 4785.8, + "clarity_ratio": 2.46, + "median_distance_km": 4407.3, + "distances_to_centroid": { + "Lokoja": 829.7, + "Soweto": 4785.8, + "Bek’ojī": 4407.3, + "Finote Selam": 4194.1, + "Blythe": 11754.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lokoja: (7.80°, 6.74°)", + " Soweto: (-26.27°, 27.86°)", + " Bek’ojī: (7.53°, 39.25°)", + " Finote Selam: (10.70°, 37.27°)", + " Blythe: (33.61°, -114.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blythe: 11754.6 km from centroid", + " Soweto: 4785.8 km from centroid", + " Bek’ojī: 4407.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blythe", + "FINAL ANSWER: Blythe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.52694, + "lon": -41.945, + "name": "Rio das Ostras" + }, + { + "lat": -21.60333, + "lon": -48.36583, + "name": "Matão" + }, + { + "lat": -1.9175, + "lon": -55.51806, + "name": "Óbidos" + }, + { + "lat": -34.98279, + "lon": -71.23943, + "name": "Curicó" + }, + { + "lat": 38.84622, + "lon": -77.30637, + "name": "Fairfax" + } + ], + "question": "Which location is the geographic outlier among: Rio das Ostras, Matão, Óbidos, Curicó, Fairfax?", + "ground_truth": { + "answer": "Fairfax", + "outlier_distance_km": 5592.4, + "second_furthest_km": 3209.4, + "clarity_ratio": 1.74, + "median_distance_km": 2392.5, + "distances_to_centroid": { + "Rio das Ostras": 2392.5, + "Matão": 1846.7, + "Óbidos": 814.6, + "Curicó": 3209.4, + "Fairfax": 5592.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rio das Ostras: (-22.53°, -41.95°)", + " Matão: (-21.60°, -48.37°)", + " Óbidos: (-1.92°, -55.52°)", + " Curicó: (-34.98°, -71.24°)", + " Fairfax: (38.85°, -77.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fairfax: 5592.4 km from centroid", + " Curicó: 3209.4 km from centroid", + " Rio das Ostras: 2392.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fairfax", + "FINAL ANSWER: Fairfax" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.85193, + "lon": 14.47826, + "name": "Ottaviano" + }, + { + "lat": 37.40881, + "lon": -4.48522, + "name": "Lucena" + }, + { + "lat": 37.31065, + "lon": 13.57661, + "name": "Agrigento" + }, + { + "lat": 41.99771, + "lon": 12.61814, + "name": "Tor Lupara" + }, + { + "lat": 45.67965, + "lon": -111.03856, + "name": "Bozeman" + } + ], + "question": "Which location is the geographic outlier among: Ottaviano, Lucena, Agrigento, Tor Lupara, Bozeman?", + "ground_truth": { + "answer": "Bozeman", + "outlier_distance_km": 7315.9, + "second_furthest_km": 2484.2, + "clarity_ratio": 2.95, + "median_distance_km": 2468.9, + "distances_to_centroid": { + "Ottaviano": 2468.9, + "Lucena": 973.9, + "Agrigento": 2484.2, + "Tor Lupara": 2298.7, + "Bozeman": 7315.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ottaviano: (40.85°, 14.48°)", + " Lucena: (37.41°, -4.49°)", + " Agrigento: (37.31°, 13.58°)", + " Tor Lupara: (42.00°, 12.62°)", + " Bozeman: (45.68°, -111.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bozeman: 7315.9 km from centroid", + " Agrigento: 2484.2 km from centroid", + " Ottaviano: 2468.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bozeman", + "FINAL ANSWER: Bozeman" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.67717, + "lon": 100.48407, + "name": "Chom Thong" + }, + { + "lat": 23.21337, + "lon": 82.20232, + "name": "Manendragarh" + }, + { + "lat": 30.67399, + "lon": 74.75579, + "name": "Farīdkot" + }, + { + "lat": 29.71607, + "lon": 107.5976, + "name": "Jiaoshi" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + } + ], + "question": "Which location is the geographic outlier among: Chom Thong, Manendragarh, Farīdkot, Jiaoshi, Hampton Park?", + "ground_truth": { + "answer": "Hampton Park", + "outlier_distance_km": 7136.8, + "second_furthest_km": 3501.4, + "clarity_ratio": 2.04, + "median_distance_km": 2450.7, + "distances_to_centroid": { + "Chom Thong": 265.4, + "Manendragarh": 2450.7, + "Farīdkot": 3501.4, + "Jiaoshi": 2067.5, + "Hampton Park": 7136.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chom Thong: (13.68°, 100.48°)", + " Manendragarh: (23.21°, 82.20°)", + " Farīdkot: (30.67°, 74.76°)", + " Jiaoshi: (29.72°, 107.60°)", + " Hampton Park: (-38.03°, 145.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hampton Park: 7136.8 km from centroid", + " Farīdkot: 3501.4 km from centroid", + " Manendragarh: 2450.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hampton Park", + "FINAL ANSWER: Hampton Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.84861, + "lon": -50.18778, + "name": "Ibaiti" + }, + { + "lat": -20.91694, + "lon": -46.99139, + "name": "São Sebastião do Paraíso" + }, + { + "lat": -27.21787, + "lon": -61.18738, + "name": "Charata" + }, + { + "lat": -3.85444, + "lon": -40.92111, + "name": "Ubajara" + }, + { + "lat": -26.68443, + "lon": 153.05705, + "name": "Buderim" + } + ], + "question": "Which location is the geographic outlier among: Ibaiti, São Sebastião do Paraíso, Charata, Ubajara, Buderim?", + "ground_truth": { + "answer": "Buderim", + "outlier_distance_km": 14432.0, + "second_furthest_km": 5298.2, + "clarity_ratio": 2.72, + "median_distance_km": 4217.9, + "distances_to_centroid": { + "Ibaiti": 4217.9, + "São Sebastião do Paraíso": 3916.9, + "Charata": 5298.2, + "Ubajara": 3895.0, + "Buderim": 14432.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ibaiti: (-23.85°, -50.19°)", + " São Sebastião do Paraíso: (-20.92°, -46.99°)", + " Charata: (-27.22°, -61.19°)", + " Ubajara: (-3.85°, -40.92°)", + " Buderim: (-26.68°, 153.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Buderim: 14432.0 km from centroid", + " Charata: 5298.2 km from centroid", + " Ibaiti: 4217.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Buderim", + "FINAL ANSWER: Buderim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.11396, + "lon": 24.84753, + "name": "Warrenton" + }, + { + "lat": 25.91544, + "lon": 32.76287, + "name": "Qūş" + }, + { + "lat": 6.58412, + "lon": 3.98336, + "name": "Epe" + }, + { + "lat": 6.95766, + "lon": 35.55746, + "name": "Komtikas" + }, + { + "lat": 33.78252, + "lon": -117.22865, + "name": "Perris" + } + ], + "question": "Which location is the geographic outlier among: Warrenton, Qūş, Epe, Komtikas, Perris?", + "ground_truth": { + "answer": "Perris", + "outlier_distance_km": 11527.5, + "second_furthest_km": 5165.2, + "clarity_ratio": 2.23, + "median_distance_km": 4361.6, + "distances_to_centroid": { + "Warrenton": 5165.2, + "Qūş": 4307.1, + "Epe": 922.0, + "Komtikas": 4361.6, + "Perris": 11527.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warrenton: (-28.11°, 24.85°)", + " Qūş: (25.92°, 32.76°)", + " Epe: (6.58°, 3.98°)", + " Komtikas: (6.96°, 35.56°)", + " Perris: (33.78°, -117.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perris: 11527.5 km from centroid", + " Warrenton: 5165.2 km from centroid", + " Komtikas: 4361.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perris", + "FINAL ANSWER: Perris" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.14931, + "lon": -0.97469, + "name": "Alton" + }, + { + "lat": 47.21997, + "lon": 39.70769, + "name": "Rostov-na-Donu" + }, + { + "lat": 51.52609, + "lon": -0.01665, + "name": "Bow" + }, + { + "lat": 40.4724, + "lon": -3.64709, + "name": "Pinar del Rey" + }, + { + "lat": 15.7118, + "lon": 121.1061, + "name": "Rizal" + } + ], + "question": "Which location is the geographic outlier among: Alton, Rostov-na-Donu, Bow, Pinar del Rey, Rizal?", + "ground_truth": { + "answer": "Rizal", + "outlier_distance_km": 8854.1, + "second_furthest_km": 2915.6, + "clarity_ratio": 3.04, + "median_distance_km": 2686.7, + "distances_to_centroid": { + "Alton": 2686.7, + "Rostov-na-Donu": 948.5, + "Bow": 2630.9, + "Pinar del Rey": 2915.6, + "Rizal": 8854.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alton: (51.15°, -0.97°)", + " Rostov-na-Donu: (47.22°, 39.71°)", + " Bow: (51.53°, -0.02°)", + " Pinar del Rey: (40.47°, -3.65°)", + " Rizal: (15.71°, 121.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rizal: 8854.1 km from centroid", + " Pinar del Rey: 2915.6 km from centroid", + " Alton: 2686.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rizal", + "FINAL ANSWER: Rizal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.31401, + "lon": 26.82223, + "name": "Ventersdorp" + }, + { + "lat": 11.80937, + "lon": 8.84422, + "name": "Wudil" + }, + { + "lat": 5.55874, + "lon": 7.63359, + "name": "Bende" + }, + { + "lat": -1.4275, + "lon": 36.6865, + "name": "Kiserian" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + } + ], + "question": "Which location is the geographic outlier among: Ventersdorp, Wudil, Bende, Kiserian, Porirua?", + "ground_truth": { + "answer": "Porirua", + "outlier_distance_km": 11918.7, + "second_furthest_km": 5263.4, + "clarity_ratio": 2.26, + "median_distance_km": 5112.3, + "distances_to_centroid": { + "Ventersdorp": 3098.6, + "Wudil": 5263.4, + "Bende": 5112.3, + "Kiserian": 1861.1, + "Porirua": 11918.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ventersdorp: (-26.31°, 26.82°)", + " Wudil: (11.81°, 8.84°)", + " Bende: (5.56°, 7.63°)", + " Kiserian: (-1.43°, 36.69°)", + " Porirua: (-41.13°, 174.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Porirua: 11918.7 km from centroid", + " Wudil: 5263.4 km from centroid", + " Bende: 5112.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Porirua", + "FINAL ANSWER: Porirua" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.51868, + "lon": -1.9945, + "name": "West Bromwich" + }, + { + "lat": 38.19165, + "lon": -0.5658, + "name": "Santa Pola" + }, + { + "lat": 52.31394, + "lon": 9.9682, + "name": "Sehnde" + }, + { + "lat": 52.60242, + "lon": 13.43019, + "name": "Französisch Buchholz" + }, + { + "lat": 35.76417, + "lon": 116.79139, + "name": "Ningyang" + } + ], + "question": "Which location is the geographic outlier among: West Bromwich, Santa Pola, Sehnde, Französisch Buchholz, Ningyang?", + "ground_truth": { + "answer": "Ningyang", + "outlier_distance_km": 7178.7, + "second_furthest_km": 2465.3, + "clarity_ratio": 2.91, + "median_distance_km": 2227.9, + "distances_to_centroid": { + "West Bromwich": 2227.9, + "Santa Pola": 2465.3, + "Sehnde": 1434.1, + "Französisch Buchholz": 1234.8, + "Ningyang": 7178.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Bromwich: (52.52°, -1.99°)", + " Santa Pola: (38.19°, -0.57°)", + " Sehnde: (52.31°, 9.97°)", + " Französisch Buchholz: (52.60°, 13.43°)", + " Ningyang: (35.76°, 116.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ningyang: 7178.7 km from centroid", + " Santa Pola: 2465.3 km from centroid", + " West Bromwich: 2227.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ningyang", + "FINAL ANSWER: Ningyang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.2789, + "lon": -38.99584, + "name": "Itacaré" + }, + { + "lat": -21.69694, + "lon": -45.25333, + "name": "Três Corações" + }, + { + "lat": -21.37583, + "lon": -46.52556, + "name": "Muzambinho" + }, + { + "lat": -18.87056, + "lon": -48.88083, + "name": "Monte Alegre de Minas" + }, + { + "lat": 13.82735, + "lon": 100.55531, + "name": "Chatuchak subdistrict" + } + ], + "question": "Which location is the geographic outlier among: Itacaré, Três Corações, Muzambinho, Monte Alegre de Minas, Chatuchak subdistrict?", + "ground_truth": { + "answer": "Chatuchak subdistrict", + "outlier_distance_km": 13145.2, + "second_furthest_km": 3604.3, + "clarity_ratio": 3.65, + "median_distance_km": 3405.6, + "distances_to_centroid": { + "Itacaré": 2514.0, + "Três Corações": 3284.9, + "Muzambinho": 3405.6, + "Monte Alegre de Minas": 3604.3, + "Chatuchak subdistrict": 13145.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itacaré: (-14.28°, -39.00°)", + " Três Corações: (-21.70°, -45.25°)", + " Muzambinho: (-21.38°, -46.53°)", + " Monte Alegre de Minas: (-18.87°, -48.88°)", + " Chatuchak subdistrict: (13.83°, 100.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chatuchak subdistrict: 13145.2 km from centroid", + " Monte Alegre de Minas: 3604.3 km from centroid", + " Muzambinho: 3405.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chatuchak subdistrict", + "FINAL ANSWER: Chatuchak subdistrict" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.65145, + "lon": -41.84564, + "name": "Livramento do Brumado" + }, + { + "lat": -6.26617, + "lon": -35.20969, + "name": "Goianinha" + }, + { + "lat": -19.32556, + "lon": -41.25528, + "name": "Resplendor" + }, + { + "lat": -14.20361, + "lon": -41.66528, + "name": "Brumado" + }, + { + "lat": 25.47758, + "lon": 80.33491, + "name": "Bānda" + } + ], + "question": "Which location is the geographic outlier among: Livramento do Brumado, Goianinha, Resplendor, Brumado, Bānda?", + "ground_truth": { + "answer": "Bānda", + "outlier_distance_km": 10902.1, + "second_furthest_km": 3137.8, + "clarity_ratio": 3.47, + "median_distance_km": 2976.2, + "distances_to_centroid": { + "Livramento do Brumado": 2976.2, + "Goianinha": 2133.7, + "Resplendor": 3137.8, + "Brumado": 2973.9, + "Bānda": 10902.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Livramento do Brumado: (-13.65°, -41.85°)", + " Goianinha: (-6.27°, -35.21°)", + " Resplendor: (-19.33°, -41.26°)", + " Brumado: (-14.20°, -41.67°)", + " Bānda: (25.48°, 80.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bānda: 10902.1 km from centroid", + " Resplendor: 3137.8 km from centroid", + " Livramento do Brumado: 2976.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bānda", + "FINAL ANSWER: Bānda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.73265, + "lon": -78.85029, + "name": "Apex" + }, + { + "lat": 39.31111, + "lon": -94.92246, + "name": "Leavenworth" + }, + { + "lat": 43.46004, + "lon": -84.00674, + "name": "Saginaw Township North" + }, + { + "lat": 39.26674, + "lon": -81.56151, + "name": "Parkersburg" + }, + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + } + ], + "question": "Which location is the geographic outlier among: Apex, Leavenworth, Saginaw Township North, Parkersburg, Werribee?", + "ground_truth": { + "answer": "Werribee", + "outlier_distance_km": 18429.3, + "second_furthest_km": 5475.4, + "clarity_ratio": 3.37, + "median_distance_km": 4624.9, + "distances_to_centroid": { + "Apex": 4033.6, + "Leavenworth": 5475.4, + "Saginaw Township North": 4624.9, + "Parkersburg": 4331.2, + "Werribee": 18429.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Apex: (35.73°, -78.85°)", + " Leavenworth: (39.31°, -94.92°)", + " Saginaw Township North: (43.46°, -84.01°)", + " Parkersburg: (39.27°, -81.56°)", + " Werribee: (-37.90°, 144.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Werribee: 18429.3 km from centroid", + " Leavenworth: 5475.4 km from centroid", + " Saginaw Township North: 4624.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Werribee", + "FINAL ANSWER: Werribee" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -36.8282, + "lon": 174.62019, + "name": "Massey East" + }, + { + "lat": -26.41663, + "lon": 29.08668, + "name": "Kinross" + } + ], + "question": "Which location is the geographic outlier among: Maroochydore, Caboolture, Dandenong North, Massey East, Kinross?", + "ground_truth": { + "answer": "Kinross", + "outlier_distance_km": 9556.8, + "second_furthest_km": 4042.8, + "clarity_ratio": 2.36, + "median_distance_km": 2202.7, + "distances_to_centroid": { + "Maroochydore": 2202.7, + "Caboolture": 2174.6, + "Dandenong North": 1513.8, + "Massey East": 4042.8, + "Kinross": 9556.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maroochydore: (-26.66°, 153.10°)", + " Caboolture: (-27.08°, 152.95°)", + " Dandenong North: (-37.97°, 145.21°)", + " Massey East: (-36.83°, 174.62°)", + " Kinross: (-26.42°, 29.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kinross: 9556.8 km from centroid", + " Massey East: 4042.8 km from centroid", + " Maroochydore: 2202.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kinross", + "FINAL ANSWER: Kinross" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.28333, + "lon": 37.78333, + "name": "Welk’īt’ē" + }, + { + "lat": 30.06263, + "lon": 31.24967, + "name": "Cairo" + }, + { + "lat": -24.72459, + "lon": 31.19939, + "name": "Thulamahashi" + }, + { + "lat": 6.41667, + "lon": 39.85, + "name": "Mena" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + } + ], + "question": "Which location is the geographic outlier among: Welk’īt’ē, Cairo, Thulamahashi, Mena, Liverpool?", + "ground_truth": { + "answer": "Liverpool", + "outlier_distance_km": 10086.3, + "second_furthest_km": 4640.0, + "clarity_ratio": 2.17, + "median_distance_km": 3785.4, + "distances_to_centroid": { + "Welk’īt’ē": 2576.6, + "Cairo": 4640.0, + "Thulamahashi": 3785.4, + "Mena": 2279.4, + "Liverpool": 10086.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Welk’īt’ē: (8.28°, 37.78°)", + " Cairo: (30.06°, 31.25°)", + " Thulamahashi: (-24.72°, 31.20°)", + " Mena: (6.42°, 39.85°)", + " Liverpool: (-33.92°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Liverpool: 10086.3 km from centroid", + " Cairo: 4640.0 km from centroid", + " Thulamahashi: 3785.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Liverpool", + "FINAL ANSWER: Liverpool" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.08122, + "lon": -75.08017, + "name": "Fox Chase" + }, + { + "lat": 41.62666, + "lon": -93.71217, + "name": "Urbandale" + }, + { + "lat": 42.24587, + "lon": -84.40135, + "name": "Jackson" + }, + { + "lat": 29.66301, + "lon": -95.23549, + "name": "South Houston" + }, + { + "lat": -37.95855, + "lon": 176.98545, + "name": "Whakatane" + } + ], + "question": "Which location is the geographic outlier among: Fox Chase, Urbandale, Jackson, South Houston, Whakatane?", + "ground_truth": { + "answer": "Whakatane", + "outlier_distance_km": 16620.1, + "second_furthest_km": 6046.2, + "clarity_ratio": 2.75, + "median_distance_km": 5822.7, + "distances_to_centroid": { + "Fox Chase": 4249.8, + "Urbandale": 5822.7, + "Jackson": 5061.5, + "South Houston": 6046.2, + "Whakatane": 16620.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fox Chase: (40.08°, -75.08°)", + " Urbandale: (41.63°, -93.71°)", + " Jackson: (42.25°, -84.40°)", + " South Houston: (29.66°, -95.24°)", + " Whakatane: (-37.96°, 176.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whakatane: 16620.1 km from centroid", + " South Houston: 6046.2 km from centroid", + " Urbandale: 5822.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whakatane", + "FINAL ANSWER: Whakatane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.56061, + "lon": -0.10887, + "name": "Primrose Place" + }, + { + "lat": 28.96108, + "lon": -13.64502, + "name": "Tías" + }, + { + "lat": 40.97259, + "lon": 14.20745, + "name": "Aversa" + }, + { + "lat": 49.59786, + "lon": 8.4725, + "name": "Lampertheim" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + } + ], + "question": "Which location is the geographic outlier among: Primrose Place, Tías, Aversa, Lampertheim, Mornington?", + "ground_truth": { + "answer": "Mornington", + "outlier_distance_km": 13846.3, + "second_furthest_km": 4349.5, + "clarity_ratio": 3.18, + "median_distance_km": 3844.6, + "distances_to_centroid": { + "Primrose Place": 3844.6, + "Tías": 4349.5, + "Aversa": 2191.7, + "Lampertheim": 3175.3, + "Mornington": 13846.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Primrose Place: (52.56°, -0.11°)", + " Tías: (28.96°, -13.65°)", + " Aversa: (40.97°, 14.21°)", + " Lampertheim: (49.60°, 8.47°)", + " Mornington: (-38.22°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mornington: 13846.3 km from centroid", + " Tías: 4349.5 km from centroid", + " Primrose Place: 3844.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mornington", + "FINAL ANSWER: Mornington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.81009, + "lon": 9.63863, + "name": "Weingarten" + }, + { + "lat": 43.06425, + "lon": 12.54612, + "name": "Bastia umbra" + }, + { + "lat": 43.44775, + "lon": 3.75524, + "name": "Frontignan" + }, + { + "lat": 53.72821, + "lon": 9.91078, + "name": "Quickborn" + }, + { + "lat": 16.02781, + "lon": 100.37917, + "name": "Bang Mun Nak" + } + ], + "question": "Which location is the geographic outlier among: Weingarten, Bastia umbra, Frontignan, Quickborn, Bang Mun Nak?", + "ground_truth": { + "answer": "Bang Mun Nak", + "outlier_distance_km": 7444.6, + "second_furthest_km": 1952.4, + "clarity_ratio": 3.81, + "median_distance_km": 1931.9, + "distances_to_centroid": { + "Weingarten": 1597.0, + "Bastia umbra": 1239.6, + "Frontignan": 1952.4, + "Quickborn": 1931.9, + "Bang Mun Nak": 7444.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Weingarten: (47.81°, 9.64°)", + " Bastia umbra: (43.06°, 12.55°)", + " Frontignan: (43.45°, 3.76°)", + " Quickborn: (53.73°, 9.91°)", + " Bang Mun Nak: (16.03°, 100.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bang Mun Nak: 7444.6 km from centroid", + " Frontignan: 1952.4 km from centroid", + " Quickborn: 1931.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bang Mun Nak", + "FINAL ANSWER: Bang Mun Nak" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.86931, + "lon": 37.72966, + "name": "Babushkin" + }, + { + "lat": 40.54746, + "lon": -3.64197, + "name": "Alcobendas" + }, + { + "lat": 45.43713, + "lon": 12.33265, + "name": "Venice" + }, + { + "lat": 54.36677, + "lon": 77.3068, + "name": "Kupino" + }, + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + } + ], + "question": "Which location is the geographic outlier among: Babushkin, Alcobendas, Venice, Kupino, Te Atatu South?", + "ground_truth": { + "answer": "Te Atatu South", + "outlier_distance_km": 14136.1, + "second_furthest_km": 5640.5, + "clarity_ratio": 2.51, + "median_distance_km": 4307.7, + "distances_to_centroid": { + "Babushkin": 3166.2, + "Alcobendas": 5640.5, + "Venice": 4307.7, + "Kupino": 2863.7, + "Te Atatu South": 14136.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Babushkin: (55.87°, 37.73°)", + " Alcobendas: (40.55°, -3.64°)", + " Venice: (45.44°, 12.33°)", + " Kupino: (54.37°, 77.31°)", + " Te Atatu South: (-36.86°, 174.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Te Atatu South: 14136.1 km from centroid", + " Alcobendas: 5640.5 km from centroid", + " Venice: 4307.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Te Atatu South", + "FINAL ANSWER: Te Atatu South" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.23377, + "lon": -93.27006, + "name": "Villaflores" + }, + { + "lat": 32.4425, + "lon": -117.03417, + "name": "Pórticos de San Antonio" + }, + { + "lat": 40.05039, + "lon": -75.09156, + "name": "Lawndale" + }, + { + "lat": 41.71087, + "lon": -87.75811, + "name": "Oak Lawn" + }, + { + "lat": -20.44306, + "lon": -53.75917, + "name": "Ribas do Rio Pardo" + } + ], + "question": "Which location is the geographic outlier among: Villaflores, Pórticos de San Antonio, Lawndale, Oak Lawn, Ribas do Rio Pardo?", + "ground_truth": { + "answer": "Ribas do Rio Pardo", + "outlier_distance_km": 5836.2, + "second_furthest_km": 3322.9, + "clarity_ratio": 1.76, + "median_distance_km": 2230.1, + "distances_to_centroid": { + "Villaflores": 1047.3, + "Pórticos de San Antonio": 3322.9, + "Lawndale": 2230.1, + "Oak Lawn": 2203.1, + "Ribas do Rio Pardo": 5836.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Villaflores: (16.23°, -93.27°)", + " Pórticos de San Antonio: (32.44°, -117.03°)", + " Lawndale: (40.05°, -75.09°)", + " Oak Lawn: (41.71°, -87.76°)", + " Ribas do Rio Pardo: (-20.44°, -53.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ribas do Rio Pardo: 5836.2 km from centroid", + " Pórticos de San Antonio: 3322.9 km from centroid", + " Lawndale: 2230.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ribas do Rio Pardo", + "FINAL ANSWER: Ribas do Rio Pardo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.88724, + "lon": -118.35257, + "name": "Lawndale" + }, + { + "lat": 19.29513, + "lon": -99.16206, + "name": "Tlalpan" + }, + { + "lat": 33.73585, + "lon": -118.29229, + "name": "San Pedro" + }, + { + "lat": 40.88232, + "lon": -74.0832, + "name": "Lodi" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + } + ], + "question": "Which location is the geographic outlier among: Lawndale, Tlalpan, San Pedro, Lodi, Porirua?", + "ground_truth": { + "answer": "Porirua", + "outlier_distance_km": 15234.9, + "second_furthest_km": 7248.9, + "clarity_ratio": 2.1, + "median_distance_km": 7244.8, + "distances_to_centroid": { + "Lawndale": 7248.9, + "Tlalpan": 5489.2, + "San Pedro": 7244.8, + "Lodi": 3681.6, + "Porirua": 15234.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lawndale: (33.89°, -118.35°)", + " Tlalpan: (19.30°, -99.16°)", + " San Pedro: (33.74°, -118.29°)", + " Lodi: (40.88°, -74.08°)", + " Porirua: (-41.13°, 174.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Porirua: 15234.9 km from centroid", + " Lawndale: 7248.9 km from centroid", + " San Pedro: 7244.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Porirua", + "FINAL ANSWER: Porirua" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.83333, + "lon": 38.23333, + "name": "Ciro" + }, + { + "lat": -3.21799, + "lon": 40.11692, + "name": "Malindi" + }, + { + "lat": 6.90412, + "lon": -2.56114, + "name": "Mim" + }, + { + "lat": 5.78333, + "lon": 36.56667, + "name": "Bako" + }, + { + "lat": -12.15278, + "lon": -44.99, + "name": "Barreiras" + } + ], + "question": "Which location is the geographic outlier among: Ciro, Malindi, Mim, Bako, Barreiras?", + "ground_truth": { + "answer": "Barreiras", + "outlier_distance_km": 6616.7, + "second_furthest_km": 2998.9, + "clarity_ratio": 2.21, + "median_distance_km": 2845.6, + "distances_to_centroid": { + "Ciro": 2845.6, + "Malindi": 2998.9, + "Mim": 1894.0, + "Bako": 2616.5, + "Barreiras": 6616.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ciro: (7.83°, 38.23°)", + " Malindi: (-3.22°, 40.12°)", + " Mim: (6.90°, -2.56°)", + " Bako: (5.78°, 36.57°)", + " Barreiras: (-12.15°, -44.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barreiras: 6616.7 km from centroid", + " Malindi: 2998.9 km from centroid", + " Ciro: 2845.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barreiras", + "FINAL ANSWER: Barreiras" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.65883, + "lon": 77.4664, + "name": "Azhatebage" + }, + { + "lat": 27.79836, + "lon": 73.34297, + "name": "Deshnoke" + }, + { + "lat": 11.94646, + "lon": 108.44193, + "name": "Ðà Lạt" + }, + { + "lat": 10.95818, + "lon": 76.92013, + "name": "Rāmachettipālaiyam" + }, + { + "lat": -32.78749, + "lon": 26.8344, + "name": "Alice" + } + ], + "question": "Which location is the geographic outlier among: Azhatebage, Deshnoke, Ðà Lạt, Rāmachettipālaiyam, Alice?", + "ground_truth": { + "answer": "Alice", + "outlier_distance_km": 6898.9, + "second_furthest_km": 3901.4, + "clarity_ratio": 1.77, + "median_distance_km": 3078.6, + "distances_to_centroid": { + "Azhatebage": 3078.6, + "Deshnoke": 1834.5, + "Ðà Lạt": 3901.4, + "Rāmachettipālaiyam": 472.9, + "Alice": 6898.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Azhatebage: (38.66°, 77.47°)", + " Deshnoke: (27.80°, 73.34°)", + " Ðà Lạt: (11.95°, 108.44°)", + " Rāmachettipālaiyam: (10.96°, 76.92°)", + " Alice: (-32.79°, 26.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alice: 6898.9 km from centroid", + " Ðà Lạt: 3901.4 km from centroid", + " Azhatebage: 3078.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alice", + "FINAL ANSWER: Alice" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.77538, + "lon": 7.197, + "name": "Sankt Augustin" + }, + { + "lat": 48.01676, + "lon": 9.50064, + "name": "Bad Saulgau" + }, + { + "lat": 49.44287, + "lon": 11.86267, + "name": "Amberg" + }, + { + "lat": 50.89741, + "lon": 7.87415, + "name": "Freudenberg" + }, + { + "lat": -26.55, + "lon": 29.16667, + "name": "Secunda" + } + ], + "question": "Which location is the geographic outlier among: Sankt Augustin, Bad Saulgau, Amberg, Freudenberg, Secunda?", + "ground_truth": { + "answer": "Secunda", + "outlier_distance_km": 6997.5, + "second_furthest_km": 1870.2, + "clarity_ratio": 3.74, + "median_distance_km": 1870.0, + "distances_to_centroid": { + "Sankt Augustin": 1870.2, + "Bad Saulgau": 1530.9, + "Amberg": 1662.9, + "Freudenberg": 1870.0, + "Secunda": 6997.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sankt Augustin: (50.78°, 7.20°)", + " Bad Saulgau: (48.02°, 9.50°)", + " Amberg: (49.44°, 11.86°)", + " Freudenberg: (50.90°, 7.87°)", + " Secunda: (-26.55°, 29.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Secunda: 6997.5 km from centroid", + " Sankt Augustin: 1870.2 km from centroid", + " Freudenberg: 1870.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Secunda", + "FINAL ANSWER: Secunda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.98065, + "lon": -73.68374, + "name": "Rye" + }, + { + "lat": 39.48623, + "lon": -75.02573, + "name": "Vineland" + }, + { + "lat": 33.63967, + "lon": -117.84164, + "name": "UC Irvine" + }, + { + "lat": 34.00288, + "lon": -84.14464, + "name": "Duluth" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + } + ], + "question": "Which location is the geographic outlier among: Rye, Vineland, UC Irvine, Duluth, Melbourne?", + "ground_truth": { + "answer": "Melbourne", + "outlier_distance_km": 18168.1, + "second_furthest_km": 7485.4, + "clarity_ratio": 2.43, + "median_distance_km": 4388.8, + "distances_to_centroid": { + "Rye": 3698.9, + "Vineland": 3739.2, + "UC Irvine": 7485.4, + "Duluth": 4388.8, + "Melbourne": 18168.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rye: (40.98°, -73.68°)", + " Vineland: (39.49°, -75.03°)", + " UC Irvine: (33.64°, -117.84°)", + " Duluth: (34.00°, -84.14°)", + " Melbourne: (-37.81°, 144.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Melbourne: 18168.1 km from centroid", + " UC Irvine: 7485.4 km from centroid", + " Duluth: 4388.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Melbourne", + "FINAL ANSWER: Melbourne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.43482, + "lon": 31.67506, + "name": "Dumyāţ al Jadīdah" + }, + { + "lat": -27.00805, + "lon": 27.3646, + "name": "Vredefort" + }, + { + "lat": -0.15816, + "lon": 35.19645, + "name": "Muhoroni" + }, + { + "lat": -24.72459, + "lon": 31.19939, + "name": "Thulamahashi" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + } + ], + "question": "Which location is the geographic outlier among: Dumyāţ al Jadīdah, Vredefort, Muhoroni, Thulamahashi, Dandenong?", + "ground_truth": { + "answer": "Dandenong", + "outlier_distance_km": 9303.9, + "second_furthest_km": 5359.4, + "clarity_ratio": 1.74, + "median_distance_km": 3271.8, + "distances_to_centroid": { + "Dumyāţ al Jadīdah": 5359.4, + "Vredefort": 3271.8, + "Muhoroni": 2451.9, + "Thulamahashi": 2815.2, + "Dandenong": 9303.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dumyāţ al Jadīdah: (31.43°, 31.68°)", + " Vredefort: (-27.01°, 27.36°)", + " Muhoroni: (-0.16°, 35.20°)", + " Thulamahashi: (-24.72°, 31.20°)", + " Dandenong: (-37.98°, 145.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dandenong: 9303.9 km from centroid", + " Dumyāţ al Jadīdah: 5359.4 km from centroid", + " Vredefort: 3271.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dandenong", + "FINAL ANSWER: Dandenong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.57573, + "lon": -103.32442, + "name": "Las Pintas de Arriba" + }, + { + "lat": 49.16667, + "lon": -122.91667, + "name": "North Delta" + }, + { + "lat": 29.91465, + "lon": -90.05396, + "name": "Gretna" + }, + { + "lat": 23.64824, + "lon": -100.64334, + "name": "Matehuala" + }, + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + } + ], + "question": "Which location is the geographic outlier among: Las Pintas de Arriba, North Delta, Gretna, Matehuala, Pakenham?", + "ground_truth": { + "answer": "Pakenham", + "outlier_distance_km": 16986.0, + "second_furthest_km": 7036.2, + "clarity_ratio": 2.41, + "median_distance_km": 5157.2, + "distances_to_centroid": { + "Las Pintas de Arriba": 5157.2, + "North Delta": 7036.2, + "Gretna": 3897.4, + "Matehuala": 4867.3, + "Pakenham": 16986.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Las Pintas de Arriba: (20.58°, -103.32°)", + " North Delta: (49.17°, -122.92°)", + " Gretna: (29.91°, -90.05°)", + " Matehuala: (23.65°, -100.64°)", + " Pakenham: (-38.07°, 145.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pakenham: 16986.0 km from centroid", + " North Delta: 7036.2 km from centroid", + " Las Pintas de Arriba: 5157.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pakenham", + "FINAL ANSWER: Pakenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -37.81667, + "lon": 145.2, + "name": "Mitcham" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": 6.60086, + "lon": 3.48818, + "name": "Ebute Ikorodu" + } + ], + "question": "Which location is the geographic outlier among: Gosnells, Whangarei, Mitcham, Southport, Ebute Ikorodu?", + "ground_truth": { + "answer": "Ebute Ikorodu", + "outlier_distance_km": 12828.6, + "second_furthest_km": 5396.3, + "clarity_ratio": 2.38, + "median_distance_km": 3469.0, + "distances_to_centroid": { + "Gosnells": 781.2, + "Whangarei": 5396.3, + "Mitcham": 2867.4, + "Southport": 3469.0, + "Ebute Ikorodu": 12828.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gosnells: (-32.08°, 116.01°)", + " Whangarei: (-35.73°, 174.32°)", + " Mitcham: (-37.82°, 145.20°)", + " Southport: (-27.97°, 153.40°)", + " Ebute Ikorodu: (6.60°, 3.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ebute Ikorodu: 12828.6 km from centroid", + " Whangarei: 5396.3 km from centroid", + " Southport: 3469.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ebute Ikorodu", + "FINAL ANSWER: Ebute Ikorodu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.51868, + "lon": -1.9945, + "name": "West Bromwich" + }, + { + "lat": 58.37884, + "lon": 42.34633, + "name": "Galich" + }, + { + "lat": 43.69415, + "lon": 5.50291, + "name": "Pertuis" + }, + { + "lat": 50.86874, + "lon": 6.09317, + "name": "Herzogenrath" + }, + { + "lat": -37.83382, + "lon": 144.93834, + "name": "City of Port Phillip" + } + ], + "question": "Which location is the geographic outlier among: West Bromwich, Galich, Pertuis, Herzogenrath, City of Port Phillip?", + "ground_truth": { + "answer": "City of Port Phillip", + "outlier_distance_km": 13457.3, + "second_furthest_km": 3894.0, + "clarity_ratio": 3.46, + "median_distance_km": 3307.6, + "distances_to_centroid": { + "West Bromwich": 3894.0, + "Galich": 2772.5, + "Pertuis": 3126.5, + "Herzogenrath": 3307.6, + "City of Port Phillip": 13457.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Bromwich: (52.52°, -1.99°)", + " Galich: (58.38°, 42.35°)", + " Pertuis: (43.69°, 5.50°)", + " Herzogenrath: (50.87°, 6.09°)", + " City of Port Phillip: (-37.83°, 144.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " City of Port Phillip: 13457.3 km from centroid", + " West Bromwich: 3894.0 km from centroid", + " Herzogenrath: 3307.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: City of Port Phillip", + "FINAL ANSWER: City of Port Phillip" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.79722, + "lon": -57.28806, + "name": "Nova Olímpia" + }, + { + "lat": -6.02583, + "lon": -44.24917, + "name": "Colinas" + }, + { + "lat": -32.02957, + "lon": -61.22097, + "name": "Gálvez" + }, + { + "lat": -42.76848, + "lon": -65.03827, + "name": "Puerto Madryn" + }, + { + "lat": 13.94521, + "lon": 121.43065, + "name": "Malabanban Norte" + } + ], + "question": "Which location is the geographic outlier among: Nova Olímpia, Colinas, Gálvez, Puerto Madryn, Malabanban Norte?", + "ground_truth": { + "answer": "Malabanban Norte", + "outlier_distance_km": 16008.4, + "second_furthest_km": 5069.8, + "clarity_ratio": 3.16, + "median_distance_km": 4379.8, + "distances_to_centroid": { + "Nova Olímpia": 3856.7, + "Colinas": 2752.0, + "Gálvez": 4379.8, + "Puerto Madryn": 5069.8, + "Malabanban Norte": 16008.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nova Olímpia: (-14.80°, -57.29°)", + " Colinas: (-6.03°, -44.25°)", + " Gálvez: (-32.03°, -61.22°)", + " Puerto Madryn: (-42.77°, -65.04°)", + " Malabanban Norte: (13.95°, 121.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Malabanban Norte: 16008.4 km from centroid", + " Puerto Madryn: 5069.8 km from centroid", + " Gálvez: 4379.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Malabanban Norte", + "FINAL ANSWER: Malabanban Norte" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.07538, + "lon": -75.73422, + "name": "Ica" + }, + { + "lat": -4.22583, + "lon": -38.73056, + "name": "Redenção" + }, + { + "lat": -23.49283, + "lon": -46.66916, + "name": "Limão" + }, + { + "lat": 4.43139, + "lon": -61.14639, + "name": "Pacaraima" + }, + { + "lat": -25.67031, + "lon": 31.86288, + "name": "Kamaqhekeza" + } + ], + "question": "Which location is the geographic outlier among: Ica, Redenção, Limão, Pacaraima, Kamaqhekeza?", + "ground_truth": { + "answer": "Kamaqhekeza", + "outlier_distance_km": 7412.5, + "second_furthest_km": 4072.7, + "clarity_ratio": 1.82, + "median_distance_km": 3175.3, + "distances_to_centroid": { + "Ica": 4072.7, + "Redenção": 934.6, + "Limão": 1511.9, + "Pacaraima": 3175.3, + "Kamaqhekeza": 7412.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ica: (-14.08°, -75.73°)", + " Redenção: (-4.23°, -38.73°)", + " Limão: (-23.49°, -46.67°)", + " Pacaraima: (4.43°, -61.15°)", + " Kamaqhekeza: (-25.67°, 31.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kamaqhekeza: 7412.5 km from centroid", + " Ica: 4072.7 km from centroid", + " Pacaraima: 3175.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kamaqhekeza", + "FINAL ANSWER: Kamaqhekeza" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.92979, + "lon": -1.12537, + "name": "West Bridgford" + }, + { + "lat": 50.81667, + "lon": 8.1, + "name": "Wilnsdorf" + }, + { + "lat": 41.72722, + "lon": 13.00481, + "name": "Colleferro" + }, + { + "lat": 42.54664, + "lon": -6.59619, + "name": "Ponferrada" + }, + { + "lat": -23.57381, + "lon": -46.51561, + "name": "Aricanduva" + } + ], + "question": "Which location is the geographic outlier among: West Bridgford, Wilnsdorf, Colleferro, Ponferrada, Aricanduva?", + "ground_truth": { + "answer": "Aricanduva", + "outlier_distance_km": 7569.8, + "second_furthest_km": 2327.3, + "clarity_ratio": 3.25, + "median_distance_km": 2271.3, + "distances_to_centroid": { + "West Bridgford": 2271.3, + "Wilnsdorf": 2327.3, + "Colleferro": 1988.2, + "Ponferrada": 1073.9, + "Aricanduva": 7569.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Bridgford: (52.93°, -1.13°)", + " Wilnsdorf: (50.82°, 8.10°)", + " Colleferro: (41.73°, 13.00°)", + " Ponferrada: (42.55°, -6.60°)", + " Aricanduva: (-23.57°, -46.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aricanduva: 7569.8 km from centroid", + " Wilnsdorf: 2327.3 km from centroid", + " West Bridgford: 2271.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aricanduva", + "FINAL ANSWER: Aricanduva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.90877, + "lon": 88.39674, + "name": "Hugli" + }, + { + "lat": 36.67444, + "lon": 119.87528, + "name": "Liaolan" + }, + { + "lat": 10.93314, + "lon": 108.28327, + "name": "Mui Ne" + }, + { + "lat": 36.31865, + "lon": 138.27329, + "name": "Kamimaruko" + }, + { + "lat": 38.26993, + "lon": 16.29607, + "name": "Siderno" + } + ], + "question": "Which location is the geographic outlier among: Hugli, Liaolan, Mui Ne, Kamimaruko, Siderno?", + "ground_truth": { + "answer": "Siderno", + "outlier_distance_km": 7076.2, + "second_furthest_km": 4165.7, + "clarity_ratio": 1.7, + "median_distance_km": 2533.4, + "distances_to_centroid": { + "Hugli": 894.9, + "Liaolan": 2533.4, + "Mui Ne": 2485.4, + "Kamimaruko": 4165.7, + "Siderno": 7076.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hugli: (22.91°, 88.40°)", + " Liaolan: (36.67°, 119.88°)", + " Mui Ne: (10.93°, 108.28°)", + " Kamimaruko: (36.32°, 138.27°)", + " Siderno: (38.27°, 16.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Siderno: 7076.2 km from centroid", + " Kamimaruko: 4165.7 km from centroid", + " Liaolan: 2533.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Siderno", + "FINAL ANSWER: Siderno" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.20704, + "lon": -71.68562, + "name": "Grafton" + }, + { + "lat": 26.43814, + "lon": -81.80675, + "name": "Estero" + }, + { + "lat": 20.7421, + "lon": -100.44783, + "name": "Santa Rosa Jáuregui" + }, + { + "lat": 33.96057, + "lon": -118.18535, + "name": "Cudahy" + }, + { + "lat": 34.41667, + "lon": 135.31667, + "name": "Izumisano" + } + ], + "question": "Which location is the geographic outlier among: Grafton, Estero, Santa Rosa Jáuregui, Cudahy, Izumisano?", + "ground_truth": { + "answer": "Izumisano", + "outlier_distance_km": 12674.2, + "second_furthest_km": 6490.0, + "clarity_ratio": 1.95, + "median_distance_km": 5381.4, + "distances_to_centroid": { + "Grafton": 2454.0, + "Estero": 3383.8, + "Santa Rosa Jáuregui": 5381.4, + "Cudahy": 6490.0, + "Izumisano": 12674.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Grafton: (42.21°, -71.69°)", + " Estero: (26.44°, -81.81°)", + " Santa Rosa Jáuregui: (20.74°, -100.45°)", + " Cudahy: (33.96°, -118.19°)", + " Izumisano: (34.42°, 135.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Izumisano: 12674.2 km from centroid", + " Cudahy: 6490.0 km from centroid", + " Santa Rosa Jáuregui: 5381.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Izumisano", + "FINAL ANSWER: Izumisano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.335, + "lon": -50.35, + "name": "Santana do Araguaia" + }, + { + "lat": -22.77944, + "lon": -46.59056, + "name": "Pinhalzinho" + }, + { + "lat": -6.09401, + "lon": -36.47219, + "name": "Lagoa Nova" + }, + { + "lat": -5.56667, + "lon": -46.74222, + "name": "Amarante do Maranhão" + }, + { + "lat": 53.03333, + "lon": 8.75, + "name": "Stuhr" + } + ], + "question": "Which location is the geographic outlier among: Santana do Araguaia, Pinhalzinho, Lagoa Nova, Amarante do Maranhão, Stuhr?", + "ground_truth": { + "answer": "Stuhr", + "outlier_distance_km": 6925.1, + "second_furthest_km": 3046.6, + "clarity_ratio": 2.27, + "median_distance_km": 2171.6, + "distances_to_centroid": { + "Santana do Araguaia": 2171.6, + "Pinhalzinho": 3046.6, + "Lagoa Nova": 916.4, + "Amarante do Maranhão": 1611.1, + "Stuhr": 6925.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santana do Araguaia: (-9.34°, -50.35°)", + " Pinhalzinho: (-22.78°, -46.59°)", + " Lagoa Nova: (-6.09°, -36.47°)", + " Amarante do Maranhão: (-5.57°, -46.74°)", + " Stuhr: (53.03°, 8.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stuhr: 6925.1 km from centroid", + " Pinhalzinho: 3046.6 km from centroid", + " Santana do Araguaia: 2171.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stuhr", + "FINAL ANSWER: Stuhr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.73475, + "lon": 105.38817, + "name": "Xigaoshan" + }, + { + "lat": 15.3275, + "lon": 120.9192, + "name": "Jaen" + }, + { + "lat": 23.53878, + "lon": 86.6735, + "name": "Raghunathpur" + }, + { + "lat": 28.19874, + "lon": 112.97087, + "name": "Changsha" + }, + { + "lat": -16.02511, + "lon": -48.07121, + "name": "Gama" + } + ], + "question": "Which location is the geographic outlier among: Xigaoshan, Jaen, Raghunathpur, Changsha, Gama?", + "ground_truth": { + "answer": "Gama", + "outlier_distance_km": 14027.3, + "second_furthest_km": 4836.0, + "clarity_ratio": 2.9, + "median_distance_km": 4019.0, + "distances_to_centroid": { + "Xigaoshan": 3508.6, + "Jaen": 4836.0, + "Raghunathpur": 1368.8, + "Changsha": 4019.0, + "Gama": 14027.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Xigaoshan: (33.73°, 105.39°)", + " Jaen: (15.33°, 120.92°)", + " Raghunathpur: (23.54°, 86.67°)", + " Changsha: (28.20°, 112.97°)", + " Gama: (-16.03°, -48.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gama: 14027.3 km from centroid", + " Jaen: 4836.0 km from centroid", + " Changsha: 4019.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gama", + "FINAL ANSWER: Gama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.26667, + "lon": 9.98333, + "name": "Takum" + }, + { + "lat": 9.03528, + "lon": 38.66083, + "name": "Burayu" + }, + { + "lat": -3.63045, + "lon": 39.84992, + "name": "Kilifi" + }, + { + "lat": 5.96667, + "lon": 41.03333, + "name": "Ara Ali" + }, + { + "lat": 49.45421, + "lon": 11.07752, + "name": "Nürnberg" + } + ], + "question": "Which location is the geographic outlier among: Takum, Burayu, Kilifi, Ara Ali, Nürnberg?", + "ground_truth": { + "answer": "Nürnberg", + "outlier_distance_km": 4277.5, + "second_furthest_km": 2313.8, + "clarity_ratio": 1.85, + "median_distance_km": 2104.1, + "distances_to_centroid": { + "Takum": 2104.1, + "Burayu": 1256.7, + "Kilifi": 2313.8, + "Ara Ali": 1649.9, + "Nürnberg": 4277.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Takum: (7.27°, 9.98°)", + " Burayu: (9.04°, 38.66°)", + " Kilifi: (-3.63°, 39.85°)", + " Ara Ali: (5.97°, 41.03°)", + " Nürnberg: (49.45°, 11.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nürnberg: 4277.5 km from centroid", + " Kilifi: 2313.8 km from centroid", + " Takum: 2104.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nürnberg", + "FINAL ANSWER: Nürnberg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.99116, + "lon": 145.17385, + "name": "Keysborough" + }, + { + "lat": -32.23013, + "lon": 115.78128, + "name": "Kwinana" + }, + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": -35.28346, + "lon": 149.12807, + "name": "Canberra" + }, + { + "lat": 55.93924, + "lon": 92.37513, + "name": "Divnogorsk" + } + ], + "question": "Which location is the geographic outlier among: Keysborough, Kwinana, Frankston East, Canberra, Divnogorsk?", + "ground_truth": { + "answer": "Divnogorsk", + "outlier_distance_km": 8880.2, + "second_furthest_km": 2765.1, + "clarity_ratio": 3.21, + "median_distance_km": 2747.9, + "distances_to_centroid": { + "Keysborough": 2737.6, + "Kwinana": 2137.6, + "Frankston East": 2747.9, + "Canberra": 2765.1, + "Divnogorsk": 8880.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Keysborough: (-37.99°, 145.17°)", + " Kwinana: (-32.23°, 115.78°)", + " Frankston East: (-38.13°, 145.13°)", + " Canberra: (-35.28°, 149.13°)", + " Divnogorsk: (55.94°, 92.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Divnogorsk: 8880.2 km from centroid", + " Canberra: 2765.1 km from centroid", + " Frankston East: 2747.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Divnogorsk", + "FINAL ANSWER: Divnogorsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.56337, + "lon": 110.00404, + "name": "Huaihua" + }, + { + "lat": 37.02444, + "lon": 111.9125, + "name": "Jiexiu" + }, + { + "lat": 35.02107, + "lon": 135.75385, + "name": "Kyoto" + }, + { + "lat": 26.7469, + "lon": 89.35385, + "name": "Hāsimāra" + }, + { + "lat": 51.30417, + "lon": 5.58889, + "name": "Cranendonck" + } + ], + "question": "Which location is the geographic outlier among: Huaihua, Jiexiu, Kyoto, Hāsimāra, Cranendonck?", + "ground_truth": { + "answer": "Cranendonck", + "outlier_distance_km": 6682.7, + "second_furthest_km": 4069.3, + "clarity_ratio": 1.64, + "median_distance_km": 2042.6, + "distances_to_centroid": { + "Huaihua": 2042.6, + "Jiexiu": 1920.5, + "Kyoto": 4069.3, + "Hāsimāra": 983.1, + "Cranendonck": 6682.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huaihua: (27.56°, 110.00°)", + " Jiexiu: (37.02°, 111.91°)", + " Kyoto: (35.02°, 135.75°)", + " Hāsimāra: (26.75°, 89.35°)", + " Cranendonck: (51.30°, 5.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cranendonck: 6682.7 km from centroid", + " Kyoto: 4069.3 km from centroid", + " Huaihua: 2042.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cranendonck", + "FINAL ANSWER: Cranendonck" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.85444, + "lon": -40.92111, + "name": "Ubajara" + }, + { + "lat": -33.00777, + "lon": -58.51836, + "name": "Gualeguaychú" + }, + { + "lat": -18.47333, + "lon": -47.20028, + "name": "Coromandel" + }, + { + "lat": -28.93575, + "lon": -49.49538, + "name": "Araranguá" + }, + { + "lat": 30.42059, + "lon": -86.61707, + "name": "Fort Walton Beach" + } + ], + "question": "Which location is the geographic outlier among: Ubajara, Gualeguaychú, Coromandel, Araranguá, Fort Walton Beach?", + "ground_truth": { + "answer": "Fort Walton Beach", + "outlier_distance_km": 5595.0, + "second_furthest_km": 2480.9, + "clarity_ratio": 2.26, + "median_distance_km": 2149.0, + "distances_to_centroid": { + "Ubajara": 1886.4, + "Gualeguaychú": 2480.9, + "Coromandel": 1320.5, + "Araranguá": 2149.0, + "Fort Walton Beach": 5595.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ubajara: (-3.85°, -40.92°)", + " Gualeguaychú: (-33.01°, -58.52°)", + " Coromandel: (-18.47°, -47.20°)", + " Araranguá: (-28.94°, -49.50°)", + " Fort Walton Beach: (30.42°, -86.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fort Walton Beach: 5595.0 km from centroid", + " Gualeguaychú: 2480.9 km from centroid", + " Araranguá: 2149.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fort Walton Beach", + "FINAL ANSWER: Fort Walton Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.86709, + "lon": 11.22594, + "name": "Biliri" + }, + { + "lat": -28.55874, + "lon": 29.77896, + "name": "Ladysmith" + }, + { + "lat": 0.6004, + "lon": 34.77119, + "name": "Webuye" + }, + { + "lat": 11.28333, + "lon": 36.21667, + "name": "Mambuk" + }, + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + } + ], + "question": "Which location is the geographic outlier among: Biliri, Ladysmith, Webuye, Mambuk, Mernda?", + "ground_truth": { + "answer": "Mernda", + "outlier_distance_km": 9727.2, + "second_furthest_km": 4913.0, + "clarity_ratio": 1.98, + "median_distance_km": 3147.2, + "distances_to_centroid": { + "Biliri": 4913.0, + "Ladysmith": 3147.2, + "Webuye": 2124.1, + "Mambuk": 2802.5, + "Mernda": 9727.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Biliri: (9.87°, 11.23°)", + " Ladysmith: (-28.56°, 29.78°)", + " Webuye: (0.60°, 34.77°)", + " Mambuk: (11.28°, 36.22°)", + " Mernda: (-37.60°, 145.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mernda: 9727.2 km from centroid", + " Biliri: 4913.0 km from centroid", + " Ladysmith: 3147.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mernda", + "FINAL ANSWER: Mernda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -16.47583, + "lon": -43.48833, + "name": "Francisco Sá" + }, + { + "lat": -22.4625, + "lon": -42.65306, + "name": "Cachoeiras de Macacu" + }, + { + "lat": -23.54333, + "lon": -46.41083, + "name": "Guaianases" + }, + { + "lat": -9.645, + "lon": -36.49722, + "name": "Taquarana" + }, + { + "lat": 41.81371, + "lon": -71.37005, + "name": "East Providence" + } + ], + "question": "Which location is the geographic outlier among: Francisco Sá, Cachoeiras de Macacu, Guaianases, Taquarana, East Providence?", + "ground_truth": { + "answer": "East Providence", + "outlier_distance_km": 5824.9, + "second_furthest_km": 1952.0, + "clarity_ratio": 2.98, + "median_distance_km": 1914.5, + "distances_to_centroid": { + "Francisco Sá": 1261.4, + "Cachoeiras de Macacu": 1914.5, + "Guaianases": 1952.0, + "Taquarana": 1336.8, + "East Providence": 5824.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Francisco Sá: (-16.48°, -43.49°)", + " Cachoeiras de Macacu: (-22.46°, -42.65°)", + " Guaianases: (-23.54°, -46.41°)", + " Taquarana: (-9.64°, -36.50°)", + " East Providence: (41.81°, -71.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " East Providence: 5824.9 km from centroid", + " Guaianases: 1952.0 km from centroid", + " Cachoeiras de Macacu: 1914.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: East Providence", + "FINAL ANSWER: East Providence" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.10383, + "lon": 84.46185, + "name": "Narkatiāganj" + }, + { + "lat": 44.05305, + "lon": 80.87173, + "name": "Huocheng" + }, + { + "lat": 20.28333, + "lon": 73.01667, + "name": "Āmli" + }, + { + "lat": 22.05236, + "lon": 72.80074, + "name": "Jambusar" + }, + { + "lat": -26.68443, + "lon": 153.05705, + "name": "Buderim" + } + ], + "question": "Which location is the geographic outlier among: Narkatiāganj, Huocheng, Āmli, Jambusar, Buderim?", + "ground_truth": { + "answer": "Buderim", + "outlier_distance_km": 8135.6, + "second_furthest_km": 3173.0, + "clarity_ratio": 2.56, + "median_distance_km": 2159.8, + "distances_to_centroid": { + "Narkatiāganj": 1383.7, + "Huocheng": 3173.0, + "Āmli": 2110.3, + "Jambusar": 2159.8, + "Buderim": 8135.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Narkatiāganj: (27.10°, 84.46°)", + " Huocheng: (44.05°, 80.87°)", + " Āmli: (20.28°, 73.02°)", + " Jambusar: (22.05°, 72.80°)", + " Buderim: (-26.68°, 153.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Buderim: 8135.6 km from centroid", + " Huocheng: 3173.0 km from centroid", + " Jambusar: 2159.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Buderim", + "FINAL ANSWER: Buderim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.37477, + "lon": -95.75444, + "name": "Carlos A. Carrillo" + }, + { + "lat": 28.19013, + "lon": -105.47012, + "name": "Ciudad Delicias" + }, + { + "lat": 26.05731, + "lon": -80.27172, + "name": "Cooper City" + }, + { + "lat": 32.76783, + "lon": -117.02308, + "name": "La Mesa" + }, + { + "lat": 26.26265, + "lon": 127.76147, + "name": "Ginowan" + } + ], + "question": "Which location is the geographic outlier among: Carlos A. Carrillo, Ciudad Delicias, Cooper City, La Mesa, Ginowan?", + "ground_truth": { + "answer": "Ginowan", + "outlier_distance_km": 14163.4, + "second_furthest_km": 6036.6, + "clarity_ratio": 2.35, + "median_distance_km": 5038.5, + "distances_to_centroid": { + "Carlos A. Carrillo": 4349.9, + "Ciudad Delicias": 5038.5, + "Cooper City": 2601.9, + "La Mesa": 6036.6, + "Ginowan": 14163.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlos A. Carrillo: (18.37°, -95.75°)", + " Ciudad Delicias: (28.19°, -105.47°)", + " Cooper City: (26.06°, -80.27°)", + " La Mesa: (32.77°, -117.02°)", + " Ginowan: (26.26°, 127.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ginowan: 14163.4 km from centroid", + " La Mesa: 6036.6 km from centroid", + " Ciudad Delicias: 5038.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ginowan", + "FINAL ANSWER: Ginowan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.68927, + "lon": -73.85791, + "name": "Woodhaven" + }, + { + "lat": 45.40008, + "lon": -73.58248, + "name": "Sainte-Catherine" + }, + { + "lat": 39.48309, + "lon": -88.37283, + "name": "Mattoon" + }, + { + "lat": 32.84069, + "lon": -83.6324, + "name": "Macon" + }, + { + "lat": 14.277, + "lon": 39.462, + "name": "Ādīgrat" + } + ], + "question": "Which location is the geographic outlier among: Woodhaven, Sainte-Catherine, Mattoon, Macon, Ādīgrat?", + "ground_truth": { + "answer": "Ādīgrat", + "outlier_distance_km": 9600.3, + "second_furthest_km": 2910.6, + "clarity_ratio": 3.3, + "median_distance_km": 2555.9, + "distances_to_centroid": { + "Woodhaven": 1711.4, + "Sainte-Catherine": 1917.4, + "Mattoon": 2910.6, + "Macon": 2555.9, + "Ādīgrat": 9600.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Woodhaven: (40.69°, -73.86°)", + " Sainte-Catherine: (45.40°, -73.58°)", + " Mattoon: (39.48°, -88.37°)", + " Macon: (32.84°, -83.63°)", + " Ādīgrat: (14.28°, 39.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ādīgrat: 9600.3 km from centroid", + " Mattoon: 2910.6 km from centroid", + " Macon: 2555.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ādīgrat", + "FINAL ANSWER: Ādīgrat" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.26667, + "lon": 140.86667, + "name": "Sendai" + }, + { + "lat": 44.08436, + "lon": 131.11841, + "name": "Dongning" + }, + { + "lat": 29.56227, + "lon": 103.76386, + "name": "Leshan" + }, + { + "lat": 33.71706, + "lon": 130.64117, + "name": "Miyawaka" + }, + { + "lat": -32.035, + "lon": -52.09861, + "name": "Rio Grande" + } + ], + "question": "Which location is the geographic outlier among: Sendai, Dongning, Leshan, Miyawaka, Rio Grande?", + "ground_truth": { + "answer": "Rio Grande", + "outlier_distance_km": 16234.0, + "second_furthest_km": 5026.1, + "clarity_ratio": 3.23, + "median_distance_km": 4365.1, + "distances_to_centroid": { + "Sendai": 5026.1, + "Dongning": 4365.1, + "Leshan": 1494.6, + "Miyawaka": 4057.1, + "Rio Grande": 16234.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sendai: (38.27°, 140.87°)", + " Dongning: (44.08°, 131.12°)", + " Leshan: (29.56°, 103.76°)", + " Miyawaka: (33.72°, 130.64°)", + " Rio Grande: (-32.03°, -52.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rio Grande: 16234.0 km from centroid", + " Sendai: 5026.1 km from centroid", + " Dongning: 4365.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rio Grande", + "FINAL ANSWER: Rio Grande" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.50083, + "lon": -117.18588, + "name": "Apple Valley" + }, + { + "lat": 46.82666, + "lon": -100.88958, + "name": "Mandan" + }, + { + "lat": 35.07681, + "lon": -80.66924, + "name": "Indian Trail" + }, + { + "lat": 37.52966, + "lon": -122.04024, + "name": "Newark" + }, + { + "lat": -22.49472, + "lon": -48.55806, + "name": "Barra Bonita" + } + ], + "question": "Which location is the geographic outlier among: Apple Valley, Mandan, Indian Trail, Newark, Barra Bonita?", + "ground_truth": { + "answer": "Barra Bonita", + "outlier_distance_km": 7294.3, + "second_furthest_km": 2923.0, + "clarity_ratio": 2.5, + "median_distance_km": 2408.4, + "distances_to_centroid": { + "Apple Valley": 2408.4, + "Mandan": 2365.9, + "Indian Trail": 1593.8, + "Newark": 2923.0, + "Barra Bonita": 7294.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Apple Valley: (34.50°, -117.19°)", + " Mandan: (46.83°, -100.89°)", + " Indian Trail: (35.08°, -80.67°)", + " Newark: (37.53°, -122.04°)", + " Barra Bonita: (-22.49°, -48.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barra Bonita: 7294.3 km from centroid", + " Newark: 2923.0 km from centroid", + " Apple Valley: 2408.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barra Bonita", + "FINAL ANSWER: Barra Bonita" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.60591, + "lon": 74.7334, + "name": "R.S. Pora" + }, + { + "lat": 8.5138, + "lon": 77.54944, + "name": "Kalakkādu" + }, + { + "lat": 10.15033, + "lon": 76.73544, + "name": "Kuttampuzha" + }, + { + "lat": 1.8548, + "lon": 102.9325, + "name": "Batu Pahat" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + } + ], + "question": "Which location is the geographic outlier among: R.S. Pora, Kalakkādu, Kuttampuzha, Batu Pahat, Te Atatu Peninsula?", + "ground_truth": { + "answer": "Te Atatu Peninsula", + "outlier_distance_km": 8756.4, + "second_furthest_km": 4279.9, + "clarity_ratio": 2.05, + "median_distance_km": 2819.3, + "distances_to_centroid": { + "R.S. Pora": 4279.9, + "Kalakkādu": 2692.4, + "Kuttampuzha": 2819.3, + "Batu Pahat": 237.4, + "Te Atatu Peninsula": 8756.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " R.S. Pora: (32.61°, 74.73°)", + " Kalakkādu: (8.51°, 77.55°)", + " Kuttampuzha: (10.15°, 76.74°)", + " Batu Pahat: (1.85°, 102.93°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Te Atatu Peninsula: 8756.4 km from centroid", + " R.S. Pora: 4279.9 km from centroid", + " Kuttampuzha: 2819.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Te Atatu Peninsula", + "FINAL ANSWER: Te Atatu Peninsula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -33.91972, + "lon": 151.07592, + "name": "Lakemba" + }, + { + "lat": -38.68333, + "lon": 176.08333, + "name": "Taupo" + }, + { + "lat": -3.45361, + "lon": -44.78, + "name": "Arari" + } + ], + "question": "Which location is the geographic outlier among: Townsville, Canning Vale, Lakemba, Taupo, Arari?", + "ground_truth": { + "answer": "Arari", + "outlier_distance_km": 15734.3, + "second_furthest_km": 6346.9, + "clarity_ratio": 2.48, + "median_distance_km": 4139.3, + "distances_to_centroid": { + "Townsville": 3932.9, + "Canning Vale": 993.3, + "Lakemba": 4139.3, + "Taupo": 6346.9, + "Arari": 15734.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Townsville: (-19.27°, 146.81°)", + " Canning Vale: (-32.06°, 115.92°)", + " Lakemba: (-33.92°, 151.08°)", + " Taupo: (-38.68°, 176.08°)", + " Arari: (-3.45°, -44.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arari: 15734.3 km from centroid", + " Taupo: 6346.9 km from centroid", + " Lakemba: 4139.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arari", + "FINAL ANSWER: Arari" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.32361, + "lon": 91.93614, + "name": "Shushenskoye" + }, + { + "lat": 53.16675, + "lon": 48.69723, + "name": "Oktyabr’sk" + }, + { + "lat": 42.03539, + "lon": 12.64413, + "name": "Mentana" + }, + { + "lat": 53.72405, + "lon": -1.71294, + "name": "Cleckheaton" + }, + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + } + ], + "question": "Which location is the geographic outlier among: Shushenskoye, Oktyabr’sk, Mentana, Cleckheaton, Masterton?", + "ground_truth": { + "answer": "Masterton", + "outlier_distance_km": 13875.7, + "second_furthest_km": 5710.2, + "clarity_ratio": 2.43, + "median_distance_km": 4727.2, + "distances_to_centroid": { + "Shushenskoye": 3151.4, + "Oktyabr’sk": 2682.7, + "Mentana": 4727.2, + "Cleckheaton": 5710.2, + "Masterton": 13875.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shushenskoye: (53.32°, 91.94°)", + " Oktyabr’sk: (53.17°, 48.70°)", + " Mentana: (42.04°, 12.64°)", + " Cleckheaton: (53.72°, -1.71°)", + " Masterton: (-40.96°, 175.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Masterton: 13875.7 km from centroid", + " Cleckheaton: 5710.2 km from centroid", + " Mentana: 4727.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Masterton", + "FINAL ANSWER: Masterton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + { + "lat": -27.35364, + "lon": 152.96848, + "name": "Albany Creek" + }, + { + "lat": -33.90741, + "lon": 151.15546, + "name": "Marrickville" + }, + { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + { + "lat": 21.32608, + "lon": -157.87594, + "name": "Kalihi-Palama" + } + ], + "question": "Which location is the geographic outlier among: Cabramatta, Albany Creek, Marrickville, Kellyville, Kalihi-Palama?", + "ground_truth": { + "answer": "Kalihi-Palama", + "outlier_distance_km": 13088.5, + "second_furthest_km": 6379.2, + "clarity_ratio": 2.05, + "median_distance_km": 6123.1, + "distances_to_centroid": { + "Cabramatta": 6102.8, + "Albany Creek": 6379.2, + "Marrickville": 6123.1, + "Kellyville": 6105.8, + "Kalihi-Palama": 13088.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cabramatta: (-33.90°, 150.93°)", + " Albany Creek: (-27.35°, 152.97°)", + " Marrickville: (-33.91°, 151.16°)", + " Kellyville: (-33.71°, 150.95°)", + " Kalihi-Palama: (21.33°, -157.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kalihi-Palama: 13088.5 km from centroid", + " Albany Creek: 6379.2 km from centroid", + " Marrickville: 6123.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kalihi-Palama", + "FINAL ANSWER: Kalihi-Palama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.31451, + "lon": -97.9252, + "name": "Huamantla" + }, + { + "lat": 29.66578, + "lon": -95.01937, + "name": "La Porte" + }, + { + "lat": 19.35985, + "lon": -99.35016, + "name": "Huixquilucan" + }, + { + "lat": 44.76774, + "lon": -93.27772, + "name": "Burnsville" + }, + { + "lat": 5.53532, + "lon": -0.39827, + "name": "Amanfrom" + } + ], + "question": "Which location is the geographic outlier among: Huamantla, La Porte, Huixquilucan, Burnsville, Amanfrom?", + "ground_truth": { + "answer": "Amanfrom", + "outlier_distance_km": 8417.8, + "second_furthest_km": 2755.8, + "clarity_ratio": 3.05, + "median_distance_km": 2339.7, + "distances_to_centroid": { + "Huamantla": 2197.6, + "La Porte": 1887.2, + "Huixquilucan": 2339.7, + "Burnsville": 2755.8, + "Amanfrom": 8417.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huamantla: (19.31°, -97.93°)", + " La Porte: (29.67°, -95.02°)", + " Huixquilucan: (19.36°, -99.35°)", + " Burnsville: (44.77°, -93.28°)", + " Amanfrom: (5.54°, -0.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amanfrom: 8417.8 km from centroid", + " Burnsville: 2755.8 km from centroid", + " Huixquilucan: 2339.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amanfrom", + "FINAL ANSWER: Amanfrom" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.21452, + "lon": 31.35798, + "name": "Bilqās" + }, + { + "lat": 30.76128, + "lon": 30.69972, + "name": "Kawm Ḩamādah" + }, + { + "lat": 10.9202, + "lon": 39.78714, + "name": "Harbu" + }, + { + "lat": 8.9, + "lon": 39.91667, + "name": "Metahāra" + }, + { + "lat": 17.30097, + "lon": 101.7685, + "name": "Wang Saphung" + } + ], + "question": "Which location is the geographic outlier among: Bilqās, Kawm Ḩamādah, Harbu, Metahāra, Wang Saphung?", + "ground_truth": { + "answer": "Wang Saphung", + "outlier_distance_km": 5577.9, + "second_furthest_km": 2176.2, + "clarity_ratio": 2.56, + "median_distance_km": 2148.2, + "distances_to_centroid": { + "Bilqās": 2148.2, + "Kawm Ḩamādah": 2176.2, + "Harbu": 1375.2, + "Metahāra": 1538.6, + "Wang Saphung": 5577.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bilqās: (31.21°, 31.36°)", + " Kawm Ḩamādah: (30.76°, 30.70°)", + " Harbu: (10.92°, 39.79°)", + " Metahāra: (8.90°, 39.92°)", + " Wang Saphung: (17.30°, 101.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wang Saphung: 5577.9 km from centroid", + " Kawm Ḩamādah: 2176.2 km from centroid", + " Bilqās: 2148.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wang Saphung", + "FINAL ANSWER: Wang Saphung" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.47278, + "lon": -47.36306, + "name": "Santa Rosa de Viterbo" + }, + { + "lat": -7.04159, + "lon": -35.62699, + "name": "Alagoa Grande" + }, + { + "lat": -12.62639, + "lon": -38.99, + "name": "Muritiba" + }, + { + "lat": -31.66274, + "lon": -60.7653, + "name": "Santo Tomé" + }, + { + "lat": 28.43597, + "lon": 77.17601, + "name": "Dera Māndi" + } + ], + "question": "Which location is the geographic outlier among: Santa Rosa de Viterbo, Alagoa Grande, Muritiba, Santo Tomé, Dera Māndi?", + "ground_truth": { + "answer": "Dera Māndi", + "outlier_distance_km": 11282.1, + "second_furthest_km": 4808.3, + "clarity_ratio": 2.35, + "median_distance_km": 3138.4, + "distances_to_centroid": { + "Santa Rosa de Viterbo": 3138.4, + "Alagoa Grande": 1611.0, + "Muritiba": 1996.3, + "Santo Tomé": 4808.3, + "Dera Māndi": 11282.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Rosa de Viterbo: (-21.47°, -47.36°)", + " Alagoa Grande: (-7.04°, -35.63°)", + " Muritiba: (-12.63°, -38.99°)", + " Santo Tomé: (-31.66°, -60.77°)", + " Dera Māndi: (28.44°, 77.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dera Māndi: 11282.1 km from centroid", + " Santo Tomé: 4808.3 km from centroid", + " Santa Rosa de Viterbo: 3138.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dera Māndi", + "FINAL ANSWER: Dera Māndi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.29306, + "lon": -98.84167, + "name": "San Jerónimo Cuatro Vientos" + }, + { + "lat": 36.10803, + "lon": -115.245, + "name": "Spring Valley" + }, + { + "lat": 41.34559, + "lon": -88.84258, + "name": "Ottawa" + }, + { + "lat": 41.7942, + "lon": -87.59394, + "name": "Hyde Park" + }, + { + "lat": -37.66667, + "lon": 145.06667, + "name": "Mill Park" + } + ], + "question": "Which location is the geographic outlier among: San Jerónimo Cuatro Vientos, Spring Valley, Ottawa, Hyde Park, Mill Park?", + "ground_truth": { + "answer": "Mill Park", + "outlier_distance_km": 17637.9, + "second_furthest_km": 6599.1, + "clarity_ratio": 2.67, + "median_distance_km": 5188.0, + "distances_to_centroid": { + "San Jerónimo Cuatro Vientos": 5188.0, + "Spring Valley": 6599.1, + "Ottawa": 4412.4, + "Hyde Park": 4333.0, + "Mill Park": 17637.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Jerónimo Cuatro Vientos: (19.29°, -98.84°)", + " Spring Valley: (36.11°, -115.25°)", + " Ottawa: (41.35°, -88.84°)", + " Hyde Park: (41.79°, -87.59°)", + " Mill Park: (-37.67°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mill Park: 17637.9 km from centroid", + " Spring Valley: 6599.1 km from centroid", + " San Jerónimo Cuatro Vientos: 5188.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mill Park", + "FINAL ANSWER: Mill Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -27.56056, + "lon": 151.95386, + "name": "Toowoomba" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": 41.38022, + "lon": 2.17319, + "name": "Ciutat Vella" + } + ], + "question": "Which location is the geographic outlier among: Bundoora, Broken Hill, Toowoomba, Cheltenham, Ciutat Vella?", + "ground_truth": { + "answer": "Ciutat Vella", + "outlier_distance_km": 13435.6, + "second_furthest_km": 3677.7, + "clarity_ratio": 3.65, + "median_distance_km": 3442.8, + "distances_to_centroid": { + "Bundoora": 3428.5, + "Broken Hill": 2839.4, + "Toowoomba": 3677.7, + "Cheltenham": 3442.8, + "Ciutat Vella": 13435.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bundoora: (-37.70°, 145.06°)", + " Broken Hill: (-31.97°, 141.45°)", + " Toowoomba: (-27.56°, 151.95°)", + " Cheltenham: (-37.97°, 145.05°)", + " Ciutat Vella: (41.38°, 2.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciutat Vella: 13435.6 km from centroid", + " Toowoomba: 3677.7 km from centroid", + " Cheltenham: 3442.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciutat Vella", + "FINAL ANSWER: Ciutat Vella" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -33.94185, + "lon": 150.8717, + "name": "Prestons" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -3.22028, + "lon": -45.00361, + "name": "Viana" + } + ], + "question": "Which location is the geographic outlier among: Greystanes, Seven Hills, Prestons, Mount Martha, Viana?", + "ground_truth": { + "answer": "Viana", + "outlier_distance_km": 15617.4, + "second_furthest_km": 3860.1, + "clarity_ratio": 4.05, + "median_distance_km": 3859.2, + "distances_to_centroid": { + "Greystanes": 3860.1, + "Seven Hills": 3859.2, + "Prestons": 3852.7, + "Mount Martha": 3350.9, + "Viana": 15617.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Greystanes: (-33.82°, 150.95°)", + " Seven Hills: (-33.78°, 150.93°)", + " Prestons: (-33.94°, 150.87°)", + " Mount Martha: (-38.27°, 145.02°)", + " Viana: (-3.22°, -45.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viana: 15617.4 km from centroid", + " Greystanes: 3860.1 km from centroid", + " Seven Hills: 3859.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viana", + "FINAL ANSWER: Viana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + }, + { + "lat": -37.73333, + "lon": 145.15, + "name": "Eltham" + }, + { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + }, + { + "lat": 9.24391, + "lon": -75.14675, + "name": "San Luis de Sincé" + } + ], + "question": "Which location is the geographic outlier among: Albany, Eltham, Kellyville, Te Atatu Peninsula, San Luis de Sincé?", + "ground_truth": { + "answer": "San Luis de Sincé", + "outlier_distance_km": 18048.3, + "second_furthest_km": 6732.4, + "clarity_ratio": 2.68, + "median_distance_km": 4655.5, + "distances_to_centroid": { + "Albany": 1709.3, + "Eltham": 4133.0, + "Kellyville": 4655.5, + "Te Atatu Peninsula": 6732.4, + "San Luis de Sincé": 18048.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albany: (-35.03°, 117.88°)", + " Eltham: (-37.73°, 145.15°)", + " Kellyville: (-33.71°, 150.95°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + " San Luis de Sincé: (9.24°, -75.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Luis de Sincé: 18048.3 km from centroid", + " Te Atatu Peninsula: 6732.4 km from centroid", + " Kellyville: 4655.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Luis de Sincé", + "FINAL ANSWER: San Luis de Sincé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.81667, + "lon": 40.51667, + "name": "Gelemso" + }, + { + "lat": 5.70119, + "lon": -1.28657, + "name": "Foso" + }, + { + "lat": -0.17344, + "lon": 35.86313, + "name": "Rongai" + }, + { + "lat": 30.15293, + "lon": 31.31501, + "name": "Al Khuşūş" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + } + ], + "question": "Which location is the geographic outlier among: Gelemso, Foso, Rongai, Al Khuşūş, Greystanes?", + "ground_truth": { + "answer": "Greystanes", + "outlier_distance_km": 11014.5, + "second_furthest_km": 5864.0, + "clarity_ratio": 1.88, + "median_distance_km": 3771.0, + "distances_to_centroid": { + "Gelemso": 1421.4, + "Foso": 5864.0, + "Rongai": 1754.0, + "Al Khuşūş": 3771.0, + "Greystanes": 11014.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gelemso: (8.82°, 40.52°)", + " Foso: (5.70°, -1.29°)", + " Rongai: (-0.17°, 35.86°)", + " Al Khuşūş: (30.15°, 31.32°)", + " Greystanes: (-33.82°, 150.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greystanes: 11014.5 km from centroid", + " Foso: 5864.0 km from centroid", + " Al Khuşūş: 3771.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greystanes", + "FINAL ANSWER: Greystanes" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.26722, + "lon": -43.16194, + "name": "Palmas de Monte Alto" + }, + { + "lat": -2.12583, + "lon": -45.88528, + "name": "Governador Nunes Freire" + }, + { + "lat": -21.53944, + "lon": -42.18028, + "name": "Santo Antônio de Pádua" + }, + { + "lat": -33.2914, + "lon": -66.32467, + "name": "San Luis" + }, + { + "lat": -38.16667, + "lon": 145.16667, + "name": "Langwarrin" + } + ], + "question": "Which location is the geographic outlier among: Palmas de Monte Alto, Governador Nunes Freire, Santo Antônio de Pádua, San Luis, Langwarrin?", + "ground_truth": { + "answer": "Langwarrin", + "outlier_distance_km": 12870.4, + "second_furthest_km": 5582.8, + "clarity_ratio": 2.31, + "median_distance_km": 4412.0, + "distances_to_centroid": { + "Palmas de Monte Alto": 3549.4, + "Governador Nunes Freire": 4412.0, + "Santo Antônio de Pádua": 3269.6, + "San Luis": 5582.8, + "Langwarrin": 12870.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palmas de Monte Alto: (-14.27°, -43.16°)", + " Governador Nunes Freire: (-2.13°, -45.89°)", + " Santo Antônio de Pádua: (-21.54°, -42.18°)", + " San Luis: (-33.29°, -66.32°)", + " Langwarrin: (-38.17°, 145.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Langwarrin: 12870.4 km from centroid", + " San Luis: 5582.8 km from centroid", + " Governador Nunes Freire: 4412.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Langwarrin", + "FINAL ANSWER: Langwarrin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.98889, + "lon": -39.58056, + "name": "Tejuçuoca" + }, + { + "lat": 1.90999, + "lon": -75.15931, + "name": "Puerto Rico" + }, + { + "lat": 6.96321, + "lon": -75.41738, + "name": "Yarumal" + }, + { + "lat": -26.81298, + "lon": -65.29543, + "name": "Yerba Buena" + }, + { + "lat": 45.57438, + "lon": 9.07537, + "name": "Garbagnate Milanese" + } + ], + "question": "Which location is the geographic outlier among: Tejuçuoca, Puerto Rico, Yarumal, Yerba Buena, Garbagnate Milanese?", + "ground_truth": { + "answer": "Garbagnate Milanese", + "outlier_distance_km": 7211.5, + "second_furthest_km": 3907.8, + "clarity_ratio": 1.85, + "median_distance_km": 2901.9, + "distances_to_centroid": { + "Tejuçuoca": 1449.0, + "Puerto Rico": 2890.0, + "Yarumal": 2901.9, + "Yerba Buena": 3907.8, + "Garbagnate Milanese": 7211.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tejuçuoca: (-3.99°, -39.58°)", + " Puerto Rico: (1.91°, -75.16°)", + " Yarumal: (6.96°, -75.42°)", + " Yerba Buena: (-26.81°, -65.30°)", + " Garbagnate Milanese: (45.57°, 9.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Garbagnate Milanese: 7211.5 km from centroid", + " Yerba Buena: 3907.8 km from centroid", + " Yarumal: 2901.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Garbagnate Milanese", + "FINAL ANSWER: Garbagnate Milanese" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": -37.69863, + "lon": 144.78631, + "name": "Taylors Lakes" + }, + { + "lat": -27.56056, + "lon": 151.95386, + "name": "Toowoomba" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": -24.24423, + "lon": -49.70932, + "name": "Jaguariaíva" + } + ], + "question": "Which location is the geographic outlier among: Cheltenham, Taylors Lakes, Toowoomba, Boronia, Jaguariaíva?", + "ground_truth": { + "answer": "Jaguariaíva", + "outlier_distance_km": 13199.1, + "second_furthest_km": 4281.9, + "clarity_ratio": 3.08, + "median_distance_km": 3441.8, + "distances_to_centroid": { + "Cheltenham": 3420.7, + "Taylors Lakes": 3399.1, + "Toowoomba": 4281.9, + "Boronia": 3441.8, + "Jaguariaíva": 13199.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cheltenham: (-37.97°, 145.05°)", + " Taylors Lakes: (-37.70°, 144.79°)", + " Toowoomba: (-27.56°, 151.95°)", + " Boronia: (-37.87°, 145.28°)", + " Jaguariaíva: (-24.24°, -49.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaguariaíva: 13199.1 km from centroid", + " Toowoomba: 4281.9 km from centroid", + " Boronia: 3441.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaguariaíva", + "FINAL ANSWER: Jaguariaíva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.29695, + "lon": 5.38107, + "name": "Marseille" + }, + { + "lat": 59.88333, + "lon": 29.9, + "name": "Peterhof" + }, + { + "lat": 53.55, + "lon": -2.2, + "name": "Middleton" + }, + { + "lat": 53.46667, + "lon": -3.01667, + "name": "Bootle" + }, + { + "lat": -23.31861, + "lon": -46.58667, + "name": "Mairiporã" + } + ], + "question": "Which location is the geographic outlier among: Marseille, Peterhof, Middleton, Bootle, Mairiporã?", + "ground_truth": { + "answer": "Mairiporã", + "outlier_distance_km": 8126.6, + "second_furthest_km": 3427.7, + "clarity_ratio": 2.37, + "median_distance_km": 1800.5, + "distances_to_centroid": { + "Marseille": 986.7, + "Peterhof": 3427.7, + "Middleton": 1800.5, + "Bootle": 1789.4, + "Mairiporã": 8126.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marseille: (43.30°, 5.38°)", + " Peterhof: (59.88°, 29.90°)", + " Middleton: (53.55°, -2.20°)", + " Bootle: (53.47°, -3.02°)", + " Mairiporã: (-23.32°, -46.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mairiporã: 8126.6 km from centroid", + " Peterhof: 3427.7 km from centroid", + " Middleton: 1800.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mairiporã", + "FINAL ANSWER: Mairiporã" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.39144, + "lon": -86.93111, + "name": "Jasper" + }, + { + "lat": 41.83809, + "lon": -87.65116, + "name": "Bridgeport" + }, + { + "lat": 44.18582, + "lon": -88.46261, + "name": "Neenah" + }, + { + "lat": 45.84041, + "lon": -119.28946, + "name": "Hermiston" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + } + ], + "question": "Which location is the geographic outlier among: Jasper, Bridgeport, Neenah, Hermiston, Bairnsdale?", + "ground_truth": { + "answer": "Bairnsdale", + "outlier_distance_km": 18157.6, + "second_furthest_km": 6604.8, + "clarity_ratio": 2.75, + "median_distance_km": 4190.1, + "distances_to_centroid": { + "Jasper": 3943.5, + "Bridgeport": 4067.9, + "Neenah": 4190.1, + "Hermiston": 6604.8, + "Bairnsdale": 18157.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jasper: (38.39°, -86.93°)", + " Bridgeport: (41.84°, -87.65°)", + " Neenah: (44.19°, -88.46°)", + " Hermiston: (45.84°, -119.29°)", + " Bairnsdale: (-37.82°, 147.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bairnsdale: 18157.6 km from centroid", + " Hermiston: 6604.8 km from centroid", + " Neenah: 4190.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bairnsdale", + "FINAL ANSWER: Bairnsdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.10467, + "lon": 93.69518, + "name": "Naharlagun" + }, + { + "lat": 28.9629, + "lon": 106.92844, + "name": "Wansheng" + }, + { + "lat": 29.16242, + "lon": 78.48458, + "name": "Tājpur" + }, + { + "lat": 31.16946, + "lon": 108.4031, + "name": "Hanfeng" + }, + { + "lat": 36.81904, + "lon": -76.27494, + "name": "Chesapeake" + } + ], + "question": "Which location is the geographic outlier among: Naharlagun, Wansheng, Tājpur, Hanfeng, Chesapeake?", + "ground_truth": { + "answer": "Chesapeake", + "outlier_distance_km": 11359.1, + "second_furthest_km": 4371.0, + "clarity_ratio": 2.6, + "median_distance_km": 4286.7, + "distances_to_centroid": { + "Naharlagun": 3077.3, + "Wansheng": 4286.7, + "Tājpur": 1572.4, + "Hanfeng": 4371.0, + "Chesapeake": 11359.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Naharlagun: (27.10°, 93.70°)", + " Wansheng: (28.96°, 106.93°)", + " Tājpur: (29.16°, 78.48°)", + " Hanfeng: (31.17°, 108.40°)", + " Chesapeake: (36.82°, -76.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chesapeake: 11359.1 km from centroid", + " Hanfeng: 4371.0 km from centroid", + " Wansheng: 4286.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chesapeake", + "FINAL ANSWER: Chesapeake" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.05997, + "lon": 17.09001, + "name": "Mola di Bari" + }, + { + "lat": 52.84754, + "lon": 8.045, + "name": "Cloppenburg" + }, + { + "lat": 46.70241, + "lon": 41.72487, + "name": "Proletarsk" + }, + { + "lat": 45.35383, + "lon": 40.69465, + "name": "Gul’kevichi" + }, + { + "lat": -28.77897, + "lon": 114.61459, + "name": "Geraldton" + } + ], + "question": "Which location is the geographic outlier among: Mola di Bari, Cloppenburg, Proletarsk, Gul’kevichi, Geraldton?", + "ground_truth": { + "answer": "Geraldton", + "outlier_distance_km": 9991.9, + "second_furthest_km": 3763.8, + "clarity_ratio": 2.65, + "median_distance_km": 2660.8, + "distances_to_centroid": { + "Mola di Bari": 2660.8, + "Cloppenburg": 3763.8, + "Proletarsk": 1713.2, + "Gul’kevichi": 1580.9, + "Geraldton": 9991.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mola di Bari: (41.06°, 17.09°)", + " Cloppenburg: (52.85°, 8.04°)", + " Proletarsk: (46.70°, 41.72°)", + " Gul’kevichi: (45.35°, 40.69°)", + " Geraldton: (-28.78°, 114.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Geraldton: 9991.9 km from centroid", + " Cloppenburg: 3763.8 km from centroid", + " Mola di Bari: 2660.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Geraldton", + "FINAL ANSWER: Geraldton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.46538, + "lon": -73.2531, + "name": "Valledupar" + }, + { + "lat": -23.43861, + "lon": -47.06139, + "name": "Araçariguama" + }, + { + "lat": -15.80976, + "lon": -47.97202, + "name": "Guará" + }, + { + "lat": -30.18111, + "lon": -50.20556, + "name": "Cidreira" + }, + { + "lat": 28.73548, + "lon": 77.03522, + "name": "Karāla" + } + ], + "question": "Which location is the geographic outlier among: Valledupar, Araçariguama, Guará, Cidreira, Karāla?", + "ground_truth": { + "answer": "Karāla", + "outlier_distance_km": 11823.0, + "second_furthest_km": 5305.8, + "clarity_ratio": 2.23, + "median_distance_km": 3529.0, + "distances_to_centroid": { + "Valledupar": 5305.8, + "Araçariguama": 2788.2, + "Guará": 2404.5, + "Cidreira": 3529.0, + "Karāla": 11823.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Valledupar: (10.47°, -73.25°)", + " Araçariguama: (-23.44°, -47.06°)", + " Guará: (-15.81°, -47.97°)", + " Cidreira: (-30.18°, -50.21°)", + " Karāla: (28.74°, 77.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karāla: 11823.0 km from centroid", + " Valledupar: 5305.8 km from centroid", + " Cidreira: 3529.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karāla", + "FINAL ANSWER: Karāla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": -41.13827, + "lon": 175.0502, + "name": "Upper Hutt" + }, + { + "lat": 53.11125, + "lon": 9.41082, + "name": "Rotenburg" + } + ], + "question": "Which location is the geographic outlier among: Wollongong, Saint Kilda, Shepparton, Upper Hutt, Rotenburg?", + "ground_truth": { + "answer": "Rotenburg", + "outlier_distance_km": 13423.2, + "second_furthest_km": 5281.9, + "clarity_ratio": 2.54, + "median_distance_km": 3040.4, + "distances_to_centroid": { + "Wollongong": 3040.4, + "Saint Kilda": 2814.7, + "Shepparton": 2736.9, + "Upper Hutt": 5281.9, + "Rotenburg": 13423.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wollongong: (-34.42°, 150.89°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Shepparton: (-36.38°, 145.40°)", + " Upper Hutt: (-41.14°, 175.05°)", + " Rotenburg: (53.11°, 9.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rotenburg: 13423.2 km from centroid", + " Upper Hutt: 5281.9 km from centroid", + " Wollongong: 3040.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rotenburg", + "FINAL ANSWER: Rotenburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.52944, + "lon": -46.64389, + "name": "Caconde" + }, + { + "lat": -3.87667, + "lon": -38.62556, + "name": "Maracanaú" + }, + { + "lat": -13.64136, + "lon": -41.84319, + "name": "Livramento de Nossa Senhora" + }, + { + "lat": -8.96389, + "lon": -37.62833, + "name": "Manari" + }, + { + "lat": 13.99904, + "lon": 100.54962, + "name": "Ban Bang Kadi" + } + ], + "question": "Which location is the geographic outlier among: Caconde, Maracanaú, Livramento de Nossa Senhora, Manari, Ban Bang Kadi?", + "ground_truth": { + "answer": "Ban Bang Kadi", + "outlier_distance_km": 12706.7, + "second_furthest_km": 3981.7, + "clarity_ratio": 3.19, + "median_distance_km": 3260.7, + "distances_to_centroid": { + "Caconde": 3981.7, + "Maracanaú": 2872.9, + "Livramento de Nossa Senhora": 3260.7, + "Manari": 2740.5, + "Ban Bang Kadi": 12706.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caconde: (-21.53°, -46.64°)", + " Maracanaú: (-3.88°, -38.63°)", + " Livramento de Nossa Senhora: (-13.64°, -41.84°)", + " Manari: (-8.96°, -37.63°)", + " Ban Bang Kadi: (14.00°, 100.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ban Bang Kadi: 12706.7 km from centroid", + " Caconde: 3981.7 km from centroid", + " Livramento de Nossa Senhora: 3260.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ban Bang Kadi", + "FINAL ANSWER: Ban Bang Kadi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": 40.54184, + "lon": 81.26566, + "name": "Aral" + } + ], + "question": "Which location is the geographic outlier among: Saint Albans, Miranda, Tuggeranong Administrative District, Avondale, Aral?", + "ground_truth": { + "answer": "Aral", + "outlier_distance_km": 9131.2, + "second_furthest_km": 3784.2, + "clarity_ratio": 2.41, + "median_distance_km": 1944.8, + "distances_to_centroid": { + "Saint Albans": 1944.8, + "Miranda": 1830.0, + "Tuggeranong Administrative District": 1851.3, + "Avondale": 3784.2, + "Aral": 9131.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Albans: (-37.73°, 144.80°)", + " Miranda: (-34.04°, 151.10°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + " Avondale: (-36.88°, 174.70°)", + " Aral: (40.54°, 81.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aral: 9131.2 km from centroid", + " Avondale: 3784.2 km from centroid", + " Saint Albans: 1944.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aral", + "FINAL ANSWER: Aral" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.35778, + "lon": -36.69639, + "name": "Pesqueira" + }, + { + "lat": -17.02306, + "lon": -72.01472, + "name": "Mollendo" + }, + { + "lat": -4.17972, + "lon": -38.13056, + "name": "Beberibe" + }, + { + "lat": -31.63349, + "lon": -71.16967, + "name": "Illapel" + }, + { + "lat": 48.86342, + "lon": 2.506, + "name": "Neuilly-Plaisance" + } + ], + "question": "Which location is the geographic outlier among: Pesqueira, Mollendo, Beberibe, Illapel, Neuilly-Plaisance?", + "ground_truth": { + "answer": "Neuilly-Plaisance", + "outlier_distance_km": 7194.1, + "second_furthest_km": 4376.9, + "clarity_ratio": 1.64, + "median_distance_km": 3549.0, + "distances_to_centroid": { + "Pesqueira": 965.1, + "Mollendo": 3549.0, + "Beberibe": 583.7, + "Illapel": 4376.9, + "Neuilly-Plaisance": 7194.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pesqueira: (-8.36°, -36.70°)", + " Mollendo: (-17.02°, -72.01°)", + " Beberibe: (-4.18°, -38.13°)", + " Illapel: (-31.63°, -71.17°)", + " Neuilly-Plaisance: (48.86°, 2.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Neuilly-Plaisance: 7194.1 km from centroid", + " Illapel: 4376.9 km from centroid", + " Mollendo: 3549.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Neuilly-Plaisance", + "FINAL ANSWER: Neuilly-Plaisance" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + { + "lat": 46.91054, + "lon": -98.70844, + "name": "Jamestown" + } + ], + "question": "Which location is the geographic outlier among: Caroline Springs, Pakenham, Burwood, Cabramatta, Jamestown?", + "ground_truth": { + "answer": "Jamestown", + "outlier_distance_km": 16564.3, + "second_furthest_km": 5392.9, + "clarity_ratio": 3.07, + "median_distance_km": 5377.7, + "distances_to_centroid": { + "Caroline Springs": 4879.7, + "Pakenham": 4950.4, + "Burwood": 5392.9, + "Cabramatta": 5377.7, + "Jamestown": 16564.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caroline Springs: (-37.74°, 144.74°)", + " Pakenham: (-38.07°, 145.47°)", + " Burwood: (-33.88°, 151.10°)", + " Cabramatta: (-33.90°, 150.93°)", + " Jamestown: (46.91°, -98.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jamestown: 16564.3 km from centroid", + " Burwood: 5392.9 km from centroid", + " Cabramatta: 5377.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jamestown", + "FINAL ANSWER: Jamestown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + }, + { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + { + "lat": -38.11342, + "lon": 145.28326, + "name": "Cranbourne" + }, + { + "lat": 51.93333, + "lon": 7.35, + "name": "Nottuln" + } + ], + "question": "Which location is the geographic outlier among: Coogee, Mulgrave, Hawthorn South, Cranbourne, Nottuln?", + "ground_truth": { + "answer": "Nottuln", + "outlier_distance_km": 13137.2, + "second_furthest_km": 3597.3, + "clarity_ratio": 3.65, + "median_distance_km": 3310.7, + "distances_to_centroid": { + "Coogee": 3597.3, + "Mulgrave": 3292.0, + "Hawthorn South": 3275.9, + "Cranbourne": 3310.7, + "Nottuln": 13137.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coogee: (-33.92°, 151.26°)", + " Mulgrave: (-37.93°, 145.18°)", + " Hawthorn South: (-37.83°, 145.04°)", + " Cranbourne: (-38.11°, 145.28°)", + " Nottuln: (51.93°, 7.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nottuln: 13137.2 km from centroid", + " Coogee: 3597.3 km from centroid", + " Cranbourne: 3310.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nottuln", + "FINAL ANSWER: Nottuln" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.43476, + "lon": 0.09311, + "name": "Alençon" + }, + { + "lat": 50.64358, + "lon": 2.98715, + "name": "Lomme" + }, + { + "lat": 51.69689, + "lon": 7.46809, + "name": "Selm" + }, + { + "lat": 53.70291, + "lon": -1.6337, + "name": "Batley" + }, + { + "lat": 37.97806, + "lon": 76.86722, + "name": "Kaqun" + } + ], + "question": "Which location is the geographic outlier among: Alençon, Lomme, Selm, Batley, Kaqun?", + "ground_truth": { + "answer": "Kaqun", + "outlier_distance_km": 4847.0, + "second_furthest_km": 1428.8, + "clarity_ratio": 3.39, + "median_distance_km": 1255.5, + "distances_to_centroid": { + "Alençon": 1255.5, + "Lomme": 1047.7, + "Selm": 776.8, + "Batley": 1428.8, + "Kaqun": 4847.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alençon: (48.43°, 0.09°)", + " Lomme: (50.64°, 2.99°)", + " Selm: (51.70°, 7.47°)", + " Batley: (53.70°, -1.63°)", + " Kaqun: (37.98°, 76.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kaqun: 4847.0 km from centroid", + " Batley: 1428.8 km from centroid", + " Alençon: 1255.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kaqun", + "FINAL ANSWER: Kaqun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.55, + "lon": 37.78333, + "name": "Petrovskaya" + }, + { + "lat": 48.73961, + "lon": 9.30473, + "name": "Esslingen" + }, + { + "lat": 48.87143, + "lon": 2.22929, + "name": "Suresnes" + }, + { + "lat": 50.27593, + "lon": 127.52637, + "name": "Blagoveshchensk" + }, + { + "lat": 6.91002, + "lon": 3.66557, + "name": "Iperu" + } + ], + "question": "Which location is the geographic outlier among: Petrovskaya, Esslingen, Suresnes, Blagoveshchensk, Iperu?", + "ground_truth": { + "answer": "Blagoveshchensk", + "outlier_distance_km": 6645.6, + "second_furthest_km": 5044.4, + "clarity_ratio": 1.32, + "median_distance_km": 2722.3, + "distances_to_centroid": { + "Petrovskaya": 1503.9, + "Esslingen": 2205.9, + "Suresnes": 2722.3, + "Blagoveshchensk": 6645.6, + "Iperu": 5044.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Petrovskaya: (55.55°, 37.78°)", + " Esslingen: (48.74°, 9.30°)", + " Suresnes: (48.87°, 2.23°)", + " Blagoveshchensk: (50.28°, 127.53°)", + " Iperu: (6.91°, 3.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blagoveshchensk: 6645.6 km from centroid", + " Iperu: 5044.4 km from centroid", + " Suresnes: 2722.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blagoveshchensk", + "FINAL ANSWER: Blagoveshchensk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + }, + { + "lat": -41.13827, + "lon": 175.0502, + "name": "Upper Hutt" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -21.90389, + "lon": -47.61944, + "name": "Descalvado" + } + ], + "question": "Which location is the geographic outlier among: Te Atatu South, Upper Hutt, Engadine, Bairnsdale, Descalvado?", + "ground_truth": { + "answer": "Descalvado", + "outlier_distance_km": 13626.4, + "second_furthest_km": 4867.7, + "clarity_ratio": 2.8, + "median_distance_km": 4806.2, + "distances_to_centroid": { + "Te Atatu South": 4867.7, + "Upper Hutt": 4806.2, + "Engadine": 2827.9, + "Bairnsdale": 2489.0, + "Descalvado": 13626.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Te Atatu South: (-36.86°, 174.65°)", + " Upper Hutt: (-41.14°, 175.05°)", + " Engadine: (-34.07°, 151.01°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Descalvado: (-21.90°, -47.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Descalvado: 13626.4 km from centroid", + " Te Atatu South: 4867.7 km from centroid", + " Upper Hutt: 4806.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Descalvado", + "FINAL ANSWER: Descalvado" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.67501, + "lon": 20.13473, + "name": "Svetlyy" + }, + { + "lat": 45.90878, + "lon": 6.12565, + "name": "Annecy" + }, + { + "lat": 51.48026, + "lon": -0.1993, + "name": "Fulham" + }, + { + "lat": 46.66817, + "lon": 11.15953, + "name": "Merano" + }, + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + } + ], + "question": "Which location is the geographic outlier among: Svetlyy, Annecy, Fulham, Merano, Umina Beach?", + "ground_truth": { + "answer": "Umina Beach", + "outlier_distance_km": 13957.1, + "second_furthest_km": 3671.2, + "clarity_ratio": 3.8, + "median_distance_km": 3037.2, + "distances_to_centroid": { + "Svetlyy": 2770.2, + "Annecy": 3037.2, + "Fulham": 3671.2, + "Merano": 2705.1, + "Umina Beach": 13957.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Svetlyy: (54.68°, 20.13°)", + " Annecy: (45.91°, 6.13°)", + " Fulham: (51.48°, -0.20°)", + " Merano: (46.67°, 11.16°)", + " Umina Beach: (-33.52°, 151.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Umina Beach: 13957.1 km from centroid", + " Fulham: 3671.2 km from centroid", + " Annecy: 3037.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Umina Beach", + "FINAL ANSWER: Umina Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.01769, + "lon": -82.50619, + "name": "Egypt Lake-Leto" + }, + { + "lat": 49.17003, + "lon": -123.13683, + "name": "Richmond" + }, + { + "lat": 40.91149, + "lon": -73.78235, + "name": "New Rochelle" + }, + { + "lat": 48.46686, + "lon": -81.33312, + "name": "Timmins" + }, + { + "lat": 21.23391, + "lon": 110.38749, + "name": "Zhanjiang" + } + ], + "question": "Which location is the geographic outlier among: Egypt Lake-Leto, Richmond, New Rochelle, Timmins, Zhanjiang?", + "ground_truth": { + "answer": "Zhanjiang", + "outlier_distance_km": 13165.1, + "second_furthest_km": 5809.7, + "clarity_ratio": 2.27, + "median_distance_km": 3193.1, + "distances_to_centroid": { + "Egypt Lake-Leto": 3193.1, + "Richmond": 5809.7, + "New Rochelle": 2069.0, + "Timmins": 2790.0, + "Zhanjiang": 13165.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Egypt Lake-Leto: (28.02°, -82.51°)", + " Richmond: (49.17°, -123.14°)", + " New Rochelle: (40.91°, -73.78°)", + " Timmins: (48.47°, -81.33°)", + " Zhanjiang: (21.23°, 110.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhanjiang: 13165.1 km from centroid", + " Richmond: 5809.7 km from centroid", + " Egypt Lake-Leto: 3193.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhanjiang", + "FINAL ANSWER: Zhanjiang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.72459, + "lon": 31.19939, + "name": "Thulamahashi" + }, + { + "lat": 7.01667, + "lon": 39.98333, + "name": "Goba" + }, + { + "lat": 3.93726, + "lon": 41.85688, + "name": "Mandera" + }, + { + "lat": 9.40079, + "lon": -0.8393, + "name": "Tamale" + }, + { + "lat": 19.34361, + "lon": -98.97472, + "name": "Emiliano Zapata" + } + ], + "question": "Which location is the geographic outlier among: Thulamahashi, Goba, Mandera, Tamale, Emiliano Zapata?", + "ground_truth": { + "answer": "Emiliano Zapata", + "outlier_distance_km": 11112.0, + "second_furthest_km": 4359.3, + "clarity_ratio": 2.55, + "median_distance_km": 4353.1, + "distances_to_centroid": { + "Thulamahashi": 4359.3, + "Goba": 4158.6, + "Mandera": 4353.1, + "Tamale": 809.7, + "Emiliano Zapata": 11112.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thulamahashi: (-24.72°, 31.20°)", + " Goba: (7.02°, 39.98°)", + " Mandera: (3.94°, 41.86°)", + " Tamale: (9.40°, -0.84°)", + " Emiliano Zapata: (19.34°, -98.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Emiliano Zapata: 11112.0 km from centroid", + " Thulamahashi: 4359.3 km from centroid", + " Mandera: 4353.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Emiliano Zapata", + "FINAL ANSWER: Emiliano Zapata" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.41371, + "lon": 9.5899, + "name": "Garbsen" + }, + { + "lat": 52.0825, + "lon": 4.75, + "name": "Bodegraven" + }, + { + "lat": 52.46106, + "lon": 13.52108, + "name": "Oberschöneweide" + }, + { + "lat": 47.54612, + "lon": 9.68431, + "name": "Lindau" + }, + { + "lat": 42.49999, + "lon": -96.40031, + "name": "Sioux City" + } + ], + "question": "Which location is the geographic outlier among: Garbsen, Bodegraven, Oberschöneweide, Lindau, Sioux City?", + "ground_truth": { + "answer": "Sioux City", + "outlier_distance_km": 6237.1, + "second_furthest_km": 1795.2, + "clarity_ratio": 3.47, + "median_distance_km": 1589.6, + "distances_to_centroid": { + "Garbsen": 1528.7, + "Bodegraven": 1197.2, + "Oberschöneweide": 1795.2, + "Lindau": 1589.6, + "Sioux City": 6237.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Garbsen: (52.41°, 9.59°)", + " Bodegraven: (52.08°, 4.75°)", + " Oberschöneweide: (52.46°, 13.52°)", + " Lindau: (47.55°, 9.68°)", + " Sioux City: (42.50°, -96.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sioux City: 6237.1 km from centroid", + " Oberschöneweide: 1795.2 km from centroid", + " Lindau: 1589.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sioux City", + "FINAL ANSWER: Sioux City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.45232, + "lon": -71.137, + "name": "Winchester" + }, + { + "lat": 42.24177, + "lon": -71.16616, + "name": "Dedham" + }, + { + "lat": 40.60843, + "lon": -75.49018, + "name": "Allentown" + }, + { + "lat": 34.09529, + "lon": -118.12701, + "name": "Alhambra" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + } + ], + "question": "Which location is the geographic outlier among: Winchester, Dedham, Allentown, Alhambra, Levin?", + "ground_truth": { + "answer": "Levin", + "outlier_distance_km": 16848.0, + "second_furthest_km": 8208.2, + "clarity_ratio": 2.05, + "median_distance_km": 4434.7, + "distances_to_centroid": { + "Winchester": 4135.2, + "Dedham": 4130.4, + "Allentown": 4434.7, + "Alhambra": 8208.2, + "Levin": 16848.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Winchester: (42.45°, -71.14°)", + " Dedham: (42.24°, -71.17°)", + " Allentown: (40.61°, -75.49°)", + " Alhambra: (34.10°, -118.13°)", + " Levin: (-40.63°, 175.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Levin: 16848.0 km from centroid", + " Alhambra: 8208.2 km from centroid", + " Allentown: 4434.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Levin", + "FINAL ANSWER: Levin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -16.3775, + "lon": -39.58028, + "name": "Eunápolis" + } + ], + "question": "Which location is the geographic outlier among: Reservoir, Avondale, Maroubra, Karori, Eunápolis?", + "ground_truth": { + "answer": "Eunápolis", + "outlier_distance_km": 14133.0, + "second_furthest_km": 4820.9, + "clarity_ratio": 2.93, + "median_distance_km": 4744.2, + "distances_to_centroid": { + "Reservoir": 2203.6, + "Avondale": 4820.9, + "Maroubra": 2771.1, + "Karori": 4744.2, + "Eunápolis": 14133.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reservoir: (-37.72°, 145.00°)", + " Avondale: (-36.88°, 174.70°)", + " Maroubra: (-33.95°, 151.23°)", + " Karori: (-41.28°, 174.74°)", + " Eunápolis: (-16.38°, -39.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eunápolis: 14133.0 km from centroid", + " Avondale: 4820.9 km from centroid", + " Karori: 4744.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eunápolis", + "FINAL ANSWER: Eunápolis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.41222, + "lon": -2.20056, + "name": "Neston" + }, + { + "lat": 45.4981, + "lon": 9.42043, + "name": "Melzo" + }, + { + "lat": 48.70354, + "lon": 9.65209, + "name": "Göppingen" + }, + { + "lat": 50.85162, + "lon": -1.17929, + "name": "Fareham" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + } + ], + "question": "Which location is the geographic outlier among: Neston, Melzo, Göppingen, Fareham, Chatswood?", + "ground_truth": { + "answer": "Chatswood", + "outlier_distance_km": 14317.0, + "second_furthest_km": 3558.2, + "clarity_ratio": 4.02, + "median_distance_km": 3468.5, + "distances_to_centroid": { + "Neston": 3558.2, + "Melzo": 2506.4, + "Göppingen": 2670.6, + "Fareham": 3468.5, + "Chatswood": 14317.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Neston: (51.41°, -2.20°)", + " Melzo: (45.50°, 9.42°)", + " Göppingen: (48.70°, 9.65°)", + " Fareham: (50.85°, -1.18°)", + " Chatswood: (-33.80°, 151.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chatswood: 14317.0 km from centroid", + " Neston: 3558.2 km from centroid", + " Fareham: 3468.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chatswood", + "FINAL ANSWER: Chatswood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.1665, + "lon": -75.52001, + "name": "Neira" + }, + { + "lat": -33.02457, + "lon": -71.55183, + "name": "Viña del Mar" + }, + { + "lat": -13.74389, + "lon": -39.48667, + "name": "Gandu" + }, + { + "lat": -39.64355, + "lon": -72.33269, + "name": "Panguipulli" + }, + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + } + ], + "question": "Which location is the geographic outlier among: Neira, Viña del Mar, Gandu, Panguipulli, Frankston East?", + "ground_truth": { + "answer": "Frankston East", + "outlier_distance_km": 13005.0, + "second_furthest_km": 6564.0, + "clarity_ratio": 1.98, + "median_distance_km": 4934.3, + "distances_to_centroid": { + "Neira": 6564.0, + "Viña del Mar": 4834.9, + "Gandu": 2087.8, + "Panguipulli": 4934.3, + "Frankston East": 13005.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Neira: (5.17°, -75.52°)", + " Viña del Mar: (-33.02°, -71.55°)", + " Gandu: (-13.74°, -39.49°)", + " Panguipulli: (-39.64°, -72.33°)", + " Frankston East: (-38.13°, 145.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Frankston East: 13005.0 km from centroid", + " Neira: 6564.0 km from centroid", + " Panguipulli: 4934.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Frankston East", + "FINAL ANSWER: Frankston East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.59811, + "lon": 131.1883, + "name": "Nakatsu" + }, + { + "lat": 3.5078, + "lon": 98.6839, + "name": "Deli Tua" + }, + { + "lat": 35.73264, + "lon": 139.76961, + "name": "Nishinippori" + }, + { + "lat": 44.02127, + "lon": 144.26971, + "name": "Abashiri" + }, + { + "lat": 52.46833, + "lon": 4.74306, + "name": "Assendelft" + } + ], + "question": "Which location is the geographic outlier among: Nakatsu, Deli Tua, Nishinippori, Abashiri, Assendelft?", + "ground_truth": { + "answer": "Assendelft", + "outlier_distance_km": 7641.6, + "second_furthest_km": 3642.0, + "clarity_ratio": 2.1, + "median_distance_km": 3415.9, + "distances_to_centroid": { + "Nakatsu": 2531.7, + "Deli Tua": 3415.9, + "Nishinippori": 3278.7, + "Abashiri": 3642.0, + "Assendelft": 7641.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nakatsu: (33.60°, 131.19°)", + " Deli Tua: (3.51°, 98.68°)", + " Nishinippori: (35.73°, 139.77°)", + " Abashiri: (44.02°, 144.27°)", + " Assendelft: (52.47°, 4.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Assendelft: 7641.6 km from centroid", + " Abashiri: 3642.0 km from centroid", + " Deli Tua: 3415.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Assendelft", + "FINAL ANSWER: Assendelft" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75, + "lon": 144.96667, + "name": "Coburg" + }, + { + "lat": -41.31667, + "lon": 173.23333, + "name": "Stoke" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + }, + { + "lat": 30.77967, + "lon": 108.45506, + "name": "Wuqiao" + } + ], + "question": "Which location is the geographic outlier among: Coburg, Stoke, Granville, Hamilton, Wuqiao?", + "ground_truth": { + "answer": "Wuqiao", + "outlier_distance_km": 7564.6, + "second_furthest_km": 2848.8, + "clarity_ratio": 2.66, + "median_distance_km": 2798.1, + "distances_to_centroid": { + "Coburg": 1621.3, + "Stoke": 2848.8, + "Granville": 1097.0, + "Hamilton": 2798.1, + "Wuqiao": 7564.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coburg: (-37.75°, 144.97°)", + " Stoke: (-41.32°, 173.23°)", + " Granville: (-33.84°, 151.01°)", + " Hamilton: (-37.78°, 175.28°)", + " Wuqiao: (30.78°, 108.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wuqiao: 7564.6 km from centroid", + " Stoke: 2848.8 km from centroid", + " Hamilton: 2798.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wuqiao", + "FINAL ANSWER: Wuqiao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.15, + "lon": 39.35, + "name": "Huruta" + }, + { + "lat": 8.456, + "lon": 36.35302, + "name": "Bedelē" + }, + { + "lat": 10.65, + "lon": 36.21667, + "name": "Dibate" + }, + { + "lat": 31.20176, + "lon": 29.91582, + "name": "Alexandria" + }, + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + } + ], + "question": "Which location is the geographic outlier among: Huruta, Bedelē, Dibate, Alexandria, Hornsby?", + "ground_truth": { + "answer": "Hornsby", + "outlier_distance_km": 10544.7, + "second_furthest_km": 4180.0, + "clarity_ratio": 2.52, + "median_distance_km": 2543.3, + "distances_to_centroid": { + "Huruta": 2154.2, + "Bedelē": 2485.5, + "Dibate": 2543.3, + "Alexandria": 4180.0, + "Hornsby": 10544.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huruta: (8.15°, 39.35°)", + " Bedelē: (8.46°, 36.35°)", + " Dibate: (10.65°, 36.22°)", + " Alexandria: (31.20°, 29.92°)", + " Hornsby: (-33.70°, 151.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hornsby: 10544.7 km from centroid", + " Alexandria: 4180.0 km from centroid", + " Dibate: 2543.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hornsby", + "FINAL ANSWER: Hornsby" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.39899, + "lon": 17.63726, + "name": "Manduria" + }, + { + "lat": 51.06314, + "lon": -0.32757, + "name": "Horsham" + }, + { + "lat": 46.09534, + "lon": 38.97691, + "name": "Kanevskaya" + }, + { + "lat": 59.15838, + "lon": 57.5705, + "name": "Aleksandrovsk" + }, + { + "lat": 41.18454, + "lon": -73.13317, + "name": "Stratford" + } + ], + "question": "Which location is the geographic outlier among: Manduria, Horsham, Kanevskaya, Aleksandrovsk, Stratford?", + "ground_truth": { + "answer": "Stratford", + "outlier_distance_km": 6196.9, + "second_furthest_km": 3427.3, + "clarity_ratio": 1.81, + "median_distance_km": 2335.6, + "distances_to_centroid": { + "Manduria": 1100.4, + "Horsham": 725.3, + "Kanevskaya": 2335.6, + "Aleksandrovsk": 3427.3, + "Stratford": 6196.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manduria: (40.40°, 17.64°)", + " Horsham: (51.06°, -0.33°)", + " Kanevskaya: (46.10°, 38.98°)", + " Aleksandrovsk: (59.16°, 57.57°)", + " Stratford: (41.18°, -73.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stratford: 6196.9 km from centroid", + " Aleksandrovsk: 3427.3 km from centroid", + " Kanevskaya: 2335.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stratford", + "FINAL ANSWER: Stratford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.80802, + "lon": 136.86441, + "name": "Kaminoma" + }, + { + "lat": 32.40732, + "lon": 104.52738, + "name": "Pingwu County" + }, + { + "lat": 10.69694, + "lon": 122.56444, + "name": "Iloilo" + }, + { + "lat": 34.5, + "lon": 116.75, + "name": "Liangzhai" + }, + { + "lat": 6.92471, + "lon": 37.65263, + "name": "Gununo" + } + ], + "question": "Which location is the geographic outlier among: Kaminoma, Pingwu County, Iloilo, Liangzhai, Gununo?", + "ground_truth": { + "answer": "Gununo", + "outlier_distance_km": 7261.9, + "second_furthest_km": 3420.4, + "clarity_ratio": 2.12, + "median_distance_km": 2478.4, + "distances_to_centroid": { + "Kaminoma": 3420.4, + "Pingwu County": 953.3, + "Iloilo": 2478.4, + "Liangzhai": 1731.8, + "Gununo": 7261.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kaminoma: (34.81°, 136.86°)", + " Pingwu County: (32.41°, 104.53°)", + " Iloilo: (10.70°, 122.56°)", + " Liangzhai: (34.50°, 116.75°)", + " Gununo: (6.92°, 37.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gununo: 7261.9 km from centroid", + " Kaminoma: 3420.4 km from centroid", + " Iloilo: 2478.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gununo", + "FINAL ANSWER: Gununo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": -23.69748, + "lon": 133.88362, + "name": "Alice Springs" + }, + { + "lat": 10.26858, + "lon": 13.26701, + "name": "Mubi" + } + ], + "question": "Which location is the geographic outlier among: Newcastle, Lincoln, Nerang, Alice Springs, Mubi?", + "ground_truth": { + "answer": "Mubi", + "outlier_distance_km": 12701.0, + "second_furthest_km": 4972.7, + "clarity_ratio": 2.55, + "median_distance_km": 2879.7, + "distances_to_centroid": { + "Newcastle": 2849.8, + "Lincoln": 4972.7, + "Nerang": 2879.7, + "Alice Springs": 885.6, + "Mubi": 12701.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newcastle: (-32.93°, 151.78°)", + " Lincoln: (-36.86°, 174.62°)", + " Nerang: (-27.99°, 153.34°)", + " Alice Springs: (-23.70°, 133.88°)", + " Mubi: (10.27°, 13.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mubi: 12701.0 km from centroid", + " Lincoln: 4972.7 km from centroid", + " Nerang: 2879.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mubi", + "FINAL ANSWER: Mubi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.25221, + "lon": 21.26902, + "name": "Sulejówek" + }, + { + "lat": 40.46438, + "lon": 17.24707, + "name": "Taranto" + }, + { + "lat": 44.07926, + "lon": 10.09789, + "name": "Carrara" + }, + { + "lat": 36.76419, + "lon": -2.61475, + "name": "Roquetas de Mar" + }, + { + "lat": 9.59111, + "lon": 123.12278, + "name": "Bais" + } + ], + "question": "Which location is the geographic outlier among: Sulejówek, Taranto, Carrara, Roquetas de Mar, Bais?", + "ground_truth": { + "answer": "Bais", + "outlier_distance_km": 9311.1, + "second_furthest_km": 3228.8, + "clarity_ratio": 2.88, + "median_distance_km": 2164.6, + "distances_to_centroid": { + "Sulejówek": 1996.3, + "Taranto": 1500.7, + "Carrara": 2164.6, + "Roquetas de Mar": 3228.8, + "Bais": 9311.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sulejówek: (52.25°, 21.27°)", + " Taranto: (40.46°, 17.25°)", + " Carrara: (44.08°, 10.10°)", + " Roquetas de Mar: (36.76°, -2.61°)", + " Bais: (9.59°, 123.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bais: 9311.1 km from centroid", + " Roquetas de Mar: 3228.8 km from centroid", + " Carrara: 2164.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bais", + "FINAL ANSWER: Bais" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.50222, + "lon": -48.71139, + "name": "Macatuba" + }, + { + "lat": -23.66389, + "lon": -46.53833, + "name": "Santo André" + }, + { + "lat": -3.56516, + "lon": -44.58018, + "name": "Miranda do Norte" + }, + { + "lat": -13.18222, + "lon": -39.425, + "name": "Laje" + }, + { + "lat": 14.58617, + "lon": 100.99758, + "name": "Kaeng Khoi" + } + ], + "question": "Which location is the geographic outlier among: Macatuba, Santo André, Miranda do Norte, Laje, Kaeng Khoi?", + "ground_truth": { + "answer": "Kaeng Khoi", + "outlier_distance_km": 13126.2, + "second_furthest_km": 3797.5, + "clarity_ratio": 3.46, + "median_distance_km": 3627.3, + "distances_to_centroid": { + "Macatuba": 3797.5, + "Santo André": 3627.3, + "Miranda do Norte": 3264.5, + "Laje": 2619.3, + "Kaeng Khoi": 13126.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macatuba: (-22.50°, -48.71°)", + " Santo André: (-23.66°, -46.54°)", + " Miranda do Norte: (-3.57°, -44.58°)", + " Laje: (-13.18°, -39.42°)", + " Kaeng Khoi: (14.59°, 101.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kaeng Khoi: 13126.2 km from centroid", + " Macatuba: 3797.5 km from centroid", + " Santo André: 3627.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kaeng Khoi", + "FINAL ANSWER: Kaeng Khoi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.71417, + "lon": -52.42222, + "name": "Bataguassu" + }, + { + "lat": -20.10194, + "lon": -42.4525, + "name": "Raul Soares" + }, + { + "lat": -3.66667, + "lon": -45.38, + "name": "Santa Inês" + }, + { + "lat": -22.28556, + "lon": -46.61222, + "name": "Jacutinga" + }, + { + "lat": 31.13259, + "lon": 30.64784, + "name": "Disūq" + } + ], + "question": "Which location is the geographic outlier among: Bataguassu, Raul Soares, Santa Inês, Jacutinga, Disūq?", + "ground_truth": { + "answer": "Disūq", + "outlier_distance_km": 7837.6, + "second_furthest_km": 2778.4, + "clarity_ratio": 2.82, + "median_distance_km": 2340.1, + "distances_to_centroid": { + "Bataguassu": 2778.4, + "Raul Soares": 1864.5, + "Santa Inês": 1616.4, + "Jacutinga": 2340.1, + "Disūq": 7837.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bataguassu: (-21.71°, -52.42°)", + " Raul Soares: (-20.10°, -42.45°)", + " Santa Inês: (-3.67°, -45.38°)", + " Jacutinga: (-22.29°, -46.61°)", + " Disūq: (31.13°, 30.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Disūq: 7837.6 km from centroid", + " Bataguassu: 2778.4 km from centroid", + " Jacutinga: 2340.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Disūq", + "FINAL ANSWER: Disūq" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.7565, + "lon": -103.44297, + "name": "Nuevo México" + }, + { + "lat": 35.68698, + "lon": -105.9378, + "name": "Santa Fe" + }, + { + "lat": 40.80427, + "lon": -74.01208, + "name": "North Bergen" + }, + { + "lat": 42.29732, + "lon": -71.43701, + "name": "Framingham Center" + }, + { + "lat": -15.32333, + "lon": -58.00361, + "name": "Lambari d'Oeste" + } + ], + "question": "Which location is the geographic outlier among: Nuevo México, Santa Fe, North Bergen, Framingham Center, Lambari d'Oeste?", + "ground_truth": { + "answer": "Lambari d'Oeste", + "outlier_distance_km": 5200.3, + "second_furthest_km": 2538.3, + "clarity_ratio": 2.05, + "median_distance_km": 2193.0, + "distances_to_centroid": { + "Nuevo México": 2185.3, + "Santa Fe": 2538.3, + "North Bergen": 1943.9, + "Framingham Center": 2193.0, + "Lambari d'Oeste": 5200.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nuevo México: (20.76°, -103.44°)", + " Santa Fe: (35.69°, -105.94°)", + " North Bergen: (40.80°, -74.01°)", + " Framingham Center: (42.30°, -71.44°)", + " Lambari d'Oeste: (-15.32°, -58.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lambari d'Oeste: 5200.3 km from centroid", + " Santa Fe: 2538.3 km from centroid", + " Framingham Center: 2193.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lambari d'Oeste", + "FINAL ANSWER: Lambari d'Oeste" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.39458, + "lon": 2.17946, + "name": "Fort Pienc" + }, + { + "lat": 47.1069, + "lon": 39.41486, + "name": "Azov" + }, + { + "lat": 55.9825, + "lon": 37.18139, + "name": "Zelenograd" + }, + { + "lat": 41.69993, + "lon": 2.84565, + "name": "Lloret de Mar" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + } + ], + "question": "Which location is the geographic outlier among: Fort Pienc, Azov, Zelenograd, Lloret de Mar, South Morang?", + "ground_truth": { + "answer": "South Morang", + "outlier_distance_km": 12763.7, + "second_furthest_km": 4068.4, + "clarity_ratio": 3.14, + "median_distance_km": 4016.1, + "distances_to_centroid": { + "Fort Pienc": 4068.4, + "Azov": 2001.1, + "Zelenograd": 2991.8, + "Lloret de Mar": 4016.1, + "South Morang": 12763.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fort Pienc: (41.39°, 2.18°)", + " Azov: (47.11°, 39.41°)", + " Zelenograd: (55.98°, 37.18°)", + " Lloret de Mar: (41.70°, 2.85°)", + " South Morang: (-37.65°, 145.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " South Morang: 12763.7 km from centroid", + " Fort Pienc: 4068.4 km from centroid", + " Lloret de Mar: 4016.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: South Morang", + "FINAL ANSWER: South Morang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.5842, + "lon": 45.7338, + "name": "Znamensk" + }, + { + "lat": 44.8546, + "lon": 38.3031, + "name": "Akhtyrskiy" + }, + { + "lat": 50.53439, + "lon": 36.68462, + "name": "Razumnoye" + }, + { + "lat": 48.75568, + "lon": 2.32241, + "name": "Fresnes" + }, + { + "lat": 20.14085, + "lon": -101.18251, + "name": "Uriangato" + } + ], + "question": "Which location is the geographic outlier among: Znamensk, Akhtyrskiy, Razumnoye, Fresnes, Uriangato?", + "ground_truth": { + "answer": "Uriangato", + "outlier_distance_km": 9704.5, + "second_furthest_km": 3246.0, + "clarity_ratio": 2.99, + "median_distance_km": 2718.9, + "distances_to_centroid": { + "Znamensk": 3246.0, + "Akhtyrskiy": 2718.9, + "Razumnoye": 2599.9, + "Fresnes": 705.5, + "Uriangato": 9704.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Znamensk: (48.58°, 45.73°)", + " Akhtyrskiy: (44.85°, 38.30°)", + " Razumnoye: (50.53°, 36.68°)", + " Fresnes: (48.76°, 2.32°)", + " Uriangato: (20.14°, -101.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uriangato: 9704.5 km from centroid", + " Znamensk: 3246.0 km from centroid", + " Akhtyrskiy: 2718.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uriangato", + "FINAL ANSWER: Uriangato" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.99004, + "lon": 2.25804, + "name": "Ermont" + }, + { + "lat": 42.39996, + "lon": -8.80698, + "name": "Sanxenxo" + }, + { + "lat": 40.43285, + "lon": -3.70113, + "name": "Trafalgar" + }, + { + "lat": 43.31083, + "lon": 3.47583, + "name": "Agde" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + } + ], + "question": "Which location is the geographic outlier among: Ermont, Sanxenxo, Trafalgar, Agde, Corio?", + "ground_truth": { + "answer": "Corio", + "outlier_distance_km": 14104.7, + "second_furthest_km": 3670.8, + "clarity_ratio": 3.84, + "median_distance_km": 3230.3, + "distances_to_centroid": { + "Ermont": 3230.3, + "Sanxenxo": 3670.8, + "Trafalgar": 3201.1, + "Agde": 2789.3, + "Corio": 14104.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ermont: (48.99°, 2.26°)", + " Sanxenxo: (42.40°, -8.81°)", + " Trafalgar: (40.43°, -3.70°)", + " Agde: (43.31°, 3.48°)", + " Corio: (-38.08°, 144.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Corio: 14104.7 km from centroid", + " Sanxenxo: 3670.8 km from centroid", + " Ermont: 3230.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Corio", + "FINAL ANSWER: Corio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.52611, + "lon": -49.94861, + "name": "Piraí do Sul" + }, + { + "lat": -10.24111, + "lon": -76.64556, + "name": "Yanacancha" + }, + { + "lat": -4.75639, + "lon": -42.57556, + "name": "José de Freitas" + }, + { + "lat": -9.53694, + "lon": -36.63361, + "name": "Igaci" + }, + { + "lat": 53.64904, + "lon": -1.78416, + "name": "Huddersfield" + } + ], + "question": "Which location is the geographic outlier among: Piraí do Sul, Yanacancha, José de Freitas, Igaci, Huddersfield?", + "ground_truth": { + "answer": "Huddersfield", + "outlier_distance_km": 6899.9, + "second_furthest_km": 4079.7, + "clarity_ratio": 1.69, + "median_distance_km": 2971.7, + "distances_to_centroid": { + "Piraí do Sul": 2971.7, + "Yanacancha": 4079.7, + "José de Freitas": 641.8, + "Igaci": 1282.1, + "Huddersfield": 6899.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piraí do Sul: (-24.53°, -49.95°)", + " Yanacancha: (-10.24°, -76.65°)", + " José de Freitas: (-4.76°, -42.58°)", + " Igaci: (-9.54°, -36.63°)", + " Huddersfield: (53.65°, -1.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huddersfield: 6899.9 km from centroid", + " Yanacancha: 4079.7 km from centroid", + " Piraí do Sul: 2971.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huddersfield", + "FINAL ANSWER: Huddersfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.84853, + "lon": 174.76349, + "name": "Auckland" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + }, + { + "lat": 29.63482, + "lon": 105.3911, + "name": "Wujia" + } + ], + "question": "Which location is the geographic outlier among: Auckland, Launceston, Mount Isa, Moonee Ponds, Wujia?", + "ground_truth": { + "answer": "Wujia", + "outlier_distance_km": 6919.4, + "second_furthest_km": 3560.2, + "clarity_ratio": 1.94, + "median_distance_km": 2270.0, + "distances_to_centroid": { + "Auckland": 3560.2, + "Launceston": 2270.0, + "Mount Isa": 305.2, + "Moonee Ponds": 1833.4, + "Wujia": 6919.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auckland: (-36.85°, 174.76°)", + " Launceston: (-41.44°, 147.13°)", + " Mount Isa: (-20.73°, 139.50°)", + " Moonee Ponds: (-37.77°, 144.92°)", + " Wujia: (29.63°, 105.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wujia: 6919.4 km from centroid", + " Auckland: 3560.2 km from centroid", + " Launceston: 2270.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wujia", + "FINAL ANSWER: Wujia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.52667, + "lon": -43.73278, + "name": "Mendes" + }, + { + "lat": 9.36238, + "lon": -73.60313, + "name": "Chiriguaná" + }, + { + "lat": -28.25504, + "lon": -58.62386, + "name": "Saladas" + }, + { + "lat": -22.31472, + "lon": -49.06056, + "name": "Bauru" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + } + ], + "question": "Which location is the geographic outlier among: Mendes, Chiriguaná, Saladas, Bauru, Armidale?", + "ground_truth": { + "answer": "Armidale", + "outlier_distance_km": 14336.5, + "second_furthest_km": 7180.4, + "clarity_ratio": 2.0, + "median_distance_km": 4575.0, + "distances_to_centroid": { + "Mendes": 3045.9, + "Chiriguaná": 7180.4, + "Saladas": 4575.0, + "Bauru": 3593.0, + "Armidale": 14336.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mendes: (-22.53°, -43.73°)", + " Chiriguaná: (9.36°, -73.60°)", + " Saladas: (-28.26°, -58.62°)", + " Bauru: (-22.31°, -49.06°)", + " Armidale: (-30.50°, 151.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Armidale: 14336.5 km from centroid", + " Chiriguaná: 7180.4 km from centroid", + " Saladas: 4575.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Armidale", + "FINAL ANSWER: Armidale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.90747, + "lon": 14.95634, + "name": "Bogatynia" + }, + { + "lat": 53.01532, + "lon": 39.14458, + "name": "Lebedyan’" + }, + { + "lat": 42.35055, + "lon": 13.39954, + "name": "L'Aquila" + }, + { + "lat": 48.8, + "lon": 9.01667, + "name": "Leonberg" + }, + { + "lat": 5.05127, + "lon": 7.9335, + "name": "Uyo" + } + ], + "question": "Which location is the geographic outlier among: Bogatynia, Lebedyan’, L'Aquila, Leonberg, Uyo?", + "ground_truth": { + "answer": "Uyo", + "outlier_distance_km": 3991.1, + "second_furthest_km": 2216.5, + "clarity_ratio": 1.8, + "median_distance_km": 1219.3, + "distances_to_centroid": { + "Bogatynia": 1219.3, + "Lebedyan’": 2216.5, + "L'Aquila": 390.1, + "Leonberg": 1157.5, + "Uyo": 3991.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bogatynia: (50.91°, 14.96°)", + " Lebedyan’: (53.02°, 39.14°)", + " L'Aquila: (42.35°, 13.40°)", + " Leonberg: (48.80°, 9.02°)", + " Uyo: (5.05°, 7.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uyo: 3991.1 km from centroid", + " Lebedyan’: 2216.5 km from centroid", + " Bogatynia: 1219.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uyo", + "FINAL ANSWER: Uyo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.35682, + "lon": -77.44165, + "name": "Chester" + }, + { + "lat": 27.29393, + "lon": -80.35033, + "name": "Port Saint Lucie" + }, + { + "lat": 41.76198, + "lon": -87.57783, + "name": "South Shore" + }, + { + "lat": 42.81259, + "lon": -70.87728, + "name": "Newburyport" + }, + { + "lat": 45.76758, + "lon": 4.8345, + "name": "Lyon 01" + } + ], + "question": "Which location is the geographic outlier among: Chester, Port Saint Lucie, South Shore, Newburyport, Lyon 01?", + "ground_truth": { + "answer": "Lyon 01", + "outlier_distance_km": 5400.7, + "second_furthest_km": 2156.6, + "clarity_ratio": 2.5, + "median_distance_km": 2119.9, + "distances_to_centroid": { + "Chester": 1336.0, + "Port Saint Lucie": 2119.9, + "South Shore": 2156.6, + "Newburyport": 837.0, + "Lyon 01": 5400.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chester: (37.36°, -77.44°)", + " Port Saint Lucie: (27.29°, -80.35°)", + " South Shore: (41.76°, -87.58°)", + " Newburyport: (42.81°, -70.88°)", + " Lyon 01: (45.77°, 4.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lyon 01: 5400.7 km from centroid", + " South Shore: 2156.6 km from centroid", + " Port Saint Lucie: 2119.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lyon 01", + "FINAL ANSWER: Lyon 01" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.36006, + "lon": 72.93106, + "name": "Vapi INA" + }, + { + "lat": 10.95356, + "lon": 75.9468, + "name": "Ponmundam" + }, + { + "lat": 21.53889, + "lon": 71.57737, + "name": "Gariadhar" + }, + { + "lat": 21.73359, + "lon": 70.45004, + "name": "Dhoraji" + }, + { + "lat": 6.88658, + "lon": 46.21508, + "name": "Waal" + } + ], + "question": "Which location is the geographic outlier among: Vapi INA, Ponmundam, Gariadhar, Dhoraji, Waal?", + "ground_truth": { + "answer": "Waal", + "outlier_distance_km": 2532.9, + "second_furthest_km": 1095.5, + "clarity_ratio": 2.31, + "median_distance_km": 736.2, + "distances_to_centroid": { + "Vapi INA": 736.2, + "Ponmundam": 1095.5, + "Gariadhar": 728.5, + "Dhoraji": 683.3, + "Waal": 2532.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vapi INA: (20.36°, 72.93°)", + " Ponmundam: (10.95°, 75.95°)", + " Gariadhar: (21.54°, 71.58°)", + " Dhoraji: (21.73°, 70.45°)", + " Waal: (6.89°, 46.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Waal: 2532.9 km from centroid", + " Ponmundam: 1095.5 km from centroid", + " Vapi INA: 736.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Waal", + "FINAL ANSWER: Waal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.25612, + "lon": 72.17928, + "name": "Deesa" + }, + { + "lat": 33.3213, + "lon": 130.94098, + "name": "Hita" + }, + { + "lat": 28.72249, + "lon": 78.28436, + "name": "Hasanpur" + }, + { + "lat": 42.99167, + "lon": 143.20028, + "name": "Otofuke" + }, + { + "lat": -27.78324, + "lon": 24.68768, + "name": "Pampierstad" + } + ], + "question": "Which location is the geographic outlier among: Deesa, Hita, Hasanpur, Otofuke, Pampierstad?", + "ground_truth": { + "answer": "Pampierstad", + "outlier_distance_km": 8811.1, + "second_furthest_km": 5531.6, + "clarity_ratio": 1.59, + "median_distance_km": 4294.2, + "distances_to_centroid": { + "Deesa": 1869.9, + "Hita": 4294.2, + "Hasanpur": 1497.7, + "Otofuke": 5531.6, + "Pampierstad": 8811.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deesa: (24.26°, 72.18°)", + " Hita: (33.32°, 130.94°)", + " Hasanpur: (28.72°, 78.28°)", + " Otofuke: (42.99°, 143.20°)", + " Pampierstad: (-27.78°, 24.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pampierstad: 8811.1 km from centroid", + " Otofuke: 5531.6 km from centroid", + " Hita: 4294.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pampierstad", + "FINAL ANSWER: Pampierstad" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.48417, + "lon": -51.99056, + "name": "Palmas" + }, + { + "lat": -6.60667, + "lon": -39.06222, + "name": "Cedro" + }, + { + "lat": -13.54232, + "lon": -43.57968, + "name": "Serra do Ramalho" + }, + { + "lat": -27.77333, + "lon": -54.24, + "name": "Três de Maio" + }, + { + "lat": 2.3829, + "lon": 102.3311, + "name": "Kampung Machap Baru" + } + ], + "question": "Which location is the geographic outlier among: Palmas, Cedro, Serra do Ramalho, Três de Maio, Kampung Machap Baru?", + "ground_truth": { + "answer": "Kampung Machap Baru", + "outlier_distance_km": 13262.2, + "second_furthest_km": 4089.6, + "clarity_ratio": 3.24, + "median_distance_km": 3839.6, + "distances_to_centroid": { + "Palmas": 3839.6, + "Cedro": 2529.2, + "Serra do Ramalho": 2834.9, + "Três de Maio": 4089.6, + "Kampung Machap Baru": 13262.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palmas: (-26.48°, -51.99°)", + " Cedro: (-6.61°, -39.06°)", + " Serra do Ramalho: (-13.54°, -43.58°)", + " Três de Maio: (-27.77°, -54.24°)", + " Kampung Machap Baru: (2.38°, 102.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kampung Machap Baru: 13262.2 km from centroid", + " Três de Maio: 4089.6 km from centroid", + " Palmas: 3839.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kampung Machap Baru", + "FINAL ANSWER: Kampung Machap Baru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.6241, + "lon": -90.7512, + "name": "Bayou Cane" + }, + { + "lat": 40.57538, + "lon": -74.32237, + "name": "Iselin" + }, + { + "lat": 38.88101, + "lon": -77.10428, + "name": "Arlington" + }, + { + "lat": 32.95373, + "lon": -96.89028, + "name": "Carrollton" + }, + { + "lat": 53.32498, + "lon": -3.83148, + "name": "Llandudno" + } + ], + "question": "Which location is the geographic outlier among: Bayou Cane, Iselin, Arlington, Carrollton, Llandudno?", + "ground_truth": { + "answer": "Llandudno", + "outlier_distance_km": 5037.7, + "second_furthest_km": 2623.8, + "clarity_ratio": 1.92, + "median_distance_km": 2282.0, + "distances_to_centroid": { + "Bayou Cane": 2282.0, + "Iselin": 518.0, + "Arlington": 736.9, + "Carrollton": 2623.8, + "Llandudno": 5037.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bayou Cane: (29.62°, -90.75°)", + " Iselin: (40.58°, -74.32°)", + " Arlington: (38.88°, -77.10°)", + " Carrollton: (32.95°, -96.89°)", + " Llandudno: (53.32°, -3.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Llandudno: 5037.7 km from centroid", + " Carrollton: 2623.8 km from centroid", + " Bayou Cane: 2282.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Llandudno", + "FINAL ANSWER: Llandudno" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.52278, + "lon": -46.18833, + "name": "Mogi das Cruzes" + }, + { + "lat": -14.52472, + "lon": -49.14083, + "name": "Uruaçu" + }, + { + "lat": -23.43088, + "lon": -46.79295, + "name": "Anhanguera" + }, + { + "lat": -23.60333, + "lon": -47.02639, + "name": "Vargem Grande Paulista" + }, + { + "lat": 36.96655, + "lon": -2.20595, + "name": "Níjar" + } + ], + "question": "Which location is the geographic outlier among: Mogi das Cruzes, Uruaçu, Anhanguera, Vargem Grande Paulista, Níjar?", + "ground_truth": { + "answer": "Níjar", + "outlier_distance_km": 6401.6, + "second_furthest_km": 1811.4, + "clarity_ratio": 3.53, + "median_distance_km": 1782.5, + "distances_to_centroid": { + "Mogi das Cruzes": 1759.6, + "Uruaçu": 1301.1, + "Anhanguera": 1782.5, + "Vargem Grande Paulista": 1811.4, + "Níjar": 6401.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mogi das Cruzes: (-23.52°, -46.19°)", + " Uruaçu: (-14.52°, -49.14°)", + " Anhanguera: (-23.43°, -46.79°)", + " Vargem Grande Paulista: (-23.60°, -47.03°)", + " Níjar: (36.97°, -2.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Níjar: 6401.6 km from centroid", + " Vargem Grande Paulista: 1811.4 km from centroid", + " Anhanguera: 1782.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Níjar", + "FINAL ANSWER: Níjar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.48329, + "lon": 44.13781, + "name": "Terek" + }, + { + "lat": 51.6503, + "lon": 11.51146, + "name": "Hettstedt" + }, + { + "lat": 51.05224, + "lon": 8.39227, + "name": "Bad Berleburg" + }, + { + "lat": 51.21898, + "lon": 22.69621, + "name": "Świdnik" + }, + { + "lat": -29.20932, + "lon": 26.83898, + "name": "Thaba Nchu" + } + ], + "question": "Which location is the geographic outlier among: Terek, Hettstedt, Bad Berleburg, Świdnik, Thaba Nchu?", + "ground_truth": { + "answer": "Thaba Nchu", + "outlier_distance_km": 7001.9, + "second_furthest_km": 2257.0, + "clarity_ratio": 3.1, + "median_distance_km": 2196.6, + "distances_to_centroid": { + "Terek": 2151.0, + "Hettstedt": 2196.6, + "Bad Berleburg": 2257.0, + "Świdnik": 1954.8, + "Thaba Nchu": 7001.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Terek: (43.48°, 44.14°)", + " Hettstedt: (51.65°, 11.51°)", + " Bad Berleburg: (51.05°, 8.39°)", + " Świdnik: (51.22°, 22.70°)", + " Thaba Nchu: (-29.21°, 26.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thaba Nchu: 7001.9 km from centroid", + " Bad Berleburg: 2257.0 km from centroid", + " Hettstedt: 2196.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thaba Nchu", + "FINAL ANSWER: Thaba Nchu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + }, + { + "lat": 49.00158, + "lon": 2.09694, + "name": "Conflans-Sainte-Honorine" + } + ], + "question": "Which location is the geographic outlier among: Willetton, Coorparoo, Ashfield, Springfield Lakes, Conflans-Sainte-Honorine?", + "ground_truth": { + "answer": "Conflans-Sainte-Honorine", + "outlier_distance_km": 12877.6, + "second_furthest_km": 4221.2, + "clarity_ratio": 3.05, + "median_distance_km": 4188.3, + "distances_to_centroid": { + "Willetton": 1962.6, + "Coorparoo": 4188.3, + "Ashfield": 4221.2, + "Springfield Lakes": 4179.6, + "Conflans-Sainte-Honorine": 12877.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Willetton: (-32.05°, 115.89°)", + " Coorparoo: (-27.49°, 153.06°)", + " Ashfield: (-33.89°, 151.12°)", + " Springfield Lakes: (-27.67°, 152.92°)", + " Conflans-Sainte-Honorine: (49.00°, 2.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Conflans-Sainte-Honorine: 12877.6 km from centroid", + " Ashfield: 4221.2 km from centroid", + " Coorparoo: 4188.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Conflans-Sainte-Honorine", + "FINAL ANSWER: Conflans-Sainte-Honorine" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.2509, + "lon": 10.41409, + "name": "Lüneburg" + }, + { + "lat": 51.83843, + "lon": 8.03093, + "name": "Ennigerloh" + }, + { + "lat": 51.62355, + "lon": 12.32395, + "name": "Bitterfeld-Wolfen" + }, + { + "lat": 52.7025, + "lon": 21.08276, + "name": "Pułtusk" + }, + { + "lat": 9.61524, + "lon": 6.54776, + "name": "Minna" + } + ], + "question": "Which location is the geographic outlier among: Lüneburg, Ennigerloh, Bitterfeld-Wolfen, Pułtusk, Minna?", + "ground_truth": { + "answer": "Minna", + "outlier_distance_km": 3834.1, + "second_furthest_km": 1207.5, + "clarity_ratio": 3.18, + "median_distance_km": 1054.3, + "distances_to_centroid": { + "Lüneburg": 1054.3, + "Ennigerloh": 933.5, + "Bitterfeld-Wolfen": 870.6, + "Pułtusk": 1207.5, + "Minna": 3834.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lüneburg: (53.25°, 10.41°)", + " Ennigerloh: (51.84°, 8.03°)", + " Bitterfeld-Wolfen: (51.62°, 12.32°)", + " Pułtusk: (52.70°, 21.08°)", + " Minna: (9.62°, 6.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Minna: 3834.1 km from centroid", + " Pułtusk: 1207.5 km from centroid", + " Lüneburg: 1054.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Minna", + "FINAL ANSWER: Minna" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": -25.095, + "lon": -50.16194, + "name": "Ponta Grossa" + } + ], + "question": "Which location is the geographic outlier among: Saint Albans, Melbourne City Centre, Blacktown, Palm Beach, Ponta Grossa?", + "ground_truth": { + "answer": "Ponta Grossa", + "outlier_distance_km": 13232.9, + "second_furthest_km": 4284.7, + "clarity_ratio": 3.09, + "median_distance_km": 3896.8, + "distances_to_centroid": { + "Saint Albans": 3304.9, + "Melbourne City Centre": 3319.4, + "Blacktown": 3896.8, + "Palm Beach": 4284.7, + "Ponta Grossa": 13232.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Albans: (-37.73°, 144.80°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Blacktown: (-33.77°, 150.92°)", + " Palm Beach: (-28.12°, 153.47°)", + " Ponta Grossa: (-25.09°, -50.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ponta Grossa: 13232.9 km from centroid", + " Palm Beach: 4284.7 km from centroid", + " Blacktown: 3896.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ponta Grossa", + "FINAL ANSWER: Ponta Grossa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.25444, + "lon": -75.34389, + "name": "Arjona" + }, + { + "lat": -5.12056, + "lon": -60.37972, + "name": "Novo Aripuanã" + }, + { + "lat": -13.54232, + "lon": -43.57968, + "name": "Serra do Ramalho" + }, + { + "lat": -17.70306, + "lon": -40.76639, + "name": "Carlos Chagas" + }, + { + "lat": 28.70146, + "lon": 76.57708, + "name": "Beri Khās" + } + ], + "question": "Which location is the geographic outlier among: Arjona, Novo Aripuanã, Serra do Ramalho, Carlos Chagas, Beri Khās?", + "ground_truth": { + "answer": "Beri Khās", + "outlier_distance_km": 11464.8, + "second_furthest_km": 5268.5, + "clarity_ratio": 2.18, + "median_distance_km": 3573.9, + "distances_to_centroid": { + "Arjona": 5268.5, + "Novo Aripuanã": 3573.9, + "Serra do Ramalho": 2265.6, + "Carlos Chagas": 2418.6, + "Beri Khās": 11464.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arjona: (10.25°, -75.34°)", + " Novo Aripuanã: (-5.12°, -60.38°)", + " Serra do Ramalho: (-13.54°, -43.58°)", + " Carlos Chagas: (-17.70°, -40.77°)", + " Beri Khās: (28.70°, 76.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Beri Khās: 11464.8 km from centroid", + " Arjona: 5268.5 km from centroid", + " Novo Aripuanã: 3573.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Beri Khās", + "FINAL ANSWER: Beri Khās" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.94167, + "lon": 83.56111, + "name": "Mau" + }, + { + "lat": 5.90702, + "lon": 116.10146, + "name": "Donggongon" + }, + { + "lat": 49.17405, + "lon": 125.21967, + "name": "Nenjiang" + }, + { + "lat": 34.53333, + "lon": 135.95, + "name": "Haibara-akanedai" + }, + { + "lat": 10.42949, + "lon": 3.81495, + "name": "Babana" + } + ], + "question": "Which location is the geographic outlier among: Mau, Donggongon, Nenjiang, Haibara-akanedai, Babana?", + "ground_truth": { + "answer": "Babana", + "outlier_distance_km": 9428.1, + "second_furthest_km": 4242.9, + "clarity_ratio": 2.22, + "median_distance_km": 3857.5, + "distances_to_centroid": { + "Mau": 943.1, + "Donggongon": 3268.7, + "Nenjiang": 3857.5, + "Haibara-akanedai": 4242.9, + "Babana": 9428.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mau: (25.94°, 83.56°)", + " Donggongon: (5.91°, 116.10°)", + " Nenjiang: (49.17°, 125.22°)", + " Haibara-akanedai: (34.53°, 135.95°)", + " Babana: (10.43°, 3.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Babana: 9428.1 km from centroid", + " Haibara-akanedai: 4242.9 km from centroid", + " Nenjiang: 3857.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Babana", + "FINAL ANSWER: Babana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.7511, + "lon": 151.28886, + "name": "Dee Why" + }, + { + "lat": -33.79068, + "lon": 150.6693, + "name": "Glenmore Park" + }, + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": 48.86158, + "lon": 9.18569, + "name": "Kornwestheim" + } + ], + "question": "Which location is the geographic outlier among: Dee Why, Glenmore Park, Traralgon, Greystanes, Kornwestheim?", + "ground_truth": { + "answer": "Kornwestheim", + "outlier_distance_km": 13154.7, + "second_furthest_km": 3408.7, + "clarity_ratio": 3.86, + "median_distance_km": 3382.9, + "distances_to_centroid": { + "Dee Why": 3408.7, + "Glenmore Park": 3358.0, + "Traralgon": 3279.7, + "Greystanes": 3382.9, + "Kornwestheim": 13154.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dee Why: (-33.75°, 151.29°)", + " Glenmore Park: (-33.79°, 150.67°)", + " Traralgon: (-38.20°, 146.54°)", + " Greystanes: (-33.82°, 150.95°)", + " Kornwestheim: (48.86°, 9.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kornwestheim: 13154.7 km from centroid", + " Dee Why: 3408.7 km from centroid", + " Greystanes: 3382.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kornwestheim", + "FINAL ANSWER: Kornwestheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.71524, + "lon": 31.2592, + "name": "Mīt Ghamr" + }, + { + "lat": 8.21896, + "lon": 5.50757, + "name": "Egbe" + }, + { + "lat": 1.01572, + "lon": 35.00622, + "name": "Kitale" + }, + { + "lat": 31.3073, + "lon": 30.2981, + "name": "Idkū" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + } + ], + "question": "Which location is the geographic outlier among: Mīt Ghamr, Egbe, Kitale, Idkū, Perth?", + "ground_truth": { + "answer": "Perth", + "outlier_distance_km": 8831.7, + "second_furthest_km": 4191.2, + "clarity_ratio": 2.11, + "median_distance_km": 2949.0, + "distances_to_centroid": { + "Mīt Ghamr": 2846.2, + "Egbe": 4191.2, + "Kitale": 1217.8, + "Idkū": 2949.0, + "Perth": 8831.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mīt Ghamr: (30.72°, 31.26°)", + " Egbe: (8.22°, 5.51°)", + " Kitale: (1.02°, 35.01°)", + " Idkū: (31.31°, 30.30°)", + " Perth: (-31.95°, 115.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perth: 8831.7 km from centroid", + " Egbe: 4191.2 km from centroid", + " Idkū: 2949.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perth", + "FINAL ANSWER: Perth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.8045, + "lon": 135.76681, + "name": "Kyōtanabe" + }, + { + "lat": 22.89396, + "lon": 88.41521, + "name": "Naihāti" + }, + { + "lat": 14.00774, + "lon": 77.60846, + "name": "Somandepalle" + }, + { + "lat": 10.1664, + "lon": 76.20179, + "name": "Vadakakarai" + }, + { + "lat": -37.90232, + "lon": 145.01734, + "name": "Brighton East" + } + ], + "question": "Which location is the geographic outlier among: Kyōtanabe, Naihāti, Somandepalle, Vadakakarai, Brighton East?", + "ground_truth": { + "answer": "Brighton East", + "outlier_distance_km": 6673.3, + "second_furthest_km": 4291.2, + "clarity_ratio": 1.56, + "median_distance_km": 3117.6, + "distances_to_centroid": { + "Kyōtanabe": 4291.2, + "Naihāti": 2331.5, + "Somandepalle": 2996.7, + "Vadakakarai": 3117.6, + "Brighton East": 6673.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kyōtanabe: (34.80°, 135.77°)", + " Naihāti: (22.89°, 88.42°)", + " Somandepalle: (14.01°, 77.61°)", + " Vadakakarai: (10.17°, 76.20°)", + " Brighton East: (-37.90°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brighton East: 6673.3 km from centroid", + " Kyōtanabe: 4291.2 km from centroid", + " Vadakakarai: 3117.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brighton East", + "FINAL ANSWER: Brighton East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.83615, + "lon": -87.59001, + "name": "Henderson" + }, + { + "lat": 40.63371, + "lon": -74.40737, + "name": "Plainfield" + }, + { + "lat": 34.48888, + "lon": -118.62287, + "name": "Castaic" + }, + { + "lat": 29.55718, + "lon": -95.80856, + "name": "Rosenberg" + }, + { + "lat": 32.06167, + "lon": 118.77778, + "name": "Nanjing" + } + ], + "question": "Which location is the geographic outlier among: Henderson, Plainfield, Castaic, Rosenberg, Nanjing?", + "ground_truth": { + "answer": "Nanjing", + "outlier_distance_km": 12499.1, + "second_furthest_km": 6009.3, + "clarity_ratio": 2.08, + "median_distance_km": 4173.2, + "distances_to_centroid": { + "Henderson": 3224.6, + "Plainfield": 2101.8, + "Castaic": 6009.3, + "Rosenberg": 4173.2, + "Nanjing": 12499.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Henderson: (37.84°, -87.59°)", + " Plainfield: (40.63°, -74.41°)", + " Castaic: (34.49°, -118.62°)", + " Rosenberg: (29.56°, -95.81°)", + " Nanjing: (32.06°, 118.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nanjing: 12499.1 km from centroid", + " Castaic: 6009.3 km from centroid", + " Rosenberg: 4173.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nanjing", + "FINAL ANSWER: Nanjing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -37.77988, + "lon": 144.92276, + "name": "Ascot Vale" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": 7.55632, + "lon": 3.44107, + "name": "Orita-Eruwa" + } + ], + "question": "Which location is the geographic outlier among: Carlton, Ascot Vale, Greystanes, Yarraville, Orita-Eruwa?", + "ground_truth": { + "answer": "Orita-Eruwa", + "outlier_distance_km": 12792.4, + "second_furthest_km": 3212.6, + "clarity_ratio": 3.98, + "median_distance_km": 2748.3, + "distances_to_centroid": { + "Carlton": 2748.3, + "Ascot Vale": 2744.0, + "Greystanes": 3212.6, + "Yarraville": 2743.2, + "Orita-Eruwa": 12792.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlton: (-37.80°, 144.97°)", + " Ascot Vale: (-37.78°, 144.92°)", + " Greystanes: (-33.82°, 150.95°)", + " Yarraville: (-37.82°, 144.90°)", + " Orita-Eruwa: (7.56°, 3.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Orita-Eruwa: 12792.4 km from centroid", + " Greystanes: 3212.6 km from centroid", + " Carlton: 2748.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Orita-Eruwa", + "FINAL ANSWER: Orita-Eruwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -43.53333, + "lon": 172.63333, + "name": "Christchurch" + }, + { + "lat": -38.03333, + "lon": 145.3, + "name": "Narre Warren" + }, + { + "lat": -1.45583, + "lon": -48.50444, + "name": "Belém" + } + ], + "question": "Which location is the geographic outlier among: Caboolture, Greenvale, Christchurch, Narre Warren, Belém?", + "ground_truth": { + "answer": "Belém", + "outlier_distance_km": 16070.2, + "second_furthest_km": 5391.7, + "clarity_ratio": 2.98, + "median_distance_km": 3858.1, + "distances_to_centroid": { + "Caboolture": 3858.1, + "Greenvale": 3029.5, + "Christchurch": 5391.7, + "Narre Warren": 3073.4, + "Belém": 16070.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caboolture: (-27.08°, 152.95°)", + " Greenvale: (-37.63°, 144.87°)", + " Christchurch: (-43.53°, 172.63°)", + " Narre Warren: (-38.03°, 145.30°)", + " Belém: (-1.46°, -48.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Belém: 16070.2 km from centroid", + " Christchurch: 5391.7 km from centroid", + " Caboolture: 3858.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Belém", + "FINAL ANSWER: Belém" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.1913, + "lon": 78.75904, + "name": "Parāsia" + }, + { + "lat": 35.48778, + "lon": 119.34583, + "name": "Nanhu" + }, + { + "lat": 46.3223, + "lon": 129.56081, + "name": "Yilan" + }, + { + "lat": 35.24762, + "lon": 136.97229, + "name": "Kasugai" + }, + { + "lat": -37.2, + "lon": 174.95, + "name": "Pukekohe East" + } + ], + "question": "Which location is the geographic outlier among: Parāsia, Nanhu, Yilan, Kasugai, Pukekohe East?", + "ground_truth": { + "answer": "Pukekohe East", + "outlier_distance_km": 8079.9, + "second_furthest_km": 5074.4, + "clarity_ratio": 1.59, + "median_distance_km": 2885.2, + "distances_to_centroid": { + "Parāsia": 5074.4, + "Nanhu": 1874.0, + "Yilan": 2885.2, + "Kasugai": 1872.5, + "Pukekohe East": 8079.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Parāsia: (22.19°, 78.76°)", + " Nanhu: (35.49°, 119.35°)", + " Yilan: (46.32°, 129.56°)", + " Kasugai: (35.25°, 136.97°)", + " Pukekohe East: (-37.20°, 174.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pukekohe East: 8079.9 km from centroid", + " Parāsia: 5074.4 km from centroid", + " Yilan: 2885.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pukekohe East", + "FINAL ANSWER: Pukekohe East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.01667, + "lon": 39.63333, + "name": "Robīt" + }, + { + "lat": -29.01269, + "lon": 29.86619, + "name": "Estcourt" + }, + { + "lat": 7.87377, + "lon": 5.07691, + "name": "Ipoti" + }, + { + "lat": 7.32275, + "lon": 9.00108, + "name": "Gboko" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + } + ], + "question": "Which location is the geographic outlier among: Robīt, Estcourt, Ipoti, Gboko, Lalor?", + "ground_truth": { + "answer": "Lalor", + "outlier_distance_km": 10280.1, + "second_furthest_km": 4833.9, + "clarity_ratio": 2.13, + "median_distance_km": 4408.3, + "distances_to_centroid": { + "Robīt": 2313.9, + "Estcourt": 2875.2, + "Ipoti": 4833.9, + "Gboko": 4408.3, + "Lalor": 10280.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robīt: (12.02°, 39.63°)", + " Estcourt: (-29.01°, 29.87°)", + " Ipoti: (7.87°, 5.08°)", + " Gboko: (7.32°, 9.00°)", + " Lalor: (-37.67°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lalor: 10280.1 km from centroid", + " Ipoti: 4833.9 km from centroid", + " Gboko: 4408.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lalor", + "FINAL ANSWER: Lalor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.83375, + "lon": 8.40531, + "name": "Porto Torres" + }, + { + "lat": 53.54899, + "lon": -2.52464, + "name": "Westhoughton" + }, + { + "lat": 52.67631, + "lon": 13.27775, + "name": "Hohen Neuendorf" + }, + { + "lat": 48.16925, + "lon": 12.83139, + "name": "Burghausen" + }, + { + "lat": 42.90339, + "lon": -78.75475, + "name": "Cheektowaga" + } + ], + "question": "Which location is the geographic outlier among: Porto Torres, Westhoughton, Hohen Neuendorf, Burghausen, Cheektowaga?", + "ground_truth": { + "answer": "Cheektowaga", + "outlier_distance_km": 5273.0, + "second_furthest_km": 1698.9, + "clarity_ratio": 3.1, + "median_distance_km": 1649.2, + "distances_to_centroid": { + "Porto Torres": 1598.6, + "Westhoughton": 815.4, + "Hohen Neuendorf": 1698.9, + "Burghausen": 1649.2, + "Cheektowaga": 5273.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porto Torres: (40.83°, 8.41°)", + " Westhoughton: (53.55°, -2.52°)", + " Hohen Neuendorf: (52.68°, 13.28°)", + " Burghausen: (48.17°, 12.83°)", + " Cheektowaga: (42.90°, -78.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cheektowaga: 5273.0 km from centroid", + " Hohen Neuendorf: 1698.9 km from centroid", + " Burghausen: 1649.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cheektowaga", + "FINAL ANSWER: Cheektowaga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.26074, + "lon": 30.82545, + "name": "Redhill" + }, + { + "lat": -24.59165, + "lon": 27.41155, + "name": "Thabazimbi" + }, + { + "lat": 6.71897, + "lon": -1.61188, + "name": "New Tafo" + }, + { + "lat": -26.9033, + "lon": 27.45727, + "name": "Parys" + }, + { + "lat": 52.31667, + "lon": 8.33333, + "name": "Bad Essen" + } + ], + "question": "Which location is the geographic outlier among: Redhill, Thabazimbi, New Tafo, Parys, Bad Essen?", + "ground_truth": { + "answer": "Bad Essen", + "outlier_distance_km": 6306.7, + "second_furthest_km": 2828.1, + "clarity_ratio": 2.23, + "median_distance_km": 2746.3, + "distances_to_centroid": { + "Redhill": 2828.1, + "Thabazimbi": 2507.6, + "New Tafo": 2515.8, + "Parys": 2746.3, + "Bad Essen": 6306.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Redhill: (-26.26°, 30.83°)", + " Thabazimbi: (-24.59°, 27.41°)", + " New Tafo: (6.72°, -1.61°)", + " Parys: (-26.90°, 27.46°)", + " Bad Essen: (52.32°, 8.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bad Essen: 6306.7 km from centroid", + " Redhill: 2828.1 km from centroid", + " Parys: 2746.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bad Essen", + "FINAL ANSWER: Bad Essen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.5702, + "lon": -46.72628, + "name": "Butanta" + }, + { + "lat": -22.84278, + "lon": -45.25139, + "name": "Potim" + }, + { + "lat": -24.32083, + "lon": -47.63472, + "name": "Juquiá" + }, + { + "lat": -11.04833, + "lon": -45.19306, + "name": "Formosa do Rio Preto" + }, + { + "lat": 44.7133, + "lon": -93.42273, + "name": "Prior Lake" + } + ], + "question": "Which location is the geographic outlier among: Butanta, Potim, Juquiá, Formosa do Rio Preto, Prior Lake?", + "ground_truth": { + "answer": "Prior Lake", + "outlier_distance_km": 6917.6, + "second_furthest_km": 2064.4, + "clarity_ratio": 3.35, + "median_distance_km": 2044.2, + "distances_to_centroid": { + "Butanta": 2033.1, + "Potim": 2044.2, + "Juquiá": 2064.4, + "Formosa do Rio Preto": 1216.1, + "Prior Lake": 6917.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Butanta: (-23.57°, -46.73°)", + " Potim: (-22.84°, -45.25°)", + " Juquiá: (-24.32°, -47.63°)", + " Formosa do Rio Preto: (-11.05°, -45.19°)", + " Prior Lake: (44.71°, -93.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Prior Lake: 6917.6 km from centroid", + " Juquiá: 2064.4 km from centroid", + " Potim: 2044.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Prior Lake", + "FINAL ANSWER: Prior Lake" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.22097, + "lon": 18.56964, + "name": "Wieluń" + }, + { + "lat": 51.11303, + "lon": -0.18312, + "name": "Crawley" + }, + { + "lat": 51.02496, + "lon": 7.65599, + "name": "Bergneustadt" + }, + { + "lat": 50.72136, + "lon": 10.44386, + "name": "Schmalkalden" + }, + { + "lat": -41.05584, + "lon": 145.90375, + "name": "Burnie" + } + ], + "question": "Which location is the geographic outlier among: Wieluń, Crawley, Bergneustadt, Schmalkalden, Burnie?", + "ground_truth": { + "answer": "Burnie", + "outlier_distance_km": 13834.3, + "second_furthest_km": 3610.6, + "clarity_ratio": 3.83, + "median_distance_km": 3111.0, + "distances_to_centroid": { + "Wieluń": 2531.1, + "Crawley": 3610.6, + "Bergneustadt": 3111.0, + "Schmalkalden": 2926.9, + "Burnie": 13834.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wieluń: (51.22°, 18.57°)", + " Crawley: (51.11°, -0.18°)", + " Bergneustadt: (51.02°, 7.66°)", + " Schmalkalden: (50.72°, 10.44°)", + " Burnie: (-41.06°, 145.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Burnie: 13834.3 km from centroid", + " Crawley: 3610.6 km from centroid", + " Bergneustadt: 3111.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Burnie", + "FINAL ANSWER: Burnie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.46723, + "lon": -2.68166, + "name": "Haydock" + }, + { + "lat": 53.18463, + "lon": 18.60466, + "name": "Chełmża" + }, + { + "lat": 40.3818, + "lon": -3.77109, + "name": "Las Águilas" + }, + { + "lat": 50.15441, + "lon": -5.07113, + "name": "Falmouth" + }, + { + "lat": -37.69047, + "lon": 144.74172, + "name": "Hillside" + } + ], + "question": "Which location is the geographic outlier among: Haydock, Chełmża, Las Águilas, Falmouth, Hillside?", + "ground_truth": { + "answer": "Hillside", + "outlier_distance_km": 14110.2, + "second_furthest_km": 3556.1, + "clarity_ratio": 3.97, + "median_distance_km": 3547.8, + "distances_to_centroid": { + "Haydock": 3556.1, + "Chełmża": 2547.6, + "Las Águilas": 3184.7, + "Falmouth": 3547.8, + "Hillside": 14110.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Haydock: (53.47°, -2.68°)", + " Chełmża: (53.18°, 18.60°)", + " Las Águilas: (40.38°, -3.77°)", + " Falmouth: (50.15°, -5.07°)", + " Hillside: (-37.69°, 144.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hillside: 14110.2 km from centroid", + " Haydock: 3556.1 km from centroid", + " Falmouth: 3547.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hillside", + "FINAL ANSWER: Hillside" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.05192, + "lon": 136.66958, + "name": "Kuwana" + }, + { + "lat": 34.13333, + "lon": 118.43333, + "name": "Shaodian" + }, + { + "lat": 38.04139, + "lon": 114.47861, + "name": "Shijiazhuang" + }, + { + "lat": 19.98533, + "lon": 76.52046, + "name": "Lonar" + }, + { + "lat": 33.03699, + "lon": -117.29198, + "name": "Encinitas" + } + ], + "question": "Which location is the geographic outlier among: Kuwana, Shaodian, Shijiazhuang, Lonar, Encinitas?", + "ground_truth": { + "answer": "Encinitas", + "outlier_distance_km": 12770.7, + "second_furthest_km": 6435.7, + "clarity_ratio": 1.98, + "median_distance_km": 4857.2, + "distances_to_centroid": { + "Kuwana": 6435.7, + "Shaodian": 4857.2, + "Shijiazhuang": 4434.0, + "Lonar": 1716.8, + "Encinitas": 12770.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kuwana: (35.05°, 136.67°)", + " Shaodian: (34.13°, 118.43°)", + " Shijiazhuang: (38.04°, 114.48°)", + " Lonar: (19.99°, 76.52°)", + " Encinitas: (33.04°, -117.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Encinitas: 12770.7 km from centroid", + " Kuwana: 6435.7 km from centroid", + " Shaodian: 4857.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Encinitas", + "FINAL ANSWER: Encinitas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.3527, + "lon": 36.6699, + "name": "Ngong" + }, + { + "lat": 28.92095, + "lon": 30.85367, + "name": "Sumusţā al Waqf" + }, + { + "lat": 25.66477, + "lon": 32.63539, + "name": "Al Bayāḑīyah" + }, + { + "lat": -26.23656, + "lon": 28.36938, + "name": "Brakpan" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + } + ], + "question": "Which location is the geographic outlier among: Ngong, Sumusţā al Waqf, Al Bayāḑīyah, Brakpan, Maitland?", + "ground_truth": { + "answer": "Maitland", + "outlier_distance_km": 10456.2, + "second_furthest_km": 4283.3, + "clarity_ratio": 2.44, + "median_distance_km": 4065.1, + "distances_to_centroid": { + "Ngong": 2150.9, + "Sumusţā al Waqf": 4283.3, + "Al Bayāḑīyah": 3899.2, + "Brakpan": 4065.1, + "Maitland": 10456.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ngong: (-1.35°, 36.67°)", + " Sumusţā al Waqf: (28.92°, 30.85°)", + " Al Bayāḑīyah: (25.66°, 32.64°)", + " Brakpan: (-26.24°, 28.37°)", + " Maitland: (-32.73°, 151.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maitland: 10456.2 km from centroid", + " Sumusţā al Waqf: 4283.3 km from centroid", + " Brakpan: 4065.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maitland", + "FINAL ANSWER: Maitland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.61617, + "lon": -64.28991, + "name": "Santa Rosa" + }, + { + "lat": -20.10667, + "lon": -43.04889, + "name": "Alvinópolis" + }, + { + "lat": -2.69795, + "lon": -59.70172, + "name": "Rio Preto da Eva" + }, + { + "lat": -40.29313, + "lon": -73.08167, + "name": "La Unión" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + } + ], + "question": "Which location is the geographic outlier among: Santa Rosa, Alvinópolis, Rio Preto da Eva, La Unión, Carlton?", + "ground_truth": { + "answer": "Carlton", + "outlier_distance_km": 12564.6, + "second_furthest_km": 5123.1, + "clarity_ratio": 2.45, + "median_distance_km": 5104.7, + "distances_to_centroid": { + "Santa Rosa": 4342.4, + "Alvinópolis": 2572.8, + "Rio Preto da Eva": 5123.1, + "La Unión": 5104.7, + "Carlton": 12564.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Rosa: (-36.62°, -64.29°)", + " Alvinópolis: (-20.11°, -43.05°)", + " Rio Preto da Eva: (-2.70°, -59.70°)", + " La Unión: (-40.29°, -73.08°)", + " Carlton: (-37.80°, 144.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carlton: 12564.6 km from centroid", + " Rio Preto da Eva: 5123.1 km from centroid", + " La Unión: 5104.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carlton", + "FINAL ANSWER: Carlton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.42603, + "lon": -58.57962, + "name": "Tigre" + }, + { + "lat": -21.68528, + "lon": -51.0725, + "name": "Adamantina" + }, + { + "lat": -12.77778, + "lon": -38.91944, + "name": "Maragogipe" + }, + { + "lat": -10.6, + "lon": -38.38333, + "name": "Cícero Dantas" + }, + { + "lat": 40.44682, + "lon": -3.70347, + "name": "Cuatro Caminos" + } + ], + "question": "Which location is the geographic outlier among: Tigre, Adamantina, Maragogipe, Cícero Dantas, Cuatro Caminos?", + "ground_truth": { + "answer": "Cuatro Caminos", + "outlier_distance_km": 6420.5, + "second_furthest_km": 3624.1, + "clarity_ratio": 1.77, + "median_distance_km": 2074.9, + "distances_to_centroid": { + "Tigre": 3624.1, + "Adamantina": 2074.9, + "Maragogipe": 559.2, + "Cícero Dantas": 311.6, + "Cuatro Caminos": 6420.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tigre: (-34.43°, -58.58°)", + " Adamantina: (-21.69°, -51.07°)", + " Maragogipe: (-12.78°, -38.92°)", + " Cícero Dantas: (-10.60°, -38.38°)", + " Cuatro Caminos: (40.45°, -3.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cuatro Caminos: 6420.5 km from centroid", + " Tigre: 3624.1 km from centroid", + " Adamantina: 2074.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cuatro Caminos", + "FINAL ANSWER: Cuatro Caminos" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.41333, + "lon": -98.14358, + "name": "Apizaco" + }, + { + "lat": 41.0051, + "lon": -73.78458, + "name": "Scarsdale" + }, + { + "lat": 29.84576, + "lon": -90.10674, + "name": "Estelle" + }, + { + "lat": 25.5783, + "lon": -80.3377, + "name": "Cutler Bay" + }, + { + "lat": -26.1466, + "lon": 28.68322, + "name": "Delmas" + } + ], + "question": "Which location is the geographic outlier among: Apizaco, Scarsdale, Estelle, Cutler Bay, Delmas?", + "ground_truth": { + "answer": "Delmas", + "outlier_distance_km": 11011.4, + "second_furthest_km": 3726.8, + "clarity_ratio": 2.95, + "median_distance_km": 3070.2, + "distances_to_centroid": { + "Apizaco": 3726.8, + "Scarsdale": 2773.2, + "Estelle": 3070.2, + "Cutler Bay": 2003.6, + "Delmas": 11011.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Apizaco: (19.41°, -98.14°)", + " Scarsdale: (41.01°, -73.78°)", + " Estelle: (29.85°, -90.11°)", + " Cutler Bay: (25.58°, -80.34°)", + " Delmas: (-26.15°, 28.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Delmas: 11011.4 km from centroid", + " Apizaco: 3726.8 km from centroid", + " Estelle: 3070.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Delmas", + "FINAL ANSWER: Delmas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.47599, + "lon": 77.86637, + "name": "Sankagiri" + }, + { + "lat": -8.36667, + "lon": 114.15, + "name": "Genteng" + }, + { + "lat": 26.66667, + "lon": 107.91667, + "name": "Longchang" + }, + { + "lat": 3.14657, + "lon": 101.71023, + "name": "Bukit Bintang" + }, + { + "lat": -54.81084, + "lon": -68.31591, + "name": "Ushuaia" + } + ], + "question": "Which location is the geographic outlier among: Sankagiri, Genteng, Longchang, Bukit Bintang, Ushuaia?", + "ground_truth": { + "answer": "Ushuaia", + "outlier_distance_km": 12243.4, + "second_furthest_km": 5619.0, + "clarity_ratio": 2.18, + "median_distance_km": 5263.0, + "distances_to_centroid": { + "Sankagiri": 2154.7, + "Genteng": 5263.0, + "Longchang": 5619.0, + "Bukit Bintang": 3982.6, + "Ushuaia": 12243.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sankagiri: (11.48°, 77.87°)", + " Genteng: (-8.37°, 114.15°)", + " Longchang: (26.67°, 107.92°)", + " Bukit Bintang: (3.15°, 101.71°)", + " Ushuaia: (-54.81°, -68.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ushuaia: 12243.4 km from centroid", + " Longchang: 5619.0 km from centroid", + " Genteng: 5263.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ushuaia", + "FINAL ANSWER: Ushuaia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.83658, + "lon": -83.97878, + "name": "Thomasville" + }, + { + "lat": 39.08289, + "lon": -77.26498, + "name": "North Potomac" + }, + { + "lat": 25.7076, + "lon": -80.32561, + "name": "Glenvar Heights" + }, + { + "lat": 40.3934, + "lon": -82.48572, + "name": "Mount Vernon" + }, + { + "lat": 5.45303, + "lon": -75.65072, + "name": "Supía" + } + ], + "question": "Which location is the geographic outlier among: Thomasville, North Potomac, Glenvar Heights, Mount Vernon, Supía?", + "ground_truth": { + "answer": "Supía", + "outlier_distance_km": 2579.9, + "second_furthest_km": 1365.3, + "clarity_ratio": 1.89, + "median_distance_km": 1224.7, + "distances_to_centroid": { + "Thomasville": 482.0, + "North Potomac": 1224.7, + "Glenvar Heights": 290.2, + "Mount Vernon": 1365.3, + "Supía": 2579.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thomasville: (30.84°, -83.98°)", + " North Potomac: (39.08°, -77.26°)", + " Glenvar Heights: (25.71°, -80.33°)", + " Mount Vernon: (40.39°, -82.49°)", + " Supía: (5.45°, -75.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Supía: 2579.9 km from centroid", + " Mount Vernon: 1365.3 km from centroid", + " North Potomac: 1224.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Supía", + "FINAL ANSWER: Supía" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.33316, + "lon": 37.64587, + "name": "Chuka" + }, + { + "lat": 4.64231, + "lon": 7.92438, + "name": "Eket" + }, + { + "lat": 27.06309, + "lon": 31.34425, + "name": "As Sāḩil" + }, + { + "lat": 27.18096, + "lon": 31.18368, + "name": "Assiut" + }, + { + "lat": -25.51626, + "lon": -48.52537, + "name": "Paranaguá" + } + ], + "question": "Which location is the geographic outlier among: Chuka, Eket, As Sāḩil, Assiut, Paranaguá?", + "ground_truth": { + "answer": "Paranaguá", + "outlier_distance_km": 7436.5, + "second_furthest_km": 3064.0, + "clarity_ratio": 2.43, + "median_distance_km": 3061.9, + "distances_to_centroid": { + "Chuka": 2957.5, + "Eket": 492.6, + "As Sāḩil": 3064.0, + "Assiut": 3061.9, + "Paranaguá": 7436.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chuka: (-0.33°, 37.65°)", + " Eket: (4.64°, 7.92°)", + " As Sāḩil: (27.06°, 31.34°)", + " Assiut: (27.18°, 31.18°)", + " Paranaguá: (-25.52°, -48.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paranaguá: 7436.5 km from centroid", + " As Sāḩil: 3064.0 km from centroid", + " Assiut: 3061.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paranaguá", + "FINAL ANSWER: Paranaguá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.06258, + "lon": -94.15743, + "name": "Fayetteville" + }, + { + "lat": 40.42331, + "lon": -104.70913, + "name": "Greeley" + }, + { + "lat": 43.63552, + "lon": -79.50113, + "name": "Stonegate-Queensway" + }, + { + "lat": 21.93115, + "lon": -99.99488, + "name": "Rioverde" + }, + { + "lat": -9.31833, + "lon": -35.56111, + "name": "São Luís do Quitunde" + } + ], + "question": "Which location is the geographic outlier among: Fayetteville, Greeley, Stonegate-Queensway, Rioverde, São Luís do Quitunde?", + "ground_truth": { + "answer": "São Luís do Quitunde", + "outlier_distance_km": 6470.1, + "second_furthest_km": 2540.2, + "clarity_ratio": 2.55, + "median_distance_km": 1923.1, + "distances_to_centroid": { + "Fayetteville": 1510.1, + "Greeley": 2540.2, + "Stonegate-Queensway": 1923.1, + "Rioverde": 1817.1, + "São Luís do Quitunde": 6470.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fayetteville: (36.06°, -94.16°)", + " Greeley: (40.42°, -104.71°)", + " Stonegate-Queensway: (43.64°, -79.50°)", + " Rioverde: (21.93°, -99.99°)", + " São Luís do Quitunde: (-9.32°, -35.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Luís do Quitunde: 6470.1 km from centroid", + " Greeley: 2540.2 km from centroid", + " Stonegate-Queensway: 1923.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Luís do Quitunde", + "FINAL ANSWER: São Luís do Quitunde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.30136, + "lon": 6.7482, + "name": "Borne" + }, + { + "lat": 52.56395, + "lon": 13.33552, + "name": "Reinickendorf" + }, + { + "lat": 55.68333, + "lon": 37.55, + "name": "Semënovskoye" + }, + { + "lat": 50.00377, + "lon": 18.47205, + "name": "Wodzisław Śląski" + }, + { + "lat": 28.90314, + "lon": 78.46984, + "name": "Amroha" + } + ], + "question": "Which location is the geographic outlier among: Borne, Reinickendorf, Semënovskoye, Wodzisław Śląski, Amroha?", + "ground_truth": { + "answer": "Amroha", + "outlier_distance_km": 4558.7, + "second_furthest_km": 1782.8, + "clarity_ratio": 2.56, + "median_distance_km": 1349.8, + "distances_to_centroid": { + "Borne": 1782.8, + "Reinickendorf": 1349.8, + "Semënovskoye": 978.3, + "Wodzisław Śląski": 937.3, + "Amroha": 4558.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Borne: (52.30°, 6.75°)", + " Reinickendorf: (52.56°, 13.34°)", + " Semënovskoye: (55.68°, 37.55°)", + " Wodzisław Śląski: (50.00°, 18.47°)", + " Amroha: (28.90°, 78.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amroha: 4558.7 km from centroid", + " Borne: 1782.8 km from centroid", + " Reinickendorf: 1349.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amroha", + "FINAL ANSWER: Amroha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.92485, + "lon": 78.12786, + "name": "Amla" + }, + { + "lat": 21.32855, + "lon": 71.02645, + "name": "Dhāri" + }, + { + "lat": 40.19956, + "lon": 140.39388, + "name": "Kita-Akita" + }, + { + "lat": 2.5148, + "lon": 102.8158, + "name": "Segamat" + }, + { + "lat": 23.64824, + "lon": -100.64334, + "name": "Matehuala" + } + ], + "question": "Which location is the geographic outlier among: Amla, Dhāri, Kita-Akita, Segamat, Matehuala?", + "ground_truth": { + "answer": "Matehuala", + "outlier_distance_km": 14461.4, + "second_furthest_km": 7804.2, + "clarity_ratio": 1.85, + "median_distance_km": 5263.2, + "distances_to_centroid": { + "Amla": 2039.3, + "Dhāri": 1312.2, + "Kita-Akita": 7804.2, + "Segamat": 5263.2, + "Matehuala": 14461.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Amla: (21.92°, 78.13°)", + " Dhāri: (21.33°, 71.03°)", + " Kita-Akita: (40.20°, 140.39°)", + " Segamat: (2.51°, 102.82°)", + " Matehuala: (23.65°, -100.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Matehuala: 14461.4 km from centroid", + " Kita-Akita: 7804.2 km from centroid", + " Segamat: 5263.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Matehuala", + "FINAL ANSWER: Matehuala" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.43293, + "lon": -123.48591, + "name": "Colwood" + }, + { + "lat": 18.68415, + "lon": -99.24577, + "name": "Xoxocotla" + }, + { + "lat": 43.63388, + "lon": -79.3772, + "name": "Waterfront Communities-The Island" + }, + { + "lat": 47.14121, + "lon": -122.27012, + "name": "South Hill" + }, + { + "lat": 51.55103, + "lon": 43.17069, + "name": "Balashov" + } + ], + "question": "Which location is the geographic outlier among: Colwood, Xoxocotla, Waterfront Communities-The Island, South Hill, Balashov?", + "ground_truth": { + "answer": "Balashov", + "outlier_distance_km": 8095.9, + "second_furthest_km": 3713.7, + "clarity_ratio": 2.18, + "median_distance_km": 3642.0, + "distances_to_centroid": { + "Colwood": 3713.7, + "Xoxocotla": 3373.9, + "Waterfront Communities-The Island": 321.2, + "South Hill": 3642.0, + "Balashov": 8095.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Colwood: (48.43°, -123.49°)", + " Xoxocotla: (18.68°, -99.25°)", + " Waterfront Communities-The Island: (43.63°, -79.38°)", + " South Hill: (47.14°, -122.27°)", + " Balashov: (51.55°, 43.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Balashov: 8095.9 km from centroid", + " Colwood: 3713.7 km from centroid", + " South Hill: 3642.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Balashov", + "FINAL ANSWER: Balashov" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.41692, + "lon": 3.14058, + "name": "Irewe" + }, + { + "lat": -26.98023, + "lon": 26.67272, + "name": "Orkney" + }, + { + "lat": 6.21269, + "lon": 7.07199, + "name": "Awka" + }, + { + "lat": 31.0539, + "lon": 31.37787, + "name": "Ţalkhā" + }, + { + "lat": 24.91389, + "lon": 118.58583, + "name": "Quanzhou" + } + ], + "question": "Which location is the geographic outlier among: Irewe, Orkney, Awka, Ţalkhā, Quanzhou?", + "ground_truth": { + "answer": "Quanzhou", + "outlier_distance_km": 8737.6, + "second_furthest_km": 4091.5, + "clarity_ratio": 2.14, + "median_distance_km": 3779.5, + "distances_to_centroid": { + "Irewe": 3779.5, + "Orkney": 4091.5, + "Awka": 3349.3, + "Ţalkhā": 2602.8, + "Quanzhou": 8737.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Irewe: (6.42°, 3.14°)", + " Orkney: (-26.98°, 26.67°)", + " Awka: (6.21°, 7.07°)", + " Ţalkhā: (31.05°, 31.38°)", + " Quanzhou: (24.91°, 118.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Quanzhou: 8737.6 km from centroid", + " Orkney: 4091.5 km from centroid", + " Irewe: 3779.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Quanzhou", + "FINAL ANSWER: Quanzhou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.33341, + "lon": -79.21632, + "name": "Huntsville" + }, + { + "lat": 40.72149, + "lon": -73.7693, + "name": "Terrace Heights" + }, + { + "lat": 45.27413, + "lon": -93.59135, + "name": "Otsego" + }, + { + "lat": 19.26757, + "lon": -99.53214, + "name": "San Mateo Atenco" + }, + { + "lat": -23.56729, + "lon": -46.69232, + "name": "Pinheiros" + } + ], + "question": "Which location is the geographic outlier among: Huntsville, Terrace Heights, Otsego, San Mateo Atenco, Pinheiros?", + "ground_truth": { + "answer": "Pinheiros", + "outlier_distance_km": 6436.6, + "second_furthest_km": 2586.3, + "clarity_ratio": 2.49, + "median_distance_km": 2259.2, + "distances_to_centroid": { + "Huntsville": 2216.6, + "Terrace Heights": 1759.8, + "Otsego": 2586.3, + "San Mateo Atenco": 2259.2, + "Pinheiros": 6436.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huntsville: (45.33°, -79.22°)", + " Terrace Heights: (40.72°, -73.77°)", + " Otsego: (45.27°, -93.59°)", + " San Mateo Atenco: (19.27°, -99.53°)", + " Pinheiros: (-23.57°, -46.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pinheiros: 6436.6 km from centroid", + " Otsego: 2586.3 km from centroid", + " San Mateo Atenco: 2259.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pinheiros", + "FINAL ANSWER: Pinheiros" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": 41.37471, + "lon": 2.12775, + "name": "Sants - Badal" + } + ], + "question": "Which location is the geographic outlier among: Lidcombe, Lilydale, Southport, Forest Lake, Sants - Badal?", + "ground_truth": { + "answer": "Sants - Badal", + "outlier_distance_km": 13649.6, + "second_furthest_km": 3525.6, + "clarity_ratio": 3.87, + "median_distance_km": 3521.3, + "distances_to_centroid": { + "Lidcombe": 3521.3, + "Lilydale": 3299.9, + "Southport": 3525.6, + "Forest Lake": 3476.0, + "Sants - Badal": 13649.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lidcombe: (-33.86°, 151.04°)", + " Lilydale: (-37.75°, 145.35°)", + " Southport: (-27.97°, 153.40°)", + " Forest Lake: (-27.63°, 152.97°)", + " Sants - Badal: (41.37°, 2.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sants - Badal: 13649.6 km from centroid", + " Southport: 3525.6 km from centroid", + " Lidcombe: 3521.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sants - Badal", + "FINAL ANSWER: Sants - Badal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.78842, + "lon": 31.05319, + "name": "Barberton" + }, + { + "lat": 5.30383, + "lon": -1.98956, + "name": "Tarkwa" + }, + { + "lat": 7.84855, + "lon": 4.32981, + "name": "Inisa" + }, + { + "lat": 5.85475, + "lon": 6.85944, + "name": "Ihiala" + }, + { + "lat": 29.45609, + "lon": 106.85776, + "name": "Dongwenquan" + } + ], + "question": "Which location is the geographic outlier among: Barberton, Tarkwa, Inisa, Ihiala, Dongwenquan?", + "ground_truth": { + "answer": "Dongwenquan", + "outlier_distance_km": 8544.0, + "second_furthest_km": 3480.6, + "clarity_ratio": 2.45, + "median_distance_km": 3376.4, + "distances_to_centroid": { + "Barberton": 3376.4, + "Tarkwa": 3480.6, + "Inisa": 2797.6, + "Ihiala": 2502.7, + "Dongwenquan": 8544.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Barberton: (-25.79°, 31.05°)", + " Tarkwa: (5.30°, -1.99°)", + " Inisa: (7.85°, 4.33°)", + " Ihiala: (5.85°, 6.86°)", + " Dongwenquan: (29.46°, 106.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dongwenquan: 8544.0 km from centroid", + " Tarkwa: 3480.6 km from centroid", + " Barberton: 3376.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dongwenquan", + "FINAL ANSWER: Dongwenquan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.50727, + "lon": 45.83493, + "name": "Golwayn" + }, + { + "lat": 7.5758, + "lon": -2.78516, + "name": "Japekrom" + }, + { + "lat": 7.01667, + "lon": 39.98333, + "name": "Goba" + }, + { + "lat": 31.32977, + "lon": 31.71507, + "name": "Fāraskūr" + }, + { + "lat": -5.89056, + "lon": -38.62194, + "name": "Jaguaribe" + } + ], + "question": "Which location is the geographic outlier among: Golwayn, Japekrom, Goba, Fāraskūr, Jaguaribe?", + "ground_truth": { + "answer": "Jaguaribe", + "outlier_distance_km": 6201.5, + "second_furthest_km": 3384.5, + "clarity_ratio": 1.83, + "median_distance_km": 2983.1, + "distances_to_centroid": { + "Golwayn": 3384.5, + "Japekrom": 1990.1, + "Goba": 2736.3, + "Fāraskūr": 2983.1, + "Jaguaribe": 6201.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Golwayn: (6.51°, 45.83°)", + " Japekrom: (7.58°, -2.79°)", + " Goba: (7.02°, 39.98°)", + " Fāraskūr: (31.33°, 31.72°)", + " Jaguaribe: (-5.89°, -38.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaguaribe: 6201.5 km from centroid", + " Golwayn: 3384.5 km from centroid", + " Fāraskūr: 2983.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaguaribe", + "FINAL ANSWER: Jaguaribe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + { + "lat": -37.73261, + "lon": 144.86504, + "name": "Keilor East" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -33.8178, + "lon": 151.00348, + "name": "Parramatta" + }, + { + "lat": 40.40525, + "lon": -3.64249, + "name": "Vinateros" + } + ], + "question": "Which location is the geographic outlier among: Kellyville, Keilor East, Auburn, Parramatta, Vinateros?", + "ground_truth": { + "answer": "Vinateros", + "outlier_distance_km": 14138.2, + "second_furthest_km": 3538.7, + "clarity_ratio": 4.0, + "median_distance_km": 3535.0, + "distances_to_centroid": { + "Kellyville": 3526.7, + "Keilor East": 3211.3, + "Auburn": 3538.7, + "Parramatta": 3535.0, + "Vinateros": 14138.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kellyville: (-33.71°, 150.95°)", + " Keilor East: (-37.73°, 144.87°)", + " Auburn: (-33.85°, 151.03°)", + " Parramatta: (-33.82°, 151.00°)", + " Vinateros: (40.41°, -3.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vinateros: 14138.2 km from centroid", + " Auburn: 3538.7 km from centroid", + " Parramatta: 3535.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vinateros", + "FINAL ANSWER: Vinateros" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.85843, + "lon": -74.16376, + "name": "Clifton" + }, + { + "lat": 18.01932, + "lon": -102.21225, + "name": "Guacamayas" + }, + { + "lat": 42.49044, + "lon": -83.01304, + "name": "Warren" + }, + { + "lat": 43.4668, + "lon": -80.51639, + "name": "Waterloo" + }, + { + "lat": -15.56222, + "lon": -49.94861, + "name": "Itapuranga" + } + ], + "question": "Which location is the geographic outlier among: Clifton, Guacamayas, Warren, Waterloo, Itapuranga?", + "ground_truth": { + "answer": "Itapuranga", + "outlier_distance_km": 5513.9, + "second_furthest_km": 2642.6, + "clarity_ratio": 2.09, + "median_distance_km": 1971.9, + "distances_to_centroid": { + "Clifton": 1704.9, + "Guacamayas": 2642.6, + "Warren": 1906.1, + "Waterloo": 1971.9, + "Itapuranga": 5513.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Clifton: (40.86°, -74.16°)", + " Guacamayas: (18.02°, -102.21°)", + " Warren: (42.49°, -83.01°)", + " Waterloo: (43.47°, -80.52°)", + " Itapuranga: (-15.56°, -49.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itapuranga: 5513.9 km from centroid", + " Guacamayas: 2642.6 km from centroid", + " Waterloo: 1971.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itapuranga", + "FINAL ANSWER: Itapuranga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.95559, + "lon": -86.01387, + "name": "Fishers" + }, + { + "lat": 40.52927, + "lon": -74.31598, + "name": "Fords" + }, + { + "lat": 41.8317, + "lon": -87.67366, + "name": "McKinley Park" + }, + { + "lat": 20.03557, + "lon": -98.31015, + "name": "Cuautepec de Hinojosa" + }, + { + "lat": -4.90389, + "lon": -80.68528, + "name": "Sullana" + } + ], + "question": "Which location is the geographic outlier among: Fishers, Fords, McKinley Park, Cuautepec de Hinojosa, Sullana?", + "ground_truth": { + "answer": "Sullana", + "outlier_distance_km": 3637.4, + "second_furthest_km": 1770.4, + "clarity_ratio": 2.05, + "median_distance_km": 1608.1, + "distances_to_centroid": { + "Fishers": 1387.3, + "Fords": 1770.4, + "McKinley Park": 1608.1, + "Cuautepec de Hinojosa": 1551.8, + "Sullana": 3637.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fishers: (39.96°, -86.01°)", + " Fords: (40.53°, -74.32°)", + " McKinley Park: (41.83°, -87.67°)", + " Cuautepec de Hinojosa: (20.04°, -98.31°)", + " Sullana: (-4.90°, -80.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sullana: 3637.4 km from centroid", + " Fords: 1770.4 km from centroid", + " McKinley Park: 1608.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sullana", + "FINAL ANSWER: Sullana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.67086, + "lon": -0.02748, + "name": "Enfield Lock" + }, + { + "lat": 53.01499, + "lon": 13.99924, + "name": "Angermünde" + }, + { + "lat": 37.57465, + "lon": 15.04964, + "name": "Mascalucia" + }, + { + "lat": 49.23262, + "lon": 7.00982, + "name": "Saarbrücken" + }, + { + "lat": 11.45207, + "lon": 9.47856, + "name": "Birnin Kudu" + } + ], + "question": "Which location is the geographic outlier among: Enfield Lock, Angermünde, Mascalucia, Saarbrücken, Birnin Kudu?", + "ground_truth": { + "answer": "Birnin Kudu", + "outlier_distance_km": 3240.1, + "second_furthest_km": 1430.2, + "clarity_ratio": 2.27, + "median_distance_km": 1416.4, + "distances_to_centroid": { + "Enfield Lock": 1416.4, + "Angermünde": 1430.2, + "Mascalucia": 612.9, + "Saarbrücken": 975.0, + "Birnin Kudu": 3240.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Enfield Lock: (51.67°, -0.03°)", + " Angermünde: (53.01°, 14.00°)", + " Mascalucia: (37.57°, 15.05°)", + " Saarbrücken: (49.23°, 7.01°)", + " Birnin Kudu: (11.45°, 9.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Birnin Kudu: 3240.1 km from centroid", + " Angermünde: 1430.2 km from centroid", + " Enfield Lock: 1416.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Birnin Kudu", + "FINAL ANSWER: Birnin Kudu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.13994, + "lon": 85.84096, + "name": "Sheikhpura" + }, + { + "lat": 12.42602, + "lon": 75.7382, + "name": "Madikeri" + }, + { + "lat": 27.68806, + "lon": 111.42944, + "name": "Lengshuijiang" + }, + { + "lat": 29.6544, + "lon": 105.78416, + "name": "Zhifeng" + }, + { + "lat": 34.17426, + "lon": -97.14363, + "name": "Ardmore" + } + ], + "question": "Which location is the geographic outlier among: Sheikhpura, Madikeri, Lengshuijiang, Zhifeng, Ardmore?", + "ground_truth": { + "answer": "Ardmore", + "outlier_distance_km": 12781.2, + "second_furthest_km": 5428.6, + "clarity_ratio": 2.35, + "median_distance_km": 4849.7, + "distances_to_centroid": { + "Sheikhpura": 2957.1, + "Madikeri": 2518.8, + "Lengshuijiang": 5428.6, + "Zhifeng": 4849.7, + "Ardmore": 12781.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sheikhpura: (25.14°, 85.84°)", + " Madikeri: (12.43°, 75.74°)", + " Lengshuijiang: (27.69°, 111.43°)", + " Zhifeng: (29.65°, 105.78°)", + " Ardmore: (34.17°, -97.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ardmore: 12781.2 km from centroid", + " Lengshuijiang: 5428.6 km from centroid", + " Zhifeng: 4849.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ardmore", + "FINAL ANSWER: Ardmore" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": -41.21667, + "lon": 174.91667, + "name": "Lower Hutt" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + { + "lat": 33.86726, + "lon": -112.14682, + "name": "Anthem" + } + ], + "question": "Which location is the geographic outlier among: Officer, Altona Meadows, Lower Hutt, Lincoln, Anthem?", + "ground_truth": { + "answer": "Anthem", + "outlier_distance_km": 16214.3, + "second_furthest_km": 6635.5, + "clarity_ratio": 2.44, + "median_distance_km": 6597.6, + "distances_to_centroid": { + "Officer": 4070.0, + "Altona Meadows": 4012.5, + "Lower Hutt": 6597.6, + "Lincoln": 6635.5, + "Anthem": 16214.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Officer: (-38.06°, 145.41°)", + " Altona Meadows: (-37.88°, 144.78°)", + " Lower Hutt: (-41.22°, 174.92°)", + " Lincoln: (-36.86°, 174.62°)", + " Anthem: (33.87°, -112.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Anthem: 16214.3 km from centroid", + " Lincoln: 6635.5 km from centroid", + " Lower Hutt: 6597.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Anthem", + "FINAL ANSWER: Anthem" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.22426, + "lon": 153.02075, + "name": "North Lakes" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -37.75405, + "lon": 145.14864, + "name": "Templestowe" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": 50.40704, + "lon": 1.56446, + "name": "Berck-Plage" + } + ], + "question": "Which location is the geographic outlier among: North Lakes, Canning Vale, Templestowe, Shepparton, Berck-Plage?", + "ground_truth": { + "answer": "Berck-Plage", + "outlier_distance_km": 12878.4, + "second_furthest_km": 4351.4, + "clarity_ratio": 2.96, + "median_distance_km": 3983.3, + "distances_to_centroid": { + "North Lakes": 4351.4, + "Canning Vale": 1758.8, + "Templestowe": 3983.3, + "Shepparton": 3936.1, + "Berck-Plage": 12878.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Lakes: (-27.22°, 153.02°)", + " Canning Vale: (-32.06°, 115.92°)", + " Templestowe: (-37.75°, 145.15°)", + " Shepparton: (-36.38°, 145.40°)", + " Berck-Plage: (50.41°, 1.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Berck-Plage: 12878.4 km from centroid", + " North Lakes: 4351.4 km from centroid", + " Templestowe: 3983.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Berck-Plage", + "FINAL ANSWER: Berck-Plage" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.21266, + "lon": 79.36369, + "name": "Jayamkondacholapuram" + }, + { + "lat": 17.56425, + "lon": 76.56854, + "name": "Aland" + }, + { + "lat": 26.23111, + "lon": 109.13139, + "name": "Liping" + }, + { + "lat": 24.62361, + "lon": 76.70783, + "name": "Chhipa Barod" + }, + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + } + ], + "question": "Which location is the geographic outlier among: Jayamkondacholapuram, Aland, Liping, Chhipa Barod, Wangaratta?", + "ground_truth": { + "answer": "Wangaratta", + "outlier_distance_km": 7131.6, + "second_furthest_km": 2840.9, + "clarity_ratio": 2.51, + "median_distance_km": 2482.5, + "distances_to_centroid": { + "Jayamkondacholapuram": 2019.1, + "Aland": 2482.5, + "Liping": 2301.2, + "Chhipa Barod": 2840.9, + "Wangaratta": 7131.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jayamkondacholapuram: (11.21°, 79.36°)", + " Aland: (17.56°, 76.57°)", + " Liping: (26.23°, 109.13°)", + " Chhipa Barod: (24.62°, 76.71°)", + " Wangaratta: (-36.36°, 146.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wangaratta: 7131.6 km from centroid", + " Chhipa Barod: 2840.9 km from centroid", + " Aland: 2482.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wangaratta", + "FINAL ANSWER: Wangaratta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + }, + { + "lat": -36.8, + "lon": 174.75, + "name": "North Shore" + }, + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": 41.09978, + "lon": -80.64952, + "name": "Youngstown" + } + ], + "question": "Which location is the geographic outlier among: Levin, North Shore, Greenvale, Whangarei, Youngstown?", + "ground_truth": { + "answer": "Youngstown", + "outlier_distance_km": 17276.3, + "second_furthest_km": 5739.7, + "clarity_ratio": 3.01, + "median_distance_km": 5682.3, + "distances_to_centroid": { + "Levin": 5739.7, + "North Shore": 5682.3, + "Greenvale": 3129.5, + "Whangarei": 5644.2, + "Youngstown": 17276.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Levin: (-40.63°, 175.28°)", + " North Shore: (-36.80°, 174.75°)", + " Greenvale: (-37.63°, 144.87°)", + " Whangarei: (-35.73°, 174.32°)", + " Youngstown: (41.10°, -80.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Youngstown: 17276.3 km from centroid", + " Levin: 5739.7 km from centroid", + " North Shore: 5682.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Youngstown", + "FINAL ANSWER: Youngstown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75, + "lon": 145.01667, + "name": "Preston" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + }, + { + "lat": -33.73333, + "lon": 150.88333, + "name": "Quakers Hill" + }, + { + "lat": -32.22099, + "lon": 116.009, + "name": "Byford" + }, + { + "lat": 8.3, + "lon": 38.95, + "name": "‘Alem T’ēna" + } + ], + "question": "Which location is the geographic outlier among: Preston, Seaford, Quakers Hill, Byford, ‘Alem T’ēna?", + "ground_truth": { + "answer": "‘Alem T’ēna", + "outlier_distance_km": 9466.2, + "second_furthest_km": 3129.8, + "clarity_ratio": 3.02, + "median_distance_km": 2731.7, + "distances_to_centroid": { + "Preston": 2709.0, + "Seaford": 2731.7, + "Quakers Hill": 3129.8, + "Byford": 687.0, + "‘Alem T’ēna": 9466.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Preston: (-37.75°, 145.02°)", + " Seaford: (-38.10°, 145.13°)", + " Quakers Hill: (-33.73°, 150.88°)", + " Byford: (-32.22°, 116.01°)", + " ‘Alem T’ēna: (8.30°, 38.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " ‘Alem T’ēna: 9466.2 km from centroid", + " Quakers Hill: 3129.8 km from centroid", + " Seaford: 2731.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: ‘Alem T’ēna", + "FINAL ANSWER: ‘Alem T’ēna" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.49004, + "lon": 76.3264, + "name": "Alappuzha" + }, + { + "lat": 25.31258, + "lon": 86.48888, + "name": "Jamālpur" + }, + { + "lat": 36.8, + "lon": 118.5, + "name": "Gaoliu" + }, + { + "lat": 4.85, + "lon": 100.73333, + "name": "Taiping" + }, + { + "lat": 43.46589, + "lon": -3.80493, + "name": "Santander" + } + ], + "question": "Which location is the geographic outlier among: Alappuzha, Jamālpur, Gaoliu, Taiping, Santander?", + "ground_truth": { + "answer": "Santander", + "outlier_distance_km": 7378.8, + "second_furthest_km": 4309.3, + "clarity_ratio": 1.71, + "median_distance_km": 3425.7, + "distances_to_centroid": { + "Alappuzha": 1613.2, + "Jamālpur": 1105.1, + "Gaoliu": 4309.3, + "Taiping": 3425.7, + "Santander": 7378.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alappuzha: (9.49°, 76.33°)", + " Jamālpur: (25.31°, 86.49°)", + " Gaoliu: (36.80°, 118.50°)", + " Taiping: (4.85°, 100.73°)", + " Santander: (43.47°, -3.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santander: 7378.8 km from centroid", + " Gaoliu: 4309.3 km from centroid", + " Taiping: 3425.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santander", + "FINAL ANSWER: Santander" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.34077, + "lon": -3.68843, + "name": "San Cristobal" + }, + { + "lat": 48.88333, + "lon": 2.5, + "name": "Villemomble" + }, + { + "lat": 51.01122, + "lon": 13.82029, + "name": "Leuben" + }, + { + "lat": 51.50403, + "lon": 14.64017, + "name": "Weißwasser" + }, + { + "lat": 40.76844, + "lon": -73.77708, + "name": "Bayside" + } + ], + "question": "Which location is the geographic outlier among: San Cristobal, Villemomble, Leuben, Weißwasser, Bayside?", + "ground_truth": { + "answer": "Bayside", + "outlier_distance_km": 5082.5, + "second_furthest_km": 1823.3, + "clarity_ratio": 2.79, + "median_distance_km": 1759.2, + "distances_to_centroid": { + "San Cristobal": 820.9, + "Villemomble": 921.0, + "Leuben": 1759.2, + "Weißwasser": 1823.3, + "Bayside": 5082.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Cristobal: (40.34°, -3.69°)", + " Villemomble: (48.88°, 2.50°)", + " Leuben: (51.01°, 13.82°)", + " Weißwasser: (51.50°, 14.64°)", + " Bayside: (40.77°, -73.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bayside: 5082.5 km from centroid", + " Weißwasser: 1823.3 km from centroid", + " Leuben: 1759.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bayside", + "FINAL ANSWER: Bayside" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.41333, + "lon": -119.86097, + "name": "Isla Vista" + }, + { + "lat": 20.44655, + "lon": -97.32494, + "name": "Papantla de Olarte" + }, + { + "lat": 51.30011, + "lon": -114.03528, + "name": "Airdrie" + }, + { + "lat": 40.89288, + "lon": -73.97264, + "name": "Englewood" + }, + { + "lat": -2.23111, + "lon": -45.3, + "name": "Santa Helena" + } + ], + "question": "Which location is the geographic outlier among: Isla Vista, Papantla de Olarte, Airdrie, Englewood, Santa Helena?", + "ground_truth": { + "answer": "Santa Helena", + "outlier_distance_km": 5895.8, + "second_furthest_km": 3180.9, + "clarity_ratio": 1.85, + "median_distance_km": 2869.5, + "distances_to_centroid": { + "Isla Vista": 2869.5, + "Papantla de Olarte": 1195.1, + "Airdrie": 3180.9, + "Englewood": 1974.0, + "Santa Helena": 5895.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Isla Vista: (34.41°, -119.86°)", + " Papantla de Olarte: (20.45°, -97.32°)", + " Airdrie: (51.30°, -114.04°)", + " Englewood: (40.89°, -73.97°)", + " Santa Helena: (-2.23°, -45.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Helena: 5895.8 km from centroid", + " Airdrie: 3180.9 km from centroid", + " Isla Vista: 2869.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Helena", + "FINAL ANSWER: Santa Helena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + }, + { + "lat": -20.02194, + "lon": -44.05889, + "name": "Ibirité" + } + ], + "question": "Which location is the geographic outlier among: Tarneit, Balwyn North, Liverpool, Hornsby, Ibirité?", + "ground_truth": { + "answer": "Ibirité", + "outlier_distance_km": 13520.2, + "second_furthest_km": 3842.8, + "clarity_ratio": 3.52, + "median_distance_km": 3822.8, + "distances_to_centroid": { + "Tarneit": 3221.1, + "Balwyn North": 3259.3, + "Liverpool": 3822.8, + "Hornsby": 3842.8, + "Ibirité": 13520.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tarneit: (-37.84°, 144.66°)", + " Balwyn North: (-37.79°, 145.09°)", + " Liverpool: (-33.92°, 150.93°)", + " Hornsby: (-33.70°, 151.10°)", + " Ibirité: (-20.02°, -44.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ibirité: 13520.2 km from centroid", + " Hornsby: 3842.8 km from centroid", + " Liverpool: 3822.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ibirité", + "FINAL ANSWER: Ibirité" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + { + "lat": -33.78269, + "lon": 151.04888, + "name": "Carlingford" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": 36.76419, + "lon": -2.61475, + "name": "Roquetas de Mar" + } + ], + "question": "Which location is the geographic outlier among: Werribee, Carlingford, Hobart, Perth, Roquetas de Mar?", + "ground_truth": { + "answer": "Roquetas de Mar", + "outlier_distance_km": 13524.7, + "second_furthest_km": 4097.6, + "clarity_ratio": 3.3, + "median_distance_km": 4060.1, + "distances_to_centroid": { + "Werribee": 3647.1, + "Carlingford": 4097.6, + "Hobart": 4060.1, + "Perth": 1201.7, + "Roquetas de Mar": 13524.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Werribee: (-37.90°, 144.67°)", + " Carlingford: (-33.78°, 151.05°)", + " Hobart: (-42.88°, 147.33°)", + " Perth: (-31.95°, 115.86°)", + " Roquetas de Mar: (36.76°, -2.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Roquetas de Mar: 13524.7 km from centroid", + " Carlingford: 4097.6 km from centroid", + " Hobart: 4060.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Roquetas de Mar", + "FINAL ANSWER: Roquetas de Mar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + }, + { + "lat": -33.91667, + "lon": 151.03333, + "name": "Bankstown" + }, + { + "lat": -26.68443, + "lon": 153.05705, + "name": "Buderim" + }, + { + "lat": -37.90561, + "lon": 145.00279, + "name": "Brighton" + }, + { + "lat": 28.77718, + "lon": 76.77165, + "name": "Sāmpla" + } + ], + "question": "Which location is the geographic outlier among: Northcote, Bankstown, Buderim, Brighton, Sāmpla?", + "ground_truth": { + "answer": "Sāmpla", + "outlier_distance_km": 8312.5, + "second_furthest_km": 2153.4, + "clarity_ratio": 3.86, + "median_distance_km": 2099.2, + "distances_to_centroid": { + "Northcote": 2086.1, + "Bankstown": 2153.4, + "Buderim": 1999.3, + "Brighton": 2099.2, + "Sāmpla": 8312.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Northcote: (-37.77°, 145.00°)", + " Bankstown: (-33.92°, 151.03°)", + " Buderim: (-26.68°, 153.06°)", + " Brighton: (-37.91°, 145.00°)", + " Sāmpla: (28.78°, 76.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sāmpla: 8312.5 km from centroid", + " Bankstown: 2153.4 km from centroid", + " Brighton: 2099.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sāmpla", + "FINAL ANSWER: Sāmpla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 56.10921, + "lon": 94.58698, + "name": "Zelenogorsk" + }, + { + "lat": 51.20219, + "lon": 7.36027, + "name": "Radevormwald" + }, + { + "lat": 48.81568, + "lon": 2.38487, + "name": "Ivry-sur-Seine" + }, + { + "lat": 50.48333, + "lon": 2.55, + "name": "Bruay-la-Buissière" + }, + { + "lat": -36.8, + "lon": 174.75, + "name": "North Shore" + } + ], + "question": "Which location is the geographic outlier among: Zelenogorsk, Radevormwald, Ivry-sur-Seine, Bruay-la-Buissière, North Shore?", + "ground_truth": { + "answer": "North Shore", + "outlier_distance_km": 14521.9, + "second_furthest_km": 4682.0, + "clarity_ratio": 3.1, + "median_distance_km": 4673.2, + "distances_to_centroid": { + "Zelenogorsk": 3805.2, + "Radevormwald": 4342.5, + "Ivry-sur-Seine": 4682.0, + "Bruay-la-Buissière": 4673.2, + "North Shore": 14521.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zelenogorsk: (56.11°, 94.59°)", + " Radevormwald: (51.20°, 7.36°)", + " Ivry-sur-Seine: (48.82°, 2.38°)", + " Bruay-la-Buissière: (50.48°, 2.55°)", + " North Shore: (-36.80°, 174.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " North Shore: 14521.9 km from centroid", + " Ivry-sur-Seine: 4682.0 km from centroid", + " Bruay-la-Buissière: 4673.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: North Shore", + "FINAL ANSWER: North Shore" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.04183, + "lon": -77.21646, + "name": "Balboa" + }, + { + "lat": -32.2375, + "lon": -53.08694, + "name": "Arroio Grande" + }, + { + "lat": -23.53306, + "lon": -49.24444, + "name": "Taquarituba" + }, + { + "lat": -21.68528, + "lon": -51.0725, + "name": "Adamantina" + }, + { + "lat": 17.99913, + "lon": -94.6359, + "name": "Cosoleacaque" + } + ], + "question": "Which location is the geographic outlier among: Balboa, Arroio Grande, Taquarituba, Adamantina, Cosoleacaque?", + "ground_truth": { + "answer": "Cosoleacaque", + "outlier_distance_km": 4614.2, + "second_furthest_km": 2612.4, + "clarity_ratio": 1.77, + "median_distance_km": 2142.4, + "distances_to_centroid": { + "Balboa": 2017.5, + "Arroio Grande": 2612.4, + "Taquarituba": 2142.4, + "Adamantina": 1870.3, + "Cosoleacaque": 4614.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Balboa: (2.04°, -77.22°)", + " Arroio Grande: (-32.24°, -53.09°)", + " Taquarituba: (-23.53°, -49.24°)", + " Adamantina: (-21.69°, -51.07°)", + " Cosoleacaque: (18.00°, -94.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cosoleacaque: 4614.2 km from centroid", + " Arroio Grande: 2612.4 km from centroid", + " Taquarituba: 2142.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cosoleacaque", + "FINAL ANSWER: Cosoleacaque" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.95559, + "lon": -86.01387, + "name": "Fishers" + }, + { + "lat": 44.54394, + "lon": -73.14791, + "name": "Colchester" + }, + { + "lat": 32.64541, + "lon": -85.37828, + "name": "Opelika" + }, + { + "lat": 43.69468, + "lon": -79.26509, + "name": "Birchcliffe-Cliffside" + }, + { + "lat": 45.38193, + "lon": 9.1559, + "name": "Rozzano" + } + ], + "question": "Which location is the geographic outlier among: Fishers, Colchester, Opelika, Birchcliffe-Cliffside, Rozzano?", + "ground_truth": { + "answer": "Rozzano", + "outlier_distance_km": 5651.3, + "second_furthest_km": 2203.5, + "clarity_ratio": 2.56, + "median_distance_km": 1948.4, + "distances_to_centroid": { + "Fishers": 1948.4, + "Colchester": 908.8, + "Opelika": 2203.5, + "Birchcliffe-Cliffside": 1364.9, + "Rozzano": 5651.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fishers: (39.96°, -86.01°)", + " Colchester: (44.54°, -73.15°)", + " Opelika: (32.65°, -85.38°)", + " Birchcliffe-Cliffside: (43.69°, -79.27°)", + " Rozzano: (45.38°, 9.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rozzano: 5651.3 km from centroid", + " Opelika: 2203.5 km from centroid", + " Fishers: 1948.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rozzano", + "FINAL ANSWER: Rozzano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.46026, + "lon": 22.60952, + "name": "Lubartów" + }, + { + "lat": 47.8082, + "lon": 7.63035, + "name": "Müllheim" + }, + { + "lat": 49.95542, + "lon": 18.57479, + "name": "Jastrzębie Zdrój" + }, + { + "lat": 51.88056, + "lon": 45.00609, + "name": "Atkarsk" + }, + { + "lat": 28.45433, + "lon": 104.71498, + "name": "Xunchang" + } + ], + "question": "Which location is the geographic outlier among: Lubartów, Müllheim, Jastrzębie Zdrój, Atkarsk, Xunchang?", + "ground_truth": { + "answer": "Xunchang", + "outlier_distance_km": 5902.5, + "second_furthest_km": 2430.4, + "clarity_ratio": 2.43, + "median_distance_km": 1631.1, + "distances_to_centroid": { + "Lubartów": 1394.0, + "Müllheim": 2430.4, + "Jastrzębie Zdrój": 1631.1, + "Atkarsk": 768.0, + "Xunchang": 5902.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lubartów: (51.46°, 22.61°)", + " Müllheim: (47.81°, 7.63°)", + " Jastrzębie Zdrój: (49.96°, 18.57°)", + " Atkarsk: (51.88°, 45.01°)", + " Xunchang: (28.45°, 104.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xunchang: 5902.5 km from centroid", + " Müllheim: 2430.4 km from centroid", + " Jastrzębie Zdrój: 1631.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xunchang", + "FINAL ANSWER: Xunchang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.42827, + "lon": -121.90662, + "name": "Milpitas" + }, + { + "lat": 40.84985, + "lon": -73.86641, + "name": "The Bronx" + }, + { + "lat": 33.41421, + "lon": -111.94348, + "name": "Tempe Junction" + }, + { + "lat": 34.30778, + "lon": -118.44925, + "name": "Sylmar" + }, + { + "lat": 5.65825, + "lon": -0.25223, + "name": "Taifa" + } + ], + "question": "Which location is the geographic outlier among: Milpitas, The Bronx, Tempe Junction, Sylmar, Taifa?", + "ground_truth": { + "answer": "Taifa", + "outlier_distance_km": 9214.3, + "second_furthest_km": 3448.8, + "clarity_ratio": 2.67, + "median_distance_km": 3133.8, + "distances_to_centroid": { + "Milpitas": 3448.8, + "The Bronx": 1557.2, + "Tempe Junction": 2533.7, + "Sylmar": 3133.8, + "Taifa": 9214.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Milpitas: (37.43°, -121.91°)", + " The Bronx: (40.85°, -73.87°)", + " Tempe Junction: (33.41°, -111.94°)", + " Sylmar: (34.31°, -118.45°)", + " Taifa: (5.66°, -0.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taifa: 9214.3 km from centroid", + " Milpitas: 3448.8 km from centroid", + " Sylmar: 3133.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taifa", + "FINAL ANSWER: Taifa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.43944, + "lon": -39.14833, + "name": "Paraipaba" + }, + { + "lat": -23.76639, + "lon": -53.325, + "name": "Umuarama" + }, + { + "lat": -13.4425, + "lon": -42.23889, + "name": "Paramirim" + }, + { + "lat": -9.51656, + "lon": -77.53045, + "name": "Centenario" + }, + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + } + ], + "question": "Which location is the geographic outlier among: Paraipaba, Umuarama, Paramirim, Centenario, Malvern East?", + "ground_truth": { + "answer": "Malvern East", + "outlier_distance_km": 13448.6, + "second_furthest_km": 6956.8, + "clarity_ratio": 1.93, + "median_distance_km": 4191.6, + "distances_to_centroid": { + "Paraipaba": 3214.4, + "Umuarama": 4191.6, + "Paramirim": 3116.8, + "Centenario": 6956.8, + "Malvern East": 13448.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paraipaba: (-3.44°, -39.15°)", + " Umuarama: (-23.77°, -53.33°)", + " Paramirim: (-13.44°, -42.24°)", + " Centenario: (-9.52°, -77.53°)", + " Malvern East: (-37.87°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Malvern East: 13448.6 km from centroid", + " Centenario: 6956.8 km from centroid", + " Umuarama: 4191.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Malvern East", + "FINAL ANSWER: Malvern East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73378, + "lon": 18.97523, + "name": "Paarl" + }, + { + "lat": 6.91002, + "lon": 3.66557, + "name": "Iperu" + }, + { + "lat": 7.62329, + "lon": 5.22087, + "name": "Ado-Ekiti" + }, + { + "lat": 26.04949, + "lon": 32.24142, + "name": "Nag Hammâdi" + }, + { + "lat": 39.57916, + "lon": -104.87692, + "name": "Centennial" + } + ], + "question": "Which location is the geographic outlier among: Paarl, Iperu, Ado-Ekiti, Nag Hammâdi, Centennial?", + "ground_truth": { + "answer": "Centennial", + "outlier_distance_km": 9852.5, + "second_furthest_km": 5619.9, + "clarity_ratio": 1.75, + "median_distance_km": 4718.8, + "distances_to_centroid": { + "Paarl": 5619.9, + "Iperu": 1414.1, + "Ado-Ekiti": 1569.9, + "Nag Hammâdi": 4718.8, + "Centennial": 9852.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paarl: (-33.73°, 18.98°)", + " Iperu: (6.91°, 3.67°)", + " Ado-Ekiti: (7.62°, 5.22°)", + " Nag Hammâdi: (26.05°, 32.24°)", + " Centennial: (39.58°, -104.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Centennial: 9852.5 km from centroid", + " Paarl: 5619.9 km from centroid", + " Nag Hammâdi: 4718.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Centennial", + "FINAL ANSWER: Centennial" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.75018, + "lon": -122.43369, + "name": "Noe Valley" + }, + { + "lat": 35.68698, + "lon": -105.9378, + "name": "Santa Fe" + }, + { + "lat": 42.49999, + "lon": -96.40031, + "name": "Sioux City" + }, + { + "lat": 19.79919, + "lon": -99.875, + "name": "Atlacomulco de Fabela" + }, + { + "lat": 28.21024, + "lon": 76.86056, + "name": "Bhiwadi" + } + ], + "question": "Which location is the geographic outlier among: Noe Valley, Santa Fe, Sioux City, Atlacomulco de Fabela, Bhiwadi?", + "ground_truth": { + "answer": "Bhiwadi", + "outlier_distance_km": 12361.8, + "second_furthest_km": 4768.6, + "clarity_ratio": 2.59, + "median_distance_km": 3340.8, + "distances_to_centroid": { + "Noe Valley": 4768.6, + "Santa Fe": 3340.8, + "Sioux City": 2583.8, + "Atlacomulco de Fabela": 3333.2, + "Bhiwadi": 12361.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Noe Valley: (37.75°, -122.43°)", + " Santa Fe: (35.69°, -105.94°)", + " Sioux City: (42.50°, -96.40°)", + " Atlacomulco de Fabela: (19.80°, -99.88°)", + " Bhiwadi: (28.21°, 76.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhiwadi: 12361.8 km from centroid", + " Noe Valley: 4768.6 km from centroid", + " Santa Fe: 3340.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhiwadi", + "FINAL ANSWER: Bhiwadi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.75106, + "lon": 104.83134, + "name": "Shandan" + }, + { + "lat": 30.83424, + "lon": 76.57677, + "name": "Kūrāli" + }, + { + "lat": 21.69482, + "lon": 72.9805, + "name": "Bharūch" + }, + { + "lat": 36.75541, + "lon": 81.60765, + "name": "Arix" + }, + { + "lat": 41.44718, + "lon": -71.52494, + "name": "South Kingstown" + } + ], + "question": "Which location is the geographic outlier among: Shandan, Kūrāli, Bharūch, Arix, South Kingstown?", + "ground_truth": { + "answer": "South Kingstown", + "outlier_distance_km": 9966.1, + "second_furthest_km": 4741.3, + "clarity_ratio": 2.1, + "median_distance_km": 2639.1, + "distances_to_centroid": { + "Shandan": 4741.3, + "Kūrāli": 2243.4, + "Bharūch": 2346.8, + "Arix": 2639.1, + "South Kingstown": 9966.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shandan: (34.75°, 104.83°)", + " Kūrāli: (30.83°, 76.58°)", + " Bharūch: (21.69°, 72.98°)", + " Arix: (36.76°, 81.61°)", + " South Kingstown: (41.45°, -71.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " South Kingstown: 9966.1 km from centroid", + " Shandan: 4741.3 km from centroid", + " Arix: 2639.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: South Kingstown", + "FINAL ANSWER: South Kingstown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.24522, + "lon": 105.95663, + "name": "Linjiang" + }, + { + "lat": 24.63925, + "lon": 87.84239, + "name": "Pakur" + }, + { + "lat": 26.02401, + "lon": 75.48182, + "name": "Todaraisingh" + }, + { + "lat": 13.2563, + "lon": 76.47768, + "name": "Tiptūr" + }, + { + "lat": -26.47306, + "lon": -49.00278, + "name": "Guaramirim" + } + ], + "question": "Which location is the geographic outlier among: Linjiang, Pakur, Todaraisingh, Tiptūr, Guaramirim?", + "ground_truth": { + "answer": "Guaramirim", + "outlier_distance_km": 12471.0, + "second_furthest_km": 5103.2, + "clarity_ratio": 2.44, + "median_distance_km": 3239.4, + "distances_to_centroid": { + "Linjiang": 5103.2, + "Pakur": 3239.4, + "Todaraisingh": 2196.3, + "Tiptūr": 1853.0, + "Guaramirim": 12471.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Linjiang: (29.25°, 105.96°)", + " Pakur: (24.64°, 87.84°)", + " Todaraisingh: (26.02°, 75.48°)", + " Tiptūr: (13.26°, 76.48°)", + " Guaramirim: (-26.47°, -49.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guaramirim: 12471.0 km from centroid", + " Linjiang: 5103.2 km from centroid", + " Pakur: 3239.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guaramirim", + "FINAL ANSWER: Guaramirim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.66917, + "lon": -42.07611, + "name": "Itaocara" + }, + { + "lat": -3.74611, + "lon": -39.78333, + "name": "Irauçuba" + }, + { + "lat": -22.84333, + "lon": -47.60611, + "name": "Rio das Pedras" + }, + { + "lat": -9.56333, + "lon": -35.82444, + "name": "Satuba" + }, + { + "lat": 9.8, + "lon": 38.4, + "name": "Gebre Guracha" + } + ], + "question": "Which location is the geographic outlier among: Itaocara, Irauçuba, Rio das Pedras, Satuba, Gebre Guracha?", + "ground_truth": { + "answer": "Gebre Guracha", + "outlier_distance_km": 7379.5, + "second_furthest_km": 2786.1, + "clarity_ratio": 2.65, + "median_distance_km": 2231.7, + "distances_to_centroid": { + "Itaocara": 2231.7, + "Irauçuba": 1718.4, + "Rio das Pedras": 2786.1, + "Satuba": 1145.3, + "Gebre Guracha": 7379.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itaocara: (-21.67°, -42.08°)", + " Irauçuba: (-3.75°, -39.78°)", + " Rio das Pedras: (-22.84°, -47.61°)", + " Satuba: (-9.56°, -35.82°)", + " Gebre Guracha: (9.80°, 38.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gebre Guracha: 7379.5 km from centroid", + " Rio das Pedras: 2786.1 km from centroid", + " Itaocara: 2231.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gebre Guracha", + "FINAL ANSWER: Gebre Guracha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": 40.73566, + "lon": -74.17237, + "name": "Newark" + } + ], + "question": "Which location is the geographic outlier among: Springvale, Miranda, Wellington, Porirua, Newark?", + "ground_truth": { + "answer": "Newark", + "outlier_distance_km": 17860.3, + "second_furthest_km": 5938.1, + "clarity_ratio": 3.01, + "median_distance_km": 5932.0, + "distances_to_centroid": { + "Springvale": 3383.0, + "Miranda": 3785.2, + "Wellington": 5932.0, + "Porirua": 5938.1, + "Newark": 17860.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Springvale: (-37.95°, 145.15°)", + " Miranda: (-34.04°, 151.10°)", + " Wellington: (-41.29°, 174.78°)", + " Porirua: (-41.13°, 174.85°)", + " Newark: (40.74°, -74.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Newark: 17860.3 km from centroid", + " Porirua: 5938.1 km from centroid", + " Wellington: 5932.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Newark", + "FINAL ANSWER: Newark" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.75389, + "lon": -42.88194, + "name": "Viçosa" + }, + { + "lat": -38.93424, + "lon": -69.23052, + "name": "Cutral-Có" + }, + { + "lat": -13.55222, + "lon": -52.26833, + "name": "Canarana" + }, + { + "lat": -22.97056, + "lon": -46.99583, + "name": "Valinhos" + }, + { + "lat": 54.56759, + "lon": 100.57659, + "name": "Tulun" + } + ], + "question": "Which location is the geographic outlier among: Viçosa, Cutral-Có, Canarana, Valinhos, Tulun?", + "ground_truth": { + "answer": "Tulun", + "outlier_distance_km": 12826.9, + "second_furthest_km": 5785.5, + "clarity_ratio": 2.22, + "median_distance_km": 3335.3, + "distances_to_centroid": { + "Vi��osa": 2618.5, + "Cutral-Có": 5785.5, + "Canarana": 3335.3, + "Valinhos": 3109.1, + "Tulun": 12826.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viçosa: (-20.75°, -42.88°)", + " Cutral-Có: (-38.93°, -69.23°)", + " Canarana: (-13.55°, -52.27°)", + " Valinhos: (-22.97°, -47.00°)", + " Tulun: (54.57°, 100.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tulun: 12826.9 km from centroid", + " Cutral-Có: 5785.5 km from centroid", + " Canarana: 3335.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tulun", + "FINAL ANSWER: Tulun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88374, + "lon": 151.21282, + "name": "Surry Hills" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": 50.39431, + "lon": -3.51585, + "name": "Brixham" + } + ], + "question": "Which location is the geographic outlier among: Surry Hills, Baldivis, Mangere East, Hobart, Brixham?", + "ground_truth": { + "answer": "Brixham", + "outlier_distance_km": 13791.1, + "second_furthest_km": 5903.1, + "clarity_ratio": 2.34, + "median_distance_km": 3866.6, + "distances_to_centroid": { + "Surry Hills": 3742.5, + "Baldivis": 1473.1, + "Mangere East": 5903.1, + "Hobart": 3866.6, + "Brixham": 13791.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Surry Hills: (-33.88°, 151.21°)", + " Baldivis: (-32.33°, 115.83°)", + " Mangere East: (-36.97°, 174.82°)", + " Hobart: (-42.88°, 147.33°)", + " Brixham: (50.39°, -3.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brixham: 13791.1 km from centroid", + " Mangere East: 5903.1 km from centroid", + " Hobart: 3866.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brixham", + "FINAL ANSWER: Brixham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": -27.20338, + "lon": 152.95923, + "name": "Narangba" + }, + { + "lat": 18.79284, + "lon": 78.27666, + "name": "Āmūr" + } + ], + "question": "Which location is the geographic outlier among: Ashfield, Wainuiomata, Dunedin, Narangba, Āmūr?", + "ground_truth": { + "answer": "Āmūr", + "outlier_distance_km": 8801.2, + "second_furthest_km": 3190.9, + "clarity_ratio": 2.76, + "median_distance_km": 3134.9, + "distances_to_centroid": { + "Ashfield": 1038.1, + "Wainuiomata": 3190.9, + "Dunedin": 3134.9, + "Narangba": 750.0, + "Āmūr": 8801.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ashfield: (-33.89°, 151.12°)", + " Wainuiomata: (-41.27°, 174.95°)", + " Dunedin: (-45.87°, 170.50°)", + " Narangba: (-27.20°, 152.96°)", + " Āmūr: (18.79°, 78.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Āmūr: 8801.2 km from centroid", + " Wainuiomata: 3190.9 km from centroid", + " Dunedin: 3134.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Āmūr", + "FINAL ANSWER: Āmūr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": -19.30323, + "lon": 146.72531, + "name": "Kirwan" + }, + { + "lat": 9.04439, + "lon": 6.57089, + "name": "Lapai" + } + ], + "question": "Which location is the geographic outlier among: Ashburton, Mandurah, Campsie, Kirwan, Lapai?", + "ground_truth": { + "answer": "Lapai", + "outlier_distance_km": 12622.1, + "second_furthest_km": 5279.7, + "clarity_ratio": 2.39, + "median_distance_km": 3347.0, + "distances_to_centroid": { + "Ashburton": 5279.7, + "Mandurah": 970.0, + "Campsie": 3347.0, + "Kirwan": 2972.5, + "Lapai": 12622.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ashburton: (-43.90°, 171.73°)", + " Mandurah: (-32.53°, 115.72°)", + " Campsie: (-33.91°, 151.10°)", + " Kirwan: (-19.30°, 146.73°)", + " Lapai: (9.04°, 6.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lapai: 12622.1 km from centroid", + " Ashburton: 5279.7 km from centroid", + " Campsie: 3347.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lapai", + "FINAL ANSWER: Lapai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.61972, + "lon": 31.2575, + "name": "Al ‘Ayyāţ" + }, + { + "lat": -28.88649, + "lon": 31.4699, + "name": "Eshowe" + }, + { + "lat": 10.17506, + "lon": 11.16458, + "name": "Garko" + }, + { + "lat": 7.67344, + "lon": 36.83441, + "name": "Jimma" + }, + { + "lat": 38.98223, + "lon": -94.67079, + "name": "Overland Park" + } + ], + "question": "Which location is the geographic outlier among: Al ‘Ayyāţ, Eshowe, Garko, Jimma, Overland Park?", + "ground_truth": { + "answer": "Overland Park", + "outlier_distance_km": 9873.1, + "second_furthest_km": 5421.2, + "clarity_ratio": 1.82, + "median_distance_km": 3708.8, + "distances_to_centroid": { + "Al ‘Ayyāţ": 3529.3, + "Eshowe": 5421.2, + "Garko": 881.2, + "Jimma": 3708.8, + "Overland Park": 9873.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al ‘Ayyāţ: (29.62°, 31.26°)", + " Eshowe: (-28.89°, 31.47°)", + " Garko: (10.18°, 11.16°)", + " Jimma: (7.67°, 36.83°)", + " Overland Park: (38.98°, -94.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Overland Park: 9873.1 km from centroid", + " Eshowe: 5421.2 km from centroid", + " Jimma: 3708.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Overland Park", + "FINAL ANSWER: Overland Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.81705, + "lon": 0.54518, + "name": "Châtellerault" + }, + { + "lat": 50.6, + "lon": 6.3, + "name": "Simmerath" + }, + { + "lat": 48.94754, + "lon": 8.83675, + "name": "Mühlacker" + }, + { + "lat": 51.48363, + "lon": -0.37577, + "name": "Heston" + }, + { + "lat": 25.78976, + "lon": 84.63596, + "name": "Revelganj" + } + ], + "question": "Which location is the geographic outlier among: Châtellerault, Simmerath, Mühlacker, Heston, Revelganj?", + "ground_truth": { + "answer": "Revelganj", + "outlier_distance_km": 6065.0, + "second_furthest_km": 1680.7, + "clarity_ratio": 3.61, + "median_distance_km": 1521.8, + "distances_to_centroid": { + "Châtellerault": 1521.8, + "Simmerath": 1212.5, + "Mühlacker": 968.0, + "Heston": 1680.7, + "Revelganj": 6065.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Châtellerault: (46.82°, 0.55°)", + " Simmerath: (50.60°, 6.30°)", + " Mühlacker: (48.95°, 8.84°)", + " Heston: (51.48°, -0.38°)", + " Revelganj: (25.79°, 84.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Revelganj: 6065.0 km from centroid", + " Heston: 1680.7 km from centroid", + " Châtellerault: 1521.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Revelganj", + "FINAL ANSWER: Revelganj" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.5657, + "lon": 2.50621, + "name": "Calvià" + }, + { + "lat": 45.61278, + "lon": 5.15058, + "name": "Villefontaine" + }, + { + "lat": 40.87822, + "lon": 14.14352, + "name": "Quarto" + }, + { + "lat": 51.20148, + "lon": 11.96843, + "name": "Weißenfels" + }, + { + "lat": 34.80472, + "lon": 105.57778, + "name": "Qianhu" + } + ], + "question": "Which location is the geographic outlier among: Calvià, Villefontaine, Quarto, Weißenfels, Qianhu?", + "ground_truth": { + "answer": "Qianhu", + "outlier_distance_km": 6568.0, + "second_furthest_km": 2144.0, + "clarity_ratio": 3.06, + "median_distance_km": 1844.8, + "distances_to_centroid": { + "Calvià": 2144.0, + "Villefontaine": 1844.8, + "Quarto": 1151.9, + "Weißenfels": 1549.8, + "Qianhu": 6568.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Calvià: (39.57°, 2.51°)", + " Villefontaine: (45.61°, 5.15°)", + " Quarto: (40.88°, 14.14°)", + " Weißenfels: (51.20°, 11.97°)", + " Qianhu: (34.80°, 105.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qianhu: 6568.0 km from centroid", + " Calvià: 2144.0 km from centroid", + " Villefontaine: 1844.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qianhu", + "FINAL ANSWER: Qianhu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -38.14458, + "lon": 145.12291, + "name": "Frankston" + }, + { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": 44.9133, + "lon": -93.50329, + "name": "Minnetonka" + } + ], + "question": "Which location is the geographic outlier among: Ashfield, Frankston, Dianella, Porirua, Minnetonka?", + "ground_truth": { + "answer": "Minnetonka", + "outlier_distance_km": 17028.7, + "second_furthest_km": 7423.3, + "clarity_ratio": 2.29, + "median_distance_km": 5359.8, + "distances_to_centroid": { + "Ashfield": 5359.8, + "Frankston": 4879.1, + "Dianella": 2160.2, + "Porirua": 7423.3, + "Minnetonka": 17028.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ashfield: (-33.89°, 151.12°)", + " Frankston: (-38.14°, 145.12°)", + " Dianella: (-31.89°, 115.87°)", + " Porirua: (-41.13°, 174.85°)", + " Minnetonka: (44.91°, -93.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Minnetonka: 17028.7 km from centroid", + " Porirua: 7423.3 km from centroid", + " Ashfield: 5359.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Minnetonka", + "FINAL ANSWER: Minnetonka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + { + "lat": -37.78828, + "lon": 145.12373, + "name": "Doncaster" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -13.03667, + "lon": -46.77167, + "name": "Campos Belos" + } + ], + "question": "Which location is the geographic outlier among: Papatoetoe, Doncaster, Mount Martha, Mandurah, Campos Belos?", + "ground_truth": { + "answer": "Campos Belos", + "outlier_distance_km": 14296.1, + "second_furthest_km": 6142.2, + "clarity_ratio": 2.33, + "median_distance_km": 3541.5, + "distances_to_centroid": { + "Papatoetoe": 6142.2, + "Doncaster": 3541.5, + "Mount Martha": 3531.9, + "Mandurah": 846.0, + "Campos Belos": 14296.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Papatoetoe: (-36.97°, 174.84°)", + " Doncaster: (-37.79°, 145.12°)", + " Mount Martha: (-38.27°, 145.02°)", + " Mandurah: (-32.53°, 115.72°)", + " Campos Belos: (-13.04°, -46.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Campos Belos: 14296.1 km from centroid", + " Papatoetoe: 6142.2 km from centroid", + " Doncaster: 3541.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Campos Belos", + "FINAL ANSWER: Campos Belos" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.2163, + "lon": 34.11074, + "name": "Ash Shaykh Zuwayd" + }, + { + "lat": 4.73614, + "lon": 6.86236, + "name": "Buguma" + }, + { + "lat": 14.10307, + "lon": 38.28289, + "name": "Inda Silasē" + }, + { + "lat": 30.42039, + "lon": 31.56223, + "name": "Bilbeis" + }, + { + "lat": -15.675, + "lon": -38.94722, + "name": "Canavieiras" + } + ], + "question": "Which location is the geographic outlier among: Ash Shaykh Zuwayd, Buguma, Inda Silasē, Bilbeis, Canavieiras?", + "ground_truth": { + "answer": "Canavieiras", + "outlier_distance_km": 6672.7, + "second_furthest_km": 2863.2, + "clarity_ratio": 2.33, + "median_distance_km": 2623.7, + "distances_to_centroid": { + "Ash Shaykh Zuwayd": 2863.2, + "Buguma": 1231.3, + "Inda Silasē": 2586.8, + "Bilbeis": 2623.7, + "Canavieiras": 6672.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ash Shaykh Zuwayd: (31.22°, 34.11°)", + " Buguma: (4.74°, 6.86°)", + " Inda Silasē: (14.10°, 38.28°)", + " Bilbeis: (30.42°, 31.56°)", + " Canavieiras: (-15.68°, -38.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Canavieiras: 6672.7 km from centroid", + " Ash Shaykh Zuwayd: 2863.2 km from centroid", + " Bilbeis: 2623.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Canavieiras", + "FINAL ANSWER: Canavieiras" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.24889, + "lon": 119.62417, + "name": "Chaigou" + }, + { + "lat": 30.31097, + "lon": 78.08979, + "name": "Rāipur" + }, + { + "lat": 14.2906, + "lon": 122.6917, + "name": "Jose Pañganiban" + }, + { + "lat": 20.9013, + "lon": 74.77737, + "name": "Dhule" + }, + { + "lat": -0.72889, + "lon": -47.84806, + "name": "Curuçá" + } + ], + "question": "Which location is the geographic outlier among: Chaigou, Rāipur, Jose Pañganiban, Dhule, Curuçá?", + "ground_truth": { + "answer": "Curuçá", + "outlier_distance_km": 12874.8, + "second_furthest_km": 5667.8, + "clarity_ratio": 2.27, + "median_distance_km": 5164.0, + "distances_to_centroid": { + "Chaigou": 5164.0, + "Rāipur": 1418.2, + "Jose Pañganiban": 5667.8, + "Dhule": 558.3, + "Curuçá": 12874.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chaigou: (36.25°, 119.62°)", + " Rāipur: (30.31°, 78.09°)", + " Jose Pañganiban: (14.29°, 122.69°)", + " Dhule: (20.90°, 74.78°)", + " Curuçá: (-0.73°, -47.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Curuçá: 12874.8 km from centroid", + " Jose Pañganiban: 5667.8 km from centroid", + " Chaigou: 5164.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Curuçá", + "FINAL ANSWER: Curuçá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.14612, + "lon": -82.75677, + "name": "Tarpon Springs" + }, + { + "lat": 33.95015, + "lon": -118.03917, + "name": "South Whittier" + }, + { + "lat": 39.09928, + "lon": -76.84831, + "name": "Laurel" + }, + { + "lat": 42.58342, + "lon": -71.8023, + "name": "Fitchburg" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + } + ], + "question": "Which location is the geographic outlier among: Tarpon Springs, South Whittier, Laurel, Fitchburg, Pacific Pines?", + "ground_truth": { + "answer": "Pacific Pines", + "outlier_distance_km": 18650.7, + "second_furthest_km": 7608.8, + "clarity_ratio": 2.45, + "median_distance_km": 4375.3, + "distances_to_centroid": { + "Tarpon Springs": 4375.3, + "South Whittier": 7608.8, + "Laurel": 3957.1, + "Fitchburg": 3693.1, + "Pacific Pines": 18650.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tarpon Springs: (28.15°, -82.76°)", + " South Whittier: (33.95°, -118.04°)", + " Laurel: (39.10°, -76.85°)", + " Fitchburg: (42.58°, -71.80°)", + " Pacific Pines: (-27.94°, 153.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pacific Pines: 18650.7 km from centroid", + " South Whittier: 7608.8 km from centroid", + " Tarpon Springs: 4375.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pacific Pines", + "FINAL ANSWER: Pacific Pines" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.73028, + "lon": -40.55528, + "name": "Piritiba" + }, + { + "lat": -3.22083, + "lon": -64.80417, + "name": "Alvarães" + }, + { + "lat": -11.01611, + "lon": -68.74806, + "name": "Brasiléia" + }, + { + "lat": -11.80361, + "lon": -61.80333, + "name": "Rolim de Moura" + }, + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + } + ], + "question": "Which location is the geographic outlier among: Piritiba, Alvarães, Brasiléia, Rolim de Moura, Robina?", + "ground_truth": { + "answer": "Robina", + "outlier_distance_km": 15302.2, + "second_furthest_km": 5675.7, + "clarity_ratio": 2.7, + "median_distance_km": 5419.4, + "distances_to_centroid": { + "Piritiba": 2615.5, + "Alvarães": 5419.4, + "Brasiléia": 5675.7, + "Rolim de Moura": 4913.8, + "Robina": 15302.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piritiba: (-11.73°, -40.56°)", + " Alvarães: (-3.22°, -64.80°)", + " Brasiléia: (-11.02°, -68.75°)", + " Rolim de Moura: (-11.80°, -61.80°)", + " Robina: (-28.07°, 153.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Robina: 15302.2 km from centroid", + " Brasiléia: 5675.7 km from centroid", + " Alvarães: 5419.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Robina", + "FINAL ANSWER: Robina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.8282, + "lon": 174.62019, + "name": "Massey East" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": -35.28346, + "lon": 149.12807, + "name": "Canberra" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": 43.90012, + "lon": -79.13289, + "name": "Pickering" + } + ], + "question": "Which location is the geographic outlier among: Massey East, South Morang, Canberra, Maroubra, Pickering?", + "ground_truth": { + "answer": "Pickering", + "outlier_distance_km": 17267.9, + "second_furthest_km": 6631.3, + "clarity_ratio": 2.6, + "median_distance_km": 4502.6, + "distances_to_centroid": { + "Massey East": 6631.3, + "South Morang": 4061.6, + "Canberra": 4340.1, + "Maroubra": 4502.6, + "Pickering": 17267.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Massey East: (-36.83°, 174.62°)", + " South Morang: (-37.65°, 145.10°)", + " Canberra: (-35.28°, 149.13°)", + " Maroubra: (-33.95°, 151.23°)", + " Pickering: (43.90°, -79.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pickering: 17267.9 km from centroid", + " Massey East: 6631.3 km from centroid", + " Maroubra: 4502.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pickering", + "FINAL ANSWER: Pickering" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.22323, + "lon": -85.39049, + "name": "Dothan" + }, + { + "lat": 26.90687, + "lon": -101.42056, + "name": "Monclova" + }, + { + "lat": 28.01769, + "lon": -82.50619, + "name": "Egypt Lake-Leto" + }, + { + "lat": 19.66194, + "lon": -99.06889, + "name": "Alborada Jaltenco" + }, + { + "lat": 28.75815, + "lon": 77.13087, + "name": "Siraspur" + } + ], + "question": "Which location is the geographic outlier among: Dothan, Monclova, Egypt Lake-Leto, Alborada Jaltenco, Siraspur?", + "ground_truth": { + "answer": "Siraspur", + "outlier_distance_km": 12208.6, + "second_furthest_km": 4258.8, + "clarity_ratio": 2.87, + "median_distance_km": 4227.8, + "distances_to_centroid": { + "Dothan": 2673.8, + "Monclova": 4258.8, + "Egypt Lake-Leto": 2392.3, + "Alborada Jaltenco": 4227.8, + "Siraspur": 12208.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dothan: (31.22°, -85.39°)", + " Monclova: (26.91°, -101.42°)", + " Egypt Lake-Leto: (28.02°, -82.51°)", + " Alborada Jaltenco: (19.66°, -99.07°)", + " Siraspur: (28.76°, 77.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Siraspur: 12208.6 km from centroid", + " Monclova: 4258.8 km from centroid", + " Alborada Jaltenco: 4227.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Siraspur", + "FINAL ANSWER: Siraspur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -33.79728, + "lon": 150.7847, + "name": "St Clair" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -28.66449, + "lon": 27.43048, + "name": "Marquard" + } + ], + "question": "Which location is the geographic outlier among: Highton, Seven Hills, St Clair, Ashburton, Marquard?", + "ground_truth": { + "answer": "Marquard", + "outlier_distance_km": 9137.0, + "second_furthest_km": 3717.3, + "clarity_ratio": 2.46, + "median_distance_km": 2007.8, + "distances_to_centroid": { + "Highton": 1384.5, + "Seven Hills": 2007.8, + "St Clair": 1994.0, + "Ashburton": 3717.3, + "Marquard": 9137.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Highton: (-38.17°, 144.31°)", + " Seven Hills: (-33.78°, 150.93°)", + " St Clair: (-33.80°, 150.78°)", + " Ashburton: (-43.90°, 171.73°)", + " Marquard: (-28.66°, 27.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marquard: 9137.0 km from centroid", + " Ashburton: 3717.3 km from centroid", + " Seven Hills: 2007.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marquard", + "FINAL ANSWER: Marquard" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.36737, + "lon": -70.33219, + "name": "Copiapó" + }, + { + "lat": -8.33556, + "lon": -36.42417, + "name": "Belo Jardim" + }, + { + "lat": -7.62759, + "lon": -72.67756, + "name": "Cruzeiro do Sul" + }, + { + "lat": -10.26389, + "lon": -40.19583, + "name": "Jaguarari" + }, + { + "lat": 53.86828, + "lon": 8.69902, + "name": "Cuxhaven" + } + ], + "question": "Which location is the geographic outlier among: Copiapó, Belo Jardim, Cruzeiro do Sul, Jaguarari, Cuxhaven?", + "ground_truth": { + "answer": "Cuxhaven", + "outlier_distance_km": 7573.9, + "second_furthest_km": 4280.9, + "clarity_ratio": 1.77, + "median_distance_km": 3486.6, + "distances_to_centroid": { + "Copiapó": 4280.9, + "Belo Jardim": 1130.5, + "Cruzeiro do Sul": 3486.6, + "Jaguarari": 1168.3, + "Cuxhaven": 7573.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Copiapó: (-27.37°, -70.33°)", + " Belo Jardim: (-8.34°, -36.42°)", + " Cruzeiro do Sul: (-7.63°, -72.68°)", + " Jaguarari: (-10.26°, -40.20°)", + " Cuxhaven: (53.87°, 8.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cuxhaven: 7573.9 km from centroid", + " Copiapó: 4280.9 km from centroid", + " Cruzeiro do Sul: 3486.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cuxhaven", + "FINAL ANSWER: Cuxhaven" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.52917, + "lon": -47.13528, + "name": "São Roque" + }, + { + "lat": 4.86242, + "lon": -74.90977, + "name": "Lérida" + }, + { + "lat": -20.97194, + "lon": -46.11889, + "name": "Carmo do Rio Claro" + }, + { + "lat": -10.99806, + "lon": -37.31056, + "name": "Itaporanga d'Ajuda" + }, + { + "lat": 53.25741, + "lon": -1.90982, + "name": "Buxton" + } + ], + "question": "Which location is the geographic outlier among: São Roque, Lérida, Carmo do Rio Claro, Itaporanga d'Ajuda, Buxton?", + "ground_truth": { + "answer": "Buxton", + "outlier_distance_km": 6901.3, + "second_furthest_km": 3743.7, + "clarity_ratio": 1.84, + "median_distance_km": 2743.6, + "distances_to_centroid": { + "São Roque": 2743.6, + "Lérida": 3743.7, + "Carmo do Rio Claro": 2443.0, + "Itaporanga d'Ajuda": 1361.5, + "Buxton": 6901.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Roque: (-23.53°, -47.14°)", + " Lérida: (4.86°, -74.91°)", + " Carmo do Rio Claro: (-20.97°, -46.12°)", + " Itaporanga d'Ajuda: (-11.00°, -37.31°)", + " Buxton: (53.26°, -1.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Buxton: 6901.3 km from centroid", + " Lérida: 3743.7 km from centroid", + " São Roque: 2743.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Buxton", + "FINAL ANSWER: Buxton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.77271, + "lon": 151.08184, + "name": "Epping" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + { + "lat": 19.2588, + "lon": 76.43412, + "name": "Pāthri" + } + ], + "question": "Which location is the geographic outlier among: Epping, North Melbourne, Lidcombe, Orange, Pāthri?", + "ground_truth": { + "answer": "Pāthri", + "outlier_distance_km": 7914.1, + "second_furthest_km": 1949.4, + "clarity_ratio": 4.06, + "median_distance_km": 1947.6, + "distances_to_centroid": { + "Epping": 1947.6, + "North Melbourne": 1835.9, + "Lidcombe": 1949.4, + "Orange": 1762.4, + "Pāthri": 7914.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epping: (-33.77°, 151.08°)", + " North Melbourne: (-37.80°, 144.95°)", + " Lidcombe: (-33.86°, 151.04°)", + " Orange: (-33.28°, 149.10°)", + " Pāthri: (19.26°, 76.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pāthri: 7914.1 km from centroid", + " Lidcombe: 1949.4 km from centroid", + " Epping: 1947.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pāthri", + "FINAL ANSWER: Pāthri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + }, + { + "lat": -37.73333, + "lon": 145.15, + "name": "Eltham" + }, + { + "lat": 50.72391, + "lon": 3.16117, + "name": "Tourcoing" + } + ], + "question": "Which location is the geographic outlier among: Ellenbrook, Townsville, Southbank, Eltham, Tourcoing?", + "ground_truth": { + "answer": "Tourcoing", + "outlier_distance_km": 12573.2, + "second_furthest_km": 4169.0, + "clarity_ratio": 3.02, + "median_distance_km": 4159.2, + "distances_to_centroid": { + "Ellenbrook": 1907.3, + "Townsville": 3801.4, + "Southbank": 4159.2, + "Eltham": 4169.0, + "Tourcoing": 12573.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ellenbrook: (-31.77°, 115.97°)", + " Townsville: (-19.27°, 146.81°)", + " Southbank: (-37.82°, 144.96°)", + " Eltham: (-37.73°, 145.15°)", + " Tourcoing: (50.72°, 3.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tourcoing: 12573.2 km from centroid", + " Eltham: 4169.0 km from centroid", + " Southbank: 4159.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tourcoing", + "FINAL ANSWER: Tourcoing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.69995, + "lon": -111.81049, + "name": "East Millcreek" + }, + { + "lat": 41.08871, + "lon": -74.14376, + "name": "Mahwah" + }, + { + "lat": 38.89511, + "lon": -77.03637, + "name": "Washington" + }, + { + "lat": 33.99084, + "lon": -118.46008, + "name": "Venice" + }, + { + "lat": 37.40202, + "lon": -6.03314, + "name": "Camas" + } + ], + "question": "Which location is the geographic outlier among: East Millcreek, Mahwah, Washington, Venice, Camas?", + "ground_truth": { + "answer": "Camas", + "outlier_distance_km": 6102.4, + "second_furthest_km": 3678.0, + "clarity_ratio": 1.66, + "median_distance_km": 2933.9, + "distances_to_centroid": { + "East Millcreek": 2933.9, + "Mahwah": 412.9, + "Washington": 66.7, + "Venice": 3678.0, + "Camas": 6102.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " East Millcreek: (40.70°, -111.81°)", + " Mahwah: (41.09°, -74.14°)", + " Washington: (38.90°, -77.04°)", + " Venice: (33.99°, -118.46°)", + " Camas: (37.40°, -6.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camas: 6102.4 km from centroid", + " Venice: 3678.0 km from centroid", + " East Millcreek: 2933.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camas", + "FINAL ANSWER: Camas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.22834, + "lon": -2.32211, + "name": "Frome" + }, + { + "lat": 48.39029, + "lon": -4.48628, + "name": "Brest" + }, + { + "lat": 50.96643, + "lon": -1.32832, + "name": "Bishopstoke" + }, + { + "lat": 52.28927, + "lon": -0.60184, + "name": "Rushden" + }, + { + "lat": -18.71056, + "lon": -40.40056, + "name": "Nova Venécia" + } + ], + "question": "Which location is the geographic outlier among: Frome, Brest, Bishopstoke, Rushden, Nova Venécia?", + "ground_truth": { + "answer": "Nova Venécia", + "outlier_distance_km": 6959.4, + "second_furthest_km": 1864.1, + "clarity_ratio": 3.73, + "median_distance_km": 1710.1, + "distances_to_centroid": { + "Frome": 1707.3, + "Brest": 1356.6, + "Bishopstoke": 1710.1, + "Rushden": 1864.1, + "Nova Venécia": 6959.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frome: (51.23°, -2.32°)", + " Brest: (48.39°, -4.49°)", + " Bishopstoke: (50.97°, -1.33°)", + " Rushden: (52.29°, -0.60°)", + " Nova Venécia: (-18.71°, -40.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nova Venécia: 6959.4 km from centroid", + " Rushden: 1864.1 km from centroid", + " Bishopstoke: 1710.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nova Venécia", + "FINAL ANSWER: Nova Venécia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87552, + "lon": -67.79451, + "name": "Catriel" + }, + { + "lat": -23.54771, + "lon": -46.63145, + "name": "Se" + }, + { + "lat": -21.8025, + "lon": -49.61, + "name": "Cafelândia" + }, + { + "lat": -1.9175, + "lon": -55.51806, + "name": "Óbidos" + }, + { + "lat": 17.61577, + "lon": 121.72285, + "name": "Tuguegarao" + } + ], + "question": "Which location is the geographic outlier among: Catriel, Se, Cafelândia, Óbidos, Tuguegarao?", + "ground_truth": { + "answer": "Tuguegarao", + "outlier_distance_km": 15850.3, + "second_furthest_km": 5460.2, + "clarity_ratio": 2.9, + "median_distance_km": 4157.8, + "distances_to_centroid": { + "Catriel": 5460.2, + "Se": 3057.1, + "Cafelândia": 3307.6, + "Óbidos": 4157.8, + "Tuguegarao": 15850.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Catriel: (-37.88°, -67.79°)", + " Se: (-23.55°, -46.63°)", + " Cafelândia: (-21.80°, -49.61°)", + " Óbidos: (-1.92°, -55.52°)", + " Tuguegarao: (17.62°, 121.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tuguegarao: 15850.3 km from centroid", + " Catriel: 5460.2 km from centroid", + " Óbidos: 4157.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tuguegarao", + "FINAL ANSWER: Tuguegarao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + { + "lat": -37.8, + "lon": 145.28333, + "name": "Croydon" + }, + { + "lat": -37.74981, + "lon": 144.9109, + "name": "Essendon" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + { + "lat": 7.27386, + "lon": -2.87348, + "name": "Domaa-Ahenkro" + } + ], + "question": "Which location is the geographic outlier among: Papatoetoe, Croydon, Essendon, Cabramatta, Domaa-Ahenkro?", + "ground_truth": { + "answer": "Domaa-Ahenkro", + "outlier_distance_km": 13859.4, + "second_furthest_km": 4945.1, + "clarity_ratio": 2.8, + "median_distance_km": 2776.0, + "distances_to_centroid": { + "Papatoetoe": 4945.1, + "Croydon": 2381.7, + "Essendon": 2349.2, + "Cabramatta": 2776.0, + "Domaa-Ahenkro": 13859.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Papatoetoe: (-36.97°, 174.84°)", + " Croydon: (-37.80°, 145.28°)", + " Essendon: (-37.75°, 144.91°)", + " Cabramatta: (-33.90°, 150.93°)", + " Domaa-Ahenkro: (7.27°, -2.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Domaa-Ahenkro: 13859.4 km from centroid", + " Papatoetoe: 4945.1 km from centroid", + " Cabramatta: 2776.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Domaa-Ahenkro", + "FINAL ANSWER: Domaa-Ahenkro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.05354, + "lon": -77.09802, + "name": "Carmen De La Legua Reynoso" + }, + { + "lat": -28.4602, + "lon": -62.83354, + "name": "Añatuya" + }, + { + "lat": -23.49696, + "lon": -46.52045, + "name": "Cangaiba" + }, + { + "lat": -29.35622, + "lon": -50.81357, + "name": "Canela" + }, + { + "lat": 25.66705, + "lon": -80.30811, + "name": "Pinecrest" + } + ], + "question": "Which location is the geographic outlier among: Carmen De La Legua Reynoso, Añatuya, Cangaiba, Canela, Pinecrest?", + "ground_truth": { + "answer": "Pinecrest", + "outlier_distance_km": 4723.7, + "second_furthest_km": 2191.8, + "clarity_ratio": 2.16, + "median_distance_km": 2103.2, + "distances_to_centroid": { + "Carmen De La Legua Reynoso": 1481.9, + "Añatuya": 1660.5, + "Cangaiba": 2103.2, + "Canela": 2191.8, + "Pinecrest": 4723.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carmen De La Legua Reynoso: (-12.05°, -77.10°)", + " Añatuya: (-28.46°, -62.83°)", + " Cangaiba: (-23.50°, -46.52°)", + " Canela: (-29.36°, -50.81°)", + " Pinecrest: (25.67°, -80.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pinecrest: 4723.7 km from centroid", + " Canela: 2191.8 km from centroid", + " Cangaiba: 2103.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pinecrest", + "FINAL ANSWER: Pinecrest" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.67323, + "lon": 7.19, + "name": "Saint-Laurent-du-Var" + }, + { + "lat": 55.45978, + "lon": 38.44358, + "name": "Beloozyorskiy" + }, + { + "lat": 52.49376, + "lon": 13.44469, + "name": "Treptow" + }, + { + "lat": 52.25973, + "lon": 43.78678, + "name": "Rtishchevo" + }, + { + "lat": 21.92485, + "lon": 78.12786, + "name": "Amla" + } + ], + "question": "Which location is the geographic outlier among: Saint-Laurent-du-Var, Beloozyorskiy, Treptow, Rtishchevo, Amla?", + "ground_truth": { + "answer": "Amla", + "outlier_distance_km": 4591.0, + "second_furthest_km": 2297.4, + "clarity_ratio": 2.0, + "median_distance_km": 1843.8, + "distances_to_centroid": { + "Saint-Laurent-du-Var": 2297.4, + "Beloozyorskiy": 1155.9, + "Treptow": 1843.8, + "Rtishchevo": 964.7, + "Amla": 4591.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint-Laurent-du-Var: (43.67°, 7.19°)", + " Beloozyorskiy: (55.46°, 38.44°)", + " Treptow: (52.49°, 13.44°)", + " Rtishchevo: (52.26°, 43.79°)", + " Amla: (21.92°, 78.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amla: 4591.0 km from centroid", + " Saint-Laurent-du-Var: 2297.4 km from centroid", + " Treptow: 1843.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amla", + "FINAL ANSWER: Amla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.9701, + "lon": -84.22159, + "name": "Peachtree Corners" + }, + { + "lat": 38.75095, + "lon": -77.47527, + "name": "Manassas" + }, + { + "lat": 40.86815, + "lon": -73.42568, + "name": "Huntington" + }, + { + "lat": 40.68038, + "lon": -73.45512, + "name": "Massapequa Park" + }, + { + "lat": 31.20864, + "lon": 31.63528, + "name": "Az Zarqā" + } + ], + "question": "Which location is the geographic outlier among: Peachtree Corners, Manassas, Huntington, Massapequa Park, Az Zarqā?", + "ground_truth": { + "answer": "Az Zarqā", + "outlier_distance_km": 7743.4, + "second_furthest_km": 2621.9, + "clarity_ratio": 2.95, + "median_distance_km": 1941.3, + "distances_to_centroid": { + "Peachtree Corners": 2621.9, + "Manassas": 1941.3, + "Huntington": 1611.2, + "Massapequa Park": 1610.5, + "Az Zarqā": 7743.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Peachtree Corners: (33.97°, -84.22°)", + " Manassas: (38.75°, -77.48°)", + " Huntington: (40.87°, -73.43°)", + " Massapequa Park: (40.68°, -73.46°)", + " Az Zarqā: (31.21°, 31.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Az Zarqā: 7743.4 km from centroid", + " Peachtree Corners: 2621.9 km from centroid", + " Manassas: 1941.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Az Zarqā", + "FINAL ANSWER: Az Zarqā" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.2, + "lon": 174.95, + "name": "Pukekohe East" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -37.6, + "lon": 144.95, + "name": "Craigieburn" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": 51.925, + "lon": 6.58056, + "name": "Aalten" + } + ], + "question": "Which location is the geographic outlier among: Pukekohe East, Balwyn North, Craigieburn, Wollongong, Aalten?", + "ground_truth": { + "answer": "Aalten", + "outlier_distance_km": 13562.3, + "second_furthest_km": 5274.2, + "clarity_ratio": 2.57, + "median_distance_km": 3116.3, + "distances_to_centroid": { + "Pukekohe East": 5274.2, + "Balwyn North": 2887.6, + "Craigieburn": 2864.2, + "Wollongong": 3116.3, + "Aalten": 13562.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pukekohe East: (-37.20°, 174.95°)", + " Balwyn North: (-37.79°, 145.09°)", + " Craigieburn: (-37.60°, 144.95°)", + " Wollongong: (-34.42°, 150.89°)", + " Aalten: (51.92°, 6.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aalten: 13562.3 km from centroid", + " Pukekohe East: 5274.2 km from centroid", + " Wollongong: 3116.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aalten", + "FINAL ANSWER: Aalten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.05278, + "lon": -49.68833, + "name": "José Bonifácio" + }, + { + "lat": -16.10971, + "lon": -47.93261, + "name": "Cidade Ocidental" + }, + { + "lat": -20.26389, + "lon": -40.42, + "name": "Cariacica" + }, + { + "lat": -14.66429, + "lon": -52.35859, + "name": "Nova Xavantina" + }, + { + "lat": 55.80202, + "lon": 37.67159, + "name": "Sokol’niki" + } + ], + "question": "Which location is the geographic outlier among: José Bonifácio, Cidade Ocidental, Cariacica, Nova Xavantina, Sokol’niki?", + "ground_truth": { + "answer": "Sokol’niki", + "outlier_distance_km": 8975.8, + "second_furthest_km": 2864.2, + "clarity_ratio": 3.13, + "median_distance_km": 2706.8, + "distances_to_centroid": { + "José Bonifácio": 2864.2, + "Cidade Ocidental": 2378.4, + "Cariacica": 2172.9, + "Nova Xavantina": 2706.8, + "Sokol’niki": 8975.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " José Bonifácio: (-21.05°, -49.69°)", + " Cidade Ocidental: (-16.11°, -47.93°)", + " Cariacica: (-20.26°, -40.42°)", + " Nova Xavantina: (-14.66°, -52.36°)", + " Sokol’niki: (55.80°, 37.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sokol’niki: 8975.8 km from centroid", + " José Bonifácio: 2864.2 km from centroid", + " Nova Xavantina: 2706.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sokol’niki", + "FINAL ANSWER: Sokol’niki" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.15194, + "lon": -41.77278, + "name": "Piatã" + }, + { + "lat": -5.70556, + "lon": -35.30722, + "name": "Extremoz" + }, + { + "lat": -22.8075, + "lon": -43.41389, + "name": "Nilópolis" + }, + { + "lat": -3.68444, + "lon": -42.75028, + "name": "Brejo" + }, + { + "lat": 12.80351, + "lon": 74.86472, + "name": "Sōmēshvara" + } + ], + "question": "Which location is the geographic outlier among: Piatã, Extremoz, Nilópolis, Brejo, Sōmēshvara?", + "ground_truth": { + "answer": "Sōmēshvara", + "outlier_distance_km": 10441.5, + "second_furthest_km": 3298.4, + "clarity_ratio": 3.17, + "median_distance_km": 2794.4, + "distances_to_centroid": { + "Piatã": 2739.4, + "Extremoz": 1951.3, + "Nilópolis": 3298.4, + "Brejo": 2794.4, + "Sōmēshvara": 10441.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piatã: (-13.15°, -41.77°)", + " Extremoz: (-5.71°, -35.31°)", + " Nilópolis: (-22.81°, -43.41°)", + " Brejo: (-3.68°, -42.75°)", + " Sōmēshvara: (12.80°, 74.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sōmēshvara: 10441.5 km from centroid", + " Nilópolis: 3298.4 km from centroid", + " Brejo: 2794.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sōmēshvara", + "FINAL ANSWER: Sōmēshvara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.16852, + "lon": 9.87134, + "name": "Sondrio" + }, + { + "lat": 44.59445, + "lon": 11.04979, + "name": "Castelfranco Emilia" + }, + { + "lat": 44.73188, + "lon": 37.76176, + "name": "Novorossiysk" + }, + { + "lat": 48.82345, + "lon": 2.29025, + "name": "Vanves" + }, + { + "lat": 34.82083, + "lon": 105.03389, + "name": "Jutou" + } + ], + "question": "Which location is the geographic outlier among: Sondrio, Castelfranco Emilia, Novorossiysk, Vanves, Jutou?", + "ground_truth": { + "answer": "Jutou", + "outlier_distance_km": 6065.0, + "second_furthest_km": 2419.7, + "clarity_ratio": 2.51, + "median_distance_km": 1846.0, + "distances_to_centroid": { + "Sondrio": 1846.0, + "Castelfranco Emilia": 1762.2, + "Novorossiysk": 376.6, + "Vanves": 2419.7, + "Jutou": 6065.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sondrio: (46.17°, 9.87°)", + " Castelfranco Emilia: (44.59°, 11.05°)", + " Novorossiysk: (44.73°, 37.76°)", + " Vanves: (48.82°, 2.29°)", + " Jutou: (34.82°, 105.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jutou: 6065.0 km from centroid", + " Vanves: 2419.7 km from centroid", + " Sondrio: 1846.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jutou", + "FINAL ANSWER: Jutou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -36.8, + "lon": 174.75, + "name": "North Shore" + }, + { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + }, + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + }, + { + "lat": -27.08819, + "lon": -61.08217, + "name": "Las Breñas" + } + ], + "question": "Which location is the geographic outlier among: Glen Iris, North Shore, Whanganui, Northcote, Las Breñas?", + "ground_truth": { + "answer": "Las Breñas", + "outlier_distance_km": 13004.3, + "second_furthest_km": 5196.9, + "clarity_ratio": 2.5, + "median_distance_km": 5125.0, + "distances_to_centroid": { + "Glen Iris": 2605.5, + "North Shore": 5196.9, + "Whanganui": 5125.0, + "Northcote": 2600.5, + "Las Breñas": 13004.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Iris: (-37.87°, 145.07°)", + " North Shore: (-36.80°, 174.75°)", + " Whanganui: (-39.93°, 175.05°)", + " Northcote: (-37.77°, 145.00°)", + " Las Breñas: (-27.09°, -61.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Las Breñas: 13004.3 km from centroid", + " North Shore: 5196.9 km from centroid", + " Whanganui: 5125.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Las Breñas", + "FINAL ANSWER: Las Breñas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.57509, + "lon": -71.99813, + "name": "Gardner" + }, + { + "lat": 21.00153, + "lon": -100.38416, + "name": "San José Iturbide" + }, + { + "lat": 46.73239, + "lon": -117.00017, + "name": "Moscow" + }, + { + "lat": 40.53078, + "lon": -112.29828, + "name": "Tooele" + }, + { + "lat": -22.25222, + "lon": -45.70333, + "name": "Santa Rita do Sapucaí" + } + ], + "question": "Which location is the geographic outlier among: Gardner, San José Iturbide, Moscow, Tooele, Santa Rita do Sapucaí?", + "ground_truth": { + "answer": "Santa Rita do Sapucaí", + "outlier_distance_km": 7120.7, + "second_furthest_km": 3366.6, + "clarity_ratio": 2.12, + "median_distance_km": 2674.7, + "distances_to_centroid": { + "Gardner": 2459.6, + "San José Iturbide": 1230.1, + "Moscow": 3366.6, + "Tooele": 2674.7, + "Santa Rita do Sapucaí": 7120.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gardner: (42.58°, -72.00°)", + " San José Iturbide: (21.00°, -100.38°)", + " Moscow: (46.73°, -117.00°)", + " Tooele: (40.53°, -112.30°)", + " Santa Rita do Sapucaí: (-22.25°, -45.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Rita do Sapucaí: 7120.7 km from centroid", + " Moscow: 3366.6 km from centroid", + " Tooele: 2674.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Rita do Sapucaí", + "FINAL ANSWER: Santa Rita do Sapucaí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.63873, + "lon": -122.66149, + "name": "Vancouver" + }, + { + "lat": 40.88621, + "lon": -73.25734, + "name": "Kings Park" + }, + { + "lat": 33.74141, + "lon": -118.10479, + "name": "Seal Beach" + }, + { + "lat": 33.87529, + "lon": -117.56644, + "name": "Corona" + }, + { + "lat": -22.36611, + "lon": -48.38028, + "name": "Dois Córregos" + } + ], + "question": "Which location is the geographic outlier among: Vancouver, Kings Park, Seal Beach, Corona, Dois Córregos?", + "ground_truth": { + "answer": "Dois Córregos", + "outlier_distance_km": 7457.3, + "second_furthest_km": 3189.9, + "clarity_ratio": 2.34, + "median_distance_km": 2640.0, + "distances_to_centroid": { + "Vancouver": 3189.9, + "Kings Park": 2640.0, + "Seal Beach": 2275.3, + "Corona": 2231.4, + "Dois Córregos": 7457.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vancouver: (45.64°, -122.66°)", + " Kings Park: (40.89°, -73.26°)", + " Seal Beach: (33.74°, -118.10°)", + " Corona: (33.88°, -117.57°)", + " Dois Córregos: (-22.37°, -48.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dois Córregos: 7457.3 km from centroid", + " Vancouver: 3189.9 km from centroid", + " Kings Park: 2640.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dois Córregos", + "FINAL ANSWER: Dois Córregos" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": -37.78821, + "lon": 175.2902, + "name": "Hamilton East" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": 51.14931, + "lon": -0.97469, + "name": "Alton" + } + ], + "question": "Which location is the geographic outlier among: Yagoona, South Morang, Hamilton East, Launceston, Alton?", + "ground_truth": { + "answer": "Alton", + "outlier_distance_km": 14102.2, + "second_furthest_km": 5342.5, + "clarity_ratio": 2.64, + "median_distance_km": 3268.1, + "distances_to_centroid": { + "Yagoona": 3123.8, + "South Morang": 2868.6, + "Hamilton East": 5342.5, + "Launceston": 3268.1, + "Alton": 14102.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yagoona: (-33.90°, 151.02°)", + " South Morang: (-37.65°, 145.10°)", + " Hamilton East: (-37.79°, 175.29°)", + " Launceston: (-41.44°, 147.13°)", + " Alton: (51.15°, -0.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alton: 14102.2 km from centroid", + " Hamilton East: 5342.5 km from centroid", + " Launceston: 3268.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alton", + "FINAL ANSWER: Alton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.63361, + "lon": -47.83478, + "name": "Sobradinho II" + }, + { + "lat": -8.62306, + "lon": -37.15583, + "name": "Buíque" + }, + { + "lat": -3.76806, + "lon": -60.36917, + "name": "Careiro" + }, + { + "lat": -16.33333, + "lon": -55.93333, + "name": "Lucas" + }, + { + "lat": -38.03333, + "lon": 145.35, + "name": "Berwick" + } + ], + "question": "Which location is the geographic outlier among: Sobradinho II, Buíque, Careiro, Lucas, Berwick?", + "ground_truth": { + "answer": "Berwick", + "outlier_distance_km": 13477.3, + "second_furthest_km": 5548.7, + "clarity_ratio": 2.43, + "median_distance_km": 4762.6, + "distances_to_centroid": { + "Sobradinho II": 3911.7, + "Buíque": 2947.1, + "Careiro": 5548.7, + "Lucas": 4762.6, + "Berwick": 13477.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sobradinho II: (-15.63°, -47.83°)", + " Buíque: (-8.62°, -37.16°)", + " Careiro: (-3.77°, -60.37°)", + " Lucas: (-16.33°, -55.93°)", + " Berwick: (-38.03°, 145.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Berwick: 13477.3 km from centroid", + " Careiro: 5548.7 km from centroid", + " Lucas: 4762.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Berwick", + "FINAL ANSWER: Berwick" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.84306, + "lon": -51.835, + "name": "Oiapoque" + }, + { + "lat": -4.00092, + "lon": -49.5068, + "name": "Breu Branco" + }, + { + "lat": 8.09419, + "lon": -74.77573, + "name": "Nechí" + }, + { + "lat": -7.02194, + "lon": -45.48111, + "name": "São Raimundo das Mangabeiras" + }, + { + "lat": 50.58286, + "lon": 22.05334, + "name": "Stalowa Wola" + } + ], + "question": "Which location is the geographic outlier among: Oiapoque, Breu Branco, Nechí, São Raimundo das Mangabeiras, Stalowa Wola?", + "ground_truth": { + "answer": "Stalowa Wola", + "outlier_distance_km": 7163.1, + "second_furthest_km": 3833.2, + "clarity_ratio": 1.87, + "median_distance_km": 2022.5, + "distances_to_centroid": { + "Oiapoque": 1498.4, + "Breu Branco": 1912.6, + "Nechí": 3833.2, + "São Raimundo das Mangabeiras": 2022.5, + "Stalowa Wola": 7163.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oiapoque: (3.84°, -51.84°)", + " Breu Branco: (-4.00°, -49.51°)", + " Nechí: (8.09°, -74.78°)", + " São Raimundo das Mangabeiras: (-7.02°, -45.48°)", + " Stalowa Wola: (50.58°, 22.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stalowa Wola: 7163.1 km from centroid", + " Nechí: 3833.2 km from centroid", + " São Raimundo das Mangabeiras: 2022.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stalowa Wola", + "FINAL ANSWER: Stalowa Wola" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.9218, + "lon": -75.06232, + "name": "Líbano" + }, + { + "lat": -10.43889, + "lon": -62.46639, + "name": "Jaru" + }, + { + "lat": -54.81084, + "lon": -68.31591, + "name": "Ushuaia" + }, + { + "lat": -18.64722, + "lon": -48.18722, + "name": "Araguari" + }, + { + "lat": 51.5567, + "lon": -0.21549, + "name": "Cricklewood" + } + ], + "question": "Which location is the geographic outlier among: Líbano, Jaru, Ushuaia, Araguari, Cricklewood?", + "ground_truth": { + "answer": "Cricklewood", + "outlier_distance_km": 7947.8, + "second_furthest_km": 5703.9, + "clarity_ratio": 1.39, + "median_distance_km": 2927.0, + "distances_to_centroid": { + "Líbano": 2927.0, + "Jaru": 1392.5, + "Ushuaia": 5703.9, + "Araguari": 1491.9, + "Cricklewood": 7947.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Líbano: (4.92°, -75.06°)", + " Jaru: (-10.44°, -62.47°)", + " Ushuaia: (-54.81°, -68.32°)", + " Araguari: (-18.65°, -48.19°)", + " Cricklewood: (51.56°, -0.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cricklewood: 7947.8 km from centroid", + " Ushuaia: 5703.9 km from centroid", + " Líbano: 2927.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cricklewood", + "FINAL ANSWER: Cricklewood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.21667, + "lon": 1.53333, + "name": "El Vendrell" + }, + { + "lat": 51.43787, + "lon": 14.23549, + "name": "Hoyerswerda" + }, + { + "lat": 41.07663, + "lon": 1.14163, + "name": "Salou" + }, + { + "lat": 53.36592, + "lon": -1.99986, + "name": "New Mills" + }, + { + "lat": 6.99536, + "lon": 0.29306, + "name": "Kpandu" + } + ], + "question": "Which location is the geographic outlier among: El Vendrell, Hoyerswerda, Salou, New Mills, Kpandu?", + "ground_truth": { + "answer": "Kpandu", + "outlier_distance_km": 3549.3, + "second_furthest_km": 1662.6, + "clarity_ratio": 2.13, + "median_distance_km": 1651.2, + "distances_to_centroid": { + "El Vendrell": 295.9, + "Hoyerswerda": 1651.2, + "Salou": 298.7, + "New Mills": 1662.6, + "Kpandu": 3549.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " El Vendrell: (41.22°, 1.53°)", + " Hoyerswerda: (51.44°, 14.24°)", + " Salou: (41.08°, 1.14°)", + " New Mills: (53.37°, -2.00°)", + " Kpandu: (7.00°, 0.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kpandu: 3549.3 km from centroid", + " New Mills: 1662.6 km from centroid", + " Hoyerswerda: 1651.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kpandu", + "FINAL ANSWER: Kpandu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.34447, + "lon": 5.38004, + "name": "Marseille 14" + }, + { + "lat": 40.83255, + "lon": 14.22677, + "name": "Chiaia" + }, + { + "lat": 40.74248, + "lon": 14.67447, + "name": "Nocera Superiore" + }, + { + "lat": 44.4258, + "lon": 39.5362, + "name": "Khadyzhensk" + }, + { + "lat": 7.11345, + "lon": 6.73866, + "name": "Idah" + } + ], + "question": "Which location is the geographic outlier among: Marseille 14, Chiaia, Nocera Superiore, Khadyzhensk, Idah?", + "ground_truth": { + "answer": "Idah", + "outlier_distance_km": 3276.2, + "second_furthest_km": 2231.6, + "clarity_ratio": 1.47, + "median_distance_km": 1284.0, + "distances_to_centroid": { + "Marseille 14": 1284.0, + "Chiaia": 637.8, + "Nocera Superiore": 619.0, + "Khadyzhensk": 2231.6, + "Idah": 3276.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marseille 14: (43.34°, 5.38°)", + " Chiaia: (40.83°, 14.23°)", + " Nocera Superiore: (40.74°, 14.67°)", + " Khadyzhensk: (44.43°, 39.54°)", + " Idah: (7.11°, 6.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Idah: 3276.2 km from centroid", + " Khadyzhensk: 2231.6 km from centroid", + " Marseille 14: 1284.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Idah", + "FINAL ANSWER: Idah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.47205, + "lon": -123.39483, + "name": "Carey" + }, + { + "lat": 19.87444, + "lon": -98.93472, + "name": "Don Antonio" + }, + { + "lat": 18.90815, + "lon": -98.43613, + "name": "Atlixco" + }, + { + "lat": 35.14778, + "lon": -114.5683, + "name": "Bullhead City" + }, + { + "lat": 50.25937, + "lon": 10.96384, + "name": "Coburg" + } + ], + "question": "Which location is the geographic outlier among: Carey, Don Antonio, Atlixco, Bullhead City, Coburg?", + "ground_truth": { + "answer": "Coburg", + "outlier_distance_km": 7508.1, + "second_furthest_km": 3514.2, + "clarity_ratio": 2.14, + "median_distance_km": 2700.8, + "distances_to_centroid": { + "Carey": 3514.2, + "Don Antonio": 2137.5, + "Atlixco": 2193.4, + "Bullhead City": 2700.8, + "Coburg": 7508.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carey: (48.47°, -123.39°)", + " Don Antonio: (19.87°, -98.93°)", + " Atlixco: (18.91°, -98.44°)", + " Bullhead City: (35.15°, -114.57°)", + " Coburg: (50.26°, 10.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coburg: 7508.1 km from centroid", + " Carey: 3514.2 km from centroid", + " Bullhead City: 2700.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coburg", + "FINAL ANSWER: Coburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + }, + { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + { + "lat": -37.93333, + "lon": 145.23333, + "name": "Rowville" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": 34.58333, + "lon": 133.76667, + "name": "Kurashiki" + } + ], + "question": "Which location is the geographic outlier among: Strathfield, Landsdale, Rowville, Carlton, Kurashiki?", + "ground_truth": { + "answer": "Kurashiki", + "outlier_distance_km": 6239.0, + "second_furthest_km": 2497.1, + "clarity_ratio": 2.5, + "median_distance_km": 1962.3, + "distances_to_centroid": { + "Strathfield": 1880.8, + "Landsdale": 2497.1, + "Rowville": 1962.3, + "Carlton": 1939.9, + "Kurashiki": 6239.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Strathfield: (-33.88°, 151.08°)", + " Landsdale: (-31.81°, 115.87°)", + " Rowville: (-37.93°, 145.23°)", + " Carlton: (-37.80°, 144.97°)", + " Kurashiki: (34.58°, 133.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kurashiki: 6239.0 km from centroid", + " Landsdale: 2497.1 km from centroid", + " Rowville: 1962.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kurashiki", + "FINAL ANSWER: Kurashiki" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.9128, + "lon": 30.29019, + "name": "Ḩawsh ‘Īsá" + }, + { + "lat": 9.29482, + "lon": 5.05412, + "name": "Mokwa" + }, + { + "lat": 7.01667, + "lon": 39.98333, + "name": "Goba" + }, + { + "lat": 7.91283, + "lon": 4.66741, + "name": "Ikirun" + }, + { + "lat": -37.90561, + "lon": 145.00279, + "name": "Brighton" + } + ], + "question": "Which location is the geographic outlier among: Ḩawsh ‘Īsá, Mokwa, Goba, Ikirun, Brighton?", + "ground_truth": { + "answer": "Brighton", + "outlier_distance_km": 11120.1, + "second_furthest_km": 4488.2, + "clarity_ratio": 2.48, + "median_distance_km": 4458.8, + "distances_to_centroid": { + "Ḩawsh ‘Īsá": 3421.7, + "Mokwa": 4458.8, + "Goba": 682.7, + "Ikirun": 4488.2, + "Brighton": 11120.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ḩawsh ‘Īsá: (30.91°, 30.29°)", + " Mokwa: (9.29°, 5.05°)", + " Goba: (7.02°, 39.98°)", + " Ikirun: (7.91°, 4.67°)", + " Brighton: (-37.91°, 145.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brighton: 11120.1 km from centroid", + " Ikirun: 4488.2 km from centroid", + " Mokwa: 4458.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brighton", + "FINAL ANSWER: Brighton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.76602, + "lon": 88.36336, + "name": "Bārākpur" + }, + { + "lat": 17.53909, + "lon": 78.36355, + "name": "Bāspalli" + }, + { + "lat": -7.68333, + "lon": 112.61667, + "name": "Prigen" + }, + { + "lat": 28.8457, + "lon": 78.2396, + "name": "Gajraula" + }, + { + "lat": 33.51623, + "lon": -90.17953, + "name": "Greenwood" + } + ], + "question": "Which location is the geographic outlier among: Bārākpur, Bāspalli, Prigen, Gajraula, Greenwood?", + "ground_truth": { + "answer": "Greenwood", + "outlier_distance_km": 13018.9, + "second_furthest_km": 7124.9, + "clarity_ratio": 1.83, + "median_distance_km": 3639.9, + "distances_to_centroid": { + "Bārākpur": 3639.9, + "Bāspalli": 2630.2, + "Prigen": 7124.9, + "Gajraula": 2737.0, + "Greenwood": 13018.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bārākpur: (22.77°, 88.36°)", + " Bāspalli: (17.54°, 78.36°)", + " Prigen: (-7.68°, 112.62°)", + " Gajraula: (28.85°, 78.24°)", + " Greenwood: (33.52°, -90.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greenwood: 13018.9 km from centroid", + " Prigen: 7124.9 km from centroid", + " Bārākpur: 3639.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greenwood", + "FINAL ANSWER: Greenwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.54861, + "lon": -42.55694, + "name": "Peçanha" + }, + { + "lat": -9.89667, + "lon": -39.02639, + "name": "Canudos" + }, + { + "lat": -8.1654, + "lon": -70.35486, + "name": "Feijó" + }, + { + "lat": -27.09571, + "lon": -54.89344, + "name": "Aristóbulo del Valle" + }, + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + } + ], + "question": "Which location is the geographic outlier among: Peçanha, Canudos, Feijó, Aristóbulo del Valle, Hoppers Crossing?", + "ground_truth": { + "answer": "Hoppers Crossing", + "outlier_distance_km": 13115.8, + "second_furthest_km": 6356.6, + "clarity_ratio": 2.06, + "median_distance_km": 4368.4, + "distances_to_centroid": { + "Peçanha": 3161.3, + "Canudos": 3075.6, + "Feijó": 6356.6, + "Aristóbulo del Valle": 4368.4, + "Hoppers Crossing": 13115.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Peçanha: (-18.55°, -42.56°)", + " Canudos: (-9.90°, -39.03°)", + " Feijó: (-8.17°, -70.35°)", + " Aristóbulo del Valle: (-27.10°, -54.89°)", + " Hoppers Crossing: (-37.88°, 144.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hoppers Crossing: 13115.8 km from centroid", + " Feijó: 6356.6 km from centroid", + " Aristóbulo del Valle: 4368.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hoppers Crossing", + "FINAL ANSWER: Hoppers Crossing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + { + "lat": 40.4842, + "lon": -88.99369, + "name": "Bloomington" + } + ], + "question": "Which location is the geographic outlier among: Maroochydore, Saint Ives, Melbourne City Centre, Sunbury, Bloomington?", + "ground_truth": { + "answer": "Bloomington", + "outlier_distance_km": 17449.5, + "second_furthest_km": 5370.0, + "clarity_ratio": 3.25, + "median_distance_km": 5201.4, + "distances_to_centroid": { + "Maroochydore": 5370.0, + "Saint Ives": 5201.4, + "Melbourne City Centre": 4723.1, + "Sunbury": 4696.3, + "Bloomington": 17449.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maroochydore: (-26.66°, 153.10°)", + " Saint Ives: (-33.73°, 151.16°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Sunbury: (-37.58°, 144.73°)", + " Bloomington: (40.48°, -88.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bloomington: 17449.5 km from centroid", + " Maroochydore: 5370.0 km from centroid", + " Saint Ives: 5201.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bloomington", + "FINAL ANSWER: Bloomington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.78269, + "lon": 151.04888, + "name": "Carlingford" + }, + { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + { + "lat": 49.31406, + "lon": -123.0725, + "name": "Lower Lonsdale" + } + ], + "question": "Which location is the geographic outlier among: Carlingford, Papatoetoe, Australind, Wyndham Vale, Lower Lonsdale?", + "ground_truth": { + "answer": "Lower Lonsdale", + "outlier_distance_km": 15342.0, + "second_furthest_km": 8108.2, + "clarity_ratio": 1.89, + "median_distance_km": 5992.0, + "distances_to_centroid": { + "Carlingford": 5992.0, + "Papatoetoe": 8108.2, + "Australind": 2821.3, + "Wyndham Vale": 5450.1, + "Lower Lonsdale": 15342.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlingford: (-33.78°, 151.05°)", + " Papatoetoe: (-36.97°, 174.84°)", + " Australind: (-33.28°, 115.72°)", + " Wyndham Vale: (-37.89°, 144.62°)", + " Lower Lonsdale: (49.31°, -123.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lower Lonsdale: 15342.0 km from centroid", + " Papatoetoe: 8108.2 km from centroid", + " Carlingford: 5992.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lower Lonsdale", + "FINAL ANSWER: Lower Lonsdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.93548, + "lon": 15.50643, + "name": "Zielona Góra" + }, + { + "lat": 51.46246, + "lon": 0.10759, + "name": "Welling" + }, + { + "lat": 55.88333, + "lon": 37.6, + "name": "Bibirevo" + }, + { + "lat": 54.53333, + "lon": -1.3, + "name": "Thornaby-on-Tees" + }, + { + "lat": 41.15376, + "lon": -87.88754, + "name": "Bourbonnais" + } + ], + "question": "Which location is the geographic outlier among: Zielona Góra, Welling, Bibirevo, Thornaby-on-Tees, Bourbonnais?", + "ground_truth": { + "answer": "Bourbonnais", + "outlier_distance_km": 6002.6, + "second_furthest_km": 2962.0, + "clarity_ratio": 2.03, + "median_distance_km": 1569.7, + "distances_to_centroid": { + "Zielona Góra": 1569.7, + "Welling": 510.9, + "Bibirevo": 2962.0, + "Thornaby-on-Tees": 558.4, + "Bourbonnais": 6002.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zielona Góra: (51.94°, 15.51°)", + " Welling: (51.46°, 0.11°)", + " Bibirevo: (55.88°, 37.60°)", + " Thornaby-on-Tees: (54.53°, -1.30°)", + " Bourbonnais: (41.15°, -87.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bourbonnais: 6002.6 km from centroid", + " Bibirevo: 2962.0 km from centroid", + " Zielona Góra: 1569.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bourbonnais", + "FINAL ANSWER: Bourbonnais" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.31004, + "lon": 106.09828, + "name": "Tây Ninh" + }, + { + "lat": 39.87869, + "lon": 139.99767, + "name": "Katagami" + }, + { + "lat": 23.29549, + "lon": 113.82465, + "name": "Licheng" + }, + { + "lat": 33.73333, + "lon": 130.46667, + "name": "Koga" + }, + { + "lat": -40.80255, + "lon": -62.98349, + "name": "Carmen de Patagones" + } + ], + "question": "Which location is the geographic outlier among: Tây Ninh, Katagami, Licheng, Koga, Carmen de Patagones?", + "ground_truth": { + "answer": "Carmen de Patagones", + "outlier_distance_km": 15704.9, + "second_furthest_km": 6044.8, + "clarity_ratio": 2.6, + "median_distance_km": 5054.4, + "distances_to_centroid": { + "Tây Ninh": 2251.4, + "Katagami": 6044.8, + "Licheng": 3176.0, + "Koga": 5054.4, + "Carmen de Patagones": 15704.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tây Ninh: (11.31°, 106.10°)", + " Katagami: (39.88°, 140.00°)", + " Licheng: (23.30°, 113.82°)", + " Koga: (33.73°, 130.47°)", + " Carmen de Patagones: (-40.80°, -62.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carmen de Patagones: 15704.9 km from centroid", + " Katagami: 6044.8 km from centroid", + " Koga: 5054.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carmen de Patagones", + "FINAL ANSWER: Carmen de Patagones" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.87497, + "lon": -96.90036, + "name": "West Fargo" + }, + { + "lat": 38.73289, + "lon": -77.05803, + "name": "Fort Hunt" + }, + { + "lat": 35.19807, + "lon": -111.65127, + "name": "Flagstaff" + }, + { + "lat": 25.18909, + "lon": -99.82865, + "name": "Montemorelos" + }, + { + "lat": 22.59373, + "lon": 75.29774, + "name": "Dhār" + } + ], + "question": "Which location is the geographic outlier among: West Fargo, Fort Hunt, Flagstaff, Montemorelos, Dhār?", + "ground_truth": { + "answer": "Dhār", + "outlier_distance_km": 12294.8, + "second_furthest_km": 4504.6, + "clarity_ratio": 2.73, + "median_distance_km": 3758.3, + "distances_to_centroid": { + "West Fargo": 3263.5, + "Fort Hunt": 1456.7, + "Flagstaff": 4504.6, + "Montemorelos": 3758.3, + "Dhār": 12294.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Fargo: (46.87°, -96.90°)", + " Fort Hunt: (38.73°, -77.06°)", + " Flagstaff: (35.20°, -111.65°)", + " Montemorelos: (25.19°, -99.83°)", + " Dhār: (22.59°, 75.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dhār: 12294.8 km from centroid", + " Flagstaff: 4504.6 km from centroid", + " Montemorelos: 3758.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dhār", + "FINAL ANSWER: Dhār" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -31.91099, + "lon": 152.45387, + "name": "Taree" + }, + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": -33.32711, + "lon": 115.64137, + "name": "Bunbury" + }, + { + "lat": -29.45986, + "lon": -60.21315, + "name": "Vera" + } + ], + "question": "Which location is the geographic outlier among: Avondale, Taree, Forest Lake, Bunbury, Vera?", + "ground_truth": { + "answer": "Vera", + "outlier_distance_km": 13068.5, + "second_furthest_km": 6099.3, + "clarity_ratio": 2.14, + "median_distance_km": 4420.3, + "distances_to_centroid": { + "Avondale": 6099.3, + "Taree": 4249.1, + "Forest Lake": 4420.3, + "Bunbury": 815.9, + "Vera": 13068.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Avondale: (-36.88°, 174.70°)", + " Taree: (-31.91°, 152.45°)", + " Forest Lake: (-27.63°, 152.97°)", + " Bunbury: (-33.33°, 115.64°)", + " Vera: (-29.46°, -60.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vera: 13068.5 km from centroid", + " Avondale: 6099.3 km from centroid", + " Forest Lake: 4420.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vera", + "FINAL ANSWER: Vera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.69919, + "lon": 30.7673, + "name": "Al ‘Idwah" + }, + { + "lat": 7.87377, + "lon": 5.07691, + "name": "Ipoti" + }, + { + "lat": 31.16844, + "lon": 31.7655, + "name": "Kafr al Kurdī" + }, + { + "lat": 7.55632, + "lon": 3.44107, + "name": "Orita-Eruwa" + }, + { + "lat": -29.11761, + "lon": -59.65834, + "name": "Avellaneda" + } + ], + "question": "Which location is the geographic outlier among: Al ‘Idwah, Ipoti, Kafr al Kurdī, Orita-Eruwa, Avellaneda?", + "ground_truth": { + "answer": "Avellaneda", + "outlier_distance_km": 7881.4, + "second_furthest_km": 3902.1, + "clarity_ratio": 2.02, + "median_distance_km": 3677.1, + "distances_to_centroid": { + "Al ‘Idwah": 3677.1, + "Ipoti": 343.0, + "Kafr al Kurdī": 3902.1, + "Orita-Eruwa": 226.4, + "Avellaneda": 7881.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al ‘Idwah: (28.70°, 30.77°)", + " Ipoti: (7.87°, 5.08°)", + " Kafr al Kurdī: (31.17°, 31.77°)", + " Orita-Eruwa: (7.56°, 3.44°)", + " Avellaneda: (-29.12°, -59.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Avellaneda: 7881.4 km from centroid", + " Kafr al Kurdī: 3902.1 km from centroid", + " Al ‘Idwah: 3677.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Avellaneda", + "FINAL ANSWER: Avellaneda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -33.8188, + "lon": 151.1062, + "name": "Ryde" + }, + { + "lat": -37.58333, + "lon": 145.03333, + "name": "Wollert" + }, + { + "lat": -14.61222, + "lon": -41.13556, + "name": "Anagé" + } + ], + "question": "Which location is the geographic outlier among: Blacktown, Karori, Ryde, Wollert, Anagé?", + "ground_truth": { + "answer": "Anagé", + "outlier_distance_km": 14273.2, + "second_furthest_km": 5218.5, + "clarity_ratio": 2.74, + "median_distance_km": 3250.2, + "distances_to_centroid": { + "Blacktown": 3233.5, + "Karori": 5218.5, + "Ryde": 3250.2, + "Wollert": 2691.1, + "Anagé": 14273.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blacktown: (-33.77°, 150.92°)", + " Karori: (-41.28°, 174.74°)", + " Ryde: (-33.82°, 151.11°)", + " Wollert: (-37.58°, 145.03°)", + " Anagé: (-14.61°, -41.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Anagé: 14273.2 km from centroid", + " Karori: 5218.5 km from centroid", + " Ryde: 3250.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Anagé", + "FINAL ANSWER: Anagé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.45867, + "lon": -58.91398, + "name": "Pilar" + }, + { + "lat": 9.31847, + "lon": -75.2933, + "name": "Corozal" + }, + { + "lat": -24.28389, + "lon": -53.84, + "name": "Palotina" + }, + { + "lat": -0.72889, + "lon": -47.84806, + "name": "Curuçá" + }, + { + "lat": 42.69764, + "lon": 2.89541, + "name": "Perpignan" + } + ], + "question": "Which location is the geographic outlier among: Pilar, Corozal, Palotina, Curuçá, Perpignan?", + "ground_truth": { + "answer": "Perpignan", + "outlier_distance_km": 6965.5, + "second_furthest_km": 3882.2, + "clarity_ratio": 1.79, + "median_distance_km": 3397.8, + "distances_to_centroid": { + "Pilar": 3882.2, + "Corozal": 3397.8, + "Palotina": 2651.4, + "Curuçá": 162.6, + "Perpignan": 6965.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pilar: (-34.46°, -58.91°)", + " Corozal: (9.32°, -75.29°)", + " Palotina: (-24.28°, -53.84°)", + " Curuçá: (-0.73°, -47.85°)", + " Perpignan: (42.70°, 2.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perpignan: 6965.5 km from centroid", + " Pilar: 3882.2 km from centroid", + " Corozal: 3397.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perpignan", + "FINAL ANSWER: Perpignan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.98639, + "lon": -44.42778, + "name": "Mateus Leme" + }, + { + "lat": -6.85306, + "lon": -35.38111, + "name": "Araçagi" + }, + { + "lat": -28.40833, + "lon": -54.96083, + "name": "São Luiz Gonzaga" + }, + { + "lat": -31.09321, + "lon": -64.48448, + "name": "La Falda" + }, + { + "lat": 21.23853, + "lon": 77.74713, + "name": "Chāndūr Bāzār" + } + ], + "question": "Which location is the geographic outlier among: Mateus Leme, Araçagi, São Luiz Gonzaga, La Falda, Chāndūr Bāzār?", + "ground_truth": { + "answer": "Chāndūr Bāzār", + "outlier_distance_km": 11757.1, + "second_furthest_km": 4568.3, + "clarity_ratio": 2.57, + "median_distance_km": 3602.3, + "distances_to_centroid": { + "Mateus Leme": 2278.9, + "Araçagi": 1393.3, + "São Luiz Gonzaga": 3602.3, + "La Falda": 4568.3, + "Chāndūr Bāzār": 11757.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mateus Leme: (-19.99°, -44.43°)", + " Araçagi: (-6.85°, -35.38°)", + " São Luiz Gonzaga: (-28.41°, -54.96°)", + " La Falda: (-31.09°, -64.48°)", + " Chāndūr Bāzār: (21.24°, 77.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chāndūr Bāzār: 11757.1 km from centroid", + " La Falda: 4568.3 km from centroid", + " São Luiz Gonzaga: 3602.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chāndūr Bāzār", + "FINAL ANSWER: Chāndūr Bāzār" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.38176, + "lon": 142.48799, + "name": "Warrnambool" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": -9.93361, + "lon": -36.55417, + "name": "São Sebastião" + } + ], + "question": "Which location is the geographic outlier among: Warrnambool, Mackay, Mount Eden, Nerang, São Sebastião?", + "ground_truth": { + "answer": "São Sebastião", + "outlier_distance_km": 15004.0, + "second_furthest_km": 5515.8, + "clarity_ratio": 2.72, + "median_distance_km": 3610.3, + "distances_to_centroid": { + "Warrnambool": 2725.0, + "Mackay": 3354.7, + "Mount Eden": 5515.8, + "Nerang": 3610.3, + "São Sebastião": 15004.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warrnambool: (-38.38°, 142.49°)", + " Mackay: (-21.15°, 149.17°)", + " Mount Eden: (-36.88°, 174.76°)", + " Nerang: (-27.99°, 153.34°)", + " São Sebastião: (-9.93°, -36.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Sebastião: 15004.0 km from centroid", + " Mount Eden: 5515.8 km from centroid", + " Nerang: 3610.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Sebastião", + "FINAL ANSWER: São Sebastião" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + }, + { + "lat": -22.46889, + "lon": -44.44667, + "name": "Resende" + } + ], + "question": "Which location is the geographic outlier among: Chatswood, Baldivis, Wellington, Hampton Park, Resende?", + "ground_truth": { + "answer": "Resende", + "outlier_distance_km": 13156.0, + "second_furthest_km": 5771.1, + "clarity_ratio": 2.28, + "median_distance_km": 3918.2, + "distances_to_centroid": { + "Chatswood": 3918.2, + "Baldivis": 696.2, + "Wellington": 5771.1, + "Hampton Park": 3327.2, + "Resende": 13156.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chatswood: (-33.80°, 151.18°)", + " Baldivis: (-32.33°, 115.83°)", + " Wellington: (-41.29°, 174.78°)", + " Hampton Park: (-38.03°, 145.25°)", + " Resende: (-22.47°, -44.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Resende: 13156.0 km from centroid", + " Wellington: 5771.1 km from centroid", + " Chatswood: 3918.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Resende", + "FINAL ANSWER: Resende" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.86085, + "lon": 8.5725, + "name": "Griesheim" + }, + { + "lat": 51.14648, + "lon": 0.87376, + "name": "Ashford" + }, + { + "lat": 55.57957, + "lon": 36.70392, + "name": "Kubinka" + }, + { + "lat": 48.8, + "lon": 8.33333, + "name": "Gaggenau" + }, + { + "lat": -37.87709, + "lon": 145.12939, + "name": "Mount Waverley" + } + ], + "question": "Which location is the geographic outlier among: Griesheim, Ashford, Kubinka, Gaggenau, Mount Waverley?", + "ground_truth": { + "answer": "Mount Waverley", + "outlier_distance_km": 13428.6, + "second_furthest_km": 3699.4, + "clarity_ratio": 3.63, + "median_distance_km": 3139.3, + "distances_to_centroid": { + "Griesheim": 3139.3, + "Ashford": 3699.4, + "Kubinka": 2467.5, + "Gaggenau": 3110.3, + "Mount Waverley": 13428.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Griesheim: (49.86°, 8.57°)", + " Ashford: (51.15°, 0.87°)", + " Kubinka: (55.58°, 36.70°)", + " Gaggenau: (48.80°, 8.33°)", + " Mount Waverley: (-37.88°, 145.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Waverley: 13428.6 km from centroid", + " Ashford: 3699.4 km from centroid", + " Griesheim: 3139.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Waverley", + "FINAL ANSWER: Mount Waverley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + }, + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": -33.88374, + "lon": 151.21282, + "name": "Surry Hills" + }, + { + "lat": 6.33815, + "lon": 5.62575, + "name": "Benin City" + } + ], + "question": "Which location is the geographic outlier among: Tamworth, Springfield Lakes, Wangaratta, Surry Hills, Benin City?", + "ground_truth": { + "answer": "Benin City", + "outlier_distance_km": 12903.3, + "second_furthest_km": 3158.4, + "clarity_ratio": 4.09, + "median_distance_km": 3061.1, + "distances_to_centroid": { + "Tamworth": 2984.3, + "Springfield Lakes": 3158.4, + "Wangaratta": 2714.8, + "Surry Hills": 3061.1, + "Benin City": 12903.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tamworth: (-31.09°, 150.93°)", + " Springfield Lakes: (-27.67°, 152.92°)", + " Wangaratta: (-36.36°, 146.32°)", + " Surry Hills: (-33.88°, 151.21°)", + " Benin City: (6.34°, 5.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Benin City: 12903.3 km from centroid", + " Springfield Lakes: 3158.4 km from centroid", + " Surry Hills: 3061.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Benin City", + "FINAL ANSWER: Benin City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.18848, + "lon": 28.32078, + "name": "Benoni" + }, + { + "lat": -25.0999, + "lon": 30.78001, + "name": "Sabie" + }, + { + "lat": -26.25, + "lon": 28.4, + "name": "Springs" + }, + { + "lat": -0.10221, + "lon": 34.76171, + "name": "Kisumu" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + } + ], + "question": "Which location is the geographic outlier among: Benoni, Sabie, Springs, Kisumu, Ringwood?", + "ground_truth": { + "answer": "Ringwood", + "outlier_distance_km": 8604.3, + "second_furthest_km": 3261.2, + "clarity_ratio": 2.64, + "median_distance_km": 2563.9, + "distances_to_centroid": { + "Benoni": 2563.9, + "Sabie": 2314.2, + "Springs": 2556.3, + "Kisumu": 3261.2, + "Ringwood": 8604.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Benoni: (-26.19°, 28.32°)", + " Sabie: (-25.10°, 30.78°)", + " Springs: (-26.25°, 28.40°)", + " Kisumu: (-0.10°, 34.76°)", + " Ringwood: (-37.82°, 145.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ringwood: 8604.3 km from centroid", + " Kisumu: 3261.2 km from centroid", + " Benoni: 2563.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ringwood", + "FINAL ANSWER: Ringwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8149, + "lon": 144.95052, + "name": "Docklands" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + }, + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": 43.78609, + "lon": -79.33502, + "name": "Pleasant View" + } + ], + "question": "Which location is the geographic outlier among: Docklands, Mount Martha, Hampton Park, Tamworth, Pleasant View?", + "ground_truth": { + "answer": "Pleasant View", + "outlier_distance_km": 17401.0, + "second_furthest_km": 5067.7, + "clarity_ratio": 3.43, + "median_distance_km": 4642.5, + "distances_to_centroid": { + "Docklands": 4611.6, + "Mount Martha": 4628.2, + "Hampton Park": 4642.5, + "Tamworth": 5067.7, + "Pleasant View": 17401.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Docklands: (-37.81°, 144.95°)", + " Mount Martha: (-38.27°, 145.02°)", + " Hampton Park: (-38.03°, 145.25°)", + " Tamworth: (-31.09°, 150.93°)", + " Pleasant View: (43.79°, -79.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pleasant View: 17401.0 km from centroid", + " Tamworth: 5067.7 km from centroid", + " Hampton Park: 4642.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pleasant View", + "FINAL ANSWER: Pleasant View" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.695, + "lon": -79.2959, + "name": "Taylor-Massey" + }, + { + "lat": 45.63076, + "lon": -72.95699, + "name": "Saint-Hyacinthe" + }, + { + "lat": 26.13397, + "lon": -80.1131, + "name": "Sunrise" + }, + { + "lat": 45.40008, + "lon": -74.03251, + "name": "Vaudreuil-Dorion" + }, + { + "lat": 34.66799, + "lon": 137.26736, + "name": "Tahara" + } + ], + "question": "Which location is the geographic outlier among: Taylor-Massey, Saint-Hyacinthe, Sunrise, Vaudreuil-Dorion, Tahara?", + "ground_truth": { + "answer": "Tahara", + "outlier_distance_km": 11760.8, + "second_furthest_km": 4514.7, + "clarity_ratio": 2.6, + "median_distance_km": 3778.8, + "distances_to_centroid": { + "Taylor-Massey": 3778.8, + "Saint-Hyacinthe": 3261.3, + "Sunrise": 4514.7, + "Vaudreuil-Dorion": 3345.9, + "Tahara": 11760.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taylor-Massey: (43.70°, -79.30°)", + " Saint-Hyacinthe: (45.63°, -72.96°)", + " Sunrise: (26.13°, -80.11°)", + " Vaudreuil-Dorion: (45.40°, -74.03°)", + " Tahara: (34.67°, 137.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tahara: 11760.8 km from centroid", + " Sunrise: 4514.7 km from centroid", + " Taylor-Massey: 3778.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tahara", + "FINAL ANSWER: Tahara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.36217, + "lon": -0.09421, + "name": "South Croydon" + }, + { + "lat": 51.66361, + "lon": 16.0845, + "name": "Głogów" + }, + { + "lat": 41.67041, + "lon": -3.6892, + "name": "Aranda de Duero" + }, + { + "lat": 47.91303, + "lon": 1.97705, + "name": "Saint-Jean-de-Braye" + }, + { + "lat": 19.845, + "lon": -99.23333, + "name": "Santa Teresa" + } + ], + "question": "Which location is the geographic outlier among: South Croydon, Głogów, Aranda de Duero, Saint-Jean-de-Braye, Santa Teresa?", + "ground_truth": { + "answer": "Santa Teresa", + "outlier_distance_km": 7912.6, + "second_furthest_km": 2675.7, + "clarity_ratio": 2.96, + "median_distance_km": 1612.0, + "distances_to_centroid": { + "South Croydon": 1612.0, + "Głogów": 2675.7, + "Aranda de Duero": 1100.4, + "Saint-Jean-de-Braye": 1598.5, + "Santa Teresa": 7912.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " South Croydon: (51.36°, -0.09°)", + " Głogów: (51.66°, 16.08°)", + " Aranda de Duero: (41.67°, -3.69°)", + " Saint-Jean-de-Braye: (47.91°, 1.98°)", + " Santa Teresa: (19.84°, -99.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Teresa: 7912.6 km from centroid", + " Głogów: 2675.7 km from centroid", + " South Croydon: 1612.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Teresa", + "FINAL ANSWER: Santa Teresa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.43869, + "lon": 108.31324, + "name": "Baojia" + }, + { + "lat": 8.95583, + "lon": 76.67388, + "name": "Elampalloor" + }, + { + "lat": 28.70958, + "lon": 77.2587, + "name": "Khajoori Khas" + }, + { + "lat": 25.04493, + "lon": 100.51437, + "name": "Nanjian" + }, + { + "lat": -28.84556, + "lon": -51.89028, + "name": "Guaporé" + } + ], + "question": "Which location is the geographic outlier among: Baojia, Elampalloor, Khajoori Khas, Nanjian, Guaporé?", + "ground_truth": { + "answer": "Guaporé", + "outlier_distance_km": 13011.5, + "second_furthest_km": 5098.7, + "clarity_ratio": 2.55, + "median_distance_km": 4245.2, + "distances_to_centroid": { + "Baojia": 5098.7, + "Elampalloor": 1636.0, + "Khajoori Khas": 2371.1, + "Nanjian": 4245.2, + "Guaporé": 13011.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baojia: (29.44°, 108.31°)", + " Elampalloor: (8.96°, 76.67°)", + " Khajoori Khas: (28.71°, 77.26°)", + " Nanjian: (25.04°, 100.51°)", + " Guaporé: (-28.85°, -51.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guaporé: 13011.5 km from centroid", + " Baojia: 5098.7 km from centroid", + " Nanjian: 4245.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guaporé", + "FINAL ANSWER: Guaporé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.78705, + "lon": -73.97542, + "name": "Upper West Side" + }, + { + "lat": 42.29669, + "lon": -89.62123, + "name": "Freeport" + }, + { + "lat": 43.36679, + "lon": -80.94972, + "name": "Stratford" + }, + { + "lat": 41.43982, + "lon": -72.01424, + "name": "Ledyard" + }, + { + "lat": 34.29722, + "lon": 117.77222, + "name": "Nianzhuang" + } + ], + "question": "Which location is the geographic outlier among: Upper West Side, Freeport, Stratford, Ledyard, Nianzhuang?", + "ground_truth": { + "answer": "Nianzhuang", + "outlier_distance_km": 11391.7, + "second_furthest_km": 4106.1, + "clarity_ratio": 2.77, + "median_distance_km": 3389.9, + "distances_to_centroid": { + "Upper West Side": 2870.1, + "Freeport": 4106.1, + "Stratford": 3389.9, + "Ledyard": 2696.1, + "Nianzhuang": 11391.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Upper West Side: (40.79°, -73.98°)", + " Freeport: (42.30°, -89.62°)", + " Stratford: (43.37°, -80.95°)", + " Ledyard: (41.44°, -72.01°)", + " Nianzhuang: (34.30°, 117.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nianzhuang: 11391.7 km from centroid", + " Freeport: 4106.1 km from centroid", + " Stratford: 3389.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nianzhuang", + "FINAL ANSWER: Nianzhuang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.15, + "lon": -0.43333, + "name": "Alzira" + }, + { + "lat": 55.61171, + "lon": 40.65023, + "name": "Gus’-Khrustal’nyy" + }, + { + "lat": 37.60197, + "lon": -0.98397, + "name": "Cartagena" + }, + { + "lat": 53.37596, + "lon": 51.3452, + "name": "Otradnyy" + }, + { + "lat": 49.27784, + "lon": -123.12794, + "name": "Downtown" + } + ], + "question": "Which location is the geographic outlier among: Alzira, Gus’-Khrustal’nyy, Cartagena, Otradnyy, Downtown?", + "ground_truth": { + "answer": "Downtown", + "outlier_distance_km": 7695.6, + "second_furthest_km": 4063.0, + "clarity_ratio": 1.89, + "median_distance_km": 3343.0, + "distances_to_centroid": { + "Alzira": 1002.3, + "Gus’-Khrustal’nyy": 3343.0, + "Cartagena": 1139.2, + "Otradnyy": 4063.0, + "Downtown": 7695.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alzira: (39.15°, -0.43°)", + " Gus’-Khrustal’nyy: (55.61°, 40.65°)", + " Cartagena: (37.60°, -0.98°)", + " Otradnyy: (53.38°, 51.35°)", + " Downtown: (49.28°, -123.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Downtown: 7695.6 km from centroid", + " Otradnyy: 4063.0 km from centroid", + " Gus’-Khrustal’nyy: 3343.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Downtown", + "FINAL ANSWER: Downtown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.8423, + "lon": -90.70428, + "name": "Jonesboro" + }, + { + "lat": 42.96083, + "lon": -89.46984, + "name": "Fitchburg" + }, + { + "lat": 40.42331, + "lon": -104.70913, + "name": "Greeley" + }, + { + "lat": 38.96122, + "lon": -77.02748, + "name": "Brightwood" + }, + { + "lat": 54.84034, + "lon": -1.46427, + "name": "Houghton-Le-Spring" + } + ], + "question": "Which location is the geographic outlier among: Jonesboro, Fitchburg, Greeley, Brightwood, Houghton-Le-Spring?", + "ground_truth": { + "answer": "Houghton-Le-Spring", + "outlier_distance_km": 5156.5, + "second_furthest_km": 2662.2, + "clarity_ratio": 1.94, + "median_distance_km": 1720.8, + "distances_to_centroid": { + "Jonesboro": 1720.8, + "Fitchburg": 1368.9, + "Greeley": 2662.2, + "Brightwood": 546.2, + "Houghton-Le-Spring": 5156.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jonesboro: (35.84°, -90.70°)", + " Fitchburg: (42.96°, -89.47°)", + " Greeley: (40.42°, -104.71°)", + " Brightwood: (38.96°, -77.03°)", + " Houghton-Le-Spring: (54.84°, -1.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Houghton-Le-Spring: 5156.5 km from centroid", + " Greeley: 2662.2 km from centroid", + " Jonesboro: 1720.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Houghton-Le-Spring", + "FINAL ANSWER: Houghton-Le-Spring" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.50054, + "lon": -1.82657, + "name": "Washwood Heath" + }, + { + "lat": 40.46041, + "lon": -3.69413, + "name": "Castillejos" + }, + { + "lat": 53.34174, + "lon": -2.73124, + "name": "Runcorn" + }, + { + "lat": 55.86515, + "lon": -4.25763, + "name": "Glasgow" + }, + { + "lat": -31.4183, + "lon": -64.49008, + "name": "Villa Carlos Paz" + } + ], + "question": "Which location is the geographic outlier among: Washwood Heath, Castillejos, Runcorn, Glasgow, Villa Carlos Paz?", + "ground_truth": { + "answer": "Villa Carlos Paz", + "outlier_distance_km": 8920.0, + "second_furthest_km": 2561.1, + "clarity_ratio": 3.48, + "median_distance_km": 2356.1, + "distances_to_centroid": { + "Washwood Heath": 2308.3, + "Castillejos": 1249.0, + "Runcorn": 2356.1, + "Glasgow": 2561.1, + "Villa Carlos Paz": 8920.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Washwood Heath: (52.50°, -1.83°)", + " Castillejos: (40.46°, -3.69°)", + " Runcorn: (53.34°, -2.73°)", + " Glasgow: (55.87°, -4.26°)", + " Villa Carlos Paz: (-31.42°, -64.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Villa Carlos Paz: 8920.0 km from centroid", + " Glasgow: 2561.1 km from centroid", + " Runcorn: 2356.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Villa Carlos Paz", + "FINAL ANSWER: Villa Carlos Paz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.03528, + "lon": 38.66083, + "name": "Burayu" + }, + { + "lat": 30.36056, + "lon": 31.3776, + "name": "Mashtūl as Sūq" + }, + { + "lat": 9.21667, + "lon": 41.1, + "name": "Hīrna" + }, + { + "lat": -26.1625, + "lon": 27.8725, + "name": "Roodepoort" + }, + { + "lat": -37.69047, + "lon": 144.74172, + "name": "Hillside" + } + ], + "question": "Which location is the geographic outlier among: Burayu, Mashtūl as Sūq, Hīrna, Roodepoort, Hillside?", + "ground_truth": { + "answer": "Hillside", + "outlier_distance_km": 9623.7, + "second_furthest_km": 4588.6, + "clarity_ratio": 2.1, + "median_distance_km": 4011.1, + "distances_to_centroid": { + "Burayu": 2413.5, + "Mashtūl as Sūq": 4588.6, + "Hīrna": 2206.3, + "Roodepoort": 4011.1, + "Hillside": 9623.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Burayu: (9.04°, 38.66°)", + " Mashtūl as Sūq: (30.36°, 31.38°)", + " Hīrna: (9.22°, 41.10°)", + " Roodepoort: (-26.16°, 27.87°)", + " Hillside: (-37.69°, 144.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hillside: 9623.7 km from centroid", + " Mashtūl as Sūq: 4588.6 km from centroid", + " Roodepoort: 4011.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hillside", + "FINAL ANSWER: Hillside" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": -23.69748, + "lon": 133.88362, + "name": "Alice Springs" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -23.49417, + "lon": -46.43222, + "name": "São Miguel" + } + ], + "question": "Which location is the geographic outlier among: Officer, Alice Springs, North Melbourne, Broken Hill, São Miguel?", + "ground_truth": { + "answer": "São Miguel", + "outlier_distance_km": 13178.1, + "second_furthest_km": 3854.0, + "clarity_ratio": 3.42, + "median_distance_km": 3813.8, + "distances_to_centroid": { + "Officer": 3854.0, + "Alice Springs": 3064.8, + "North Melbourne": 3813.8, + "Broken Hill": 3549.0, + "São Miguel": 13178.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Officer: (-38.06°, 145.41°)", + " Alice Springs: (-23.70°, 133.88°)", + " North Melbourne: (-37.80°, 144.95°)", + " Broken Hill: (-31.97°, 141.45°)", + " São Miguel: (-23.49°, -46.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Miguel: 13178.1 km from centroid", + " Officer: 3854.0 km from centroid", + " North Melbourne: 3813.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Miguel", + "FINAL ANSWER: São Miguel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.42896, + "lon": 39.92391, + "name": "Adler" + }, + { + "lat": 53.64789, + "lon": -2.31683, + "name": "Ramsbottom" + }, + { + "lat": 53.3618, + "lon": -2.73406, + "name": "Widnes" + }, + { + "lat": 50.81809, + "lon": 6.1347, + "name": "Würselen" + }, + { + "lat": -7.55472, + "lon": -35.45306, + "name": "Macaparana" + } + ], + "question": "Which location is the geographic outlier among: Adler, Ramsbottom, Widnes, Würselen, Macaparana?", + "ground_truth": { + "answer": "Macaparana", + "outlier_distance_km": 6382.6, + "second_furthest_km": 3264.4, + "clarity_ratio": 1.96, + "median_distance_km": 1678.0, + "distances_to_centroid": { + "Adler": 3264.4, + "Ramsbottom": 1678.0, + "Widnes": 1652.1, + "Würselen": 1399.4, + "Macaparana": 6382.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adler: (43.43°, 39.92°)", + " Ramsbottom: (53.65°, -2.32°)", + " Widnes: (53.36°, -2.73°)", + " Würselen: (50.82°, 6.13°)", + " Macaparana: (-7.55°, -35.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Macaparana: 6382.6 km from centroid", + " Adler: 3264.4 km from centroid", + " Ramsbottom: 1678.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Macaparana", + "FINAL ANSWER: Macaparana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.46179, + "lon": 85.53179, + "name": "Bakhtiyārpur" + }, + { + "lat": 30.06603, + "lon": 105.80934, + "name": "Tai’an" + }, + { + "lat": 16.41639, + "lon": 120.59306, + "name": "Baguio" + }, + { + "lat": 11.13849, + "lon": 79.07556, + "name": "Ariyalūr" + }, + { + "lat": 48.82586, + "lon": 2.3508, + "name": "Maison Blanche" + } + ], + "question": "Which location is the geographic outlier among: Bakhtiyārpur, Tai’an, Baguio, Ariyalūr, Maison Blanche?", + "ground_truth": { + "answer": "Maison Blanche", + "outlier_distance_km": 6861.8, + "second_furthest_km": 4458.3, + "clarity_ratio": 1.54, + "median_distance_km": 2683.7, + "distances_to_centroid": { + "Bakhtiyārpur": 693.5, + "Tai’an": 2683.7, + "Baguio": 4458.3, + "Ariyalūr": 1695.5, + "Maison Blanche": 6861.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bakhtiyārpur: (25.46°, 85.53°)", + " Tai’an: (30.07°, 105.81°)", + " Baguio: (16.42°, 120.59°)", + " Ariyalūr: (11.14°, 79.08°)", + " Maison Blanche: (48.83°, 2.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maison Blanche: 6861.8 km from centroid", + " Baguio: 4458.3 km from centroid", + " Tai’an: 2683.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maison Blanche", + "FINAL ANSWER: Maison Blanche" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + }, + { + "lat": -37.75405, + "lon": 145.14864, + "name": "Templestowe" + }, + { + "lat": 5.10535, + "lon": -1.2466, + "name": "Cape Coast" + } + ], + "question": "Which location is the geographic outlier among: Landsdale, Boronia, Upper Coomera, Templestowe, Cape Coast?", + "ground_truth": { + "answer": "Cape Coast", + "outlier_distance_km": 12542.7, + "second_furthest_km": 4110.2, + "clarity_ratio": 3.05, + "median_distance_km": 3409.9, + "distances_to_centroid": { + "Landsdale": 760.3, + "Boronia": 3409.9, + "Upper Coomera": 4110.2, + "Templestowe": 3395.6, + "Cape Coast": 12542.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Landsdale: (-31.81°, 115.87°)", + " Boronia: (-37.87°, 145.28°)", + " Upper Coomera: (-27.88°, 153.29°)", + " Templestowe: (-37.75°, 145.15°)", + " Cape Coast: (5.11°, -1.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cape Coast: 12542.7 km from centroid", + " Upper Coomera: 4110.2 km from centroid", + " Boronia: 3409.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cape Coast", + "FINAL ANSWER: Cape Coast" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.11667, + "lon": 2.76667, + "name": "Banyoles" + }, + { + "lat": 51.0555, + "lon": 6.22658, + "name": "Hückelhoven" + }, + { + "lat": 52.41667, + "lon": 0.75, + "name": "Thetford" + }, + { + "lat": 51.26371, + "lon": 6.54734, + "name": "Willich" + }, + { + "lat": 32.63958, + "lon": -96.53832, + "name": "Seagoville" + } + ], + "question": "Which location is the geographic outlier among: Banyoles, Hückelhoven, Thetford, Willich, Seagoville?", + "ground_truth": { + "answer": "Seagoville", + "outlier_distance_km": 6787.7, + "second_furthest_km": 1757.6, + "clarity_ratio": 3.86, + "median_distance_km": 1731.3, + "distances_to_centroid": { + "Banyoles": 1558.3, + "Hückelhoven": 1731.3, + "Thetford": 1415.5, + "Willich": 1757.6, + "Seagoville": 6787.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banyoles: (42.12°, 2.77°)", + " Hückelhoven: (51.06°, 6.23°)", + " Thetford: (52.42°, 0.75°)", + " Willich: (51.26°, 6.55°)", + " Seagoville: (32.64°, -96.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Seagoville: 6787.7 km from centroid", + " Willich: 1757.6 km from centroid", + " Hückelhoven: 1731.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Seagoville", + "FINAL ANSWER: Seagoville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.24295, + "lon": 148.60484, + "name": "Dubbo" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": 19.31556, + "lon": -98.88284, + "name": "Ixtapaluca" + } + ], + "question": "Which location is the geographic outlier among: Dubbo, Townsville, Te Atatu South, Officer, Ixtapaluca?", + "ground_truth": { + "answer": "Ixtapaluca", + "outlier_distance_km": 17691.1, + "second_furthest_km": 6979.9, + "clarity_ratio": 2.53, + "median_distance_km": 4616.0, + "distances_to_centroid": { + "Dubbo": 4616.0, + "Townsville": 4526.2, + "Te Atatu South": 6979.9, + "Officer": 4417.6, + "Ixtapaluca": 17691.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dubbo: (-32.24°, 148.60°)", + " Townsville: (-19.27°, 146.81°)", + " Te Atatu South: (-36.86°, 174.65°)", + " Officer: (-38.06°, 145.41°)", + " Ixtapaluca: (19.32°, -98.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ixtapaluca: 17691.1 km from centroid", + " Te Atatu South: 6979.9 km from centroid", + " Dubbo: 4616.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ixtapaluca", + "FINAL ANSWER: Ixtapaluca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.4532, + "lon": -45.72831, + "name": "Cândido Mendes" + }, + { + "lat": -22.23, + "lon": -45.93639, + "name": "Pouso Alegre" + }, + { + "lat": -1.81361, + "lon": -49.79528, + "name": "Curralinho" + }, + { + "lat": -10.22306, + "lon": -54.97972, + "name": "Peixoto de Azevedo" + }, + { + "lat": 27.89232, + "lon": -101.42319, + "name": "Palau" + } + ], + "question": "Which location is the geographic outlier among: Cândido Mendes, Pouso Alegre, Curralinho, Peixoto de Azevedo, Palau?", + "ground_truth": { + "answer": "Palau", + "outlier_distance_km": 5538.6, + "second_furthest_km": 2730.1, + "clarity_ratio": 2.03, + "median_distance_km": 1538.9, + "distances_to_centroid": { + "Cândido Mendes": 1538.9, + "Pouso Alegre": 2730.1, + "Curralinho": 1087.1, + "Peixoto de Azevedo": 1088.3, + "Palau": 5538.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cândido Mendes: (-1.45°, -45.73°)", + " Pouso Alegre: (-22.23°, -45.94°)", + " Curralinho: (-1.81°, -49.80°)", + " Peixoto de Azevedo: (-10.22°, -54.98°)", + " Palau: (27.89°, -101.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Palau: 5538.6 km from centroid", + " Pouso Alegre: 2730.1 km from centroid", + " Cândido Mendes: 1538.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Palau", + "FINAL ANSWER: Palau" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": 45.52345, + "lon": -122.67621, + "name": "Portland" + } + ], + "question": "Which location is the geographic outlier among: Hawthorn, Lalor, Bundoora, Earlwood, Portland?", + "ground_truth": { + "answer": "Portland", + "outlier_distance_km": 15742.0, + "second_furthest_km": 5896.9, + "clarity_ratio": 2.67, + "median_distance_km": 5367.6, + "distances_to_centroid": { + "Hawthorn": 5366.9, + "Lalor": 5363.5, + "Bundoora": 5367.6, + "Earlwood": 5896.9, + "Portland": 15742.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hawthorn: (-37.82°, 145.04°)", + " Lalor: (-37.67°, 145.02°)", + " Bundoora: (-37.70°, 145.06°)", + " Earlwood: (-33.92°, 151.13°)", + " Portland: (45.52°, -122.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Portland: 15742.0 km from centroid", + " Earlwood: 5896.9 km from centroid", + " Bundoora: 5367.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Portland", + "FINAL ANSWER: Portland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.2855, + "lon": -157.83594, + "name": "Waikīkī" + }, + { + "lat": 43.69899, + "lon": -79.54786, + "name": "Kingsview Village-The Westway" + }, + { + "lat": 33.83335, + "lon": -117.29615, + "name": "Mead Valley" + }, + { + "lat": 38.10409, + "lon": -122.25664, + "name": "Vallejo" + }, + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + } + ], + "question": "Which location is the geographic outlier among: Waikīkī, Kingsview Village-The Westway, Mead Valley, Vallejo, Mulgrave?", + "ground_truth": { + "answer": "Mulgrave", + "outlier_distance_km": 16370.6, + "second_furthest_km": 9367.8, + "clarity_ratio": 1.75, + "median_distance_km": 5714.0, + "distances_to_centroid": { + "Waikīkī": 9367.8, + "Kingsview Village-The Westway": 2927.2, + "Mead Valley": 5234.6, + "Vallejo": 5714.0, + "Mulgrave": 16370.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waikīkī: (21.29°, -157.84°)", + " Kingsview Village-The Westway: (43.70°, -79.55°)", + " Mead Valley: (33.83°, -117.30°)", + " Vallejo: (38.10°, -122.26°)", + " Mulgrave: (-37.93°, 145.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mulgrave: 16370.6 km from centroid", + " Waikīkī: 9367.8 km from centroid", + " Vallejo: 5714.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mulgrave", + "FINAL ANSWER: Mulgrave" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": 48.22786, + "lon": 9.87874, + "name": "Laupheim" + } + ], + "question": "Which location is the geographic outlier among: Gosnells, Thornlie, Kingsford, Wheelers Hill, Laupheim?", + "ground_truth": { + "answer": "Laupheim", + "outlier_distance_km": 12020.6, + "second_furthest_km": 4686.6, + "clarity_ratio": 2.56, + "median_distance_km": 4289.0, + "distances_to_centroid": { + "Gosnells": 1821.1, + "Thornlie": 1816.7, + "Kingsford": 4686.6, + "Wheelers Hill": 4289.0, + "Laupheim": 12020.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gosnells: (-32.08°, 116.01°)", + " Thornlie: (-32.06°, 115.95°)", + " Kingsford: (-33.92°, 151.23°)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Laupheim: (48.23°, 9.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Laupheim: 12020.6 km from centroid", + " Kingsford: 4686.6 km from centroid", + " Wheelers Hill: 4289.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Laupheim", + "FINAL ANSWER: Laupheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.36723, + "lon": -72.51852, + "name": "Amherst" + }, + { + "lat": 41.62666, + "lon": -93.71217, + "name": "Urbandale" + }, + { + "lat": 35.04275, + "lon": -120.476, + "name": "Nipomo" + }, + { + "lat": 15.76889, + "lon": -96.135, + "name": "Crucecita" + }, + { + "lat": 5.92665, + "lon": -0.98577, + "name": "Akim Oda" + } + ], + "question": "Which location is the geographic outlier among: Amherst, Urbandale, Nipomo, Crucecita, Akim Oda?", + "ground_truth": { + "answer": "Akim Oda", + "outlier_distance_km": 8304.4, + "second_furthest_km": 4176.8, + "clarity_ratio": 1.99, + "median_distance_km": 2419.9, + "distances_to_centroid": { + "Amherst": 1627.0, + "Urbandale": 2145.5, + "Nipomo": 4176.8, + "Crucecita": 2419.9, + "Akim Oda": 8304.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Amherst: (42.37°, -72.52°)", + " Urbandale: (41.63°, -93.71°)", + " Nipomo: (35.04°, -120.48°)", + " Crucecita: (15.77°, -96.14°)", + " Akim Oda: (5.93°, -0.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Akim Oda: 8304.4 km from centroid", + " Nipomo: 4176.8 km from centroid", + " Crucecita: 2419.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Akim Oda", + "FINAL ANSWER: Akim Oda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + }, + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + }, + { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + }, + { + "lat": -21.83222, + "lon": -46.89361, + "name": "Vargem Grande do Sul" + } + ], + "question": "Which location is the geographic outlier among: Hoppers Crossing, Warragul, Dandenong, Cessnock, Vargem Grande do Sul?", + "ground_truth": { + "answer": "Vargem Grande do Sul", + "outlier_distance_km": 13290.6, + "second_furthest_km": 3995.9, + "clarity_ratio": 3.33, + "median_distance_km": 3420.5, + "distances_to_centroid": { + "Hoppers Crossing": 3314.7, + "Warragul": 3420.5, + "Dandenong": 3357.8, + "Cessnock": 3995.9, + "Vargem Grande do Sul": 13290.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hoppers Crossing: (-37.88°, 144.70°)", + " Warragul: (-38.16°, 145.93°)", + " Dandenong: (-37.98°, 145.20°)", + " Cessnock: (-32.83°, 151.36°)", + " Vargem Grande do Sul: (-21.83°, -46.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vargem Grande do Sul: 13290.6 km from centroid", + " Cessnock: 3995.9 km from centroid", + " Warragul: 3420.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vargem Grande do Sul", + "FINAL ANSWER: Vargem Grande do Sul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": 19.3467, + "lon": -99.16174, + "name": "Coyoacán" + } + ], + "question": "Which location is the geographic outlier among: Otahuhu, Avondale, Engadine, Maroubra, Coyoacán?", + "ground_truth": { + "answer": "Coyoacán", + "outlier_distance_km": 16906.0, + "second_furthest_km": 6186.6, + "clarity_ratio": 2.73, + "median_distance_km": 6174.9, + "distances_to_centroid": { + "Otahuhu": 6186.6, + "Avondale": 6174.9, + "Engadine": 4040.1, + "Maroubra": 4059.4, + "Coyoacán": 16906.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Otahuhu: (-36.94°, 174.84°)", + " Avondale: (-36.88°, 174.70°)", + " Engadine: (-34.07°, 151.01°)", + " Maroubra: (-33.95°, 151.23°)", + " Coyoacán: (19.35°, -99.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coyoacán: 16906.0 km from centroid", + " Otahuhu: 6186.6 km from centroid", + " Avondale: 6174.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coyoacán", + "FINAL ANSWER: Coyoacán" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": 26.33863, + "lon": -80.1869, + "name": "Sandalfoot Cove" + } + ], + "question": "Which location is the geographic outlier among: Warragul, Dunedin, Wahroonga, Chatswood, Sandalfoot Cove?", + "ground_truth": { + "answer": "Sandalfoot Cove", + "outlier_distance_km": 19211.0, + "second_furthest_km": 5969.4, + "clarity_ratio": 3.22, + "median_distance_km": 4289.1, + "distances_to_centroid": { + "Warragul": 3869.1, + "Dunedin": 5969.4, + "Wahroonga": 4282.6, + "Chatswood": 4289.1, + "Sandalfoot Cove": 19211.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warragul: (-38.16°, 145.93°)", + " Dunedin: (-45.87°, 170.50°)", + " Wahroonga: (-33.72°, 151.12°)", + " Chatswood: (-33.80°, 151.18°)", + " Sandalfoot Cove: (26.34°, -80.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sandalfoot Cove: 19211.0 km from centroid", + " Dunedin: 5969.4 km from centroid", + " Chatswood: 4289.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sandalfoot Cove", + "FINAL ANSWER: Sandalfoot Cove" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + }, + { + "lat": -37.90561, + "lon": 145.00279, + "name": "Brighton" + }, + { + "lat": 1.01659, + "lon": 39.49122, + "name": "Habaswein" + } + ], + "question": "Which location is the geographic outlier among: Blacktown, Armidale, Merrylands, Brighton, Habaswein?", + "ground_truth": { + "answer": "Habaswein", + "outlier_distance_km": 9872.7, + "second_furthest_km": 2372.4, + "clarity_ratio": 4.16, + "median_distance_km": 2360.1, + "distances_to_centroid": { + "Blacktown": 2352.5, + "Armidale": 2372.4, + "Merrylands": 2360.1, + "Brighton": 2027.3, + "Habaswein": 9872.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blacktown: (-33.77°, 150.92°)", + " Armidale: (-30.50°, 151.67°)", + " Merrylands: (-33.83°, 150.98°)", + " Brighton: (-37.91°, 145.00°)", + " Habaswein: (1.02°, 39.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Habaswein: 9872.7 km from centroid", + " Armidale: 2372.4 km from centroid", + " Merrylands: 2360.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Habaswein", + "FINAL ANSWER: Habaswein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.40717, + "lon": 79.12216, + "name": "Tittagudi" + }, + { + "lat": 33.84103, + "lon": 105.23117, + "name": "Luoyu" + }, + { + "lat": 23.33062, + "lon": 86.36303, + "name": "Puruliya" + }, + { + "lat": 22.20928, + "lon": 75.47057, + "name": "Dhāmnod" + }, + { + "lat": 51.62867, + "lon": 0.41963, + "name": "Billericay" + } + ], + "question": "Which location is the geographic outlier among: Tittagudi, Luoyu, Puruliya, Dhāmnod, Billericay?", + "ground_truth": { + "answer": "Billericay", + "outlier_distance_km": 6141.2, + "second_furthest_km": 3450.6, + "clarity_ratio": 1.78, + "median_distance_km": 2154.9, + "distances_to_centroid": { + "Tittagudi": 2154.9, + "Luoyu": 3450.6, + "Puruliya": 1796.2, + "Dhāmnod": 931.6, + "Billericay": 6141.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tittagudi: (11.41°, 79.12°)", + " Luoyu: (33.84°, 105.23°)", + " Puruliya: (23.33°, 86.36°)", + " Dhāmnod: (22.21°, 75.47°)", + " Billericay: (51.63°, 0.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Billericay: 6141.2 km from centroid", + " Luoyu: 3450.6 km from centroid", + " Tittagudi: 2154.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Billericay", + "FINAL ANSWER: Billericay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -19.30323, + "lon": 146.72531, + "name": "Kirwan" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": 53.03333, + "lon": -1.4, + "name": "Ripley" + } + ], + "question": "Which location is the geographic outlier among: Frankston East, Greystanes, Kirwan, Hobart, Ripley?", + "ground_truth": { + "answer": "Ripley", + "outlier_distance_km": 13376.0, + "second_furthest_km": 4078.7, + "clarity_ratio": 3.28, + "median_distance_km": 3849.2, + "distances_to_centroid": { + "Frankston East": 3617.2, + "Greystanes": 3849.2, + "Kirwan": 3084.2, + "Hobart": 4078.7, + "Ripley": 13376.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frankston East: (-38.13°, 145.13°)", + " Greystanes: (-33.82°, 150.95°)", + " Kirwan: (-19.30°, 146.73°)", + " Hobart: (-42.88°, 147.33°)", + " Ripley: (53.03°, -1.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ripley: 13376.0 km from centroid", + " Hobart: 4078.7 km from centroid", + " Greystanes: 3849.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ripley", + "FINAL ANSWER: Ripley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.8231, + "lon": 116.0466, + "name": "Kinarut" + }, + { + "lat": 24.94824, + "lon": 114.06572, + "name": "Shixing" + }, + { + "lat": 19.02475, + "lon": 73.31688, + "name": "Neral" + }, + { + "lat": 28.30766, + "lon": 105.0522, + "name": "Bowangshan" + }, + { + "lat": 7.85868, + "lon": 10.97187, + "name": "Beli" + } + ], + "question": "Which location is the geographic outlier among: Kinarut, Shixing, Neral, Bowangshan, Beli?", + "ground_truth": { + "answer": "Beli", + "outlier_distance_km": 7943.2, + "second_furthest_km": 3716.9, + "clarity_ratio": 2.14, + "median_distance_km": 3239.6, + "distances_to_centroid": { + "Kinarut": 3716.9, + "Shixing": 3239.6, + "Neral": 1135.7, + "Bowangshan": 2491.1, + "Beli": 7943.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kinarut: (5.82°, 116.05°)", + " Shixing: (24.95°, 114.07°)", + " Neral: (19.02°, 73.32°)", + " Bowangshan: (28.31°, 105.05°)", + " Beli: (7.86°, 10.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Beli: 7943.2 km from centroid", + " Kinarut: 3716.9 km from centroid", + " Shixing: 3239.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Beli", + "FINAL ANSWER: Beli" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.21644, + "lon": 9.02596, + "name": "Albstadt" + }, + { + "lat": 50.41038, + "lon": 2.83053, + "name": "Avion" + }, + { + "lat": 46.5599, + "lon": 39.6321, + "name": "Kushchyovskaya" + }, + { + "lat": 41.37857, + "lon": 2.15937, + "name": "Sant Antoni" + }, + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + } + ], + "question": "Which location is the geographic outlier among: Albstadt, Avion, Kushchyovskaya, Sant Antoni, Surfers Paradise?", + "ground_truth": { + "answer": "Surfers Paradise", + "outlier_distance_km": 13554.0, + "second_furthest_km": 3782.6, + "clarity_ratio": 3.58, + "median_distance_km": 3633.3, + "distances_to_centroid": { + "Albstadt": 3276.9, + "Avion": 3782.6, + "Kushchyovskaya": 1658.0, + "Sant Antoni": 3633.3, + "Surfers Paradise": 13554.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albstadt: (48.22°, 9.03°)", + " Avion: (50.41°, 2.83°)", + " Kushchyovskaya: (46.56°, 39.63°)", + " Sant Antoni: (41.38°, 2.16°)", + " Surfers Paradise: (-28.00°, 153.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Surfers Paradise: 13554.0 km from centroid", + " Avion: 3782.6 km from centroid", + " Sant Antoni: 3633.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Surfers Paradise", + "FINAL ANSWER: Surfers Paradise" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.66028, + "lon": -43.78611, + "name": "Conselheiro Lafaiete" + }, + { + "lat": -19.61806, + "lon": -44.04306, + "name": "Pedro Leopoldo" + }, + { + "lat": -27.87083, + "lon": -54.48139, + "name": "Santa Rosa" + }, + { + "lat": -3.10056, + "lon": -45.03361, + "name": "Matinha" + }, + { + "lat": 30.63965, + "lon": 108.23701, + "name": "Longsha" + } + ], + "question": "Which location is the geographic outlier among: Conselheiro Lafaiete, Pedro Leopoldo, Santa Rosa, Matinha, Longsha?", + "ground_truth": { + "answer": "Longsha", + "outlier_distance_km": 13710.3, + "second_furthest_km": 4610.2, + "clarity_ratio": 2.97, + "median_distance_km": 3310.7, + "distances_to_centroid": { + "Conselheiro Lafaiete": 3310.7, + "Pedro Leopoldo": 3296.6, + "Santa Rosa": 4610.2, + "Matinha": 3279.2, + "Longsha": 13710.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Conselheiro Lafaiete: (-20.66°, -43.79°)", + " Pedro Leopoldo: (-19.62°, -44.04°)", + " Santa Rosa: (-27.87°, -54.48°)", + " Matinha: (-3.10°, -45.03°)", + " Longsha: (30.64°, 108.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Longsha: 13710.3 km from centroid", + " Santa Rosa: 4610.2 km from centroid", + " Conselheiro Lafaiete: 3310.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Longsha", + "FINAL ANSWER: Longsha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.02333, + "lon": 106.42963, + "name": "Shuangfeng" + }, + { + "lat": 18.71364, + "lon": 76.06718, + "name": "Kaij" + }, + { + "lat": 3.6253, + "lon": 98.864, + "name": "Percut" + }, + { + "lat": 5.02917, + "lon": 119.77306, + "name": "Bongao" + }, + { + "lat": -6.89028, + "lon": -38.55528, + "name": "Cajazeiras" + } + ], + "question": "Which location is the geographic outlier among: Shuangfeng, Kaij, Percut, Bongao, Cajazeiras?", + "ground_truth": { + "answer": "Cajazeiras", + "outlier_distance_km": 12438.9, + "second_furthest_km": 5234.9, + "clarity_ratio": 2.38, + "median_distance_km": 4151.1, + "distances_to_centroid": { + "Shuangfeng": 4151.1, + "Kaij": 1031.2, + "Percut": 2994.6, + "Bongao": 5234.9, + "Cajazeiras": 12438.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shuangfeng: (30.02°, 106.43°)", + " Kaij: (18.71°, 76.07°)", + " Percut: (3.63°, 98.86°)", + " Bongao: (5.03°, 119.77°)", + " Cajazeiras: (-6.89°, -38.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cajazeiras: 12438.9 km from centroid", + " Bongao: 5234.9 km from centroid", + " Shuangfeng: 4151.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cajazeiras", + "FINAL ANSWER: Cajazeiras" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.98693, + "lon": 2.44892, + "name": "Gonesse" + }, + { + "lat": 45.61236, + "lon": 9.23985, + "name": "Lissone" + }, + { + "lat": 49.3, + "lon": 6.81667, + "name": "Schwalbach" + }, + { + "lat": 40.4165, + "lon": -3.70256, + "name": "Madrid" + }, + { + "lat": -33.8178, + "lon": 151.00348, + "name": "Parramatta" + } + ], + "question": "Which location is the geographic outlier among: Gonesse, Lissone, Schwalbach, Madrid, Parramatta?", + "ground_truth": { + "answer": "Parramatta", + "outlier_distance_km": 14226.1, + "second_furthest_km": 3508.8, + "clarity_ratio": 4.05, + "median_distance_km": 3329.5, + "distances_to_centroid": { + "Gonesse": 3329.5, + "Lissone": 2699.2, + "Schwalbach": 3074.8, + "Madrid": 3508.8, + "Parramatta": 14226.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gonesse: (48.99°, 2.45°)", + " Lissone: (45.61°, 9.24°)", + " Schwalbach: (49.30°, 6.82°)", + " Madrid: (40.42°, -3.70°)", + " Parramatta: (-33.82°, 151.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Parramatta: 14226.1 km from centroid", + " Madrid: 3508.8 km from centroid", + " Gonesse: 3329.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Parramatta", + "FINAL ANSWER: Parramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.4807, + "lon": -94.27134, + "name": "Bella Vista" + }, + { + "lat": 42.15843, + "lon": -71.14477, + "name": "Canton" + }, + { + "lat": 38.9556, + "lon": -90.18678, + "name": "Godfrey" + }, + { + "lat": 25.77583, + "lon": -100.42583, + "name": "Mitras Poniente" + }, + { + "lat": -36.8382, + "lon": 174.61019, + "name": "Massey" + } + ], + "question": "Which location is the geographic outlier among: Bella Vista, Canton, Godfrey, Mitras Poniente, Massey?", + "ground_truth": { + "answer": "Massey", + "outlier_distance_km": 16574.5, + "second_furthest_km": 6494.4, + "clarity_ratio": 2.55, + "median_distance_km": 5802.5, + "distances_to_centroid": { + "Bella Vista": 5802.5, + "Canton": 3986.2, + "Godfrey": 5455.1, + "Mitras Poniente": 6494.4, + "Massey": 16574.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bella Vista: (36.48°, -94.27°)", + " Canton: (42.16°, -71.14°)", + " Godfrey: (38.96°, -90.19°)", + " Mitras Poniente: (25.78°, -100.43°)", + " Massey: (-36.84°, 174.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Massey: 16574.5 km from centroid", + " Mitras Poniente: 6494.4 km from centroid", + " Bella Vista: 5802.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Massey", + "FINAL ANSWER: Massey" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.03333, + "lon": 105.9, + "name": "Long Bien" + }, + { + "lat": 39.71667, + "lon": 140.11667, + "name": "Akita" + }, + { + "lat": 9.61827, + "lon": 76.53127, + "name": "Perumbaikad" + }, + { + "lat": 11.23052, + "lon": 75.85178, + "name": "Pantheeramkavu" + }, + { + "lat": 27.94752, + "lon": -82.45843, + "name": "Tampa" + } + ], + "question": "Which location is the geographic outlier among: Long Bien, Akita, Perumbaikad, Pantheeramkavu, Tampa?", + "ground_truth": { + "answer": "Tampa", + "outlier_distance_km": 13356.2, + "second_furthest_km": 7386.9, + "clarity_ratio": 1.81, + "median_distance_km": 4406.4, + "distances_to_centroid": { + "Long Bien": 4406.4, + "Akita": 7386.9, + "Perumbaikad": 1973.9, + "Pantheeramkavu": 1795.6, + "Tampa": 13356.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Long Bien: (21.03°, 105.90°)", + " Akita: (39.72°, 140.12°)", + " Perumbaikad: (9.62°, 76.53°)", + " Pantheeramkavu: (11.23°, 75.85°)", + " Tampa: (27.95°, -82.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tampa: 13356.2 km from centroid", + " Akita: 7386.9 km from centroid", + " Long Bien: 4406.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tampa", + "FINAL ANSWER: Tampa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.13019, + "lon": 104.38198, + "name": "Deyang" + }, + { + "lat": 9.60886, + "lon": 76.36083, + "name": "Muhamma" + }, + { + "lat": -6.8487, + "lon": 108.6422, + "name": "Karangsembung" + }, + { + "lat": 28.1722, + "lon": 78.06376, + "name": "Pahāsu" + }, + { + "lat": -4.75639, + "lon": -42.57556, + "name": "José de Freitas" + } + ], + "question": "Which location is the geographic outlier among: Deyang, Muhamma, Karangsembung, Pahāsu, José de Freitas?", + "ground_truth": { + "answer": "José de Freitas", + "outlier_distance_km": 12022.3, + "second_furthest_km": 5242.0, + "clarity_ratio": 2.29, + "median_distance_km": 4595.6, + "distances_to_centroid": { + "Deyang": 4595.6, + "Muhamma": 1261.5, + "Karangsembung": 5242.0, + "Pahāsu": 2304.0, + "José de Freitas": 12022.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deyang: (31.13°, 104.38°)", + " Muhamma: (9.61°, 76.36°)", + " Karangsembung: (-6.85°, 108.64°)", + " Pahāsu: (28.17°, 78.06°)", + " José de Freitas: (-4.76°, -42.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " José de Freitas: 12022.3 km from centroid", + " Karangsembung: 5242.0 km from centroid", + " Deyang: 4595.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: José de Freitas", + "FINAL ANSWER: José de Freitas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.27194, + "lon": -101.98602, + "name": "Loreto" + }, + { + "lat": 47.40177, + "lon": -122.32429, + "name": "Des Moines" + }, + { + "lat": 33.86726, + "lon": -112.14682, + "name": "Anthem" + }, + { + "lat": 39.52963, + "lon": -119.8138, + "name": "Reno" + }, + { + "lat": -7.50528, + "lon": -35.31833, + "name": "Timbaúba" + } + ], + "question": "Which location is the geographic outlier among: Loreto, Des Moines, Anthem, Reno, Timbaúba?", + "ground_truth": { + "answer": "Timbaúba", + "outlier_distance_km": 7789.8, + "second_furthest_km": 3073.9, + "clarity_ratio": 2.53, + "median_distance_km": 2417.7, + "distances_to_centroid": { + "Loreto": 653.4, + "Des Moines": 3073.9, + "Anthem": 1521.0, + "Reno": 2417.7, + "Timbaúba": 7789.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Loreto: (22.27°, -101.99°)", + " Des Moines: (47.40°, -122.32°)", + " Anthem: (33.87°, -112.15°)", + " Reno: (39.53°, -119.81°)", + " Timbaúba: (-7.51°, -35.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Timbaúba: 7789.8 km from centroid", + " Des Moines: 3073.9 km from centroid", + " Reno: 2417.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Timbaúba", + "FINAL ANSWER: Timbaúba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -31.88775, + "lon": 115.9099, + "name": "Morley" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + { + "lat": -14.75583, + "lon": -43.93222, + "name": "Manga" + } + ], + "question": "Which location is the geographic outlier among: Hobart, Balwyn North, Morley, Orange, Manga?", + "ground_truth": { + "answer": "Manga", + "outlier_distance_km": 13707.0, + "second_furthest_km": 4307.2, + "clarity_ratio": 3.18, + "median_distance_km": 4062.7, + "distances_to_centroid": { + "Hobart": 4062.7, + "Balwyn North": 3881.2, + "Morley": 1245.1, + "Orange": 4307.2, + "Manga": 13707.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hobart: (-42.88°, 147.33°)", + " Balwyn North: (-37.79°, 145.09°)", + " Morley: (-31.89°, 115.91°)", + " Orange: (-33.28°, 149.10°)", + " Manga: (-14.76°, -43.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manga: 13707.0 km from centroid", + " Orange: 4307.2 km from centroid", + " Hobart: 4062.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manga", + "FINAL ANSWER: Manga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.88583, + "lon": -46.005, + "name": "Arame" + }, + { + "lat": -11.01472, + "lon": -37.20639, + "name": "São Cristóvão" + }, + { + "lat": -19.11333, + "lon": -51.73417, + "name": "Cassilândia" + }, + { + "lat": -16.62375, + "lon": -72.71055, + "name": "Camaná" + }, + { + "lat": 50.9236, + "lon": 22.22706, + "name": "Kraśnik" + } + ], + "question": "Which location is the geographic outlier among: Arame, São Cristóvão, Cassilândia, Camaná, Kraśnik?", + "ground_truth": { + "answer": "Kraśnik", + "outlier_distance_km": 7933.9, + "second_furthest_km": 4311.8, + "clarity_ratio": 1.84, + "median_distance_km": 2646.2, + "distances_to_centroid": { + "Arame": 1122.2, + "São Cristóvão": 1209.0, + "Cassilândia": 2646.2, + "Camaná": 4311.8, + "Kraśnik": 7933.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arame: (-4.89°, -46.01°)", + " São Cristóvão: (-11.01°, -37.21°)", + " Cassilândia: (-19.11°, -51.73°)", + " Camaná: (-16.62°, -72.71°)", + " Kraśnik: (50.92°, 22.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kraśnik: 7933.9 km from centroid", + " Camaná: 4311.8 km from centroid", + " Cassilândia: 2646.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kraśnik", + "FINAL ANSWER: Kraśnik" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.43351, + "lon": 129.057, + "name": "Cheongsong gun" + }, + { + "lat": 25.66742, + "lon": 116.75429, + "name": "Wenheng" + }, + { + "lat": 12.99623, + "lon": 80.07514, + "name": "Kavanur" + }, + { + "lat": 35.63424, + "lon": 139.57546, + "name": "Komae" + }, + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + } + ], + "question": "Which location is the geographic outlier among: Cheongsong gun, Wenheng, Kavanur, Komae, Lilydale?", + "ground_truth": { + "answer": "Lilydale", + "outlier_distance_km": 6304.3, + "second_furthest_km": 4542.1, + "clarity_ratio": 1.39, + "median_distance_km": 2912.7, + "distances_to_centroid": { + "Cheongsong gun": 2522.9, + "Wenheng": 1353.8, + "Kavanur": 4542.1, + "Komae": 2912.7, + "Lilydale": 6304.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cheongsong gun: (36.43°, 129.06°)", + " Wenheng: (25.67°, 116.75°)", + " Kavanur: (13.00°, 80.08°)", + " Komae: (35.63°, 139.58°)", + " Lilydale: (-37.75°, 145.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lilydale: 6304.3 km from centroid", + " Kavanur: 4542.1 km from centroid", + " Komae: 2912.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lilydale", + "FINAL ANSWER: Lilydale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -29.8175, + "lon": -50.51972, + "name": "Santo Antônio da Patrulha" + }, + { + "lat": -18.54861, + "lon": -42.55694, + "name": "Peçanha" + }, + { + "lat": -8.76194, + "lon": -63.90389, + "name": "Porto Velho" + }, + { + "lat": -23.5725, + "lon": -46.03861, + "name": "Biritiba Mirim" + }, + { + "lat": 44.85157, + "lon": 0.48171, + "name": "Bergerac" + } + ], + "question": "Which location is the geographic outlier among: Santo Antônio da Patrulha, Peçanha, Porto Velho, Biritiba Mirim, Bergerac?", + "ground_truth": { + "answer": "Bergerac", + "outlier_distance_km": 7084.2, + "second_furthest_km": 2727.1, + "clarity_ratio": 2.6, + "median_distance_km": 2582.1, + "distances_to_centroid": { + "Santo Antônio da Patrulha": 2727.1, + "Peçanha": 1284.6, + "Porto Velho": 2582.1, + "Biritiba Mirim": 1917.1, + "Bergerac": 7084.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santo Antônio da Patrulha: (-29.82°, -50.52°)", + " Peçanha: (-18.55°, -42.56°)", + " Porto Velho: (-8.76°, -63.90°)", + " Biritiba Mirim: (-23.57°, -46.04°)", + " Bergerac: (44.85°, 0.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bergerac: 7084.2 km from centroid", + " Santo Antônio da Patrulha: 2727.1 km from centroid", + " Porto Velho: 2582.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bergerac", + "FINAL ANSWER: Bergerac" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.1974, + "lon": 25.98311, + "name": "Wolmaransstad" + }, + { + "lat": -30.99766, + "lon": 26.32862, + "name": "Burgersdorp" + }, + { + "lat": 0.5635, + "lon": 34.56055, + "name": "Bungoma" + }, + { + "lat": -0.33316, + "lon": 37.64587, + "name": "Chuka" + }, + { + "lat": -17.18889, + "lon": -41.69472, + "name": "Caraí" + } + ], + "question": "Which location is the geographic outlier among: Wolmaransstad, Burgersdorp, Bungoma, Chuka, Caraí?", + "ground_truth": { + "answer": "Caraí", + "outlier_distance_km": 6205.1, + "second_furthest_km": 2834.6, + "clarity_ratio": 2.19, + "median_distance_km": 2630.8, + "distances_to_centroid": { + "Wolmaransstad": 1667.1, + "Burgersdorp": 2034.8, + "Bungoma": 2630.8, + "Chuka": 2834.6, + "Caraí": 6205.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wolmaransstad: (-27.20°, 25.98°)", + " Burgersdorp: (-31.00°, 26.33°)", + " Bungoma: (0.56°, 34.56°)", + " Chuka: (-0.33°, 37.65°)", + " Caraí: (-17.19°, -41.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caraí: 6205.1 km from centroid", + " Chuka: 2834.6 km from centroid", + " Bungoma: 2630.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caraí", + "FINAL ANSWER: Caraí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": 36.59634, + "lon": -119.4504, + "name": "Reedley" + } + ], + "question": "Which location is the geographic outlier among: Shepparton, Hobart, Cranbourne North, Mackay, Reedley?", + "ground_truth": { + "answer": "Reedley", + "outlier_distance_km": 16347.2, + "second_furthest_km": 5752.1, + "clarity_ratio": 2.84, + "median_distance_km": 5559.3, + "distances_to_centroid": { + "Shepparton": 5306.3, + "Hobart": 5559.3, + "Cranbourne North": 5316.2, + "Mackay": 5752.1, + "Reedley": 16347.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shepparton: (-36.38°, 145.40°)", + " Hobart: (-42.88°, 147.33°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Mackay: (-21.15°, 149.17°)", + " Reedley: (36.60°, -119.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Reedley: 16347.2 km from centroid", + " Mackay: 5752.1 km from centroid", + " Hobart: 5559.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Reedley", + "FINAL ANSWER: Reedley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.61357, + "lon": 79.37442, + "name": "Peddapalli" + }, + { + "lat": 29.409, + "lon": 106.14228, + "name": "Dingjia" + }, + { + "lat": 38.13387, + "lon": 85.52992, + "name": "Qiemo" + }, + { + "lat": 34.72083, + "lon": 104.88583, + "name": "Wushan" + }, + { + "lat": 53.4614, + "lon": -2.92863, + "name": "Fazakerley" + } + ], + "question": "Which location is the geographic outlier among: Peddapalli, Dingjia, Qiemo, Wushan, Fazakerley?", + "ground_truth": { + "answer": "Fazakerley", + "outlier_distance_km": 6183.7, + "second_furthest_km": 3018.2, + "clarity_ratio": 2.05, + "median_distance_km": 2754.8, + "distances_to_centroid": { + "Peddapalli": 1867.8, + "Dingjia": 3018.2, + "Qiemo": 1041.4, + "Wushan": 2754.8, + "Fazakerley": 6183.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Peddapalli: (18.61°, 79.37°)", + " Dingjia: (29.41°, 106.14°)", + " Qiemo: (38.13°, 85.53°)", + " Wushan: (34.72°, 104.89°)", + " Fazakerley: (53.46°, -2.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fazakerley: 6183.7 km from centroid", + " Dingjia: 3018.2 km from centroid", + " Wushan: 2754.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fazakerley", + "FINAL ANSWER: Fazakerley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.79554, + "lon": 108.65921, + "name": "Tai’an" + }, + { + "lat": 10.06667, + "lon": 76.28333, + "name": "Elūr" + }, + { + "lat": 14.37917, + "lon": 121.0525, + "name": "Tunasan" + }, + { + "lat": 6.86814, + "lon": 101.25009, + "name": "Pattani" + }, + { + "lat": 53.95387, + "lon": 32.86409, + "name": "Roslavl’" + } + ], + "question": "Which location is the geographic outlier among: Tai’an, Elūr, Tunasan, Pattani, Roslavl’?", + "ground_truth": { + "answer": "Roslavl’", + "outlier_distance_km": 5684.6, + "second_furthest_km": 3603.6, + "clarity_ratio": 1.58, + "median_distance_km": 2303.0, + "distances_to_centroid": { + "Tai’an": 2207.0, + "Elūr": 1921.4, + "Tunasan": 3603.6, + "Pattani": 2303.0, + "Roslavl’": 5684.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tai’an: (30.80°, 108.66°)", + " Elūr: (10.07°, 76.28°)", + " Tunasan: (14.38°, 121.05°)", + " Pattani: (6.87°, 101.25°)", + " Roslavl’: (53.95°, 32.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Roslavl’: 5684.6 km from centroid", + " Tunasan: 3603.6 km from centroid", + " Pattani: 2303.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Roslavl’", + "FINAL ANSWER: Roslavl’" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.28026, + "lon": 75.46818, + "name": "Adampur" + }, + { + "lat": 2.691, + "lon": 101.989, + "name": "Taman Senawang Indah" + }, + { + "lat": 34.53333, + "lon": 117.88333, + "name": "Chahe" + }, + { + "lat": -0.8006, + "lon": 100.6571, + "name": "Solok" + }, + { + "lat": 6.23669, + "lon": 0.99578, + "name": "Dzodze" + } + ], + "question": "Which location is the geographic outlier among: Adampur, Taman Senawang Indah, Chahe, Solok, Dzodze?", + "ground_truth": { + "answer": "Dzodze", + "outlier_distance_km": 8590.7, + "second_furthest_km": 4453.3, + "clarity_ratio": 1.93, + "median_distance_km": 2885.7, + "distances_to_centroid": { + "Adampur": 1704.5, + "Taman Senawang Indah": 2799.6, + "Chahe": 4453.3, + "Solok": 2885.7, + "Dzodze": 8590.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adampur: (29.28°, 75.47°)", + " Taman Senawang Indah: (2.69°, 101.99°)", + " Chahe: (34.53°, 117.88°)", + " Solok: (-0.80°, 100.66°)", + " Dzodze: (6.24°, 1.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dzodze: 8590.7 km from centroid", + " Chahe: 4453.3 km from centroid", + " Solok: 2885.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dzodze", + "FINAL ANSWER: Dzodze" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.35528, + "lon": -48.34194, + "name": "Marituba" + }, + { + "lat": -22.84333, + "lon": -47.60611, + "name": "Rio das Pedras" + }, + { + "lat": 8.81136, + "lon": -74.72084, + "name": "Sucre" + }, + { + "lat": -19.80139, + "lon": -45.68556, + "name": "Luz" + }, + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + } + ], + "question": "Which location is the geographic outlier among: Marituba, Rio das Pedras, Sucre, Luz, Adelaide?", + "ground_truth": { + "answer": "Adelaide", + "outlier_distance_km": 13926.8, + "second_furthest_km": 7003.5, + "clarity_ratio": 1.99, + "median_distance_km": 3870.1, + "distances_to_centroid": { + "Marituba": 3870.1, + "Rio das Pedras": 3512.1, + "Sucre": 7003.5, + "Luz": 3264.8, + "Adelaide": 13926.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marituba: (-1.36°, -48.34°)", + " Rio das Pedras: (-22.84°, -47.61°)", + " Sucre: (8.81°, -74.72°)", + " Luz: (-19.80°, -45.69°)", + " Adelaide: (-34.93°, 138.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adelaide: 13926.8 km from centroid", + " Sucre: 7003.5 km from centroid", + " Marituba: 3870.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adelaide", + "FINAL ANSWER: Adelaide" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.67618, + "lon": 16.10094, + "name": "Vibo Valentia" + }, + { + "lat": 48.82104, + "lon": 2.27718, + "name": "Issy-les-Moulineaux" + }, + { + "lat": 51.56387, + "lon": 0.50859, + "name": "Pitsea" + }, + { + "lat": 41.20036, + "lon": 16.59905, + "name": "Molfetta" + }, + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + } + ], + "question": "Which location is the geographic outlier among: Vibo Valentia, Issy-les-Moulineaux, Pitsea, Molfetta, Titirangi?", + "ground_truth": { + "answer": "Titirangi", + "outlier_distance_km": 15539.4, + "second_furthest_km": 4265.4, + "clarity_ratio": 3.64, + "median_distance_km": 4044.2, + "distances_to_centroid": { + "Vibo Valentia": 2632.7, + "Issy-les-Moulineaux": 4044.2, + "Pitsea": 4265.4, + "Molfetta": 2689.7, + "Titirangi": 15539.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vibo Valentia: (38.68°, 16.10°)", + " Issy-les-Moulineaux: (48.82°, 2.28°)", + " Pitsea: (51.56°, 0.51°)", + " Molfetta: (41.20°, 16.60°)", + " Titirangi: (-36.94°, 174.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Titirangi: 15539.4 km from centroid", + " Pitsea: 4265.4 km from centroid", + " Issy-les-Moulineaux: 4044.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Titirangi", + "FINAL ANSWER: Titirangi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.65466, + "lon": -122.40775, + "name": "South San Francisco" + }, + { + "lat": 37.38522, + "lon": -122.11413, + "name": "Los Altos" + }, + { + "lat": 21.43434, + "lon": -102.57427, + "name": "Teocaltiche" + }, + { + "lat": 40.66205, + "lon": -73.73541, + "name": "Rosedale" + }, + { + "lat": 35.68463, + "lon": 138.50979, + "name": "Kai" + } + ], + "question": "Which location is the geographic outlier among: South San Francisco, Los Altos, Teocaltiche, Rosedale, Kai?", + "ground_truth": { + "answer": "Kai", + "outlier_distance_km": 12050.7, + "second_furthest_km": 5808.9, + "clarity_ratio": 2.07, + "median_distance_km": 5793.5, + "distances_to_centroid": { + "South San Francisco": 5808.9, + "Los Altos": 5793.5, + "Teocaltiche": 4711.9, + "Rosedale": 1661.8, + "Kai": 12050.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " South San Francisco: (37.65°, -122.41°)", + " Los Altos: (37.39°, -122.11°)", + " Teocaltiche: (21.43°, -102.57°)", + " Rosedale: (40.66°, -73.74°)", + " Kai: (35.68°, 138.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kai: 12050.7 km from centroid", + " South San Francisco: 5808.9 km from centroid", + " Los Altos: 5793.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kai", + "FINAL ANSWER: Kai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + { + "lat": -26.06566, + "lon": 27.64765, + "name": "Bagale" + } + ], + "question": "Which location is the geographic outlier among: Mernda, Mount Isa, Coorparoo, Tarneit, Bagale?", + "ground_truth": { + "answer": "Bagale", + "outlier_distance_km": 8981.4, + "second_furthest_km": 3032.6, + "clarity_ratio": 2.96, + "median_distance_km": 2291.3, + "distances_to_centroid": { + "Mernda": 2291.3, + "Mount Isa": 2032.3, + "Coorparoo": 3032.6, + "Tarneit": 2261.3, + "Bagale": 8981.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mernda: (-37.60°, 145.10°)", + " Mount Isa: (-20.73°, 139.50°)", + " Coorparoo: (-27.49°, 153.06°)", + " Tarneit: (-37.84°, 144.66°)", + " Bagale: (-26.07°, 27.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bagale: 8981.4 km from centroid", + " Coorparoo: 3032.6 km from centroid", + " Mernda: 2291.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bagale", + "FINAL ANSWER: Bagale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.10148, + "lon": -72.58981, + "name": "Springfield" + }, + { + "lat": 28.6, + "lon": -81.33924, + "name": "Winter Park" + }, + { + "lat": 40.52927, + "lon": -74.31598, + "name": "Fords" + }, + { + "lat": 40.57927, + "lon": -74.41154, + "name": "South Plainfield" + }, + { + "lat": 42.66085, + "lon": -8.11285, + "name": "Lalín" + } + ], + "question": "Which location is the geographic outlier among: Springfield, Winter Park, Fords, South Plainfield, Lalín?", + "ground_truth": { + "answer": "Lalín", + "outlier_distance_km": 4491.9, + "second_furthest_km": 2104.2, + "clarity_ratio": 2.13, + "median_distance_km": 1063.8, + "distances_to_centroid": { + "Springfield": 950.9, + "Winter Park": 2104.2, + "Fords": 1055.2, + "South Plainfield": 1063.8, + "Lalín": 4491.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Springfield: (42.10°, -72.59°)", + " Winter Park: (28.60°, -81.34°)", + " Fords: (40.53°, -74.32°)", + " South Plainfield: (40.58°, -74.41°)", + " Lalín: (42.66°, -8.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lalín: 4491.9 km from centroid", + " Winter Park: 2104.2 km from centroid", + " South Plainfield: 1063.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lalín", + "FINAL ANSWER: Lalín" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.87224, + "lon": -117.87034, + "name": "Placentia" + }, + { + "lat": 19.22201, + "lon": -99.20242, + "name": "San Miguel Ajusco" + }, + { + "lat": 43.30453, + "lon": -70.97562, + "name": "Rochester" + }, + { + "lat": 19.19251, + "lon": -99.02317, + "name": "Milpa Alta" + }, + { + "lat": 27.95243, + "lon": 30.78082, + "name": "Banī ‘Ubayd" + } + ], + "question": "Which location is the geographic outlier among: Placentia, San Miguel Ajusco, Rochester, Milpa Alta, Banī ‘Ubayd?", + "ground_truth": { + "answer": "Banī ‘Ubayd", + "outlier_distance_km": 9602.3, + "second_furthest_km": 4428.8, + "clarity_ratio": 2.17, + "median_distance_km": 3019.7, + "distances_to_centroid": { + "Placentia": 4428.8, + "San Miguel Ajusco": 3019.7, + "Rochester": 1623.2, + "Milpa Alta": 3004.2, + "Banī ‘Ubayd": 9602.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Placentia: (33.87°, -117.87°)", + " San Miguel Ajusco: (19.22°, -99.20°)", + " Rochester: (43.30°, -70.98°)", + " Milpa Alta: (19.19°, -99.02°)", + " Banī ‘Ubayd: (27.95°, 30.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Banī ‘Ubayd: 9602.3 km from centroid", + " Placentia: 4428.8 km from centroid", + " San Miguel Ajusco: 3019.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Banī ‘Ubayd", + "FINAL ANSWER: Banī ‘Ubayd" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": 3.71363, + "lon": 34.8572, + "name": "Kakuma" + } + ], + "question": "Which location is the geographic outlier among: Morphett Vale, Townsville, Ashfield, Port Macquarie, Kakuma?", + "ground_truth": { + "answer": "Kakuma", + "outlier_distance_km": 10168.6, + "second_furthest_km": 2910.2, + "clarity_ratio": 3.49, + "median_distance_km": 2817.6, + "distances_to_centroid": { + "Morphett Vale": 1873.2, + "Townsville": 2315.6, + "Ashfield": 2817.6, + "Port Macquarie": 2910.2, + "Kakuma": 10168.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morphett Vale: (-35.13°, 138.52°)", + " Townsville: (-19.27°, 146.81°)", + " Ashfield: (-33.89°, 151.12°)", + " Port Macquarie: (-31.43°, 152.91°)", + " Kakuma: (3.71°, 34.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kakuma: 10168.6 km from centroid", + " Port Macquarie: 2910.2 km from centroid", + " Ashfield: 2817.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kakuma", + "FINAL ANSWER: Kakuma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.68859, + "lon": 78.37985, + "name": "Sikandra Rao" + }, + { + "lat": 15.6321, + "lon": 121.1448, + "name": "Bongabon" + }, + { + "lat": 34.9802, + "lon": 136.15752, + "name": "Kōka" + }, + { + "lat": 26.04327, + "lon": 84.05298, + "name": "Sikandarpur" + }, + { + "lat": 29.77606, + "lon": -95.11465, + "name": "Channelview" + } + ], + "question": "Which location is the geographic outlier among: Sikandra Rao, Bongabon, Kōka, Sikandarpur, Channelview?", + "ground_truth": { + "answer": "Channelview", + "outlier_distance_km": 13372.5, + "second_furthest_km": 6716.2, + "clarity_ratio": 1.99, + "median_distance_km": 5912.5, + "distances_to_centroid": { + "Sikandra Rao": 1332.9, + "Bongabon": 5912.5, + "Kōka": 6716.2, + "Sikandarpur": 1904.8, + "Channelview": 13372.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sikandra Rao: (27.69°, 78.38°)", + " Bongabon: (15.63°, 121.14°)", + " Kōka: (34.98°, 136.16°)", + " Sikandarpur: (26.04°, 84.05°)", + " Channelview: (29.78°, -95.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Channelview: 13372.5 km from centroid", + " Kōka: 6716.2 km from centroid", + " Bongabon: 5912.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Channelview", + "FINAL ANSWER: Channelview" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.84755, + "lon": -115.56944, + "name": "Imperial" + }, + { + "lat": 29.55718, + "lon": -95.80856, + "name": "Rosenberg" + }, + { + "lat": 41.68199, + "lon": -85.97667, + "name": "Elkhart" + }, + { + "lat": 45.52289, + "lon": -122.98983, + "name": "Hillsboro" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + } + ], + "question": "Which location is the geographic outlier among: Imperial, Rosenberg, Elkhart, Hillsboro, Tuggeranong Administrative District?", + "ground_truth": { + "answer": "Tuggeranong Administrative District", + "outlier_distance_km": 17363.3, + "second_furthest_km": 6589.5, + "clarity_ratio": 2.63, + "median_distance_km": 6048.6, + "distances_to_centroid": { + "Imperial": 6048.6, + "Rosenberg": 4190.4, + "Elkhart": 3611.6, + "Hillsboro": 6589.5, + "Tuggeranong Administrative District": 17363.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Imperial: (32.85°, -115.57°)", + " Rosenberg: (29.56°, -95.81°)", + " Elkhart: (41.68°, -85.98°)", + " Hillsboro: (45.52°, -122.99°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tuggeranong Administrative District: 17363.3 km from centroid", + " Hillsboro: 6589.5 km from centroid", + " Imperial: 6048.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tuggeranong Administrative District", + "FINAL ANSWER: Tuggeranong Administrative District" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + }, + { + "lat": 34.09751, + "lon": -117.64839, + "name": "Upland" + } + ], + "question": "Which location is the geographic outlier among: Kensington, Umina Beach, Eastwood, Hampton Park, Upland?", + "ground_truth": { + "answer": "Upland", + "outlier_distance_km": 16394.2, + "second_furthest_km": 5551.7, + "clarity_ratio": 2.95, + "median_distance_km": 5543.2, + "distances_to_centroid": { + "Kensington": 5543.2, + "Umina Beach": 5551.7, + "Eastwood": 5530.1, + "Hampton Park": 5037.2, + "Upland": 16394.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kensington: (-33.92°, 151.22°)", + " Umina Beach: (-33.52°, 151.31°)", + " Eastwood: (-33.79°, 151.08°)", + " Hampton Park: (-38.03°, 145.25°)", + " Upland: (34.10°, -117.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upland: 16394.2 km from centroid", + " Umina Beach: 5551.7 km from centroid", + " Kensington: 5543.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upland", + "FINAL ANSWER: Upland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.77606, + "lon": -95.11465, + "name": "Channelview" + }, + { + "lat": 34.41333, + "lon": -119.86097, + "name": "Isla Vista" + }, + { + "lat": 40.69365, + "lon": -89.58899, + "name": "Peoria" + }, + { + "lat": 41.45532, + "lon": -81.91792, + "name": "Westlake" + }, + { + "lat": 35.29778, + "lon": 126.78444, + "name": "Jangseong" + } + ], + "question": "Which location is the geographic outlier among: Channelview, Isla Vista, Peoria, Westlake, Jangseong?", + "ground_truth": { + "answer": "Jangseong", + "outlier_distance_km": 12049.7, + "second_furthest_km": 6029.4, + "clarity_ratio": 2.0, + "median_distance_km": 4055.5, + "distances_to_centroid": { + "Channelview": 4055.5, + "Isla Vista": 6029.4, + "Peoria": 3286.2, + "Westlake": 2642.4, + "Jangseong": 12049.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Channelview: (29.78°, -95.11°)", + " Isla Vista: (34.41°, -119.86°)", + " Peoria: (40.69°, -89.59°)", + " Westlake: (41.46°, -81.92°)", + " Jangseong: (35.30°, 126.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jangseong: 12049.7 km from centroid", + " Isla Vista: 6029.4 km from centroid", + " Channelview: 4055.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jangseong", + "FINAL ANSWER: Jangseong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.66, + "lon": -37.78944, + "name": "Canindé de São Francisco" + }, + { + "lat": -6.18667, + "lon": -35.09194, + "name": "Tibau do Sul" + }, + { + "lat": -30.60106, + "lon": -71.19901, + "name": "Ovalle" + }, + { + "lat": -5.08, + "lon": -37.61667, + "name": "Baraúna" + }, + { + "lat": -37.95855, + "lon": 176.98545, + "name": "Whakatane" + } + ], + "question": "Which location is the geographic outlier among: Canindé de São Francisco, Tibau do Sul, Ovalle, Baraúna, Whakatane?", + "ground_truth": { + "answer": "Whakatane", + "outlier_distance_km": 13800.4, + "second_furthest_km": 7153.6, + "clarity_ratio": 1.93, + "median_distance_km": 4231.3, + "distances_to_centroid": { + "Canindé de São Francisco": 4075.4, + "Tibau do Sul": 3926.0, + "Ovalle": 7153.6, + "Baraúna": 4231.3, + "Whakatane": 13800.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canindé de São Francisco: (-9.66°, -37.79°)", + " Tibau do Sul: (-6.19°, -35.09°)", + " Ovalle: (-30.60°, -71.20°)", + " Baraúna: (-5.08°, -37.62°)", + " Whakatane: (-37.96°, 176.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whakatane: 13800.4 km from centroid", + " Ovalle: 7153.6 km from centroid", + " Baraúna: 4231.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whakatane", + "FINAL ANSWER: Whakatane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.43285, + "lon": -3.69354, + "name": "Almagro" + }, + { + "lat": 48.9482, + "lon": 2.19169, + "name": "Sartrouville" + }, + { + "lat": 51.11112, + "lon": 13.91199, + "name": "Radeberg" + }, + { + "lat": 48.96115, + "lon": 2.06882, + "name": "Achères" + }, + { + "lat": 6.09392, + "lon": -0.83599, + "name": "Kade" + } + ], + "question": "Which location is the geographic outlier among: Almagro, Sartrouville, Radeberg, Achères, Kade?", + "ground_truth": { + "answer": "Kade", + "outlier_distance_km": 3688.6, + "second_furthest_km": 1593.3, + "clarity_ratio": 2.32, + "median_distance_km": 1096.7, + "distances_to_centroid": { + "Almagro": 568.1, + "Sartrouville": 1094.9, + "Radeberg": 1593.3, + "Achères": 1096.7, + "Kade": 3688.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Almagro: (40.43°, -3.69°)", + " Sartrouville: (48.95°, 2.19°)", + " Radeberg: (51.11°, 13.91°)", + " Achères: (48.96°, 2.07°)", + " Kade: (6.09°, -0.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kade: 3688.6 km from centroid", + " Radeberg: 1593.3 km from centroid", + " Achères: 1096.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kade", + "FINAL ANSWER: Kade" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.92678, + "lon": -1.75773, + "name": "Sekondi-Takoradi" + }, + { + "lat": 27.55642, + "lon": 30.81057, + "name": "Dayrūţ" + }, + { + "lat": 31.24193, + "lon": 30.94504, + "name": "Ar Riyāḑ" + }, + { + "lat": -27.98299, + "lon": 30.71769, + "name": "Mondlo" + }, + { + "lat": 1.31678, + "lon": 124.80379, + "name": "Tomohon" + } + ], + "question": "Which location is the geographic outlier among: Sekondi-Takoradi, Dayrūţ, Ar Riyāḑ, Mondlo, Tomohon?", + "ground_truth": { + "answer": "Tomohon", + "outlier_distance_km": 9073.5, + "second_furthest_km": 4965.2, + "clarity_ratio": 1.83, + "median_distance_km": 4154.7, + "distances_to_centroid": { + "Sekondi-Takoradi": 4965.2, + "Dayrūţ": 2587.3, + "Ar Riyāḑ": 2935.3, + "Mondlo": 4154.7, + "Tomohon": 9073.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sekondi-Takoradi: (4.93°, -1.76°)", + " Dayrūţ: (27.56°, 30.81°)", + " Ar Riyāḑ: (31.24°, 30.95°)", + " Mondlo: (-27.98°, 30.72°)", + " Tomohon: (1.32°, 124.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tomohon: 9073.5 km from centroid", + " Sekondi-Takoradi: 4965.2 km from centroid", + " Mondlo: 4154.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tomohon", + "FINAL ANSWER: Tomohon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.11667, + "lon": 8.83333, + "name": "Mühlheim am Main" + }, + { + "lat": 44.20199, + "lon": 0.62055, + "name": "Agen" + }, + { + "lat": 43.51345, + "lon": 4.98747, + "name": "Istres" + }, + { + "lat": 50.83673, + "lon": -0.78003, + "name": "Chichester" + }, + { + "lat": 11.28333, + "lon": 36.21667, + "name": "Mambuk" + } + ], + "question": "Which location is the geographic outlier among: Mühlheim am Main, Agen, Istres, Chichester, Mambuk?", + "ground_truth": { + "answer": "Mambuk", + "outlier_distance_km": 4103.4, + "second_furthest_km": 1466.2, + "clarity_ratio": 2.8, + "median_distance_km": 1129.5, + "distances_to_centroid": { + "Mühlheim am Main": 1129.5, + "Agen": 902.0, + "Istres": 569.6, + "Chichester": 1466.2, + "Mambuk": 4103.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mühlheim am Main: (50.12°, 8.83°)", + " Agen: (44.20°, 0.62°)", + " Istres: (43.51°, 4.99°)", + " Chichester: (50.84°, -0.78°)", + " Mambuk: (11.28°, 36.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mambuk: 4103.4 km from centroid", + " Chichester: 1466.2 km from centroid", + " Mühlheim am Main: 1129.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mambuk", + "FINAL ANSWER: Mambuk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.42102, + "lon": -121.42384, + "name": "Laguna" + }, + { + "lat": 34.7698, + "lon": -84.97022, + "name": "Dalton" + }, + { + "lat": 34.14862, + "lon": -118.39647, + "name": "Studio City" + }, + { + "lat": 40.97926, + "lon": -74.11653, + "name": "Ridgewood" + }, + { + "lat": 6.41667, + "lon": 38.31667, + "name": "Dīla" + } + ], + "question": "Which location is the geographic outlier among: Laguna, Dalton, Studio City, Ridgewood, Dīla?", + "ground_truth": { + "answer": "Dīla", + "outlier_distance_km": 11552.3, + "second_furthest_km": 4530.0, + "clarity_ratio": 2.55, + "median_distance_km": 4315.5, + "distances_to_centroid": { + "Laguna": 4530.0, + "Dalton": 1272.3, + "Studio City": 4315.5, + "Ridgewood": 1129.8, + "Dīla": 11552.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Laguna: (38.42°, -121.42°)", + " Dalton: (34.77°, -84.97°)", + " Studio City: (34.15°, -118.40°)", + " Ridgewood: (40.98°, -74.12°)", + " Dīla: (6.42°, 38.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dīla: 11552.3 km from centroid", + " Laguna: 4530.0 km from centroid", + " Studio City: 4315.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dīla", + "FINAL ANSWER: Dīla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.42528, + "lon": -51.93861, + "name": "Maringá" + }, + { + "lat": -4.19444, + "lon": -40.47667, + "name": "Varjota" + }, + { + "lat": -25.76889, + "lon": -53.5325, + "name": "Realeza" + }, + { + "lat": -23.03556, + "lon": -49.16611, + "name": "Cerqueira César" + }, + { + "lat": 40.92237, + "lon": 14.42386, + "name": "Brusciano" + } + ], + "question": "Which location is the geographic outlier among: Maringá, Varjota, Realeza, Cerqueira César, Brusciano?", + "ground_truth": { + "answer": "Brusciano", + "outlier_distance_km": 7418.1, + "second_furthest_km": 2776.7, + "clarity_ratio": 2.67, + "median_distance_km": 2478.5, + "distances_to_centroid": { + "Maringá": 2478.5, + "Varjota": 578.7, + "Realeza": 2776.7, + "Cerqueira César": 2254.0, + "Brusciano": 7418.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maringá: (-23.43°, -51.94°)", + " Varjota: (-4.19°, -40.48°)", + " Realeza: (-25.77°, -53.53°)", + " Cerqueira César: (-23.04°, -49.17°)", + " Brusciano: (40.92°, 14.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brusciano: 7418.1 km from centroid", + " Realeza: 2776.7 km from centroid", + " Maringá: 2478.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brusciano", + "FINAL ANSWER: Brusciano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": -33.94185, + "lon": 150.8717, + "name": "Prestons" + }, + { + "lat": 30.04477, + "lon": 107.9149, + "name": "Longkong" + } + ], + "question": "Which location is the geographic outlier among: Camberwell, Cranbourne North, Alexandra Hills, Prestons, Longkong?", + "ground_truth": { + "answer": "Longkong", + "outlier_distance_km": 6703.4, + "second_furthest_km": 1903.6, + "clarity_ratio": 3.52, + "median_distance_km": 1873.1, + "distances_to_centroid": { + "Camberwell": 1873.1, + "Cranbourne North": 1903.6, + "Alexandra Hills": 1454.5, + "Prestons": 1721.1, + "Longkong": 6703.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Camberwell: (-37.84°, 145.07°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Prestons: (-33.94°, 150.87°)", + " Longkong: (30.04°, 107.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Longkong: 6703.4 km from centroid", + " Cranbourne North: 1903.6 km from centroid", + " Camberwell: 1873.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Longkong", + "FINAL ANSWER: Longkong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.67089, + "lon": -79.52246, + "name": "Edenbridge-Humber Valley" + }, + { + "lat": 28.07418, + "lon": -82.47176, + "name": "Lake Magdalene" + }, + { + "lat": 34.18667, + "lon": -118.44897, + "name": "Van Nuys" + }, + { + "lat": 31.69261, + "lon": -106.20748, + "name": "Horizon City" + }, + { + "lat": 52.62783, + "lon": 1.29834, + "name": "Norwich" + } + ], + "question": "Which location is the geographic outlier among: Edenbridge-Humber Valley, Lake Magdalene, Van Nuys, Horizon City, Norwich?", + "ground_truth": { + "answer": "Norwich", + "outlier_distance_km": 6017.1, + "second_furthest_km": 3710.9, + "clarity_ratio": 1.62, + "median_distance_km": 2738.1, + "distances_to_centroid": { + "Edenbridge-Humber Valley": 658.0, + "Lake Magdalene": 1217.5, + "Van Nuys": 3710.9, + "Horizon City": 2738.1, + "Norwich": 6017.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Edenbridge-Humber Valley: (43.67°, -79.52°)", + " Lake Magdalene: (28.07°, -82.47°)", + " Van Nuys: (34.19°, -118.45°)", + " Horizon City: (31.69°, -106.21°)", + " Norwich: (52.63°, 1.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Norwich: 6017.1 km from centroid", + " Van Nuys: 3710.9 km from centroid", + " Horizon City: 2738.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Norwich", + "FINAL ANSWER: Norwich" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -37.89359, + "lon": 145.05534, + "name": "Carnegie" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": 30.8248, + "lon": 30.81805, + "name": "Kafr az Zayyāt" + } + ], + "question": "Which location is the geographic outlier among: Maitland, Carnegie, Mandurah, Frankston East, Kafr az Zayyāt?", + "ground_truth": { + "answer": "Kafr az Zayyāt", + "outlier_distance_km": 10959.4, + "second_furthest_km": 3531.0, + "clarity_ratio": 3.1, + "median_distance_km": 3168.5, + "distances_to_centroid": { + "Maitland": 3531.0, + "Carnegie": 3150.6, + "Mandurah": 1175.8, + "Frankston East": 3168.5, + "Kafr az Zayyāt": 10959.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maitland: (-32.73°, 151.56°)", + " Carnegie: (-37.89°, 145.06°)", + " Mandurah: (-32.53°, 115.72°)", + " Frankston East: (-38.13°, 145.13°)", + " Kafr az Zayyāt: (30.82°, 30.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kafr az Zayyāt: 10959.4 km from centroid", + " Maitland: 3531.0 km from centroid", + " Frankston East: 3168.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kafr az Zayyāt", + "FINAL ANSWER: Kafr az Zayyāt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.98735, + "lon": 18.49746, + "name": "Lansdowne" + }, + { + "lat": -25.99636, + "lon": 28.2268, + "name": "Thembisa" + }, + { + "lat": 9.21866, + "lon": 3.20117, + "name": "Okuta" + }, + { + "lat": -23.04385, + "lon": 29.90319, + "name": "Louis Trichardt" + }, + { + "lat": 45.36551, + "lon": 38.21194, + "name": "Krasnoarmeyskaya" + } + ], + "question": "Which location is the geographic outlier among: Lansdowne, Thembisa, Okuta, Louis Trichardt, Krasnoarmeyskaya?", + "ground_truth": { + "answer": "Krasnoarmeyskaya", + "outlier_distance_km": 5859.9, + "second_furthest_km": 3190.5, + "clarity_ratio": 1.84, + "median_distance_km": 2804.0, + "distances_to_centroid": { + "Lansdowne": 3190.5, + "Thembisa": 2310.8, + "Okuta": 2804.0, + "Louis Trichardt": 2044.4, + "Krasnoarmeyskaya": 5859.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lansdowne: (-33.99°, 18.50°)", + " Thembisa: (-26.00°, 28.23°)", + " Okuta: (9.22°, 3.20°)", + " Louis Trichardt: (-23.04°, 29.90°)", + " Krasnoarmeyskaya: (45.37°, 38.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Krasnoarmeyskaya: 5859.9 km from centroid", + " Lansdowne: 3190.5 km from centroid", + " Okuta: 2804.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Krasnoarmeyskaya", + "FINAL ANSWER: Krasnoarmeyskaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.52754, + "lon": 11.54835, + "name": "Eisleben Lutherstadt" + }, + { + "lat": 53.41667, + "lon": -1.2, + "name": "Maltby" + }, + { + "lat": 38.01328, + "lon": -3.3705, + "name": "Úbeda" + }, + { + "lat": 43.31195, + "lon": 45.68895, + "name": "Grozny" + }, + { + "lat": -11.79667, + "lon": -49.52889, + "name": "Formoso do Araguaia" + } + ], + "question": "Which location is the geographic outlier among: Eisleben Lutherstadt, Maltby, Úbeda, Grozny, Formoso do Araguaia?", + "ground_truth": { + "answer": "Formoso do Araguaia", + "outlier_distance_km": 7403.5, + "second_furthest_km": 3949.0, + "clarity_ratio": 1.87, + "median_distance_km": 2064.5, + "distances_to_centroid": { + "Eisleben Lutherstadt": 2045.2, + "Maltby": 2064.5, + "Úbeda": 498.0, + "Grozny": 3949.0, + "Formoso do Araguaia": 7403.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eisleben Lutherstadt: (51.53°, 11.55°)", + " Maltby: (53.42°, -1.20°)", + " Úbeda: (38.01°, -3.37°)", + " Grozny: (43.31°, 45.69°)", + " Formoso do Araguaia: (-11.80°, -49.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Formoso do Araguaia: 7403.5 km from centroid", + " Grozny: 3949.0 km from centroid", + " Maltby: 2064.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Formoso do Araguaia", + "FINAL ANSWER: Formoso do Araguaia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.01907, + "lon": 20.88029, + "name": "Przasnysz" + }, + { + "lat": 48.83337, + "lon": 2.37513, + "name": "Gare" + }, + { + "lat": 52.04479, + "lon": 39.72569, + "name": "Usman’" + }, + { + "lat": 51.24827, + "lon": -0.76389, + "name": "Aldershot" + }, + { + "lat": 33.68527, + "lon": -117.81371, + "name": "Westpark" + } + ], + "question": "Which location is the geographic outlier among: Przasnysz, Gare, Usman’, Aldershot, Westpark?", + "ground_truth": { + "answer": "Westpark", + "outlier_distance_km": 8397.8, + "second_furthest_km": 3596.6, + "clarity_ratio": 2.33, + "median_distance_km": 2321.2, + "distances_to_centroid": { + "Przasnysz": 2321.2, + "Gare": 1003.9, + "Usman’": 3596.6, + "Aldershot": 841.0, + "Westpark": 8397.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Przasnysz: (53.02°, 20.88°)", + " Gare: (48.83°, 2.38°)", + " Usman’: (52.04°, 39.73°)", + " Aldershot: (51.25°, -0.76°)", + " Westpark: (33.69°, -117.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Westpark: 8397.8 km from centroid", + " Usman’: 3596.6 km from centroid", + " Przasnysz: 2321.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Westpark", + "FINAL ANSWER: Westpark" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.72028, + "lon": -39.11389, + "name": "Abaré" + }, + { + "lat": -23.00667, + "lon": -44.31806, + "name": "Angra dos Reis" + }, + { + "lat": -1.12889, + "lon": -47.62, + "name": "Igarapé-Açu" + }, + { + "lat": -23.67379, + "lon": -46.65681, + "name": "Cidade Ademar" + }, + { + "lat": 36.52715, + "lon": 138.08943, + "name": "Chikuma" + } + ], + "question": "Which location is the geographic outlier among: Abaré, Angra dos Reis, Igarapé-Açu, Cidade Ademar, Chikuma?", + "ground_truth": { + "answer": "Chikuma", + "outlier_distance_km": 15003.1, + "second_furthest_km": 4693.4, + "clarity_ratio": 3.2, + "median_distance_km": 4444.4, + "distances_to_centroid": { + "Abaré": 3485.0, + "Angra dos Reis": 4444.4, + "Igarapé-Açu": 4420.5, + "Cidade Ademar": 4693.4, + "Chikuma": 15003.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abaré: (-8.72°, -39.11°)", + " Angra dos Reis: (-23.01°, -44.32°)", + " Igarapé-Açu: (-1.13°, -47.62°)", + " Cidade Ademar: (-23.67°, -46.66°)", + " Chikuma: (36.53°, 138.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chikuma: 15003.1 km from centroid", + " Cidade Ademar: 4693.4 km from centroid", + " Angra dos Reis: 4444.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chikuma", + "FINAL ANSWER: Chikuma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.35889, + "lon": -39.31167, + "name": "Canindé" + }, + { + "lat": -13.62611, + "lon": -41.32694, + "name": "Barra da Estiva" + }, + { + "lat": 10.44589, + "lon": -74.95869, + "name": "Manatí" + }, + { + "lat": -6.28333, + "lon": -37.75, + "name": "São Bento" + }, + { + "lat": 57.0436, + "lon": 34.96221, + "name": "Torzhok" + } + ], + "question": "Which location is the geographic outlier among: Canindé, Barra da Estiva, Manatí, São Bento, Torzhok?", + "ground_truth": { + "answer": "Torzhok", + "outlier_distance_km": 7801.6, + "second_furthest_km": 4746.8, + "clarity_ratio": 1.64, + "median_distance_km": 2695.7, + "distances_to_centroid": { + "Canindé": 1675.5, + "Barra da Estiva": 2695.7, + "Manatí": 4746.8, + "São Bento": 1791.2, + "Torzhok": 7801.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canindé: (-4.36°, -39.31°)", + " Barra da Estiva: (-13.63°, -41.33°)", + " Manatí: (10.45°, -74.96°)", + " São Bento: (-6.28°, -37.75°)", + " Torzhok: (57.04°, 34.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Torzhok: 7801.6 km from centroid", + " Manatí: 4746.8 km from centroid", + " Barra da Estiva: 2695.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Torzhok", + "FINAL ANSWER: Torzhok" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.45434, + "lon": 40.12371, + "name": "Pavlovsk" + }, + { + "lat": 51.98589, + "lon": 9.25246, + "name": "Bad Pyrmont" + }, + { + "lat": 51.40055, + "lon": 6.71187, + "name": "Rheinhausen" + }, + { + "lat": 43.16296, + "lon": 13.72274, + "name": "Fermo" + }, + { + "lat": 23.7902, + "lon": 87.37648, + "name": "Dubrājpur" + } + ], + "question": "Which location is the geographic outlier among: Pavlovsk, Bad Pyrmont, Rheinhausen, Fermo, Dubrājpur?", + "ground_truth": { + "answer": "Dubrājpur", + "outlier_distance_km": 5510.6, + "second_furthest_km": 2002.9, + "clarity_ratio": 2.75, + "median_distance_km": 1853.6, + "distances_to_centroid": { + "Pavlovsk": 957.4, + "Bad Pyrmont": 1853.6, + "Rheinhausen": 2002.9, + "Fermo": 1426.5, + "Dubrājpur": 5510.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pavlovsk: (50.45°, 40.12°)", + " Bad Pyrmont: (51.99°, 9.25°)", + " Rheinhausen: (51.40°, 6.71°)", + " Fermo: (43.16°, 13.72°)", + " Dubrājpur: (23.79°, 87.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dubrājpur: 5510.6 km from centroid", + " Rheinhausen: 2002.9 km from centroid", + " Bad Pyrmont: 1853.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dubrājpur", + "FINAL ANSWER: Dubrājpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.24303, + "lon": -123.09319, + "name": "Riley Park" + }, + { + "lat": 39.53491, + "lon": -119.75269, + "name": "Sparks" + }, + { + "lat": 41.69031, + "lon": -87.66672, + "name": "Morgan Park" + }, + { + "lat": 34.18479, + "lon": -101.70684, + "name": "Plainview" + }, + { + "lat": 32.28034, + "lon": 119.16999, + "name": "Zhenzhou" + } + ], + "question": "Which location is the geographic outlier among: Riley Park, Sparks, Morgan Park, Plainview, Zhenzhou?", + "ground_truth": { + "answer": "Zhenzhou", + "outlier_distance_km": 12044.0, + "second_furthest_km": 4818.9, + "clarity_ratio": 2.5, + "median_distance_km": 4800.9, + "distances_to_centroid": { + "Riley Park": 4800.9, + "Sparks": 4818.9, + "Morgan Park": 2125.3, + "Plainview": 3501.7, + "Zhenzhou": 12044.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Riley Park: (49.24°, -123.09°)", + " Sparks: (39.53°, -119.75°)", + " Morgan Park: (41.69°, -87.67°)", + " Plainview: (34.18°, -101.71°)", + " Zhenzhou: (32.28°, 119.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhenzhou: 12044.0 km from centroid", + " Sparks: 4818.9 km from centroid", + " Riley Park: 4800.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhenzhou", + "FINAL ANSWER: Zhenzhou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.21392, + "lon": -122.93992, + "name": "Edmonds" + }, + { + "lat": 33.55391, + "lon": -117.21392, + "name": "Murrieta" + }, + { + "lat": 33.95621, + "lon": -83.98796, + "name": "Lawrenceville" + }, + { + "lat": 39.51394, + "lon": -121.55776, + "name": "Oroville" + }, + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + } + ], + "question": "Which location is the geographic outlier among: Edmonds, Murrieta, Lawrenceville, Oroville, Frankston South?", + "ground_truth": { + "answer": "Frankston South", + "outlier_distance_km": 17128.4, + "second_furthest_km": 6091.9, + "clarity_ratio": 2.81, + "median_distance_km": 5965.3, + "distances_to_centroid": { + "Edmonds": 6091.9, + "Murrieta": 5614.7, + "Lawrenceville": 2586.4, + "Oroville": 5965.3, + "Frankston South": 17128.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Edmonds: (49.21°, -122.94°)", + " Murrieta: (33.55°, -117.21°)", + " Lawrenceville: (33.96°, -83.99°)", + " Oroville: (39.51°, -121.56°)", + " Frankston South: (-38.17°, 145.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Frankston South: 17128.4 km from centroid", + " Edmonds: 6091.9 km from centroid", + " Oroville: 5965.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Frankston South", + "FINAL ANSWER: Frankston South" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -46.4, + "lon": 168.35, + "name": "Invercargill" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -6.22944, + "lon": -36.02278, + "name": "Santa Cruz" + } + ], + "question": "Which location is the geographic outlier among: Mandurah, Invercargill, Broken Hill, Cairns, Santa Cruz?", + "ground_truth": { + "answer": "Santa Cruz", + "outlier_distance_km": 14602.9, + "second_furthest_km": 5728.9, + "clarity_ratio": 2.55, + "median_distance_km": 4125.7, + "distances_to_centroid": { + "Mandurah": 1050.8, + "Invercargill": 5728.9, + "Broken Hill": 3367.3, + "Cairns": 4125.7, + "Santa Cruz": 14602.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mandurah: (-32.53°, 115.72°)", + " Invercargill: (-46.40°, 168.35°)", + " Broken Hill: (-31.97°, 141.45°)", + " Cairns: (-16.92°, 145.77°)", + " Santa Cruz: (-6.23°, -36.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Cruz: 14602.9 km from centroid", + " Invercargill: 5728.9 km from centroid", + " Cairns: 4125.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Cruz", + "FINAL ANSWER: Santa Cruz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.73915, + "lon": -104.9847, + "name": "Denver" + }, + { + "lat": 42.00864, + "lon": -87.66672, + "name": "Rogers Park" + }, + { + "lat": 19.31451, + "lon": -97.9252, + "name": "Huamantla" + }, + { + "lat": 19.61639, + "lon": -99.14722, + "name": "Ampliación San Mateo" + }, + { + "lat": 45.26885, + "lon": 37.39752, + "name": "Temryuk" + } + ], + "question": "Which location is the geographic outlier among: Denver, Rogers Park, Huamantla, Ampliación San Mateo, Temryuk?", + "ground_truth": { + "answer": "Temryuk", + "outlier_distance_km": 8671.1, + "second_furthest_km": 3215.1, + "clarity_ratio": 2.7, + "median_distance_km": 3150.9, + "distances_to_centroid": { + "Denver": 3150.9, + "Rogers Park": 1799.8, + "Huamantla": 3128.4, + "Ampliación San Mateo": 3215.1, + "Temryuk": 8671.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Denver: (39.74°, -104.98°)", + " Rogers Park: (42.01°, -87.67°)", + " Huamantla: (19.31°, -97.93°)", + " Ampliación San Mateo: (19.62°, -99.15°)", + " Temryuk: (45.27°, 37.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Temryuk: 8671.1 km from centroid", + " Ampliación San Mateo: 3215.1 km from centroid", + " Denver: 3150.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Temryuk", + "FINAL ANSWER: Temryuk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -37.58333, + "lon": 145.03333, + "name": "Wollert" + }, + { + "lat": -37.76667, + "lon": 144.96667, + "name": "Brunswick" + }, + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + { + "lat": -29.71671, + "lon": -52.50321, + "name": "Vera Cruz" + } + ], + "question": "Which location is the geographic outlier among: Avondale, Wollert, Brunswick, Coogee, Vera Cruz?", + "ground_truth": { + "answer": "Vera Cruz", + "outlier_distance_km": 12634.7, + "second_furthest_km": 5477.7, + "clarity_ratio": 2.31, + "median_distance_km": 3512.5, + "distances_to_centroid": { + "Avondale": 5477.7, + "Wollert": 2893.6, + "Brunswick": 2886.1, + "Coogee": 3512.5, + "Vera Cruz": 12634.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Avondale: (-36.88°, 174.70°)", + " Wollert: (-37.58°, 145.03°)", + " Brunswick: (-37.77°, 144.97°)", + " Coogee: (-33.92°, 151.26°)", + " Vera Cruz: (-29.72°, -52.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vera Cruz: 12634.7 km from centroid", + " Avondale: 5477.7 km from centroid", + " Coogee: 3512.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vera Cruz", + "FINAL ANSWER: Vera Cruz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -33.78269, + "lon": 151.04888, + "name": "Carlingford" + }, + { + "lat": 3.19698, + "lon": -75.64506, + "name": "Planadas" + } + ], + "question": "Which location is the geographic outlier among: Miranda, Cherrybrook, Lidcombe, Carlingford, Planadas?", + "ground_truth": { + "answer": "Planadas", + "outlier_distance_km": 17426.3, + "second_furthest_km": 4404.5, + "clarity_ratio": 3.96, + "median_distance_km": 4400.6, + "distances_to_centroid": { + "Miranda": 4404.5, + "Cherrybrook": 4400.6, + "Lidcombe": 4399.5, + "Carlingford": 4400.6, + "Planadas": 17426.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miranda: (-34.04°, 151.10°)", + " Cherrybrook: (-33.72°, 151.05°)", + " Lidcombe: (-33.86°, 151.04°)", + " Carlingford: (-33.78°, 151.05°)", + " Planadas: (3.20°, -75.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Planadas: 17426.3 km from centroid", + " Miranda: 4404.5 km from centroid", + " Cherrybrook: 4400.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Planadas", + "FINAL ANSWER: Planadas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + }, + { + "lat": -36.9482, + "lon": 174.87019, + "name": "Otara" + }, + { + "lat": -36.8282, + "lon": 174.62019, + "name": "Massey East" + }, + { + "lat": 9.27078, + "lon": 76.43257, + "name": "Kumārapuram" + } + ], + "question": "Which location is the geographic outlier among: Wangaratta, Merrylands, Otara, Massey East, Kumārapuram?", + "ground_truth": { + "answer": "Kumārapuram", + "outlier_distance_km": 8374.2, + "second_furthest_km": 3045.2, + "clarity_ratio": 2.75, + "median_distance_km": 3020.6, + "distances_to_centroid": { + "Wangaratta": 1059.2, + "Merrylands": 977.9, + "Otara": 3045.2, + "Massey East": 3020.6, + "Kumārapuram": 8374.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wangaratta: (-36.36°, 146.32°)", + " Merrylands: (-33.83°, 150.98°)", + " Otara: (-36.95°, 174.87°)", + " Massey East: (-36.83°, 174.62°)", + " Kumārapuram: (9.27°, 76.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kumārapuram: 8374.2 km from centroid", + " Otara: 3045.2 km from centroid", + " Massey East: 3020.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kumārapuram", + "FINAL ANSWER: Kumārapuram" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.03238, + "lon": 23.11652, + "name": "Biała Podlaska" + }, + { + "lat": 53.59245, + "lon": -2.21941, + "name": "Heywood" + }, + { + "lat": 60.01375, + "lon": 30.39471, + "name": "Akademicheskoe" + }, + { + "lat": 43.12468, + "lon": 6.01033, + "name": "La Garde" + }, + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + } + ], + "question": "Which location is the geographic outlier among: Biała Podlaska, Heywood, Akademicheskoe, La Garde, Hornsby?", + "ground_truth": { + "answer": "Hornsby", + "outlier_distance_km": 13679.0, + "second_furthest_km": 3970.2, + "clarity_ratio": 3.45, + "median_distance_km": 3182.0, + "distances_to_centroid": { + "Biała Podlaska": 2398.2, + "Heywood": 3970.2, + "Akademicheskoe": 2897.1, + "La Garde": 3182.0, + "Hornsby": 13679.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Biała Podlaska: (52.03°, 23.12°)", + " Heywood: (53.59°, -2.22°)", + " Akademicheskoe: (60.01°, 30.39°)", + " La Garde: (43.12°, 6.01°)", + " Hornsby: (-33.70°, 151.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hornsby: 13679.0 km from centroid", + " Heywood: 3970.2 km from centroid", + " La Garde: 3182.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hornsby", + "FINAL ANSWER: Hornsby" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + }, + { + "lat": -31.83291, + "lon": 115.7759, + "name": "Duncraig" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": -19.80139, + "lon": -45.68556, + "name": "Luz" + } + ], + "question": "Which location is the geographic outlier among: Wheelers Hill, Papakura, Duncraig, Timaru, Luz?", + "ground_truth": { + "answer": "Luz", + "outlier_distance_km": 13574.0, + "second_furthest_km": 5566.3, + "clarity_ratio": 2.44, + "median_distance_km": 5085.6, + "distances_to_centroid": { + "Wheelers Hill": 2969.8, + "Papakura": 5566.3, + "Duncraig": 417.8, + "Timaru": 5085.6, + "Luz": 13574.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Papakura: (-37.06°, 174.94°)", + " Duncraig: (-31.83°, 115.78°)", + " Timaru: (-44.40°, 171.25°)", + " Luz: (-19.80°, -45.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Luz: 13574.0 km from centroid", + " Papakura: 5566.3 km from centroid", + " Timaru: 5085.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Luz", + "FINAL ANSWER: Luz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.1427, + "lon": 74.23946, + "name": "Lāsalgaon" + }, + { + "lat": 7.8257, + "lon": 123.437, + "name": "Pagadian" + }, + { + "lat": 27.79449, + "lon": 77.4368, + "name": "Kosi" + }, + { + "lat": 35.48333, + "lon": 136.91667, + "name": "Sekimachi" + }, + { + "lat": -2.24444, + "lon": -49.49583, + "name": "Cametá" + } + ], + "question": "Which location is the geographic outlier among: Lāsalgaon, Pagadian, Kosi, Sekimachi, Cametá?", + "ground_truth": { + "answer": "Cametá", + "outlier_distance_km": 13463.0, + "second_furthest_km": 6580.6, + "clarity_ratio": 2.05, + "median_distance_km": 5614.9, + "distances_to_centroid": { + "Lāsalgaon": 317.8, + "Pagadian": 5614.9, + "Kosi": 1220.4, + "Sekimachi": 6580.6, + "Cametá": 13463.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lāsalgaon: (20.14°, 74.24°)", + " Pagadian: (7.83°, 123.44°)", + " Kosi: (27.79°, 77.44°)", + " Sekimachi: (35.48°, 136.92°)", + " Cametá: (-2.24°, -49.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cametá: 13463.0 km from centroid", + " Sekimachi: 6580.6 km from centroid", + " Pagadian: 5614.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cametá", + "FINAL ANSWER: Cametá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.84766, + "lon": 89.37558, + "name": "Jaigaon" + }, + { + "lat": 17.55606, + "lon": 78.34824, + "name": "Bolārum" + }, + { + "lat": 12.91823, + "lon": 80.08245, + "name": "Perunkalattu" + }, + { + "lat": 14.191, + "lon": 121.7309, + "name": "Mauban" + }, + { + "lat": 16.7075, + "lon": -93.01216, + "name": "Chiapa de Corzo" + } + ], + "question": "Which location is the geographic outlier among: Jaigaon, Bolārum, Perunkalattu, Mauban, Chiapa de Corzo?", + "ground_truth": { + "answer": "Chiapa de Corzo", + "outlier_distance_km": 14855.2, + "second_furthest_km": 7078.0, + "clarity_ratio": 2.1, + "median_distance_km": 3640.0, + "distances_to_centroid": { + "Jaigaon": 3640.0, + "Bolārum": 2440.8, + "Perunkalattu": 2706.8, + "Mauban": 7078.0, + "Chiapa de Corzo": 14855.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jaigaon: (26.85°, 89.38°)", + " Bolārum: (17.56°, 78.35°)", + " Perunkalattu: (12.92°, 80.08°)", + " Mauban: (14.19°, 121.73°)", + " Chiapa de Corzo: (16.71°, -93.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chiapa de Corzo: 14855.2 km from centroid", + " Mauban: 7078.0 km from centroid", + " Jaigaon: 3640.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chiapa de Corzo", + "FINAL ANSWER: Chiapa de Corzo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.04949, + "lon": 32.24142, + "name": "Nag Hammâdi" + }, + { + "lat": -27.18871, + "lon": 25.32931, + "name": "Schweizer-Reneke" + }, + { + "lat": 29.56472, + "lon": 31.28111, + "name": "Aş Şaff" + }, + { + "lat": 10.04807, + "lon": 11.21055, + "name": "Kumo" + }, + { + "lat": 19.41018, + "lon": 109.55024, + "name": "Nanfeng" + } + ], + "question": "Which location is the geographic outlier among: Nag Hammâdi, Schweizer-Reneke, Aş Şaff, Kumo, Nanfeng?", + "ground_truth": { + "answer": "Nanfeng", + "outlier_distance_km": 7257.4, + "second_furthest_km": 4667.5, + "clarity_ratio": 1.55, + "median_distance_km": 3357.1, + "distances_to_centroid": { + "Nag Hammâdi": 1902.7, + "Schweizer-Reneke": 4667.5, + "Aş Şaff": 2283.2, + "Kumo": 3357.1, + "Nanfeng": 7257.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nag Hammâdi: (26.05°, 32.24°)", + " Schweizer-Reneke: (-27.19°, 25.33°)", + " Aş Şaff: (29.56°, 31.28°)", + " Kumo: (10.05°, 11.21°)", + " Nanfeng: (19.41°, 109.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nanfeng: 7257.4 km from centroid", + " Schweizer-Reneke: 4667.5 km from centroid", + " Kumo: 3357.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nanfeng", + "FINAL ANSWER: Nanfeng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -46.4, + "lon": 168.35, + "name": "Invercargill" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": 26.50358, + "lon": -100.18187, + "name": "Ciudad Sabinas Hidalgo" + } + ], + "question": "Which location is the geographic outlier among: Epsom, Corio, Invercargill, Balwyn North, Ciudad Sabinas Hidalgo?", + "ground_truth": { + "answer": "Ciudad Sabinas Hidalgo", + "outlier_distance_km": 17366.8, + "second_furthest_km": 6427.2, + "clarity_ratio": 2.7, + "median_distance_km": 5792.3, + "distances_to_centroid": { + "Epsom": 6427.2, + "Corio": 3755.8, + "Invercargill": 5792.3, + "Balwyn North": 3812.8, + "Ciudad Sabinas Hidalgo": 17366.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epsom: (-36.89°, 174.77°)", + " Corio: (-38.08°, 144.38°)", + " Invercargill: (-46.40°, 168.35°)", + " Balwyn North: (-37.79°, 145.09°)", + " Ciudad Sabinas Hidalgo: (26.50°, -100.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciudad Sabinas Hidalgo: 17366.8 km from centroid", + " Epsom: 6427.2 km from centroid", + " Invercargill: 5792.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciudad Sabinas Hidalgo", + "FINAL ANSWER: Ciudad Sabinas Hidalgo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": -38.65333, + "lon": 178.00417, + "name": "Gisborne" + }, + { + "lat": -37.88461, + "lon": 145.29539, + "name": "Ferntree Gully" + }, + { + "lat": 36.67777, + "lon": -5.446, + "name": "Ubrique" + } + ], + "question": "Which location is the geographic outlier among: Forest Lake, Mount Isa, Gisborne, Ferntree Gully, Ubrique?", + "ground_truth": { + "answer": "Ubrique", + "outlier_distance_km": 14485.5, + "second_furthest_km": 5859.1, + "clarity_ratio": 2.47, + "median_distance_km": 3349.1, + "distances_to_centroid": { + "Forest Lake": 3349.1, + "Mount Isa": 1861.6, + "Gisborne": 5859.1, + "Ferntree Gully": 3189.9, + "Ubrique": 14485.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Forest Lake: (-27.63°, 152.97°)", + " Mount Isa: (-20.73°, 139.50°)", + " Gisborne: (-38.65°, 178.00°)", + " Ferntree Gully: (-37.88°, 145.30°)", + " Ubrique: (36.68°, -5.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ubrique: 14485.5 km from centroid", + " Gisborne: 5859.1 km from centroid", + " Forest Lake: 3349.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ubrique", + "FINAL ANSWER: Ubrique" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.14458, + "lon": 145.12291, + "name": "Frankston" + }, + { + "lat": -33.94185, + "lon": 150.8717, + "name": "Prestons" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + { + "lat": 44.86208, + "lon": 40.07195, + "name": "Giaginskaya" + } + ], + "question": "Which location is the geographic outlier among: Frankston, Prestons, Papakura, Granville, Giaginskaya?", + "ground_truth": { + "answer": "Giaginskaya", + "outlier_distance_km": 11710.2, + "second_furthest_km": 4544.2, + "clarity_ratio": 2.58, + "median_distance_km": 2423.8, + "distances_to_centroid": { + "Frankston": 2397.2, + "Prestons": 2420.3, + "Papakura": 4544.2, + "Granville": 2423.8, + "Giaginskaya": 11710.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frankston: (-38.14°, 145.12°)", + " Prestons: (-33.94°, 150.87°)", + " Papakura: (-37.06°, 174.94°)", + " Granville: (-33.84°, 151.01°)", + " Giaginskaya: (44.86°, 40.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Giaginskaya: 11710.2 km from centroid", + " Papakura: 4544.2 km from centroid", + " Granville: 2423.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Giaginskaya", + "FINAL ANSWER: Giaginskaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.15816, + "lon": 35.19645, + "name": "Muhoroni" + }, + { + "lat": -33.83079, + "lon": 18.6486, + "name": "Durbanville" + }, + { + "lat": 4.74215, + "lon": 7.08368, + "name": "Okrika" + }, + { + "lat": -33.93462, + "lon": 18.86676, + "name": "Stellenbosch" + }, + { + "lat": -4.45194, + "lon": -37.79722, + "name": "Fortim" + } + ], + "question": "Which location is the geographic outlier among: Muhoroni, Durbanville, Okrika, Stellenbosch, Fortim?", + "ground_truth": { + "answer": "Fortim", + "outlier_distance_km": 5163.9, + "second_furthest_km": 3304.3, + "clarity_ratio": 1.56, + "median_distance_km": 2503.0, + "distances_to_centroid": { + "Muhoroni": 3304.3, + "Durbanville": 2483.5, + "Okrika": 2036.6, + "Stellenbosch": 2503.0, + "Fortim": 5163.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Muhoroni: (-0.16°, 35.20°)", + " Durbanville: (-33.83°, 18.65°)", + " Okrika: (4.74°, 7.08°)", + " Stellenbosch: (-33.93°, 18.87°)", + " Fortim: (-4.45°, -37.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fortim: 5163.9 km from centroid", + " Muhoroni: 3304.3 km from centroid", + " Stellenbosch: 2503.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fortim", + "FINAL ANSWER: Fortim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.2846, + "lon": -122.78217, + "name": "Coquitlam" + }, + { + "lat": 49.23839, + "lon": -122.86676, + "name": "Maillardville" + }, + { + "lat": 41.49899, + "lon": -72.90066, + "name": "Cheshire" + }, + { + "lat": 32.28924, + "lon": -115.10534, + "name": "Guadalupe Victoria" + }, + { + "lat": 10.7735, + "lon": 76.37758, + "name": "Ottapalam" + } + ], + "question": "Which location is the geographic outlier among: Coquitlam, Maillardville, Cheshire, Guadalupe Victoria, Ottapalam?", + "ground_truth": { + "answer": "Ottapalam", + "outlier_distance_km": 13763.4, + "second_furthest_km": 4321.4, + "clarity_ratio": 3.18, + "median_distance_km": 4315.2, + "distances_to_centroid": { + "Coquitlam": 4315.2, + "Maillardville": 4321.4, + "Cheshire": 557.0, + "Guadalupe Victoria": 3996.8, + "Ottapalam": 13763.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coquitlam: (49.28°, -122.78°)", + " Maillardville: (49.24°, -122.87°)", + " Cheshire: (41.50°, -72.90°)", + " Guadalupe Victoria: (32.29°, -115.11°)", + " Ottapalam: (10.77°, 76.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ottapalam: 13763.4 km from centroid", + " Maillardville: 4321.4 km from centroid", + " Coquitlam: 4315.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ottapalam", + "FINAL ANSWER: Ottapalam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.19444, + "lon": -40.47667, + "name": "Varjota" + }, + { + "lat": -23.71056, + "lon": -46.41333, + "name": "Ribeirão Pires" + }, + { + "lat": -10.91908, + "lon": -74.88496, + "name": "Santa Rosa" + }, + { + "lat": 3.23114, + "lon": -76.41668, + "name": "Puerto Tejada" + }, + { + "lat": 42.53306, + "lon": 124.04028, + "name": "Kaiyuan" + } + ], + "question": "Which location is the geographic outlier among: Varjota, Ribeirão Pires, Santa Rosa, Puerto Tejada, Kaiyuan?", + "ground_truth": { + "answer": "Kaiyuan", + "outlier_distance_km": 14111.6, + "second_furthest_km": 5956.6, + "clarity_ratio": 2.37, + "median_distance_km": 5915.7, + "distances_to_centroid": { + "Varjota": 2056.7, + "Ribeirão Pires": 3779.5, + "Santa Rosa": 5915.7, + "Puerto Tejada": 5956.6, + "Kaiyuan": 14111.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Varjota: (-4.19°, -40.48°)", + " Ribeirão Pires: (-23.71°, -46.41°)", + " Santa Rosa: (-10.92°, -74.88°)", + " Puerto Tejada: (3.23°, -76.42°)", + " Kaiyuan: (42.53°, 124.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kaiyuan: 14111.6 km from centroid", + " Puerto Tejada: 5956.6 km from centroid", + " Santa Rosa: 5915.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kaiyuan", + "FINAL ANSWER: Kaiyuan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": 5.0847, + "lon": -1.35093, + "name": "Elmina" + } + ], + "question": "Which location is the geographic outlier among: Blenheim, Albany, Bairnsdale, Mandurah, Elmina?", + "ground_truth": { + "answer": "Elmina", + "outlier_distance_km": 12436.4, + "second_furthest_km": 5811.2, + "clarity_ratio": 2.14, + "median_distance_km": 3564.3, + "distances_to_centroid": { + "Blenheim": 5811.2, + "Albany": 1000.9, + "Bairnsdale": 3564.3, + "Mandurah": 663.5, + "Elmina": 12436.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blenheim: (-41.52°, 173.95°)", + " Albany: (-35.03°, 117.88°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Mandurah: (-32.53°, 115.72°)", + " Elmina: (5.08°, -1.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Elmina: 12436.4 km from centroid", + " Blenheim: 5811.2 km from centroid", + " Bairnsdale: 3564.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Elmina", + "FINAL ANSWER: Elmina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.31457, + "lon": 29.50078, + "name": "Lebowakgomo" + }, + { + "lat": 8.25, + "lon": 34.58333, + "name": "Gambēla" + }, + { + "lat": -28.61961, + "lon": 28.20966, + "name": "Fouriesburg" + }, + { + "lat": 5.80865, + "lon": 8.08098, + "name": "Ugep" + }, + { + "lat": 42.97225, + "lon": -85.95365, + "name": "Allendale" + } + ], + "question": "Which location is the geographic outlier among: Lebowakgomo, Gambēla, Fouriesburg, Ugep, Allendale?", + "ground_truth": { + "answer": "Allendale", + "outlier_distance_km": 9850.9, + "second_furthest_km": 4240.8, + "clarity_ratio": 2.32, + "median_distance_km": 4005.9, + "distances_to_centroid": { + "Lebowakgomo": 4005.9, + "Gambēla": 3606.8, + "Fouriesburg": 4240.8, + "Ugep": 800.2, + "Allendale": 9850.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lebowakgomo: (-24.31°, 29.50°)", + " Gambēla: (8.25°, 34.58°)", + " Fouriesburg: (-28.62°, 28.21°)", + " Ugep: (5.81°, 8.08°)", + " Allendale: (42.97°, -85.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Allendale: 9850.9 km from centroid", + " Fouriesburg: 4240.8 km from centroid", + " Lebowakgomo: 4005.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Allendale", + "FINAL ANSWER: Allendale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.08333, + "lon": 36.55, + "name": "Nek’emtē" + }, + { + "lat": -0.68174, + "lon": 34.76666, + "name": "Kisii" + }, + { + "lat": 9.80726, + "lon": 6.15238, + "name": "Zungeru" + }, + { + "lat": 25.69893, + "lon": 32.6421, + "name": "Luxor" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + } + ], + "question": "Which location is the geographic outlier among: Nek’emtē, Kisii, Zungeru, Luxor, Cabramatta?", + "ground_truth": { + "answer": "Cabramatta", + "outlier_distance_km": 10936.7, + "second_furthest_km": 5161.9, + "clarity_ratio": 2.12, + "median_distance_km": 3365.6, + "distances_to_centroid": { + "Nek’emtē": 1902.5, + "Kisii": 1962.0, + "Zungeru": 5161.9, + "Luxor": 3365.6, + "Cabramatta": 10936.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nek’emtē: (9.08°, 36.55°)", + " Kisii: (-0.68°, 34.77°)", + " Zungeru: (9.81°, 6.15°)", + " Luxor: (25.70°, 32.64°)", + " Cabramatta: (-33.90°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cabramatta: 10936.7 km from centroid", + " Zungeru: 5161.9 km from centroid", + " Luxor: 3365.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cabramatta", + "FINAL ANSWER: Cabramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": 7.55122, + "lon": 6.23589, + "name": "Okene" + } + ], + "question": "Which location is the geographic outlier among: Springvale, Mangere East, Timaru, Seven Hills, Okene?", + "ground_truth": { + "answer": "Okene", + "outlier_distance_km": 13651.4, + "second_furthest_km": 4257.4, + "clarity_ratio": 3.21, + "median_distance_km": 4020.9, + "distances_to_centroid": { + "Springvale": 1734.9, + "Mangere East": 4257.4, + "Timaru": 4020.9, + "Seven Hills": 2077.9, + "Okene": 13651.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Springvale: (-37.95°, 145.15°)", + " Mangere East: (-36.97°, 174.82°)", + " Timaru: (-44.40°, 171.25°)", + " Seven Hills: (-33.78°, 150.93°)", + " Okene: (7.55°, 6.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Okene: 13651.4 km from centroid", + " Mangere East: 4257.4 km from centroid", + " Timaru: 4020.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Okene", + "FINAL ANSWER: Okene" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.63651, + "lon": -123.10593, + "name": "Albany" + }, + { + "lat": 16.7612, + "lon": -93.37426, + "name": "Ocozocoautla de Espinosa" + }, + { + "lat": 39.61332, + "lon": -105.01665, + "name": "Littleton" + }, + { + "lat": 38.20091, + "lon": -84.87328, + "name": "Frankfort" + }, + { + "lat": 10.59918, + "lon": 76.21801, + "name": "Killannur" + } + ], + "question": "Which location is the geographic outlier among: Albany, Ocozocoautla de Espinosa, Littleton, Frankfort, Killannur?", + "ground_truth": { + "answer": "Killannur", + "outlier_distance_km": 13960.8, + "second_furthest_km": 5191.4, + "clarity_ratio": 2.69, + "median_distance_km": 3686.4, + "distances_to_centroid": { + "Albany": 5191.4, + "Ocozocoautla de Espinosa": 3141.3, + "Littleton": 3686.4, + "Frankfort": 1957.0, + "Killannur": 13960.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albany: (44.64°, -123.11°)", + " Ocozocoautla de Espinosa: (16.76°, -93.37°)", + " Littleton: (39.61°, -105.02°)", + " Frankfort: (38.20°, -84.87°)", + " Killannur: (10.60°, 76.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Killannur: 13960.8 km from centroid", + " Albany: 5191.4 km from centroid", + " Littleton: 3686.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Killannur", + "FINAL ANSWER: Killannur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.69934, + "lon": -48.53219, + "name": "Ribeirão da Ilha" + }, + { + "lat": -7.03333, + "lon": -40.45, + "name": "Ipueiras" + }, + { + "lat": -20.15139, + "lon": -41.62278, + "name": "Lajinha" + }, + { + "lat": -12.14297, + "lon": -77.01862, + "name": "Barranco" + }, + { + "lat": 14.1737, + "lon": 122.9066, + "name": "Vinzons" + } + ], + "question": "Which location is the geographic outlier among: Ribeirão da Ilha, Ipueiras, Lajinha, Barranco, Vinzons?", + "ground_truth": { + "answer": "Vinzons", + "outlier_distance_km": 15641.0, + "second_furthest_km": 6538.4, + "clarity_ratio": 2.39, + "median_distance_km": 3807.4, + "distances_to_centroid": { + "Ribeirão da Ilha": 3807.4, + "Ipueiras": 2611.9, + "Lajinha": 2847.7, + "Barranco": 6538.4, + "Vinzons": 15641.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ribeirão da Ilha: (-27.70°, -48.53°)", + " Ipueiras: (-7.03°, -40.45°)", + " Lajinha: (-20.15°, -41.62°)", + " Barranco: (-12.14°, -77.02°)", + " Vinzons: (14.17°, 122.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vinzons: 15641.0 km from centroid", + " Barranco: 6538.4 km from centroid", + " Ribeirão da Ilha: 3807.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vinzons", + "FINAL ANSWER: Vinzons" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.76737, + "lon": -79.1795, + "name": "West Hill" + }, + { + "lat": 40.06178, + "lon": -75.05573, + "name": "Rhawnhurst" + }, + { + "lat": 30.83334, + "lon": -83.28032, + "name": "Valdosta" + }, + { + "lat": 29.91021, + "lon": -90.03257, + "name": "Terrytown" + }, + { + "lat": 44.01759, + "lon": 1.3542, + "name": "Montauban" + } + ], + "question": "Which location is the geographic outlier among: West Hill, Rhawnhurst, Valdosta, Terrytown, Montauban?", + "ground_truth": { + "answer": "Montauban", + "outlier_distance_km": 5490.4, + "second_furthest_km": 2440.5, + "clarity_ratio": 2.25, + "median_distance_km": 1821.8, + "distances_to_centroid": { + "West Hill": 1350.8, + "Rhawnhurst": 888.2, + "Valdosta": 1821.8, + "Terrytown": 2440.5, + "Montauban": 5490.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Hill: (43.77°, -79.18°)", + " Rhawnhurst: (40.06°, -75.06°)", + " Valdosta: (30.83°, -83.28°)", + " Terrytown: (29.91°, -90.03°)", + " Montauban: (44.02°, 1.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Montauban: 5490.4 km from centroid", + " Terrytown: 2440.5 km from centroid", + " Valdosta: 1821.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Montauban", + "FINAL ANSWER: Montauban" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.32711, + "lon": 115.64137, + "name": "Bunbury" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": 43.3665, + "lon": -124.21789, + "name": "Coos Bay" + } + ], + "question": "Which location is the geographic outlier among: Bunbury, Logan City, Bundoora, Cranbourne East, Coos Bay?", + "ground_truth": { + "answer": "Coos Bay", + "outlier_distance_km": 16012.4, + "second_furthest_km": 6758.3, + "clarity_ratio": 2.37, + "median_distance_km": 5993.9, + "distances_to_centroid": { + "Bunbury": 3278.2, + "Logan City": 6758.3, + "Bundoora": 5969.9, + "Cranbourne East": 5993.9, + "Coos Bay": 16012.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bunbury: (-33.33°, 115.64°)", + " Logan City: (-27.64°, 153.11°)", + " Bundoora: (-37.70°, 145.06°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Coos Bay: (43.37°, -124.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coos Bay: 16012.4 km from centroid", + " Logan City: 6758.3 km from centroid", + " Cranbourne East: 5993.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coos Bay", + "FINAL ANSWER: Coos Bay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.03624, + "lon": 4.06802, + "name": "Roanne" + }, + { + "lat": 50.98241, + "lon": 39.50412, + "name": "Liski" + }, + { + "lat": 54.50364, + "lon": -1.35793, + "name": "Yarm" + }, + { + "lat": 40.15913, + "lon": -3.62103, + "name": "Ciempozuelos" + }, + { + "lat": 11.63422, + "lon": 78.87412, + "name": "Chinna Salem" + } + ], + "question": "Which location is the geographic outlier among: Roanne, Liski, Yarm, Ciempozuelos, Chinna Salem?", + "ground_truth": { + "answer": "Chinna Salem", + "outlier_distance_km": 6270.5, + "second_furthest_km": 2394.8, + "clarity_ratio": 2.62, + "median_distance_km": 2287.2, + "distances_to_centroid": { + "Roanne": 1675.2, + "Liski": 1683.2, + "Yarm": 2394.8, + "Ciempozuelos": 2287.2, + "Chinna Salem": 6270.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Roanne: (46.04°, 4.07°)", + " Liski: (50.98°, 39.50°)", + " Yarm: (54.50°, -1.36°)", + " Ciempozuelos: (40.16°, -3.62°)", + " Chinna Salem: (11.63°, 78.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chinna Salem: 6270.5 km from centroid", + " Yarm: 2394.8 km from centroid", + " Ciempozuelos: 2287.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chinna Salem", + "FINAL ANSWER: Chinna Salem" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.77148, + "lon": 127.07996, + "name": "Boseong" + }, + { + "lat": 31.21288, + "lon": 108.34026, + "name": "Dade" + }, + { + "lat": 25.33061, + "lon": 76.50973, + "name": "Māngrol" + }, + { + "lat": 20.81717, + "lon": 105.33759, + "name": "Hòa Bình" + }, + { + "lat": -20.53389, + "lon": -49.31417, + "name": "Nova Granada" + } + ], + "question": "Which location is the geographic outlier among: Boseong, Dade, Māngrol, Hòa Bình, Nova Granada?", + "ground_truth": { + "answer": "Nova Granada", + "outlier_distance_km": 14053.3, + "second_furthest_km": 5556.2, + "clarity_ratio": 2.53, + "median_distance_km": 3769.8, + "distances_to_centroid": { + "Boseong": 5556.2, + "Dade": 3769.8, + "Māngrol": 835.7, + "Hòa Bình": 3332.5, + "Nova Granada": 14053.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boseong: (34.77°, 127.08°)", + " Dade: (31.21°, 108.34°)", + " Māngrol: (25.33°, 76.51°)", + " Hòa Bình: (20.82°, 105.34°)", + " Nova Granada: (-20.53°, -49.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nova Granada: 14053.3 km from centroid", + " Boseong: 5556.2 km from centroid", + " Dade: 3769.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nova Granada", + "FINAL ANSWER: Nova Granada" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.8, + "lon": 174.75, + "name": "North Shore" + }, + { + "lat": -33.76667, + "lon": 150.81667, + "name": "Mount Druitt" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": -27.20338, + "lon": 152.95923, + "name": "Narangba" + }, + { + "lat": 40.29081, + "lon": 141.31334, + "name": "Ninohe" + } + ], + "question": "Which location is the geographic outlier among: North Shore, Mount Druitt, Palm Beach, Narangba, Ninohe?", + "ground_truth": { + "answer": "Ninohe", + "outlier_distance_km": 6531.5, + "second_furthest_km": 2945.4, + "clarity_ratio": 2.22, + "median_distance_km": 1890.5, + "distances_to_centroid": { + "North Shore": 2945.4, + "Mount Druitt": 1890.5, + "Palm Beach": 1229.0, + "Narangba": 1134.9, + "Ninohe": 6531.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Shore: (-36.80°, 174.75°)", + " Mount Druitt: (-33.77°, 150.82°)", + " Palm Beach: (-28.12°, 153.47°)", + " Narangba: (-27.20°, 152.96°)", + " Ninohe: (40.29°, 141.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ninohe: 6531.5 km from centroid", + " North Shore: 2945.4 km from centroid", + " Mount Druitt: 1890.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ninohe", + "FINAL ANSWER: Ninohe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.61712, + "lon": -75.15146, + "name": "Luruaco" + }, + { + "lat": -0.97357, + "lon": -62.9269, + "name": "Barcelos" + }, + { + "lat": -11.30417, + "lon": -41.85583, + "name": "Irecê" + }, + { + "lat": -23.84861, + "lon": -50.18778, + "name": "Ibaiti" + }, + { + "lat": -37.83961, + "lon": 144.94228, + "name": "Port Melbourne" + } + ], + "question": "Which location is the geographic outlier among: Luruaco, Barcelos, Irecê, Ibaiti, Port Melbourne?", + "ground_truth": { + "answer": "Port Melbourne", + "outlier_distance_km": 14092.6, + "second_furthest_km": 6918.3, + "clarity_ratio": 2.04, + "median_distance_km": 5220.0, + "distances_to_centroid": { + "Luruaco": 6918.3, + "Barcelos": 5220.0, + "Irecê": 2702.9, + "Ibaiti": 3703.2, + "Port Melbourne": 14092.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Luruaco: (10.62°, -75.15°)", + " Barcelos: (-0.97°, -62.93°)", + " Irecê: (-11.30°, -41.86°)", + " Ibaiti: (-23.85°, -50.19°)", + " Port Melbourne: (-37.84°, 144.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Melbourne: 14092.6 km from centroid", + " Luruaco: 6918.3 km from centroid", + " Barcelos: 5220.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Melbourne", + "FINAL ANSWER: Port Melbourne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": -37.78828, + "lon": 145.12373, + "name": "Doncaster" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": 26.02065, + "lon": -80.18394, + "name": "West Hollywood" + } + ], + "question": "Which location is the geographic outlier among: Canning Vale, Tauranga, Doncaster, Mount Martha, West Hollywood?", + "ground_truth": { + "answer": "West Hollywood", + "outlier_distance_km": 19777.8, + "second_furthest_km": 7202.9, + "clarity_ratio": 2.75, + "median_distance_km": 4487.7, + "distances_to_centroid": { + "Canning Vale": 1766.3, + "Tauranga": 7202.9, + "Doncaster": 4487.7, + "Mount Martha": 4485.1, + "West Hollywood": 19777.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canning Vale: (-32.06°, 115.92°)", + " Tauranga: (-37.69°, 176.17°)", + " Doncaster: (-37.79°, 145.12°)", + " Mount Martha: (-38.27°, 145.02°)", + " West Hollywood: (26.02°, -80.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Hollywood: 19777.8 km from centroid", + " Tauranga: 7202.9 km from centroid", + " Doncaster: 4487.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Hollywood", + "FINAL ANSWER: West Hollywood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.81677, + "lon": -84.31326, + "name": "North Druid Hills" + }, + { + "lat": 32.38653, + "lon": -96.84833, + "name": "Waxahachie" + }, + { + "lat": 40.81204, + "lon": -74.12431, + "name": "Lyndhurst" + }, + { + "lat": 42.19697, + "lon": -88.09341, + "name": "Lake Zurich" + }, + { + "lat": -30.29831, + "lon": 29.93772, + "name": "Clydesdale" + } + ], + "question": "Which location is the geographic outlier among: North Druid Hills, Waxahachie, Lyndhurst, Lake Zurich, Clydesdale?", + "ground_truth": { + "answer": "Clydesdale", + "outlier_distance_km": 11549.4, + "second_furthest_km": 3468.5, + "clarity_ratio": 3.33, + "median_distance_km": 3109.5, + "distances_to_centroid": { + "North Druid Hills": 2377.2, + "Waxahachie": 3468.5, + "Lyndhurst": 2172.8, + "Lake Zurich": 3109.5, + "Clydesdale": 11549.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Druid Hills: (33.82°, -84.31°)", + " Waxahachie: (32.39°, -96.85°)", + " Lyndhurst: (40.81°, -74.12°)", + " Lake Zurich: (42.20°, -88.09°)", + " Clydesdale: (-30.30°, 29.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clydesdale: 11549.4 km from centroid", + " Waxahachie: 3468.5 km from centroid", + " Lake Zurich: 3109.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clydesdale", + "FINAL ANSWER: Clydesdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.58833, + "lon": -67.5325, + "name": "Porto Acre" + }, + { + "lat": -16.47583, + "lon": -43.48833, + "name": "Francisco Sá" + }, + { + "lat": -6.53389, + "lon": -64.38306, + "name": "Canutama" + }, + { + "lat": -3.47194, + "lon": -41.5575, + "name": "Cocal" + }, + { + "lat": 43.16296, + "lon": 13.72274, + "name": "Fermo" + } + ], + "question": "Which location is the geographic outlier among: Porto Acre, Francisco Sá, Canutama, Cocal, Fermo?", + "ground_truth": { + "answer": "Fermo", + "outlier_distance_km": 7092.7, + "second_furthest_km": 3218.8, + "clarity_ratio": 2.2, + "median_distance_km": 2778.9, + "distances_to_centroid": { + "Porto Acre": 3218.8, + "Francisco Sá": 2014.0, + "Canutama": 2778.9, + "Cocal": 553.1, + "Fermo": 7092.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porto Acre: (-9.59°, -67.53°)", + " Francisco Sá: (-16.48°, -43.49°)", + " Canutama: (-6.53°, -64.38°)", + " Cocal: (-3.47°, -41.56°)", + " Fermo: (43.16°, 13.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fermo: 7092.7 km from centroid", + " Porto Acre: 3218.8 km from centroid", + " Canutama: 2778.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fermo", + "FINAL ANSWER: Fermo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.43139, + "lon": -61.14639, + "name": "Pacaraima" + }, + { + "lat": -20.07528, + "lon": -44.57639, + "name": "Itaúna" + }, + { + "lat": -30.24162, + "lon": -68.74662, + "name": "San José de Jáchal" + }, + { + "lat": -23.52909, + "lon": -45.84904, + "name": "Salesópolis" + }, + { + "lat": -27.28115, + "lon": 27.9709, + "name": "Heilbron" + } + ], + "question": "Which location is the geographic outlier among: Pacaraima, Itaúna, San José de Jáchal, Salesópolis, Heilbron?", + "ground_truth": { + "answer": "Heilbron", + "outlier_distance_km": 6767.0, + "second_furthest_km": 3625.1, + "clarity_ratio": 1.87, + "median_distance_km": 3275.0, + "distances_to_centroid": { + "Pacaraima": 3625.1, + "Itaúna": 644.5, + "San José de Jáchal": 3275.0, + "Salesópolis": 894.4, + "Heilbron": 6767.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacaraima: (4.43°, -61.15°)", + " Itaúna: (-20.08°, -44.58°)", + " San José de Jáchal: (-30.24°, -68.75°)", + " Salesópolis: (-23.53°, -45.85°)", + " Heilbron: (-27.28°, 27.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Heilbron: 6767.0 km from centroid", + " Pacaraima: 3625.1 km from centroid", + " San José de Jáchal: 3275.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Heilbron", + "FINAL ANSWER: Heilbron" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + }, + { + "lat": -31.91099, + "lon": 152.45387, + "name": "Taree" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -17.13806, + "lon": -49.98806, + "name": "Indiara" + } + ], + "question": "Which location is the geographic outlier among: Te Atatu South, Taree, Epping, Glen Iris, Indiara?", + "ground_truth": { + "answer": "Indiara", + "outlier_distance_km": 14243.0, + "second_furthest_km": 5531.0, + "clarity_ratio": 2.58, + "median_distance_km": 3654.3, + "distances_to_centroid": { + "Te Atatu South": 5531.0, + "Taree": 3654.3, + "Epping": 2925.2, + "Glen Iris": 2929.1, + "Indiara": 14243.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Te Atatu South: (-36.86°, 174.65°)", + " Taree: (-31.91°, 152.45°)", + " Epping: (-37.65°, 145.03°)", + " Glen Iris: (-37.87°, 145.07°)", + " Indiara: (-17.14°, -49.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Indiara: 14243.0 km from centroid", + " Te Atatu South: 5531.0 km from centroid", + " Taree: 3654.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Indiara", + "FINAL ANSWER: Indiara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": 41.71982, + "lon": -72.83204, + "name": "Farmington" + } + ], + "question": "Which location is the geographic outlier among: Mount Martha, Thornlie, Liverpool, Palm Beach, Farmington?", + "ground_truth": { + "answer": "Farmington", + "outlier_distance_km": 17265.9, + "second_furthest_km": 5682.6, + "clarity_ratio": 3.04, + "median_distance_km": 5460.9, + "distances_to_centroid": { + "Mount Martha": 5011.7, + "Thornlie": 2336.1, + "Liverpool": 5460.9, + "Palm Beach": 5682.6, + "Farmington": 17265.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mount Martha: (-38.27°, 145.02°)", + " Thornlie: (-32.06°, 115.95°)", + " Liverpool: (-33.92°, 150.93°)", + " Palm Beach: (-28.12°, 153.47°)", + " Farmington: (41.72°, -72.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Farmington: 17265.9 km from centroid", + " Palm Beach: 5682.6 km from centroid", + " Liverpool: 5460.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Farmington", + "FINAL ANSWER: Farmington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.14978, + "lon": 6.78569, + "name": "Onitsha" + }, + { + "lat": 0.04626, + "lon": 37.65587, + "name": "Meru" + }, + { + "lat": -0.7, + "lon": 37.18333, + "name": "Karuri" + }, + { + "lat": -28.76197, + "lon": 31.89329, + "name": "Empangeni" + }, + { + "lat": -12.46113, + "lon": 130.84185, + "name": "Darwin" + } + ], + "question": "Which location is the geographic outlier among: Onitsha, Meru, Karuri, Empangeni, Darwin?", + "ground_truth": { + "answer": "Darwin", + "outlier_distance_km": 8969.7, + "second_furthest_km": 4897.4, + "clarity_ratio": 1.83, + "median_distance_km": 2991.7, + "distances_to_centroid": { + "Onitsha": 4897.4, + "Meru": 1478.8, + "Karuri": 1480.9, + "Empangeni": 2991.7, + "Darwin": 8969.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Onitsha: (6.15°, 6.79°)", + " Meru: (0.05°, 37.66°)", + " Karuri: (-0.70°, 37.18°)", + " Empangeni: (-28.76°, 31.89°)", + " Darwin: (-12.46°, 130.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Darwin: 8969.7 km from centroid", + " Onitsha: 4897.4 km from centroid", + " Empangeni: 2991.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Darwin", + "FINAL ANSWER: Darwin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.71897, + "lon": -1.61188, + "name": "New Tafo" + }, + { + "lat": 31.3529, + "lon": 27.23725, + "name": "Marsá Maţrūḩ" + }, + { + "lat": 0.89284, + "lon": 34.92468, + "name": "Kiminini" + }, + { + "lat": 28.08639, + "lon": 30.81464, + "name": "Al-Minyā al-Jadīdah" + }, + { + "lat": -28.55104, + "lon": -56.04125, + "name": "Santo Tomé" + } + ], + "question": "Which location is the geographic outlier among: New Tafo, Marsá Maţrūḩ, Kiminini, Al-Minyā al-Jadīdah, Santo Tomé?", + "ground_truth": { + "answer": "Santo Tomé", + "outlier_distance_km": 7866.9, + "second_furthest_km": 3370.1, + "clarity_ratio": 2.33, + "median_distance_km": 3360.5, + "distances_to_centroid": { + "New Tafo": 963.3, + "Marsá Maţrūḩ": 3360.5, + "Kiminini": 3178.6, + "Al-Minyā al-Jadīdah": 3370.1, + "Santo Tomé": 7866.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " New Tafo: (6.72°, -1.61°)", + " Marsá Maţrūḩ: (31.35°, 27.24°)", + " Kiminini: (0.89°, 34.92°)", + " Al-Minyā al-Jadīdah: (28.09°, 30.81°)", + " Santo Tomé: (-28.55°, -56.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santo Tomé: 7866.9 km from centroid", + " Al-Minyā al-Jadīdah: 3370.1 km from centroid", + " Marsá Maţrūḩ: 3360.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santo Tomé", + "FINAL ANSWER: Santo Tomé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.12694, + "lon": -40.36333, + "name": "Montanha" + }, + { + "lat": -33.13044, + "lon": -64.35272, + "name": "Río Cuarto" + }, + { + "lat": -13.53306, + "lon": -48.22, + "name": "Minaçu" + }, + { + "lat": -16.84972, + "lon": -42.07028, + "name": "Araçuaí" + }, + { + "lat": 29.53489, + "lon": 75.02898, + "name": "Sirsa" + } + ], + "question": "Which location is the geographic outlier among: Montanha, Río Cuarto, Minaçu, Araçuaí, Sirsa?", + "ground_truth": { + "answer": "Sirsa", + "outlier_distance_km": 11442.9, + "second_furthest_km": 4826.8, + "clarity_ratio": 2.37, + "median_distance_km": 2656.4, + "distances_to_centroid": { + "Montanha": 1959.2, + "Río Cuarto": 4826.8, + "Minaçu": 2656.4, + "Araçuaí": 2078.3, + "Sirsa": 11442.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Montanha: (-18.13°, -40.36°)", + " Río Cuarto: (-33.13°, -64.35°)", + " Minaçu: (-13.53°, -48.22°)", + " Araçuaí: (-16.85°, -42.07°)", + " Sirsa: (29.53°, 75.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sirsa: 11442.9 km from centroid", + " Río Cuarto: 4826.8 km from centroid", + " Minaçu: 2656.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sirsa", + "FINAL ANSWER: Sirsa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.36363, + "lon": -87.84479, + "name": "Waukegan" + }, + { + "lat": 28.05002, + "lon": -82.49287, + "name": "Carrollwood" + }, + { + "lat": 33.5806, + "lon": -112.23738, + "name": "Peoria" + }, + { + "lat": 33.97751, + "lon": -118.18702, + "name": "Bell" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + } + ], + "question": "Which location is the geographic outlier among: Waukegan, Carrollwood, Peoria, Bell, Eight Mile Plains?", + "ground_truth": { + "answer": "Eight Mile Plains", + "outlier_distance_km": 17654.5, + "second_furthest_km": 6746.7, + "clarity_ratio": 2.62, + "median_distance_km": 6205.9, + "distances_to_centroid": { + "Waukegan": 4199.4, + "Carrollwood": 3375.0, + "Peoria": 6205.9, + "Bell": 6746.7, + "Eight Mile Plains": 17654.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waukegan: (42.36°, -87.84°)", + " Carrollwood: (28.05°, -82.49°)", + " Peoria: (33.58°, -112.24°)", + " Bell: (33.98°, -118.19°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eight Mile Plains: 17654.5 km from centroid", + " Bell: 6746.7 km from centroid", + " Peoria: 6205.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eight Mile Plains", + "FINAL ANSWER: Eight Mile Plains" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + }, + { + "lat": -26.65682, + "lon": 153.07955, + "name": "Sunshine Coast" + }, + { + "lat": -30.8063, + "lon": 30.33484, + "name": "Ga-Malakhe" + } + ], + "question": "Which location is the geographic outlier among: Paralowie, Palmerston, Manukau City, Sunshine Coast, Ga-Malakhe?", + "ground_truth": { + "answer": "Ga-Malakhe", + "outlier_distance_km": 8893.1, + "second_furthest_km": 4661.8, + "clarity_ratio": 1.91, + "median_distance_km": 2713.3, + "distances_to_centroid": { + "Paralowie": 1424.3, + "Palmerston": 1849.9, + "Manukau City": 4661.8, + "Sunshine Coast": 2713.3, + "Ga-Malakhe": 8893.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paralowie: (-34.76°, 138.61°)", + " Palmerston: (-12.49°, 130.98°)", + " Manukau City: (-36.99°, 174.88°)", + " Sunshine Coast: (-26.66°, 153.08°)", + " Ga-Malakhe: (-30.81°, 30.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ga-Malakhe: 8893.1 km from centroid", + " Manukau City: 4661.8 km from centroid", + " Sunshine Coast: 2713.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ga-Malakhe", + "FINAL ANSWER: Ga-Malakhe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.36333, + "lon": -44.97333, + "name": "São Desidério" + }, + { + "lat": -17.19747, + "lon": -70.93587, + "name": "Moquegua" + }, + { + "lat": -23.87444, + "lon": -53.90167, + "name": "Altônia" + }, + { + "lat": -10.74167, + "lon": -40.36083, + "name": "Pindobaçu" + }, + { + "lat": -28.44776, + "lon": 21.25612, + "name": "Upington" + } + ], + "question": "Which location is the geographic outlier among: São Desidério, Moquegua, Altônia, Pindobaçu, Upington?", + "ground_truth": { + "answer": "Upington", + "outlier_distance_km": 6063.7, + "second_furthest_km": 3507.0, + "clarity_ratio": 1.73, + "median_distance_km": 1772.2, + "distances_to_centroid": { + "São Desidério": 1030.8, + "Moquegua": 3507.0, + "Altônia": 1772.2, + "Pindobaçu": 908.7, + "Upington": 6063.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Desidério: (-12.36°, -44.97°)", + " Moquegua: (-17.20°, -70.94°)", + " Altônia: (-23.87°, -53.90°)", + " Pindobaçu: (-10.74°, -40.36°)", + " Upington: (-28.45°, 21.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upington: 6063.7 km from centroid", + " Moquegua: 3507.0 km from centroid", + " Altônia: 1772.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upington", + "FINAL ANSWER: Upington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.37224, + "lon": 5.35386, + "name": "Marseille 15" + }, + { + "lat": 52.58713, + "lon": 14.64953, + "name": "Kostrzyn nad Odrą" + }, + { + "lat": 53.48095, + "lon": -2.23743, + "name": "Manchester" + }, + { + "lat": 52.5511, + "lon": 13.19921, + "name": "Spandau" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + } + ], + "question": "Which location is the geographic outlier among: Marseille 15, Kostrzyn nad Odrą, Manchester, Spandau, Blenheim?", + "ground_truth": { + "answer": "Blenheim", + "outlier_distance_km": 15753.9, + "second_furthest_km": 4159.0, + "clarity_ratio": 3.79, + "median_distance_km": 3343.7, + "distances_to_centroid": { + "Marseille 15": 3343.7, + "Kostrzyn nad Odrą": 3108.6, + "Manchester": 4159.0, + "Spandau": 3185.9, + "Blenheim": 15753.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marseille 15: (43.37°, 5.35°)", + " Kostrzyn nad Odrą: (52.59°, 14.65°)", + " Manchester: (53.48°, -2.24°)", + " Spandau: (52.55°, 13.20°)", + " Blenheim: (-41.52°, 173.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blenheim: 15753.9 km from centroid", + " Manchester: 4159.0 km from centroid", + " Marseille 15: 3343.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blenheim", + "FINAL ANSWER: Blenheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.12711, + "lon": -84.51439, + "name": "Cincinnati" + }, + { + "lat": 20.52353, + "lon": -100.8157, + "name": "Celaya" + }, + { + "lat": 33.76446, + "lon": -117.79394, + "name": "North Tustin" + }, + { + "lat": 37.35682, + "lon": -77.44165, + "name": "Chester" + }, + { + "lat": -7.53306, + "lon": 110.59583, + "name": "Boyolali" + } + ], + "question": "Which location is the geographic outlier among: Cincinnati, Celaya, North Tustin, Chester, Boyolali?", + "ground_truth": { + "answer": "Boyolali", + "outlier_distance_km": 17504.0, + "second_furthest_km": 6179.3, + "clarity_ratio": 2.83, + "median_distance_km": 4806.5, + "distances_to_centroid": { + "Cincinnati": 3277.7, + "Celaya": 4806.5, + "North Tustin": 6179.3, + "Chester": 2632.5, + "Boyolali": 17504.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cincinnati: (39.13°, -84.51°)", + " Celaya: (20.52°, -100.82°)", + " North Tustin: (33.76°, -117.79°)", + " Chester: (37.36°, -77.44°)", + " Boyolali: (-7.53°, 110.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Boyolali: 17504.0 km from centroid", + " North Tustin: 6179.3 km from centroid", + " Celaya: 4806.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Boyolali", + "FINAL ANSWER: Boyolali" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -33.86667, + "lon": 150.95, + "name": "Fairfield" + }, + { + "lat": -36.90694, + "lon": 174.68704, + "name": "New Lynn" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": 40.59161, + "lon": -111.8841, + "name": "Sandy" + } + ], + "question": "Which location is the geographic outlier among: Gosnells, Fairfield, New Lynn, The Gap, Sandy?", + "ground_truth": { + "answer": "Sandy", + "outlier_distance_km": 16312.0, + "second_furthest_km": 7789.0, + "clarity_ratio": 2.09, + "median_distance_km": 5834.1, + "distances_to_centroid": { + "Gosnells": 2506.1, + "Fairfield": 5653.9, + "New Lynn": 7789.0, + "The Gap": 5834.1, + "Sandy": 16312.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gosnells: (-32.08°, 116.01°)", + " Fairfield: (-33.87°, 150.95°)", + " New Lynn: (-36.91°, 174.69°)", + " The Gap: (-27.44°, 152.94°)", + " Sandy: (40.59°, -111.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sandy: 16312.0 km from centroid", + " New Lynn: 7789.0 km from centroid", + " The Gap: 5834.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sandy", + "FINAL ANSWER: Sandy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.83222, + "lon": -46.89361, + "name": "Vargem Grande do Sul" + }, + { + "lat": -17.72194, + "lon": -48.15972, + "name": "Ipameri" + }, + { + "lat": -1.35528, + "lon": -48.34194, + "name": "Marituba" + }, + { + "lat": -23.72576, + "lon": -46.7024, + "name": "Cidade Dutra" + }, + { + "lat": 42.37093, + "lon": -71.18283, + "name": "Watertown" + } + ], + "question": "Which location is the geographic outlier among: Vargem Grande do Sul, Ipameri, Marituba, Cidade Dutra, Watertown?", + "ground_truth": { + "answer": "Watertown", + "outlier_distance_km": 5546.1, + "second_furthest_km": 2224.3, + "clarity_ratio": 2.49, + "median_distance_km": 2017.1, + "distances_to_centroid": { + "Vargem Grande do Sul": 2017.1, + "Ipameri": 1541.4, + "Marituba": 554.6, + "Cidade Dutra": 2224.3, + "Watertown": 5546.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vargem Grande do Sul: (-21.83°, -46.89°)", + " Ipameri: (-17.72°, -48.16°)", + " Marituba: (-1.36°, -48.34°)", + " Cidade Dutra: (-23.73°, -46.70°)", + " Watertown: (42.37°, -71.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Watertown: 5546.1 km from centroid", + " Cidade Dutra: 2224.3 km from centroid", + " Vargem Grande do Sul: 2017.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Watertown", + "FINAL ANSWER: Watertown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.15722, + "lon": 43.35417, + "name": "Hartīshēk" + }, + { + "lat": -3.39879, + "lon": 37.68336, + "name": "Taveta" + }, + { + "lat": 8.72851, + "lon": 5.75561, + "name": "Patigi" + }, + { + "lat": 9.17031, + "lon": 35.83491, + "name": "Gimbi" + }, + { + "lat": -23.295, + "lon": -50.07722, + "name": "Santo Antônio da Platina" + } + ], + "question": "Which location is the geographic outlier among: Hartīshēk, Taveta, Patigi, Gimbi, Santo Antônio da Platina?", + "ground_truth": { + "answer": "Santo Antônio da Platina", + "outlier_distance_km": 7429.8, + "second_furthest_km": 3349.2, + "clarity_ratio": 2.22, + "median_distance_km": 2604.0, + "distances_to_centroid": { + "Hartīshēk": 3349.2, + "Taveta": 2604.0, + "Patigi": 1366.3, + "Gimbi": 2568.5, + "Santo Antônio da Platina": 7429.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hartīshēk: (9.16°, 43.35°)", + " Taveta: (-3.40°, 37.68°)", + " Patigi: (8.73°, 5.76°)", + " Gimbi: (9.17°, 35.83°)", + " Santo Antônio da Platina: (-23.30°, -50.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santo Antônio da Platina: 7429.8 km from centroid", + " Hartīshēk: 3349.2 km from centroid", + " Taveta: 2604.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santo Antônio da Platina", + "FINAL ANSWER: Santo Antônio da Platina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.10545, + "lon": -82.52594, + "name": "Greater Northdale" + }, + { + "lat": 43.65355, + "lon": -79.39724, + "name": "Kensington-Chinatown" + }, + { + "lat": 50.03928, + "lon": -110.67661, + "name": "Medicine Hat" + }, + { + "lat": 39.53983, + "lon": -76.35496, + "name": "North Bel Air" + }, + { + "lat": -41.13827, + "lon": 175.0502, + "name": "Upper Hutt" + } + ], + "question": "Which location is the geographic outlier among: Greater Northdale, Kensington-Chinatown, Medicine Hat, North Bel Air, Upper Hutt?", + "ground_truth": { + "answer": "Upper Hutt", + "outlier_distance_km": 16661.9, + "second_furthest_km": 6996.8, + "clarity_ratio": 2.38, + "median_distance_km": 4760.3, + "distances_to_centroid": { + "Greater Northdale": 4760.3, + "Kensington-Chinatown": 4589.5, + "Medicine Hat": 6996.8, + "North Bel Air": 4243.9, + "Upper Hutt": 16661.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Greater Northdale: (28.11°, -82.53°)", + " Kensington-Chinatown: (43.65°, -79.40°)", + " Medicine Hat: (50.04°, -110.68°)", + " North Bel Air: (39.54°, -76.35°)", + " Upper Hutt: (-41.14°, 175.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upper Hutt: 16661.9 km from centroid", + " Medicine Hat: 6996.8 km from centroid", + " Greater Northdale: 4760.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upper Hutt", + "FINAL ANSWER: Upper Hutt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.71171, + "lon": 27.83795, + "name": "Vanderbijlpark" + }, + { + "lat": 6.15038, + "lon": 6.83042, + "name": "Nkpor" + }, + { + "lat": 4.77742, + "lon": 7.0134, + "name": "Port Harcourt" + }, + { + "lat": -27.27888, + "lon": 28.49696, + "name": "Frankfort" + }, + { + "lat": -30.98278, + "lon": -54.67306, + "name": "Dom Pedrito" + } + ], + "question": "Which location is the geographic outlier among: Vanderbijlpark, Nkpor, Port Harcourt, Frankfort, Dom Pedrito?", + "ground_truth": { + "answer": "Dom Pedrito", + "outlier_distance_km": 6115.8, + "second_furthest_km": 2968.8, + "clarity_ratio": 2.06, + "median_distance_km": 2884.4, + "distances_to_centroid": { + "Vanderbijlpark": 2884.4, + "Nkpor": 2366.6, + "Port Harcourt": 2220.2, + "Frankfort": 2968.8, + "Dom Pedrito": 6115.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vanderbijlpark: (-26.71°, 27.84°)", + " Nkpor: (6.15°, 6.83°)", + " Port Harcourt: (4.78°, 7.01°)", + " Frankfort: (-27.28°, 28.50°)", + " Dom Pedrito: (-30.98°, -54.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dom Pedrito: 6115.8 km from centroid", + " Frankfort: 2968.8 km from centroid", + " Vanderbijlpark: 2884.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dom Pedrito", + "FINAL ANSWER: Dom Pedrito" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.37477, + "lon": -95.75444, + "name": "Carlos A. Carrillo" + }, + { + "lat": 33.71372, + "lon": -117.76091, + "name": "Northwood" + }, + { + "lat": 19.76613, + "lon": -97.24514, + "name": "Altotonga" + }, + { + "lat": 49.26418, + "lon": -123.239, + "name": "University Endowment Lands" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + } + ], + "question": "Which location is the geographic outlier among: Carlos A. Carrillo, Northwood, Altotonga, University Endowment Lands, Liverpool?", + "ground_truth": { + "answer": "Liverpool", + "outlier_distance_km": 16720.1, + "second_furthest_km": 6860.6, + "clarity_ratio": 2.44, + "median_distance_km": 6302.5, + "distances_to_centroid": { + "Carlos A. Carrillo": 4134.6, + "Northwood": 6302.5, + "Altotonga": 4279.7, + "University Endowment Lands": 6860.6, + "Liverpool": 16720.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlos A. Carrillo: (18.37°, -95.75°)", + " Northwood: (33.71°, -117.76°)", + " Altotonga: (19.77°, -97.25°)", + " University Endowment Lands: (49.26°, -123.24°)", + " Liverpool: (-33.92°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Liverpool: 16720.1 km from centroid", + " University Endowment Lands: 6860.6 km from centroid", + " Northwood: 6302.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Liverpool", + "FINAL ANSWER: Liverpool" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.02858, + "lon": 8.11754, + "name": "Eltville" + }, + { + "lat": 53.54846, + "lon": -2.00455, + "name": "Saddleworth" + }, + { + "lat": 37.329, + "lon": -5.41681, + "name": "Marchena" + }, + { + "lat": 40.86543, + "lon": 14.28877, + "name": "Poggioreale" + }, + { + "lat": 42.46254, + "lon": -83.10409, + "name": "Hazel Park" + } + ], + "question": "Which location is the geographic outlier among: Eltville, Saddleworth, Marchena, Poggioreale, Hazel Park?", + "ground_truth": { + "answer": "Hazel Park", + "outlier_distance_km": 5420.0, + "second_furthest_km": 2306.0, + "clarity_ratio": 2.35, + "median_distance_km": 1726.3, + "distances_to_centroid": { + "Eltville": 1726.3, + "Saddleworth": 1280.9, + "Marchena": 1081.3, + "Poggioreale": 2306.0, + "Hazel Park": 5420.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eltville: (50.03°, 8.12°)", + " Saddleworth: (53.55°, -2.00°)", + " Marchena: (37.33°, -5.42°)", + " Poggioreale: (40.87°, 14.29°)", + " Hazel Park: (42.46°, -83.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hazel Park: 5420.0 km from centroid", + " Poggioreale: 2306.0 km from centroid", + " Eltville: 1726.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hazel Park", + "FINAL ANSWER: Hazel Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.18333, + "lon": 78.01667, + "name": "Agra" + }, + { + "lat": 20.28845, + "lon": 82.7606, + "name": "Kharhiāl" + }, + { + "lat": 19.31151, + "lon": 84.7929, + "name": "Brahmapur" + }, + { + "lat": 32.9, + "lon": 115.81667, + "name": "Fuyang" + }, + { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + } + ], + "question": "Which location is the geographic outlier among: Agra, Kharhiāl, Brahmapur, Fuyang, Dianella?", + "ground_truth": { + "answer": "Dianella", + "outlier_distance_km": 5502.1, + "second_furthest_km": 2980.6, + "clarity_ratio": 1.85, + "median_distance_km": 2360.7, + "distances_to_centroid": { + "Agra": 2360.7, + "Kharhiāl": 1542.5, + "Brahmapur": 1303.7, + "Fuyang": 2980.6, + "Dianella": 5502.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Agra: (27.18°, 78.02°)", + " Kharhiāl: (20.29°, 82.76°)", + " Brahmapur: (19.31°, 84.79°)", + " Fuyang: (32.90°, 115.82°)", + " Dianella: (-31.89°, 115.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dianella: 5502.1 km from centroid", + " Fuyang: 2980.6 km from centroid", + " Agra: 2360.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dianella", + "FINAL ANSWER: Dianella" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.73006, + "lon": -92.63825, + "name": "San Cristóbal de las Casas" + }, + { + "lat": 21.33999, + "lon": -158.03039, + "name": "‘Ewa Gentry" + }, + { + "lat": 39.94035, + "lon": -82.01319, + "name": "Zanesville" + }, + { + "lat": 34.86676, + "lon": -92.40432, + "name": "Maumelle" + }, + { + "lat": -4.085, + "lon": -63.14139, + "name": "Coari" + } + ], + "question": "Which location is the geographic outlier among: San Cristóbal de las Casas, ‘Ewa Gentry, Zanesville, Maumelle, Coari?", + "ground_truth": { + "answer": "‘Ewa Gentry", + "outlier_distance_km": 6202.3, + "second_furthest_km": 4728.2, + "clarity_ratio": 1.31, + "median_distance_km": 2504.4, + "distances_to_centroid": { + "San Cristóbal de las Casas": 767.3, + "‘Ewa Gentry": 6202.3, + "Zanesville": 2504.4, + "Maumelle": 1544.5, + "Coari": 4728.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Cristóbal de las Casas: (16.73°, -92.64°)", + " ‘Ewa Gentry: (21.34°, -158.03°)", + " Zanesville: (39.94°, -82.01°)", + " Maumelle: (34.87°, -92.40°)", + " Coari: (-4.08°, -63.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " ‘Ewa Gentry: 6202.3 km from centroid", + " Coari: 4728.2 km from centroid", + " Zanesville: 2504.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: ‘Ewa Gentry", + "FINAL ANSWER: ‘Ewa Gentry" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.68282, + "lon": -79.37967, + "name": "Rosedale-Moore Park" + }, + { + "lat": 34.7698, + "lon": -84.97022, + "name": "Dalton" + }, + { + "lat": 34.27834, + "lon": -119.29317, + "name": "Ventura" + }, + { + "lat": 20.03557, + "lon": -98.31015, + "name": "Cuautepec de Hinojosa" + }, + { + "lat": -8.14583, + "lon": -36.37111, + "name": "Brejo da Madre de Deus" + } + ], + "question": "Which location is the geographic outlier among: Rosedale-Moore Park, Dalton, Ventura, Cuautepec de Hinojosa, Brejo da Madre de Deus?", + "ground_truth": { + "answer": "Brejo da Madre de Deus", + "outlier_distance_km": 6303.7, + "second_furthest_km": 3577.6, + "clarity_ratio": 1.76, + "median_distance_km": 2121.9, + "distances_to_centroid": { + "Rosedale-Moore Park": 2121.9, + "Dalton": 1102.0, + "Ventura": 3577.6, + "Cuautepec de Hinojosa": 1598.7, + "Brejo da Madre de Deus": 6303.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rosedale-Moore Park: (43.68°, -79.38°)", + " Dalton: (34.77°, -84.97°)", + " Ventura: (34.28°, -119.29°)", + " Cuautepec de Hinojosa: (20.04°, -98.31°)", + " Brejo da Madre de Deus: (-8.15°, -36.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brejo da Madre de Deus: 6303.7 km from centroid", + " Ventura: 3577.6 km from centroid", + " Rosedale-Moore Park: 2121.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brejo da Madre de Deus", + "FINAL ANSWER: Brejo da Madre de Deus" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.82882, + "lon": -0.32247, + "name": "Lancing" + }, + { + "lat": 48.91667, + "lon": 2.28333, + "name": "Asnières-sur-Seine" + }, + { + "lat": 51.40944, + "lon": 46.04833, + "name": "Privolzhskiy" + }, + { + "lat": 43.4028, + "lon": 3.69278, + "name": "Sète" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + } + ], + "question": "Which location is the geographic outlier among: Lancing, Asnières-sur-Seine, Privolzhskiy, Sète, Shepparton?", + "ground_truth": { + "answer": "Shepparton", + "outlier_distance_km": 13341.9, + "second_furthest_km": 3880.8, + "clarity_ratio": 3.44, + "median_distance_km": 3637.5, + "distances_to_centroid": { + "Lancing": 3880.8, + "Asnières-sur-Seine": 3637.5, + "Privolzhskiy": 2264.7, + "Sète": 3379.6, + "Shepparton": 13341.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lancing: (50.83°, -0.32°)", + " Asnières-sur-Seine: (48.92°, 2.28°)", + " Privolzhskiy: (51.41°, 46.05°)", + " Sète: (43.40°, 3.69°)", + " Shepparton: (-36.38°, 145.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shepparton: 13341.9 km from centroid", + " Lancing: 3880.8 km from centroid", + " Asnières-sur-Seine: 3637.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shepparton", + "FINAL ANSWER: Shepparton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.09639, + "lon": -35.23278, + "name": "Sapé" + }, + { + "lat": -22.99835, + "lon": -43.36545, + "name": "Barra da Tijuca" + }, + { + "lat": -30.00018, + "lon": -51.07632, + "name": "Alvorada" + }, + { + "lat": -8.96389, + "lon": -37.62833, + "name": "Manari" + }, + { + "lat": 30.71877, + "lon": 31.56299, + "name": "Al Ibrāhīmīyah" + } + ], + "question": "Which location is the geographic outlier among: Sapé, Barra da Tijuca, Alvorada, Manari, Al Ibrāhīmīyah?", + "ground_truth": { + "answer": "Al Ibrāhīmīyah", + "outlier_distance_km": 7563.2, + "second_furthest_km": 3519.8, + "clarity_ratio": 2.15, + "median_distance_km": 2430.4, + "distances_to_centroid": { + "Sapé": 893.8, + "Barra da Tijuca": 2430.4, + "Alvorada": 3519.8, + "Manari": 1162.0, + "Al Ibrāhīmīyah": 7563.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sapé: (-7.10°, -35.23°)", + " Barra da Tijuca: (-23.00°, -43.37°)", + " Alvorada: (-30.00°, -51.08°)", + " Manari: (-8.96°, -37.63°)", + " Al Ibrāhīmīyah: (30.72°, 31.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Ibrāhīmīyah: 7563.2 km from centroid", + " Alvorada: 3519.8 km from centroid", + " Barra da Tijuca: 2430.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Ibrāhīmīyah", + "FINAL ANSWER: Al Ibrāhīmīyah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 67.93972, + "lon": 32.87389, + "name": "Monchegorsk" + }, + { + "lat": 47.40769, + "lon": 47.25391, + "name": "Kharabali" + }, + { + "lat": 40.93591, + "lon": 14.25983, + "name": "Grumo Nevano" + }, + { + "lat": 52.9911, + "lon": 22.88422, + "name": "Łapy" + }, + { + "lat": -26.71667, + "lon": 27.1, + "name": "Potchefstroom" + } + ], + "question": "Which location is the geographic outlier among: Monchegorsk, Kharabali, Grumo Nevano, Łapy, Potchefstroom?", + "ground_truth": { + "answer": "Potchefstroom", + "outlier_distance_km": 7033.1, + "second_furthest_km": 3503.6, + "clarity_ratio": 2.01, + "median_distance_km": 1935.1, + "distances_to_centroid": { + "Monchegorsk": 3503.6, + "Kharabali": 1935.1, + "Grumo Nevano": 1357.8, + "Łapy": 1890.9, + "Potchefstroom": 7033.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Monchegorsk: (67.94°, 32.87°)", + " Kharabali: (47.41°, 47.25°)", + " Grumo Nevano: (40.94°, 14.26°)", + " Łapy: (52.99°, 22.88°)", + " Potchefstroom: (-26.72°, 27.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Potchefstroom: 7033.1 km from centroid", + " Monchegorsk: 3503.6 km from centroid", + " Kharabali: 1935.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Potchefstroom", + "FINAL ANSWER: Potchefstroom" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.81568, + "lon": 2.38487, + "name": "Ivry-sur-Seine" + }, + { + "lat": 55.91797, + "lon": 39.17242, + "name": "Pokrov" + }, + { + "lat": 46.46671, + "lon": -0.80624, + "name": "Fontenay-le-Comte" + }, + { + "lat": 52.58128, + "lon": -1.09248, + "name": "Wigston Magna" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + } + ], + "question": "Which location is the geographic outlier among: Ivry-sur-Seine, Pokrov, Fontenay-le-Comte, Wigston Magna, Mount Eden?", + "ground_truth": { + "answer": "Mount Eden", + "outlier_distance_km": 15667.7, + "second_furthest_km": 4077.3, + "clarity_ratio": 3.84, + "median_distance_km": 3940.4, + "distances_to_centroid": { + "Ivry-sur-Seine": 3744.5, + "Pokrov": 2522.4, + "Fontenay-le-Comte": 3940.4, + "Wigston Magna": 4077.3, + "Mount Eden": 15667.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ivry-sur-Seine: (48.82°, 2.38°)", + " Pokrov: (55.92°, 39.17°)", + " Fontenay-le-Comte: (46.47°, -0.81°)", + " Wigston Magna: (52.58°, -1.09°)", + " Mount Eden: (-36.88°, 174.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Eden: 15667.7 km from centroid", + " Wigston Magna: 4077.3 km from centroid", + " Fontenay-le-Comte: 3940.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Eden", + "FINAL ANSWER: Mount Eden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.09826, + "lon": -16.61708, + "name": "San Miguel De Abona" + }, + { + "lat": 52.63333, + "lon": -1.93333, + "name": "Brownhills" + }, + { + "lat": 51.39323, + "lon": 0.47713, + "name": "Strood" + }, + { + "lat": 49.38417, + "lon": 8.3775, + "name": "Schifferstadt" + }, + { + "lat": 39.084, + "lon": -76.70025, + "name": "Odenton" + } + ], + "question": "Which location is the geographic outlier among: San Miguel De Abona, Brownhills, Strood, Schifferstadt, Odenton?", + "ground_truth": { + "answer": "Odenton", + "outlier_distance_km": 4864.6, + "second_furthest_km": 2029.2, + "clarity_ratio": 2.4, + "median_distance_km": 1782.4, + "distances_to_centroid": { + "San Miguel De Abona": 1782.4, + "Brownhills": 1471.6, + "Strood": 1548.4, + "Schifferstadt": 2029.2, + "Odenton": 4864.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Miguel De Abona: (28.10°, -16.62°)", + " Brownhills: (52.63°, -1.93°)", + " Strood: (51.39°, 0.48°)", + " Schifferstadt: (49.38°, 8.38°)", + " Odenton: (39.08°, -76.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Odenton: 4864.6 km from centroid", + " Schifferstadt: 2029.2 km from centroid", + " San Miguel De Abona: 1782.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Odenton", + "FINAL ANSWER: Odenton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.28333, + "lon": 36.21667, + "name": "Mambuk" + }, + { + "lat": 6.98333, + "lon": 39.18333, + "name": "Dodola" + }, + { + "lat": -27.342, + "lon": 31.58, + "name": "Ncotshane" + }, + { + "lat": 9.88333, + "lon": 36.61667, + "name": "Āyana" + }, + { + "lat": 18.37035, + "lon": -97.29966, + "name": "Altepexi" + } + ], + "question": "Which location is the geographic outlier among: Mambuk, Dodola, Ncotshane, Āyana, Altepexi?", + "ground_truth": { + "answer": "Altepexi", + "outlier_distance_km": 11609.4, + "second_furthest_km": 4213.5, + "clarity_ratio": 2.76, + "median_distance_km": 3330.2, + "distances_to_centroid": { + "Mambuk": 3082.1, + "Dodola": 3330.2, + "Ncotshane": 4213.5, + "Āyana": 3092.3, + "Altepexi": 11609.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mambuk: (11.28°, 36.22°)", + " Dodola: (6.98°, 39.18°)", + " Ncotshane: (-27.34°, 31.58°)", + " Āyana: (9.88°, 36.62°)", + " Altepexi: (18.37°, -97.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Altepexi: 11609.4 km from centroid", + " Ncotshane: 4213.5 km from centroid", + " Dodola: 3330.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Altepexi", + "FINAL ANSWER: Altepexi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.08595, + "lon": -48.96765, + "name": "Guabiruba" + }, + { + "lat": -8.17111, + "lon": -79.00917, + "name": "Moche" + }, + { + "lat": -4.52889, + "lon": -39.62222, + "name": "Itatira" + }, + { + "lat": 7.00017, + "lon": -76.26915, + "name": "Dabeiba" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + } + ], + "question": "Which location is the geographic outlier among: Guabiruba, Moche, Itatira, Dabeiba, Hervey Bay?", + "ground_truth": { + "answer": "Hervey Bay", + "outlier_distance_km": 15797.1, + "second_furthest_km": 6745.4, + "clarity_ratio": 2.34, + "median_distance_km": 6658.5, + "distances_to_centroid": { + "Guabiruba": 3640.1, + "Moche": 6658.5, + "Itatira": 2482.7, + "Dabeiba": 6745.4, + "Hervey Bay": 15797.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guabiruba: (-27.09°, -48.97°)", + " Moche: (-8.17°, -79.01°)", + " Itatira: (-4.53°, -39.62°)", + " Dabeiba: (7.00°, -76.27°)", + " Hervey Bay: (-25.29°, 152.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hervey Bay: 15797.1 km from centroid", + " Dabeiba: 6745.4 km from centroid", + " Moche: 6658.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hervey Bay", + "FINAL ANSWER: Hervey Bay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.70567, + "lon": -70.22863, + "name": "Yarmouth" + }, + { + "lat": 40.59161, + "lon": -111.8841, + "name": "Sandy" + }, + { + "lat": 19.25934, + "lon": -99.60175, + "name": "Metepec" + }, + { + "lat": 42.4251, + "lon": -71.06616, + "name": "Malden" + }, + { + "lat": 16.78854, + "lon": 80.84593, + "name": "Nūzvīd" + } + ], + "question": "Which location is the geographic outlier among: Yarmouth, Sandy, Metepec, Malden, Nūzvīd?", + "ground_truth": { + "answer": "Nūzvīd", + "outlier_distance_km": 12781.2, + "second_furthest_km": 5140.8, + "clarity_ratio": 2.49, + "median_distance_km": 4713.6, + "distances_to_centroid": { + "Yarmouth": 1758.9, + "Sandy": 5140.8, + "Metepec": 4713.6, + "Malden": 1860.1, + "Nūzvīd": 12781.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yarmouth: (41.71°, -70.23°)", + " Sandy: (40.59°, -111.88°)", + " Metepec: (19.26°, -99.60°)", + " Malden: (42.43°, -71.07°)", + " Nūzvīd: (16.79°, 80.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nūzvīd: 12781.2 km from centroid", + " Sandy: 5140.8 km from centroid", + " Metepec: 4713.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nūzvīd", + "FINAL ANSWER: Nūzvīd" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.36861, + "lon": -49.45139, + "name": "Campo Magro" + }, + { + "lat": -5.19917, + "lon": -39.29278, + "name": "Quixeramobim" + }, + { + "lat": -7.19111, + "lon": -48.20722, + "name": "Araguaína" + }, + { + "lat": -18.03028, + "lon": -40.15056, + "name": "Pedro Canário" + }, + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + } + ], + "question": "Which location is the geographic outlier among: Campo Magro, Quixeramobim, Araguaína, Pedro Canário, Epsom?", + "ground_truth": { + "answer": "Epsom", + "outlier_distance_km": 13832.1, + "second_furthest_km": 5309.5, + "clarity_ratio": 2.61, + "median_distance_km": 5081.7, + "distances_to_centroid": { + "Campo Magro": 5081.7, + "Quixeramobim": 4464.0, + "Araguaína": 5309.5, + "Pedro Canário": 4181.7, + "Epsom": 13832.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Campo Magro: (-25.37°, -49.45°)", + " Quixeramobim: (-5.20°, -39.29°)", + " Araguaína: (-7.19°, -48.21°)", + " Pedro Canário: (-18.03°, -40.15°)", + " Epsom: (-36.89°, 174.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Epsom: 13832.1 km from centroid", + " Araguaína: 5309.5 km from centroid", + " Campo Magro: 5081.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Epsom", + "FINAL ANSWER: Epsom" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.85711, + "lon": 32.31183, + "name": "Al Qanţarah" + }, + { + "lat": 11.28333, + "lon": 36.21667, + "name": "Mambuk" + }, + { + "lat": -25.68991, + "lon": 30.03504, + "name": "Belfast" + }, + { + "lat": 8.72851, + "lon": 5.75561, + "name": "Patigi" + }, + { + "lat": -5.0925, + "lon": -80.1625, + "name": "Chulucanas" + } + ], + "question": "Which location is the geographic outlier among: Al Qanţarah, Mambuk, Belfast, Patigi, Chulucanas?", + "ground_truth": { + "answer": "Chulucanas", + "outlier_distance_km": 9494.2, + "second_furthest_km": 4277.1, + "clarity_ratio": 2.22, + "median_distance_km": 4145.7, + "distances_to_centroid": { + "Al Qanţarah": 4145.7, + "Mambuk": 3548.8, + "Belfast": 4277.1, + "Patigi": 533.7, + "Chulucanas": 9494.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Qanţarah: (30.86°, 32.31°)", + " Mambuk: (11.28°, 36.22°)", + " Belfast: (-25.69°, 30.04°)", + " Patigi: (8.73°, 5.76°)", + " Chulucanas: (-5.09°, -80.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chulucanas: 9494.2 km from centroid", + " Belfast: 4277.1 km from centroid", + " Al Qanţarah: 4145.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chulucanas", + "FINAL ANSWER: Chulucanas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.4625, + "lon": -42.65306, + "name": "Cachoeiras de Macacu" + }, + { + "lat": -6.35944, + "lon": -39.29861, + "name": "Iguatu" + }, + { + "lat": -26.56849, + "lon": -54.7579, + "name": "Montecarlo" + }, + { + "lat": -32.43289, + "lon": -63.24811, + "name": "Villa Nueva" + }, + { + "lat": 34.41728, + "lon": 74.64308, + "name": "Bandipura" + } + ], + "question": "Which location is the geographic outlier among: Cachoeiras de Macacu, Iguatu, Montecarlo, Villa Nueva, Bandipura?", + "ground_truth": { + "answer": "Bandipura", + "outlier_distance_km": 11561.0, + "second_furthest_km": 4591.8, + "clarity_ratio": 2.52, + "median_distance_km": 3578.2, + "distances_to_centroid": { + "Cachoeiras de Macacu": 2283.1, + "Iguatu": 1637.1, + "Montecarlo": 3578.2, + "Villa Nueva": 4591.8, + "Bandipura": 11561.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cachoeiras de Macacu: (-22.46°, -42.65°)", + " Iguatu: (-6.36°, -39.30°)", + " Montecarlo: (-26.57°, -54.76°)", + " Villa Nueva: (-32.43°, -63.25°)", + " Bandipura: (34.42°, 74.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bandipura: 11561.0 km from centroid", + " Villa Nueva: 4591.8 km from centroid", + " Montecarlo: 3578.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bandipura", + "FINAL ANSWER: Bandipura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.75398, + "lon": 100.50144, + "name": "Bangkok" + }, + { + "lat": 36.84666, + "lon": 136.98355, + "name": "Himi" + }, + { + "lat": 33.83916, + "lon": 132.76574, + "name": "Matsuyama" + }, + { + "lat": 20.74238, + "lon": 78.5871, + "name": "Sindi" + }, + { + "lat": -10.64389, + "lon": -51.56889, + "name": "Confresa" + } + ], + "question": "Which location is the geographic outlier among: Bangkok, Himi, Matsuyama, Sindi, Confresa?", + "ground_truth": { + "answer": "Confresa", + "outlier_distance_km": 14686.1, + "second_furthest_km": 5901.7, + "clarity_ratio": 2.49, + "median_distance_km": 5500.2, + "distances_to_centroid": { + "Bangkok": 2316.0, + "Himi": 5901.7, + "Matsuyama": 5500.2, + "Sindi": 223.2, + "Confresa": 14686.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bangkok: (13.75°, 100.50°)", + " Himi: (36.85°, 136.98°)", + " Matsuyama: (33.84°, 132.77°)", + " Sindi: (20.74°, 78.59°)", + " Confresa: (-10.64°, -51.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Confresa: 14686.1 km from centroid", + " Himi: 5901.7 km from centroid", + " Matsuyama: 5500.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Confresa", + "FINAL ANSWER: Confresa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.31946, + "lon": -72.98538, + "name": "Puerto Varas" + }, + { + "lat": -23.64889, + "lon": -46.85222, + "name": "Embu das Artes" + }, + { + "lat": -20.76361, + "lon": -41.53306, + "name": "Alegre" + }, + { + "lat": -22.74389, + "lon": -43.7075, + "name": "Seropédica" + }, + { + "lat": 41.31755, + "lon": -81.34539, + "name": "Aurora" + } + ], + "question": "Which location is the geographic outlier among: Puerto Varas, Embu das Artes, Alegre, Seropédica, Aurora?", + "ground_truth": { + "answer": "Aurora", + "outlier_distance_km": 6570.6, + "second_furthest_km": 3453.9, + "clarity_ratio": 1.9, + "median_distance_km": 1860.3, + "distances_to_centroid": { + "Puerto Varas": 3453.9, + "Embu das Artes": 1579.8, + "Alegre": 1860.3, + "Seropédica": 1767.7, + "Aurora": 6570.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Puerto Varas: (-41.32°, -72.99°)", + " Embu das Artes: (-23.65°, -46.85°)", + " Alegre: (-20.76°, -41.53°)", + " Seropédica: (-22.74°, -43.71°)", + " Aurora: (41.32°, -81.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aurora: 6570.6 km from centroid", + " Puerto Varas: 3453.9 km from centroid", + " Alegre: 1860.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aurora", + "FINAL ANSWER: Aurora" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.11694, + "lon": -40.07028, + "name": "Itororó" + }, + { + "lat": -11.03194, + "lon": -37.475, + "name": "Salgado" + }, + { + "lat": -38.73628, + "lon": -72.59738, + "name": "Temuco" + }, + { + "lat": -7.05614, + "lon": -76.5911, + "name": "Bellavista" + }, + { + "lat": 31.21093, + "lon": 109.32154, + "name": "Dashu" + } + ], + "question": "Which location is the geographic outlier among: Itororó, Salgado, Temuco, Bellavista, Dashu?", + "ground_truth": { + "answer": "Dashu", + "outlier_distance_km": 14504.7, + "second_furthest_km": 5954.8, + "clarity_ratio": 2.44, + "median_distance_km": 5850.7, + "distances_to_centroid": { + "Itororó": 1964.5, + "Salgado": 1567.1, + "Temuco": 5954.8, + "Bellavista": 5850.7, + "Dashu": 14504.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itororó: (-15.12°, -40.07°)", + " Salgado: (-11.03°, -37.48°)", + " Temuco: (-38.74°, -72.60°)", + " Bellavista: (-7.06°, -76.59°)", + " Dashu: (31.21°, 109.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dashu: 14504.7 km from centroid", + " Temuco: 5954.8 km from centroid", + " Bellavista: 5850.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dashu", + "FINAL ANSWER: Dashu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.455, + "lon": 120.5875, + "name": "La Trinidad" + }, + { + "lat": 4.18333, + "lon": 114.31667, + "name": "Marudi" + }, + { + "lat": 33.59993, + "lon": 130.81495, + "name": "Kawasaki" + }, + { + "lat": 1.7497, + "lon": 103.277, + "name": "Kawasan Penempatan Ulu Benut Tiga" + }, + { + "lat": 41.81843, + "lon": -73.14372, + "name": "West Torrington" + } + ], + "question": "Which location is the geographic outlier among: La Trinidad, Marudi, Kawasaki, Kawasan Penempatan Ulu Benut Tiga, West Torrington?", + "ground_truth": { + "answer": "West Torrington", + "outlier_distance_km": 12619.6, + "second_furthest_km": 5310.0, + "clarity_ratio": 2.38, + "median_distance_km": 4383.1, + "distances_to_centroid": { + "La Trinidad": 4383.1, + "Marudi": 4174.9, + "Kawasaki": 5310.0, + "Kawasan Penempatan Ulu Benut Tiga": 3285.8, + "West Torrington": 12619.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Trinidad: (16.45°, 120.59°)", + " Marudi: (4.18°, 114.32°)", + " Kawasaki: (33.60°, 130.81°)", + " Kawasan Penempatan Ulu Benut Tiga: (1.75°, 103.28°)", + " West Torrington: (41.82°, -73.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Torrington: 12619.6 km from centroid", + " Kawasaki: 5310.0 km from centroid", + " La Trinidad: 4383.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Torrington", + "FINAL ANSWER: West Torrington" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.92665, + "lon": -0.98577, + "name": "Akim Oda" + }, + { + "lat": 31.40398, + "lon": 31.73778, + "name": "Kafr al Baţţīkh" + }, + { + "lat": 10.48536, + "lon": 5.14501, + "name": "Ibeto" + }, + { + "lat": 27.93043, + "lon": 30.83826, + "name": "Abū Qurqāş" + }, + { + "lat": 8.33702, + "lon": 77.86776, + "name": "Tisaiyanvilai" + } + ], + "question": "Which location is the geographic outlier among: Akim Oda, Kafr al Baţţīkh, Ibeto, Abū Qurqāş, Tisaiyanvilai?", + "ground_truth": { + "answer": "Tisaiyanvilai", + "outlier_distance_km": 5381.4, + "second_furthest_km": 3471.2, + "clarity_ratio": 1.55, + "median_distance_km": 2661.3, + "distances_to_centroid": { + "Akim Oda": 3471.2, + "Kafr al Baţţīkh": 1646.8, + "Ibeto": 2661.3, + "Abū Qurqāş": 1251.4, + "Tisaiyanvilai": 5381.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Akim Oda: (5.93°, -0.99°)", + " Kafr al Baţţīkh: (31.40°, 31.74°)", + " Ibeto: (10.49°, 5.15°)", + " Abū Qurqāş: (27.93°, 30.84°)", + " Tisaiyanvilai: (8.34°, 77.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tisaiyanvilai: 5381.4 km from centroid", + " Akim Oda: 3471.2 km from centroid", + " Ibeto: 2661.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tisaiyanvilai", + "FINAL ANSWER: Tisaiyanvilai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.1305, + "lon": -121.65439, + "name": "Morgan Hill" + }, + { + "lat": 41.69031, + "lon": -87.66672, + "name": "Morgan Park" + }, + { + "lat": 40.70121, + "lon": -74.23015, + "name": "Hillside" + }, + { + "lat": 37.67748, + "lon": -113.06189, + "name": "Cedar City" + }, + { + "lat": 23.00959, + "lon": 74.57747, + "name": "Thandla" + } + ], + "question": "Which location is the geographic outlier among: Morgan Hill, Morgan Park, Hillside, Cedar City, Thandla?", + "ground_truth": { + "answer": "Thandla", + "outlier_distance_km": 12160.8, + "second_furthest_km": 5032.3, + "clarity_ratio": 2.42, + "median_distance_km": 4283.3, + "distances_to_centroid": { + "Morgan Hill": 5032.3, + "Morgan Park": 2101.9, + "Hillside": 999.9, + "Cedar City": 4283.3, + "Thandla": 12160.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morgan Hill: (37.13°, -121.65°)", + " Morgan Park: (41.69°, -87.67°)", + " Hillside: (40.70°, -74.23°)", + " Cedar City: (37.68°, -113.06°)", + " Thandla: (23.01°, 74.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thandla: 12160.8 km from centroid", + " Morgan Hill: 5032.3 km from centroid", + " Cedar City: 4283.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thandla", + "FINAL ANSWER: Thandla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -6.82972, + "lon": -35.24722, + "name": "Itapororoca" + } + ], + "question": "Which location is the geographic outlier among: Kellyville, Helensvale, Thomastown, Port Macquarie, Itapororoca?", + "ground_truth": { + "answer": "Itapororoca", + "outlier_distance_km": 14921.0, + "second_furthest_km": 3914.0, + "clarity_ratio": 3.81, + "median_distance_km": 3829.8, + "distances_to_centroid": { + "Kellyville": 3639.2, + "Helensvale": 3914.0, + "Thomastown": 3152.4, + "Port Macquarie": 3829.8, + "Itapororoca": 14921.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kellyville: (-33.71°, 150.95°)", + " Helensvale: (-27.92°, 153.33°)", + " Thomastown: (-37.68°, 145.02°)", + " Port Macquarie: (-31.43°, 152.91°)", + " Itapororoca: (-6.83°, -35.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itapororoca: 14921.0 km from centroid", + " Helensvale: 3914.0 km from centroid", + " Port Macquarie: 3829.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itapororoca", + "FINAL ANSWER: Itapororoca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.90018, + "lon": 2.30952, + "name": "Clichy" + }, + { + "lat": 53.56414, + "lon": 13.27532, + "name": "Neubrandenburg" + }, + { + "lat": 50.96667, + "lon": -1.35, + "name": "Eastleigh" + }, + { + "lat": 46.49067, + "lon": 11.33982, + "name": "Bolzano" + }, + { + "lat": 43.85037, + "lon": 81.78308, + "name": "Onyar" + } + ], + "question": "Which location is the geographic outlier among: Clichy, Neubrandenburg, Eastleigh, Bolzano, Onyar?", + "ground_truth": { + "answer": "Onyar", + "outlier_distance_km": 4542.8, + "second_furthest_km": 1647.5, + "clarity_ratio": 2.76, + "median_distance_km": 1399.1, + "distances_to_centroid": { + "Clichy": 1399.1, + "Neubrandenburg": 781.9, + "Eastleigh": 1647.5, + "Bolzano": 799.2, + "Onyar": 4542.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Clichy: (48.90°, 2.31°)", + " Neubrandenburg: (53.56°, 13.28°)", + " Eastleigh: (50.97°, -1.35°)", + " Bolzano: (46.49°, 11.34°)", + " Onyar: (43.85°, 81.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Onyar: 4542.8 km from centroid", + " Eastleigh: 1647.5 km from centroid", + " Clichy: 1399.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Onyar", + "FINAL ANSWER: Onyar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.35149, + "lon": 8.96317, + "name": "Hechingen" + }, + { + "lat": 45.46903, + "lon": 10.85371, + "name": "Bussolengo" + }, + { + "lat": 53.58705, + "lon": -1.52676, + "name": "Darton" + }, + { + "lat": 42.1115, + "lon": 14.70649, + "name": "Vasto" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + } + ], + "question": "Which location is the geographic outlier among: Hechingen, Bussolengo, Darton, Vasto, Tuggeranong Administrative District?", + "ground_truth": { + "answer": "Tuggeranong Administrative District", + "outlier_distance_km": 13844.5, + "second_furthest_km": 3944.8, + "clarity_ratio": 3.51, + "median_distance_km": 3026.1, + "distances_to_centroid": { + "Hechingen": 3026.1, + "Bussolengo": 2745.8, + "Darton": 3944.8, + "Vasto": 2301.3, + "Tuggeranong Administrative District": 13844.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hechingen: (48.35°, 8.96°)", + " Bussolengo: (45.47°, 10.85°)", + " Darton: (53.59°, -1.53°)", + " Vasto: (42.11°, 14.71°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tuggeranong Administrative District: 13844.5 km from centroid", + " Darton: 3944.8 km from centroid", + " Hechingen: 3026.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tuggeranong Administrative District", + "FINAL ANSWER: Tuggeranong Administrative District" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.31401, + "lon": 26.82223, + "name": "Ventersdorp" + }, + { + "lat": 30.97478, + "lon": 31.87231, + "name": "Şān al Ḩajar al Qiblīyah" + }, + { + "lat": -28.70025, + "lon": 26.4581, + "name": "Winnie Mandela" + }, + { + "lat": 6.75, + "lon": 38.41667, + "name": "Yirga ‘Alem" + }, + { + "lat": 7.07444, + "lon": 125.70833, + "name": "Samal" + } + ], + "question": "Which location is the geographic outlier among: Ventersdorp, Şān al Ḩajar al Qiblīyah, Winnie Mandela, Yirga ‘Alem, Samal?", + "ground_truth": { + "answer": "Samal", + "outlier_distance_km": 8476.5, + "second_furthest_km": 4135.3, + "clarity_ratio": 2.05, + "median_distance_km": 3864.2, + "distances_to_centroid": { + "Ventersdorp": 3651.6, + "Şān al Ḩajar al Qiblīyah": 4135.3, + "Winnie Mandela": 3864.2, + "Yirga ‘Alem": 1602.5, + "Samal": 8476.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ventersdorp: (-26.31°, 26.82°)", + " Şān al Ḩajar al Qiblīyah: (30.97°, 31.87°)", + " Winnie Mandela: (-28.70°, 26.46°)", + " Yirga ‘Alem: (6.75°, 38.42°)", + " Samal: (7.07°, 125.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Samal: 8476.5 km from centroid", + " Şān al Ḩajar al Qiblīyah: 4135.3 km from centroid", + " Winnie Mandela: 3864.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Samal", + "FINAL ANSWER: Samal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + }, + { + "lat": 42.61405, + "lon": -70.66313, + "name": "Gloucester" + } + ], + "question": "Which location is the geographic outlier among: Mount Martha, Hervey Bay, Porirua, Pascoe Vale, Gloucester?", + "ground_truth": { + "answer": "Gloucester", + "outlier_distance_km": 17496.2, + "second_furthest_km": 6534.8, + "clarity_ratio": 2.68, + "median_distance_km": 4473.6, + "distances_to_centroid": { + "Mount Martha": 3979.2, + "Hervey Bay": 4473.6, + "Porirua": 6534.8, + "Pascoe Vale": 3951.9, + "Gloucester": 17496.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mount Martha: (-38.27°, 145.02°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Porirua: (-41.13°, 174.85°)", + " Pascoe Vale: (-37.73°, 144.93°)", + " Gloucester: (42.61°, -70.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gloucester: 17496.2 km from centroid", + " Porirua: 6534.8 km from centroid", + " Hervey Bay: 4473.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gloucester", + "FINAL ANSWER: Gloucester" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.93964, + "lon": 9.25995, + "name": "Marbach am Neckar" + }, + { + "lat": 42.82562, + "lon": -1.61671, + "name": "Burlata" + }, + { + "lat": 44.74471, + "lon": -0.68194, + "name": "Cestas" + }, + { + "lat": 51.41505, + "lon": -0.0927, + "name": "Upper Norwood" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + } + ], + "question": "Which location is the geographic outlier among: Marbach am Neckar, Burlata, Cestas, Upper Norwood, Griffith?", + "ground_truth": { + "answer": "Griffith", + "outlier_distance_km": 14053.6, + "second_furthest_km": 3405.6, + "clarity_ratio": 4.13, + "median_distance_km": 3142.3, + "distances_to_centroid": { + "Marbach am Neckar": 2704.4, + "Burlata": 3142.3, + "Cestas": 3132.3, + "Upper Norwood": 3405.6, + "Griffith": 14053.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marbach am Neckar: (48.94°, 9.26°)", + " Burlata: (42.83°, -1.62°)", + " Cestas: (44.74°, -0.68°)", + " Upper Norwood: (51.42°, -0.09°)", + " Griffith: (-34.29°, 146.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Griffith: 14053.6 km from centroid", + " Upper Norwood: 3405.6 km from centroid", + " Burlata: 3142.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Griffith", + "FINAL ANSWER: Griffith" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.11667, + "lon": 37.78333, + "name": "Ādīs Zemen" + }, + { + "lat": 30.90711, + "lon": 32.02341, + "name": "Munsha‘at Abū ‘Umar" + }, + { + "lat": 25.29336, + "lon": 32.55402, + "name": "Esna" + }, + { + "lat": 12.37299, + "lon": 14.2069, + "name": "Gamboru" + }, + { + "lat": 34.81667, + "lon": 137.4, + "name": "Toyokawa" + } + ], + "question": "Which location is the geographic outlier among: Ādīs Zemen, Munsha‘at Abū ‘Umar, Esna, Gamboru, Toyokawa?", + "ground_truth": { + "answer": "Toyokawa", + "outlier_distance_km": 8274.2, + "second_furthest_km": 4041.1, + "clarity_ratio": 2.05, + "median_distance_km": 2048.3, + "distances_to_centroid": { + "Ādīs Zemen": 1839.8, + "Munsha‘at Abū ‘Umar": 2048.3, + "Esna": 1864.4, + "Gamboru": 4041.1, + "Toyokawa": 8274.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ādīs Zemen: (12.12°, 37.78°)", + " Munsha‘at Abū ‘Umar: (30.91°, 32.02°)", + " Esna: (25.29°, 32.55°)", + " Gamboru: (12.37°, 14.21°)", + " Toyokawa: (34.82°, 137.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Toyokawa: 8274.2 km from centroid", + " Gamboru: 4041.1 km from centroid", + " Munsha‘at Abū ‘Umar: 2048.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Toyokawa", + "FINAL ANSWER: Toyokawa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.31694, + "lon": -42.89611, + "name": "Oliveira dos Brejinhos" + }, + { + "lat": -14.64083, + "lon": -39.55111, + "name": "Coaraci" + }, + { + "lat": -23.69389, + "lon": -46.565, + "name": "São Bernardo do Campo" + }, + { + "lat": -7.83306, + "lon": -35.75472, + "name": "Surubim" + }, + { + "lat": 40.61872, + "lon": -74.0332, + "name": "Fort Hamilton" + } + ], + "question": "Which location is the geographic outlier among: Oliveira dos Brejinhos, Coaraci, São Bernardo do Campo, Surubim, Fort Hamilton?", + "ground_truth": { + "answer": "Fort Hamilton", + "outlier_distance_km": 5593.3, + "second_furthest_km": 2241.0, + "clarity_ratio": 2.5, + "median_distance_km": 1524.5, + "distances_to_centroid": { + "Oliveira dos Brejinhos": 1109.8, + "Coaraci": 1524.5, + "São Bernardo do Campo": 2241.0, + "Surubim": 1409.9, + "Fort Hamilton": 5593.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oliveira dos Brejinhos: (-12.32°, -42.90°)", + " Coaraci: (-14.64°, -39.55°)", + " São Bernardo do Campo: (-23.69°, -46.56°)", + " Surubim: (-7.83°, -35.75°)", + " Fort Hamilton: (40.62°, -74.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fort Hamilton: 5593.3 km from centroid", + " São Bernardo do Campo: 2241.0 km from centroid", + " Coaraci: 1524.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fort Hamilton", + "FINAL ANSWER: Fort Hamilton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.87482, + "lon": 137.17086, + "name": "Kōta" + }, + { + "lat": 36.24083, + "lon": 128.2975, + "name": "Jenzan" + }, + { + "lat": 28.24341, + "lon": 79.95135, + "name": "Bilsanda" + }, + { + "lat": 22.52383, + "lon": 113.90969, + "name": "Wushipai" + }, + { + "lat": 40.61747, + "lon": 15.05693, + "name": "Eboli" + } + ], + "question": "Which location is the geographic outlier among: Kōta, Jenzan, Bilsanda, Wushipai, Eboli?", + "ground_truth": { + "answer": "Eboli", + "outlier_distance_km": 6941.2, + "second_furthest_km": 3893.1, + "clarity_ratio": 1.78, + "median_distance_km": 3080.1, + "distances_to_centroid": { + "Kōta": 3893.1, + "Jenzan": 3080.1, + "Bilsanda": 1506.5, + "Wushipai": 2175.0, + "Eboli": 6941.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kōta: (34.87°, 137.17°)", + " Jenzan: (36.24°, 128.30°)", + " Bilsanda: (28.24°, 79.95°)", + " Wushipai: (22.52°, 113.91°)", + " Eboli: (40.62°, 15.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eboli: 6941.2 km from centroid", + " Kōta: 3893.1 km from centroid", + " Jenzan: 3080.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eboli", + "FINAL ANSWER: Eboli" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.55376, + "lon": -77.46026, + "name": "Richmond" + }, + { + "lat": 34.05168, + "lon": -117.9684, + "name": "West Puente Valley" + }, + { + "lat": 19.22708, + "lon": -99.67083, + "name": "Santiago Tlacotepec" + }, + { + "lat": 39.34589, + "lon": -84.5605, + "name": "Fairfield" + }, + { + "lat": 11.85, + "lon": 38.01667, + "name": "Debre Tabor" + } + ], + "question": "Which location is the geographic outlier among: Richmond, West Puente Valley, Santiago Tlacotepec, Fairfield, Debre Tabor?", + "ground_truth": { + "answer": "Debre Tabor", + "outlier_distance_km": 10931.9, + "second_furthest_km": 4715.9, + "clarity_ratio": 2.32, + "median_distance_km": 3336.2, + "distances_to_centroid": { + "Richmond": 1325.3, + "West Puente Valley": 4715.9, + "Santiago Tlacotepec": 3336.2, + "Fairfield": 1924.7, + "Debre Tabor": 10931.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Richmond: (37.55°, -77.46°)", + " West Puente Valley: (34.05°, -117.97°)", + " Santiago Tlacotepec: (19.23°, -99.67°)", + " Fairfield: (39.35°, -84.56°)", + " Debre Tabor: (11.85°, 38.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Debre Tabor: 10931.9 km from centroid", + " West Puente Valley: 4715.9 km from centroid", + " Santiago Tlacotepec: 3336.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Debre Tabor", + "FINAL ANSWER: Debre Tabor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.3125, + "lon": -39.32333, + "name": "Ubaitaba" + }, + { + "lat": -23.63083, + "lon": -46.59817, + "name": "Sacomã" + }, + { + "lat": -5.14556, + "lon": -38.09806, + "name": "Limoeiro do Norte" + }, + { + "lat": -2.18611, + "lon": -56.71306, + "name": "Nhamundá" + }, + { + "lat": 52.66917, + "lon": 4.70417, + "name": "Bergen" + } + ], + "question": "Which location is the geographic outlier among: Ubaitaba, Sacomã, Limoeiro do Norte, Nhamundá, Bergen?", + "ground_truth": { + "answer": "Bergen", + "outlier_distance_km": 6777.7, + "second_furthest_km": 3051.8, + "clarity_ratio": 2.22, + "median_distance_km": 2425.5, + "distances_to_centroid": { + "Ubaitaba": 1813.5, + "Sacomã": 3051.8, + "Limoeiro do Norte": 803.6, + "Nhamundá": 2425.5, + "Bergen": 6777.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ubaitaba: (-14.31°, -39.32°)", + " Sacomã: (-23.63°, -46.60°)", + " Limoeiro do Norte: (-5.15°, -38.10°)", + " Nhamundá: (-2.19°, -56.71°)", + " Bergen: (52.67°, 4.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bergen: 6777.7 km from centroid", + " Sacomã: 3051.8 km from centroid", + " Nhamundá: 2425.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bergen", + "FINAL ANSWER: Bergen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.82306, + "lon": 30.89903, + "name": "Al Fashn" + }, + { + "lat": 10.83333, + "lon": 38.26667, + "name": "Mertule Maryam" + }, + { + "lat": 10.3121, + "lon": 39.65888, + "name": "Mehal Mēda" + }, + { + "lat": -32.17588, + "lon": 26.82437, + "name": "Whittlesea" + }, + { + "lat": -23.04639, + "lon": -50.07361, + "name": "Cambará" + } + ], + "question": "Which location is the geographic outlier among: Al Fashn, Mertule Maryam, Mehal Mēda, Whittlesea, Cambará?", + "ground_truth": { + "answer": "Cambará", + "outlier_distance_km": 7634.8, + "second_furthest_km": 3631.5, + "clarity_ratio": 2.1, + "median_distance_km": 3607.6, + "distances_to_centroid": { + "Al Fashn": 3631.5, + "Mertule Maryam": 2686.5, + "Mehal Mēda": 2796.0, + "Whittlesea": 3607.6, + "Cambará": 7634.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Fashn: (28.82°, 30.90°)", + " Mertule Maryam: (10.83°, 38.27°)", + " Mehal Mēda: (10.31°, 39.66°)", + " Whittlesea: (-32.18°, 26.82°)", + " Cambará: (-23.05°, -50.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cambará: 7634.8 km from centroid", + " Al Fashn: 3631.5 km from centroid", + " Whittlesea: 3607.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cambará", + "FINAL ANSWER: Cambará" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.27088, + "lon": 36.37917, + "name": "Ol Kalou" + }, + { + "lat": 31.28837, + "lon": 31.67719, + "name": "Mīt Abū Ghālib" + }, + { + "lat": 8.66762, + "lon": 3.39393, + "name": "Saki" + }, + { + "lat": 6.09408, + "lon": -0.25913, + "name": "Koforidua" + }, + { + "lat": -23.69748, + "lon": 133.88362, + "name": "Alice Springs" + } + ], + "question": "Which location is the geographic outlier among: Ol Kalou, Mīt Abū Ghālib, Saki, Koforidua, Alice Springs?", + "ground_truth": { + "answer": "Alice Springs", + "outlier_distance_km": 10496.3, + "second_furthest_km": 4572.9, + "clarity_ratio": 2.3, + "median_distance_km": 4180.8, + "distances_to_centroid": { + "Ol Kalou": 732.7, + "Mīt Abū Ghālib": 3143.4, + "Saki": 4180.8, + "Koforidua": 4572.9, + "Alice Springs": 10496.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ol Kalou: (-0.27°, 36.38°)", + " Mīt Abū Ghālib: (31.29°, 31.68°)", + " Saki: (8.67°, 3.39°)", + " Koforidua: (6.09°, -0.26°)", + " Alice Springs: (-23.70°, 133.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alice Springs: 10496.3 km from centroid", + " Koforidua: 4572.9 km from centroid", + " Saki: 4180.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alice Springs", + "FINAL ANSWER: Alice Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -27.19354, + "lon": 153.02631, + "name": "Deception Bay" + }, + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": 13.7567, + "lon": 121.0584, + "name": "Batangas" + } + ], + "question": "Which location is the geographic outlier among: Engadine, Deception Bay, Highton, Morayfield, Batangas?", + "ground_truth": { + "answer": "Batangas", + "outlier_distance_km": 4775.9, + "second_furthest_km": 1736.3, + "clarity_ratio": 2.75, + "median_distance_km": 1430.1, + "distances_to_centroid": { + "Engadine": 1430.1, + "Deception Bay": 1004.8, + "Highton": 1736.3, + "Morayfield": 993.6, + "Batangas": 4775.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Engadine: (-34.07°, 151.01°)", + " Deception Bay: (-27.19°, 153.03°)", + " Highton: (-38.17°, 144.31°)", + " Morayfield: (-27.11°, 152.95°)", + " Batangas: (13.76°, 121.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Batangas: 4775.9 km from centroid", + " Highton: 1736.3 km from centroid", + " Engadine: 1430.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Batangas", + "FINAL ANSWER: Batangas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.69676, + "lon": 8.13523, + "name": "Bühl" + }, + { + "lat": 52.0862, + "lon": 8.74434, + "name": "Bad Salzuflen" + }, + { + "lat": 52.48333, + "lon": 4.65694, + "name": "Beverwijk" + }, + { + "lat": 68.1432, + "lon": 33.25287, + "name": "Olenegorsk" + }, + { + "lat": 23.69356, + "lon": 71.907, + "name": "Hārij" + } + ], + "question": "Which location is the geographic outlier among: Bühl, Bad Salzuflen, Beverwijk, Olenegorsk, Hārij?", + "ground_truth": { + "answer": "Hārij", + "outlier_distance_km": 4921.1, + "second_furthest_km": 2171.1, + "clarity_ratio": 2.27, + "median_distance_km": 1499.3, + "distances_to_centroid": { + "Bühl": 1256.4, + "Bad Salzuflen": 1217.9, + "Beverwijk": 1499.3, + "Olenegorsk": 2171.1, + "Hārij": 4921.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bühl: (48.70°, 8.14°)", + " Bad Salzuflen: (52.09°, 8.74°)", + " Beverwijk: (52.48°, 4.66°)", + " Olenegorsk: (68.14°, 33.25°)", + " Hārij: (23.69°, 71.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hārij: 4921.1 km from centroid", + " Olenegorsk: 2171.1 km from centroid", + " Beverwijk: 1499.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hārij", + "FINAL ANSWER: Hārij" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.87198, + "lon": 32.75585, + "name": "Jarājūs" + }, + { + "lat": 6.919, + "lon": 37.529, + "name": "Bale Hawassa" + }, + { + "lat": 30.03103, + "lon": 31.11109, + "name": "Kirdāsah" + }, + { + "lat": 30.53766, + "lon": 31.67875, + "name": "Abū Ḩammād" + }, + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + } + ], + "question": "Which location is the geographic outlier among: Jarājūs, Bale Hawassa, Kirdāsah, Abū Ḩammād, Busselton?", + "ground_truth": { + "answer": "Busselton", + "outlier_distance_km": 8588.0, + "second_furthest_km": 2777.6, + "clarity_ratio": 3.09, + "median_distance_km": 2776.6, + "distances_to_centroid": { + "Jarājūs": 2355.2, + "Bale Hawassa": 1445.1, + "Kirdāsah": 2777.6, + "Abū Ḩammād": 2776.6, + "Busselton": 8588.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jarājūs: (25.87°, 32.76°)", + " Bale Hawassa: (6.92°, 37.53°)", + " Kirdāsah: (30.03°, 31.11°)", + " Abū Ḩammād: (30.54°, 31.68°)", + " Busselton: (-33.65°, 115.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Busselton: 8588.0 km from centroid", + " Kirdāsah: 2777.6 km from centroid", + " Abū Ḩammād: 2776.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Busselton", + "FINAL ANSWER: Busselton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -38.11342, + "lon": 145.28326, + "name": "Cranbourne" + }, + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + }, + { + "lat": 40.72152, + "lon": 14.54021, + "name": "Sant'Antonio Abate" + } + ], + "question": "Which location is the geographic outlier among: Epping, Highton, Cranbourne, Northcote, Sant'Antonio Abate?", + "ground_truth": { + "answer": "Sant'Antonio Abate", + "outlier_distance_km": 12766.9, + "second_furthest_km": 3080.0, + "clarity_ratio": 4.15, + "median_distance_km": 3040.2, + "distances_to_centroid": { + "Epping": 3036.9, + "Highton": 3008.0, + "Cranbourne": 3080.0, + "Northcote": 3040.2, + "Sant'Antonio Abate": 12766.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epping: (-37.65°, 145.03°)", + " Highton: (-38.17°, 144.31°)", + " Cranbourne: (-38.11°, 145.28°)", + " Northcote: (-37.77°, 145.00°)", + " Sant'Antonio Abate: (40.72°, 14.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sant'Antonio Abate: 12766.9 km from centroid", + " Cranbourne: 3080.0 km from centroid", + " Northcote: 3040.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sant'Antonio Abate", + "FINAL ANSWER: Sant'Antonio Abate" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -37.0182, + "lon": 174.88019, + "name": "Manurewa" + }, + { + "lat": 52.20333, + "lon": 4.39861, + "name": "Katwijk aan Zee" + } + ], + "question": "Which location is the geographic outlier among: Robina, Morayfield, Armidale, Manurewa, Katwijk aan Zee?", + "ground_truth": { + "answer": "Katwijk aan Zee", + "outlier_distance_km": 13467.2, + "second_furthest_km": 5324.7, + "clarity_ratio": 2.53, + "median_distance_km": 3096.1, + "distances_to_centroid": { + "Robina": 3096.1, + "Morayfield": 3012.4, + "Armidale": 3074.3, + "Manurewa": 5324.7, + "Katwijk aan Zee": 13467.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Morayfield: (-27.11°, 152.95°)", + " Armidale: (-30.50°, 151.67°)", + " Manurewa: (-37.02°, 174.88°)", + " Katwijk aan Zee: (52.20°, 4.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Katwijk aan Zee: 13467.2 km from centroid", + " Manurewa: 5324.7 km from centroid", + " Robina: 3096.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Katwijk aan Zee", + "FINAL ANSWER: Katwijk aan Zee" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + }, + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -26.95659, + "lon": 24.7284, + "name": "Vryburg" + } + ], + "question": "Which location is the geographic outlier among: Mulgrave, Mildura, Mosman, Camberwell, Vryburg?", + "ground_truth": { + "answer": "Vryburg", + "outlier_distance_km": 8949.8, + "second_furthest_km": 2716.1, + "clarity_ratio": 3.3, + "median_distance_km": 2148.4, + "distances_to_centroid": { + "Mulgrave": 2148.4, + "Mildura": 1881.7, + "Mosman": 2716.1, + "Camberwell": 2138.3, + "Vryburg": 8949.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mulgrave: (-37.93°, 145.18°)", + " Mildura: (-34.19°, 142.16°)", + " Mosman: (-33.84°, 151.24°)", + " Camberwell: (-37.84°, 145.07°)", + " Vryburg: (-26.96°, 24.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vryburg: 8949.8 km from centroid", + " Mosman: 2716.1 km from centroid", + " Mulgrave: 2148.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vryburg", + "FINAL ANSWER: Vryburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.12705, + "lon": 83.89148, + "name": "Bilthra" + }, + { + "lat": 23.67595, + "lon": 91.28325, + "name": "Bisālgarh" + }, + { + "lat": 30.12796, + "lon": 77.28371, + "name": "Yamuna Nagar" + }, + { + "lat": 37.31739, + "lon": 79.70532, + "name": "Puqiakeqi" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + } + ], + "question": "Which location is the geographic outlier among: Bilthra, Bisālgarh, Yamuna Nagar, Puqiakeqi, Hawthorn?", + "ground_truth": { + "answer": "Hawthorn", + "outlier_distance_km": 7901.2, + "second_furthest_km": 2841.3, + "clarity_ratio": 2.78, + "median_distance_km": 2435.0, + "distances_to_centroid": { + "Bilthra": 1651.6, + "Bisālgarh": 969.1, + "Yamuna Nagar": 2435.0, + "Puqiakeqi": 2841.3, + "Hawthorn": 7901.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bilthra: (26.13°, 83.89°)", + " Bisālgarh: (23.68°, 91.28°)", + " Yamuna Nagar: (30.13°, 77.28°)", + " Puqiakeqi: (37.32°, 79.71°)", + " Hawthorn: (-37.82°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hawthorn: 7901.2 km from centroid", + " Puqiakeqi: 2841.3 km from centroid", + " Yamuna Nagar: 2435.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hawthorn", + "FINAL ANSWER: Hawthorn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.29005, + "lon": -74.81612, + "name": "Flandes" + }, + { + "lat": -30.74179, + "lon": -59.64517, + "name": "La Paz" + }, + { + "lat": -21.38111, + "lon": -51.57056, + "name": "Tupi Paulista" + }, + { + "lat": -18.755, + "lon": -40.89083, + "name": "Barra de São Francisco" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + } + ], + "question": "Which location is the geographic outlier among: Flandes, La Paz, Tupi Paulista, Barra de São Francisco, Punchbowl?", + "ground_truth": { + "answer": "Punchbowl", + "outlier_distance_km": 13832.3, + "second_furthest_km": 7051.1, + "clarity_ratio": 1.96, + "median_distance_km": 4588.5, + "distances_to_centroid": { + "Flandes": 7051.1, + "La Paz": 4588.5, + "Tupi Paulista": 3779.0, + "Barra de São Francisco": 2698.2, + "Punchbowl": 13832.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Flandes: (4.29°, -74.82°)", + " La Paz: (-30.74°, -59.65°)", + " Tupi Paulista: (-21.38°, -51.57°)", + " Barra de São Francisco: (-18.75°, -40.89°)", + " Punchbowl: (-33.93°, 151.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Punchbowl: 13832.3 km from centroid", + " Flandes: 7051.1 km from centroid", + " La Paz: 4588.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Punchbowl", + "FINAL ANSWER: Punchbowl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": 22.52383, + "lon": 113.90969, + "name": "Wushipai" + } + ], + "question": "Which location is the geographic outlier among: Truganina, Logan City, Mernda, Boronia, Wushipai?", + "ground_truth": { + "answer": "Wushipai", + "outlier_distance_km": 5883.2, + "second_furthest_km": 1643.5, + "clarity_ratio": 3.58, + "median_distance_km": 1624.7, + "distances_to_centroid": { + "Truganina": 1624.7, + "Logan City": 1344.1, + "Mernda": 1610.4, + "Boronia": 1643.5, + "Wushipai": 5883.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Truganina: (-37.82°, 144.75°)", + " Logan City: (-27.64°, 153.11°)", + " Mernda: (-37.60°, 145.10°)", + " Boronia: (-37.87°, 145.28°)", + " Wushipai: (22.52°, 113.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wushipai: 5883.2 km from centroid", + " Boronia: 1643.5 km from centroid", + " Truganina: 1624.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wushipai", + "FINAL ANSWER: Wushipai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.67147, + "lon": 116.49213, + "name": "Wanggou" + }, + { + "lat": 36.21494, + "lon": 136.14832, + "name": "Mikuni" + }, + { + "lat": 39.71183, + "lon": 118.44954, + "name": "Linxi" + }, + { + "lat": 40.78341, + "lon": 114.87139, + "name": "Zhangjiakou" + }, + { + "lat": 8.27515, + "lon": -76.37641, + "name": "San Pedro de Urabá" + } + ], + "question": "Which location is the geographic outlier among: Wanggou, Mikuni, Linxi, Zhangjiakou, San Pedro de Urabá?", + "ground_truth": { + "answer": "San Pedro de Urabá", + "outlier_distance_km": 14984.9, + "second_furthest_km": 4953.0, + "clarity_ratio": 3.03, + "median_distance_km": 3380.3, + "distances_to_centroid": { + "Wanggou": 3212.0, + "Mikuni": 4953.0, + "Linxi": 3380.3, + "Zhangjiakou": 3089.7, + "San Pedro de Urabá": 14984.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wanggou: (34.67°, 116.49°)", + " Mikuni: (36.21°, 136.15°)", + " Linxi: (39.71°, 118.45°)", + " Zhangjiakou: (40.78°, 114.87°)", + " San Pedro de Urabá: (8.28°, -76.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Pedro de Urabá: 14984.9 km from centroid", + " Mikuni: 4953.0 km from centroid", + " Linxi: 3380.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Pedro de Urabá", + "FINAL ANSWER: San Pedro de Urabá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": 51.50372, + "lon": 0.11982, + "name": "Thamesmead" + } + ], + "question": "Which location is the geographic outlier among: Thomastown, Eight Mile Plains, Logan City, Wahroonga, Thamesmead?", + "ground_truth": { + "answer": "Thamesmead", + "outlier_distance_km": 13393.9, + "second_furthest_km": 3709.8, + "clarity_ratio": 3.61, + "median_distance_km": 3643.0, + "distances_to_centroid": { + "Thomastown": 3487.8, + "Eight Mile Plains": 3640.4, + "Logan City": 3643.0, + "Wahroonga": 3709.8, + "Thamesmead": 13393.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thomastown: (-37.68°, 145.02°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Logan City: (-27.64°, 153.11°)", + " Wahroonga: (-33.72°, 151.12°)", + " Thamesmead: (51.50°, 0.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thamesmead: 13393.9 km from centroid", + " Wahroonga: 3709.8 km from centroid", + " Logan City: 3643.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thamesmead", + "FINAL ANSWER: Thamesmead" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.91336, + "lon": -85.70531, + "name": "Wyoming" + }, + { + "lat": 45.78329, + "lon": -108.50069, + "name": "Billings" + }, + { + "lat": 18.42131, + "lon": -95.11398, + "name": "Catemaco" + }, + { + "lat": 53.27237, + "lon": -110.02256, + "name": "Lloydminster" + }, + { + "lat": 51.11357, + "lon": -0.86245, + "name": "Bordon" + } + ], + "question": "Which location is the geographic outlier among: Wyoming, Billings, Catemaco, Lloydminster, Bordon?", + "ground_truth": { + "answer": "Bordon", + "outlier_distance_km": 5819.3, + "second_furthest_km": 3012.8, + "clarity_ratio": 1.93, + "median_distance_km": 2524.2, + "distances_to_centroid": { + "Wyoming": 468.5, + "Billings": 2294.9, + "Catemaco": 3012.8, + "Lloydminster": 2524.2, + "Bordon": 5819.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wyoming: (42.91°, -85.71°)", + " Billings: (45.78°, -108.50°)", + " Catemaco: (18.42°, -95.11°)", + " Lloydminster: (53.27°, -110.02°)", + " Bordon: (51.11°, -0.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bordon: 5819.3 km from centroid", + " Catemaco: 3012.8 km from centroid", + " Lloydminster: 2524.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bordon", + "FINAL ANSWER: Bordon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.52356, + "lon": 27.6952, + "name": "Cala" + }, + { + "lat": -33.73378, + "lon": 18.97523, + "name": "Paarl" + }, + { + "lat": 12.67059, + "lon": 13.61224, + "name": "Monguno" + }, + { + "lat": 31.24193, + "lon": 30.94504, + "name": "Ar Riyāḑ" + }, + { + "lat": 27.29393, + "lon": -80.35033, + "name": "Port Saint Lucie" + } + ], + "question": "Which location is the geographic outlier among: Cala, Paarl, Monguno, Ar Riyāḑ, Port Saint Lucie?", + "ground_truth": { + "answer": "Port Saint Lucie", + "outlier_distance_km": 9208.5, + "second_furthest_km": 4524.6, + "clarity_ratio": 2.04, + "median_distance_km": 4506.8, + "distances_to_centroid": { + "Cala": 4524.6, + "Paarl": 4262.3, + "Monguno": 1793.8, + "Ar Riyāḑ": 4506.8, + "Port Saint Lucie": 9208.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cala: (-31.52°, 27.70°)", + " Paarl: (-33.73°, 18.98°)", + " Monguno: (12.67°, 13.61°)", + " Ar Riyāḑ: (31.24°, 30.95°)", + " Port Saint Lucie: (27.29°, -80.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Saint Lucie: 9208.5 km from centroid", + " Cala: 4524.6 km from centroid", + " Ar Riyāḑ: 4506.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Saint Lucie", + "FINAL ANSWER: Port Saint Lucie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.05048, + "lon": -76.97335, + "name": "Santa Anita - Los Ficus" + }, + { + "lat": -29.44806, + "lon": -50.58361, + "name": "São Francisco de Paula" + }, + { + "lat": -17.345, + "lon": -44.94194, + "name": "Pirapora" + }, + { + "lat": -10.34472, + "lon": -39.83556, + "name": "Andorinha" + }, + { + "lat": 49.12426, + "lon": 8.59804, + "name": "Bruchsal" + } + ], + "question": "Which location is the geographic outlier among: Santa Anita - Los Ficus, São Francisco de Paula, Pirapora, Andorinha, Bruchsal?", + "ground_truth": { + "answer": "Bruchsal", + "outlier_distance_km": 7576.4, + "second_furthest_km": 4082.8, + "clarity_ratio": 1.86, + "median_distance_km": 3012.1, + "distances_to_centroid": { + "Santa Anita - Los Ficus": 4082.8, + "São Francisco de Paula": 3012.1, + "Pirapora": 1551.4, + "Andorinha": 711.2, + "Bruchsal": 7576.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Anita - Los Ficus: (-12.05°, -76.97°)", + " São Francisco de Paula: (-29.45°, -50.58°)", + " Pirapora: (-17.34°, -44.94°)", + " Andorinha: (-10.34°, -39.84°)", + " Bruchsal: (49.12°, 8.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bruchsal: 7576.4 km from centroid", + " Santa Anita - Los Ficus: 4082.8 km from centroid", + " São Francisco de Paula: 3012.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bruchsal", + "FINAL ANSWER: Bruchsal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": -37.8, + "lon": 145.28333, + "name": "Croydon" + }, + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": 14.11168, + "lon": 78.15982, + "name": "Kadiri" + } + ], + "question": "Which location is the geographic outlier among: Yarraville, Launceston, Croydon, Seven Hills, Kadiri?", + "ground_truth": { + "answer": "Kadiri", + "outlier_distance_km": 7520.0, + "second_furthest_km": 2012.3, + "clarity_ratio": 3.74, + "median_distance_km": 1832.1, + "distances_to_centroid": { + "Yarraville": 1591.3, + "Launceston": 2012.3, + "Croydon": 1614.6, + "Seven Hills": 1832.1, + "Kadiri": 7520.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yarraville: (-37.82°, 144.90°)", + " Launceston: (-41.44°, 147.13°)", + " Croydon: (-37.80°, 145.28°)", + " Seven Hills: (-33.78°, 150.93°)", + " Kadiri: (14.11°, 78.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kadiri: 7520.0 km from centroid", + " Launceston: 2012.3 km from centroid", + " Seven Hills: 1832.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kadiri", + "FINAL ANSWER: Kadiri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.54964, + "lon": -123.36931, + "name": "Saanich" + }, + { + "lat": 33.56042, + "lon": -81.71955, + "name": "Aiken" + }, + { + "lat": 35.62246, + "lon": -117.6709, + "name": "Ridgecrest" + }, + { + "lat": 39.26674, + "lon": -81.56151, + "name": "Parkersburg" + }, + { + "lat": 51.20099, + "lon": 58.31318, + "name": "Novotroitsk" + } + ], + "question": "Which location is the geographic outlier among: Saanich, Aiken, Ridgecrest, Parkersburg, Novotroitsk?", + "ground_truth": { + "answer": "Novotroitsk", + "outlier_distance_km": 8511.5, + "second_furthest_km": 4229.3, + "clarity_ratio": 2.01, + "median_distance_km": 4207.1, + "distances_to_centroid": { + "Saanich": 4229.3, + "Aiken": 1419.8, + "Ridgecrest": 4207.1, + "Parkersburg": 1077.5, + "Novotroitsk": 8511.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saanich: (48.55°, -123.37°)", + " Aiken: (33.56°, -81.72°)", + " Ridgecrest: (35.62°, -117.67°)", + " Parkersburg: (39.27°, -81.56°)", + " Novotroitsk: (51.20°, 58.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Novotroitsk: 8511.5 km from centroid", + " Saanich: 4229.3 km from centroid", + " Ridgecrest: 4207.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Novotroitsk", + "FINAL ANSWER: Novotroitsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.45977, + "lon": 31.1842, + "name": "Banhā" + }, + { + "lat": 5.93576, + "lon": 7.0793, + "name": "Uga" + }, + { + "lat": 7.71393, + "lon": 3.91665, + "name": "Fiditi" + }, + { + "lat": -33.89058, + "lon": 19.10328, + "name": "Le Roux" + }, + { + "lat": 33.9, + "lon": 118.13333, + "name": "Shaji" + } + ], + "question": "Which location is the geographic outlier among: Banhā, Uga, Fiditi, Le Roux, Shaji?", + "ground_truth": { + "answer": "Shaji", + "outlier_distance_km": 8749.7, + "second_furthest_km": 5069.1, + "clarity_ratio": 1.73, + "median_distance_km": 3518.7, + "distances_to_centroid": { + "Banhā": 2454.8, + "Uga": 3191.6, + "Fiditi": 3518.7, + "Le Roux": 5069.1, + "Shaji": 8749.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banhā: (30.46°, 31.18°)", + " Uga: (5.94°, 7.08°)", + " Fiditi: (7.71°, 3.92°)", + " Le Roux: (-33.89°, 19.10°)", + " Shaji: (33.90°, 118.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shaji: 8749.7 km from centroid", + " Le Roux: 5069.1 km from centroid", + " Fiditi: 3518.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shaji", + "FINAL ANSWER: Shaji" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.96, + "lon": 9.06472, + "name": "Sachsenheim" + }, + { + "lat": 54.11175, + "lon": 22.93087, + "name": "Suwałki" + }, + { + "lat": 42.26199, + "lon": 3.17689, + "name": "Roses" + }, + { + "lat": 54.37648, + "lon": 18.60753, + "name": "Wrzeszcz" + }, + { + "lat": 4.6192, + "lon": 101.0685, + "name": "Kampung Manjoi" + } + ], + "question": "Which location is the geographic outlier among: Sachsenheim, Suwałki, Roses, Wrzeszcz, Kampung Manjoi?", + "ground_truth": { + "answer": "Kampung Manjoi", + "outlier_distance_km": 8004.3, + "second_furthest_km": 2307.2, + "clarity_ratio": 3.47, + "median_distance_km": 1935.9, + "distances_to_centroid": { + "Sachsenheim": 1935.9, + "Suwałki": 1589.5, + "Roses": 2307.2, + "Wrzeszcz": 1759.3, + "Kampung Manjoi": 8004.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sachsenheim: (48.96°, 9.06°)", + " Suwałki: (54.11°, 22.93°)", + " Roses: (42.26°, 3.18°)", + " Wrzeszcz: (54.38°, 18.61°)", + " Kampung Manjoi: (4.62°, 101.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kampung Manjoi: 8004.3 km from centroid", + " Roses: 2307.2 km from centroid", + " Sachsenheim: 1935.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kampung Manjoi", + "FINAL ANSWER: Kampung Manjoi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.69689, + "lon": -71.52194, + "name": "West Warwick" + }, + { + "lat": 43.65751, + "lon": -79.38572, + "name": "Bay Street Corridor" + }, + { + "lat": 32.46402, + "lon": -86.4597, + "name": "Prattville" + }, + { + "lat": 41.67176, + "lon": -72.94927, + "name": "Bristol" + }, + { + "lat": 28.61052, + "lon": -13.92912, + "name": "La Oliva" + } + ], + "question": "Which location is the geographic outlier among: West Warwick, Bay Street Corridor, Prattville, Bristol, La Oliva?", + "ground_truth": { + "answer": "La Oliva", + "outlier_distance_km": 4787.9, + "second_furthest_km": 2043.9, + "clarity_ratio": 2.34, + "median_distance_km": 1395.4, + "distances_to_centroid": { + "West Warwick": 728.8, + "Bay Street Corridor": 1395.4, + "Prattville": 2043.9, + "Bristol": 826.4, + "La Oliva": 4787.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Warwick: (41.70°, -71.52°)", + " Bay Street Corridor: (43.66°, -79.39°)", + " Prattville: (32.46°, -86.46°)", + " Bristol: (41.67°, -72.95°)", + " La Oliva: (28.61°, -13.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " La Oliva: 4787.9 km from centroid", + " Prattville: 2043.9 km from centroid", + " Bay Street Corridor: 1395.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: La Oliva", + "FINAL ANSWER: La Oliva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.18111, + "lon": -50.64667, + "name": "Cornélio Procópio" + }, + { + "lat": 4.57937, + "lon": -74.21682, + "name": "Soacha" + }, + { + "lat": -23.58833, + "lon": -46.63464, + "name": "Vila Mariana" + }, + { + "lat": -14.54114, + "lon": -52.79508, + "name": "Campinápolis" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + } + ], + "question": "Which location is the geographic outlier among: Cornélio Procópio, Soacha, Vila Mariana, Campinápolis, Otahuhu?", + "ground_truth": { + "answer": "Otahuhu", + "outlier_distance_km": 13804.8, + "second_furthest_km": 7501.1, + "clarity_ratio": 1.84, + "median_distance_km": 4584.3, + "distances_to_centroid": { + "Cornélio Procópio": 4247.5, + "Soacha": 7501.1, + "Vila Mariana": 3837.9, + "Campinápolis": 4584.3, + "Otahuhu": 13804.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cornélio Procópio: (-23.18°, -50.65°)", + " Soacha: (4.58°, -74.22°)", + " Vila Mariana: (-23.59°, -46.63°)", + " Campinápolis: (-14.54°, -52.80°)", + " Otahuhu: (-36.94°, 174.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Otahuhu: 13804.8 km from centroid", + " Soacha: 7501.1 km from centroid", + " Campinápolis: 4584.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Otahuhu", + "FINAL ANSWER: Otahuhu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.15109, + "lon": 35.81703, + "name": "Wacha" + }, + { + "lat": 14.27889, + "lon": 39.15, + "name": "Intich’o" + }, + { + "lat": 5.43385, + "lon": -2.14295, + "name": "Prestea" + }, + { + "lat": -26.26781, + "lon": 27.85849, + "name": "Soweto" + }, + { + "lat": -33.75881, + "lon": 150.99292, + "name": "Baulkham Hills" + } + ], + "question": "Which location is the geographic outlier among: Wacha, Intich’o, Prestea, Soweto, Baulkham Hills?", + "ground_truth": { + "answer": "Baulkham Hills", + "outlier_distance_km": 10572.4, + "second_furthest_km": 5976.5, + "clarity_ratio": 1.77, + "median_distance_km": 3230.3, + "distances_to_centroid": { + "Wacha": 2223.2, + "Intich’o": 2632.4, + "Prestea": 5976.5, + "Soweto": 3230.3, + "Baulkham Hills": 10572.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wacha: (7.15°, 35.82°)", + " Intich’o: (14.28°, 39.15°)", + " Prestea: (5.43°, -2.14°)", + " Soweto: (-26.27°, 27.86°)", + " Baulkham Hills: (-33.76°, 150.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baulkham Hills: 10572.4 km from centroid", + " Prestea: 5976.5 km from centroid", + " Soweto: 3230.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Baulkham Hills", + "FINAL ANSWER: Baulkham Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.85, + "lon": 107.91667, + "name": "Sumedang Utara" + }, + { + "lat": 36.98874, + "lon": 119.92224, + "name": "Dazeshan" + }, + { + "lat": 6.35196, + "lon": 99.78791, + "name": "Kampung Baru Ulu Melaka" + }, + { + "lat": 22.42114, + "lon": 87.32257, + "name": "Medinīpur" + }, + { + "lat": -2.4041, + "lon": -44.41669, + "name": "Alcântara" + } + ], + "question": "Which location is the geographic outlier among: Sumedang Utara, Dazeshan, Kampung Baru Ulu Melaka, Medinīpur, Alcântara?", + "ground_truth": { + "answer": "Alcântara", + "outlier_distance_km": 13168.7, + "second_furthest_km": 5382.7, + "clarity_ratio": 2.45, + "median_distance_km": 4250.4, + "distances_to_centroid": { + "Sumedang Utara": 4250.4, + "Dazeshan": 5382.7, + "Kampung Baru Ulu Melaka": 2873.5, + "Medinīpur": 1870.3, + "Alcântara": 13168.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sumedang Utara: (-6.85°, 107.92°)", + " Dazeshan: (36.99°, 119.92°)", + " Kampung Baru Ulu Melaka: (6.35°, 99.79°)", + " Medinīpur: (22.42°, 87.32°)", + " Alcântara: (-2.40°, -44.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alcântara: 13168.7 km from centroid", + " Dazeshan: 5382.7 km from centroid", + " Sumedang Utara: 4250.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alcântara", + "FINAL ANSWER: Alcântara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.0925, + "lon": -80.1625, + "name": "Chulucanas" + }, + { + "lat": -23.53872, + "lon": -46.68093, + "name": "Perdizes" + }, + { + "lat": -4.30028, + "lon": -38.49778, + "name": "Chorozinho" + }, + { + "lat": -25.8725, + "lon": -49.49778, + "name": "Quitandinha" + }, + { + "lat": 43.61616, + "lon": -79.51269, + "name": "Mimico" + } + ], + "question": "Which location is the geographic outlier among: Chulucanas, Perdizes, Chorozinho, Quitandinha, Mimico?", + "ground_truth": { + "answer": "Mimico", + "outlier_distance_km": 5583.0, + "second_furthest_km": 2729.3, + "clarity_ratio": 2.05, + "median_distance_km": 2629.6, + "distances_to_centroid": { + "Chulucanas": 2372.5, + "Perdizes": 2629.6, + "Chorozinho": 2264.9, + "Quitandinha": 2729.3, + "Mimico": 5583.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chulucanas: (-5.09°, -80.16°)", + " Perdizes: (-23.54°, -46.68°)", + " Chorozinho: (-4.30°, -38.50°)", + " Quitandinha: (-25.87°, -49.50°)", + " Mimico: (43.62°, -79.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mimico: 5583.0 km from centroid", + " Quitandinha: 2729.3 km from centroid", + " Perdizes: 2629.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mimico", + "FINAL ANSWER: Mimico" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.98654, + "lon": -75.19349, + "name": "Caucasia" + }, + { + "lat": -27.89944, + "lon": -53.31361, + "name": "Palmeira das Missões" + }, + { + "lat": -20.54139, + "lon": -44.635, + "name": "Carmópolis de Minas" + }, + { + "lat": -34.98279, + "lon": -71.23943, + "name": "Curicó" + }, + { + "lat": 39.09112, + "lon": -94.41551, + "name": "Independence" + } + ], + "question": "Which location is the geographic outlier among: Caucasia, Palmeira das Missões, Carmópolis de Minas, Curicó, Independence?", + "ground_truth": { + "answer": "Independence", + "outlier_distance_km": 5841.5, + "second_furthest_km": 3102.1, + "clarity_ratio": 1.88, + "median_distance_km": 2893.0, + "distances_to_centroid": { + "Caucasia": 1886.0, + "Palmeira das Missões": 2751.9, + "Carmópolis de Minas": 2893.0, + "Curicó": 3102.1, + "Independence": 5841.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caucasia: (7.99°, -75.19°)", + " Palmeira das Missões: (-27.90°, -53.31°)", + " Carmópolis de Minas: (-20.54°, -44.63°)", + " Curicó: (-34.98°, -71.24°)", + " Independence: (39.09°, -94.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Independence: 5841.5 km from centroid", + " Curicó: 3102.1 km from centroid", + " Carmópolis de Minas: 2893.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Independence", + "FINAL ANSWER: Independence" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73333, + "lon": 150.93284, + "name": "Glenwood" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": -32.24295, + "lon": 148.60484, + "name": "Dubbo" + }, + { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + }, + { + "lat": 35.43515, + "lon": 139.4256, + "name": "Ayase" + } + ], + "question": "Which location is the geographic outlier among: Glenwood, South Morang, Dubbo, Hurstville, Ayase?", + "ground_truth": { + "answer": "Ayase", + "outlier_distance_km": 6263.7, + "second_furthest_km": 1923.6, + "clarity_ratio": 3.26, + "median_distance_km": 1557.5, + "distances_to_centroid": { + "Glenwood": 1528.2, + "South Morang": 1923.6, + "Dubbo": 1322.6, + "Hurstville": 1557.5, + "Ayase": 6263.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenwood: (-33.73°, 150.93°)", + " South Morang: (-37.65°, 145.10°)", + " Dubbo: (-32.24°, 148.60°)", + " Hurstville: (-33.97°, 151.10°)", + " Ayase: (35.44°, 139.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ayase: 6263.7 km from centroid", + " South Morang: 1923.6 km from centroid", + " Hurstville: 1557.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ayase", + "FINAL ANSWER: Ayase" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + }, + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": 5.68476, + "lon": -0.04011, + "name": "Lashibi" + } + ], + "question": "Which location is the geographic outlier among: Hoppers Crossing, Upper Coomera, Whangarei, Nerang, Lashibi?", + "ground_truth": { + "answer": "Lashibi", + "outlier_distance_km": 13808.7, + "second_furthest_km": 4829.2, + "clarity_ratio": 2.86, + "median_distance_km": 2827.4, + "distances_to_centroid": { + "Hoppers Crossing": 2355.2, + "Upper Coomera": 2822.2, + "Whangarei": 4829.2, + "Nerang": 2827.4, + "Lashibi": 13808.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hoppers Crossing: (-37.88°, 144.70°)", + " Upper Coomera: (-27.88°, 153.29°)", + " Whangarei: (-35.73°, 174.32°)", + " Nerang: (-27.99°, 153.34°)", + " Lashibi: (5.68°, -0.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lashibi: 13808.7 km from centroid", + " Whangarei: 4829.2 km from centroid", + " Nerang: 2827.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lashibi", + "FINAL ANSWER: Lashibi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.77437, + "lon": 4.77758, + "name": "Écully" + }, + { + "lat": 51.55109, + "lon": 8.55956, + "name": "Büren" + }, + { + "lat": 50.73438, + "lon": 7.09549, + "name": "Bonn" + }, + { + "lat": 48.82206, + "lon": 1.98677, + "name": "Les Clayes-sous-Bois" + }, + { + "lat": -3.89174, + "lon": -59.09542, + "name": "Nova Olinda do Norte" + } + ], + "question": "Which location is the geographic outlier among: Écully, Büren, Bonn, Les Clayes-sous-Bois, Nova Olinda do Norte?", + "ground_truth": { + "answer": "Nova Olinda do Norte", + "outlier_distance_km": 7102.9, + "second_furthest_km": 1897.5, + "clarity_ratio": 3.74, + "median_distance_km": 1761.0, + "distances_to_centroid": { + "Écully": 1275.4, + "Büren": 1897.5, + "Bonn": 1761.0, + "Les Clayes-sous-Bois": 1359.3, + "Nova Olinda do Norte": 7102.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Écully: (45.77°, 4.78°)", + " Büren: (51.55°, 8.56°)", + " Bonn: (50.73°, 7.10°)", + " Les Clayes-sous-Bois: (48.82°, 1.99°)", + " Nova Olinda do Norte: (-3.89°, -59.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nova Olinda do Norte: 7102.9 km from centroid", + " Büren: 1897.5 km from centroid", + " Bonn: 1761.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nova Olinda do Norte", + "FINAL ANSWER: Nova Olinda do Norte" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.50246, + "lon": -98.75358, + "name": "Axochiapan" + }, + { + "lat": 34.77453, + "lon": -96.67834, + "name": "Ada" + }, + { + "lat": 38.784, + "lon": -77.46971, + "name": "Manassas Park" + }, + { + "lat": 19.13325, + "lon": -97.64167, + "name": "San Salvador El Seco" + }, + { + "lat": 43.38285, + "lon": -3.22043, + "name": "Castro-Urdiales" + } + ], + "question": "Which location is the geographic outlier among: Axochiapan, Ada, Manassas Park, San Salvador El Seco, Castro-Urdiales?", + "ground_truth": { + "answer": "Castro-Urdiales", + "outlier_distance_km": 6294.2, + "second_furthest_km": 2780.3, + "clarity_ratio": 2.26, + "median_distance_km": 2644.1, + "distances_to_centroid": { + "Axochiapan": 2780.3, + "Ada": 2088.3, + "Manassas Park": 909.3, + "San Salvador El Seco": 2644.1, + "Castro-Urdiales": 6294.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Axochiapan: (18.50°, -98.75°)", + " Ada: (34.77°, -96.68°)", + " Manassas Park: (38.78°, -77.47°)", + " San Salvador El Seco: (19.13°, -97.64°)", + " Castro-Urdiales: (43.38°, -3.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castro-Urdiales: 6294.2 km from centroid", + " Axochiapan: 2780.3 km from centroid", + " San Salvador El Seco: 2644.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castro-Urdiales", + "FINAL ANSWER: Castro-Urdiales" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.05594, + "lon": 17.99088, + "name": "Gallipoli" + }, + { + "lat": 54.03811, + "lon": 21.76441, + "name": "Giżycko" + }, + { + "lat": 51.02288, + "lon": 2.39359, + "name": "Coudekerque-Branche" + }, + { + "lat": 54.12226, + "lon": 17.98119, + "name": "Kościerzyna" + }, + { + "lat": 8.1, + "lon": 36.95, + "name": "Suntu" + } + ], + "question": "Which location is the geographic outlier among: Gallipoli, Giżycko, Coudekerque-Branche, Kościerzyna, Suntu?", + "ground_truth": { + "answer": "Suntu", + "outlier_distance_km": 4092.4, + "second_furthest_km": 1678.9, + "clarity_ratio": 2.44, + "median_distance_km": 1411.1, + "distances_to_centroid": { + "Gallipoli": 197.6, + "Giżycko": 1408.5, + "Coudekerque-Branche": 1678.9, + "Kościerzyna": 1411.1, + "Suntu": 4092.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gallipoli: (40.06°, 17.99°)", + " Giżycko: (54.04°, 21.76°)", + " Coudekerque-Branche: (51.02°, 2.39°)", + " Kościerzyna: (54.12°, 17.98°)", + " Suntu: (8.10°, 36.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Suntu: 4092.4 km from centroid", + " Coudekerque-Branche: 1678.9 km from centroid", + " Kościerzyna: 1411.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Suntu", + "FINAL ANSWER: Suntu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.74496, + "lon": 144.80049, + "name": "St Albans" + }, + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": -32.23013, + "lon": 115.78128, + "name": "Kwinana" + }, + { + "lat": 31.01887, + "lon": 33.0098, + "name": "Bi’r al ‘Abd" + } + ], + "question": "Which location is the geographic outlier among: St Albans, Bexley, Randwick, Kwinana, Bi’r al ‘Abd?", + "ground_truth": { + "answer": "Bi’r al ‘Abd", + "outlier_distance_km": 10867.6, + "second_furthest_km": 3433.5, + "clarity_ratio": 3.17, + "median_distance_km": 3422.8, + "distances_to_centroid": { + "St Albans": 3057.1, + "Bexley": 3422.8, + "Randwick": 3433.5, + "Kwinana": 1254.5, + "Bi’r al ‘Abd": 10867.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " St Albans: (-37.74°, 144.80°)", + " Bexley: (-33.95°, 151.12°)", + " Randwick: (-33.91°, 151.25°)", + " Kwinana: (-32.23°, 115.78°)", + " Bi’r al ‘Abd: (31.02°, 33.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bi’r al ‘Abd: 10867.6 km from centroid", + " Randwick: 3433.5 km from centroid", + " Bexley: 3422.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bi’r al ‘Abd", + "FINAL ANSWER: Bi’r al ‘Abd" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.84069, + "lon": -83.6324, + "name": "Macon" + }, + { + "lat": 35.71126, + "lon": -78.61417, + "name": "Garner" + }, + { + "lat": 18.55462, + "lon": -99.60592, + "name": "Taxco de Alarcón" + }, + { + "lat": 40.83899, + "lon": -73.86041, + "name": "Parkchester" + }, + { + "lat": 34.37664, + "lon": 118.60308, + "name": "Ahu" + } + ], + "question": "Which location is the geographic outlier among: Macon, Garner, Taxco de Alarcón, Parkchester, Ahu?", + "ground_truth": { + "answer": "Ahu", + "outlier_distance_km": 12349.0, + "second_furthest_km": 5779.8, + "clarity_ratio": 2.14, + "median_distance_km": 3741.5, + "distances_to_centroid": { + "Macon": 3741.5, + "Garner": 3243.5, + "Taxco de Alarcón": 5779.8, + "Parkchester": 2853.6, + "Ahu": 12349.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macon: (32.84°, -83.63°)", + " Garner: (35.71°, -78.61°)", + " Taxco de Alarcón: (18.55°, -99.61°)", + " Parkchester: (40.84°, -73.86°)", + " Ahu: (34.38°, 118.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ahu: 12349.0 km from centroid", + " Taxco de Alarcón: 5779.8 km from centroid", + " Macon: 3741.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ahu", + "FINAL ANSWER: Ahu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.15152, + "lon": 19.01509, + "name": "Grabouw" + }, + { + "lat": -28.23078, + "lon": 28.30707, + "name": "Bethlehem" + }, + { + "lat": 13.49667, + "lon": 39.47528, + "name": "Mek'ele" + }, + { + "lat": 9.56561, + "lon": 36.63569, + "name": "Gutin" + }, + { + "lat": 31.64615, + "lon": 120.74221, + "name": "Changshu" + } + ], + "question": "Which location is the geographic outlier among: Grabouw, Bethlehem, Mek'ele, Gutin, Changshu?", + "ground_truth": { + "answer": "Changshu", + "outlier_distance_km": 8396.2, + "second_furthest_km": 4768.2, + "clarity_ratio": 1.76, + "median_distance_km": 3683.4, + "distances_to_centroid": { + "Grabouw": 4768.2, + "Bethlehem": 3683.4, + "Mek'ele": 1964.4, + "Gutin": 1830.0, + "Changshu": 8396.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Grabouw: (-34.15°, 19.02°)", + " Bethlehem: (-28.23°, 28.31°)", + " Mek'ele: (13.50°, 39.48°)", + " Gutin: (9.57°, 36.64°)", + " Changshu: (31.65°, 120.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Changshu: 8396.2 km from centroid", + " Grabouw: 4768.2 km from centroid", + " Bethlehem: 3683.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Changshu", + "FINAL ANSWER: Changshu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.67344, + "lon": 84.39463, + "name": "Bolotnoye" + }, + { + "lat": 47.99597, + "lon": -4.09795, + "name": "Quimper" + }, + { + "lat": 60.76186, + "lon": 46.31352, + "name": "Velikiy Ustyug" + }, + { + "lat": 28.10178, + "lon": -15.41573, + "name": "Las Palmas de Gran Canaria" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + } + ], + "question": "Which location is the geographic outlier among: Bolotnoye, Quimper, Velikiy Ustyug, Las Palmas de Gran Canaria, Clayton?", + "ground_truth": { + "answer": "Clayton", + "outlier_distance_km": 12362.6, + "second_furthest_km": 6360.8, + "clarity_ratio": 1.94, + "median_distance_km": 4994.1, + "distances_to_centroid": { + "Bolotnoye": 3775.5, + "Quimper": 4994.1, + "Velikiy Ustyug": 3337.8, + "Las Palmas de Gran Canaria": 6360.8, + "Clayton": 12362.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bolotnoye: (55.67°, 84.39°)", + " Quimper: (48.00°, -4.10°)", + " Velikiy Ustyug: (60.76°, 46.31°)", + " Las Palmas de Gran Canaria: (28.10°, -15.42°)", + " Clayton: (-37.92°, 145.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clayton: 12362.6 km from centroid", + " Las Palmas de Gran Canaria: 6360.8 km from centroid", + " Quimper: 4994.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clayton", + "FINAL ANSWER: Clayton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.5635, + "lon": 34.56055, + "name": "Bungoma" + }, + { + "lat": 7.25256, + "lon": 5.19312, + "name": "Akure" + }, + { + "lat": 8.4, + "lon": 38.85, + "name": "Dēra" + }, + { + "lat": 30.37746, + "lon": 30.35032, + "name": "Madīnat Wādī an Naţrūn" + }, + { + "lat": -6.02583, + "lon": -44.24917, + "name": "Colinas" + } + ], + "question": "Which location is the geographic outlier among: Bungoma, Akure, Dēra, Madīnat Wādī an Naţrūn, Colinas?", + "ground_truth": { + "answer": "Colinas", + "outlier_distance_km": 6533.6, + "second_furthest_km": 3067.3, + "clarity_ratio": 2.13, + "median_distance_km": 2850.8, + "distances_to_centroid": { + "Bungoma": 2538.1, + "Akure": 859.1, + "Dēra": 2850.8, + "Madīnat Wādī an Naţrūn": 3067.3, + "Colinas": 6533.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bungoma: (0.56°, 34.56°)", + " Akure: (7.25°, 5.19°)", + " Dēra: (8.40°, 38.85°)", + " Madīnat Wādī an Naţrūn: (30.38°, 30.35°)", + " Colinas: (-6.03°, -44.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Colinas: 6533.6 km from centroid", + " Madīnat Wādī an Naţrūn: 3067.3 km from centroid", + " Dēra: 2850.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Colinas", + "FINAL ANSWER: Colinas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -27.35364, + "lon": 152.96848, + "name": "Albany Creek" + }, + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + }, + { + "lat": 44.85614, + "lon": -0.53355, + "name": "Cenon" + } + ], + "question": "Which location is the geographic outlier among: Rotorua, Albany Creek, Upper Coomera, Mount Eden, Cenon?", + "ground_truth": { + "answer": "Cenon", + "outlier_distance_km": 14595.6, + "second_furthest_km": 4942.0, + "clarity_ratio": 2.95, + "median_distance_km": 4778.6, + "distances_to_centroid": { + "Rotorua": 4942.0, + "Albany Creek": 2496.2, + "Upper Coomera": 2547.8, + "Mount Eden": 4778.6, + "Cenon": 14595.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rotorua: (-38.14°, 176.25°)", + " Albany Creek: (-27.35°, 152.97°)", + " Upper Coomera: (-27.88°, 153.29°)", + " Mount Eden: (-36.88°, 174.76°)", + " Cenon: (44.86°, -0.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cenon: 14595.6 km from centroid", + " Rotorua: 4942.0 km from centroid", + " Mount Eden: 4778.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cenon", + "FINAL ANSWER: Cenon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.91177, + "lon": -94.09646, + "name": "Las Choapas" + }, + { + "lat": 43.19472, + "lon": -88.72899, + "name": "Watertown" + }, + { + "lat": 40.64372, + "lon": -73.90069, + "name": "Canarsie" + }, + { + "lat": 39.11417, + "lon": -94.62746, + "name": "Kansas City" + }, + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + } + ], + "question": "Which location is the geographic outlier among: Las Choapas, Watertown, Canarsie, Kansas City, Merrylands?", + "ground_truth": { + "answer": "Merrylands", + "outlier_distance_km": 18258.1, + "second_furthest_km": 5643.3, + "clarity_ratio": 3.24, + "median_distance_km": 5506.4, + "distances_to_centroid": { + "Las Choapas": 5643.3, + "Watertown": 5083.6, + "Canarsie": 3831.1, + "Kansas City": 5506.4, + "Merrylands": 18258.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Las Choapas: (17.91°, -94.10°)", + " Watertown: (43.19°, -88.73°)", + " Canarsie: (40.64°, -73.90°)", + " Kansas City: (39.11°, -94.63°)", + " Merrylands: (-33.83°, 150.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Merrylands: 18258.1 km from centroid", + " Las Choapas: 5643.3 km from centroid", + " Kansas City: 5506.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Merrylands", + "FINAL ANSWER: Merrylands" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.06847, + "lon": -78.88947, + "name": "Waynesboro" + }, + { + "lat": 37.97476, + "lon": -87.55585, + "name": "Evansville" + }, + { + "lat": 40.73121, + "lon": -74.27348, + "name": "Maplewood" + }, + { + "lat": 33.78391, + "lon": -116.95864, + "name": "San Jacinto" + }, + { + "lat": -28.33057, + "lon": 28.99087, + "name": "Tshiame" + } + ], + "question": "Which location is the geographic outlier among: Waynesboro, Evansville, Maplewood, San Jacinto, Tshiame?", + "ground_truth": { + "answer": "Tshiame", + "outlier_distance_km": 11699.3, + "second_furthest_km": 5031.7, + "clarity_ratio": 2.33, + "median_distance_km": 2551.9, + "distances_to_centroid": { + "Waynesboro": 1959.6, + "Evansville": 2551.9, + "Maplewood": 1977.1, + "San Jacinto": 5031.7, + "Tshiame": 11699.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Waynesboro: (38.07°, -78.89°)", + " Evansville: (37.97°, -87.56°)", + " Maplewood: (40.73°, -74.27°)", + " San Jacinto: (33.78°, -116.96°)", + " Tshiame: (-28.33°, 28.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tshiame: 11699.3 km from centroid", + " San Jacinto: 5031.7 km from centroid", + " Evansville: 2551.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tshiame", + "FINAL ANSWER: Tshiame" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": 11.19152, + "lon": 40.01675, + "name": "Batī" + } + ], + "question": "Which location is the geographic outlier among: Banora Point, Truganina, Papatoetoe, Otahuhu, Batī?", + "ground_truth": { + "answer": "Batī", + "outlier_distance_km": 11296.1, + "second_furthest_km": 3722.2, + "clarity_ratio": 3.03, + "median_distance_km": 3721.6, + "distances_to_centroid": { + "Banora Point": 1601.8, + "Truganina": 1501.3, + "Papatoetoe": 3722.2, + "Otahuhu": 3721.6, + "Batī": 11296.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banora Point: (-28.21°, 153.54°)", + " Truganina: (-37.82°, 144.75°)", + " Papatoetoe: (-36.97°, 174.84°)", + " Otahuhu: (-36.94°, 174.84°)", + " Batī: (11.19°, 40.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Batī: 11296.1 km from centroid", + " Papatoetoe: 3722.2 km from centroid", + " Otahuhu: 3721.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Batī", + "FINAL ANSWER: Batī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.63864, + "lon": -80.39727, + "name": "Vero Beach" + }, + { + "lat": 41.0706, + "lon": -85.01441, + "name": "New Haven" + }, + { + "lat": 41.70037, + "lon": -73.92097, + "name": "Poughkeepsie" + }, + { + "lat": 42.097, + "lon": -79.23533, + "name": "Jamestown" + }, + { + "lat": -13.74389, + "lon": -39.48667, + "name": "Gandu" + } + ], + "question": "Which location is the geographic outlier among: Vero Beach, New Haven, Poughkeepsie, Jamestown, Gandu?", + "ground_truth": { + "answer": "Gandu", + "outlier_distance_km": 5768.2, + "second_furthest_km": 1920.0, + "clarity_ratio": 3.0, + "median_distance_km": 1738.1, + "distances_to_centroid": { + "Vero Beach": 865.0, + "New Haven": 1920.0, + "Poughkeepsie": 1565.1, + "Jamestown": 1738.1, + "Gandu": 5768.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vero Beach: (27.64°, -80.40°)", + " New Haven: (41.07°, -85.01°)", + " Poughkeepsie: (41.70°, -73.92°)", + " Jamestown: (42.10°, -79.24°)", + " Gandu: (-13.74°, -39.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gandu: 5768.2 km from centroid", + " New Haven: 1920.0 km from centroid", + " Jamestown: 1738.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gandu", + "FINAL ANSWER: Gandu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.53333, + "lon": 138.93333, + "name": "Mitsuke" + }, + { + "lat": 32.77856, + "lon": 130.74537, + "name": "Kotō" + }, + { + "lat": 3.14657, + "lon": 101.71023, + "name": "Bukit Bintang" + }, + { + "lat": 16.3865, + "lon": 121.1066, + "name": "Bambang" + }, + { + "lat": 30.4013, + "lon": -91.00094, + "name": "Shenandoah" + } + ], + "question": "Which location is the geographic outlier among: Mitsuke, Kotō, Bukit Bintang, Bambang, Shenandoah?", + "ground_truth": { + "answer": "Shenandoah", + "outlier_distance_km": 13889.8, + "second_furthest_km": 5704.7, + "clarity_ratio": 2.43, + "median_distance_km": 4981.7, + "distances_to_centroid": { + "Mitsuke": 5704.7, + "Kotō": 4981.7, + "Bukit Bintang": 3268.6, + "Bambang": 4327.0, + "Shenandoah": 13889.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mitsuke: (37.53°, 138.93°)", + " Kotō: (32.78°, 130.75°)", + " Bukit Bintang: (3.15°, 101.71°)", + " Bambang: (16.39°, 121.11°)", + " Shenandoah: (30.40°, -91.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shenandoah: 13889.8 km from centroid", + " Mitsuke: 5704.7 km from centroid", + " Kotō: 4981.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shenandoah", + "FINAL ANSWER: Shenandoah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + { + "lat": 39.11417, + "lon": -94.62746, + "name": "Kansas City" + } + ], + "question": "Which location is the geographic outlier among: Pakenham, Coorparoo, Kensington, Kingsford, Kansas City?", + "ground_truth": { + "answer": "Kansas City", + "outlier_distance_km": 17292.5, + "second_furthest_km": 5342.9, + "clarity_ratio": 3.24, + "median_distance_km": 5194.8, + "distances_to_centroid": { + "Pakenham": 4762.4, + "Coorparoo": 5342.9, + "Kensington": 5194.3, + "Kingsford": 5194.8, + "Kansas City": 17292.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pakenham: (-38.07°, 145.47°)", + " Coorparoo: (-27.49°, 153.06°)", + " Kensington: (-33.92°, 151.22°)", + " Kingsford: (-33.92°, 151.23°)", + " Kansas City: (39.11°, -94.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kansas City: 17292.5 km from centroid", + " Coorparoo: 5342.9 km from centroid", + " Kingsford: 5194.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kansas City", + "FINAL ANSWER: Kansas City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.21773, + "lon": 8.26679, + "name": "Idstein" + }, + { + "lat": 51.75742, + "lon": 11.46084, + "name": "Aschersleben" + }, + { + "lat": 52.86195, + "lon": -3.05497, + "name": "Oswestry" + }, + { + "lat": 44.55858, + "lon": 6.07868, + "name": "Gap" + }, + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + } + ], + "question": "Which location is the geographic outlier among: Idstein, Aschersleben, Oswestry, Gap, Hoppers Crossing?", + "ground_truth": { + "answer": "Hoppers Crossing", + "outlier_distance_km": 13867.7, + "second_furthest_km": 3700.8, + "clarity_ratio": 3.75, + "median_distance_km": 2874.3, + "distances_to_centroid": { + "Idstein": 2874.3, + "Aschersleben": 2803.9, + "Oswestry": 3700.8, + "Gap": 2730.0, + "Hoppers Crossing": 13867.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Idstein: (50.22°, 8.27°)", + " Aschersleben: (51.76°, 11.46°)", + " Oswestry: (52.86°, -3.05°)", + " Gap: (44.56°, 6.08°)", + " Hoppers Crossing: (-37.88°, 144.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hoppers Crossing: 13867.7 km from centroid", + " Oswestry: 3700.8 km from centroid", + " Idstein: 2874.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hoppers Crossing", + "FINAL ANSWER: Hoppers Crossing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.31387, + "lon": 42.11815, + "name": "Harar" + }, + { + "lat": 30.72508, + "lon": 31.67148, + "name": "Abū Kabīr" + }, + { + "lat": 10.31032, + "lon": 9.84388, + "name": "Bauchi" + }, + { + "lat": 31.61166, + "lon": 25.92539, + "name": "Sīdī Barānī" + }, + { + "lat": 13.08449, + "lon": 79.67053, + "name": "Arakkonam" + } + ], + "question": "Which location is the geographic outlier among: Harar, Abū Kabīr, Bauchi, Sīdī Barānī, Arakkonam?", + "ground_truth": { + "answer": "Arakkonam", + "outlier_distance_km": 4507.4, + "second_furthest_km": 3158.6, + "clarity_ratio": 1.43, + "median_distance_km": 1840.9, + "distances_to_centroid": { + "Harar": 1172.1, + "Abū Kabīr": 1443.2, + "Bauchi": 3158.6, + "Sīdī Barānī": 1840.9, + "Arakkonam": 4507.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Harar: (9.31°, 42.12°)", + " Abū Kabīr: (30.73°, 31.67°)", + " Bauchi: (10.31°, 9.84°)", + " Sīdī Barānī: (31.61°, 25.93°)", + " Arakkonam: (13.08°, 79.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arakkonam: 4507.4 km from centroid", + " Bauchi: 3158.6 km from centroid", + " Sīdī Barānī: 1840.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arakkonam", + "FINAL ANSWER: Arakkonam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.64773, + "lon": 10.04149, + "name": "Hummelsbüttel" + }, + { + "lat": 48.35103, + "lon": 41.829, + "name": "Morozovsk" + }, + { + "lat": 55.71667, + "lon": 37.53333, + "name": "Vorob’yovo" + }, + { + "lat": 51.46072, + "lon": -0.21814, + "name": "Putney" + }, + { + "lat": -23.18111, + "lon": -46.395, + "name": "Nazaré Paulista" + } + ], + "question": "Which location is the geographic outlier among: Hummelsbüttel, Morozovsk, Vorob’yovo, Putney, Nazaré Paulista?", + "ground_truth": { + "answer": "Nazaré Paulista", + "outlier_distance_km": 8838.3, + "second_furthest_km": 2987.4, + "clarity_ratio": 2.96, + "median_distance_km": 2955.0, + "distances_to_centroid": { + "Hummelsbüttel": 1832.6, + "Morozovsk": 2955.0, + "Vorob’yovo": 2987.4, + "Putney": 1729.7, + "Nazaré Paulista": 8838.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hummelsbüttel: (53.65°, 10.04°)", + " Morozovsk: (48.35°, 41.83°)", + " Vorob’yovo: (55.72°, 37.53°)", + " Putney: (51.46°, -0.22°)", + " Nazaré Paulista: (-23.18°, -46.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nazaré Paulista: 8838.3 km from centroid", + " Vorob’yovo: 2987.4 km from centroid", + " Morozovsk: 2955.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nazaré Paulista", + "FINAL ANSWER: Nazaré Paulista" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": -37.2, + "lon": 174.95, + "name": "Pukekohe East" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": 51.33678, + "lon": -0.11201, + "name": "Purley" + } + ], + "question": "Which location is the geographic outlier among: Yarraville, Pukekohe East, New Plymouth, Lara, Purley?", + "ground_truth": { + "answer": "Purley", + "outlier_distance_km": 14334.6, + "second_furthest_km": 4928.9, + "clarity_ratio": 2.91, + "median_distance_km": 4891.7, + "distances_to_centroid": { + "Yarraville": 2574.1, + "Pukekohe East": 4928.9, + "New Plymouth": 4891.7, + "Lara": 2560.2, + "Purley": 14334.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yarraville: (-37.82°, 144.90°)", + " Pukekohe East: (-37.20°, 174.95°)", + " New Plymouth: (-39.07°, 174.08°)", + " Lara: (-38.02°, 144.41°)", + " Purley: (51.34°, -0.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Purley: 14334.6 km from centroid", + " Pukekohe East: 4928.9 km from centroid", + " New Plymouth: 4891.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Purley", + "FINAL ANSWER: Purley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.31577, + "lon": 76.31502, + "name": "Jīnd" + }, + { + "lat": 37.37575, + "lon": 101.62199, + "name": "Haomen" + }, + { + "lat": 20.28845, + "lon": 82.7606, + "name": "Kharhiāl" + }, + { + "lat": 19.79632, + "lon": 75.22648, + "name": "Waluj Buzurg" + }, + { + "lat": 35.14953, + "lon": -90.04898, + "name": "Memphis" + } + ], + "question": "Which location is the geographic outlier among: Jīnd, Haomen, Kharhiāl, Waluj Buzurg, Memphis?", + "ground_truth": { + "answer": "Memphis", + "outlier_distance_km": 11756.3, + "second_furthest_km": 4935.0, + "clarity_ratio": 2.38, + "median_distance_km": 3507.1, + "distances_to_centroid": { + "Jīnd": 2639.4, + "Haomen": 4935.0, + "Kharhiāl": 3507.1, + "Waluj Buzurg": 2804.3, + "Memphis": 11756.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jīnd: (29.32°, 76.32°)", + " Haomen: (37.38°, 101.62°)", + " Kharhiāl: (20.29°, 82.76°)", + " Waluj Buzurg: (19.80°, 75.23°)", + " Memphis: (35.15°, -90.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Memphis: 11756.3 km from centroid", + " Haomen: 4935.0 km from centroid", + " Kharhiāl: 3507.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Memphis", + "FINAL ANSWER: Memphis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.17655, + "lon": 4.50885, + "name": "Merenwijk" + }, + { + "lat": 41.39458, + "lon": 2.17946, + "name": "Fort Pienc" + }, + { + "lat": 40.68907, + "lon": 14.52036, + "name": "Gragnano" + }, + { + "lat": 40.32718, + "lon": -3.7635, + "name": "Leganés" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + } + ], + "question": "Which location is the geographic outlier among: Merenwijk, Fort Pienc, Gragnano, Leganés, Cherrybrook?", + "ground_truth": { + "answer": "Cherrybrook", + "outlier_distance_km": 14098.8, + "second_furthest_km": 3665.8, + "clarity_ratio": 3.85, + "median_distance_km": 3596.2, + "distances_to_centroid": { + "Merenwijk": 3596.2, + "Fort Pienc": 3207.4, + "Gragnano": 2234.2, + "Leganés": 3665.8, + "Cherrybrook": 14098.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Merenwijk: (52.18°, 4.51°)", + " Fort Pienc: (41.39°, 2.18°)", + " Gragnano: (40.69°, 14.52°)", + " Leganés: (40.33°, -3.76°)", + " Cherrybrook: (-33.72°, 151.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cherrybrook: 14098.8 km from centroid", + " Leganés: 3665.8 km from centroid", + " Merenwijk: 3596.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cherrybrook", + "FINAL ANSWER: Cherrybrook" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.77972, + "lon": -108.2967, + "name": "North Battleford" + }, + { + "lat": 25.90232, + "lon": -80.25033, + "name": "Opa-locka" + }, + { + "lat": 26.39823, + "lon": -99.02857, + "name": "Ciudad Miguel Alemán" + }, + { + "lat": 25.64205, + "lon": -80.39839, + "name": "Three Lakes" + }, + { + "lat": 6.34656, + "lon": 45.47811, + "name": "El Bahay" + } + ], + "question": "Which location is the geographic outlier among: North Battleford, Opa-locka, Ciudad Miguel Alemán, Three Lakes, El Bahay?", + "ground_truth": { + "answer": "El Bahay", + "outlier_distance_km": 11620.8, + "second_furthest_km": 4563.9, + "clarity_ratio": 2.55, + "median_distance_km": 3414.7, + "distances_to_centroid": { + "North Battleford": 4563.9, + "Opa-locka": 1573.2, + "Ciudad Miguel Alemán": 3414.7, + "Three Lakes": 1592.9, + "El Bahay": 11620.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Battleford: (52.78°, -108.30°)", + " Opa-locka: (25.90°, -80.25°)", + " Ciudad Miguel Alemán: (26.40°, -99.03°)", + " Three Lakes: (25.64°, -80.40°)", + " El Bahay: (6.35°, 45.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " El Bahay: 11620.8 km from centroid", + " North Battleford: 4563.9 km from centroid", + " Ciudad Miguel Alemán: 3414.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: El Bahay", + "FINAL ANSWER: El Bahay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.60333, + "lon": -47.02639, + "name": "Vargem Grande Paulista" + }, + { + "lat": -23.81305, + "lon": -64.79353, + "name": "Libertador General San Martín" + }, + { + "lat": -10.855, + "lon": -37.12611, + "name": "Nossa Senhora do Socorro" + }, + { + "lat": 8.92901, + "lon": -75.02709, + "name": "San Benito Abad" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + } + ], + "question": "Which location is the geographic outlier among: Vargem Grande Paulista, Libertador General San Martín, Nossa Senhora do Socorro, San Benito Abad, Whangarei?", + "ground_truth": { + "answer": "Whangarei", + "outlier_distance_km": 14132.8, + "second_furthest_km": 7713.5, + "clarity_ratio": 1.83, + "median_distance_km": 5733.8, + "distances_to_centroid": { + "Vargem Grande Paulista": 3926.0, + "Libertador General San Martín": 5733.8, + "Nossa Senhora do Socorro": 3010.7, + "San Benito Abad": 7713.5, + "Whangarei": 14132.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vargem Grande Paulista: (-23.60°, -47.03°)", + " Libertador General San Martín: (-23.81°, -64.79°)", + " Nossa Senhora do Socorro: (-10.86°, -37.13°)", + " San Benito Abad: (8.93°, -75.03°)", + " Whangarei: (-35.73°, 174.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whangarei: 14132.8 km from centroid", + " San Benito Abad: 7713.5 km from centroid", + " Libertador General San Martín: 5733.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whangarei", + "FINAL ANSWER: Whangarei" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.75888, + "lon": -81.31784, + "name": "Lake Mary" + }, + { + "lat": 22.91273, + "lon": -109.92655, + "name": "Colonia del Sol" + }, + { + "lat": 43.68341, + "lon": -79.76633, + "name": "Brampton" + }, + { + "lat": 19.36357, + "lon": -98.97707, + "name": "Los Reyes Acaquilpan" + }, + { + "lat": -26.26786, + "lon": 28.12225, + "name": "Alberton" + } + ], + "question": "Which location is the geographic outlier among: Lake Mary, Colonia del Sol, Brampton, Los Reyes Acaquilpan, Alberton?", + "ground_truth": { + "answer": "Alberton", + "outlier_distance_km": 11493.5, + "second_furthest_km": 4358.2, + "clarity_ratio": 2.64, + "median_distance_km": 3227.9, + "distances_to_centroid": { + "Lake Mary": 1804.1, + "Colonia del Sol": 4358.2, + "Brampton": 3081.8, + "Los Reyes Acaquilpan": 3227.9, + "Alberton": 11493.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lake Mary: (28.76°, -81.32°)", + " Colonia del Sol: (22.91°, -109.93°)", + " Brampton: (43.68°, -79.77°)", + " Los Reyes Acaquilpan: (19.36°, -98.98°)", + " Alberton: (-26.27°, 28.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alberton: 11493.5 km from centroid", + " Colonia del Sol: 4358.2 km from centroid", + " Los Reyes Acaquilpan: 3227.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alberton", + "FINAL ANSWER: Alberton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + }, + { + "lat": -37.75, + "lon": 144.96667, + "name": "Coburg" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": 27.91667, + "lon": 112.51667, + "name": "Shaoshan" + } + ], + "question": "Which location is the geographic outlier among: Taylors Hill, Coburg, Lara, Melbourne, Shaoshan?", + "ground_truth": { + "answer": "Shaoshan", + "outlier_distance_km": 6468.2, + "second_furthest_km": 1591.7, + "clarity_ratio": 4.06, + "median_distance_km": 1590.3, + "distances_to_centroid": { + "Taylors Hill": 1572.1, + "Coburg": 1584.0, + "Lara": 1591.7, + "Melbourne": 1590.3, + "Shaoshan": 6468.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taylors Hill: (-37.71°, 144.75°)", + " Coburg: (-37.75°, 144.97°)", + " Lara: (-38.02°, 144.41°)", + " Melbourne: (-37.81°, 144.96°)", + " Shaoshan: (27.92°, 112.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shaoshan: 6468.2 km from centroid", + " Lara: 1591.7 km from centroid", + " Melbourne: 1590.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shaoshan", + "FINAL ANSWER: Shaoshan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.25008, + "lon": -74.13253, + "name": "Salaberry-de-Valleyfield" + }, + { + "lat": 36.19617, + "lon": -86.6225, + "name": "Hermitage" + }, + { + "lat": 41.43333, + "lon": -96.49808, + "name": "Fremont" + }, + { + "lat": 21.38667, + "lon": -158.00917, + "name": "Waipahu" + }, + { + "lat": 10.32944, + "lon": -75.41137, + "name": "Turbaco" + } + ], + "question": "Which location is the geographic outlier among: Salaberry-de-Valleyfield, Hermitage, Fremont, Waipahu, Turbaco?", + "ground_truth": { + "answer": "Waipahu", + "outlier_distance_km": 6000.5, + "second_furthest_km": 3276.9, + "clarity_ratio": 1.83, + "median_distance_km": 2619.5, + "distances_to_centroid": { + "Salaberry-de-Valleyfield": 2619.5, + "Hermitage": 1216.2, + "Fremont": 1178.3, + "Waipahu": 6000.5, + "Turbaco": 3276.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Salaberry-de-Valleyfield: (45.25°, -74.13°)", + " Hermitage: (36.20°, -86.62°)", + " Fremont: (41.43°, -96.50°)", + " Waipahu: (21.39°, -158.01°)", + " Turbaco: (10.33°, -75.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Waipahu: 6000.5 km from centroid", + " Turbaco: 3276.9 km from centroid", + " Salaberry-de-Valleyfield: 2619.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Waipahu", + "FINAL ANSWER: Waipahu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.66667, + "lon": 38.8, + "name": "Filakit" + }, + { + "lat": -33.15388, + "lon": 18.66031, + "name": "Moorreesburg" + }, + { + "lat": -29.81292, + "lon": 30.63646, + "name": "Mpumalanga" + }, + { + "lat": 5.20131, + "lon": 7.98373, + "name": "Itu" + }, + { + "lat": -23.68611, + "lon": -46.62278, + "name": "Diadema" + } + ], + "question": "Which location is the geographic outlier among: Filakit, Moorreesburg, Mpumalanga, Itu, Diadema?", + "ground_truth": { + "answer": "Diadema", + "outlier_distance_km": 6008.9, + "second_furthest_km": 4274.7, + "clarity_ratio": 1.41, + "median_distance_km": 2764.0, + "distances_to_centroid": { + "Filakit": 4274.7, + "Moorreesburg": 2311.6, + "Mpumalanga": 2764.0, + "Itu": 2140.7, + "Diadema": 6008.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Filakit: (11.67°, 38.80°)", + " Moorreesburg: (-33.15°, 18.66°)", + " Mpumalanga: (-29.81°, 30.64°)", + " Itu: (5.20°, 7.98°)", + " Diadema: (-23.69°, -46.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Diadema: 6008.9 km from centroid", + " Filakit: 4274.7 km from centroid", + " Mpumalanga: 2764.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Diadema", + "FINAL ANSWER: Diadema" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.77819, + "lon": 135.59512, + "name": "Settsu" + }, + { + "lat": -3.2945, + "lon": 102.8614, + "name": "Lubuklinggau" + }, + { + "lat": 35.75202, + "lon": 139.51169, + "name": "Higashikurume" + }, + { + "lat": 42.81944, + "lon": 141.65222, + "name": "Chitose" + }, + { + "lat": -24.04309, + "lon": -52.37929, + "name": "Campo Mourão" + } + ], + "question": "Which location is the geographic outlier among: Settsu, Lubuklinggau, Higashikurume, Chitose, Campo Mourão?", + "ground_truth": { + "answer": "Campo Mourão", + "outlier_distance_km": 16387.9, + "second_furthest_km": 5346.9, + "clarity_ratio": 3.06, + "median_distance_km": 4971.2, + "distances_to_centroid": { + "Settsu": 4600.3, + "Lubuklinggau": 2502.4, + "Higashikurume": 4971.2, + "Chitose": 5346.9, + "Campo Mourão": 16387.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Settsu: (34.78°, 135.60°)", + " Lubuklinggau: (-3.29°, 102.86°)", + " Higashikurume: (35.75°, 139.51°)", + " Chitose: (42.82°, 141.65°)", + " Campo Mourão: (-24.04°, -52.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Campo Mourão: 16387.9 km from centroid", + " Chitose: 5346.9 km from centroid", + " Higashikurume: 4971.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Campo Mourão", + "FINAL ANSWER: Campo Mourão" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.1466, + "lon": 28.68322, + "name": "Delmas" + }, + { + "lat": 10.89469, + "lon": -1.09083, + "name": "Navrongo" + }, + { + "lat": 11.01537, + "lon": 6.78036, + "name": "Sofo-Birnin-Gwari" + }, + { + "lat": 5.71417, + "lon": -0.15418, + "name": "Adenta" + }, + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + } + ], + "question": "Which location is the geographic outlier among: Delmas, Navrongo, Sofo-Birnin-Gwari, Adenta, Coogee?", + "ground_truth": { + "answer": "Coogee", + "outlier_distance_km": 11778.5, + "second_furthest_km": 4647.3, + "clarity_ratio": 2.53, + "median_distance_km": 4350.9, + "distances_to_centroid": { + "Delmas": 2360.9, + "Navrongo": 4647.3, + "Sofo-Birnin-Gwari": 3878.6, + "Adenta": 4350.9, + "Coogee": 11778.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Delmas: (-26.15°, 28.68°)", + " Navrongo: (10.89°, -1.09°)", + " Sofo-Birnin-Gwari: (11.02°, 6.78°)", + " Adenta: (5.71°, -0.15°)", + " Coogee: (-33.92°, 151.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coogee: 11778.5 km from centroid", + " Navrongo: 4647.3 km from centroid", + " Adenta: 4350.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coogee", + "FINAL ANSWER: Coogee" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": 35.64595, + "lon": 139.7155, + "name": "Ebisu" + } + ], + "question": "Which location is the geographic outlier among: Titirangi, Launceston, Logan City, Melbourne City Centre, Ebisu?", + "ground_truth": { + "answer": "Ebisu", + "outlier_distance_km": 6497.9, + "second_furthest_km": 2772.4, + "clarity_ratio": 2.34, + "median_distance_km": 2247.0, + "distances_to_centroid": { + "Titirangi": 2772.4, + "Launceston": 2247.0, + "Logan City": 678.2, + "Melbourne City Centre": 1918.4, + "Ebisu": 6497.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Titirangi: (-36.94°, 174.66°)", + " Launceston: (-41.44°, 147.13°)", + " Logan City: (-27.64°, 153.11°)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Ebisu: (35.65°, 139.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ebisu: 6497.9 km from centroid", + " Titirangi: 2772.4 km from centroid", + " Launceston: 2247.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ebisu", + "FINAL ANSWER: Ebisu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.93462, + "lon": 18.86676, + "name": "Stellenbosch" + }, + { + "lat": -26.53333, + "lon": 29.06667, + "name": "eMbalenhle" + }, + { + "lat": -4.05466, + "lon": 39.66359, + "name": "Mombasa" + }, + { + "lat": 5.86006, + "lon": -0.6635, + "name": "Asamankese" + }, + { + "lat": 37.06217, + "lon": 114.49272, + "name": "Xingtai" + } + ], + "question": "Which location is the geographic outlier among: Stellenbosch, eMbalenhle, Mombasa, Asamankese, Xingtai?", + "ground_truth": { + "answer": "Xingtai", + "outlier_distance_km": 8911.7, + "second_furthest_km": 4685.6, + "clarity_ratio": 1.9, + "median_distance_km": 3968.0, + "distances_to_centroid": { + "Stellenbosch": 3968.0, + "eMbalenhle": 2743.0, + "Mombasa": 75.0, + "Asamankese": 4685.6, + "Xingtai": 8911.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stellenbosch: (-33.93°, 18.87°)", + " eMbalenhle: (-26.53°, 29.07°)", + " Mombasa: (-4.05°, 39.66°)", + " Asamankese: (5.86°, -0.66°)", + " Xingtai: (37.06°, 114.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xingtai: 8911.7 km from centroid", + " Asamankese: 4685.6 km from centroid", + " Stellenbosch: 3968.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xingtai", + "FINAL ANSWER: Xingtai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.16951, + "lon": 94.8006, + "name": "Along" + }, + { + "lat": 26.12583, + "lon": 109.40889, + "name": "Hongzhou" + }, + { + "lat": 34.8262, + "lon": 126.10863, + "name": "Sinan" + }, + { + "lat": 27.25097, + "lon": 75.17893, + "name": "Rāmgarh" + }, + { + "lat": 51.66083, + "lon": 5.61944, + "name": "Uden" + } + ], + "question": "Which location is the geographic outlier among: Along, Hongzhou, Sinan, Rāmgarh, Uden?", + "ground_truth": { + "answer": "Uden", + "outlier_distance_km": 6268.1, + "second_furthest_km": 4004.9, + "clarity_ratio": 1.57, + "median_distance_km": 2740.8, + "distances_to_centroid": { + "Along": 1342.5, + "Hongzhou": 2740.8, + "Sinan": 4004.9, + "Rāmgarh": 977.0, + "Uden": 6268.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Along: (28.17°, 94.80°)", + " Hongzhou: (26.13°, 109.41°)", + " Sinan: (34.83°, 126.11°)", + " Rāmgarh: (27.25°, 75.18°)", + " Uden: (51.66°, 5.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uden: 6268.1 km from centroid", + " Sinan: 4004.9 km from centroid", + " Hongzhou: 2740.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uden", + "FINAL ANSWER: Uden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.98533, + "lon": 76.52046, + "name": "Lonar" + }, + { + "lat": 18.04348, + "lon": 77.206, + "name": "Bhālki" + }, + { + "lat": 13.83576, + "lon": 100.46001, + "name": "Bang O" + }, + { + "lat": 25.43745, + "lon": 81.9055, + "name": "Jhūsi" + }, + { + "lat": -43.58333, + "lon": 172.38333, + "name": "Rolleston" + } + ], + "question": "Which location is the geographic outlier among: Lonar, Bhālki, Bang O, Jhūsi, Rolleston?", + "ground_truth": { + "answer": "Rolleston", + "outlier_distance_km": 9003.5, + "second_furthest_km": 3088.7, + "clarity_ratio": 2.91, + "median_distance_km": 2956.0, + "distances_to_centroid": { + "Lonar": 3088.7, + "Bhālki": 2936.1, + "Bang O": 800.1, + "Jhūsi": 2956.0, + "Rolleston": 9003.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lonar: (19.99°, 76.52°)", + " Bhālki: (18.04°, 77.21°)", + " Bang O: (13.84°, 100.46°)", + " Jhūsi: (25.44°, 81.91°)", + " Rolleston: (-43.58°, 172.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rolleston: 9003.5 km from centroid", + " Lonar: 3088.7 km from centroid", + " Jhūsi: 2956.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rolleston", + "FINAL ANSWER: Rolleston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": 2.2186, + "lon": 102.1995, + "name": "Klebang Besar" + } + ], + "question": "Which location is the geographic outlier among: Traralgon, Caulfield North, Hawthorn, Carrum Downs, Klebang Besar?", + "ground_truth": { + "answer": "Klebang Besar", + "outlier_distance_km": 5126.4, + "second_furthest_km": 1281.3, + "clarity_ratio": 4.0, + "median_distance_km": 1189.0, + "distances_to_centroid": { + "Traralgon": 1281.3, + "Caulfield North": 1161.8, + "Hawthorn": 1158.1, + "Carrum Downs": 1189.0, + "Klebang Besar": 5126.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Traralgon: (-38.20°, 146.54°)", + " Caulfield North: (-37.87°, 145.02°)", + " Hawthorn: (-37.82°, 145.04°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Klebang Besar: (2.22°, 102.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Klebang Besar: 5126.4 km from centroid", + " Traralgon: 1281.3 km from centroid", + " Carrum Downs: 1189.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Klebang Besar", + "FINAL ANSWER: Klebang Besar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + }, + { + "lat": 41.82399, + "lon": -71.41283, + "name": "Providence" + } + ], + "question": "Which location is the geographic outlier among: Saint Albans, Ashfield, Hervey Bay, Dandenong, Providence?", + "ground_truth": { + "answer": "Providence", + "outlier_distance_km": 17405.3, + "second_furthest_km": 5007.8, + "clarity_ratio": 3.48, + "median_distance_km": 4902.7, + "distances_to_centroid": { + "Saint Albans": 4439.1, + "Ashfield": 4902.7, + "Hervey Bay": 5007.8, + "Dandenong": 4480.9, + "Providence": 17405.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Albans: (-37.73°, 144.80°)", + " Ashfield: (-33.89°, 151.12°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Dandenong: (-37.98°, 145.20°)", + " Providence: (41.82°, -71.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Providence: 17405.3 km from centroid", + " Hervey Bay: 5007.8 km from centroid", + " Ashfield: 4902.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Providence", + "FINAL ANSWER: Providence" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.63513, + "lon": 34.28165, + "name": "Malaba" + }, + { + "lat": -24.95911, + "lon": 31.17025, + "name": "Hlanganani" + }, + { + "lat": 8.43497, + "lon": 12.05107, + "name": "Ganye" + }, + { + "lat": -34.02903, + "lon": 24.76912, + "name": "Humansdorp" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + } + ], + "question": "Which location is the geographic outlier among: Malaba, Hlanganani, Ganye, Humansdorp, Footscray?", + "ground_truth": { + "answer": "Footscray", + "outlier_distance_km": 9286.1, + "second_furthest_km": 5020.7, + "clarity_ratio": 1.85, + "median_distance_km": 3060.8, + "distances_to_centroid": { + "Malaba": 2615.0, + "Hlanganani": 2061.8, + "Ganye": 5020.7, + "Humansdorp": 3060.8, + "Footscray": 9286.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Malaba: (0.64°, 34.28°)", + " Hlanganani: (-24.96°, 31.17°)", + " Ganye: (8.43°, 12.05°)", + " Humansdorp: (-34.03°, 24.77°)", + " Footscray: (-37.80°, 144.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Footscray: 9286.1 km from centroid", + " Ganye: 5020.7 km from centroid", + " Humansdorp: 3060.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Footscray", + "FINAL ANSWER: Footscray" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.18369, + "lon": -98.12306, + "name": "Alamo" + }, + { + "lat": 40.80482, + "lon": -73.33623, + "name": "Dix Hills" + }, + { + "lat": 25.94065, + "lon": -80.2456, + "name": "Carol City" + }, + { + "lat": 32.42389, + "lon": -116.97167, + "name": "Villa del Prado 2da Sección" + }, + { + "lat": 26.99306, + "lon": 31.41605, + "name": "Al Badārī" + } + ], + "question": "Which location is the geographic outlier among: Alamo, Dix Hills, Carol City, Villa del Prado 2da Sección, Al Badārī?", + "ground_truth": { + "answer": "Al Badārī", + "outlier_distance_km": 9294.1, + "second_furthest_km": 4660.2, + "clarity_ratio": 1.99, + "median_distance_km": 3030.2, + "distances_to_centroid": { + "Alamo": 3030.2, + "Dix Hills": 1265.5, + "Carol City": 1349.9, + "Villa del Prado 2da Sección": 4660.2, + "Al Badārī": 9294.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alamo: (26.18°, -98.12°)", + " Dix Hills: (40.80°, -73.34°)", + " Carol City: (25.94°, -80.25°)", + " Villa del Prado 2da Sección: (32.42°, -116.97°)", + " Al Badārī: (26.99°, 31.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Badārī: 9294.1 km from centroid", + " Villa del Prado 2da Sección: 4660.2 km from centroid", + " Alamo: 3030.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Badārī", + "FINAL ANSWER: Al Badārī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -26.68443, + "lon": 153.05705, + "name": "Buderim" + }, + { + "lat": 19.45229, + "lon": -96.96148, + "name": "Coatepec" + } + ], + "question": "Which location is the geographic outlier among: Epping, The Gap, Cranbourne North, Buderim, Coatepec?", + "ground_truth": { + "answer": "Coatepec", + "outlier_distance_km": 18241.5, + "second_furthest_km": 5373.0, + "clarity_ratio": 3.4, + "median_distance_km": 5352.1, + "distances_to_centroid": { + "Epping": 4633.7, + "The Gap": 5352.1, + "Cranbourne North": 4664.1, + "Buderim": 5373.0, + "Coatepec": 18241.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epping: (-37.65°, 145.03°)", + " The Gap: (-27.44°, 152.94°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Buderim: (-26.68°, 153.06°)", + " Coatepec: (19.45°, -96.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coatepec: 18241.5 km from centroid", + " Buderim: 5373.0 km from centroid", + " The Gap: 5352.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coatepec", + "FINAL ANSWER: Coatepec" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.0653, + "lon": -81.78869, + "name": "Auburndale" + }, + { + "lat": 28.38612, + "lon": -80.742, + "name": "Cocoa" + }, + { + "lat": 40.58612, + "lon": -98.38839, + "name": "Hastings" + }, + { + "lat": 45.01052, + "lon": -93.45551, + "name": "Plymouth" + }, + { + "lat": -23.5325, + "lon": -46.79167, + "name": "Osasco" + } + ], + "question": "Which location is the geographic outlier among: Auburndale, Cocoa, Hastings, Plymouth, Osasco?", + "ground_truth": { + "answer": "Osasco", + "outlier_distance_km": 6373.2, + "second_furthest_km": 2653.9, + "clarity_ratio": 2.4, + "median_distance_km": 2528.3, + "distances_to_centroid": { + "Auburndale": 509.4, + "Cocoa": 523.2, + "Hastings": 2528.3, + "Plymouth": 2653.9, + "Osasco": 6373.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auburndale: (28.07°, -81.79°)", + " Cocoa: (28.39°, -80.74°)", + " Hastings: (40.59°, -98.39°)", + " Plymouth: (45.01°, -93.46°)", + " Osasco: (-23.53°, -46.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Osasco: 6373.2 km from centroid", + " Plymouth: 2653.9 km from centroid", + " Hastings: 2528.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Osasco", + "FINAL ANSWER: Osasco" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.8661, + "lon": 12.64973, + "name": "Wittenberg" + }, + { + "lat": 49.95542, + "lon": 18.57479, + "name": "Jastrzębie Zdrój" + }, + { + "lat": 49.63984, + "lon": -1.61636, + "name": "Cherbourg" + }, + { + "lat": 50.58008, + "lon": 16.50164, + "name": "Nowa Ruda" + }, + { + "lat": -11.64083, + "lon": -42.01111, + "name": "Ibipeba" + } + ], + "question": "Which location is the geographic outlier among: Wittenberg, Jastrzębie Zdrój, Cherbourg, Nowa Ruda, Ibipeba?", + "ground_truth": { + "answer": "Ibipeba", + "outlier_distance_km": 7098.2, + "second_furthest_km": 1929.8, + "clarity_ratio": 3.68, + "median_distance_km": 1859.9, + "distances_to_centroid": { + "Wittenberg": 1788.2, + "Jastrzębie Zdrój": 1929.8, + "Cherbourg": 1299.9, + "Nowa Ruda": 1859.9, + "Ibipeba": 7098.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wittenberg: (51.87°, 12.65°)", + " Jastrzębie Zdrój: (49.96°, 18.57°)", + " Cherbourg: (49.64°, -1.62°)", + " Nowa Ruda: (50.58°, 16.50°)", + " Ibipeba: (-11.64°, -42.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ibipeba: 7098.2 km from centroid", + " Jastrzębie Zdrój: 1929.8 km from centroid", + " Nowa Ruda: 1859.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ibipeba", + "FINAL ANSWER: Ibipeba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.67418, + "lon": 31.49686, + "name": "Juhaynah" + }, + { + "lat": 9.03333, + "lon": 38.4, + "name": "Ādīs ‘Alem" + }, + { + "lat": 6.66819, + "lon": 9.16453, + "name": "Obudu" + }, + { + "lat": 8.75225, + "lon": 38.97846, + "name": "Bishoftu" + }, + { + "lat": 25.58896, + "lon": -100.00156, + "name": "Cadereyta Jiménez" + } + ], + "question": "Which location is the geographic outlier among: Juhaynah, Ādīs ‘Alem, Obudu, Bishoftu, Cadereyta Jiménez?", + "ground_truth": { + "answer": "Cadereyta Jiménez", + "outlier_distance_km": 10584.1, + "second_furthest_km": 3910.5, + "clarity_ratio": 2.71, + "median_distance_km": 3841.3, + "distances_to_centroid": { + "Juhaynah": 3147.5, + "Ādīs ‘Alem": 3841.3, + "Obudu": 1139.1, + "Bishoftu": 3910.5, + "Cadereyta Jiménez": 10584.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Juhaynah: (26.67°, 31.50°)", + " Ādīs ‘Alem: (9.03°, 38.40°)", + " Obudu: (6.67°, 9.16°)", + " Bishoftu: (8.75°, 38.98°)", + " Cadereyta Jiménez: (25.59°, -100.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cadereyta Jiménez: 10584.1 km from centroid", + " Bishoftu: 3910.5 km from centroid", + " Ādīs ‘Alem: 3841.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cadereyta Jiménez", + "FINAL ANSWER: Cadereyta Jiménez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -37.0182, + "lon": 174.88019, + "name": "Manurewa" + }, + { + "lat": 33.89205, + "lon": -84.29881, + "name": "Chamblee" + } + ], + "question": "Which location is the geographic outlier among: Wellington, Glen Iris, Gosnells, Manurewa, Chamblee?", + "ground_truth": { + "answer": "Chamblee", + "outlier_distance_km": 18473.9, + "second_furthest_km": 6741.3, + "clarity_ratio": 2.74, + "median_distance_km": 6678.8, + "distances_to_centroid": { + "Wellington": 6678.8, + "Glen Iris": 4125.6, + "Gosnells": 1470.3, + "Manurewa": 6741.3, + "Chamblee": 18473.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wellington: (-41.29°, 174.78°)", + " Glen Iris: (-37.87°, 145.07°)", + " Gosnells: (-32.08°, 116.01°)", + " Manurewa: (-37.02°, 174.88°)", + " Chamblee: (33.89°, -84.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chamblee: 18473.9 km from centroid", + " Manurewa: 6741.3 km from centroid", + " Wellington: 6678.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chamblee", + "FINAL ANSWER: Chamblee" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.46528, + "lon": -45.95806, + "name": "Piumhi" + }, + { + "lat": -26.08111, + "lon": -53.055, + "name": "Francisco Beltrão" + }, + { + "lat": -29.2975, + "lon": -51.50361, + "name": "Carlos Barbosa" + }, + { + "lat": -23.87389, + "lon": -49.80278, + "name": "Wenceslau Braz" + }, + { + "lat": -28.87097, + "lon": 31.89961, + "name": "eSikhaleni" + } + ], + "question": "Which location is the geographic outlier among: Piumhi, Francisco Beltrão, Carlos Barbosa, Wenceslau Braz, eSikhaleni?", + "ground_truth": { + "answer": "eSikhaleni", + "outlier_distance_km": 6406.1, + "second_furthest_km": 1936.3, + "clarity_ratio": 3.31, + "median_distance_km": 1800.0, + "distances_to_centroid": { + "Piumhi": 1383.7, + "Francisco Beltrão": 1936.3, + "Carlos Barbosa": 1800.0, + "Wenceslau Braz": 1638.9, + "eSikhaleni": 6406.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piumhi: (-20.47°, -45.96°)", + " Francisco Beltrão: (-26.08°, -53.05°)", + " Carlos Barbosa: (-29.30°, -51.50°)", + " Wenceslau Braz: (-23.87°, -49.80°)", + " eSikhaleni: (-28.87°, 31.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " eSikhaleni: 6406.1 km from centroid", + " Francisco Beltrão: 1936.3 km from centroid", + " Carlos Barbosa: 1800.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: eSikhaleni", + "FINAL ANSWER: eSikhaleni" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + }, + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + }, + { + "lat": -9.07508, + "lon": -78.59373, + "name": "Chimbote" + } + ], + "question": "Which location is the geographic outlier among: Calamvale, Frankston South, Whangarei, West Pennant Hills, Chimbote?", + "ground_truth": { + "answer": "Chimbote", + "outlier_distance_km": 15718.2, + "second_furthest_km": 6076.2, + "clarity_ratio": 2.59, + "median_distance_km": 4292.6, + "distances_to_centroid": { + "Calamvale": 4292.6, + "Frankston South": 3481.8, + "Whangarei": 6076.2, + "West Pennant Hills": 4004.6, + "Chimbote": 15718.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Calamvale: (-27.62°, 153.05°)", + " Frankston South: (-38.17°, 145.14°)", + " Whangarei: (-35.73°, 174.32°)", + " West Pennant Hills: (-33.75°, 151.05°)", + " Chimbote: (-9.08°, -78.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chimbote: 15718.2 km from centroid", + " Whangarei: 6076.2 km from centroid", + " Calamvale: 4292.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chimbote", + "FINAL ANSWER: Chimbote" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.53139, + "lon": -40.90944, + "name": "Encruzilhada" + }, + { + "lat": -5.795, + "lon": -35.20944, + "name": "Natal" + }, + { + "lat": -30.78991, + "lon": -60.59276, + "name": "San Justo" + }, + { + "lat": -10.66585, + "lon": -76.25525, + "name": "Yanacancha" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + } + ], + "question": "Which location is the geographic outlier among: Encruzilhada, Natal, San Justo, Yanacancha, Seaford?", + "ground_truth": { + "answer": "Seaford", + "outlier_distance_km": 13163.6, + "second_furthest_km": 6766.4, + "clarity_ratio": 1.95, + "median_distance_km": 4829.3, + "distances_to_centroid": { + "Encruzilhada": 2936.1, + "Natal": 2831.9, + "San Justo": 4829.3, + "Yanacancha": 6766.4, + "Seaford": 13163.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Encruzilhada: (-15.53°, -40.91°)", + " Natal: (-5.79°, -35.21°)", + " San Justo: (-30.79°, -60.59°)", + " Yanacancha: (-10.67°, -76.26°)", + " Seaford: (-38.10°, 145.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Seaford: 13163.6 km from centroid", + " Yanacancha: 6766.4 km from centroid", + " San Justo: 4829.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Seaford", + "FINAL ANSWER: Seaford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + }, + { + "lat": 45.13338, + "lon": 8.4525, + "name": "Casale Monferrato" + } + ], + "question": "Which location is the geographic outlier among: Cheltenham, Eastwood, Wahroonga, Doncaster East, Casale Monferrato?", + "ground_truth": { + "answer": "Casale Monferrato", + "outlier_distance_km": 13225.8, + "second_furthest_km": 3432.0, + "clarity_ratio": 3.85, + "median_distance_km": 3431.6, + "distances_to_centroid": { + "Cheltenham": 3149.4, + "Eastwood": 3431.6, + "Wahroonga": 3432.0, + "Doncaster East": 3145.8, + "Casale Monferrato": 13225.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cheltenham: (-37.97°, 145.05°)", + " Eastwood: (-33.79°, 151.08°)", + " Wahroonga: (-33.72°, 151.12°)", + " Doncaster East: (-37.79°, 145.15°)", + " Casale Monferrato: (45.13°, 8.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casale Monferrato: 13225.8 km from centroid", + " Wahroonga: 3432.0 km from centroid", + " Eastwood: 3431.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casale Monferrato", + "FINAL ANSWER: Casale Monferrato" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 57.2145, + "lon": 41.92555, + "name": "Vichuga" + }, + { + "lat": 51.14979, + "lon": 7.34471, + "name": "Hückeswagen" + }, + { + "lat": 47.51683, + "lon": 40.80831, + "name": "Semikarakorsk" + }, + { + "lat": 53.06878, + "lon": -2.52051, + "name": "Nantwich" + }, + { + "lat": 20.967, + "lon": -89.62318, + "name": "Mérida" + } + ], + "question": "Which location is the geographic outlier among: Vichuga, Hückeswagen, Semikarakorsk, Nantwich, Mérida?", + "ground_truth": { + "answer": "Mérida", + "outlier_distance_km": 8290.4, + "second_furthest_km": 3116.7, + "clarity_ratio": 2.66, + "median_distance_km": 3108.2, + "distances_to_centroid": { + "Vichuga": 3116.7, + "Hückeswagen": 809.0, + "Semikarakorsk": 3108.2, + "Nantwich": 802.3, + "Mérida": 8290.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vichuga: (57.21°, 41.93°)", + " Hückeswagen: (51.15°, 7.34°)", + " Semikarakorsk: (47.52°, 40.81°)", + " Nantwich: (53.07°, -2.52°)", + " Mérida: (20.97°, -89.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mérida: 8290.4 km from centroid", + " Vichuga: 3116.7 km from centroid", + " Semikarakorsk: 3108.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mérida", + "FINAL ANSWER: Mérida" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + }, + { + "lat": -37.83834, + "lon": 144.99149, + "name": "South Yarra" + }, + { + "lat": 11.08333, + "lon": 36.88333, + "name": "Ādīs K’idamē" + } + ], + "question": "Which location is the geographic outlier among: Pakenham, Manukau City, Napier, South Yarra, Ādīs K’idamē?", + "ground_truth": { + "answer": "Ādīs K’idamē", + "outlier_distance_km": 11456.1, + "second_furthest_km": 3954.5, + "clarity_ratio": 2.9, + "median_distance_km": 3755.5, + "distances_to_centroid": { + "Pakenham": 1410.8, + "Manukau City": 3755.5, + "Napier": 3954.5, + "South Yarra": 1363.4, + "Ādīs K’idamē": 11456.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pakenham: (-38.07°, 145.47°)", + " Manukau City: (-36.99°, 174.88°)", + " Napier: (-39.49°, 176.91°)", + " South Yarra: (-37.84°, 144.99°)", + " Ādīs K’idamē: (11.08°, 36.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ādīs K’idamē: 11456.1 km from centroid", + " Napier: 3954.5 km from centroid", + " Manukau City: 3755.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ādīs K’idamē", + "FINAL ANSWER: Ādīs K’idamē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -37.75, + "lon": 144.96667, + "name": "Coburg" + }, + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + { + "lat": 35.80167, + "lon": 128.50083, + "name": "Hwawŏn" + } + ], + "question": "Which location is the geographic outlier among: Miranda, Coburg, Pakenham, Tarneit, Hwawŏn?", + "ground_truth": { + "answer": "Hwawŏn", + "outlier_distance_km": 6645.5, + "second_furthest_km": 1761.5, + "clarity_ratio": 3.77, + "median_distance_km": 1726.7, + "distances_to_centroid": { + "Miranda": 1521.8, + "Coburg": 1720.2, + "Pakenham": 1761.5, + "Tarneit": 1726.7, + "Hwawŏn": 6645.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miranda: (-34.04°, 151.10°)", + " Coburg: (-37.75°, 144.97°)", + " Pakenham: (-38.07°, 145.47°)", + " Tarneit: (-37.84°, 144.66°)", + " Hwawŏn: (35.80°, 128.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hwawŏn: 6645.5 km from centroid", + " Pakenham: 1761.5 km from centroid", + " Tarneit: 1726.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hwawŏn", + "FINAL ANSWER: Hwawŏn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + }, + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": 9.44272, + "lon": -0.00991, + "name": "Yendi" + } + ], + "question": "Which location is the geographic outlier among: Canning Vale, Southport, Casula, Frankston East, Yendi?", + "ground_truth": { + "answer": "Yendi", + "outlier_distance_km": 12768.2, + "second_furthest_km": 4022.2, + "clarity_ratio": 3.17, + "median_distance_km": 3793.4, + "distances_to_centroid": { + "Canning Vale": 881.9, + "Southport": 4022.2, + "Casula": 3793.4, + "Frankston East": 3376.8, + "Yendi": 12768.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canning Vale: (-32.06°, 115.92°)", + " Southport: (-27.97°, 153.40°)", + " Casula: (-33.95°, 150.90°)", + " Frankston East: (-38.13°, 145.13°)", + " Yendi: (9.44°, -0.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yendi: 12768.2 km from centroid", + " Southport: 4022.2 km from centroid", + " Casula: 3793.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yendi", + "FINAL ANSWER: Yendi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.71638, + "lon": -74.21195, + "name": "Funza" + }, + { + "lat": -3.20778, + "lon": -43.40361, + "name": "Urbano Santos" + }, + { + "lat": -6.52392, + "lon": -49.85167, + "name": "Canaã dos Carajás" + }, + { + "lat": 10.75773, + "lon": -74.75451, + "name": "Santo Tomás" + }, + { + "lat": 51.38333, + "lon": -0.1, + "name": "Croydon" + } + ], + "question": "Which location is the geographic outlier among: Funza, Urbano Santos, Canaã dos Carajás, Santo Tomás, Croydon?", + "ground_truth": { + "answer": "Croydon", + "outlier_distance_km": 6211.4, + "second_furthest_km": 2929.0, + "clarity_ratio": 2.12, + "median_distance_km": 2868.7, + "distances_to_centroid": { + "Funza": 2929.0, + "Urbano Santos": 1720.7, + "Canaã dos Carajás": 2001.7, + "Santo Tomás": 2868.7, + "Croydon": 6211.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Funza: (4.72°, -74.21°)", + " Urbano Santos: (-3.21°, -43.40°)", + " Canaã dos Carajás: (-6.52°, -49.85°)", + " Santo Tomás: (10.76°, -74.75°)", + " Croydon: (51.38°, -0.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Croydon: 6211.4 km from centroid", + " Funza: 2929.0 km from centroid", + " Santo Tomás: 2868.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Croydon", + "FINAL ANSWER: Croydon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.26858, + "lon": 13.26701, + "name": "Mubi" + }, + { + "lat": 29.84144, + "lon": 31.30084, + "name": "Ḩalwān" + }, + { + "lat": 1.7471, + "lon": 40.05732, + "name": "Wajir" + }, + { + "lat": -29.01269, + "lon": 29.86619, + "name": "Estcourt" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + } + ], + "question": "Which location is the geographic outlier among: Mubi, Ḩalwān, Wajir, Estcourt, Blacktown?", + "ground_truth": { + "answer": "Blacktown", + "outlier_distance_km": 10469.6, + "second_furthest_km": 4692.5, + "clarity_ratio": 2.23, + "median_distance_km": 4438.1, + "distances_to_centroid": { + "Mubi": 4692.5, + "Ḩalwān": 4438.1, + "Wajir": 1590.5, + "Estcourt": 3689.5, + "Blacktown": 10469.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mubi: (10.27°, 13.27°)", + " Ḩalwān: (29.84°, 31.30°)", + " Wajir: (1.75°, 40.06°)", + " Estcourt: (-29.01°, 29.87°)", + " Blacktown: (-33.77°, 150.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blacktown: 10469.6 km from centroid", + " Mubi: 4692.5 km from centroid", + " Ḩalwān: 4438.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blacktown", + "FINAL ANSWER: Blacktown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.1275, + "lon": -39.73222, + "name": "Boa Viagem" + }, + { + "lat": -26.56472, + "lon": -52.32833, + "name": "Abelardo Luz" + }, + { + "lat": -34.66267, + "lon": -58.69819, + "name": "San Antonio de Padua" + }, + { + "lat": -12.13556, + "lon": -38.41917, + "name": "Alagoinhas" + }, + { + "lat": 22.81027, + "lon": 115.83058, + "name": "Jieshi" + } + ], + "question": "Which location is the geographic outlier among: Boa Viagem, Abelardo Luz, San Antonio de Padua, Alagoinhas, Jieshi?", + "ground_truth": { + "answer": "Jieshi", + "outlier_distance_km": 14619.1, + "second_furthest_km": 5155.3, + "clarity_ratio": 2.84, + "median_distance_km": 4296.1, + "distances_to_centroid": { + "Boa Viagem": 2836.8, + "Abelardo Luz": 4296.1, + "San Antonio de Padua": 5155.3, + "Alagoinhas": 2588.2, + "Jieshi": 14619.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boa Viagem: (-5.13°, -39.73°)", + " Abelardo Luz: (-26.56°, -52.33°)", + " San Antonio de Padua: (-34.66°, -58.70°)", + " Alagoinhas: (-12.14°, -38.42°)", + " Jieshi: (22.81°, 115.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jieshi: 14619.1 km from centroid", + " San Antonio de Padua: 5155.3 km from centroid", + " Abelardo Luz: 4296.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jieshi", + "FINAL ANSWER: Jieshi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.94917, + "lon": 118.29583, + "name": "Suqian" + }, + { + "lat": 10.48098, + "lon": 79.39939, + "name": "Madukkūr" + }, + { + "lat": 36.2, + "lon": 139.28333, + "name": "Fukayachō" + }, + { + "lat": -6.9375, + "lon": 109.1325, + "name": "Adiwerna" + }, + { + "lat": 4.13238, + "lon": -73.62564, + "name": "Villavicencio" + } + ], + "question": "Which location is the geographic outlier among: Suqian, Madukkūr, Fukayachō, Adiwerna, Villavicencio?", + "ground_truth": { + "answer": "Villavicencio", + "outlier_distance_km": 15879.1, + "second_furthest_km": 6747.7, + "clarity_ratio": 2.35, + "median_distance_km": 4825.3, + "distances_to_centroid": { + "Suqian": 4825.3, + "Madukkūr": 775.5, + "Fukayachō": 6747.7, + "Adiwerna": 4562.0, + "Villavicencio": 15879.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Suqian: (33.95°, 118.30°)", + " Madukkūr: (10.48°, 79.40°)", + " Fukayachō: (36.20°, 139.28°)", + " Adiwerna: (-6.94°, 109.13°)", + " Villavicencio: (4.13°, -73.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Villavicencio: 15879.1 km from centroid", + " Fukayachō: 6747.7 km from centroid", + " Suqian: 4825.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Villavicencio", + "FINAL ANSWER: Villavicencio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + }, + { + "lat": -33.79068, + "lon": 150.6693, + "name": "Glenmore Park" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -22.07889, + "lon": -54.78944, + "name": "Itaporã" + } + ], + "question": "Which location is the geographic outlier among: Manly, Glenmore Park, Mackay, Banora Point, Itaporã?", + "ground_truth": { + "answer": "Itaporã", + "outlier_distance_km": 14231.7, + "second_furthest_km": 4253.0, + "clarity_ratio": 3.35, + "median_distance_km": 4017.4, + "distances_to_centroid": { + "Manly": 3975.1, + "Glenmore Park": 3917.9, + "Mackay": 4017.4, + "Banora Point": 4253.0, + "Itaporã": 14231.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manly: (-33.80°, 151.29°)", + " Glenmore Park: (-33.79°, 150.67°)", + " Mackay: (-21.15°, 149.17°)", + " Banora Point: (-28.21°, 153.54°)", + " Itaporã: (-22.08°, -54.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itaporã: 14231.7 km from centroid", + " Banora Point: 4253.0 km from centroid", + " Mackay: 4017.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itaporã", + "FINAL ANSWER: Itaporã" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.57654, + "lon": -3.92658, + "name": "Torrelodones" + }, + { + "lat": 40.94477, + "lon": 14.3714, + "name": "Acerra" + }, + { + "lat": 38.47917, + "lon": -1.325, + "name": "Jumilla" + }, + { + "lat": 51.23536, + "lon": -0.57427, + "name": "Guildford" + }, + { + "lat": 36.6, + "lon": 140.65, + "name": "Hitachi" + } + ], + "question": "Which location is the geographic outlier among: Torrelodones, Acerra, Jumilla, Guildford, Hitachi?", + "ground_truth": { + "answer": "Hitachi", + "outlier_distance_km": 8840.3, + "second_furthest_km": 2814.6, + "clarity_ratio": 3.14, + "median_distance_km": 2661.2, + "distances_to_centroid": { + "Torrelodones": 2814.6, + "Acerra": 1293.1, + "Jumilla": 2661.2, + "Guildford": 2543.9, + "Hitachi": 8840.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Torrelodones: (40.58°, -3.93°)", + " Acerra: (40.94°, 14.37°)", + " Jumilla: (38.48°, -1.32°)", + " Guildford: (51.24°, -0.57°)", + " Hitachi: (36.60°, 140.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hitachi: 8840.3 km from centroid", + " Torrelodones: 2814.6 km from centroid", + " Jumilla: 2661.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hitachi", + "FINAL ANSWER: Hitachi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.68281, + "lon": -88.35146, + "name": "Oswego" + }, + { + "lat": 19.28428, + "lon": -99.73394, + "name": "Zinacantepec" + }, + { + "lat": 33.53375, + "lon": -82.13067, + "name": "Evans" + }, + { + "lat": 43.5789, + "lon": -79.6583, + "name": "Mississauga" + }, + { + "lat": -15.84003, + "lon": -70.02198, + "name": "Puno" + } + ], + "question": "Which location is the geographic outlier among: Oswego, Zinacantepec, Evans, Mississauga, Puno?", + "ground_truth": { + "answer": "Puno", + "outlier_distance_km": 4728.9, + "second_furthest_km": 2163.4, + "clarity_ratio": 2.19, + "median_distance_km": 1958.5, + "distances_to_centroid": { + "Oswego": 1958.5, + "Zinacantepec": 1722.8, + "Evans": 1026.1, + "Mississauga": 2163.4, + "Puno": 4728.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oswego: (41.68°, -88.35°)", + " Zinacantepec: (19.28°, -99.73°)", + " Evans: (33.53°, -82.13°)", + " Mississauga: (43.58°, -79.66°)", + " Puno: (-15.84°, -70.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Puno: 4728.9 km from centroid", + " Mississauga: 2163.4 km from centroid", + " Oswego: 1958.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Puno", + "FINAL ANSWER: Puno" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.89611, + "lon": -51.37944, + "name": "Andradina" + }, + { + "lat": -37.15276, + "lon": -58.48838, + "name": "Ayacucho" + }, + { + "lat": -5.89056, + "lon": -38.62194, + "name": "Jaguaribe" + }, + { + "lat": -23.51, + "lon": -46.41566, + "name": "Vila Curuca" + }, + { + "lat": 42.69764, + "lon": 2.89541, + "name": "Perpignan" + } + ], + "question": "Which location is the geographic outlier among: Andradina, Ayacucho, Jaguaribe, Vila Curuca, Perpignan?", + "ground_truth": { + "answer": "Perpignan", + "outlier_distance_km": 7105.4, + "second_furthest_km": 3730.7, + "clarity_ratio": 1.9, + "median_distance_km": 1923.4, + "distances_to_centroid": { + "Andradina": 1923.4, + "Ayacucho": 3730.7, + "Jaguaribe": 341.1, + "Vila Curuca": 1829.7, + "Perpignan": 7105.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Andradina: (-20.90°, -51.38°)", + " Ayacucho: (-37.15°, -58.49°)", + " Jaguaribe: (-5.89°, -38.62°)", + " Vila Curuca: (-23.51°, -46.42°)", + " Perpignan: (42.70°, 2.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perpignan: 7105.4 km from centroid", + " Ayacucho: 3730.7 km from centroid", + " Andradina: 1923.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perpignan", + "FINAL ANSWER: Perpignan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.13204, + "lon": 13.58312, + "name": "Coswig" + }, + { + "lat": 52.18893, + "lon": 0.99774, + "name": "Stowmarket" + }, + { + "lat": 48.98693, + "lon": 2.44892, + "name": "Gonesse" + }, + { + "lat": 50.72044, + "lon": -3.49646, + "name": "Heavitree" + }, + { + "lat": -24.59165, + "lon": 27.41155, + "name": "Thabazimbi" + } + ], + "question": "Which location is the geographic outlier among: Coswig, Stowmarket, Gonesse, Heavitree, Thabazimbi?", + "ground_truth": { + "answer": "Thabazimbi", + "outlier_distance_km": 7000.9, + "second_furthest_km": 1920.8, + "clarity_ratio": 3.64, + "median_distance_km": 1916.0, + "distances_to_centroid": { + "Coswig": 1770.6, + "Stowmarket": 1920.8, + "Gonesse": 1551.1, + "Heavitree": 1916.0, + "Thabazimbi": 7000.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coswig: (51.13°, 13.58°)", + " Stowmarket: (52.19°, 1.00°)", + " Gonesse: (48.99°, 2.45°)", + " Heavitree: (50.72°, -3.50°)", + " Thabazimbi: (-24.59°, 27.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thabazimbi: 7000.9 km from centroid", + " Stowmarket: 1920.8 km from centroid", + " Heavitree: 1916.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thabazimbi", + "FINAL ANSWER: Thabazimbi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.26881, + "lon": 31.15232, + "name": "Abnūb" + }, + { + "lat": -29.53897, + "lon": 31.21439, + "name": "Ballitoville" + }, + { + "lat": -26.93366, + "lon": 29.24152, + "name": "Standerton" + }, + { + "lat": -34.18307, + "lon": 22.14605, + "name": "Mossel Bay" + }, + { + "lat": 32.98101, + "lon": -80.03259, + "name": "Goose Creek" + } + ], + "question": "Which location is the geographic outlier among: Abnūb, Ballitoville, Standerton, Mossel Bay, Goose Creek?", + "ground_truth": { + "answer": "Goose Creek", + "outlier_distance_km": 10076.2, + "second_furthest_km": 4543.2, + "clarity_ratio": 2.22, + "median_distance_km": 3658.0, + "distances_to_centroid": { + "Abnūb": 4543.2, + "Ballitoville": 3658.0, + "Standerton": 3323.0, + "Mossel Bay": 3503.5, + "Goose Creek": 10076.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abnūb: (27.27°, 31.15°)", + " Ballitoville: (-29.54°, 31.21°)", + " Standerton: (-26.93°, 29.24°)", + " Mossel Bay: (-34.18°, 22.15°)", + " Goose Creek: (32.98°, -80.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Goose Creek: 10076.2 km from centroid", + " Abnūb: 4543.2 km from centroid", + " Ballitoville: 3658.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Goose Creek", + "FINAL ANSWER: Goose Creek" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.96807, + "lon": 174.79875, + "name": "Mangere" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + }, + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": 0.05196, + "lon": 35.72734, + "name": "Eldama Ravine" + } + ], + "question": "Which location is the geographic outlier among: Mangere, Bracken Ridge, Adelaide, Palm Beach, Eldama Ravine?", + "ground_truth": { + "answer": "Eldama Ravine", + "outlier_distance_km": 10551.7, + "second_furthest_km": 4305.1, + "clarity_ratio": 2.45, + "median_distance_km": 2234.1, + "distances_to_centroid": { + "Mangere": 4305.1, + "Bracken Ridge": 2189.1, + "Adelaide": 1274.0, + "Palm Beach": 2234.1, + "Eldama Ravine": 10551.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mangere: (-36.97°, 174.80°)", + " Bracken Ridge: (-27.32°, 153.03°)", + " Adelaide: (-34.93°, 138.60°)", + " Palm Beach: (-28.12°, 153.47°)", + " Eldama Ravine: (0.05°, 35.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eldama Ravine: 10551.7 km from centroid", + " Mangere: 4305.1 km from centroid", + " Palm Beach: 2234.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eldama Ravine", + "FINAL ANSWER: Eldama Ravine" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.86621, + "lon": 152.3479, + "name": "Bundaberg" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + }, + { + "lat": 21.4504, + "lon": -158.01503, + "name": "Mililani Town" + } + ], + "question": "Which location is the geographic outlier among: Bundaberg, Eight Mile Plains, Busselton, Levin, Mililani Town?", + "ground_truth": { + "answer": "Mililani Town", + "outlier_distance_km": 13269.0, + "second_furthest_km": 8313.1, + "clarity_ratio": 1.6, + "median_distance_km": 6601.4, + "distances_to_centroid": { + "Bundaberg": 6579.8, + "Eight Mile Plains": 6601.4, + "Busselton": 3062.4, + "Levin": 8313.1, + "Mililani Town": 13269.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bundaberg: (-24.87°, 152.35°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Busselton: (-33.65°, 115.35°)", + " Levin: (-40.63°, 175.28°)", + " Mililani Town: (21.45°, -158.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mililani Town: 13269.0 km from centroid", + " Levin: 8313.1 km from centroid", + " Eight Mile Plains: 6601.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mililani Town", + "FINAL ANSWER: Mililani Town" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.9713, + "lon": 110.0666, + "name": "Weleri" + }, + { + "lat": 22.37303, + "lon": 110.94746, + "name": "Xinyi" + }, + { + "lat": 14.905, + "lon": 76.38527, + "name": "Kūdligi" + }, + { + "lat": 13.69634, + "lon": 100.54212, + "name": "Yan Nawa" + }, + { + "lat": -18.59333, + "lon": -39.73222, + "name": "Conceição da Barra" + } + ], + "question": "Which location is the geographic outlier among: Weleri, Xinyi, Kūdligi, Yan Nawa, Conceição da Barra?", + "ground_truth": { + "answer": "Conceição da Barra", + "outlier_distance_km": 12438.1, + "second_furthest_km": 4638.8, + "clarity_ratio": 2.68, + "median_distance_km": 4469.7, + "distances_to_centroid": { + "Weleri": 4469.7, + "Xinyi": 4638.8, + "Kūdligi": 1209.2, + "Yan Nawa": 3308.1, + "Conceição da Barra": 12438.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Weleri: (-6.97°, 110.07°)", + " Xinyi: (22.37°, 110.95°)", + " Kūdligi: (14.90°, 76.39°)", + " Yan Nawa: (13.70°, 100.54°)", + " Conceição da Barra: (-18.59°, -39.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Conceição da Barra: 12438.1 km from centroid", + " Xinyi: 4638.8 km from centroid", + " Weleri: 4469.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Conceição da Barra", + "FINAL ANSWER: Conceição da Barra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.38865, + "lon": 78.81048, + "name": "Sirsilla" + }, + { + "lat": -8.5098, + "lon": 115.2654, + "name": "Ubud" + }, + { + "lat": 42.53306, + "lon": 124.04028, + "name": "Kaiyuan" + }, + { + "lat": 37.35222, + "lon": 101.7393, + "name": "Quankou" + }, + { + "lat": -26.76083, + "lon": -53.1725, + "name": "Maravilha" + } + ], + "question": "Which location is the geographic outlier among: Sirsilla, Ubud, Kaiyuan, Quankou, Maravilha?", + "ground_truth": { + "answer": "Maravilha", + "outlier_distance_km": 14241.0, + "second_furthest_km": 5884.4, + "clarity_ratio": 2.42, + "median_distance_km": 5193.1, + "distances_to_centroid": { + "Sirsilla": 870.6, + "Ubud": 5193.1, + "Kaiyuan": 5884.4, + "Quankou": 3940.5, + "Maravilha": 14241.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sirsilla: (18.39°, 78.81°)", + " Ubud: (-8.51°, 115.27°)", + " Kaiyuan: (42.53°, 124.04°)", + " Quankou: (37.35°, 101.74°)", + " Maravilha: (-26.76°, -53.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maravilha: 14241.0 km from centroid", + " Kaiyuan: 5884.4 km from centroid", + " Ubud: 5193.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maravilha", + "FINAL ANSWER: Maravilha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + }, + { + "lat": -37.2, + "lon": 174.95, + "name": "Pukekohe East" + }, + { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + }, + { + "lat": 36.06739, + "lon": 139.67498, + "name": "Kukichūō" + } + ], + "question": "Which location is the geographic outlier among: Bairnsdale, Caboolture, Pukekohe East, Greensborough, Kukichūō?", + "ground_truth": { + "answer": "Kukichūō", + "outlier_distance_km": 6450.7, + "second_furthest_km": 2867.7, + "clarity_ratio": 2.25, + "median_distance_km": 2000.9, + "distances_to_centroid": { + "Bairnsdale": 1946.2, + "Caboolture": 710.3, + "Pukekohe East": 2867.7, + "Greensborough": 2000.9, + "Kukichūō": 6450.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bairnsdale: (-37.82°, 147.61°)", + " Caboolture: (-27.08°, 152.95°)", + " Pukekohe East: (-37.20°, 174.95°)", + " Greensborough: (-37.70°, 145.10°)", + " Kukichūō: (36.07°, 139.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kukichūō: 6450.7 km from centroid", + " Pukekohe East: 2867.7 km from centroid", + " Greensborough: 2000.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kukichūō", + "FINAL ANSWER: Kukichūō" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": 4.71131, + "lon": 6.79084, + "name": "Obonoma" + } + ], + "question": "Which location is the geographic outlier among: Miranda, Auburn, Lidcombe, Kensington, Obonoma?", + "ground_truth": { + "answer": "Obonoma", + "outlier_distance_km": 12772.5, + "second_furthest_km": 2907.6, + "clarity_ratio": 4.39, + "median_distance_km": 2898.7, + "distances_to_centroid": { + "Miranda": 2898.7, + "Auburn": 2889.1, + "Lidcombe": 2890.0, + "Kensington": 2907.6, + "Obonoma": 12772.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miranda: (-34.04°, 151.10°)", + " Auburn: (-33.85°, 151.03°)", + " Lidcombe: (-33.86°, 151.04°)", + " Kensington: (-33.92°, 151.22°)", + " Obonoma: (4.71°, 6.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Obonoma: 12772.5 km from centroid", + " Kensington: 2907.6 km from centroid", + " Miranda: 2898.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Obonoma", + "FINAL ANSWER: Obonoma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.55185, + "lon": -121.36467, + "name": "Rosemont" + }, + { + "lat": 40.58844, + "lon": -73.65791, + "name": "Long Beach" + }, + { + "lat": 32.58847, + "lon": -96.95612, + "name": "Cedar Hill" + }, + { + "lat": 45.21012, + "lon": -123.19872, + "name": "McMinnville" + }, + { + "lat": 33.68333, + "lon": 135.35, + "name": "Shirahama" + } + ], + "question": "Which location is the geographic outlier among: Rosemont, Long Beach, Cedar Hill, McMinnville, Shirahama?", + "ground_truth": { + "answer": "Shirahama", + "outlier_distance_km": 11945.3, + "second_furthest_km": 5575.7, + "clarity_ratio": 2.14, + "median_distance_km": 5477.6, + "distances_to_centroid": { + "Rosemont": 5575.7, + "Long Beach": 1542.9, + "Cedar Hill": 3737.3, + "McMinnville": 5477.6, + "Shirahama": 11945.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rosemont: (38.55°, -121.36°)", + " Long Beach: (40.59°, -73.66°)", + " Cedar Hill: (32.59°, -96.96°)", + " McMinnville: (45.21°, -123.20°)", + " Shirahama: (33.68°, 135.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shirahama: 11945.3 km from centroid", + " Rosemont: 5575.7 km from centroid", + " McMinnville: 5477.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shirahama", + "FINAL ANSWER: Shirahama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.1272, + "lon": -15.4314, + "name": "Stadtzentrum" + }, + { + "lat": 49.22565, + "lon": 12.65501, + "name": "Cham" + }, + { + "lat": 51.42167, + "lon": 5.55972, + "name": "Geldrop" + }, + { + "lat": 51.75769, + "lon": 14.32888, + "name": "Cottbus" + }, + { + "lat": 6.98789, + "lon": -73.04953, + "name": "Piedecuesta" + } + ], + "question": "Which location is the geographic outlier among: Stadtzentrum, Cham, Geldrop, Cottbus, Piedecuesta?", + "ground_truth": { + "answer": "Piedecuesta", + "outlier_distance_km": 7066.5, + "second_furthest_km": 2544.2, + "clarity_ratio": 2.78, + "median_distance_km": 2310.9, + "distances_to_centroid": { + "Stadtzentrum": 1115.2, + "Cham": 2310.9, + "Geldrop": 2030.1, + "Cottbus": 2544.2, + "Piedecuesta": 7066.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stadtzentrum: (28.13°, -15.43°)", + " Cham: (49.23°, 12.66°)", + " Geldrop: (51.42°, 5.56°)", + " Cottbus: (51.76°, 14.33°)", + " Piedecuesta: (6.99°, -73.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piedecuesta: 7066.5 km from centroid", + " Cottbus: 2544.2 km from centroid", + " Cham: 2310.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piedecuesta", + "FINAL ANSWER: Piedecuesta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.32509, + "lon": -72.6412, + "name": "Northampton" + }, + { + "lat": 18.85254, + "lon": -99.22537, + "name": "Temixco" + }, + { + "lat": 18.2025, + "lon": -98.04864, + "name": "Acatlán de Osorio" + }, + { + "lat": 41.95753, + "lon": -88.0809, + "name": "Bloomingdale" + }, + { + "lat": 31.15671, + "lon": 30.14775, + "name": "‘Izbat ‘Alī as Sayyid" + } + ], + "question": "Which location is the geographic outlier among: Northampton, Temixco, Acatlán de Osorio, Bloomingdale, ‘Izbat ‘Alī as Sayyid?", + "ground_truth": { + "answer": "‘Izbat ‘Alī as Sayyid", + "outlier_distance_km": 8795.3, + "second_furthest_km": 3621.6, + "clarity_ratio": 2.43, + "median_distance_km": 3546.4, + "distances_to_centroid": { + "Northampton": 1458.0, + "Temixco": 3621.6, + "Acatlán de Osorio": 3546.4, + "Bloomingdale": 2376.2, + "‘Izbat ‘Alī as Sayyid": 8795.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Northampton: (42.33°, -72.64°)", + " Temixco: (18.85°, -99.23°)", + " Acatlán de Osorio: (18.20°, -98.05°)", + " Bloomingdale: (41.96°, -88.08°)", + " ‘Izbat ‘Alī as Sayyid: (31.16°, 30.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " ‘Izbat ‘Alī as Sayyid: 8795.3 km from centroid", + " Temixco: 3621.6 km from centroid", + " Acatlán de Osorio: 3546.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: ‘Izbat ‘Alī as Sayyid", + "FINAL ANSWER: ‘Izbat ‘Alī as Sayyid" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.7511, + "lon": 151.28886, + "name": "Dee Why" + }, + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + }, + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": 42.37537, + "lon": -72.51925, + "name": "Amherst Center" + } + ], + "question": "Which location is the geographic outlier among: Dee Why, Pascoe Vale, Reservoir, Eastwood, Amherst Center?", + "ground_truth": { + "answer": "Amherst Center", + "outlier_distance_km": 17518.8, + "second_furthest_km": 4884.1, + "clarity_ratio": 3.59, + "median_distance_km": 4865.4, + "distances_to_centroid": { + "Dee Why": 4884.1, + "Pascoe Vale": 4396.6, + "Reservoir": 4401.8, + "Eastwood": 4865.4, + "Amherst Center": 17518.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dee Why: (-33.75°, 151.29°)", + " Pascoe Vale: (-37.73°, 144.93°)", + " Reservoir: (-37.72°, 145.00°)", + " Eastwood: (-33.79°, 151.08°)", + " Amherst Center: (42.38°, -72.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amherst Center: 17518.8 km from centroid", + " Dee Why: 4884.1 km from centroid", + " Eastwood: 4865.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amherst Center", + "FINAL ANSWER: Amherst Center" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + }, + { + "lat": -33.76667, + "lon": 150.81667, + "name": "Mount Druitt" + }, + { + "lat": 36.49889, + "lon": 111.70472, + "name": "Xinzhi" + } + ], + "question": "Which location is the geographic outlier among: Mooroolbark, Cranbourne West, Bendigo, Mount Druitt, Xinzhi?", + "ground_truth": { + "answer": "Xinzhi", + "outlier_distance_km": 7126.7, + "second_furthest_km": 1875.5, + "clarity_ratio": 3.8, + "median_distance_km": 1843.9, + "distances_to_centroid": { + "Mooroolbark": 1843.9, + "Cranbourne West": 1875.5, + "Bendigo": 1707.1, + "Mount Druitt": 1717.8, + "Xinzhi": 7126.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mooroolbark: (-37.78°, 145.32°)", + " Cranbourne West: (-38.10°, 145.27°)", + " Bendigo: (-36.76°, 144.28°)", + " Mount Druitt: (-33.77°, 150.82°)", + " Xinzhi: (36.50°, 111.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xinzhi: 7126.7 km from centroid", + " Cranbourne West: 1875.5 km from centroid", + " Mooroolbark: 1843.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xinzhi", + "FINAL ANSWER: Xinzhi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.02903, + "lon": 24.76912, + "name": "Humansdorp" + }, + { + "lat": 7.73855, + "lon": -2.1036, + "name": "Wankyi" + }, + { + "lat": -27.20841, + "lon": 26.94855, + "name": "Viljoenskroon" + }, + { + "lat": 9.8, + "lon": 38.4, + "name": "Gebre Guracha" + }, + { + "lat": -23.50167, + "lon": -47.45806, + "name": "Sorocaba" + } + ], + "question": "Which location is the geographic outlier among: Humansdorp, Wankyi, Viljoenskroon, Gebre Guracha, Sorocaba?", + "ground_truth": { + "answer": "Sorocaba", + "outlier_distance_km": 5931.7, + "second_furthest_km": 4225.2, + "clarity_ratio": 1.4, + "median_distance_km": 2839.7, + "distances_to_centroid": { + "Humansdorp": 2839.7, + "Wankyi": 2611.1, + "Viljoenskroon": 2484.2, + "Gebre Guracha": 4225.2, + "Sorocaba": 5931.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Humansdorp: (-34.03°, 24.77°)", + " Wankyi: (7.74°, -2.10°)", + " Viljoenskroon: (-27.21°, 26.95°)", + " Gebre Guracha: (9.80°, 38.40°)", + " Sorocaba: (-23.50°, -47.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sorocaba: 5931.7 km from centroid", + " Gebre Guracha: 4225.2 km from centroid", + " Humansdorp: 2839.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sorocaba", + "FINAL ANSWER: Sorocaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.26419, + "lon": 78.4056, + "name": "Babrāla" + }, + { + "lat": 21.18608, + "lon": 106.07631, + "name": "Bắc Ninh" + }, + { + "lat": 40.16667, + "lon": 94.68333, + "name": "Dunhuang" + }, + { + "lat": 22.94849, + "lon": 88.01954, + "name": "Srirāmpur" + }, + { + "lat": 21.52631, + "lon": -102.24024, + "name": "Encarnación de Díaz" + } + ], + "question": "Which location is the geographic outlier among: Babrāla, Bắc Ninh, Dunhuang, Srirāmpur, Encarnación de Díaz?", + "ground_truth": { + "answer": "Encarnación de Díaz", + "outlier_distance_km": 14014.3, + "second_furthest_km": 5391.3, + "clarity_ratio": 2.6, + "median_distance_km": 4097.2, + "distances_to_centroid": { + "Babrāla": 2506.5, + "Bắc Ninh": 5391.3, + "Dunhuang": 4097.2, + "Srirāmpur": 3548.6, + "Encarnación de Díaz": 14014.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Babrāla: (28.26°, 78.41°)", + " Bắc Ninh: (21.19°, 106.08°)", + " Dunhuang: (40.17°, 94.68°)", + " Srirāmpur: (22.95°, 88.02°)", + " Encarnación de Díaz: (21.53°, -102.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Encarnación de Díaz: 14014.3 km from centroid", + " Bắc Ninh: 5391.3 km from centroid", + " Dunhuang: 4097.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Encarnación de Díaz", + "FINAL ANSWER: Encarnación de Díaz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.79802, + "lon": -93.5269, + "name": "Shakopee" + }, + { + "lat": 41.80503, + "lon": -87.86923, + "name": "La Grange" + }, + { + "lat": 43.72267, + "lon": -79.26052, + "name": "Kennedy Park" + }, + { + "lat": 40.72371, + "lon": -73.95097, + "name": "Greenpoint" + }, + { + "lat": 49.759, + "lon": 9.50852, + "name": "Wertheim" + } + ], + "question": "Which location is the geographic outlier among: Shakopee, La Grange, Kennedy Park, Greenpoint, Wertheim?", + "ground_truth": { + "answer": "Wertheim", + "outlier_distance_km": 5453.9, + "second_furthest_km": 2251.2, + "clarity_ratio": 2.42, + "median_distance_km": 1870.9, + "distances_to_centroid": { + "Shakopee": 2251.2, + "La Grange": 1870.9, + "Kennedy Park": 1139.8, + "Greenpoint": 825.9, + "Wertheim": 5453.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shakopee: (44.80°, -93.53°)", + " La Grange: (41.81°, -87.87°)", + " Kennedy Park: (43.72°, -79.26°)", + " Greenpoint: (40.72°, -73.95°)", + " Wertheim: (49.76°, 9.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wertheim: 5453.9 km from centroid", + " Shakopee: 2251.2 km from centroid", + " La Grange: 1870.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wertheim", + "FINAL ANSWER: Wertheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.7287, + "lon": 27.87, + "name": "Hartbeespoort" + }, + { + "lat": 8.43497, + "lon": 12.05107, + "name": "Ganye" + }, + { + "lat": 6.15038, + "lon": 6.83042, + "name": "Nkpor" + }, + { + "lat": -25.44141, + "lon": 27.51114, + "name": "Hartbeestfontein-A" + }, + { + "lat": 34.24469, + "lon": 118.22113, + "name": "Qipan" + } + ], + "question": "Which location is the geographic outlier among: Hartbeespoort, Ganye, Nkpor, Hartbeestfontein-A, Qipan?", + "ground_truth": { + "answer": "Qipan", + "outlier_distance_km": 9094.3, + "second_furthest_km": 3590.9, + "clarity_ratio": 2.53, + "median_distance_km": 3093.1, + "distances_to_centroid": { + "Hartbeespoort": 3031.3, + "Ganye": 3093.1, + "Nkpor": 3590.9, + "Hartbeestfontein-A": 3017.0, + "Qipan": 9094.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hartbeespoort: (-25.73°, 27.87°)", + " Ganye: (8.43°, 12.05°)", + " Nkpor: (6.15°, 6.83°)", + " Hartbeestfontein-A: (-25.44°, 27.51°)", + " Qipan: (34.24°, 118.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qipan: 9094.3 km from centroid", + " Nkpor: 3590.9 km from centroid", + " Ganye: 3093.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qipan", + "FINAL ANSWER: Qipan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -35.28346, + "lon": 149.12807, + "name": "Canberra" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": 11.67478, + "lon": 10.19069, + "name": "Azare" + } + ], + "question": "Which location is the geographic outlier among: Kensington, Canning Vale, Canberra, Mackay, Azare?", + "ground_truth": { + "answer": "Azare", + "outlier_distance_km": 12015.9, + "second_furthest_km": 3753.5, + "clarity_ratio": 3.2, + "median_distance_km": 3600.0, + "distances_to_centroid": { + "Kensington": 3753.5, + "Canning Vale": 1104.7, + "Canberra": 3600.0, + "Mackay": 3512.5, + "Azare": 12015.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kensington: (-33.92°, 151.22°)", + " Canning Vale: (-32.06°, 115.92°)", + " Canberra: (-35.28°, 149.13°)", + " Mackay: (-21.15°, 149.17°)", + " Azare: (11.67°, 10.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Azare: 12015.9 km from centroid", + " Kensington: 3753.5 km from centroid", + " Canberra: 3600.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Azare", + "FINAL ANSWER: Azare" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.01528, + "lon": -48.01056, + "name": "Conchas" + }, + { + "lat": -1.12889, + "lon": -47.62, + "name": "Igarapé-Açu" + }, + { + "lat": -29.64833, + "lon": -51.17389, + "name": "Estância Velha" + }, + { + "lat": -10.26389, + "lon": -40.19583, + "name": "Jaguarari" + }, + { + "lat": 16.33782, + "lon": 76.13173, + "name": "Muddebihāl" + } + ], + "question": "Which location is the geographic outlier among: Conchas, Igarapé-Açu, Estância Velha, Jaguarari, Muddebihāl?", + "ground_truth": { + "answer": "Muddebihāl", + "outlier_distance_km": 11182.2, + "second_furthest_km": 3751.2, + "clarity_ratio": 2.98, + "median_distance_km": 3129.6, + "distances_to_centroid": { + "Conchas": 3129.6, + "Igarapé-Açu": 2965.9, + "Estância Velha": 3751.2, + "Jaguarari": 1975.5, + "Muddebihāl": 11182.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Conchas: (-23.02°, -48.01°)", + " Igarapé-Açu: (-1.13°, -47.62°)", + " Estância Velha: (-29.65°, -51.17°)", + " Jaguarari: (-10.26°, -40.20°)", + " Muddebihāl: (16.34°, 76.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Muddebihāl: 11182.2 km from centroid", + " Estância Velha: 3751.2 km from centroid", + " Conchas: 3129.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Muddebihāl", + "FINAL ANSWER: Muddebihāl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.75222, + "lon": -67.39778, + "name": "Boca do Acre" + }, + { + "lat": -23.26917, + "lon": -51.04806, + "name": "Ibiporã" + }, + { + "lat": 7.3915, + "lon": -73.49574, + "name": "Sabana de Torres" + }, + { + "lat": -1.515, + "lon": -48.04472, + "name": "Bujaru" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + } + ], + "question": "Which location is the geographic outlier among: Boca do Acre, Ibiporã, Sabana de Torres, Bujaru, Canning Vale?", + "ground_truth": { + "answer": "Canning Vale", + "outlier_distance_km": 13608.1, + "second_furthest_km": 5784.9, + "clarity_ratio": 2.35, + "median_distance_km": 4667.3, + "distances_to_centroid": { + "Boca do Acre": 4667.3, + "Ibiporã": 3060.9, + "Sabana de Torres": 5784.9, + "Bujaru": 2798.9, + "Canning Vale": 13608.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boca do Acre: (-8.75°, -67.40°)", + " Ibiporã: (-23.27°, -51.05°)", + " Sabana de Torres: (7.39°, -73.50°)", + " Bujaru: (-1.51°, -48.04°)", + " Canning Vale: (-32.06°, 115.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Canning Vale: 13608.1 km from centroid", + " Sabana de Torres: 5784.9 km from centroid", + " Boca do Acre: 4667.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Canning Vale", + "FINAL ANSWER: Canning Vale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + }, + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -1.17641, + "lon": 36.7564, + "name": "Karuri" + } + ], + "question": "Which location is the geographic outlier among: Wainuiomata, Adelaide, Bracken Ridge, Hastings, Karuri?", + "ground_truth": { + "answer": "Karuri", + "outlier_distance_km": 10846.4, + "second_furthest_km": 3900.2, + "clarity_ratio": 2.78, + "median_distance_km": 3762.8, + "distances_to_centroid": { + "Wainuiomata": 3762.8, + "Adelaide": 716.2, + "Bracken Ridge": 1674.5, + "Hastings": 3900.2, + "Karuri": 10846.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wainuiomata: (-41.27°, 174.95°)", + " Adelaide: (-34.93°, 138.60°)", + " Bracken Ridge: (-27.32°, 153.03°)", + " Hastings: (-39.64°, 176.85°)", + " Karuri: (-1.18°, 36.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karuri: 10846.4 km from centroid", + " Hastings: 3900.2 km from centroid", + " Wainuiomata: 3762.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karuri", + "FINAL ANSWER: Karuri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.02805, + "lon": 45.46115, + "name": "Nikolayevsk" + }, + { + "lat": 50.32124, + "lon": 17.57461, + "name": "Prudnik" + }, + { + "lat": 27.88385, + "lon": -15.72538, + "name": "Mogán" + }, + { + "lat": 63.59669, + "lon": 53.89178, + "name": "Sosnogorsk" + }, + { + "lat": -2.69795, + "lon": -59.70172, + "name": "Rio Preto da Eva" + } + ], + "question": "Which location is the geographic outlier among: Nikolayevsk, Prudnik, Mogán, Sosnogorsk, Rio Preto da Eva?", + "ground_truth": { + "answer": "Rio Preto da Eva", + "outlier_distance_km": 8287.8, + "second_furthest_km": 4151.6, + "clarity_ratio": 2.0, + "median_distance_km": 3227.9, + "distances_to_centroid": { + "Nikolayevsk": 3227.9, + "Prudnik": 1571.7, + "Mogán": 2491.6, + "Sosnogorsk": 4151.6, + "Rio Preto da Eva": 8287.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nikolayevsk: (50.03°, 45.46°)", + " Prudnik: (50.32°, 17.57°)", + " Mogán: (27.88°, -15.73°)", + " Sosnogorsk: (63.60°, 53.89°)", + " Rio Preto da Eva: (-2.70°, -59.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rio Preto da Eva: 8287.8 km from centroid", + " Sosnogorsk: 4151.6 km from centroid", + " Nikolayevsk: 3227.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rio Preto da Eva", + "FINAL ANSWER: Rio Preto da Eva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -28.27276, + "lon": 29.12946, + "name": "Harrismith" + } + ], + "question": "Which location is the geographic outlier among: Broken Hill, Wollongong city centre, Umina Beach, Engadine, Harrismith?", + "ground_truth": { + "answer": "Harrismith", + "outlier_distance_km": 8846.4, + "second_furthest_km": 2472.8, + "clarity_ratio": 3.58, + "median_distance_km": 2441.0, + "distances_to_centroid": { + "Broken Hill": 1569.7, + "Wollongong city centre": 2428.1, + "Umina Beach": 2472.8, + "Engadine": 2441.0, + "Harrismith": 8846.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Broken Hill: (-31.97°, 141.45°)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Umina Beach: (-33.52°, 151.31°)", + " Engadine: (-34.07°, 151.01°)", + " Harrismith: (-28.27°, 29.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Harrismith: 8846.4 km from centroid", + " Umina Beach: 2472.8 km from centroid", + " Engadine: 2441.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Harrismith", + "FINAL ANSWER: Harrismith" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": -33.8178, + "lon": 151.00348, + "name": "Parramatta" + }, + { + "lat": -12.05605, + "lon": -77.05295, + "name": "Breña" + } + ], + "question": "Which location is the geographic outlier among: Saint Albans, Blenheim, Wollongong, Parramatta, Breña?", + "ground_truth": { + "answer": "Breña", + "outlier_distance_km": 15087.8, + "second_furthest_km": 5774.3, + "clarity_ratio": 2.61, + "median_distance_km": 3927.3, + "distances_to_centroid": { + "Saint Albans": 3335.3, + "Blenheim": 5774.3, + "Wollongong": 3907.3, + "Parramatta": 3927.3, + "Breña": 15087.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Albans: (-37.73°, 144.80°)", + " Blenheim: (-41.52°, 173.95°)", + " Wollongong: (-34.42°, 150.89°)", + " Parramatta: (-33.82°, 151.00°)", + " Breña: (-12.06°, -77.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Breña: 15087.8 km from centroid", + " Blenheim: 5774.3 km from centroid", + " Parramatta: 3927.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Breña", + "FINAL ANSWER: Breña" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.38914, + "lon": 73.81491, + "name": "Mormugao" + }, + { + "lat": 34.28671, + "lon": 74.47228, + "name": "Sopur" + }, + { + "lat": 32.62217, + "lon": 130.66177, + "name": "Uki" + }, + { + "lat": 18.191, + "lon": 79.943, + "name": "Mulugu" + }, + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + } + ], + "question": "Which location is the geographic outlier among: Mormugao, Sopur, Uki, Mulugu, Cambridge?", + "ground_truth": { + "answer": "Cambridge", + "outlier_distance_km": 9058.8, + "second_furthest_km": 4065.7, + "clarity_ratio": 2.23, + "median_distance_km": 3577.5, + "distances_to_centroid": { + "Mormugao": 3577.5, + "Sopur": 4065.7, + "Uki": 3295.2, + "Mulugu": 2951.6, + "Cambridge": 9058.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mormugao: (15.39°, 73.81°)", + " Sopur: (34.29°, 74.47°)", + " Uki: (32.62°, 130.66°)", + " Mulugu: (18.19°, 79.94°)", + " Cambridge: (-37.88°, 175.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cambridge: 9058.8 km from centroid", + " Sopur: 4065.7 km from centroid", + " Mormugao: 3577.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cambridge", + "FINAL ANSWER: Cambridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -37.76722, + "lon": 144.76657, + "name": "Deer Park" + }, + { + "lat": -27.19354, + "lon": 153.02631, + "name": "Deception Bay" + }, + { + "lat": 0.17124, + "lon": 34.59466, + "name": "Khwisero" + } + ], + "question": "Which location is the geographic outlier among: Yarraville, Camberwell, Deer Park, Deception Bay, Khwisero?", + "ground_truth": { + "answer": "Khwisero", + "outlier_distance_km": 10004.4, + "second_furthest_km": 2808.1, + "clarity_ratio": 3.56, + "median_distance_km": 2199.2, + "distances_to_centroid": { + "Yarraville": 2184.4, + "Camberwell": 2199.2, + "Deer Park": 2171.5, + "Deception Bay": 2808.1, + "Khwisero": 10004.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yarraville: (-37.82°, 144.90°)", + " Camberwell: (-37.84°, 145.07°)", + " Deer Park: (-37.77°, 144.77°)", + " Deception Bay: (-27.19°, 153.03°)", + " Khwisero: (0.17°, 34.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Khwisero: 10004.4 km from centroid", + " Deception Bay: 2808.1 km from centroid", + " Camberwell: 2199.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Khwisero", + "FINAL ANSWER: Khwisero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.70241, + "lon": 41.72487, + "name": "Proletarsk" + }, + { + "lat": 52.41116, + "lon": 13.5355, + "name": "Altglienicke" + }, + { + "lat": 43.67954, + "lon": 10.84975, + "name": "San Miniato" + }, + { + "lat": 42.26413, + "lon": -8.78463, + "name": "Cangas do Morrazo" + }, + { + "lat": 32.63075, + "lon": -115.57039, + "name": "Santa Isabel" + } + ], + "question": "Which location is the geographic outlier among: Proletarsk, Altglienicke, San Miniato, Cangas do Morrazo, Santa Isabel?", + "ground_truth": { + "answer": "Santa Isabel", + "outlier_distance_km": 8564.6, + "second_furthest_km": 4121.7, + "clarity_ratio": 2.08, + "median_distance_km": 2103.3, + "distances_to_centroid": { + "Proletarsk": 4121.7, + "Altglienicke": 2103.3, + "San Miniato": 1805.9, + "Cangas do Morrazo": 272.9, + "Santa Isabel": 8564.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Proletarsk: (46.70°, 41.72°)", + " Altglienicke: (52.41°, 13.54°)", + " San Miniato: (43.68°, 10.85°)", + " Cangas do Morrazo: (42.26°, -8.78°)", + " Santa Isabel: (32.63°, -115.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Isabel: 8564.6 km from centroid", + " Proletarsk: 4121.7 km from centroid", + " Altglienicke: 2103.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Isabel", + "FINAL ANSWER: Santa Isabel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.86404, + "lon": 77.49937, + "name": "Ālangulam" + }, + { + "lat": 22.03177, + "lon": 111.93537, + "name": "Tangping" + }, + { + "lat": 12.9535, + "lon": 80.2572, + "name": "Palavakkam" + }, + { + "lat": 9.93653, + "lon": 76.32382, + "name": "Maradu" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + } + ], + "question": "Which location is the geographic outlier among: Ālangulam, Tangping, Palavakkam, Maradu, Mount Eden?", + "ground_truth": { + "answer": "Mount Eden", + "outlier_distance_km": 8530.6, + "second_furthest_km": 3157.0, + "clarity_ratio": 2.7, + "median_distance_km": 3008.1, + "distances_to_centroid": { + "Ālangulam": 3008.1, + "Tangping": 2237.4, + "Palavakkam": 2834.2, + "Maradu": 3157.0, + "Mount Eden": 8530.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ālangulam: (8.86°, 77.50°)", + " Tangping: (22.03°, 111.94°)", + " Palavakkam: (12.95°, 80.26°)", + " Maradu: (9.94°, 76.32°)", + " Mount Eden: (-36.88°, 174.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Eden: 8530.6 km from centroid", + " Maradu: 3157.0 km from centroid", + " Ālangulam: 3008.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Eden", + "FINAL ANSWER: Mount Eden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.09528, + "lon": -39.4525, + "name": "Acopiara" + }, + { + "lat": -7.03333, + "lon": -40.45, + "name": "Ipueiras" + }, + { + "lat": -24.32083, + "lon": -47.63472, + "name": "Juquiá" + }, + { + "lat": -9.95051, + "lon": -54.90822, + "name": "Guarantã do Norte" + }, + { + "lat": 32.21667, + "lon": 130.4, + "name": "Minamata" + } + ], + "question": "Which location is the geographic outlier among: Acopiara, Ipueiras, Juquiá, Guarantã do Norte, Minamata?", + "ground_truth": { + "answer": "Minamata", + "outlier_distance_km": 14798.0, + "second_furthest_km": 4971.3, + "clarity_ratio": 2.98, + "median_distance_km": 4639.2, + "distances_to_centroid": { + "Acopiara": 3236.5, + "Ipueiras": 3356.1, + "Juquiá": 4639.2, + "Guarantã do Norte": 4971.3, + "Minamata": 14798.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Acopiara: (-6.10°, -39.45°)", + " Ipueiras: (-7.03°, -40.45°)", + " Juquiá: (-24.32°, -47.63°)", + " Guarantã do Norte: (-9.95°, -54.91°)", + " Minamata: (32.22°, 130.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Minamata: 14798.0 km from centroid", + " Guarantã do Norte: 4971.3 km from centroid", + " Juquiá: 4639.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Minamata", + "FINAL ANSWER: Minamata" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.51957, + "lon": -88.30397, + "name": "Chetumal" + }, + { + "lat": 20.53315, + "lon": -97.45946, + "name": "Poza Rica de Hidalgo" + }, + { + "lat": 40.81538, + "lon": -73.04511, + "name": "Holtsville" + }, + { + "lat": 30.98352, + "lon": -110.29758, + "name": "Cananea" + }, + { + "lat": 24.90652, + "lon": 32.88563, + "name": "Ar Radīsīyah Qiblī" + } + ], + "question": "Which location is the geographic outlier among: Chetumal, Poza Rica de Hidalgo, Holtsville, Cananea, Ar Radīsīyah Qiblī?", + "ground_truth": { + "answer": "Ar Radīsīyah Qiblī", + "outlier_distance_km": 9687.3, + "second_furthest_km": 4180.4, + "clarity_ratio": 2.32, + "median_distance_km": 3151.5, + "distances_to_centroid": { + "Chetumal": 2357.5, + "Poza Rica de Hidalgo": 3151.5, + "Holtsville": 1609.7, + "Cananea": 4180.4, + "Ar Radīsīyah Qiblī": 9687.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chetumal: (18.52°, -88.30°)", + " Poza Rica de Hidalgo: (20.53°, -97.46°)", + " Holtsville: (40.82°, -73.05°)", + " Cananea: (30.98°, -110.30°)", + " Ar Radīsīyah Qiblī: (24.91°, 32.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ar Radīsīyah Qiblī: 9687.3 km from centroid", + " Cananea: 4180.4 km from centroid", + " Poza Rica de Hidalgo: 3151.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ar Radīsīyah Qiblī", + "FINAL ANSWER: Ar Radīsīyah Qiblī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.41359, + "lon": 2.96485, + "name": "Hénin-Beaumont" + }, + { + "lat": 49.83411, + "lon": 8.49621, + "name": "Riedstadt" + }, + { + "lat": 51.845, + "lon": 4.32917, + "name": "Spijkenisse" + }, + { + "lat": 54.57623, + "lon": -1.23483, + "name": "Middlesbrough" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + } + ], + "question": "Which location is the geographic outlier among: Hénin-Beaumont, Riedstadt, Spijkenisse, Middlesbrough, Griffith?", + "ground_truth": { + "answer": "Griffith", + "outlier_distance_km": 14068.8, + "second_furthest_km": 3407.1, + "clarity_ratio": 4.13, + "median_distance_km": 2945.7, + "distances_to_centroid": { + "Hénin-Beaumont": 2945.7, + "Riedstadt": 2570.2, + "Spijkenisse": 2936.4, + "Middlesbrough": 3407.1, + "Griffith": 14068.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hénin-Beaumont: (50.41°, 2.96°)", + " Riedstadt: (49.83°, 8.50°)", + " Spijkenisse: (51.84°, 4.33°)", + " Middlesbrough: (54.58°, -1.23°)", + " Griffith: (-34.29°, 146.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Griffith: 14068.8 km from centroid", + " Middlesbrough: 3407.1 km from centroid", + " Hénin-Beaumont: 2945.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Griffith", + "FINAL ANSWER: Griffith" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.58601, + "lon": 26.88329, + "name": "Port Alfred" + }, + { + "lat": 29.4075, + "lon": 31.2525, + "name": "Aţfīḩ" + }, + { + "lat": 6.80768, + "lon": 46.08482, + "name": "Yamarugley" + }, + { + "lat": 30.82796, + "lon": 30.53552, + "name": "Ad Dilinjāt" + }, + { + "lat": 48.43569, + "lon": -123.41174, + "name": "Esquimalt" + } + ], + "question": "Which location is the geographic outlier among: Port Alfred, Aţfīḩ, Yamarugley, Ad Dilinjāt, Esquimalt?", + "ground_truth": { + "answer": "Esquimalt", + "outlier_distance_km": 11033.2, + "second_furthest_km": 6138.6, + "clarity_ratio": 1.8, + "median_distance_km": 4878.9, + "distances_to_centroid": { + "Port Alfred": 6138.6, + "Aţfīḩ": 3290.3, + "Yamarugley": 4878.9, + "Ad Dilinjāt": 3283.2, + "Esquimalt": 11033.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Port Alfred: (-33.59°, 26.88°)", + " Aţfīḩ: (29.41°, 31.25°)", + " Yamarugley: (6.81°, 46.08°)", + " Ad Dilinjāt: (30.83°, 30.54°)", + " Esquimalt: (48.44°, -123.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Esquimalt: 11033.2 km from centroid", + " Port Alfred: 6138.6 km from centroid", + " Yamarugley: 4878.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Esquimalt", + "FINAL ANSWER: Esquimalt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.01667, + "lon": 37.45, + "name": "Gēdo" + }, + { + "lat": 11.5541, + "lon": 11.406, + "name": "Daura" + }, + { + "lat": 7.01667, + "lon": 39.98333, + "name": "Goba" + }, + { + "lat": 12.03219, + "lon": 39.04756, + "name": "Lalibela" + }, + { + "lat": -9.26083, + "lon": -37.93611, + "name": "Água Branca" + } + ], + "question": "Which location is the geographic outlier among: Gēdo, Daura, Goba, Lalibela, Água Branca?", + "ground_truth": { + "answer": "Água Branca", + "outlier_distance_km": 6427.4, + "second_furthest_km": 2431.6, + "clarity_ratio": 2.64, + "median_distance_km": 2404.0, + "distances_to_centroid": { + "Gēdo": 2169.5, + "Daura": 945.8, + "Goba": 2431.6, + "Lalibela": 2404.0, + "Água Branca": 6427.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gēdo: (9.02°, 37.45°)", + " Daura: (11.55°, 11.41°)", + " Goba: (7.02°, 39.98°)", + " Lalibela: (12.03°, 39.05°)", + " Água Branca: (-9.26°, -37.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Água Branca: 6427.4 km from centroid", + " Goba: 2431.6 km from centroid", + " Lalibela: 2404.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Água Branca", + "FINAL ANSWER: Água Branca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.5427, + "lon": -97.54667, + "name": "Hutto" + }, + { + "lat": 33.77391, + "lon": -117.94145, + "name": "Garden Grove" + }, + { + "lat": 33.23623, + "lon": -96.80111, + "name": "Prosper" + }, + { + "lat": 42.99812, + "lon": -78.18752, + "name": "Batavia" + }, + { + "lat": -4.94667, + "lon": -47.50472, + "name": "Açailândia" + } + ], + "question": "Which location is the geographic outlier among: Hutto, Garden Grove, Prosper, Batavia, Açailândia?", + "ground_truth": { + "answer": "Açailândia", + "outlier_distance_km": 5590.7, + "second_furthest_km": 2989.6, + "clarity_ratio": 1.87, + "median_distance_km": 1959.1, + "distances_to_centroid": { + "Hutto": 1040.8, + "Garden Grove": 2989.6, + "Prosper": 1115.1, + "Batavia": 1959.1, + "Açailândia": 5590.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hutto: (30.54°, -97.55°)", + " Garden Grove: (33.77°, -117.94°)", + " Prosper: (33.24°, -96.80°)", + " Batavia: (43.00°, -78.19°)", + " Açailândia: (-4.95°, -47.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Açailândia: 5590.7 km from centroid", + " Garden Grove: 2989.6 km from centroid", + " Batavia: 1959.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Açailândia", + "FINAL ANSWER: Açailândia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.5471, + "lon": 121.972, + "name": "Bungku" + }, + { + "lat": 26.70423, + "lon": 78.22678, + "name": "Ambāh" + }, + { + "lat": 10.2708, + "lon": 123.5839, + "name": "Pinamungahan" + }, + { + "lat": 26.14447, + "lon": 127.76697, + "name": "Nanjō" + }, + { + "lat": 37.84035, + "lon": -85.94913, + "name": "Radcliff" + } + ], + "question": "Which location is the geographic outlier among: Bungku, Ambāh, Pinamungahan, Nanjō, Radcliff?", + "ground_truth": { + "answer": "Radcliff", + "outlier_distance_km": 13254.7, + "second_furthest_km": 5876.0, + "clarity_ratio": 2.26, + "median_distance_km": 5603.8, + "distances_to_centroid": { + "Bungku": 5876.0, + "Ambāh": 938.9, + "Pinamungahan": 5501.0, + "Nanjō": 5603.8, + "Radcliff": 13254.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bungku: (-2.55°, 121.97°)", + " Ambāh: (26.70°, 78.23°)", + " Pinamungahan: (10.27°, 123.58°)", + " Nanjō: (26.14°, 127.77°)", + " Radcliff: (37.84°, -85.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Radcliff: 13254.7 km from centroid", + " Bungku: 5876.0 km from centroid", + " Nanjō: 5603.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Radcliff", + "FINAL ANSWER: Radcliff" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.08333, + "lon": 37.86667, + "name": "Mot’a" + }, + { + "lat": -25.40892, + "lon": 28.287, + "name": "Hammanskraal" + }, + { + "lat": 5.65003, + "lon": -0.2361, + "name": "Dome" + }, + { + "lat": -29.04912, + "lon": 29.78232, + "name": "Wembesi" + }, + { + "lat": 21.2843, + "lon": -157.73706, + "name": "Niu Valley" + } + ], + "question": "Which location is the geographic outlier among: Mot’a, Hammanskraal, Dome, Wembesi, Niu Valley?", + "ground_truth": { + "answer": "Niu Valley", + "outlier_distance_km": 15767.9, + "second_furthest_km": 5786.4, + "clarity_ratio": 2.72, + "median_distance_km": 5291.1, + "distances_to_centroid": { + "Mot’a": 5786.4, + "Hammanskraal": 4992.7, + "Dome": 1677.8, + "Wembesi": 5291.1, + "Niu Valley": 15767.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mot’a: (11.08°, 37.87°)", + " Hammanskraal: (-25.41°, 28.29°)", + " Dome: (5.65°, -0.24°)", + " Wembesi: (-29.05°, 29.78°)", + " Niu Valley: (21.28°, -157.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Niu Valley: 15767.9 km from centroid", + " Mot’a: 5786.4 km from centroid", + " Wembesi: 5291.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Niu Valley", + "FINAL ANSWER: Niu Valley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -17.35111, + "lon": -44.96222, + "name": "Buritizeiro" + }, + { + "lat": -6.72917, + "lon": -38.44889, + "name": "São João do Rio do Peixe" + }, + { + "lat": -22.37417, + "lon": -54.51389, + "name": "Fátima do Sul" + }, + { + "lat": -2.87306, + "lon": -67.80222, + "name": "Tonantins" + }, + { + "lat": -33.88374, + "lon": 151.21282, + "name": "Surry Hills" + } + ], + "question": "Which location is the geographic outlier among: Buritizeiro, São João do Rio do Peixe, Fátima do Sul, Tonantins, Surry Hills?", + "ground_truth": { + "answer": "Surry Hills", + "outlier_distance_km": 14085.8, + "second_furthest_km": 6396.5, + "clarity_ratio": 2.2, + "median_distance_km": 4599.7, + "distances_to_centroid": { + "Buritizeiro": 3617.9, + "São João do Rio do Peixe": 3190.5, + "Fátima do Sul": 4599.7, + "Tonantins": 6396.5, + "Surry Hills": 14085.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Buritizeiro: (-17.35°, -44.96°)", + " São João do Rio do Peixe: (-6.73°, -38.45°)", + " Fátima do Sul: (-22.37°, -54.51°)", + " Tonantins: (-2.87°, -67.80°)", + " Surry Hills: (-33.88°, 151.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Surry Hills: 14085.8 km from centroid", + " Tonantins: 6396.5 km from centroid", + " Fátima do Sul: 4599.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Surry Hills", + "FINAL ANSWER: Surry Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.05458, + "lon": 101.37264, + "name": "Prachin Buri Town" + }, + { + "lat": 14.94348, + "lon": 77.25494, + "name": "Uravakonda" + }, + { + "lat": 16.69746, + "lon": 74.27325, + "name": "Unchagao" + }, + { + "lat": 8.75985, + "lon": 77.73986, + "name": "Nāranammālpuram" + }, + { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + } + ], + "question": "Which location is the geographic outlier among: Prachin Buri Town, Uravakonda, Unchagao, Nāranammālpuram, Hamilton?", + "ground_truth": { + "answer": "Hamilton", + "outlier_distance_km": 8851.0, + "second_furthest_km": 3292.9, + "clarity_ratio": 2.69, + "median_distance_km": 2922.3, + "distances_to_centroid": { + "Prachin Buri Town": 1192.2, + "Uravakonda": 2922.3, + "Unchagao": 3292.9, + "Nāranammālpuram": 2660.5, + "Hamilton": 8851.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Prachin Buri Town: (14.05°, 101.37°)", + " Uravakonda: (14.94°, 77.25°)", + " Unchagao: (16.70°, 74.27°)", + " Nāranammālpuram: (8.76°, 77.74°)", + " Hamilton: (-37.78°, 175.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hamilton: 8851.0 km from centroid", + " Unchagao: 3292.9 km from centroid", + " Uravakonda: 2922.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hamilton", + "FINAL ANSWER: Hamilton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.13833, + "lon": -75.26417, + "name": "Santuario" + }, + { + "lat": -10.59333, + "lon": -36.94028, + "name": "Japaratuba" + }, + { + "lat": -2.99565, + "lon": -47.35488, + "name": "Paragominas" + }, + { + "lat": -9.38333, + "lon": -35.84167, + "name": "Messias" + }, + { + "lat": 25.96667, + "lon": 94.51667, + "name": "Zunheboto" + } + ], + "question": "Which location is the geographic outlier among: Santuario, Japaratuba, Paragominas, Messias, Zunheboto?", + "ground_truth": { + "answer": "Zunheboto", + "outlier_distance_km": 12363.6, + "second_furthest_km": 6126.7, + "clarity_ratio": 2.02, + "median_distance_km": 3068.2, + "distances_to_centroid": { + "Santuario": 6126.7, + "Japaratuba": 2312.5, + "Paragominas": 3068.2, + "Messias": 2136.5, + "Zunheboto": 12363.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santuario: (6.14°, -75.26°)", + " Japaratuba: (-10.59°, -36.94°)", + " Paragominas: (-3.00°, -47.35°)", + " Messias: (-9.38°, -35.84°)", + " Zunheboto: (25.97°, 94.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zunheboto: 12363.6 km from centroid", + " Santuario: 6126.7 km from centroid", + " Paragominas: 3068.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zunheboto", + "FINAL ANSWER: Zunheboto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.50476, + "lon": 28.35921, + "name": "Heidelberg" + }, + { + "lat": -25.87133, + "lon": 29.23323, + "name": "Emalahleni" + }, + { + "lat": 7.84855, + "lon": 4.32981, + "name": "Inisa" + }, + { + "lat": 10.65, + "lon": 36.21667, + "name": "Dibate" + }, + { + "lat": 35.65879, + "lon": 139.90055, + "name": "Urayasu" + } + ], + "question": "Which location is the geographic outlier among: Heidelberg, Emalahleni, Inisa, Dibate, Urayasu?", + "ground_truth": { + "answer": "Urayasu", + "outlier_distance_km": 10191.5, + "second_furthest_km": 4867.7, + "clarity_ratio": 2.09, + "median_distance_km": 3629.4, + "distances_to_centroid": { + "Heidelberg": 3629.4, + "Emalahleni": 3520.5, + "Inisa": 4867.7, + "Dibate": 1701.6, + "Urayasu": 10191.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Heidelberg: (-26.50°, 28.36°)", + " Emalahleni: (-25.87°, 29.23°)", + " Inisa: (7.85°, 4.33°)", + " Dibate: (10.65°, 36.22°)", + " Urayasu: (35.66°, 139.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Urayasu: 10191.5 km from centroid", + " Inisa: 4867.7 km from centroid", + " Heidelberg: 3629.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Urayasu", + "FINAL ANSWER: Urayasu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + }, + { + "lat": 32.487, + "lon": -114.78218, + "name": "San Luis" + } + ], + "question": "Which location is the geographic outlier among: Helensvale, Townsville, Glenroy, Redbank Plains, San Luis?", + "ground_truth": { + "answer": "San Luis", + "outlier_distance_km": 16362.4, + "second_furthest_km": 5944.3, + "clarity_ratio": 2.75, + "median_distance_km": 5897.7, + "distances_to_centroid": { + "Helensvale": 5944.3, + "Townsville": 5311.7, + "Glenroy": 5290.8, + "Redbank Plains": 5897.7, + "San Luis": 16362.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Helensvale: (-27.92°, 153.33°)", + " Townsville: (-19.27°, 146.81°)", + " Glenroy: (-37.70°, 144.93°)", + " Redbank Plains: (-27.65°, 152.86°)", + " San Luis: (32.49°, -114.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Luis: 16362.4 km from centroid", + " Helensvale: 5944.3 km from centroid", + " Redbank Plains: 5897.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Luis", + "FINAL ANSWER: San Luis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.52314, + "lon": -0.47718, + "name": "Buduburam" + }, + { + "lat": 6.58412, + "lon": 3.98336, + "name": "Epe" + }, + { + "lat": 5.48363, + "lon": 7.03325, + "name": "Owerri" + }, + { + "lat": -27.36541, + "lon": 29.88175, + "name": "Volksrust" + }, + { + "lat": 23.05191, + "lon": 99.82838, + "name": "Shangyun" + } + ], + "question": "Which location is the geographic outlier among: Buduburam, Epe, Owerri, Volksrust, Shangyun?", + "ground_truth": { + "answer": "Shangyun", + "outlier_distance_km": 8029.2, + "second_furthest_km": 3343.9, + "clarity_ratio": 2.4, + "median_distance_km": 3179.5, + "distances_to_centroid": { + "Buduburam": 3179.5, + "Epe": 2702.3, + "Owerri": 2351.9, + "Volksrust": 3343.9, + "Shangyun": 8029.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Buduburam: (5.52°, -0.48°)", + " Epe: (6.58°, 3.98°)", + " Owerri: (5.48°, 7.03°)", + " Volksrust: (-27.37°, 29.88°)", + " Shangyun: (23.05°, 99.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shangyun: 8029.2 km from centroid", + " Volksrust: 3343.9 km from centroid", + " Buduburam: 3179.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shangyun", + "FINAL ANSWER: Shangyun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.29713, + "lon": -157.745, + "name": "Kuliouou - Kalani Iki" + }, + { + "lat": 37.88063, + "lon": -84.573, + "name": "Nicholasville" + }, + { + "lat": 46.97537, + "lon": -123.81572, + "name": "Aberdeen" + }, + { + "lat": 42.81259, + "lon": -70.87728, + "name": "Newburyport" + }, + { + "lat": 1.53741, + "lon": 103.65779, + "name": "Skudai" + } + ], + "question": "Which location is the geographic outlier among: Kuliouou - Kalani Iki, Nicholasville, Aberdeen, Newburyport, Skudai?", + "ground_truth": { + "answer": "Skudai", + "outlier_distance_km": 16350.5, + "second_furthest_km": 8938.3, + "clarity_ratio": 1.83, + "median_distance_km": 5183.4, + "distances_to_centroid": { + "Kuliouou - Kalani Iki": 8938.3, + "Nicholasville": 1858.9, + "Aberdeen": 5183.4, + "Newburyport": 1462.2, + "Skudai": 16350.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kuliouou - Kalani Iki: (21.30°, -157.75°)", + " Nicholasville: (37.88°, -84.57°)", + " Aberdeen: (46.98°, -123.82°)", + " Newburyport: (42.81°, -70.88°)", + " Skudai: (1.54°, 103.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Skudai: 16350.5 km from centroid", + " Kuliouou - Kalani Iki: 8938.3 km from centroid", + " Aberdeen: 5183.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Skudai", + "FINAL ANSWER: Skudai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73333, + "lon": 150.88333, + "name": "Quakers Hill" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + { + "lat": 34.03612, + "lon": -117.99118, + "name": "Avocado Heights" + } + ], + "question": "Which location is the geographic outlier among: Quakers Hill, Whangarei, Punchbowl, Lincoln, Avocado Heights?", + "ground_truth": { + "answer": "Avocado Heights", + "outlier_distance_km": 15440.0, + "second_furthest_km": 6699.7, + "clarity_ratio": 2.3, + "median_distance_km": 6685.5, + "distances_to_centroid": { + "Quakers Hill": 4547.4, + "Whangarei": 6685.5, + "Punchbowl": 4565.1, + "Lincoln": 6699.7, + "Avocado Heights": 15440.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Quakers Hill: (-33.73°, 150.88°)", + " Whangarei: (-35.73°, 174.32°)", + " Punchbowl: (-33.93°, 151.05°)", + " Lincoln: (-36.86°, 174.62°)", + " Avocado Heights: (34.04°, -117.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Avocado Heights: 15440.0 km from centroid", + " Lincoln: 6699.7 km from centroid", + " Whangarei: 6685.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Avocado Heights", + "FINAL ANSWER: Avocado Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.79025, + "lon": 10.95509, + "name": "Blankenburg" + }, + { + "lat": 39.42814, + "lon": -0.41765, + "name": "Paiporta" + }, + { + "lat": 51.9725, + "lon": 6.71944, + "name": "Winterswijk" + }, + { + "lat": 45.53004, + "lon": 9.27795, + "name": "Cologno Monzese" + }, + { + "lat": 25.91544, + "lon": 32.76287, + "name": "Qūş" + } + ], + "question": "Which location is the geographic outlier among: Blankenburg, Paiporta, Winterswijk, Cologno Monzese, Qūş?", + "ground_truth": { + "answer": "Qūş", + "outlier_distance_km": 2678.8, + "second_furthest_km": 1097.4, + "clarity_ratio": 2.44, + "median_distance_km": 1076.8, + "distances_to_centroid": { + "Blankenburg": 987.8, + "Paiporta": 1097.4, + "Winterswijk": 1076.8, + "Cologno Monzese": 355.0, + "Qūş": 2678.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blankenburg: (51.79°, 10.96°)", + " Paiporta: (39.43°, -0.42°)", + " Winterswijk: (51.97°, 6.72°)", + " Cologno Monzese: (45.53°, 9.28°)", + " Qūş: (25.92°, 32.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qūş: 2678.8 km from centroid", + " Paiporta: 1097.4 km from centroid", + " Winterswijk: 1076.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qūş", + "FINAL ANSWER: Qūş" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.41972, + "lon": -50.0775, + "name": "Penápolis" + }, + { + "lat": -31.39195, + "lon": -58.01706, + "name": "Concordia" + }, + { + "lat": -17.30278, + "lon": -49.01667, + "name": "Piracanjuba" + }, + { + "lat": -2.59833, + "lon": -43.46111, + "name": "Humberto de Campos" + }, + { + "lat": -25.47288, + "lon": 28.09919, + "name": "Soshanguve" + } + ], + "question": "Which location is the geographic outlier among: Penápolis, Concordia, Piracanjuba, Humberto de Campos, Soshanguve?", + "ground_truth": { + "answer": "Soshanguve", + "outlier_distance_km": 6404.2, + "second_furthest_km": 2689.3, + "clarity_ratio": 2.38, + "median_distance_km": 2130.4, + "distances_to_centroid": { + "Penápolis": 1634.1, + "Concordia": 2689.3, + "Piracanjuba": 1552.9, + "Humberto de Campos": 2130.4, + "Soshanguve": 6404.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Penápolis: (-21.42°, -50.08°)", + " Concordia: (-31.39°, -58.02°)", + " Piracanjuba: (-17.30°, -49.02°)", + " Humberto de Campos: (-2.60°, -43.46°)", + " Soshanguve: (-25.47°, 28.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Soshanguve: 6404.2 km from centroid", + " Concordia: 2689.3 km from centroid", + " Humberto de Campos: 2130.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Soshanguve", + "FINAL ANSWER: Soshanguve" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.25665, + "lon": 77.51006, + "name": "Achalpur" + }, + { + "lat": 29.54615, + "lon": 105.81044, + "name": "Yulong" + }, + { + "lat": 22.80917, + "lon": 88.22944, + "name": "Singur" + }, + { + "lat": 33.53466, + "lon": 104.81418, + "name": "Puchi" + }, + { + "lat": -18.59222, + "lon": -48.705, + "name": "Tupaciguara" + } + ], + "question": "Which location is the geographic outlier among: Achalpur, Yulong, Singur, Puchi, Tupaciguara?", + "ground_truth": { + "answer": "Tupaciguara", + "outlier_distance_km": 13107.8, + "second_furthest_km": 4284.6, + "clarity_ratio": 3.06, + "median_distance_km": 4280.3, + "distances_to_centroid": { + "Achalpur": 1315.6, + "Yulong": 4284.6, + "Singur": 2431.7, + "Puchi": 4280.3, + "Tupaciguara": 13107.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Achalpur: (21.26°, 77.51°)", + " Yulong: (29.55°, 105.81°)", + " Singur: (22.81°, 88.23°)", + " Puchi: (33.53°, 104.81°)", + " Tupaciguara: (-18.59°, -48.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tupaciguara: 13107.8 km from centroid", + " Yulong: 4284.6 km from centroid", + " Puchi: 4280.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tupaciguara", + "FINAL ANSWER: Tupaciguara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.53674, + "lon": 125.69427, + "name": "Dehui" + }, + { + "lat": 15.94579, + "lon": 75.29785, + "name": "Rāmdurg" + }, + { + "lat": 13.17722, + "lon": 121.27806, + "name": "Victoria" + }, + { + "lat": 23.63722, + "lon": 79.06275, + "name": "Rehli" + }, + { + "lat": -31.4183, + "lon": -64.49008, + "name": "Villa Carlos Paz" + } + ], + "question": "Which location is the geographic outlier among: Dehui, Rāmdurg, Victoria, Rehli, Villa Carlos Paz?", + "ground_truth": { + "answer": "Villa Carlos Paz", + "outlier_distance_km": 14713.5, + "second_furthest_km": 6491.4, + "clarity_ratio": 2.27, + "median_distance_km": 5824.4, + "distances_to_centroid": { + "Dehui": 6491.4, + "Rāmdurg": 907.1, + "Victoria": 5824.4, + "Rehli": 1693.9, + "Villa Carlos Paz": 14713.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dehui: (44.54°, 125.69°)", + " Rāmdurg: (15.95°, 75.30°)", + " Victoria: (13.18°, 121.28°)", + " Rehli: (23.64°, 79.06°)", + " Villa Carlos Paz: (-31.42°, -64.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Villa Carlos Paz: 14713.5 km from centroid", + " Dehui: 6491.4 km from centroid", + " Victoria: 5824.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Villa Carlos Paz", + "FINAL ANSWER: Villa Carlos Paz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.8458, + "lon": -1.87942, + "name": "Challans" + }, + { + "lat": 55.7, + "lon": 37.46667, + "name": "Amin’yevo" + }, + { + "lat": 40.44682, + "lon": -3.70347, + "name": "Cuatro Caminos" + }, + { + "lat": 45.52569, + "lon": 4.87484, + "name": "Vienne" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + } + ], + "question": "Which location is the geographic outlier among: Challans, Amin’yevo, Cuatro Caminos, Vienne, Seaford?", + "ground_truth": { + "answer": "Seaford", + "outlier_distance_km": 13553.1, + "second_furthest_km": 3780.8, + "clarity_ratio": 3.58, + "median_distance_km": 3765.0, + "distances_to_centroid": { + "Challans": 3765.0, + "Amin’yevo": 2849.7, + "Cuatro Caminos": 3780.8, + "Vienne": 3225.6, + "Seaford": 13553.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Challans: (46.85°, -1.88°)", + " Amin’yevo: (55.70°, 37.47°)", + " Cuatro Caminos: (40.45°, -3.70°)", + " Vienne: (45.53°, 4.87°)", + " Seaford: (-38.10°, 145.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Seaford: 13553.1 km from centroid", + " Cuatro Caminos: 3780.8 km from centroid", + " Challans: 3765.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Seaford", + "FINAL ANSWER: Seaford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.73538, + "lon": -39.14785, + "name": "Ituberá" + }, + { + "lat": -10.40556, + "lon": -36.43444, + "name": "Piaçabuçu" + }, + { + "lat": -6.53389, + "lon": -64.38306, + "name": "Canutama" + }, + { + "lat": -23.34722, + "lon": -52.09528, + "name": "Mandaguaçu" + }, + { + "lat": 56.1325, + "lon": 101.61417, + "name": "Bratsk" + } + ], + "question": "Which location is the geographic outlier among: Ituberá, Piaçabuçu, Canutama, Mandaguaçu, Bratsk?", + "ground_truth": { + "answer": "Bratsk", + "outlier_distance_km": 11749.4, + "second_furthest_km": 5194.6, + "clarity_ratio": 2.26, + "median_distance_km": 4525.4, + "distances_to_centroid": { + "Ituberá": 2803.2, + "Piaçabuçu": 2359.3, + "Canutama": 5194.6, + "Mandaguaçu": 4525.4, + "Bratsk": 11749.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ituberá: (-13.74°, -39.15°)", + " Piaçabuçu: (-10.41°, -36.43°)", + " Canutama: (-6.53°, -64.38°)", + " Mandaguaçu: (-23.35°, -52.10°)", + " Bratsk: (56.13°, 101.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bratsk: 11749.4 km from centroid", + " Canutama: 5194.6 km from centroid", + " Mandaguaçu: 4525.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bratsk", + "FINAL ANSWER: Bratsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.86842, + "lon": 14.40196, + "name": "Sant'Anastasia" + }, + { + "lat": 51.66669, + "lon": -0.16981, + "name": "Hadley Wood" + }, + { + "lat": 51.41082, + "lon": -0.6748, + "name": "Ascot" + }, + { + "lat": 54.0887, + "lon": 12.14049, + "name": "Rostock" + }, + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + } + ], + "question": "Which location is the geographic outlier among: Sant'Anastasia, Hadley Wood, Ascot, Rostock, Calamvale?", + "ground_truth": { + "answer": "Calamvale", + "outlier_distance_km": 14078.5, + "second_furthest_km": 3489.8, + "clarity_ratio": 4.03, + "median_distance_km": 3466.5, + "distances_to_centroid": { + "Sant'Anastasia": 2022.7, + "Hadley Wood": 3466.5, + "Ascot": 3489.8, + "Rostock": 2888.1, + "Calamvale": 14078.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sant'Anastasia: (40.87°, 14.40°)", + " Hadley Wood: (51.67°, -0.17°)", + " Ascot: (51.41°, -0.67°)", + " Rostock: (54.09°, 12.14°)", + " Calamvale: (-27.62°, 153.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Calamvale: 14078.5 km from centroid", + " Ascot: 3489.8 km from centroid", + " Hadley Wood: 3466.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Calamvale", + "FINAL ANSWER: Calamvale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.33468, + "lon": 37.99086, + "name": "Marsabit" + }, + { + "lat": 30.51552, + "lon": 31.34629, + "name": "Minyā al Qamḩ" + }, + { + "lat": -28.33523, + "lon": 31.41617, + "name": "Ulundi" + }, + { + "lat": -27.78324, + "lon": 24.68768, + "name": "Pampierstad" + }, + { + "lat": 42.6225, + "lon": 126.26139, + "name": "Huinan" + } + ], + "question": "Which location is the geographic outlier among: Marsabit, Minyā al Qamḩ, Ulundi, Pampierstad, Huinan?", + "ground_truth": { + "answer": "Huinan", + "outlier_distance_km": 8566.2, + "second_furthest_km": 4465.8, + "clarity_ratio": 1.92, + "median_distance_km": 4113.9, + "distances_to_centroid": { + "Marsabit": 1381.8, + "Minyā al Qamḩ": 3570.8, + "Ulundi": 4113.9, + "Pampierstad": 4465.8, + "Huinan": 8566.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marsabit: (2.33°, 37.99°)", + " Minyā al Qamḩ: (30.52°, 31.35°)", + " Ulundi: (-28.34°, 31.42°)", + " Pampierstad: (-27.78°, 24.69°)", + " Huinan: (42.62°, 126.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huinan: 8566.2 km from centroid", + " Pampierstad: 4465.8 km from centroid", + " Ulundi: 4113.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huinan", + "FINAL ANSWER: Huinan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.80569, + "lon": 74.86058, + "name": "Ullal" + }, + { + "lat": 35.329, + "lon": 136.68051, + "name": "Hashima" + }, + { + "lat": 6.02977, + "lon": 101.96586, + "name": "Su-ngai Kolok" + }, + { + "lat": 28.45179, + "lon": 117.94287, + "name": "Shangrao" + }, + { + "lat": -26.21551, + "lon": 29.29164, + "name": "Thubelihle" + } + ], + "question": "Which location is the geographic outlier among: Ullal, Hashima, Su-ngai Kolok, Shangrao, Thubelihle?", + "ground_truth": { + "answer": "Thubelihle", + "outlier_distance_km": 7966.1, + "second_furthest_km": 5213.4, + "clarity_ratio": 1.53, + "median_distance_km": 3291.2, + "distances_to_centroid": { + "Ullal": 1887.3, + "Hashima": 5213.4, + "Su-ngai Kolok": 1226.6, + "Shangrao": 3291.2, + "Thubelihle": 7966.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ullal: (12.81°, 74.86°)", + " Hashima: (35.33°, 136.68°)", + " Su-ngai Kolok: (6.03°, 101.97°)", + " Shangrao: (28.45°, 117.94°)", + " Thubelihle: (-26.22°, 29.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thubelihle: 7966.1 km from centroid", + " Hashima: 5213.4 km from centroid", + " Shangrao: 3291.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thubelihle", + "FINAL ANSWER: Thubelihle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.1689, + "lon": -86.26395, + "name": "Norton Shores" + }, + { + "lat": 41.80892, + "lon": -88.01117, + "name": "Downers Grove" + }, + { + "lat": 42.90395, + "lon": -78.69225, + "name": "Depew" + }, + { + "lat": 42.77424, + "lon": -73.70012, + "name": "Cohoes" + }, + { + "lat": -23.84852, + "lon": 151.25775, + "name": "Gladstone" + } + ], + "question": "Which location is the geographic outlier among: Norton Shores, Downers Grove, Depew, Cohoes, Gladstone?", + "ground_truth": { + "answer": "Gladstone", + "outlier_distance_km": 19136.2, + "second_furthest_km": 4900.6, + "clarity_ratio": 3.9, + "median_distance_km": 4757.5, + "distances_to_centroid": { + "Norton Shores": 4757.5, + "Downers Grove": 4900.6, + "Depew": 4141.7, + "Cohoes": 3737.2, + "Gladstone": 19136.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Norton Shores: (43.17°, -86.26°)", + " Downers Grove: (41.81°, -88.01°)", + " Depew: (42.90°, -78.69°)", + " Cohoes: (42.77°, -73.70°)", + " Gladstone: (-23.85°, 151.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gladstone: 19136.2 km from centroid", + " Downers Grove: 4900.6 km from centroid", + " Norton Shores: 4757.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gladstone", + "FINAL ANSWER: Gladstone" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -3.05056, + "lon": -40.16778, + "name": "Bela Cruz" + } + ], + "question": "Which location is the geographic outlier among: Doreen, Nerang, Carlton, Corio, Bela Cruz?", + "ground_truth": { + "answer": "Bela Cruz", + "outlier_distance_km": 15212.3, + "second_furthest_km": 4258.9, + "clarity_ratio": 3.57, + "median_distance_km": 3427.3, + "distances_to_centroid": { + "Doreen": 3427.3, + "Nerang": 4258.9, + "Carlton": 3413.6, + "Corio": 3366.4, + "Bela Cruz": 15212.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doreen: (-37.60°, 145.15°)", + " Nerang: (-27.99°, 153.34°)", + " Carlton: (-37.80°, 144.97°)", + " Corio: (-38.08°, 144.38°)", + " Bela Cruz: (-3.05°, -40.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bela Cruz: 15212.3 km from centroid", + " Nerang: 4258.9 km from centroid", + " Doreen: 3427.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bela Cruz", + "FINAL ANSWER: Bela Cruz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 23.23756, + "lon": 69.69946, + "name": "Madhapar" + }, + { + "lat": 33.94278, + "lon": 105.06739, + "name": "Longlin" + }, + { + "lat": 24.48012, + "lon": 72.78186, + "name": "Ābu Road" + }, + { + "lat": -8.70536, + "lon": 116.27036, + "name": "Praya" + }, + { + "lat": 40.45927, + "lon": -74.36098, + "name": "Sayreville" + } + ], + "question": "Which location is the geographic outlier among: Madhapar, Longlin, Ābu Road, Praya, Sayreville?", + "ground_truth": { + "answer": "Sayreville", + "outlier_distance_km": 11432.5, + "second_furthest_km": 7247.4, + "clarity_ratio": 1.58, + "median_distance_km": 4741.4, + "distances_to_centroid": { + "Madhapar": 1210.2, + "Longlin": 4741.4, + "Ābu Road": 1529.8, + "Praya": 7247.4, + "Sayreville": 11432.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Madhapar: (23.24°, 69.70°)", + " Longlin: (33.94°, 105.07°)", + " Ābu Road: (24.48°, 72.78°)", + " Praya: (-8.71°, 116.27°)", + " Sayreville: (40.46°, -74.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sayreville: 11432.5 km from centroid", + " Praya: 7247.4 km from centroid", + " Longlin: 4741.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sayreville", + "FINAL ANSWER: Sayreville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.9, + "lon": 40.78333, + "name": "Bedēsa" + }, + { + "lat": 7.62329, + "lon": 5.22087, + "name": "Ado-Ekiti" + }, + { + "lat": -30.20672, + "lon": 30.79641, + "name": "eMkhomazi" + }, + { + "lat": 31.24193, + "lon": 30.94504, + "name": "Ar Riyāḑ" + }, + { + "lat": 31.09823, + "lon": -97.34278, + "name": "Temple" + } + ], + "question": "Which location is the geographic outlier among: Bedēsa, Ado-Ekiti, eMkhomazi, Ar Riyāḑ, Temple?", + "ground_truth": { + "answer": "Temple", + "outlier_distance_km": 10331.8, + "second_furthest_km": 5398.4, + "clarity_ratio": 1.91, + "median_distance_km": 4245.5, + "distances_to_centroid": { + "Bedēsa": 4245.5, + "Ado-Ekiti": 417.2, + "eMkhomazi": 5398.4, + "Ar Riyāḑ": 3819.0, + "Temple": 10331.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bedēsa: (8.90°, 40.78°)", + " Ado-Ekiti: (7.62°, 5.22°)", + " eMkhomazi: (-30.21°, 30.80°)", + " Ar Riyāḑ: (31.24°, 30.95°)", + " Temple: (31.10°, -97.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Temple: 10331.8 km from centroid", + " eMkhomazi: 5398.4 km from centroid", + " Bedēsa: 4245.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Temple", + "FINAL ANSWER: Temple" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.11612, + "lon": -118.15035, + "name": "South Pasadena" + }, + { + "lat": 19.35529, + "lon": -99.06224, + "name": "Iztapalapa" + }, + { + "lat": 39.48309, + "lon": -88.37283, + "name": "Mattoon" + }, + { + "lat": 36.07264, + "lon": -79.79198, + "name": "Greensboro" + }, + { + "lat": 51.37547, + "lon": 7.70281, + "name": "Iserlohn" + } + ], + "question": "Which location is the geographic outlier among: South Pasadena, Iztapalapa, Mattoon, Greensboro, Iserlohn?", + "ground_truth": { + "answer": "Iserlohn", + "outlier_distance_km": 6527.3, + "second_furthest_km": 3852.1, + "clarity_ratio": 1.69, + "median_distance_km": 2955.6, + "distances_to_centroid": { + "South Pasadena": 3852.1, + "Iztapalapa": 2955.6, + "Mattoon": 1188.7, + "Greensboro": 382.6, + "Iserlohn": 6527.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " South Pasadena: (34.12°, -118.15°)", + " Iztapalapa: (19.36°, -99.06°)", + " Mattoon: (39.48°, -88.37°)", + " Greensboro: (36.07°, -79.79°)", + " Iserlohn: (51.38°, 7.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Iserlohn: 6527.3 km from centroid", + " South Pasadena: 3852.1 km from centroid", + " Iztapalapa: 2955.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Iserlohn", + "FINAL ANSWER: Iserlohn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + }, + { + "lat": -8.81833, + "lon": -35.18639, + "name": "Barreiros" + } + ], + "question": "Which location is the geographic outlier among: Strathfield, Rochedale South, Whangarei, Calamvale, Barreiros?", + "ground_truth": { + "answer": "Barreiros", + "outlier_distance_km": 15197.0, + "second_furthest_km": 5260.5, + "clarity_ratio": 2.89, + "median_distance_km": 3339.3, + "distances_to_centroid": { + "Strathfield": 3141.1, + "Rochedale South": 3339.3, + "Whangarei": 5260.5, + "Calamvale": 3331.6, + "Barreiros": 15197.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Strathfield: (-33.88°, 151.08°)", + " Rochedale South: (-27.60°, 153.12°)", + " Whangarei: (-35.73°, 174.32°)", + " Calamvale: (-27.62°, 153.05°)", + " Barreiros: (-8.82°, -35.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barreiros: 15197.0 km from centroid", + " Whangarei: 5260.5 km from centroid", + " Rochedale South: 3339.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barreiros", + "FINAL ANSWER: Barreiros" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.6001, + "lon": 98.4854, + "name": "Binjai" + }, + { + "lat": 34.45278, + "lon": 116.9, + "name": "Heqiao" + }, + { + "lat": 13.87139, + "lon": 100.73719, + "name": "Khlong Sam Wa" + }, + { + "lat": 17.5242, + "lon": 78.32273, + "name": "Amīnpur" + }, + { + "lat": 44.64671, + "lon": 7.49309, + "name": "Saluzzo" + } + ], + "question": "Which location is the geographic outlier among: Binjai, Heqiao, Khlong Sam Wa, Amīnpur, Saluzzo?", + "ground_truth": { + "answer": "Saluzzo", + "outlier_distance_km": 6923.3, + "second_furthest_km": 3766.5, + "clarity_ratio": 1.84, + "median_distance_km": 2891.6, + "distances_to_centroid": { + "Binjai": 2891.6, + "Heqiao": 3766.5, + "Khlong Sam Wa": 2363.3, + "Amīnpur": 626.9, + "Saluzzo": 6923.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Binjai: (3.60°, 98.49°)", + " Heqiao: (34.45°, 116.90°)", + " Khlong Sam Wa: (13.87°, 100.74°)", + " Amīnpur: (17.52°, 78.32°)", + " Saluzzo: (44.65°, 7.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saluzzo: 6923.3 km from centroid", + " Heqiao: 3766.5 km from centroid", + " Binjai: 2891.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saluzzo", + "FINAL ANSWER: Saluzzo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.94541, + "lon": -66.66558, + "name": "Fredericton" + }, + { + "lat": 38.67796, + "lon": -121.17606, + "name": "Folsom" + }, + { + "lat": 29.94827, + "lon": -93.91712, + "name": "Groves" + }, + { + "lat": 34.09223, + "lon": -117.43505, + "name": "Fontana" + }, + { + "lat": 5.95753, + "lon": 6.85305, + "name": "Ozubulu" + } + ], + "question": "Which location is the geographic outlier among: Fredericton, Folsom, Groves, Fontana, Ozubulu?", + "ground_truth": { + "answer": "Ozubulu", + "outlier_distance_km": 9222.3, + "second_furthest_km": 3956.7, + "clarity_ratio": 2.33, + "median_distance_km": 3649.0, + "distances_to_centroid": { + "Fredericton": 1956.4, + "Folsom": 3956.7, + "Groves": 1483.9, + "Fontana": 3649.0, + "Ozubulu": 9222.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fredericton: (45.95°, -66.67°)", + " Folsom: (38.68°, -121.18°)", + " Groves: (29.95°, -93.92°)", + " Fontana: (34.09°, -117.44°)", + " Ozubulu: (5.96°, 6.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ozubulu: 9222.3 km from centroid", + " Folsom: 3956.7 km from centroid", + " Fontana: 3649.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ozubulu", + "FINAL ANSWER: Ozubulu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.17482, + "lon": -86.84361, + "name": "Cullman" + }, + { + "lat": 34.75405, + "lon": -77.43024, + "name": "Jacksonville" + }, + { + "lat": 40.71754, + "lon": -89.58426, + "name": "North Peoria" + }, + { + "lat": 40.68843, + "lon": -75.22073, + "name": "Easton" + }, + { + "lat": -23.39694, + "lon": -47.00222, + "name": "Pirapora do Bom Jesus" + } + ], + "question": "Which location is the geographic outlier among: Cullman, Jacksonville, North Peoria, Easton, Pirapora do Bom Jesus?", + "ground_truth": { + "answer": "Pirapora do Bom Jesus", + "outlier_distance_km": 6217.8, + "second_furthest_km": 2161.4, + "clarity_ratio": 2.88, + "median_distance_km": 1701.4, + "distances_to_centroid": { + "Cullman": 1485.9, + "Jacksonville": 1063.0, + "North Peoria": 2161.4, + "Easton": 1701.4, + "Pirapora do Bom Jesus": 6217.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cullman: (34.17°, -86.84°)", + " Jacksonville: (34.75°, -77.43°)", + " North Peoria: (40.72°, -89.58°)", + " Easton: (40.69°, -75.22°)", + " Pirapora do Bom Jesus: (-23.40°, -47.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pirapora do Bom Jesus: 6217.8 km from centroid", + " North Peoria: 2161.4 km from centroid", + " Easton: 1701.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pirapora do Bom Jesus", + "FINAL ANSWER: Pirapora do Bom Jesus" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.7471, + "lon": 40.05732, + "name": "Wajir" + }, + { + "lat": 31.40398, + "lon": 31.73778, + "name": "Kafr al Baţţīkh" + }, + { + "lat": 7.16938, + "lon": 9.28465, + "name": "Katsina-Ala" + }, + { + "lat": 5.93576, + "lon": 7.0793, + "name": "Uga" + }, + { + "lat": -4.83778, + "lon": -80.64556, + "name": "Querecotillo" + } + ], + "question": "Which location is the geographic outlier among: Wajir, Kafr al Baţţīkh, Katsina-Ala, Uga, Querecotillo?", + "ground_truth": { + "answer": "Querecotillo", + "outlier_distance_km": 9224.8, + "second_furthest_km": 4329.1, + "clarity_ratio": 2.13, + "median_distance_km": 4048.6, + "distances_to_centroid": { + "Wajir": 4329.1, + "Kafr al Baţţīkh": 4048.6, + "Katsina-Ala": 866.3, + "Uga": 668.4, + "Querecotillo": 9224.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wajir: (1.75°, 40.06°)", + " Kafr al Baţţīkh: (31.40°, 31.74°)", + " Katsina-Ala: (7.17°, 9.28°)", + " Uga: (5.94°, 7.08°)", + " Querecotillo: (-4.84°, -80.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Querecotillo: 9224.8 km from centroid", + " Wajir: 4329.1 km from centroid", + " Kafr al Baţţīkh: 4048.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Querecotillo", + "FINAL ANSWER: Querecotillo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91667, + "lon": 151.03333, + "name": "Bankstown" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": 36.77083, + "lon": 119.21083, + "name": "Hanting" + } + ], + "question": "Which location is the geographic outlier among: Bankstown, Papakura, Ashfield, Tauranga, Hanting?", + "ground_truth": { + "answer": "Hanting", + "outlier_distance_km": 7429.1, + "second_furthest_km": 2776.8, + "clarity_ratio": 2.68, + "median_distance_km": 2648.7, + "distances_to_centroid": { + "Bankstown": 1459.0, + "Papakura": 2648.7, + "Ashfield": 1453.9, + "Tauranga": 2776.8, + "Hanting": 7429.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bankstown: (-33.92°, 151.03°)", + " Papakura: (-37.06°, 174.94°)", + " Ashfield: (-33.89°, 151.12°)", + " Tauranga: (-37.69°, 176.17°)", + " Hanting: (36.77°, 119.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hanting: 7429.1 km from centroid", + " Tauranga: 2776.8 km from centroid", + " Papakura: 2648.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hanting", + "FINAL ANSWER: Hanting" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.88778, + "lon": -42.70444, + "name": "Além Paraíba" + }, + { + "lat": -19.36361, + "lon": -42.56861, + "name": "Santana do Paraíso" + }, + { + "lat": -6.24444, + "lon": -38.91361, + "name": "Orós" + }, + { + "lat": -29.95472, + "lon": -51.62528, + "name": "Charqueadas" + }, + { + "lat": 12.89439, + "lon": 11.92649, + "name": "Geidam" + } + ], + "question": "Which location is the geographic outlier among: Além Paraíba, Santana do Paraíso, Orós, Charqueadas, Geidam?", + "ground_truth": { + "answer": "Geidam", + "outlier_distance_km": 5702.6, + "second_furthest_km": 2711.4, + "clarity_ratio": 2.1, + "median_distance_km": 1450.1, + "distances_to_centroid": { + "Além Paraíba": 1450.1, + "Santana do Paraíso": 1267.7, + "Orós": 1000.8, + "Charqueadas": 2711.4, + "Geidam": 5702.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Além Paraíba: (-21.89°, -42.70°)", + " Santana do Paraíso: (-19.36°, -42.57°)", + " Orós: (-6.24°, -38.91°)", + " Charqueadas: (-29.95°, -51.63°)", + " Geidam: (12.89°, 11.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Geidam: 5702.6 km from centroid", + " Charqueadas: 2711.4 km from centroid", + " Além Paraíba: 1450.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Geidam", + "FINAL ANSWER: Geidam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.93976, + "lon": 30.81338, + "name": "Basyūn" + }, + { + "lat": 5.01806, + "lon": -1.66437, + "name": "Shama Junction" + }, + { + "lat": 30.8248, + "lon": 30.81805, + "name": "Kafr az Zayyāt" + }, + { + "lat": 12.50583, + "lon": 39.52278, + "name": "Korem" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + } + ], + "question": "Which location is the geographic outlier among: Basyūn, Shama Junction, Kafr az Zayyāt, Korem, Lincoln?", + "ground_truth": { + "answer": "Lincoln", + "outlier_distance_km": 13210.2, + "second_furthest_km": 6244.5, + "clarity_ratio": 2.12, + "median_distance_km": 3525.1, + "distances_to_centroid": { + "Basyūn": 3525.1, + "Shama Junction": 6244.5, + "Kafr az Zayyāt": 3516.5, + "Korem": 1730.9, + "Lincoln": 13210.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Basyūn: (30.94°, 30.81°)", + " Shama Junction: (5.02°, -1.66°)", + " Kafr az Zayyāt: (30.82°, 30.82°)", + " Korem: (12.51°, 39.52°)", + " Lincoln: (-36.86°, 174.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lincoln: 13210.2 km from centroid", + " Shama Junction: 6244.5 km from centroid", + " Basyūn: 3525.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lincoln", + "FINAL ANSWER: Lincoln" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.64583, + "lon": -47.19611, + "name": "Cosmópolis" + }, + { + "lat": -13.71029, + "lon": -76.20538, + "name": "Pisco" + }, + { + "lat": -22.96611, + "lon": -42.02778, + "name": "Arraial do Cabo" + }, + { + "lat": -3.56222, + "lon": -41.09222, + "name": "Viçosa do Ceará" + }, + { + "lat": 47.84965, + "lon": 12.06696, + "name": "Kolbermoor" + } + ], + "question": "Which location is the geographic outlier among: Cosmópolis, Pisco, Arraial do Cabo, Viçosa do Ceará, Kolbermoor?", + "ground_truth": { + "answer": "Kolbermoor", + "outlier_distance_km": 7501.9, + "second_furthest_km": 4266.5, + "clarity_ratio": 1.76, + "median_distance_km": 2360.1, + "distances_to_centroid": { + "Cosmópolis": 2360.1, + "Pisco": 4266.5, + "Arraial do Cabo": 2244.9, + "Viçosa do Ceará": 252.1, + "Kolbermoor": 7501.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cosmópolis: (-22.65°, -47.20°)", + " Pisco: (-13.71°, -76.21°)", + " Arraial do Cabo: (-22.97°, -42.03°)", + " Viçosa do Ceará: (-3.56°, -41.09°)", + " Kolbermoor: (47.85°, 12.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kolbermoor: 7501.9 km from centroid", + " Pisco: 4266.5 km from centroid", + " Cosmópolis: 2360.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kolbermoor", + "FINAL ANSWER: Kolbermoor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.77501, + "lon": 9.38155, + "name": "Höxter" + }, + { + "lat": 48.5842, + "lon": 45.7338, + "name": "Znamensk" + }, + { + "lat": 55.76667, + "lon": -3.91667, + "name": "Wishaw" + }, + { + "lat": 48.92161, + "lon": 2.19263, + "name": "Houilles" + }, + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + } + ], + "question": "Which location is the geographic outlier among: Höxter, Znamensk, Wishaw, Houilles, Robina?", + "ground_truth": { + "answer": "Robina", + "outlier_distance_km": 13660.2, + "second_furthest_km": 4082.9, + "clarity_ratio": 3.35, + "median_distance_km": 3511.4, + "distances_to_centroid": { + "Höxter": 3114.3, + "Znamensk": 1509.8, + "Wishaw": 4082.9, + "Houilles": 3511.4, + "Robina": 13660.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Höxter: (51.78°, 9.38°)", + " Znamensk: (48.58°, 45.73°)", + " Wishaw: (55.77°, -3.92°)", + " Houilles: (48.92°, 2.19°)", + " Robina: (-28.07°, 153.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Robina: 13660.2 km from centroid", + " Wishaw: 4082.9 km from centroid", + " Houilles: 3511.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Robina", + "FINAL ANSWER: Robina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.62914, + "lon": 31.08235, + "name": "Birkat as Sab‘" + }, + { + "lat": 9.6, + "lon": 37.83333, + "name": "Kachīsī" + }, + { + "lat": -3.86261, + "lon": 39.47458, + "name": "Mariakani" + }, + { + "lat": 8.49664, + "lon": 4.54214, + "name": "Ilorin" + }, + { + "lat": 47.92526, + "lon": -97.03285, + "name": "Grand Forks" + } + ], + "question": "Which location is the geographic outlier among: Birkat as Sab‘, Kachīsī, Mariakani, Ilorin, Grand Forks?", + "ground_truth": { + "answer": "Grand Forks", + "outlier_distance_km": 9218.1, + "second_furthest_km": 4691.5, + "clarity_ratio": 1.96, + "median_distance_km": 3860.2, + "distances_to_centroid": { + "Birkat as Sab‘": 3112.0, + "Kachīsī": 3860.2, + "Mariakani": 4691.5, + "Ilorin": 1128.4, + "Grand Forks": 9218.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Birkat as Sab‘: (30.63°, 31.08°)", + " Kachīsī: (9.60°, 37.83°)", + " Mariakani: (-3.86°, 39.47°)", + " Ilorin: (8.50°, 4.54°)", + " Grand Forks: (47.93°, -97.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Grand Forks: 9218.1 km from centroid", + " Mariakani: 4691.5 km from centroid", + " Kachīsī: 3860.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Grand Forks", + "FINAL ANSWER: Grand Forks" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.8225, + "lon": -39.42694, + "name": "Nordestina" + }, + { + "lat": -2.69795, + "lon": -59.70172, + "name": "Rio Preto da Eva" + }, + { + "lat": -25.88278, + "lon": -48.57472, + "name": "Guaratuba" + }, + { + "lat": -25.43998, + "lon": -54.40161, + "name": "Santa Terezinha de Itaipu" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + } + ], + "question": "Which location is the geographic outlier among: Nordestina, Rio Preto da Eva, Guaratuba, Santa Terezinha de Itaipu, Willetton?", + "ground_truth": { + "answer": "Willetton", + "outlier_distance_km": 12425.8, + "second_furthest_km": 4970.3, + "clarity_ratio": 2.5, + "median_distance_km": 3866.2, + "distances_to_centroid": { + "Nordestina": 2561.1, + "Rio Preto da Eva": 4970.3, + "Guaratuba": 3287.4, + "Santa Terezinha de Itaipu": 3866.2, + "Willetton": 12425.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nordestina: (-10.82°, -39.43°)", + " Rio Preto da Eva: (-2.70°, -59.70°)", + " Guaratuba: (-25.88°, -48.57°)", + " Santa Terezinha de Itaipu: (-25.44°, -54.40°)", + " Willetton: (-32.05°, 115.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Willetton: 12425.8 km from centroid", + " Rio Preto da Eva: 4970.3 km from centroid", + " Santa Terezinha de Itaipu: 3866.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Willetton", + "FINAL ANSWER: Willetton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.4232, + "lon": -71.64974, + "name": "Talca" + }, + { + "lat": -13.07541, + "lon": -76.31719, + "name": "Nuevo Imperial" + }, + { + "lat": -7.54528, + "lon": -35.7075, + "name": "Aroeiras" + }, + { + "lat": -23.52508, + "lon": -46.63889, + "name": "Bom Retiro" + }, + { + "lat": 21.6, + "lon": 109.71667, + "name": "Shankou" + } + ], + "question": "Which location is the geographic outlier among: Talca, Nuevo Imperial, Aroeiras, Bom Retiro, Shankou?", + "ground_truth": { + "answer": "Shankou", + "outlier_distance_km": 14990.6, + "second_furthest_km": 5662.7, + "clarity_ratio": 2.65, + "median_distance_km": 5453.5, + "distances_to_centroid": { + "Talca": 5453.5, + "Nuevo Imperial": 5662.7, + "Aroeiras": 1347.7, + "Bom Retiro": 2725.1, + "Shankou": 14990.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Talca: (-35.42°, -71.65°)", + " Nuevo Imperial: (-13.08°, -76.32°)", + " Aroeiras: (-7.55°, -35.71°)", + " Bom Retiro: (-23.53°, -46.64°)", + " Shankou: (21.60°, 109.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shankou: 14990.6 km from centroid", + " Nuevo Imperial: 5662.7 km from centroid", + " Talca: 5453.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shankou", + "FINAL ANSWER: Shankou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -40.80255, + "lon": -62.98349, + "name": "Carmen de Patagones" + }, + { + "lat": -4.88583, + "lon": -46.005, + "name": "Arame" + }, + { + "lat": 9.95157, + "lon": -75.08198, + "name": "San Juan Nepomuceno" + }, + { + "lat": -22.35694, + "lon": -47.38417, + "name": "Araras" + }, + { + "lat": 6.75, + "lon": 38.41667, + "name": "Yirga ‘Alem" + } + ], + "question": "Which location is the geographic outlier among: Carmen de Patagones, Arame, San Juan Nepomuceno, Araras, Yirga ‘Alem?", + "ground_truth": { + "answer": "Yirga ‘Alem", + "outlier_distance_km": 8734.7, + "second_furthest_km": 4618.7, + "clarity_ratio": 1.89, + "median_distance_km": 4153.3, + "distances_to_centroid": { + "Carmen de Patagones": 4153.3, + "Arame": 1011.2, + "San Juan Nepomuceno": 4618.7, + "Araras": 1637.0, + "Yirga ‘Alem": 8734.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carmen de Patagones: (-40.80°, -62.98°)", + " Arame: (-4.89°, -46.01°)", + " San Juan Nepomuceno: (9.95°, -75.08°)", + " Araras: (-22.36°, -47.38°)", + " Yirga ‘Alem: (6.75°, 38.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yirga ‘Alem: 8734.7 km from centroid", + " San Juan Nepomuceno: 4618.7 km from centroid", + " Carmen de Patagones: 4153.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yirga ‘Alem", + "FINAL ANSWER: Yirga ‘Alem" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.15299, + "lon": 79.10814, + "name": "Bāzpur" + }, + { + "lat": 37.24227, + "lon": 79.69283, + "name": "Tuohula" + }, + { + "lat": 11.5021, + "lon": 77.25554, + "name": "Kumārapālaiyam" + }, + { + "lat": 22.62104, + "lon": 73.11725, + "name": "Od" + }, + { + "lat": 10.64061, + "lon": 36.94684, + "name": "Shendi" + } + ], + "question": "Which location is the geographic outlier among: Bāzpur, Tuohula, Kumārapālaiyam, Od, Shendi?", + "ground_truth": { + "answer": "Shendi", + "outlier_distance_km": 3665.3, + "second_furthest_km": 1948.1, + "clarity_ratio": 1.88, + "median_distance_km": 1466.6, + "distances_to_centroid": { + "Bāzpur": 1253.3, + "Tuohula": 1948.1, + "Kumārapālaiyam": 1466.6, + "Od": 402.5, + "Shendi": 3665.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bāzpur: (29.15°, 79.11°)", + " Tuohula: (37.24°, 79.69°)", + " Kumārapālaiyam: (11.50°, 77.26°)", + " Od: (22.62°, 73.12°)", + " Shendi: (10.64°, 36.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shendi: 3665.3 km from centroid", + " Tuohula: 1948.1 km from centroid", + " Kumārapālaiyam: 1466.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shendi", + "FINAL ANSWER: Shendi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.40159, + "lon": -86.86357, + "name": "Navarre" + }, + { + "lat": 41.9659, + "lon": -87.65262, + "name": "Uptown" + }, + { + "lat": 18.14905, + "lon": -94.4447, + "name": "Coatzacoalcos" + }, + { + "lat": 42.20704, + "lon": -71.68562, + "name": "Grafton" + }, + { + "lat": 31.19688, + "lon": 31.5243, + "name": "Shirbīn" + } + ], + "question": "Which location is the geographic outlier among: Navarre, Uptown, Coatzacoalcos, Grafton, Shirbīn?", + "ground_truth": { + "answer": "Shirbīn", + "outlier_distance_km": 8473.5, + "second_furthest_km": 3635.7, + "clarity_ratio": 2.33, + "median_distance_km": 2487.5, + "distances_to_centroid": { + "Navarre": 2380.8, + "Uptown": 2487.5, + "Coatzacoalcos": 3635.7, + "Grafton": 1359.9, + "Shirbīn": 8473.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Navarre: (30.40°, -86.86°)", + " Uptown: (41.97°, -87.65°)", + " Coatzacoalcos: (18.15°, -94.44°)", + " Grafton: (42.21°, -71.69°)", + " Shirbīn: (31.20°, 31.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shirbīn: 8473.5 km from centroid", + " Coatzacoalcos: 3635.7 km from centroid", + " Uptown: 2487.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shirbīn", + "FINAL ANSWER: Shirbīn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.49482, + "lon": 77.30587, + "name": "Taj Pul" + }, + { + "lat": 17.01717, + "lon": 99.73283, + "name": "Ban Na" + }, + { + "lat": 16.55154, + "lon": 81.214, + "name": "Kaikalūr" + }, + { + "lat": 28.60922, + "lon": 76.97982, + "name": "Najafgarh" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + } + ], + "question": "Which location is the geographic outlier among: Taj Pul, Ban Na, Kaikalūr, Najafgarh, Baldivis?", + "ground_truth": { + "answer": "Baldivis", + "outlier_distance_km": 5599.3, + "second_furthest_km": 2331.5, + "clarity_ratio": 2.4, + "median_distance_km": 2301.8, + "distances_to_centroid": { + "Taj Pul": 2301.8, + "Ban Na": 1185.1, + "Kaikalūr": 1111.6, + "Najafgarh": 2331.5, + "Baldivis": 5599.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taj Pul: (28.49°, 77.31°)", + " Ban Na: (17.02°, 99.73°)", + " Kaikalūr: (16.55°, 81.21°)", + " Najafgarh: (28.61°, 76.98°)", + " Baldivis: (-32.33°, 115.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baldivis: 5599.3 km from centroid", + " Najafgarh: 2331.5 km from centroid", + " Taj Pul: 2301.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Baldivis", + "FINAL ANSWER: Baldivis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.5655, + "lon": 14.27433, + "name": "Enna" + }, + { + "lat": 48.24896, + "lon": 11.65101, + "name": "Garching" + }, + { + "lat": 54.51889, + "lon": 18.53188, + "name": "Gdynia" + }, + { + "lat": 50.89973, + "lon": 15.72899, + "name": "Jelenia Góra" + }, + { + "lat": -24.71361, + "lon": -53.74306, + "name": "Toledo" + } + ], + "question": "Which location is the geographic outlier among: Enna, Garching, Gdynia, Jelenia Góra, Toledo?", + "ground_truth": { + "answer": "Toledo", + "outlier_distance_km": 8688.5, + "second_furthest_km": 2717.1, + "clarity_ratio": 3.2, + "median_distance_km": 2281.5, + "distances_to_centroid": { + "Enna": 1266.9, + "Garching": 1873.0, + "Gdynia": 2717.1, + "Jelenia Góra": 2281.5, + "Toledo": 8688.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Enna: (37.57°, 14.27°)", + " Garching: (48.25°, 11.65°)", + " Gdynia: (54.52°, 18.53°)", + " Jelenia Góra: (50.90°, 15.73°)", + " Toledo: (-24.71°, -53.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Toledo: 8688.5 km from centroid", + " Gdynia: 2717.1 km from centroid", + " Jelenia Góra: 2281.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Toledo", + "FINAL ANSWER: Toledo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.61766, + "lon": -2.1552, + "name": "Rochdale" + }, + { + "lat": 53.55, + "lon": -2.4, + "name": "Farnworth" + }, + { + "lat": 45.88549, + "lon": 6.08831, + "name": "Seynod" + }, + { + "lat": 43.46, + "lon": 5.24861, + "name": "Vitrolles" + }, + { + "lat": -18.99111, + "lon": -50.54361, + "name": "São Simão" + } + ], + "question": "Which location is the geographic outlier among: Rochdale, Farnworth, Seynod, Vitrolles, São Simão?", + "ground_truth": { + "answer": "São Simão", + "outlier_distance_km": 7490.2, + "second_furthest_km": 2078.6, + "clarity_ratio": 3.6, + "median_distance_km": 2066.8, + "distances_to_centroid": { + "Rochdale": 2078.6, + "Farnworth": 2066.8, + "Seynod": 1697.2, + "Vitrolles": 1488.8, + "São Simão": 7490.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rochdale: (53.62°, -2.16°)", + " Farnworth: (53.55°, -2.40°)", + " Seynod: (45.89°, 6.09°)", + " Vitrolles: (43.46°, 5.25°)", + " São Simão: (-18.99°, -50.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Simão: 7490.2 km from centroid", + " Rochdale: 2078.6 km from centroid", + " Farnworth: 2066.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Simão", + "FINAL ANSWER: São Simão" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.62028, + "lon": -45.41306, + "name": "Caraguatatuba" + }, + { + "lat": -21.93472, + "lon": -50.51361, + "name": "Tupã" + }, + { + "lat": -5.895, + "lon": -35.76278, + "name": "São Paulo do Potengi" + }, + { + "lat": -33.15365, + "lon": -60.51168, + "name": "Arroyo Seco" + }, + { + "lat": 43.64506, + "lon": -79.46787, + "name": "High Park-Swansea" + } + ], + "question": "Which location is the geographic outlier among: Caraguatatuba, Tupã, São Paulo do Potengi, Arroyo Seco, High Park-Swansea?", + "ground_truth": { + "answer": "High Park-Swansea", + "outlier_distance_km": 6296.6, + "second_furthest_km": 2847.4, + "clarity_ratio": 2.21, + "median_distance_km": 2065.0, + "distances_to_centroid": { + "Caraguatatuba": 1961.2, + "Tupã": 1581.9, + "São Paulo do Potengi": 2065.0, + "Arroyo Seco": 2847.4, + "High Park-Swansea": 6296.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caraguatatuba: (-23.62°, -45.41°)", + " Tupã: (-21.93°, -50.51°)", + " São Paulo do Potengi: (-5.89°, -35.76°)", + " Arroyo Seco: (-33.15°, -60.51°)", + " High Park-Swansea: (43.65°, -79.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " High Park-Swansea: 6296.6 km from centroid", + " Arroyo Seco: 2847.4 km from centroid", + " São Paulo do Potengi: 2065.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: High Park-Swansea", + "FINAL ANSWER: High Park-Swansea" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.41069, + "lon": -80.84285, + "name": "Huntersville" + }, + { + "lat": 32.74477, + "lon": -116.99892, + "name": "Spring Valley" + }, + { + "lat": 42.99564, + "lon": -71.45479, + "name": "Manchester" + }, + { + "lat": 33.13845, + "lon": -96.11081, + "name": "Greenville" + }, + { + "lat": 10.20898, + "lon": 123.758, + "name": "Naga" + } + ], + "question": "Which location is the geographic outlier among: Huntersville, Spring Valley, Manchester, Greenville, Naga?", + "ground_truth": { + "answer": "Naga", + "outlier_distance_km": 15366.6, + "second_furthest_km": 6371.0, + "clarity_ratio": 2.41, + "median_distance_km": 4472.5, + "distances_to_centroid": { + "Huntersville": 3053.9, + "Spring Valley": 6371.0, + "Manchester": 2443.1, + "Greenville": 4472.5, + "Naga": 15366.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huntersville: (35.41°, -80.84°)", + " Spring Valley: (32.74°, -117.00°)", + " Manchester: (43.00°, -71.45°)", + " Greenville: (33.14°, -96.11°)", + " Naga: (10.21°, 123.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Naga: 15366.6 km from centroid", + " Spring Valley: 6371.0 km from centroid", + " Greenville: 4472.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Naga", + "FINAL ANSWER: Naga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.40843, + "lon": -71.01199, + "name": "Revere" + }, + { + "lat": 42.06975, + "lon": -87.78784, + "name": "Glenview" + }, + { + "lat": 42.2942, + "lon": -83.30993, + "name": "Inkster" + }, + { + "lat": 19.42155, + "lon": -98.95038, + "name": "Santa María Chimalhuacán" + }, + { + "lat": 35.73231, + "lon": 114.28616, + "name": "Hebi" + } + ], + "question": "Which location is the geographic outlier among: Revere, Glenview, Inkster, Santa María Chimalhuacán, Hebi?", + "ground_truth": { + "answer": "Hebi", + "outlier_distance_km": 11724.5, + "second_furthest_km": 5517.6, + "clarity_ratio": 2.12, + "median_distance_km": 3670.9, + "distances_to_centroid": { + "Revere": 2294.0, + "Glenview": 3670.9, + "Inkster": 3301.1, + "Santa María Chimalhuacán": 5517.6, + "Hebi": 11724.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Revere: (42.41°, -71.01°)", + " Glenview: (42.07°, -87.79°)", + " Inkster: (42.29°, -83.31°)", + " Santa María Chimalhuacán: (19.42°, -98.95°)", + " Hebi: (35.73°, 114.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hebi: 11724.5 km from centroid", + " Santa María Chimalhuacán: 5517.6 km from centroid", + " Glenview: 3670.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hebi", + "FINAL ANSWER: Hebi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": -31.88775, + "lon": 115.9099, + "name": "Morley" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": 30.03103, + "lon": 31.11109, + "name": "Kirdāsah" + } + ], + "question": "Which location is the geographic outlier among: Otahuhu, Morley, Tuggeranong Administrative District, Officer, Kirdāsah?", + "ground_truth": { + "answer": "Kirdāsah", + "outlier_distance_km": 11429.0, + "second_furthest_km": 5168.0, + "clarity_ratio": 2.21, + "median_distance_km": 2881.8, + "distances_to_centroid": { + "Otahuhu": 5168.0, + "Morley": 1275.9, + "Tuggeranong Administrative District": 2881.8, + "Officer": 2731.7, + "Kirdāsah": 11429.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Otahuhu: (-36.94°, 174.84°)", + " Morley: (-31.89°, 115.91°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + " Officer: (-38.06°, 145.41°)", + " Kirdāsah: (30.03°, 31.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kirdāsah: 11429.0 km from centroid", + " Otahuhu: 5168.0 km from centroid", + " Tuggeranong Administrative District: 2881.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kirdāsah", + "FINAL ANSWER: Kirdāsah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.79993, + "lon": 2.33256, + "name": "Arcueil" + }, + { + "lat": 43.17476, + "lon": 5.60449, + "name": "La Ciotat" + }, + { + "lat": 39.96495, + "lon": -0.26041, + "name": "Onda" + }, + { + "lat": 53.01499, + "lon": 13.99924, + "name": "Angermünde" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + } + ], + "question": "Which location is the geographic outlier among: Arcueil, La Ciotat, Onda, Angermünde, Officer?", + "ground_truth": { + "answer": "Officer", + "outlier_distance_km": 13789.5, + "second_furthest_km": 3403.3, + "clarity_ratio": 4.05, + "median_distance_km": 3273.3, + "distances_to_centroid": { + "Arcueil": 3403.3, + "La Ciotat": 2906.3, + "Onda": 3273.3, + "Angermünde": 3067.8, + "Officer": 13789.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arcueil: (48.80°, 2.33°)", + " La Ciotat: (43.17°, 5.60°)", + " Onda: (39.96°, -0.26°)", + " Angermünde: (53.01°, 14.00°)", + " Officer: (-38.06°, 145.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Officer: 13789.5 km from centroid", + " Arcueil: 3403.3 km from centroid", + " Onda: 3273.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Officer", + "FINAL ANSWER: Officer" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.62139, + "lon": -60.94417, + "name": "Novo Airão" + }, + { + "lat": -6.75917, + "lon": -38.22806, + "name": "Sousa" + }, + { + "lat": -13.44083, + "lon": -49.14861, + "name": "Porangatu" + }, + { + "lat": -38.8805, + "lon": -62.07503, + "name": "Punta Alta" + }, + { + "lat": 33.5594, + "lon": 75.23222, + "name": "Dooru Verinag" + } + ], + "question": "Which location is the geographic outlier among: Novo Airão, Sousa, Porangatu, Punta Alta, Dooru Verinag?", + "ground_truth": { + "answer": "Dooru Verinag", + "outlier_distance_km": 11488.6, + "second_furthest_km": 5104.5, + "clarity_ratio": 2.25, + "median_distance_km": 3775.1, + "distances_to_centroid": { + "Novo Airão": 3775.1, + "Sousa": 1243.9, + "Porangatu": 2573.8, + "Punta Alta": 5104.5, + "Dooru Verinag": 11488.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Novo Airão: (-2.62°, -60.94°)", + " Sousa: (-6.76°, -38.23°)", + " Porangatu: (-13.44°, -49.15°)", + " Punta Alta: (-38.88°, -62.08°)", + " Dooru Verinag: (33.56°, 75.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dooru Verinag: 11488.6 km from centroid", + " Punta Alta: 5104.5 km from centroid", + " Novo Airão: 3775.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dooru Verinag", + "FINAL ANSWER: Dooru Verinag" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.44269, + "lon": 2.182, + "name": "la Prosperitat" + }, + { + "lat": 52.4475, + "lon": 5.84306, + "name": "Elburg" + }, + { + "lat": 49.68866, + "lon": 21.77058, + "name": "Krosno" + }, + { + "lat": 53.48414, + "lon": -2.05908, + "name": "Stalybridge" + }, + { + "lat": 8.52218, + "lon": 77.04001, + "name": "Vilappil" + } + ], + "question": "Which location is the geographic outlier among: la Prosperitat, Elburg, Krosno, Stalybridge, Vilappil?", + "ground_truth": { + "answer": "Vilappil", + "outlier_distance_km": 6574.4, + "second_furthest_km": 2197.3, + "clarity_ratio": 2.99, + "median_distance_km": 1699.5, + "distances_to_centroid": { + "la Prosperitat": 1566.1, + "Elburg": 1699.5, + "Krosno": 955.2, + "Stalybridge": 2197.3, + "Vilappil": 6574.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " la Prosperitat: (41.44°, 2.18°)", + " Elburg: (52.45°, 5.84°)", + " Krosno: (49.69°, 21.77°)", + " Stalybridge: (53.48°, -2.06°)", + " Vilappil: (8.52°, 77.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vilappil: 6574.4 km from centroid", + " Stalybridge: 2197.3 km from centroid", + " Elburg: 1699.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vilappil", + "FINAL ANSWER: Vilappil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": 7.15139, + "lon": 37.17184, + "name": "Tarch’a Sodo" + } + ], + "question": "Which location is the geographic outlier among: Dandenong North, Coogee, Taylors Hill, Southport, Tarch’a Sodo?", + "ground_truth": { + "answer": "Tarch’a Sodo", + "outlier_distance_km": 10275.7, + "second_furthest_km": 2681.2, + "clarity_ratio": 3.83, + "median_distance_km": 2543.0, + "distances_to_centroid": { + "Dandenong North": 2207.2, + "Coogee": 2543.0, + "Taylors Hill": 2158.3, + "Southport": 2681.2, + "Tarch’a Sodo": 10275.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dandenong North: (-37.97°, 145.21°)", + " Coogee: (-33.92°, 151.26°)", + " Taylors Hill: (-37.71°, 144.75°)", + " Southport: (-27.97°, 153.40°)", + " Tarch’a Sodo: (7.15°, 37.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tarch’a Sodo: 10275.7 km from centroid", + " Southport: 2681.2 km from centroid", + " Coogee: 2543.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tarch’a Sodo", + "FINAL ANSWER: Tarch’a Sodo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.66578, + "lon": -95.01937, + "name": "La Porte" + }, + { + "lat": 40.81538, + "lon": -73.04511, + "name": "Holtsville" + }, + { + "lat": 25.58066, + "lon": -80.34672, + "name": "Cutler Ridge" + }, + { + "lat": 31.76072, + "lon": -93.08627, + "name": "Natchitoches" + }, + { + "lat": -20.42278, + "lon": -49.97278, + "name": "Votuporanga" + } + ], + "question": "Which location is the geographic outlier among: La Porte, Holtsville, Cutler Ridge, Natchitoches, Votuporanga?", + "ground_truth": { + "answer": "Votuporanga", + "outlier_distance_km": 5583.8, + "second_furthest_km": 2206.1, + "clarity_ratio": 2.53, + "median_distance_km": 1905.5, + "distances_to_centroid": { + "La Porte": 1905.5, + "Holtsville": 2206.1, + "Cutler Ridge": 501.7, + "Natchitoches": 1859.2, + "Votuporanga": 5583.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Porte: (29.67°, -95.02°)", + " Holtsville: (40.82°, -73.05°)", + " Cutler Ridge: (25.58°, -80.35°)", + " Natchitoches: (31.76°, -93.09°)", + " Votuporanga: (-20.42°, -49.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Votuporanga: 5583.8 km from centroid", + " Holtsville: 2206.1 km from centroid", + " La Porte: 1905.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Votuporanga", + "FINAL ANSWER: Votuporanga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.78821, + "lon": 175.2902, + "name": "Hamilton East" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": 19.15892, + "lon": -98.40824, + "name": "Huejotzingo" + } + ], + "question": "Which location is the geographic outlier among: Hamilton East, Rochedale South, Ashburton, Carlton, Huejotzingo?", + "ground_truth": { + "answer": "Huejotzingo", + "outlier_distance_km": 17079.9, + "second_furthest_km": 6258.3, + "clarity_ratio": 2.73, + "median_distance_km": 5902.7, + "distances_to_centroid": { + "Hamilton East": 6258.3, + "Rochedale South": 4336.7, + "Ashburton": 5902.7, + "Carlton": 3607.0, + "Huejotzingo": 17079.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hamilton East: (-37.79°, 175.29°)", + " Rochedale South: (-27.60°, 153.12°)", + " Ashburton: (-43.90°, 171.73°)", + " Carlton: (-37.80°, 144.97°)", + " Huejotzingo: (19.16°, -98.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huejotzingo: 17079.9 km from centroid", + " Hamilton East: 6258.3 km from centroid", + " Ashburton: 5902.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huejotzingo", + "FINAL ANSWER: Huejotzingo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.76741, + "lon": -94.48985, + "name": "Kenora" + }, + { + "lat": 42.18169, + "lon": -87.80034, + "name": "Highland Park" + }, + { + "lat": 49.01667, + "lon": -123.08333, + "name": "Tsawwassen" + }, + { + "lat": 33.56504, + "lon": -117.72712, + "name": "Aliso Viejo" + }, + { + "lat": 12.91808, + "lon": 79.27756, + "name": "Vishāram" + } + ], + "question": "Which location is the geographic outlier among: Kenora, Highland Park, Tsawwassen, Aliso Viejo, Vishāram?", + "ground_truth": { + "answer": "Vishāram", + "outlier_distance_km": 13492.3, + "second_furthest_km": 4478.1, + "clarity_ratio": 3.01, + "median_distance_km": 4402.6, + "distances_to_centroid": { + "Kenora": 2460.7, + "Highland Park": 1702.8, + "Tsawwassen": 4478.1, + "Aliso Viejo": 4402.6, + "Vishāram": 13492.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kenora: (49.77°, -94.49°)", + " Highland Park: (42.18°, -87.80°)", + " Tsawwassen: (49.02°, -123.08°)", + " Aliso Viejo: (33.57°, -117.73°)", + " Vishāram: (12.92°, 79.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vishāram: 13492.3 km from centroid", + " Tsawwassen: 4478.1 km from centroid", + " Aliso Viejo: 4402.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vishāram", + "FINAL ANSWER: Vishāram" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.74761, + "lon": -116.97307, + "name": "Hemet" + }, + { + "lat": 42.34447, + "lon": -88.04175, + "name": "Grayslake" + }, + { + "lat": 19.77189, + "lon": -104.36644, + "name": "Autlán de Navarro" + }, + { + "lat": 40.52467, + "lon": -111.86382, + "name": "Draper" + }, + { + "lat": 46.63033, + "lon": 38.66379, + "name": "Staroshcherbinovskaya" + } + ], + "question": "Which location is the geographic outlier among: Hemet, Grayslake, Autlán de Navarro, Draper, Staroshcherbinovskaya?", + "ground_truth": { + "answer": "Staroshcherbinovskaya", + "outlier_distance_km": 8731.8, + "second_furthest_km": 3663.8, + "clarity_ratio": 2.38, + "median_distance_km": 3289.3, + "distances_to_centroid": { + "Hemet": 3663.8, + "Grayslake": 1175.7, + "Autlán de Navarro": 3289.3, + "Draper": 3083.1, + "Staroshcherbinovskaya": 8731.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hemet: (33.75°, -116.97°)", + " Grayslake: (42.34°, -88.04°)", + " Autlán de Navarro: (19.77°, -104.37°)", + " Draper: (40.52°, -111.86°)", + " Staroshcherbinovskaya: (46.63°, 38.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Staroshcherbinovskaya: 8731.8 km from centroid", + " Hemet: 3663.8 km from centroid", + " Autlán de Navarro: 3289.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Staroshcherbinovskaya", + "FINAL ANSWER: Staroshcherbinovskaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + }, + { + "lat": 6.98789, + "lon": -73.04953, + "name": "Piedecuesta" + } + ], + "question": "Which location is the geographic outlier among: Hastings, Pakenham, Cranbourne West, Dandenong, Piedecuesta?", + "ground_truth": { + "answer": "Piedecuesta", + "outlier_distance_km": 17525.2, + "second_furthest_km": 6263.8, + "clarity_ratio": 2.8, + "median_distance_km": 3576.9, + "distances_to_centroid": { + "Hastings": 6263.8, + "Pakenham": 3576.9, + "Cranbourne West": 3559.1, + "Dandenong": 3552.3, + "Piedecuesta": 17525.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hastings: (-39.64°, 176.85°)", + " Pakenham: (-38.07°, 145.47°)", + " Cranbourne West: (-38.10°, 145.27°)", + " Dandenong: (-37.98°, 145.20°)", + " Piedecuesta: (6.99°, -73.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piedecuesta: 17525.2 km from centroid", + " Hastings: 6263.8 km from centroid", + " Pakenham: 3576.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piedecuesta", + "FINAL ANSWER: Piedecuesta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.66384, + "lon": 41.88915, + "name": "Rasskazovo" + }, + { + "lat": 51.10654, + "lon": 13.66047, + "name": "Radebeul" + }, + { + "lat": 52.08868, + "lon": 17.01508, + "name": "Śrem" + }, + { + "lat": 52.234, + "lon": 4.44474, + "name": "Noordwijk-Binnen" + }, + { + "lat": -28.56003, + "lon": -66.80737, + "name": "Aimogasta" + } + ], + "question": "Which location is the geographic outlier among: Rasskazovo, Radebeul, Śrem, Noordwijk-Binnen, Aimogasta?", + "ground_truth": { + "answer": "Aimogasta", + "outlier_distance_km": 10158.3, + "second_furthest_km": 3613.3, + "clarity_ratio": 2.81, + "median_distance_km": 2152.2, + "distances_to_centroid": { + "Rasskazovo": 3613.3, + "Radebeul": 1927.2, + "Śrem": 2152.2, + "Noordwijk-Binnen": 1825.4, + "Aimogasta": 10158.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rasskazovo: (52.66°, 41.89°)", + " Radebeul: (51.11°, 13.66°)", + " Śrem: (52.09°, 17.02°)", + " Noordwijk-Binnen: (52.23°, 4.44°)", + " Aimogasta: (-28.56°, -66.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aimogasta: 10158.3 km from centroid", + " Rasskazovo: 3613.3 km from centroid", + " Śrem: 2152.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aimogasta", + "FINAL ANSWER: Aimogasta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.74306, + "lon": -39.6275, + "name": "Mombaça" + }, + { + "lat": -19.53944, + "lon": -40.63056, + "name": "Colatina" + }, + { + "lat": -22.23, + "lon": -45.93639, + "name": "Pouso Alegre" + }, + { + "lat": -23.63634, + "lon": -46.76565, + "name": "Campo Limpo" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + } + ], + "question": "Which location is the geographic outlier among: Mombaça, Colatina, Pouso Alegre, Campo Limpo, Cheltenham?", + "ground_truth": { + "answer": "Cheltenham", + "outlier_distance_km": 12692.5, + "second_furthest_km": 4214.1, + "clarity_ratio": 3.01, + "median_distance_km": 4147.2, + "distances_to_centroid": { + "Mombaça": 4072.6, + "Colatina": 3647.2, + "Pouso Alegre": 4147.2, + "Campo Limpo": 4214.1, + "Cheltenham": 12692.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mombaça: (-5.74°, -39.63°)", + " Colatina: (-19.54°, -40.63°)", + " Pouso Alegre: (-22.23°, -45.94°)", + " Campo Limpo: (-23.64°, -46.77°)", + " Cheltenham: (-37.97°, 145.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cheltenham: 12692.5 km from centroid", + " Campo Limpo: 4214.1 km from centroid", + " Pouso Alegre: 4147.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cheltenham", + "FINAL ANSWER: Cheltenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + }, + { + "lat": 13.38896, + "lon": 77.86444, + "name": "Sidlaghatta" + } + ], + "question": "Which location is the geographic outlier among: Warragul, Maryborough, Lidcombe, Calamvale, Sidlaghatta?", + "ground_truth": { + "answer": "Sidlaghatta", + "outlier_distance_km": 7487.7, + "second_furthest_km": 1990.7, + "clarity_ratio": 3.76, + "median_distance_km": 1939.7, + "distances_to_centroid": { + "Warragul": 1990.7, + "Maryborough": 1721.0, + "Lidcombe": 1939.7, + "Calamvale": 1801.9, + "Sidlaghatta": 7487.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warragul: (-38.16°, 145.93°)", + " Maryborough: (-25.54°, 152.70°)", + " Lidcombe: (-33.86°, 151.04°)", + " Calamvale: (-27.62°, 153.05°)", + " Sidlaghatta: (13.39°, 77.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sidlaghatta: 7487.7 km from centroid", + " Warragul: 1990.7 km from centroid", + " Lidcombe: 1939.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sidlaghatta", + "FINAL ANSWER: Sidlaghatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.74114, + "lon": 8.28699, + "name": "Dillenburg" + }, + { + "lat": 51.44488, + "lon": 8.34851, + "name": "Warstein" + }, + { + "lat": 51.94924, + "lon": -0.28496, + "name": "Hitchin" + }, + { + "lat": 51.66446, + "lon": 7.63421, + "name": "Werne" + }, + { + "lat": 5.1665, + "lon": -75.52001, + "name": "Neira" + } + ], + "question": "Which location is the geographic outlier among: Dillenburg, Warstein, Hitchin, Werne, Neira?", + "ground_truth": { + "answer": "Neira", + "outlier_distance_km": 7594.0, + "second_furthest_km": 1744.9, + "clarity_ratio": 4.35, + "median_distance_km": 1714.2, + "distances_to_centroid": { + "Dillenburg": 1704.6, + "Warstein": 1744.9, + "Hitchin": 1321.3, + "Werne": 1714.2, + "Neira": 7594.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dillenburg: (50.74°, 8.29°)", + " Warstein: (51.44°, 8.35°)", + " Hitchin: (51.95°, -0.28°)", + " Werne: (51.66°, 7.63°)", + " Neira: (5.17°, -75.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Neira: 7594.0 km from centroid", + " Warstein: 1744.9 km from centroid", + " Werne: 1714.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Neira", + "FINAL ANSWER: Neira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": -33.41665, + "lon": 149.5806, + "name": "Bathurst" + }, + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + { + "lat": 26.33294, + "lon": 127.87403, + "name": "Katsuren-haebaru" + } + ], + "question": "Which location is the geographic outlier among: Frankston East, Bathurst, Calamvale, Sunbury, Katsuren-haebaru?", + "ground_truth": { + "answer": "Katsuren-haebaru", + "outlier_distance_km": 5659.3, + "second_furthest_km": 1787.5, + "clarity_ratio": 3.17, + "median_distance_km": 1724.0, + "distances_to_centroid": { + "Frankston East": 1787.5, + "Bathurst": 1371.2, + "Calamvale": 1094.6, + "Sunbury": 1724.0, + "Katsuren-haebaru": 5659.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frankston East: (-38.13°, 145.13°)", + " Bathurst: (-33.42°, 149.58°)", + " Calamvale: (-27.62°, 153.05°)", + " Sunbury: (-37.58°, 144.73°)", + " Katsuren-haebaru: (26.33°, 127.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Katsuren-haebaru: 5659.3 km from centroid", + " Frankston East: 1787.5 km from centroid", + " Sunbury: 1724.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Katsuren-haebaru", + "FINAL ANSWER: Katsuren-haebaru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.93206, + "lon": -77.02359, + "name": "Park View" + }, + { + "lat": 40.65871, + "lon": -73.64124, + "name": "Rockville Centre" + }, + { + "lat": 30.67436, + "lon": -96.36996, + "name": "Bryan" + }, + { + "lat": 29.59412, + "lon": -95.68078, + "name": "New Territory" + }, + { + "lat": -32.24295, + "lon": 148.60484, + "name": "Dubbo" + } + ], + "question": "Which location is the geographic outlier among: Park View, Rockville Centre, Bryan, New Territory, Dubbo?", + "ground_truth": { + "answer": "Dubbo", + "outlier_distance_km": 18614.9, + "second_furthest_km": 5775.4, + "clarity_ratio": 3.22, + "median_distance_km": 5719.2, + "distances_to_centroid": { + "Park View": 4108.0, + "Rockville Centre": 3900.2, + "Bryan": 5775.4, + "New Territory": 5719.2, + "Dubbo": 18614.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Park View: (38.93°, -77.02°)", + " Rockville Centre: (40.66°, -73.64°)", + " Bryan: (30.67°, -96.37°)", + " New Territory: (29.59°, -95.68°)", + " Dubbo: (-32.24°, 148.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dubbo: 18614.9 km from centroid", + " Bryan: 5775.4 km from centroid", + " New Territory: 5719.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dubbo", + "FINAL ANSWER: Dubbo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.9018, + "lon": 2.48931, + "name": "Bondy" + }, + { + "lat": 52.0862, + "lon": 8.74434, + "name": "Bad Salzuflen" + }, + { + "lat": 60.76186, + "lon": 46.31352, + "name": "Velikiy Ustyug" + }, + { + "lat": 52.95929, + "lon": 5.91854, + "name": "Heerenveen" + }, + { + "lat": -34.92873, + "lon": 138.60334, + "name": "Adelaide city centre" + } + ], + "question": "Which location is the geographic outlier among: Bondy, Bad Salzuflen, Velikiy Ustyug, Heerenveen, Adelaide city centre?", + "ground_truth": { + "answer": "Adelaide city centre", + "outlier_distance_km": 12844.5, + "second_furthest_km": 3384.1, + "clarity_ratio": 3.8, + "median_distance_km": 3277.7, + "distances_to_centroid": { + "Bondy": 3384.1, + "Bad Salzuflen": 3064.0, + "Velikiy Ustyug": 2789.9, + "Heerenveen": 3277.7, + "Adelaide city centre": 12844.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bondy: (48.90°, 2.49°)", + " Bad Salzuflen: (52.09°, 8.74°)", + " Velikiy Ustyug: (60.76°, 46.31°)", + " Heerenveen: (52.96°, 5.92°)", + " Adelaide city centre: (-34.93°, 138.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adelaide city centre: 12844.5 km from centroid", + " Bondy: 3384.1 km from centroid", + " Heerenveen: 3277.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adelaide city centre", + "FINAL ANSWER: Adelaide city centre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.75741, + "lon": 44.0297, + "name": "Prokhladnyy" + }, + { + "lat": 54.0887, + "lon": 12.14049, + "name": "Rostock" + }, + { + "lat": 51.12014, + "lon": 15.28768, + "name": "Lubań" + }, + { + "lat": 37.27559, + "lon": -6.83851, + "name": "Moguer" + }, + { + "lat": -33.73333, + "lon": 151.0, + "name": "Castle Hill" + } + ], + "question": "Which location is the geographic outlier among: Prokhladnyy, Rostock, Lubań, Moguer, Castle Hill?", + "ground_truth": { + "answer": "Castle Hill", + "outlier_distance_km": 13356.8, + "second_furthest_km": 4619.4, + "clarity_ratio": 2.89, + "median_distance_km": 3602.5, + "distances_to_centroid": { + "Prokhladnyy": 1476.1, + "Rostock": 3602.5, + "Lubań": 3241.1, + "Moguer": 4619.4, + "Castle Hill": 13356.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Prokhladnyy: (43.76°, 44.03°)", + " Rostock: (54.09°, 12.14°)", + " Lubań: (51.12°, 15.29°)", + " Moguer: (37.28°, -6.84°)", + " Castle Hill: (-33.73°, 151.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castle Hill: 13356.8 km from centroid", + " Moguer: 4619.4 km from centroid", + " Rostock: 3602.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castle Hill", + "FINAL ANSWER: Castle Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.01457, + "lon": 36.47185, + "name": "Maloyaroslavets" + }, + { + "lat": 53.51619, + "lon": -2.94117, + "name": "Maghull" + }, + { + "lat": 43.1165, + "lon": 1.61079, + "name": "Pamiers" + }, + { + "lat": 58.45073, + "lon": 92.17243, + "name": "Yeniseysk" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + } + ], + "question": "Which location is the geographic outlier among: Maloyaroslavets, Maghull, Pamiers, Yeniseysk, Paraparaumu?", + "ground_truth": { + "answer": "Paraparaumu", + "outlier_distance_km": 14312.8, + "second_furthest_km": 5340.3, + "clarity_ratio": 2.68, + "median_distance_km": 5119.3, + "distances_to_centroid": { + "Maloyaroslavets": 2998.1, + "Maghull": 5340.3, + "Pamiers": 5119.3, + "Yeniseysk": 3603.4, + "Paraparaumu": 14312.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maloyaroslavets: (55.01°, 36.47°)", + " Maghull: (53.52°, -2.94°)", + " Pamiers: (43.12°, 1.61°)", + " Yeniseysk: (58.45°, 92.17°)", + " Paraparaumu: (-40.92°, 175.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paraparaumu: 14312.8 km from centroid", + " Maghull: 5340.3 km from centroid", + " Pamiers: 5119.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paraparaumu", + "FINAL ANSWER: Paraparaumu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": -33.90741, + "lon": 151.15546, + "name": "Marrickville" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": 10.08333, + "lon": 39.03333, + "name": "‘Alem Ketema" + } + ], + "question": "Which location is the geographic outlier among: Pacific Pines, Marrickville, Palmerston, Ballajura, ‘Alem Ketema?", + "ground_truth": { + "answer": "‘Alem Ketema", + "outlier_distance_km": 9247.1, + "second_furthest_km": 3705.4, + "clarity_ratio": 2.5, + "median_distance_km": 3650.4, + "distances_to_centroid": { + "Pacific Pines": 3705.4, + "Marrickville": 3650.4, + "Palmerston": 1569.4, + "Ballajura": 1420.4, + "‘Alem Ketema": 9247.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacific Pines: (-27.94°, 153.31°)", + " Marrickville: (-33.91°, 151.16°)", + " Palmerston: (-12.49°, 130.98°)", + " Ballajura: (-31.84°, 115.90°)", + " ‘Alem Ketema: (10.08°, 39.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " ‘Alem Ketema: 9247.1 km from centroid", + " Pacific Pines: 3705.4 km from centroid", + " Marrickville: 3650.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: ‘Alem Ketema", + "FINAL ANSWER: ‘Alem Ketema" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.18013, + "lon": 115.02213, + "name": "Macheng" + }, + { + "lat": 29.60077, + "lon": 118.17495, + "name": "Wucheng" + }, + { + "lat": 14.83333, + "lon": 120.88333, + "name": "Guiguinto" + }, + { + "lat": 22.46787, + "lon": 88.14524, + "name": "Pujali" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + } + ], + "question": "Which location is the geographic outlier among: Macheng, Wucheng, Guiguinto, Pujali, Wainuiomata?", + "ground_truth": { + "answer": "Wainuiomata", + "outlier_distance_km": 7874.1, + "second_furthest_km": 3940.0, + "clarity_ratio": 2.0, + "median_distance_km": 2367.3, + "distances_to_centroid": { + "Macheng": 2367.3, + "Wucheng": 2099.8, + "Guiguinto": 474.6, + "Pujali": 3940.0, + "Wainuiomata": 7874.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macheng: (31.18°, 115.02°)", + " Wucheng: (29.60°, 118.17°)", + " Guiguinto: (14.83°, 120.88°)", + " Pujali: (22.47°, 88.15°)", + " Wainuiomata: (-41.27°, 174.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wainuiomata: 7874.1 km from centroid", + " Pujali: 3940.0 km from centroid", + " Macheng: 2367.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wainuiomata", + "FINAL ANSWER: Wainuiomata" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -33.94185, + "lon": 150.8717, + "name": "Prestons" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": -23.65055, + "lon": -46.64591, + "name": "Jabaquara" + } + ], + "question": "Which location is the geographic outlier among: Perth, Armidale, Prestons, Morayfield, Jabaquara?", + "ground_truth": { + "answer": "Jabaquara", + "outlier_distance_km": 13377.1, + "second_furthest_km": 4675.6, + "clarity_ratio": 2.86, + "median_distance_km": 4469.8, + "distances_to_centroid": { + "Perth": 1080.7, + "Armidale": 4469.8, + "Prestons": 4339.1, + "Morayfield": 4675.6, + "Jabaquara": 13377.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Perth: (-31.95°, 115.86°)", + " Armidale: (-30.50°, 151.67°)", + " Prestons: (-33.94°, 150.87°)", + " Morayfield: (-27.11°, 152.95°)", + " Jabaquara: (-23.65°, -46.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jabaquara: 13377.1 km from centroid", + " Morayfield: 4675.6 km from centroid", + " Armidale: 4469.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jabaquara", + "FINAL ANSWER: Jabaquara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.17869, + "lon": 5.71479, + "name": "Grenoble" + }, + { + "lat": 38.05456, + "lon": -1.20763, + "name": "Molina de Segura" + }, + { + "lat": 41.35787, + "lon": 13.42718, + "name": "Fondi" + }, + { + "lat": 51.50583, + "lon": -3.57722, + "name": "Bridgend" + }, + { + "lat": 16.92329, + "lon": 80.36308, + "name": "Madhira" + } + ], + "question": "Which location is the geographic outlier among: Grenoble, Molina de Segura, Fondi, Bridgend, Madhira?", + "ground_truth": { + "answer": "Madhira", + "outlier_distance_km": 6378.7, + "second_furthest_km": 2261.5, + "clarity_ratio": 2.82, + "median_distance_km": 1755.3, + "distances_to_centroid": { + "Grenoble": 1314.0, + "Molina de Segura": 1755.3, + "Fondi": 560.8, + "Bridgend": 2261.5, + "Madhira": 6378.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Grenoble: (45.18°, 5.71°)", + " Molina de Segura: (38.05°, -1.21°)", + " Fondi: (41.36°, 13.43°)", + " Bridgend: (51.51°, -3.58°)", + " Madhira: (16.92°, 80.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Madhira: 6378.7 km from centroid", + " Bridgend: 2261.5 km from centroid", + " Molina de Segura: 1755.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Madhira", + "FINAL ANSWER: Madhira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.96333, + "lon": -35.69167, + "name": "Areia" + }, + { + "lat": -15.86126, + "lon": -38.87982, + "name": "Belmonte" + }, + { + "lat": -22.52667, + "lon": -43.73278, + "name": "Mendes" + }, + { + "lat": -20.73722, + "lon": -48.91472, + "name": "Olímpia" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + } + ], + "question": "Which location is the geographic outlier among: Areia, Belmonte, Mendes, Olímpia, Timaru?", + "ground_truth": { + "answer": "Timaru", + "outlier_distance_km": 12557.7, + "second_furthest_km": 5126.1, + "clarity_ratio": 2.45, + "median_distance_km": 4564.5, + "distances_to_centroid": { + "Areia": 4257.1, + "Belmonte": 4218.4, + "Mendes": 4564.5, + "Olímpia": 5126.1, + "Timaru": 12557.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Areia: (-6.96°, -35.69°)", + " Belmonte: (-15.86°, -38.88°)", + " Mendes: (-22.53°, -43.73°)", + " Olímpia: (-20.74°, -48.91°)", + " Timaru: (-44.40°, 171.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Timaru: 12557.7 km from centroid", + " Olímpia: 5126.1 km from centroid", + " Mendes: 4564.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Timaru", + "FINAL ANSWER: Timaru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.18028, + "lon": -35.00139, + "name": "Jaboatão" + }, + { + "lat": -11.00861, + "lon": -44.51944, + "name": "Santa Rita de Cássia" + }, + { + "lat": -3.89, + "lon": -38.45056, + "name": "Eusébio" + }, + { + "lat": -3.76585, + "lon": -49.67923, + "name": "Tucuruí" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + } + ], + "question": "Which location is the geographic outlier among: Jaboatão, Santa Rita de Cássia, Eusébio, Tucuruí, Napier?", + "ground_truth": { + "answer": "Napier", + "outlier_distance_km": 14126.1, + "second_furthest_km": 5753.1, + "clarity_ratio": 2.46, + "median_distance_km": 5040.4, + "distances_to_centroid": { + "Jaboatão": 4062.0, + "Santa Rita de Cássia": 5040.4, + "Eusébio": 4545.1, + "Tucuruí": 5753.1, + "Napier": 14126.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jaboatão: (-8.18°, -35.00°)", + " Santa Rita de Cássia: (-11.01°, -44.52°)", + " Eusébio: (-3.89°, -38.45°)", + " Tucuruí: (-3.77°, -49.68°)", + " Napier: (-39.49°, 176.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Napier: 14126.1 km from centroid", + " Tucuruí: 5753.1 km from centroid", + " Santa Rita de Cássia: 5040.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Napier", + "FINAL ANSWER: Napier" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.45046, + "lon": -83.5085, + "name": "Tifton" + }, + { + "lat": 36.59511, + "lon": -82.18874, + "name": "Bristol" + }, + { + "lat": 42.86509, + "lon": -71.4934, + "name": "Merrimack" + }, + { + "lat": 42.74698, + "lon": -84.40108, + "name": "Haslett" + }, + { + "lat": 22.73177, + "lon": 113.81185, + "name": "Shajing Residential District" + } + ], + "question": "Which location is the geographic outlier among: Tifton, Bristol, Merrimack, Haslett, Shajing Residential District?", + "ground_truth": { + "answer": "Shajing Residential District", + "outlier_distance_km": 13061.9, + "second_furthest_km": 3890.5, + "clarity_ratio": 3.36, + "median_distance_km": 3751.7, + "distances_to_centroid": { + "Tifton": 3890.5, + "Bristol": 3633.7, + "Merrimack": 2702.0, + "Haslett": 3751.7, + "Shajing Residential District": 13061.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tifton: (31.45°, -83.51°)", + " Bristol: (36.60°, -82.19°)", + " Merrimack: (42.87°, -71.49°)", + " Haslett: (42.75°, -84.40°)", + " Shajing Residential District: (22.73°, 113.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shajing Residential District: 13061.9 km from centroid", + " Tifton: 3890.5 km from centroid", + " Haslett: 3751.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shajing Residential District", + "FINAL ANSWER: Shajing Residential District" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.76148, + "lon": -0.01144, + "name": "Hoddesdon" + }, + { + "lat": 48.82292, + "lon": 2.21757, + "name": "Sèvres" + }, + { + "lat": 45.49185, + "lon": 9.29812, + "name": "Segrate" + }, + { + "lat": 52.33953, + "lon": 21.19589, + "name": "Kobyłka" + }, + { + "lat": 8.31667, + "lon": 39.48333, + "name": "Sīrē" + } + ], + "question": "Which location is the geographic outlier among: Hoddesdon, Sèvres, Segrate, Kobyłka, Sīrē?", + "ground_truth": { + "answer": "Sīrē", + "outlier_distance_km": 4423.1, + "second_furthest_km": 1594.9, + "clarity_ratio": 2.77, + "median_distance_km": 1324.7, + "distances_to_centroid": { + "Hoddesdon": 1594.9, + "Sèvres": 1266.7, + "Segrate": 620.0, + "Kobyłka": 1324.7, + "Sīrē": 4423.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hoddesdon: (51.76°, -0.01°)", + " Sèvres: (48.82°, 2.22°)", + " Segrate: (45.49°, 9.30°)", + " Kobyłka: (52.34°, 21.20°)", + " Sīrē: (8.32°, 39.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sīrē: 4423.1 km from centroid", + " Hoddesdon: 1594.9 km from centroid", + " Kobyłka: 1324.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sīrē", + "FINAL ANSWER: Sīrē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.9802, + "lon": 136.15752, + "name": "Kōka" + }, + { + "lat": 23.42322, + "lon": 75.28185, + "name": "Khāchrod" + }, + { + "lat": 34.59845, + "lon": 119.21556, + "name": "Lianyungang" + }, + { + "lat": 11.5021, + "lon": 77.25554, + "name": "Kumārapālaiyam" + }, + { + "lat": 8.00181, + "lon": -73.51143, + "name": "San Martín" + } + ], + "question": "Which location is the geographic outlier among: Kōka, Khāchrod, Lianyungang, Kumārapālaiyam, San Martín?", + "ground_truth": { + "answer": "San Martín", + "outlier_distance_km": 14528.7, + "second_furthest_km": 6765.1, + "clarity_ratio": 2.15, + "median_distance_km": 5226.2, + "distances_to_centroid": { + "Kōka": 6765.1, + "Khāchrod": 866.2, + "Lianyungang": 5226.2, + "Kumārapālaiyam": 1645.6, + "San Martín": 14528.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kōka: (34.98°, 136.16°)", + " Khāchrod: (23.42°, 75.28°)", + " Lianyungang: (34.60°, 119.22°)", + " Kumārapālaiyam: (11.50°, 77.26°)", + " San Martín: (8.00°, -73.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Martín: 14528.7 km from centroid", + " Kōka: 6765.1 km from centroid", + " Lianyungang: 5226.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Martín", + "FINAL ANSWER: San Martín" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.0711, + "lon": 120.5423, + "name": "Porac" + }, + { + "lat": 13.725, + "lon": 100.48511, + "name": "Thon Buri" + }, + { + "lat": 29.30883, + "lon": 78.51083, + "name": "Dhāmpur" + }, + { + "lat": 14.6627, + "lon": 121.0328, + "name": "Bagong Pagasa" + }, + { + "lat": 1.23889, + "lon": 35.11194, + "name": "Kapenguria" + } + ], + "question": "Which location is the geographic outlier among: Porac, Thon Buri, Dhāmpur, Bagong Pagasa, Kapenguria?", + "ground_truth": { + "answer": "Kapenguria", + "outlier_distance_km": 6330.1, + "second_furthest_km": 3212.6, + "clarity_ratio": 1.97, + "median_distance_km": 3157.1, + "distances_to_centroid": { + "Porac": 3157.1, + "Thon Buri": 1014.5, + "Dhāmpur": 2069.0, + "Bagong Pagasa": 3212.6, + "Kapenguria": 6330.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porac: (15.07°, 120.54°)", + " Thon Buri: (13.72°, 100.49°)", + " Dhāmpur: (29.31°, 78.51°)", + " Bagong Pagasa: (14.66°, 121.03°)", + " Kapenguria: (1.24°, 35.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kapenguria: 6330.1 km from centroid", + " Bagong Pagasa: 3212.6 km from centroid", + " Porac: 3157.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kapenguria", + "FINAL ANSWER: Kapenguria" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.18871, + "lon": 25.32931, + "name": "Schweizer-Reneke" + }, + { + "lat": 11.73292, + "lon": 41.082, + "name": "Dubti" + }, + { + "lat": 6.96667, + "lon": 37.86667, + "name": "Bodītī" + }, + { + "lat": -27.24179, + "lon": 27.57422, + "name": "Koppies" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + } + ], + "question": "Which location is the geographic outlier among: Schweizer-Reneke, Dubti, Bodītī, Koppies, Officer?", + "ground_truth": { + "answer": "Officer", + "outlier_distance_km": 8999.2, + "second_furthest_km": 3406.9, + "clarity_ratio": 2.64, + "median_distance_km": 3344.0, + "distances_to_centroid": { + "Schweizer-Reneke": 3406.9, + "Dubti": 3344.0, + "Bodītī": 3097.6, + "Koppies": 3198.8, + "Officer": 8999.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Schweizer-Reneke: (-27.19°, 25.33°)", + " Dubti: (11.73°, 41.08°)", + " Bodītī: (6.97°, 37.87°)", + " Koppies: (-27.24°, 27.57°)", + " Officer: (-38.06°, 145.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Officer: 8999.2 km from centroid", + " Schweizer-Reneke: 3406.9 km from centroid", + " Dubti: 3344.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Officer", + "FINAL ANSWER: Officer" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.72143, + "lon": 128.87529, + "name": "Yichun" + }, + { + "lat": -7.11282, + "lon": 112.16354, + "name": "Babat" + }, + { + "lat": 28.1722, + "lon": 78.06376, + "name": "Pahāsu" + }, + { + "lat": 25.32356, + "lon": 98.27802, + "name": "Houqiao" + }, + { + "lat": 6.38706, + "lon": -0.37738, + "name": "Begoro" + } + ], + "question": "Which location is the geographic outlier among: Yichun, Babat, Pahāsu, Houqiao, Begoro?", + "ground_truth": { + "answer": "Begoro", + "outlier_distance_km": 9116.7, + "second_furthest_km": 5091.9, + "clarity_ratio": 1.79, + "median_distance_km": 4364.8, + "distances_to_centroid": { + "Yichun": 5091.9, + "Babat": 4364.8, + "Pahāsu": 1048.1, + "Houqiao": 1631.5, + "Begoro": 9116.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yichun: (47.72°, 128.88°)", + " Babat: (-7.11°, 112.16°)", + " Pahāsu: (28.17°, 78.06°)", + " Houqiao: (25.32°, 98.28°)", + " Begoro: (6.39°, -0.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Begoro: 9116.7 km from centroid", + " Yichun: 5091.9 km from centroid", + " Babat: 4364.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Begoro", + "FINAL ANSWER: Begoro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + }, + { + "lat": -37.68333, + "lon": 145.01667, + "name": "Thomastown" + }, + { + "lat": -34.92873, + "lon": 138.60334, + "name": "Adelaide city centre" + }, + { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + { + "lat": 31.31146, + "lon": 31.14766, + "name": "Al Ḩāmūl" + } + ], + "question": "Which location is the geographic outlier among: Adelaide, Thomastown, Adelaide city centre, Yarraville, Al Ḩāmūl?", + "ground_truth": { + "answer": "Al Ḩāmūl", + "outlier_distance_km": 11166.6, + "second_furthest_km": 2928.9, + "clarity_ratio": 3.81, + "median_distance_km": 2926.6, + "distances_to_centroid": { + "Adelaide": 2277.7, + "Thomastown": 2928.9, + "Adelaide city centre": 2278.1, + "Yarraville": 2926.6, + "Al Ḩāmūl": 11166.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adelaide: (-34.93°, 138.60°)", + " Thomastown: (-37.68°, 145.02°)", + " Adelaide city centre: (-34.93°, 138.60°)", + " Yarraville: (-37.82°, 144.90°)", + " Al Ḩāmūl: (31.31°, 31.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Ḩāmūl: 11166.6 km from centroid", + " Thomastown: 2928.9 km from centroid", + " Yarraville: 2926.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Ḩāmūl", + "FINAL ANSWER: Al Ḩāmūl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.66306, + "lon": -59.78583, + "name": "Comodoro" + }, + { + "lat": 10.45912, + "lon": -74.8797, + "name": "Candelaria" + }, + { + "lat": -7.05056, + "lon": -71.69472, + "name": "Ipixuna" + }, + { + "lat": -22.49472, + "lon": -48.55806, + "name": "Barra Bonita" + }, + { + "lat": 13.09988, + "lon": 79.93207, + "name": "Vengattūr" + } + ], + "question": "Which location is the geographic outlier among: Comodoro, Candelaria, Ipixuna, Barra Bonita, Vengattūr?", + "ground_truth": { + "answer": "Vengattūr", + "outlier_distance_km": 12804.9, + "second_furthest_km": 4696.3, + "clarity_ratio": 2.73, + "median_distance_km": 4075.5, + "distances_to_centroid": { + "Comodoro": 2927.3, + "Candelaria": 4696.3, + "Ipixuna": 4075.5, + "Barra Bonita": 2528.6, + "Vengattūr": 12804.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Comodoro: (-13.66°, -59.79°)", + " Candelaria: (10.46°, -74.88°)", + " Ipixuna: (-7.05°, -71.69°)", + " Barra Bonita: (-22.49°, -48.56°)", + " Vengattūr: (13.10°, 79.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vengattūr: 12804.9 km from centroid", + " Candelaria: 4696.3 km from centroid", + " Ipixuna: 4075.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vengattūr", + "FINAL ANSWER: Vengattūr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.26038, + "lon": 10.36491, + "name": "Vechelde" + }, + { + "lat": 47.98372, + "lon": 10.18527, + "name": "Memmingen" + }, + { + "lat": 53.25, + "lon": 8.2, + "name": "Rastede" + }, + { + "lat": 48.9018, + "lon": 2.48931, + "name": "Bondy" + }, + { + "lat": -27.42573, + "lon": 29.16585, + "name": "Vrede" + } + ], + "question": "Which location is the geographic outlier among: Vechelde, Memmingen, Rastede, Bondy, Vrede?", + "ground_truth": { + "answer": "Vrede", + "outlier_distance_km": 7169.3, + "second_furthest_km": 2052.7, + "clarity_ratio": 3.49, + "median_distance_km": 1924.8, + "distances_to_centroid": { + "Vechelde": 1924.8, + "Memmingen": 1452.9, + "Rastede": 2052.7, + "Bondy": 1734.8, + "Vrede": 7169.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vechelde: (52.26°, 10.36°)", + " Memmingen: (47.98°, 10.19°)", + " Rastede: (53.25°, 8.20°)", + " Bondy: (48.90°, 2.49°)", + " Vrede: (-27.43°, 29.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vrede: 7169.3 km from centroid", + " Rastede: 2052.7 km from centroid", + " Vechelde: 1924.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vrede", + "FINAL ANSWER: Vrede" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + }, + { + "lat": 37.7992, + "lon": 12.4367, + "name": "Marsala" + } + ], + "question": "Which location is the geographic outlier among: Hoppers Crossing, Saint Ives, Ballarat, Mascot, Marsala?", + "ground_truth": { + "answer": "Marsala", + "outlier_distance_km": 12988.0, + "second_furthest_km": 3316.0, + "clarity_ratio": 3.92, + "median_distance_km": 3306.5, + "distances_to_centroid": { + "Hoppers Crossing": 2969.0, + "Saint Ives": 3306.5, + "Ballarat": 2887.0, + "Mascot": 3316.0, + "Marsala": 12988.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hoppers Crossing: (-37.88°, 144.70°)", + " Saint Ives: (-33.73°, 151.16°)", + " Ballarat: (-37.57°, 143.85°)", + " Mascot: (-33.93°, 151.19°)", + " Marsala: (37.80°, 12.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marsala: 12988.0 km from centroid", + " Mascot: 3316.0 km from centroid", + " Saint Ives: 3306.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marsala", + "FINAL ANSWER: Marsala" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + { + "lat": -41.33333, + "lon": 173.18333, + "name": "Richmond" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + }, + { + "lat": -26.65682, + "lon": 153.07955, + "name": "Sunshine Coast" + }, + { + "lat": -31.33306, + "lon": 27.85, + "name": "Khowa" + } + ], + "question": "Which location is the geographic outlier among: Hawthorn South, Richmond, Wantirna South, Sunshine Coast, Khowa?", + "ground_truth": { + "answer": "Khowa", + "outlier_distance_km": 8954.4, + "second_furthest_km": 3893.7, + "clarity_ratio": 2.3, + "median_distance_km": 2482.6, + "distances_to_centroid": { + "Hawthorn South": 1477.9, + "Richmond": 3893.7, + "Wantirna South": 1494.3, + "Sunshine Coast": 2482.6, + "Khowa": 8954.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hawthorn South: (-37.83°, 145.04°)", + " Richmond: (-41.33°, 173.18°)", + " Wantirna South: (-37.88°, 145.22°)", + " Sunshine Coast: (-26.66°, 153.08°)", + " Khowa: (-31.33°, 27.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Khowa: 8954.4 km from centroid", + " Richmond: 3893.7 km from centroid", + " Sunshine Coast: 2482.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Khowa", + "FINAL ANSWER: Khowa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.39462, + "lon": -76.0715, + "name": "Zarzal" + }, + { + "lat": -9.335, + "lon": -50.35, + "name": "Santana do Araguaia" + }, + { + "lat": -34.57365, + "lon": -58.44924, + "name": "Colegiales" + }, + { + "lat": -16.08333, + "lon": -69.66667, + "name": "Ilave" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + } + ], + "question": "Which location is the geographic outlier among: Zarzal, Santana do Araguaia, Colegiales, Ilave, Officer?", + "ground_truth": { + "answer": "Officer", + "outlier_distance_km": 13560.9, + "second_furthest_km": 6470.3, + "clarity_ratio": 2.1, + "median_distance_km": 5069.9, + "distances_to_centroid": { + "Zarzal": 6470.3, + "Santana do Araguaia": 3243.9, + "Colegiales": 4013.3, + "Ilave": 5069.9, + "Officer": 13560.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zarzal: (4.39°, -76.07°)", + " Santana do Araguaia: (-9.34°, -50.35°)", + " Colegiales: (-34.57°, -58.45°)", + " Ilave: (-16.08°, -69.67°)", + " Officer: (-38.06°, 145.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Officer: 13560.9 km from centroid", + " Zarzal: 6470.3 km from centroid", + " Ilave: 5069.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Officer", + "FINAL ANSWER: Officer" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.88157, + "lon": -1.48681, + "name": "Sinfin" + }, + { + "lat": 48.69247, + "lon": 2.6109, + "name": "Brie-Comte-Robert" + }, + { + "lat": 45.79462, + "lon": 4.8464, + "name": "Caluire-et-Cuire" + }, + { + "lat": 56.02, + "lon": 29.92824, + "name": "Nevel’" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + } + ], + "question": "Which location is the geographic outlier among: Sinfin, Brie-Comte-Robert, Caluire-et-Cuire, Nevel’, Casula?", + "ground_truth": { + "answer": "Casula", + "outlier_distance_km": 13999.8, + "second_furthest_km": 3715.0, + "clarity_ratio": 3.77, + "median_distance_km": 3296.8, + "distances_to_centroid": { + "Sinfin": 3715.0, + "Brie-Comte-Robert": 3296.8, + "Caluire-et-Cuire": 3047.4, + "Nevel’": 2526.1, + "Casula": 13999.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sinfin: (52.88°, -1.49°)", + " Brie-Comte-Robert: (48.69°, 2.61°)", + " Caluire-et-Cuire: (45.79°, 4.85°)", + " Nevel’: (56.02°, 29.93°)", + " Casula: (-33.95°, 150.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casula: 13999.8 km from centroid", + " Sinfin: 3715.0 km from centroid", + " Brie-Comte-Robert: 3296.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casula", + "FINAL ANSWER: Casula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.43139, + "lon": -61.14639, + "name": "Pacaraima" + }, + { + "lat": -3.98417, + "lon": -38.62028, + "name": "Pacatuba" + }, + { + "lat": -42.76848, + "lon": -65.03827, + "name": "Puerto Madryn" + }, + { + "lat": -7.17846, + "lon": -38.78003, + "name": "Barro" + }, + { + "lat": 36.40265, + "lon": 138.28161, + "name": "Ueda" + } + ], + "question": "Which location is the geographic outlier among: Pacaraima, Pacatuba, Puerto Madryn, Barro, Ueda?", + "ground_truth": { + "answer": "Ueda", + "outlier_distance_km": 15245.9, + "second_furthest_km": 6797.9, + "clarity_ratio": 2.24, + "median_distance_km": 5400.0, + "distances_to_centroid": { + "Pacaraima": 5400.0, + "Pacatuba": 2841.3, + "Puerto Madryn": 6797.9, + "Barro": 2893.2, + "Ueda": 15245.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacaraima: (4.43°, -61.15°)", + " Pacatuba: (-3.98°, -38.62°)", + " Puerto Madryn: (-42.77°, -65.04°)", + " Barro: (-7.18°, -38.78°)", + " Ueda: (36.40°, 138.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ueda: 15245.9 km from centroid", + " Puerto Madryn: 6797.9 km from centroid", + " Pacaraima: 5400.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ueda", + "FINAL ANSWER: Ueda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": -41.05584, + "lon": 145.90375, + "name": "Burnie" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": 6.01798, + "lon": 7.02027, + "name": "Igbo-Ukwu" + } + ], + "question": "Which location is the geographic outlier among: Otahuhu, Burnie, Griffith, Cranbourne West, Igbo-Ukwu?", + "ground_truth": { + "answer": "Igbo-Ukwu", + "outlier_distance_km": 12933.1, + "second_furthest_km": 4790.0, + "clarity_ratio": 2.7, + "median_distance_km": 2414.9, + "distances_to_centroid": { + "Otahuhu": 4790.0, + "Burnie": 2414.9, + "Griffith": 2185.5, + "Cranbourne West": 2230.6, + "Igbo-Ukwu": 12933.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Otahuhu: (-36.94°, 174.84°)", + " Burnie: (-41.06°, 145.90°)", + " Griffith: (-34.29°, 146.05°)", + " Cranbourne West: (-38.10°, 145.27°)", + " Igbo-Ukwu: (6.02°, 7.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Igbo-Ukwu: 12933.1 km from centroid", + " Otahuhu: 4790.0 km from centroid", + " Burnie: 2414.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Igbo-Ukwu", + "FINAL ANSWER: Igbo-Ukwu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.21197, + "lon": -88.23814, + "name": "Cary" + }, + { + "lat": 19.90481, + "lon": -99.34379, + "name": "Tepeji del Río de Ocampo" + }, + { + "lat": 41.09978, + "lon": -80.64952, + "name": "Youngstown" + }, + { + "lat": 45.03274, + "lon": -93.36023, + "name": "Crystal" + }, + { + "lat": -11.80361, + "lon": -61.80333, + "name": "Rolim de Moura" + } + ], + "question": "Which location is the geographic outlier among: Cary, Tepeji del Río de Ocampo, Youngstown, Crystal, Rolim de Moura?", + "ground_truth": { + "answer": "Rolim de Moura", + "outlier_distance_km": 4998.4, + "second_furthest_km": 2118.3, + "clarity_ratio": 2.36, + "median_distance_km": 1703.0, + "distances_to_centroid": { + "Cary": 1690.5, + "Tepeji del Río de Ocampo": 1703.0, + "Youngstown": 1579.3, + "Crystal": 2118.3, + "Rolim de Moura": 4998.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cary: (42.21°, -88.24°)", + " Tepeji del Río de Ocampo: (19.90°, -99.34°)", + " Youngstown: (41.10°, -80.65°)", + " Crystal: (45.03°, -93.36°)", + " Rolim de Moura: (-11.80°, -61.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rolim de Moura: 4998.4 km from centroid", + " Crystal: 2118.3 km from centroid", + " Tepeji del Río de Ocampo: 1703.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rolim de Moura", + "FINAL ANSWER: Rolim de Moura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.18416, + "lon": 106.5558, + "name": "Shuanghuai" + }, + { + "lat": 27.72297, + "lon": 75.47178, + "name": "Udaipur" + }, + { + "lat": 36.12944, + "lon": 127.1, + "name": "Yŏnmu" + }, + { + "lat": 34.28239, + "lon": 117.55266, + "name": "Daxu" + }, + { + "lat": 37.7244, + "lon": 15.18165, + "name": "Giarre" + } + ], + "question": "Which location is the geographic outlier among: Shuanghuai, Udaipur, Yŏnmu, Daxu, Giarre?", + "ground_truth": { + "answer": "Giarre", + "outlier_distance_km": 6475.0, + "second_furthest_km": 3533.3, + "clarity_ratio": 1.83, + "median_distance_km": 2691.4, + "distances_to_centroid": { + "Shuanghuai": 1750.5, + "Udaipur": 1377.2, + "Yŏnmu": 3533.3, + "Daxu": 2691.4, + "Giarre": 6475.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shuanghuai: (30.18°, 106.56°)", + " Udaipur: (27.72°, 75.47°)", + " Yŏnmu: (36.13°, 127.10°)", + " Daxu: (34.28°, 117.55°)", + " Giarre: (37.72°, 15.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Giarre: 6475.0 km from centroid", + " Yŏnmu: 3533.3 km from centroid", + " Daxu: 2691.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Giarre", + "FINAL ANSWER: Giarre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.35163, + "lon": 77.16671, + "name": "Punjai Puliyampatti" + }, + { + "lat": 37.73908, + "lon": 115.68348, + "name": "Hengshui" + }, + { + "lat": 27.42977, + "lon": 100.79701, + "name": "Hongqiao" + }, + { + "lat": 37.44056, + "lon": 129.17083, + "name": "Santyoku" + }, + { + "lat": -33.36889, + "lon": 19.31095, + "name": "Ceres" + } + ], + "question": "Which location is the geographic outlier among: Punjai Puliyampatti, Hengshui, Hongqiao, Santyoku, Ceres?", + "ground_truth": { + "answer": "Ceres", + "outlier_distance_km": 9155.6, + "second_furthest_km": 4636.5, + "clarity_ratio": 1.97, + "median_distance_km": 3591.4, + "distances_to_centroid": { + "Punjai Puliyampatti": 1326.2, + "Hengshui": 3591.4, + "Hongqiao": 1790.3, + "Santyoku": 4636.5, + "Ceres": 9155.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Punjai Puliyampatti: (11.35°, 77.17°)", + " Hengshui: (37.74°, 115.68°)", + " Hongqiao: (27.43°, 100.80°)", + " Santyoku: (37.44°, 129.17°)", + " Ceres: (-33.37°, 19.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ceres: 9155.6 km from centroid", + " Santyoku: 4636.5 km from centroid", + " Hengshui: 3591.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ceres", + "FINAL ANSWER: Ceres" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.04639, + "lon": -47.55056, + "name": "Mãe do Rio" + }, + { + "lat": -10.28139, + "lon": -37.01861, + "name": "Aquidabã" + }, + { + "lat": -35.6593, + "lon": -63.75787, + "name": "General Pico" + }, + { + "lat": -10.5075, + "lon": -39.01583, + "name": "Euclides da Cunha" + }, + { + "lat": 7.8275, + "lon": 123.4782, + "name": "Muricay" + } + ], + "question": "Which location is the geographic outlier among: Mãe do Rio, Aquidabã, General Pico, Euclides da Cunha, Muricay?", + "ground_truth": { + "answer": "Muricay", + "outlier_distance_km": 15206.6, + "second_furthest_km": 5859.3, + "clarity_ratio": 2.6, + "median_distance_km": 3945.1, + "distances_to_centroid": { + "Mãe do Rio": 3945.1, + "Aquidabã": 2652.7, + "General Pico": 5859.3, + "Euclides da Cunha": 2870.3, + "Muricay": 15206.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mãe do Rio: (-2.05°, -47.55°)", + " Aquidabã: (-10.28°, -37.02°)", + " General Pico: (-35.66°, -63.76°)", + " Euclides da Cunha: (-10.51°, -39.02°)", + " Muricay: (7.83°, 123.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Muricay: 15206.6 km from centroid", + " General Pico: 5859.3 km from centroid", + " Mãe do Rio: 3945.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Muricay", + "FINAL ANSWER: Muricay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.59104, + "lon": -73.43605, + "name": "Boucherville" + }, + { + "lat": 41.28449, + "lon": -84.35578, + "name": "Defiance" + }, + { + "lat": 33.88399, + "lon": -84.51438, + "name": "Smyrna" + }, + { + "lat": 27.09978, + "lon": -82.45426, + "name": "Venice" + }, + { + "lat": -38.68333, + "lon": 176.08333, + "name": "Taupo" + } + ], + "question": "Which location is the geographic outlier among: Boucherville, Defiance, Smyrna, Venice, Taupo?", + "ground_truth": { + "answer": "Taupo", + "outlier_distance_km": 16926.1, + "second_furthest_km": 5505.6, + "clarity_ratio": 3.07, + "median_distance_km": 5484.5, + "distances_to_centroid": { + "Boucherville": 4744.3, + "Defiance": 5505.6, + "Smyrna": 5484.5, + "Venice": 5330.1, + "Taupo": 16926.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boucherville: (45.59°, -73.44°)", + " Defiance: (41.28°, -84.36°)", + " Smyrna: (33.88°, -84.51°)", + " Venice: (27.10°, -82.45°)", + " Taupo: (-38.68°, 176.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taupo: 16926.1 km from centroid", + " Defiance: 5505.6 km from centroid", + " Smyrna: 5484.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taupo", + "FINAL ANSWER: Taupo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.70853, + "lon": 10.4036, + "name": "Pisa" + }, + { + "lat": 52.43623, + "lon": 13.3459, + "name": "Lankwitz" + }, + { + "lat": 51.42167, + "lon": 5.55972, + "name": "Geldrop" + }, + { + "lat": 52.10577, + "lon": 21.26129, + "name": "Otwock" + }, + { + "lat": 33.8464, + "lon": -118.04673, + "name": "La Palma" + } + ], + "question": "Which location is the geographic outlier among: Pisa, Lankwitz, Geldrop, Otwock, La Palma?", + "ground_truth": { + "answer": "La Palma", + "outlier_distance_km": 8316.8, + "second_furthest_km": 2559.1, + "clarity_ratio": 3.25, + "median_distance_km": 2024.1, + "distances_to_centroid": { + "Pisa": 1894.1, + "Lankwitz": 2024.1, + "Geldrop": 1478.9, + "Otwock": 2559.1, + "La Palma": 8316.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pisa: (43.71°, 10.40°)", + " Lankwitz: (52.44°, 13.35°)", + " Geldrop: (51.42°, 5.56°)", + " Otwock: (52.11°, 21.26°)", + " La Palma: (33.85°, -118.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " La Palma: 8316.8 km from centroid", + " Otwock: 2559.1 km from centroid", + " Lankwitz: 2024.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: La Palma", + "FINAL ANSWER: La Palma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.29932, + "lon": -3.13922, + "name": "Guadix" + }, + { + "lat": 43.5252, + "lon": 11.57238, + "name": "Montevarchi" + }, + { + "lat": 49.52416, + "lon": 9.32293, + "name": "Buchen in Odenwald" + }, + { + "lat": 40.92337, + "lon": 9.49802, + "name": "Olbia" + }, + { + "lat": 35.62246, + "lon": -117.6709, + "name": "Ridgecrest" + } + ], + "question": "Which location is the geographic outlier among: Guadix, Montevarchi, Buchen in Odenwald, Olbia, Ridgecrest?", + "ground_truth": { + "answer": "Ridgecrest", + "outlier_distance_km": 8176.7, + "second_furthest_km": 2431.8, + "clarity_ratio": 3.36, + "median_distance_km": 2305.3, + "distances_to_centroid": { + "Guadix": 1360.7, + "Montevarchi": 2431.8, + "Buchen in Odenwald": 2305.3, + "Olbia": 2300.1, + "Ridgecrest": 8176.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guadix: (37.30°, -3.14°)", + " Montevarchi: (43.53°, 11.57°)", + " Buchen in Odenwald: (49.52°, 9.32°)", + " Olbia: (40.92°, 9.50°)", + " Ridgecrest: (35.62°, -117.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ridgecrest: 8176.7 km from centroid", + " Montevarchi: 2431.8 km from centroid", + " Buchen in Odenwald: 2305.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ridgecrest", + "FINAL ANSWER: Ridgecrest" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.60938, + "lon": 0.02329, + "name": "Woodford Green" + }, + { + "lat": 51.31667, + "lon": 9.5, + "name": "Kassel" + }, + { + "lat": 49.54887, + "lon": 8.66697, + "name": "Weinheim" + }, + { + "lat": 44.81592, + "lon": 9.98637, + "name": "Salsomaggiore Terme" + }, + { + "lat": 8.56688, + "lon": 76.99129, + "name": "Kidarakulam" + } + ], + "question": "Which location is the geographic outlier among: Woodford Green, Kassel, Weinheim, Salsomaggiore Terme, Kidarakulam?", + "ground_truth": { + "answer": "Kidarakulam", + "outlier_distance_km": 6562.6, + "second_furthest_km": 1974.2, + "clarity_ratio": 3.32, + "median_distance_km": 1431.5, + "distances_to_centroid": { + "Woodford Green": 1974.2, + "Kassel": 1431.5, + "Weinheim": 1338.9, + "Salsomaggiore Terme": 984.6, + "Kidarakulam": 6562.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Woodford Green: (51.61°, 0.02°)", + " Kassel: (51.32°, 9.50°)", + " Weinheim: (49.55°, 8.67°)", + " Salsomaggiore Terme: (44.82°, 9.99°)", + " Kidarakulam: (8.57°, 76.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kidarakulam: 6562.6 km from centroid", + " Woodford Green: 1974.2 km from centroid", + " Kassel: 1431.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kidarakulam", + "FINAL ANSWER: Kidarakulam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.21093, + "lon": 109.32154, + "name": "Dashu" + }, + { + "lat": 19.2425, + "lon": 110.46417, + "name": "Qionghai" + }, + { + "lat": 30.21465, + "lon": 77.04025, + "name": "Barāra" + }, + { + "lat": 14.2349, + "lon": 121.15902, + "name": "Mamatid" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + } + ], + "question": "Which location is the geographic outlier among: Dashu, Qionghai, Barāra, Mamatid, Blacktown?", + "ground_truth": { + "answer": "Blacktown", + "outlier_distance_km": 6448.9, + "second_furthest_km": 4273.3, + "clarity_ratio": 1.51, + "median_distance_km": 2159.9, + "distances_to_centroid": { + "Dashu": 2159.9, + "Qionghai": 856.9, + "Barāra": 4273.3, + "Mamatid": 829.2, + "Blacktown": 6448.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dashu: (31.21°, 109.32°)", + " Qionghai: (19.24°, 110.46°)", + " Barāra: (30.21°, 77.04°)", + " Mamatid: (14.23°, 121.16°)", + " Blacktown: (-33.77°, 150.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blacktown: 6448.9 km from centroid", + " Barāra: 4273.3 km from centroid", + " Dashu: 2159.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blacktown", + "FINAL ANSWER: Blacktown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": -26.65682, + "lon": 153.07955, + "name": "Sunshine Coast" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -37.88461, + "lon": 145.29539, + "name": "Ferntree Gully" + }, + { + "lat": 49.2, + "lon": -122.78333, + "name": "Fraser Heights" + } + ], + "question": "Which location is the geographic outlier among: Cranbourne West, Sunshine Coast, Rockingham, Ferntree Gully, Fraser Heights?", + "ground_truth": { + "answer": "Fraser Heights", + "outlier_distance_km": 15540.3, + "second_furthest_km": 6797.3, + "clarity_ratio": 2.29, + "median_distance_km": 6058.5, + "distances_to_centroid": { + "Cranbourne West": 6058.4, + "Sunshine Coast": 6797.3, + "Rockingham": 3310.6, + "Ferntree Gully": 6058.5, + "Fraser Heights": 15540.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cranbourne West: (-38.10°, 145.27°)", + " Sunshine Coast: (-26.66°, 153.08°)", + " Rockingham: (-32.28°, 115.73°)", + " Ferntree Gully: (-37.88°, 145.30°)", + " Fraser Heights: (49.20°, -122.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fraser Heights: 15540.3 km from centroid", + " Sunshine Coast: 6797.3 km from centroid", + " Ferntree Gully: 6058.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fraser Heights", + "FINAL ANSWER: Fraser Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -32.16422, + "lon": 25.61918, + "name": "Cradock" + } + ], + "question": "Which location is the geographic outlier among: Wollongong city centre, Glen Iris, Cranbourne North, Australind, Cradock?", + "ground_truth": { + "answer": "Cradock", + "outlier_distance_km": 8094.9, + "second_furthest_km": 3124.1, + "clarity_ratio": 2.59, + "median_distance_km": 2578.5, + "distances_to_centroid": { + "Wollongong city centre": 3124.1, + "Glen Iris": 2558.9, + "Cranbourne North": 2578.5, + "Australind": 222.1, + "Cradock": 8094.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Glen Iris: (-37.87°, 145.07°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Australind: (-33.28°, 115.72°)", + " Cradock: (-32.16°, 25.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cradock: 8094.9 km from centroid", + " Wollongong city centre: 3124.1 km from centroid", + " Cranbourne North: 2578.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cradock", + "FINAL ANSWER: Cradock" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + }, + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": 25.74167, + "lon": -100.30222, + "name": "San Nicolás de los Garza" + } + ], + "question": "Which location is the geographic outlier among: Wyndham Vale, Maitland, Brisbane, Frankston South, San Nicolás de los Garza?", + "ground_truth": { + "answer": "San Nicolás de los Garza", + "outlier_distance_km": 18032.9, + "second_furthest_km": 5464.2, + "clarity_ratio": 3.3, + "median_distance_km": 5284.9, + "distances_to_centroid": { + "Wyndham Vale": 4693.3, + "Maitland": 5284.9, + "Brisbane": 5464.2, + "Frankston South": 4742.2, + "San Nicolás de los Garza": 18032.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wyndham Vale: (-37.89°, 144.62°)", + " Maitland: (-32.73°, 151.56°)", + " Brisbane: (-27.47°, 153.03°)", + " Frankston South: (-38.17°, 145.14°)", + " San Nicolás de los Garza: (25.74°, -100.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Nicolás de los Garza: 18032.9 km from centroid", + " Brisbane: 5464.2 km from centroid", + " Maitland: 5284.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Nicolás de los Garza", + "FINAL ANSWER: San Nicolás de los Garza" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.07441, + "lon": 31.09785, + "name": "Banī Suwayf" + }, + { + "lat": 9.08333, + "lon": 36.55, + "name": "Nek’emtē" + }, + { + "lat": -24.95775, + "lon": 27.26543, + "name": "Northam" + }, + { + "lat": 5.18194, + "lon": 7.71481, + "name": "Ikot Ekpene" + }, + { + "lat": 28.5641, + "lon": -81.2114, + "name": "Alafaya" + } + ], + "question": "Which location is the geographic outlier among: Banī Suwayf, Nek’emtē, Northam, Ikot Ekpene, Alafaya?", + "ground_truth": { + "answer": "Alafaya", + "outlier_distance_km": 9073.6, + "second_furthest_km": 4559.7, + "clarity_ratio": 1.99, + "median_distance_km": 3548.7, + "distances_to_centroid": { + "Banī Suwayf": 3548.7, + "Nek’emtē": 3540.3, + "Northam": 4559.7, + "Ikot Ekpene": 601.7, + "Alafaya": 9073.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banī Suwayf: (29.07°, 31.10°)", + " Nek’emtē: (9.08°, 36.55°)", + " Northam: (-24.96°, 27.27°)", + " Ikot Ekpene: (5.18°, 7.71°)", + " Alafaya: (28.56°, -81.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alafaya: 9073.6 km from centroid", + " Northam: 4559.7 km from centroid", + " Banī Suwayf: 3548.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alafaya", + "FINAL ANSWER: Alafaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.02194, + "lon": -45.48111, + "name": "São Raimundo das Mangabeiras" + }, + { + "lat": -10.17647, + "lon": -59.44913, + "name": "Aripuanã" + }, + { + "lat": -7.02528, + "lon": -42.13111, + "name": "Oeiras" + }, + { + "lat": -5.74507, + "lon": -47.36395, + "name": "Governador Edison Lobão" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + } + ], + "question": "Which location is the geographic outlier among: São Raimundo das Mangabeiras, Aripuanã, Oeiras, Governador Edison Lobão, Lalor?", + "ground_truth": { + "answer": "Lalor", + "outlier_distance_km": 13748.4, + "second_furthest_km": 5398.5, + "clarity_ratio": 2.55, + "median_distance_km": 4193.7, + "distances_to_centroid": { + "São Raimundo das Mangabeiras": 3957.3, + "Aripuanã": 5398.5, + "Oeiras": 3598.2, + "Governador Edison Lobão": 4193.7, + "Lalor": 13748.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Raimundo das Mangabeiras: (-7.02°, -45.48°)", + " Aripuanã: (-10.18°, -59.45°)", + " Oeiras: (-7.03°, -42.13°)", + " Governador Edison Lobão: (-5.75°, -47.36°)", + " Lalor: (-37.67°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lalor: 13748.4 km from centroid", + " Aripuanã: 5398.5 km from centroid", + " Governador Edison Lobão: 4193.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lalor", + "FINAL ANSWER: Lalor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.73566, + "lon": -74.17237, + "name": "Newark" + }, + { + "lat": 42.29649, + "lon": -71.29256, + "name": "Wellesley" + }, + { + "lat": 41.8792, + "lon": -87.84312, + "name": "Maywood" + }, + { + "lat": 42.4251, + "lon": -71.06616, + "name": "Malden" + }, + { + "lat": 6.23669, + "lon": 0.99578, + "name": "Dzodze" + } + ], + "question": "Which location is the geographic outlier among: Newark, Wellesley, Maywood, Malden, Dzodze?", + "ground_truth": { + "answer": "Dzodze", + "outlier_distance_km": 7036.5, + "second_furthest_km": 2488.7, + "clarity_ratio": 2.83, + "median_distance_km": 1360.6, + "distances_to_centroid": { + "Newark": 1360.6, + "Wellesley": 1248.9, + "Maywood": 2488.7, + "Malden": 1243.6, + "Dzodze": 7036.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newark: (40.74°, -74.17°)", + " Wellesley: (42.30°, -71.29°)", + " Maywood: (41.88°, -87.84°)", + " Malden: (42.43°, -71.07°)", + " Dzodze: (6.24°, 1.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dzodze: 7036.5 km from centroid", + " Maywood: 2488.7 km from centroid", + " Newark: 1360.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dzodze", + "FINAL ANSWER: Dzodze" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.93938, + "lon": 39.74877, + "name": "Mtwapa" + }, + { + "lat": -24.88333, + "lon": 28.28333, + "name": "Bela Bela" + }, + { + "lat": -34.02262, + "lon": 20.44171, + "name": "Swellendam" + }, + { + "lat": 31.5084, + "lon": 31.84106, + "name": "‘Izbat al Burj" + }, + { + "lat": -34.64203, + "lon": -60.47124, + "name": "Chacabuco" + } + ], + "question": "Which location is the geographic outlier among: Mtwapa, Bela Bela, Swellendam, ‘Izbat al Burj, Chacabuco?", + "ground_truth": { + "answer": "Chacabuco", + "outlier_distance_km": 7583.1, + "second_furthest_km": 5404.0, + "clarity_ratio": 1.4, + "median_distance_km": 3219.3, + "distances_to_centroid": { + "Mtwapa": 3219.3, + "Bela Bela": 2147.9, + "Swellendam": 2468.8, + "‘Izbat al Burj": 5404.0, + "Chacabuco": 7583.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mtwapa: (-3.94°, 39.75°)", + " Bela Bela: (-24.88°, 28.28°)", + " Swellendam: (-34.02°, 20.44°)", + " ‘Izbat al Burj: (31.51°, 31.84°)", + " Chacabuco: (-34.64°, -60.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chacabuco: 7583.1 km from centroid", + " ‘Izbat al Burj: 5404.0 km from centroid", + " Mtwapa: 3219.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chacabuco", + "FINAL ANSWER: Chacabuco" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.64028, + "lon": 109.69944, + "name": "Baocheng" + }, + { + "lat": 35.34199, + "lon": 129.03358, + "name": "Yangsan" + }, + { + "lat": 10.91667, + "lon": 79.83333, + "name": "Kāraikāl" + }, + { + "lat": 19.32872, + "lon": 77.15746, + "name": "Basmat" + }, + { + "lat": 41.79586, + "lon": -87.97562, + "name": "Westmont" + } + ], + "question": "Which location is the geographic outlier among: Baocheng, Yangsan, Kāraikāl, Basmat, Westmont?", + "ground_truth": { + "answer": "Westmont", + "outlier_distance_km": 11932.3, + "second_furthest_km": 6456.4, + "clarity_ratio": 1.85, + "median_distance_km": 4994.7, + "distances_to_centroid": { + "Baocheng": 4994.7, + "Yangsan": 6456.4, + "Kāraikāl": 2496.3, + "Basmat": 1732.3, + "Westmont": 11932.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baocheng: (18.64°, 109.70°)", + " Yangsan: (35.34°, 129.03°)", + " Kāraikāl: (10.92°, 79.83°)", + " Basmat: (19.33°, 77.16°)", + " Westmont: (41.80°, -87.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Westmont: 11932.3 km from centroid", + " Yangsan: 6456.4 km from centroid", + " Baocheng: 4994.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Westmont", + "FINAL ANSWER: Westmont" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.03333, + "lon": 145.35, + "name": "Berwick" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": 6.52799, + "lon": 3.35411, + "name": "Mushin" + } + ], + "question": "Which location is the geographic outlier among: Berwick, Sunshine West, Frankston South, Carlton, Mushin?", + "ground_truth": { + "answer": "Mushin", + "outlier_distance_km": 12627.4, + "second_furthest_km": 2820.7, + "clarity_ratio": 4.48, + "median_distance_km": 2805.6, + "distances_to_centroid": { + "Berwick": 2820.7, + "Sunshine West": 2769.3, + "Frankston South": 2805.6, + "Carlton": 2782.4, + "Mushin": 12627.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Berwick: (-38.03°, 145.35°)", + " Sunshine West: (-37.79°, 144.82°)", + " Frankston South: (-38.17°, 145.14°)", + " Carlton: (-37.80°, 144.97°)", + " Mushin: (6.53°, 3.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mushin: 12627.4 km from centroid", + " Berwick: 2820.7 km from centroid", + " Frankston South: 2805.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mushin", + "FINAL ANSWER: Mushin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + }, + { + "lat": 3.17301, + "lon": -76.26275, + "name": "Corinto" + } + ], + "question": "Which location is the geographic outlier among: Hawthorn South, Cranbourne North, Saint Ives, Whanganui, Corinto?", + "ground_truth": { + "answer": "Corinto", + "outlier_distance_km": 17076.5, + "second_furthest_km": 6102.0, + "clarity_ratio": 2.8, + "median_distance_km": 4086.8, + "distances_to_centroid": { + "Hawthorn South": 3531.0, + "Cranbourne North": 3556.1, + "Saint Ives": 4086.8, + "Whanganui": 6102.0, + "Corinto": 17076.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hawthorn South: (-37.83°, 145.04°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Saint Ives: (-33.73°, 151.16°)", + " Whanganui: (-39.93°, 175.05°)", + " Corinto: (3.17°, -76.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Corinto: 17076.5 km from centroid", + " Whanganui: 6102.0 km from centroid", + " Saint Ives: 4086.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Corinto", + "FINAL ANSWER: Corinto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.17922, + "lon": 31.2056, + "name": "Qalyub" + }, + { + "lat": -30.20672, + "lon": 30.79641, + "name": "eMkhomazi" + }, + { + "lat": 28.82306, + "lon": 30.89903, + "name": "Al Fashn" + }, + { + "lat": -29.01269, + "lon": 29.86619, + "name": "Estcourt" + }, + { + "lat": 34.73706, + "lon": -82.25428, + "name": "Simpsonville" + } + ], + "question": "Which location is the geographic outlier among: Qalyub, eMkhomazi, Al Fashn, Estcourt, Simpsonville?", + "ground_truth": { + "answer": "Simpsonville", + "outlier_distance_km": 9603.3, + "second_furthest_km": 4784.2, + "clarity_ratio": 2.01, + "median_distance_km": 4623.9, + "distances_to_centroid": { + "Qalyub": 3537.2, + "eMkhomazi": 4784.2, + "Al Fashn": 3414.7, + "Estcourt": 4623.9, + "Simpsonville": 9603.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Qalyub: (30.18°, 31.21°)", + " eMkhomazi: (-30.21°, 30.80°)", + " Al Fashn: (28.82°, 30.90°)", + " Estcourt: (-29.01°, 29.87°)", + " Simpsonville: (34.74°, -82.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Simpsonville: 9603.3 km from centroid", + " eMkhomazi: 4784.2 km from centroid", + " Estcourt: 4623.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Simpsonville", + "FINAL ANSWER: Simpsonville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.59383, + "lon": 6.21798, + "name": "Ogaminana" + }, + { + "lat": -31.66833, + "lon": 18.50119, + "name": "Vredendal" + }, + { + "lat": 31.18065, + "lon": 31.86497, + "name": "Al Jammālīyah" + }, + { + "lat": 28.69919, + "lon": 30.7673, + "name": "Al ‘Idwah" + }, + { + "lat": 34.62625, + "lon": 117.97139, + "name": "Sihu" + } + ], + "question": "Which location is the geographic outlier among: Ogaminana, Vredendal, Al Jammālīyah, Al ‘Idwah, Sihu?", + "ground_truth": { + "answer": "Sihu", + "outlier_distance_km": 7938.4, + "second_furthest_km": 5628.0, + "clarity_ratio": 1.41, + "median_distance_km": 3869.1, + "distances_to_centroid": { + "Ogaminana": 3869.1, + "Vredendal": 5628.0, + "Al Jammālīyah": 2119.9, + "Al ‘Idwah": 1941.0, + "Sihu": 7938.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ogaminana: (7.59°, 6.22°)", + " Vredendal: (-31.67°, 18.50°)", + " Al Jammālīyah: (31.18°, 31.86°)", + " Al ‘Idwah: (28.70°, 30.77°)", + " Sihu: (34.63°, 117.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sihu: 7938.4 km from centroid", + " Vredendal: 5628.0 km from centroid", + " Ogaminana: 3869.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sihu", + "FINAL ANSWER: Sihu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": 46.99651, + "lon": -120.54785, + "name": "Ellensburg" + } + ], + "question": "Which location is the geographic outlier among: Busselton, Australind, Eight Mile Plains, Nerang, Ellensburg?", + "ground_truth": { + "answer": "Ellensburg", + "outlier_distance_km": 15835.1, + "second_furthest_km": 7283.9, + "clarity_ratio": 2.17, + "median_distance_km": 7264.5, + "distances_to_centroid": { + "Busselton": 3812.3, + "Australind": 3826.3, + "Eight Mile Plains": 7264.5, + "Nerang": 7283.9, + "Ellensburg": 15835.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Busselton: (-33.65°, 115.35°)", + " Australind: (-33.28°, 115.72°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Nerang: (-27.99°, 153.34°)", + " Ellensburg: (47.00°, -120.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ellensburg: 15835.1 km from centroid", + " Nerang: 7283.9 km from centroid", + " Eight Mile Plains: 7264.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ellensburg", + "FINAL ANSWER: Ellensburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.43869, + "lon": 108.31324, + "name": "Baojia" + }, + { + "lat": 29.48684, + "lon": 105.58863, + "name": "Guchang" + }, + { + "lat": 21.3236, + "lon": 74.56804, + "name": "Dondaicha" + }, + { + "lat": 22.89247, + "lon": 92.74218, + "name": "Lunglei" + }, + { + "lat": 55.85, + "lon": 37.48333, + "name": "Levoberezhnyy" + } + ], + "question": "Which location is the geographic outlier among: Baojia, Guchang, Dondaicha, Lunglei, Levoberezhnyy?", + "ground_truth": { + "answer": "Levoberezhnyy", + "outlier_distance_km": 4448.6, + "second_furthest_km": 2361.1, + "clarity_ratio": 1.88, + "median_distance_km": 2102.5, + "distances_to_centroid": { + "Baojia": 2361.1, + "Guchang": 2102.5, + "Dondaicha": 1477.9, + "Lunglei": 1329.7, + "Levoberezhnyy": 4448.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baojia: (29.44°, 108.31°)", + " Guchang: (29.49°, 105.59°)", + " Dondaicha: (21.32°, 74.57°)", + " Lunglei: (22.89°, 92.74°)", + " Levoberezhnyy: (55.85°, 37.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Levoberezhnyy: 4448.6 km from centroid", + " Baojia: 2361.1 km from centroid", + " Guchang: 2102.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Levoberezhnyy", + "FINAL ANSWER: Levoberezhnyy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.29185, + "lon": 21.04845, + "name": "Targówek" + }, + { + "lat": 50.93816, + "lon": 37.81509, + "name": "Chernyanka" + }, + { + "lat": 38.42539, + "lon": -6.41734, + "name": "Zafra" + }, + { + "lat": 52.95929, + "lon": 5.91854, + "name": "Heerenveen" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + } + ], + "question": "Which location is the geographic outlier among: Targówek, Chernyanka, Zafra, Heerenveen, Ringwood?", + "ground_truth": { + "answer": "Ringwood", + "outlier_distance_km": 13256.5, + "second_furthest_km": 4322.9, + "clarity_ratio": 3.07, + "median_distance_km": 3679.9, + "distances_to_centroid": { + "Targówek": 2821.6, + "Chernyanka": 2190.1, + "Zafra": 4322.9, + "Heerenveen": 3679.9, + "Ringwood": 13256.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Targówek: (52.29°, 21.05°)", + " Chernyanka: (50.94°, 37.82°)", + " Zafra: (38.43°, -6.42°)", + " Heerenveen: (52.96°, 5.92°)", + " Ringwood: (-37.82°, 145.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ringwood: 13256.5 km from centroid", + " Zafra: 4322.9 km from centroid", + " Heerenveen: 3679.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ringwood", + "FINAL ANSWER: Ringwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.61806, + "lon": -44.04306, + "name": "Pedro Leopoldo" + }, + { + "lat": 4.86242, + "lon": -74.90977, + "name": "Lérida" + }, + { + "lat": -24.61778, + "lon": -53.32, + "name": "Cafelândia" + }, + { + "lat": -5.17775, + "lon": -40.66949, + "name": "Crateús" + }, + { + "lat": 45.0714, + "lon": 7.70421, + "name": "Vanchiglia" + } + ], + "question": "Which location is the geographic outlier among: Pedro Leopoldo, Lérida, Cafelândia, Crateús, Vanchiglia?", + "ground_truth": { + "answer": "Vanchiglia", + "outlier_distance_km": 6912.5, + "second_furthest_km": 3797.6, + "clarity_ratio": 1.82, + "median_distance_km": 3050.1, + "distances_to_centroid": { + "Pedro Leopoldo": 2217.2, + "Lérida": 3797.6, + "Cafelândia": 3050.1, + "Crateús": 588.8, + "Vanchiglia": 6912.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pedro Leopoldo: (-19.62°, -44.04°)", + " Lérida: (4.86°, -74.91°)", + " Cafelândia: (-24.62°, -53.32°)", + " Crateús: (-5.18°, -40.67°)", + " Vanchiglia: (45.07°, 7.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vanchiglia: 6912.5 km from centroid", + " Lérida: 3797.6 km from centroid", + " Cafelândia: 3050.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vanchiglia", + "FINAL ANSWER: Vanchiglia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.66401, + "lon": -4.56139, + "name": "Alhaurín de la Torre" + }, + { + "lat": 50.34984, + "lon": 18.22606, + "name": "Kędzierzyn-Koźle" + }, + { + "lat": 51.51116, + "lon": -0.18426, + "name": "Bayswater" + }, + { + "lat": 54.57092, + "lon": 18.38802, + "name": "Rumia" + }, + { + "lat": 7.06528, + "lon": -73.85472, + "name": "Barrancabermeja" + } + ], + "question": "Which location is the geographic outlier among: Alhaurín de la Torre, Kędzierzyn-Koźle, Bayswater, Rumia, Barrancabermeja?", + "ground_truth": { + "answer": "Barrancabermeja", + "outlier_distance_km": 7422.3, + "second_furthest_km": 2560.0, + "clarity_ratio": 2.9, + "median_distance_km": 2362.6, + "distances_to_centroid": { + "Alhaurín de la Torre": 502.1, + "Kędzierzyn-Koźle": 2362.6, + "Bayswater": 1424.4, + "Rumia": 2560.0, + "Barrancabermeja": 7422.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alhaurín de la Torre: (36.66°, -4.56°)", + " Kędzierzyn-Koźle: (50.35°, 18.23°)", + " Bayswater: (51.51°, -0.18°)", + " Rumia: (54.57°, 18.39°)", + " Barrancabermeja: (7.07°, -73.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barrancabermeja: 7422.3 km from centroid", + " Rumia: 2560.0 km from centroid", + " Kędzierzyn-Koźle: 2362.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barrancabermeja", + "FINAL ANSWER: Barrancabermeja" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.39749, + "lon": 41.56104, + "name": "Chelenko" + }, + { + "lat": 30.7142, + "lon": 31.24425, + "name": "Zefta" + }, + { + "lat": 8.84651, + "lon": 7.87354, + "name": "Keffi" + }, + { + "lat": 7.59054, + "lon": -1.93947, + "name": "Techiman" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + } + ], + "question": "Which location is the geographic outlier among: Chelenko, Zefta, Keffi, Techiman, Logan City?", + "ground_truth": { + "answer": "Logan City", + "outlier_distance_km": 11952.7, + "second_furthest_km": 5336.5, + "clarity_ratio": 2.24, + "median_distance_km": 4257.5, + "distances_to_centroid": { + "Chelenko": 665.2, + "Zefta": 3190.9, + "Keffi": 4257.5, + "Techiman": 5336.5, + "Logan City": 11952.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chelenko: (9.40°, 41.56°)", + " Zefta: (30.71°, 31.24°)", + " Keffi: (8.85°, 7.87°)", + " Techiman: (7.59°, -1.94°)", + " Logan City: (-27.64°, 153.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Logan City: 11952.7 km from centroid", + " Techiman: 5336.5 km from centroid", + " Keffi: 4257.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Logan City", + "FINAL ANSWER: Logan City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.88549, + "lon": 6.08831, + "name": "Seynod" + }, + { + "lat": 54.35227, + "lon": 18.64912, + "name": "Gdańsk" + }, + { + "lat": 51.50799, + "lon": 0.28333, + "name": "South Ockendon" + }, + { + "lat": 53.01416, + "lon": 9.0263, + "name": "Achim" + }, + { + "lat": 14.84677, + "lon": 78.38314, + "name": "Jammalamadugu" + } + ], + "question": "Which location is the geographic outlier among: Seynod, Gdańsk, South Ockendon, Achim, Jammalamadugu?", + "ground_truth": { + "answer": "Jammalamadugu", + "outlier_distance_km": 6158.1, + "second_furthest_km": 1852.9, + "clarity_ratio": 3.32, + "median_distance_km": 1412.3, + "distances_to_centroid": { + "Seynod": 1307.4, + "Gdańsk": 1192.5, + "South Ockendon": 1852.9, + "Achim": 1412.3, + "Jammalamadugu": 6158.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Seynod: (45.89°, 6.09°)", + " Gdańsk: (54.35°, 18.65°)", + " South Ockendon: (51.51°, 0.28°)", + " Achim: (53.01°, 9.03°)", + " Jammalamadugu: (14.85°, 78.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jammalamadugu: 6158.1 km from centroid", + " South Ockendon: 1852.9 km from centroid", + " Achim: 1412.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jammalamadugu", + "FINAL ANSWER: Jammalamadugu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.40986, + "lon": 2.19053, + "name": "el Clot" + }, + { + "lat": 52.1275, + "lon": 4.44861, + "name": "Voorschoten" + }, + { + "lat": 51.63106, + "lon": -3.81898, + "name": "Briton Ferry" + }, + { + "lat": 54.52021, + "lon": 9.56829, + "name": "Schleswig" + }, + { + "lat": 9.8, + "lon": 38.73333, + "name": "Fichē" + } + ], + "question": "Which location is the geographic outlier among: el Clot, Voorschoten, Briton Ferry, Schleswig, Fichē?", + "ground_truth": { + "answer": "Fichē", + "outlier_distance_km": 4525.0, + "second_furthest_km": 1516.7, + "clarity_ratio": 2.98, + "median_distance_km": 1404.4, + "distances_to_centroid": { + "el Clot": 669.4, + "Voorschoten": 1217.9, + "Briton Ferry": 1516.7, + "Schleswig": 1404.4, + "Fichē": 4525.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " el Clot: (41.41°, 2.19°)", + " Voorschoten: (52.13°, 4.45°)", + " Briton Ferry: (51.63°, -3.82°)", + " Schleswig: (54.52°, 9.57°)", + " Fichē: (9.80°, 38.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fichē: 4525.0 km from centroid", + " Briton Ferry: 1516.7 km from centroid", + " Schleswig: 1404.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fichē", + "FINAL ANSWER: Fichē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.96531, + "lon": -73.91301, + "name": "Tocancipá" + }, + { + "lat": -23.66778, + "lon": -46.46139, + "name": "Mauá" + }, + { + "lat": -19.7625, + "lon": -44.31389, + "name": "Esmeraldas" + }, + { + "lat": -34.5627, + "lon": -58.45829, + "name": "Belgrano" + }, + { + "lat": 35.70749, + "lon": 139.7788, + "name": "Taito" + } + ], + "question": "Which location is the geographic outlier among: Tocancipá, Mauá, Esmeraldas, Belgrano, Taito?", + "ground_truth": { + "answer": "Taito", + "outlier_distance_km": 16065.3, + "second_furthest_km": 6499.0, + "clarity_ratio": 2.47, + "median_distance_km": 5221.4, + "distances_to_centroid": { + "Tocancipá": 6499.0, + "Mauá": 3650.5, + "Esmeraldas": 3277.6, + "Belgrano": 5221.4, + "Taito": 16065.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tocancipá: (4.97°, -73.91°)", + " Mauá: (-23.67°, -46.46°)", + " Esmeraldas: (-19.76°, -44.31°)", + " Belgrano: (-34.56°, -58.46°)", + " Taito: (35.71°, 139.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taito: 16065.3 km from centroid", + " Tocancipá: 6499.0 km from centroid", + " Belgrano: 5221.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taito", + "FINAL ANSWER: Taito" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.41919, + "lon": 45.85251, + "name": "Raqo" + }, + { + "lat": 9.61524, + "lon": 6.54776, + "name": "Minna" + }, + { + "lat": -32.93324, + "lon": 27.77656, + "name": "Mdantsane" + }, + { + "lat": 6.65915, + "lon": 7.75961, + "name": "Eha Amufu" + }, + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + } + ], + "question": "Which location is the geographic outlier among: Raqo, Minna, Mdantsane, Eha Amufu, Northcote?", + "ground_truth": { + "answer": "Northcote", + "outlier_distance_km": 10083.3, + "second_furthest_km": 4919.4, + "clarity_ratio": 2.05, + "median_distance_km": 4665.9, + "distances_to_centroid": { + "Raqo": 1783.3, + "Minna": 4919.4, + "Mdantsane": 3232.5, + "Eha Amufu": 4665.9, + "Northcote": 10083.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Raqo: (6.42°, 45.85°)", + " Minna: (9.62°, 6.55°)", + " Mdantsane: (-32.93°, 27.78°)", + " Eha Amufu: (6.66°, 7.76°)", + " Northcote: (-37.77°, 145.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Northcote: 10083.3 km from centroid", + " Minna: 4919.4 km from centroid", + " Eha Amufu: 4665.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Northcote", + "FINAL ANSWER: Northcote" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + { + "lat": -37.0182, + "lon": 174.88019, + "name": "Manurewa" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -34.78254, + "lon": 138.61077, + "name": "Parafield Gardens" + }, + { + "lat": 17.02958, + "lon": -96.73518, + "name": "Santa Cruz Xoxocotlán" + } + ], + "question": "Which location is the geographic outlier among: Ballarat, Manurewa, Cairns, Parafield Gardens, Santa Cruz Xoxocotlán?", + "ground_truth": { + "answer": "Santa Cruz Xoxocotlán", + "outlier_distance_km": 18053.6, + "second_furthest_km": 7152.6, + "clarity_ratio": 2.52, + "median_distance_km": 4683.2, + "distances_to_centroid": { + "Ballarat": 4421.5, + "Manurewa": 7152.6, + "Cairns": 4683.2, + "Parafield Gardens": 3899.8, + "Santa Cruz Xoxocotlán": 18053.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ballarat: (-37.57°, 143.85°)", + " Manurewa: (-37.02°, 174.88°)", + " Cairns: (-16.92°, 145.77°)", + " Parafield Gardens: (-34.78°, 138.61°)", + " Santa Cruz Xoxocotlán: (17.03°, -96.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Cruz Xoxocotlán: 18053.6 km from centroid", + " Manurewa: 7152.6 km from centroid", + " Cairns: 4683.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Cruz Xoxocotlán", + "FINAL ANSWER: Santa Cruz Xoxocotlán" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.6561, + "lon": 103.6032, + "name": "Kulai" + }, + { + "lat": 30.39759, + "lon": 107.3895, + "name": "Xinmin" + }, + { + "lat": 23.54109, + "lon": 74.4425, + "name": "Bānswāra" + }, + { + "lat": 17.89241, + "lon": 75.02138, + "name": "Aklūj" + }, + { + "lat": -37.74981, + "lon": 144.9109, + "name": "Essendon" + } + ], + "question": "Which location is the geographic outlier among: Kulai, Xinmin, Bānswāra, Aklūj, Essendon?", + "ground_truth": { + "answer": "Essendon", + "outlier_distance_km": 6747.0, + "second_furthest_km": 3376.2, + "clarity_ratio": 2.0, + "median_distance_km": 3064.5, + "distances_to_centroid": { + "Kulai": 671.9, + "Xinmin": 2667.9, + "Bānswāra": 3376.2, + "Aklūj": 3064.5, + "Essendon": 6747.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kulai: (1.66°, 103.60°)", + " Xinmin: (30.40°, 107.39°)", + " Bānswāra: (23.54°, 74.44°)", + " Aklūj: (17.89°, 75.02°)", + " Essendon: (-37.75°, 144.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Essendon: 6747.0 km from centroid", + " Bānswāra: 3376.2 km from centroid", + " Aklūj: 3064.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Essendon", + "FINAL ANSWER: Essendon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.4, + "lon": 106.81861, + "name": "Depok" + }, + { + "lat": 26.24942, + "lon": 91.5243, + "name": "Niz-Hajo" + }, + { + "lat": 29.37861, + "lon": 106.54, + "name": "Banan" + }, + { + "lat": 30.19953, + "lon": 74.66627, + "name": "Giddarbāha" + }, + { + "lat": -27.48683, + "lon": -55.11994, + "name": "Oberá" + } + ], + "question": "Which location is the geographic outlier among: Depok, Niz-Hajo, Banan, Giddarbāha, Oberá?", + "ground_truth": { + "answer": "Oberá", + "outlier_distance_km": 13488.5, + "second_furthest_km": 5004.1, + "clarity_ratio": 2.7, + "median_distance_km": 4804.5, + "distances_to_centroid": { + "Depok": 5004.1, + "Niz-Hajo": 3306.9, + "Banan": 4804.5, + "Giddarbāha": 2424.5, + "Oberá": 13488.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Depok: (-6.40°, 106.82°)", + " Niz-Hajo: (26.25°, 91.52°)", + " Banan: (29.38°, 106.54°)", + " Giddarbāha: (30.20°, 74.67°)", + " Oberá: (-27.49°, -55.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oberá: 13488.5 km from centroid", + " Depok: 5004.1 km from centroid", + " Banan: 4804.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oberá", + "FINAL ANSWER: Oberá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.56668, + "lon": 18.48335, + "name": "Atlantis" + }, + { + "lat": 31.02819, + "lon": 28.44498, + "name": "El Dabaa" + }, + { + "lat": -0.30037, + "lon": 35.80935, + "name": "Elburgon" + }, + { + "lat": 26.05501, + "lon": 32.16274, + "name": "Farshūţ" + }, + { + "lat": 42.33698, + "lon": -83.27326, + "name": "Dearborn Heights" + } + ], + "question": "Which location is the geographic outlier among: Atlantis, El Dabaa, Elburgon, Farshūţ, Dearborn Heights?", + "ground_truth": { + "answer": "Dearborn Heights", + "outlier_distance_km": 8997.9, + "second_furthest_km": 5347.9, + "clarity_ratio": 1.68, + "median_distance_km": 3575.6, + "distances_to_centroid": { + "Atlantis": 5347.9, + "El Dabaa": 3015.3, + "Elburgon": 3575.6, + "Farshūţ": 3056.3, + "Dearborn Heights": 8997.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Atlantis: (-33.57°, 18.48°)", + " El Dabaa: (31.03°, 28.44°)", + " Elburgon: (-0.30°, 35.81°)", + " Farshūţ: (26.06°, 32.16°)", + " Dearborn Heights: (42.34°, -83.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dearborn Heights: 8997.9 km from centroid", + " Atlantis: 5347.9 km from centroid", + " Elburgon: 3575.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dearborn Heights", + "FINAL ANSWER: Dearborn Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.90741, + "lon": 151.15546, + "name": "Marrickville" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + }, + { + "lat": -38.65333, + "lon": 178.00417, + "name": "Gisborne" + }, + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": -5.32222, + "lon": -41.5525, + "name": "Castelo do Piauí" + } + ], + "question": "Which location is the geographic outlier among: Marrickville, Ringwood, Gisborne, Alexandra Hills, Castelo do Piauí?", + "ground_truth": { + "answer": "Castelo do Piauí", + "outlier_distance_km": 15606.9, + "second_furthest_km": 5633.4, + "clarity_ratio": 2.77, + "median_distance_km": 3521.8, + "distances_to_centroid": { + "Marrickville": 3263.1, + "Ringwood": 2785.1, + "Gisborne": 5633.4, + "Alexandra Hills": 3521.8, + "Castelo do Piauí": 15606.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marrickville: (-33.91°, 151.16°)", + " Ringwood: (-37.82°, 145.23°)", + " Gisborne: (-38.65°, 178.00°)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Castelo do Piauí: (-5.32°, -41.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castelo do Piauí: 15606.9 km from centroid", + " Gisborne: 5633.4 km from centroid", + " Alexandra Hills: 3521.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castelo do Piauí", + "FINAL ANSWER: Castelo do Piauí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + }, + { + "lat": -37.93333, + "lon": 145.23333, + "name": "Rowville" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -26.11694, + "lon": -48.61611, + "name": "Itapoá" + } + ], + "question": "Which location is the geographic outlier among: Titirangi, Seaford, Rowville, Gosnells, Itapoá?", + "ground_truth": { + "answer": "Itapoá", + "outlier_distance_km": 12808.9, + "second_furthest_km": 6036.2, + "clarity_ratio": 2.12, + "median_distance_km": 3481.4, + "distances_to_centroid": { + "Titirangi": 6036.2, + "Seaford": 3471.0, + "Rowville": 3481.4, + "Gosnells": 917.8, + "Itapoá": 12808.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Titirangi: (-36.94°, 174.66°)", + " Seaford: (-38.10°, 145.13°)", + " Rowville: (-37.93°, 145.23°)", + " Gosnells: (-32.08°, 116.01°)", + " Itapoá: (-26.12°, -48.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itapoá: 12808.9 km from centroid", + " Titirangi: 6036.2 km from centroid", + " Rowville: 3481.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itapoá", + "FINAL ANSWER: Itapoá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.8226, + "lon": -73.81958, + "name": "Throgs Neck" + }, + { + "lat": 42.26391, + "lon": -88.84427, + "name": "Belvidere" + }, + { + "lat": 35.41968, + "lon": -119.01955, + "name": "Oildale" + }, + { + "lat": 32.29785, + "lon": -110.9187, + "name": "Catalina Foothills" + }, + { + "lat": 28.92406, + "lon": 30.98544, + "name": "Bibā" + } + ], + "question": "Which location is the geographic outlier among: Throgs Neck, Belvidere, Oildale, Catalina Foothills, Bibā?", + "ground_truth": { + "answer": "Bibā", + "outlier_distance_km": 9236.1, + "second_furthest_km": 4176.5, + "clarity_ratio": 2.21, + "median_distance_km": 3552.8, + "distances_to_centroid": { + "Throgs Neck": 557.7, + "Belvidere": 1585.6, + "Oildale": 4176.5, + "Catalina Foothills": 3552.8, + "Bibā": 9236.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Throgs Neck: (40.82°, -73.82°)", + " Belvidere: (42.26°, -88.84°)", + " Oildale: (35.42°, -119.02°)", + " Catalina Foothills: (32.30°, -110.92°)", + " Bibā: (28.92°, 30.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bibā: 9236.1 km from centroid", + " Oildale: 4176.5 km from centroid", + " Catalina Foothills: 3552.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bibā", + "FINAL ANSWER: Bibā" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.26321, + "lon": 75.46316, + "name": "Paranda" + }, + { + "lat": 22.59373, + "lon": 75.29774, + "name": "Dhār" + }, + { + "lat": 14.905, + "lon": 76.38527, + "name": "Kūdligi" + }, + { + "lat": 18.85779, + "lon": 79.7956, + "name": "Chinnūr" + }, + { + "lat": 47.09621, + "lon": -122.35873, + "name": "Frederickson" + } + ], + "question": "Which location is the geographic outlier among: Paranda, Dhār, Kūdligi, Chinnūr, Frederickson?", + "ground_truth": { + "answer": "Frederickson", + "outlier_distance_km": 11803.5, + "second_furthest_km": 4457.8, + "clarity_ratio": 2.65, + "median_distance_km": 4249.3, + "distances_to_centroid": { + "Paranda": 4037.2, + "Dhār": 3907.3, + "Kūdligi": 4249.3, + "Chinnūr": 4457.8, + "Frederickson": 11803.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paranda: (18.26°, 75.46°)", + " Dhār: (22.59°, 75.30°)", + " Kūdligi: (14.90°, 76.39°)", + " Chinnūr: (18.86°, 79.80°)", + " Frederickson: (47.10°, -122.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Frederickson: 11803.5 km from centroid", + " Chinnūr: 4457.8 km from centroid", + " Kūdligi: 4249.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Frederickson", + "FINAL ANSWER: Frederickson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.08469, + "lon": 101.69086, + "name": "Kuchai Lama" + }, + { + "lat": 26.14934, + "lon": 87.51323, + "name": "Arāria" + }, + { + "lat": 23.87968, + "lon": 115.72546, + "name": "Hengbei" + }, + { + "lat": 2.68982, + "lon": 101.90766, + "name": "Seremban 2" + }, + { + "lat": 10.3242, + "lon": -74.96017, + "name": "Santa Lucía" + } + ], + "question": "Which location is the geographic outlier among: Kuchai Lama, Arāria, Hengbei, Seremban 2, Santa Lucía?", + "ground_truth": { + "answer": "Santa Lucía", + "outlier_distance_km": 15008.6, + "second_furthest_km": 5308.5, + "clarity_ratio": 2.83, + "median_distance_km": 4077.7, + "distances_to_centroid": { + "Kuchai Lama": 4041.0, + "Arāria": 2632.0, + "Hengbei": 5308.5, + "Seremban 2": 4077.7, + "Santa Lucía": 15008.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kuchai Lama: (3.08°, 101.69°)", + " Arāria: (26.15°, 87.51°)", + " Hengbei: (23.88°, 115.73°)", + " Seremban 2: (2.69°, 101.91°)", + " Santa Lucía: (10.32°, -74.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Lucía: 15008.6 km from centroid", + " Hengbei: 5308.5 km from centroid", + " Seremban 2: 4077.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Lucía", + "FINAL ANSWER: Santa Lucía" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.5511, + "lon": 13.19921, + "name": "Spandau" + }, + { + "lat": 55.65608, + "lon": 37.56846, + "name": "Zyuzino" + }, + { + "lat": 44.64417, + "lon": 41.84528, + "name": "Kochubeyevskoye" + }, + { + "lat": 43.96119, + "lon": 4.86008, + "name": "Le Pontet" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + } + ], + "question": "Which location is the geographic outlier among: Spandau, Zyuzino, Kochubeyevskoye, Le Pontet, Boronia?", + "ground_truth": { + "answer": "Boronia", + "outlier_distance_km": 12643.4, + "second_furthest_km": 4013.1, + "clarity_ratio": 3.15, + "median_distance_km": 3656.6, + "distances_to_centroid": { + "Spandau": 3656.6, + "Zyuzino": 2788.9, + "Kochubeyevskoye": 1543.4, + "Le Pontet": 4013.1, + "Boronia": 12643.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Spandau: (52.55°, 13.20°)", + " Zyuzino: (55.66°, 37.57°)", + " Kochubeyevskoye: (44.64°, 41.85°)", + " Le Pontet: (43.96°, 4.86°)", + " Boronia: (-37.87°, 145.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Boronia: 12643.4 km from centroid", + " Le Pontet: 4013.1 km from centroid", + " Spandau: 3656.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Boronia", + "FINAL ANSWER: Boronia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.30328, + "lon": 127.79396, + "name": "Kishaba" + }, + { + "lat": 2.8033, + "lon": 101.7972, + "name": "Kampung Baharu Nilai" + }, + { + "lat": 17.16116, + "lon": 104.14725, + "name": "Sakon Nakhon" + }, + { + "lat": 28.96346, + "lon": 109.14147, + "name": "Youchou" + }, + { + "lat": 39.84395, + "lon": -84.12466, + "name": "Huber Heights" + } + ], + "question": "Which location is the geographic outlier among: Kishaba, Kampung Baharu Nilai, Sakon Nakhon, Youchou, Huber Heights?", + "ground_truth": { + "answer": "Huber Heights", + "outlier_distance_km": 12590.9, + "second_furthest_km": 5631.4, + "clarity_ratio": 2.24, + "median_distance_km": 3938.9, + "distances_to_centroid": { + "Kishaba": 5631.4, + "Kampung Baharu Nilai": 3938.9, + "Sakon Nakhon": 3437.8, + "Youchou": 3779.4, + "Huber Heights": 12590.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kishaba: (26.30°, 127.79°)", + " Kampung Baharu Nilai: (2.80°, 101.80°)", + " Sakon Nakhon: (17.16°, 104.15°)", + " Youchou: (28.96°, 109.14°)", + " Huber Heights: (39.84°, -84.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huber Heights: 12590.9 km from centroid", + " Kishaba: 5631.4 km from centroid", + " Kampung Baharu Nilai: 3938.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huber Heights", + "FINAL ANSWER: Huber Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": -12.50583, + "lon": -38.99861, + "name": "Conceição da Feira" + } + ], + "question": "Which location is the geographic outlier among: Northcote, Willetton, Whanganui, Cranbourne East, Conceição da Feira?", + "ground_truth": { + "answer": "Conceição da Feira", + "outlier_distance_km": 13967.4, + "second_furthest_km": 5916.7, + "clarity_ratio": 2.36, + "median_distance_km": 3396.2, + "distances_to_centroid": { + "Northcote": 3370.2, + "Willetton": 701.0, + "Whanganui": 5916.7, + "Cranbourne East": 3396.2, + "Conceição da Feira": 13967.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Northcote: (-37.77°, 145.00°)", + " Willetton: (-32.05°, 115.89°)", + " Whanganui: (-39.93°, 175.05°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Conceição da Feira: (-12.51°, -39.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Conceição da Feira: 13967.4 km from centroid", + " Whanganui: 5916.7 km from centroid", + " Cranbourne East: 3396.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Conceição da Feira", + "FINAL ANSWER: Conceição da Feira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.89326, + "lon": 126.57836, + "name": "Hulan" + }, + { + "lat": 22.67111, + "lon": 88.37472, + "name": "Kāmārhāti" + }, + { + "lat": 38.75, + "lon": 141.0, + "name": "Kurihara" + }, + { + "lat": 31.64637, + "lon": 130.99068, + "name": "Soo" + }, + { + "lat": -23.47444, + "lon": -54.185, + "name": "Itaquiraí" + } + ], + "question": "Which location is the geographic outlier among: Hulan, Kāmārhāti, Kurihara, Soo, Itaquiraí?", + "ground_truth": { + "answer": "Itaquiraí", + "outlier_distance_km": 16017.4, + "second_furthest_km": 5392.7, + "clarity_ratio": 2.97, + "median_distance_km": 4458.8, + "distances_to_centroid": { + "Hulan": 4389.2, + "Kāmārhāti": 192.7, + "Kurihara": 5392.7, + "Soo": 4458.8, + "Itaquiraí": 16017.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hulan: (45.89°, 126.58°)", + " Kāmārhāti: (22.67°, 88.37°)", + " Kurihara: (38.75°, 141.00°)", + " Soo: (31.65°, 130.99°)", + " Itaquiraí: (-23.47°, -54.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itaquiraí: 16017.4 km from centroid", + " Kurihara: 5392.7 km from centroid", + " Soo: 4458.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itaquiraí", + "FINAL ANSWER: Itaquiraí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.3527, + "lon": 36.6699, + "name": "Ngong" + }, + { + "lat": -34.18307, + "lon": 22.14605, + "name": "Mossel Bay" + }, + { + "lat": 6.17559, + "lon": 45.29866, + "name": "Fadhigaradle" + }, + { + "lat": 7.77104, + "lon": 4.55698, + "name": "Osogbo" + }, + { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + } + ], + "question": "Which location is the geographic outlier among: Ngong, Mossel Bay, Fadhigaradle, Osogbo, West Pennant Hills?", + "ground_truth": { + "answer": "West Pennant Hills", + "outlier_distance_km": 10150.8, + "second_furthest_km": 5645.7, + "clarity_ratio": 1.8, + "median_distance_km": 3966.5, + "distances_to_centroid": { + "Ngong": 2002.6, + "Mossel Bay": 3966.5, + "Fadhigaradle": 2053.5, + "Osogbo": 5645.7, + "West Pennant Hills": 10150.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ngong: (-1.35°, 36.67°)", + " Mossel Bay: (-34.18°, 22.15°)", + " Fadhigaradle: (6.18°, 45.30°)", + " Osogbo: (7.77°, 4.56°)", + " West Pennant Hills: (-33.75°, 151.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Pennant Hills: 10150.8 km from centroid", + " Osogbo: 5645.7 km from centroid", + " Mossel Bay: 3966.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Pennant Hills", + "FINAL ANSWER: West Pennant Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.09198, + "lon": -70.19792, + "name": "Tocopilla" + }, + { + "lat": -20.65028, + "lon": -41.90722, + "name": "Espera Feliz" + }, + { + "lat": -10.06806, + "lon": -78.15222, + "name": "Huarmey" + }, + { + "lat": 10.33384, + "lon": -73.18048, + "name": "San Diego" + }, + { + "lat": 8.17899, + "lon": 77.43227, + "name": "Nāgercoil" + } + ], + "question": "Which location is the geographic outlier among: Tocopilla, Espera Feliz, Huarmey, San Diego, Nāgercoil?", + "ground_truth": { + "answer": "Nāgercoil", + "outlier_distance_km": 12815.5, + "second_furthest_km": 4515.3, + "clarity_ratio": 2.84, + "median_distance_km": 4418.6, + "distances_to_centroid": { + "Tocopilla": 3921.4, + "Espera Feliz": 1615.1, + "Huarmey": 4515.3, + "San Diego": 4418.6, + "Nāgercoil": 12815.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tocopilla: (-22.09°, -70.20°)", + " Espera Feliz: (-20.65°, -41.91°)", + " Huarmey: (-10.07°, -78.15°)", + " San Diego: (10.33°, -73.18°)", + " Nāgercoil: (8.18°, 77.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nāgercoil: 12815.5 km from centroid", + " Huarmey: 4515.3 km from centroid", + " San Diego: 4418.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nāgercoil", + "FINAL ANSWER: Nāgercoil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.07247, + "lon": -0.77019, + "name": "Laval" + }, + { + "lat": 44.55858, + "lon": 6.07868, + "name": "Gap" + }, + { + "lat": 27.91174, + "lon": -15.54071, + "name": "Santa Lucía" + }, + { + "lat": 51.08169, + "lon": 1.16734, + "name": "Folkestone" + }, + { + "lat": 33.61561, + "lon": 130.55105, + "name": "Sasaguri" + } + ], + "question": "Which location is the geographic outlier among: Laval, Gap, Santa Lucía, Folkestone, Sasaguri?", + "ground_truth": { + "answer": "Sasaguri", + "outlier_distance_km": 8804.1, + "second_furthest_km": 3892.1, + "clarity_ratio": 2.26, + "median_distance_km": 2122.3, + "distances_to_centroid": { + "Laval": 2122.3, + "Gap": 1533.1, + "Santa Lucía": 3892.1, + "Folkestone": 2091.0, + "Sasaguri": 8804.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Laval: (48.07°, -0.77°)", + " Gap: (44.56°, 6.08°)", + " Santa Lucía: (27.91°, -15.54°)", + " Folkestone: (51.08°, 1.17°)", + " Sasaguri: (33.62°, 130.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sasaguri: 8804.1 km from centroid", + " Santa Lucía: 3892.1 km from centroid", + " Laval: 2122.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sasaguri", + "FINAL ANSWER: Sasaguri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.24168, + "lon": 33.6222, + "name": "El-Tor" + }, + { + "lat": -1.3666, + "lon": 36.73324, + "name": "Lang'ata" + }, + { + "lat": -32.94433, + "lon": 28.01496, + "name": "Gonubie" + }, + { + "lat": 31.55582, + "lon": 31.08918, + "name": "Balţīm" + }, + { + "lat": 5.06692, + "lon": -74.59499, + "name": "Guaduas" + } + ], + "question": "Which location is the geographic outlier among: El-Tor, Lang'ata, Gonubie, Balţīm, Guaduas?", + "ground_truth": { + "answer": "Guaduas", + "outlier_distance_km": 9459.3, + "second_furthest_km": 4701.0, + "clarity_ratio": 2.01, + "median_distance_km": 3518.8, + "distances_to_centroid": { + "El-Tor": 3427.2, + "Lang'ata": 2978.3, + "Gonubie": 4701.0, + "Balţīm": 3518.8, + "Guaduas": 9459.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " El-Tor: (28.24°, 33.62°)", + " Lang'ata: (-1.37°, 36.73°)", + " Gonubie: (-32.94°, 28.01°)", + " Balţīm: (31.56°, 31.09°)", + " Guaduas: (5.07°, -74.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guaduas: 9459.3 km from centroid", + " Gonubie: 4701.0 km from centroid", + " Balţīm: 3518.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guaduas", + "FINAL ANSWER: Guaduas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.56222, + "lon": -41.09222, + "name": "Viçosa do Ceará" + }, + { + "lat": -11.18143, + "lon": -40.51372, + "name": "Jacobina" + }, + { + "lat": 6.15769, + "lon": -75.64317, + "name": "La Estrella" + }, + { + "lat": -23.71056, + "lon": -46.41333, + "name": "Ribeirão Pires" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + } + ], + "question": "Which location is the geographic outlier among: Viçosa do Ceará, Jacobina, La Estrella, Ribeirão Pires, Bracken Ridge?", + "ground_truth": { + "answer": "Bracken Ridge", + "outlier_distance_km": 15288.7, + "second_furthest_km": 7517.4, + "clarity_ratio": 2.03, + "median_distance_km": 4044.5, + "distances_to_centroid": { + "Viçosa do Ceará": 3532.4, + "Jacobina": 3309.9, + "La Estrella": 7517.4, + "Ribeirão Pires": 4044.5, + "Bracken Ridge": 15288.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viçosa do Ceará: (-3.56°, -41.09°)", + " Jacobina: (-11.18°, -40.51°)", + " La Estrella: (6.16°, -75.64°)", + " Ribeirão Pires: (-23.71°, -46.41°)", + " Bracken Ridge: (-27.32°, 153.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bracken Ridge: 15288.7 km from centroid", + " La Estrella: 7517.4 km from centroid", + " Ribeirão Pires: 4044.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bracken Ridge", + "FINAL ANSWER: Bracken Ridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.2, + "lon": 8.63333, + "name": "Kirchlengern" + }, + { + "lat": 43.68374, + "lon": 43.53507, + "name": "Baksan" + }, + { + "lat": 58.19077, + "lon": 40.17081, + "name": "Danilov" + }, + { + "lat": 38.03922, + "lon": -4.05077, + "name": "Andújar" + }, + { + "lat": 40.06928, + "lon": -75.16629, + "name": "West Oak Lane" + } + ], + "question": "Which location is the geographic outlier among: Kirchlengern, Baksan, Danilov, Andújar, West Oak Lane?", + "ground_truth": { + "answer": "West Oak Lane", + "outlier_distance_km": 6081.4, + "second_furthest_km": 3191.8, + "clarity_ratio": 1.91, + "median_distance_km": 2817.6, + "distances_to_centroid": { + "Kirchlengern": 774.3, + "Baksan": 3191.8, + "Danilov": 2817.6, + "Andújar": 1082.5, + "West Oak Lane": 6081.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kirchlengern: (52.20°, 8.63°)", + " Baksan: (43.68°, 43.54°)", + " Danilov: (58.19°, 40.17°)", + " Andújar: (38.04°, -4.05°)", + " West Oak Lane: (40.07°, -75.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Oak Lane: 6081.4 km from centroid", + " Baksan: 3191.8 km from centroid", + " Danilov: 2817.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Oak Lane", + "FINAL ANSWER: West Oak Lane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.71404, + "lon": 4.80755, + "name": "Oullins" + }, + { + "lat": 41.64662, + "lon": 2.74135, + "name": "Malgrat de Mar" + }, + { + "lat": 42.69764, + "lon": 2.89541, + "name": "Perpignan" + }, + { + "lat": 44.73188, + "lon": 37.76176, + "name": "Novorossiysk" + }, + { + "lat": 0.0607, + "lon": 34.28806, + "name": "Siaya" + } + ], + "question": "Which location is the geographic outlier among: Oullins, Malgrat de Mar, Perpignan, Novorossiysk, Siaya?", + "ground_truth": { + "answer": "Siaya", + "outlier_distance_km": 4298.7, + "second_furthest_km": 2105.4, + "clarity_ratio": 2.04, + "median_distance_km": 1548.7, + "distances_to_centroid": { + "Oullins": 1548.7, + "Malgrat de Mar": 1408.8, + "Perpignan": 1455.3, + "Novorossiysk": 2105.4, + "Siaya": 4298.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oullins: (45.71°, 4.81°)", + " Malgrat de Mar: (41.65°, 2.74°)", + " Perpignan: (42.70°, 2.90°)", + " Novorossiysk: (44.73°, 37.76°)", + " Siaya: (0.06°, 34.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Siaya: 4298.7 km from centroid", + " Novorossiysk: 2105.4 km from centroid", + " Oullins: 1548.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Siaya", + "FINAL ANSWER: Siaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.93333, + "lon": 38.71667, + "name": "Ziway" + }, + { + "lat": -31.33306, + "lon": 27.85, + "name": "Khowa" + }, + { + "lat": -3.21799, + "lon": 40.11692, + "name": "Malindi" + }, + { + "lat": -23.88384, + "lon": 29.70557, + "name": "Mankweng" + }, + { + "lat": 43.2397, + "lon": -2.8858, + "name": "Basauri" + } + ], + "question": "Which location is the geographic outlier among: Ziway, Khowa, Malindi, Mankweng, Basauri?", + "ground_truth": { + "answer": "Basauri", + "outlier_distance_km": 5779.9, + "second_furthest_km": 3324.8, + "clarity_ratio": 1.74, + "median_distance_km": 2515.2, + "distances_to_centroid": { + "Ziway": 1692.5, + "Khowa": 3324.8, + "Malindi": 1503.4, + "Mankweng": 2515.2, + "Basauri": 5779.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ziway: (7.93°, 38.72°)", + " Khowa: (-31.33°, 27.85°)", + " Malindi: (-3.22°, 40.12°)", + " Mankweng: (-23.88°, 29.71°)", + " Basauri: (43.24°, -2.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Basauri: 5779.9 km from centroid", + " Khowa: 3324.8 km from centroid", + " Mankweng: 2515.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Basauri", + "FINAL ANSWER: Basauri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.78864, + "lon": 31.07938, + "name": "Mafemani" + }, + { + "lat": -27.75796, + "lon": 29.9318, + "name": "Newcastle" + }, + { + "lat": -33.98735, + "lon": 18.49746, + "name": "Lansdowne" + }, + { + "lat": -22.94564, + "lon": 30.48497, + "name": "Thohoyandou" + }, + { + "lat": 53.56667, + "lon": 10.08333, + "name": "Marienthal" + } + ], + "question": "Which location is the geographic outlier among: Mafemani, Newcastle, Lansdowne, Thohoyandou, Marienthal?", + "ground_truth": { + "answer": "Marienthal", + "outlier_distance_km": 7320.0, + "second_furthest_km": 2597.0, + "clarity_ratio": 2.82, + "median_distance_km": 1943.7, + "distances_to_centroid": { + "Mafemani": 1686.3, + "Newcastle": 1943.7, + "Lansdowne": 2597.0, + "Thohoyandou": 1477.0, + "Marienthal": 7320.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mafemani: (-24.79°, 31.08°)", + " Newcastle: (-27.76°, 29.93°)", + " Lansdowne: (-33.99°, 18.50°)", + " Thohoyandou: (-22.95°, 30.48°)", + " Marienthal: (53.57°, 10.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marienthal: 7320.0 km from centroid", + " Lansdowne: 2597.0 km from centroid", + " Newcastle: 1943.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marienthal", + "FINAL ANSWER: Marienthal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.75617, + "lon": 79.76693, + "name": "Cuddalore" + }, + { + "lat": 30.14453, + "lon": 74.19552, + "name": "Abohar" + }, + { + "lat": 47.33922, + "lon": 123.96154, + "name": "Qiqihar" + }, + { + "lat": 26.3248, + "lon": 94.51834, + "name": "Mokokchūng" + }, + { + "lat": -34.92873, + "lon": 138.60334, + "name": "Adelaide city centre" + } + ], + "question": "Which location is the geographic outlier among: Cuddalore, Abohar, Qiqihar, Mokokchūng, Adelaide city centre?", + "ground_truth": { + "answer": "Adelaide city centre", + "outlier_distance_km": 6854.5, + "second_furthest_km": 4004.3, + "clarity_ratio": 1.71, + "median_distance_km": 3247.3, + "distances_to_centroid": { + "Cuddalore": 2468.7, + "Abohar": 3247.3, + "Qiqihar": 4004.3, + "Mokokchūng": 1385.2, + "Adelaide city centre": 6854.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cuddalore: (11.76°, 79.77°)", + " Abohar: (30.14°, 74.20°)", + " Qiqihar: (47.34°, 123.96°)", + " Mokokchūng: (26.32°, 94.52°)", + " Adelaide city centre: (-34.93°, 138.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adelaide city centre: 6854.5 km from centroid", + " Qiqihar: 4004.3 km from centroid", + " Abohar: 3247.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adelaide city centre", + "FINAL ANSWER: Adelaide city centre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.83373, + "lon": 37.61138, + "name": "Pushchino" + }, + { + "lat": 38.10558, + "lon": -1.86343, + "name": "Caravaca" + }, + { + "lat": 51.48481, + "lon": 57.35788, + "name": "Kuvandyk" + }, + { + "lat": 51.42897, + "lon": -0.13184, + "name": "Streatham" + }, + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + } + ], + "question": "Which location is the geographic outlier among: Pushchino, Caravaca, Kuvandyk, Streatham, Brisbane?", + "ground_truth": { + "answer": "Brisbane", + "outlier_distance_km": 12855.2, + "second_furthest_km": 4568.6, + "clarity_ratio": 2.81, + "median_distance_km": 4391.9, + "distances_to_centroid": { + "Pushchino": 2519.4, + "Caravaca": 4568.6, + "Kuvandyk": 2086.6, + "Streatham": 4391.9, + "Brisbane": 12855.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pushchino: (54.83°, 37.61°)", + " Caravaca: (38.11°, -1.86°)", + " Kuvandyk: (51.48°, 57.36°)", + " Streatham: (51.43°, -0.13°)", + " Brisbane: (-27.47°, 153.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brisbane: 12855.2 km from centroid", + " Caravaca: 4568.6 km from centroid", + " Streatham: 4391.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brisbane", + "FINAL ANSWER: Brisbane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.41667, + "lon": 111.51667, + "name": "Babu" + }, + { + "lat": 20.61013, + "lon": 72.93428, + "name": "Valsād" + }, + { + "lat": 22.95387, + "lon": 88.40098, + "name": "Bānsbāria" + }, + { + "lat": 1.72837, + "lon": 128.00948, + "name": "Tobelo" + }, + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + } + ], + "question": "Which location is the geographic outlier among: Babu, Valsād, Bānsbāria, Tobelo, Doreen?", + "ground_truth": { + "answer": "Doreen", + "outlier_distance_km": 6150.2, + "second_furthest_km": 4212.1, + "clarity_ratio": 1.46, + "median_distance_km": 2887.8, + "distances_to_centroid": { + "Babu": 2016.1, + "Valsād": 4212.1, + "Bānsbāria": 2887.8, + "Tobelo": 2149.6, + "Doreen": 6150.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Babu: (24.42°, 111.52°)", + " Valsād: (20.61°, 72.93°)", + " Bānsbāria: (22.95°, 88.40°)", + " Tobelo: (1.73°, 128.01°)", + " Doreen: (-37.60°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doreen: 6150.2 km from centroid", + " Valsād: 4212.1 km from centroid", + " Bānsbāria: 2887.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doreen", + "FINAL ANSWER: Doreen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.96333, + "lon": -45.65833, + "name": "Santa Luzia" + }, + { + "lat": -16.33333, + "lon": -55.93333, + "name": "Lucas" + }, + { + "lat": 9.52392, + "lon": -75.58139, + "name": "Santiago de Tolú" + }, + { + "lat": -6.52392, + "lon": -49.85167, + "name": "Canaã dos Carajás" + }, + { + "lat": 10.02674, + "lon": 76.22229, + "name": "Elamkunnapuzha" + } + ], + "question": "Which location is the geographic outlier among: Santa Luzia, Lucas, Santiago de Tolú, Canaã dos Carajás, Elamkunnapuzha?", + "ground_truth": { + "answer": "Elamkunnapuzha", + "outlier_distance_km": 11829.4, + "second_furthest_km": 5175.5, + "clarity_ratio": 2.29, + "median_distance_km": 3271.4, + "distances_to_centroid": { + "Santa Luzia": 1743.7, + "Lucas": 3271.4, + "Santiago de Tolú": 5175.5, + "Canaã dos Carajás": 2255.1, + "Elamkunnapuzha": 11829.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Luzia: (-3.96°, -45.66°)", + " Lucas: (-16.33°, -55.93°)", + " Santiago de Tolú: (9.52°, -75.58°)", + " Canaã dos Carajás: (-6.52°, -49.85°)", + " Elamkunnapuzha: (10.03°, 76.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Elamkunnapuzha: 11829.4 km from centroid", + " Santiago de Tolú: 5175.5 km from centroid", + " Lucas: 3271.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Elamkunnapuzha", + "FINAL ANSWER: Elamkunnapuzha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.62839, + "lon": -84.15938, + "name": "Centerville" + }, + { + "lat": 14.99199, + "lon": -92.16417, + "name": "Cacahoatán" + }, + { + "lat": 40.63205, + "lon": -73.71263, + "name": "Woodmere" + }, + { + "lat": 36.37285, + "lon": -94.20882, + "name": "Bentonville" + }, + { + "lat": 28.41686, + "lon": -16.55085, + "name": "Puerto de la Cruz" + } + ], + "question": "Which location is the geographic outlier among: Centerville, Cacahoatán, Woodmere, Bentonville, Puerto de la Cruz?", + "ground_truth": { + "answer": "Puerto de la Cruz", + "outlier_distance_km": 5299.8, + "second_furthest_km": 2772.5, + "clarity_ratio": 1.91, + "median_distance_km": 2080.3, + "distances_to_centroid": { + "Centerville": 1372.1, + "Cacahoatán": 2772.5, + "Woodmere": 968.9, + "Bentonville": 2080.3, + "Puerto de la Cruz": 5299.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Centerville: (39.63°, -84.16°)", + " Cacahoatán: (14.99°, -92.16°)", + " Woodmere: (40.63°, -73.71°)", + " Bentonville: (36.37°, -94.21°)", + " Puerto de la Cruz: (28.42°, -16.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Puerto de la Cruz: 5299.8 km from centroid", + " Cacahoatán: 2772.5 km from centroid", + " Bentonville: 2080.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Puerto de la Cruz", + "FINAL ANSWER: Puerto de la Cruz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.38946, + "lon": 10.43615, + "name": "Rosignano Solvay-Castiglioncello" + }, + { + "lat": 55.76273, + "lon": 37.86303, + "name": "Reutov" + }, + { + "lat": 63.9057, + "lon": 38.09944, + "name": "Onega" + }, + { + "lat": 52.08868, + "lon": 17.01508, + "name": "Śrem" + }, + { + "lat": 30.10778, + "lon": 78.29255, + "name": "Rishīkesh" + } + ], + "question": "Which location is the geographic outlier among: Rosignano Solvay-Castiglioncello, Reutov, Onega, Śrem, Rishīkesh?", + "ground_truth": { + "answer": "Rishīkesh", + "outlier_distance_km": 4094.1, + "second_furthest_km": 2078.2, + "clarity_ratio": 1.97, + "median_distance_km": 1655.2, + "distances_to_centroid": { + "Rosignano Solvay-Castiglioncello": 2078.2, + "Reutov": 753.4, + "Onega": 1655.2, + "Śrem": 1401.5, + "Rishīkesh": 4094.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rosignano Solvay-Castiglioncello: (43.39°, 10.44°)", + " Reutov: (55.76°, 37.86°)", + " Onega: (63.91°, 38.10°)", + " Śrem: (52.09°, 17.02°)", + " Rishīkesh: (30.11°, 78.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rishīkesh: 4094.1 km from centroid", + " Rosignano Solvay-Castiglioncello: 2078.2 km from centroid", + " Onega: 1655.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rishīkesh", + "FINAL ANSWER: Rishīkesh" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.31281, + "lon": -91.98224, + "name": "Las Margaritas" + }, + { + "lat": 41.57337, + "lon": -87.78449, + "name": "Tinley Park" + }, + { + "lat": 39.46976, + "lon": -76.8319, + "name": "Reisterstown" + }, + { + "lat": 40.84288, + "lon": -73.29289, + "name": "Commack" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + } + ], + "question": "Which location is the geographic outlier among: Las Margaritas, Tinley Park, Reisterstown, Commack, Caroline Springs?", + "ground_truth": { + "answer": "Caroline Springs", + "outlier_distance_km": 18045.1, + "second_furthest_km": 5794.7, + "clarity_ratio": 3.11, + "median_distance_km": 5308.9, + "distances_to_centroid": { + "Las Margaritas": 5794.7, + "Tinley Park": 5308.9, + "Reisterstown": 4354.7, + "Commack": 4126.0, + "Caroline Springs": 18045.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Las Margaritas: (16.31°, -91.98°)", + " Tinley Park: (41.57°, -87.78°)", + " Reisterstown: (39.47°, -76.83°)", + " Commack: (40.84°, -73.29°)", + " Caroline Springs: (-37.74°, 144.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caroline Springs: 18045.1 km from centroid", + " Las Margaritas: 5794.7 km from centroid", + " Tinley Park: 5308.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caroline Springs", + "FINAL ANSWER: Caroline Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.15881, + "lon": 29.71528, + "name": "Hendrina" + }, + { + "lat": -33.60047, + "lon": 22.19955, + "name": "Oudtshoorn" + }, + { + "lat": -24.59165, + "lon": 27.41155, + "name": "Thabazimbi" + }, + { + "lat": -27.36541, + "lon": 29.88175, + "name": "Volksrust" + }, + { + "lat": 45.63873, + "lon": -122.66149, + "name": "Vancouver" + } + ], + "question": "Which location is the geographic outlier among: Hendrina, Oudtshoorn, Thabazimbi, Volksrust, Vancouver?", + "ground_truth": { + "answer": "Vancouver", + "outlier_distance_km": 13369.0, + "second_furthest_km": 3727.5, + "clarity_ratio": 3.59, + "median_distance_km": 3671.2, + "distances_to_centroid": { + "Hendrina": 3671.2, + "Oudtshoorn": 3386.1, + "Thabazimbi": 3399.8, + "Volksrust": 3727.5, + "Vancouver": 13369.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hendrina: (-26.16°, 29.72°)", + " Oudtshoorn: (-33.60°, 22.20°)", + " Thabazimbi: (-24.59°, 27.41°)", + " Volksrust: (-27.37°, 29.88°)", + " Vancouver: (45.64°, -122.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vancouver: 13369.0 km from centroid", + " Volksrust: 3727.5 km from centroid", + " Hendrina: 3671.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vancouver", + "FINAL ANSWER: Vancouver" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.59468, + "lon": -46.54359, + "name": "Sao Lucas" + }, + { + "lat": -21.01028, + "lon": -42.84056, + "name": "Visconde do Rio Branco" + }, + { + "lat": -21.99861, + "lon": -49.45722, + "name": "Pirajuí" + }, + { + "lat": -5.61278, + "lon": -38.76694, + "name": "Jaguaretama" + }, + { + "lat": 15.99126, + "lon": 77.05034, + "name": "Mānvi" + } + ], + "question": "Which location is the geographic outlier among: Sao Lucas, Visconde do Rio Branco, Pirajuí, Jaguaretama, Mānvi?", + "ground_truth": { + "answer": "Mānvi", + "outlier_distance_km": 11104.1, + "second_furthest_km": 3339.4, + "clarity_ratio": 3.33, + "median_distance_km": 3114.1, + "distances_to_centroid": { + "Sao Lucas": 3114.1, + "Visconde do Rio Branco": 2655.1, + "Pirajuí": 3339.4, + "Jaguaretama": 2144.4, + "Mānvi": 11104.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sao Lucas: (-23.59°, -46.54°)", + " Visconde do Rio Branco: (-21.01°, -42.84°)", + " Pirajuí: (-22.00°, -49.46°)", + " Jaguaretama: (-5.61°, -38.77°)", + " Mānvi: (15.99°, 77.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mānvi: 11104.1 km from centroid", + " Pirajuí: 3339.4 km from centroid", + " Sao Lucas: 3114.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mānvi", + "FINAL ANSWER: Mānvi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.11, + "lon": -42.94444, + "name": "Canto do Buriti" + }, + { + "lat": -28.83208, + "lon": -49.2366, + "name": "Balneário Rincão" + }, + { + "lat": 10.32944, + "lon": -75.41137, + "name": "Turbaco" + }, + { + "lat": -19.98639, + "lon": -44.42778, + "name": "Mateus Leme" + }, + { + "lat": 52.50833, + "lon": 5.475, + "name": "Lelystad" + } + ], + "question": "Which location is the geographic outlier among: Canto do Buriti, Balneário Rincão, Turbaco, Mateus Leme, Lelystad?", + "ground_truth": { + "answer": "Lelystad", + "outlier_distance_km": 7154.2, + "second_furthest_km": 3903.0, + "clarity_ratio": 1.83, + "median_distance_km": 3442.5, + "distances_to_centroid": { + "Canto do Buriti": 1049.0, + "Balneário Rincão": 3442.5, + "Turbaco": 3903.0, + "Mateus Leme": 2378.2, + "Lelystad": 7154.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canto do Buriti: (-8.11°, -42.94°)", + " Balneário Rincão: (-28.83°, -49.24°)", + " Turbaco: (10.33°, -75.41°)", + " Mateus Leme: (-19.99°, -44.43°)", + " Lelystad: (52.51°, 5.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lelystad: 7154.2 km from centroid", + " Turbaco: 3903.0 km from centroid", + " Balneário Rincão: 3442.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lelystad", + "FINAL ANSWER: Lelystad" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.3145, + "lon": -81.83569, + "name": "Strongsville" + }, + { + "lat": 41.95781, + "lon": -87.76506, + "name": "Portage Park" + }, + { + "lat": 19.07275, + "lon": -97.04685, + "name": "Coscomatepec de Bravo" + }, + { + "lat": 45.67151, + "lon": -122.66288, + "name": "Hazel Dell" + }, + { + "lat": -37.75, + "lon": 144.96667, + "name": "Coburg" + } + ], + "question": "Which location is the geographic outlier among: Strongsville, Portage Park, Coscomatepec de Bravo, Hazel Dell, Coburg?", + "ground_truth": { + "answer": "Coburg", + "outlier_distance_km": 17824.1, + "second_furthest_km": 7038.5, + "clarity_ratio": 2.53, + "median_distance_km": 5006.6, + "distances_to_centroid": { + "Strongsville": 3747.5, + "Portage Park": 4231.2, + "Coscomatepec de Bravo": 5006.6, + "Hazel Dell": 7038.5, + "Coburg": 17824.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Strongsville: (41.31°, -81.84°)", + " Portage Park: (41.96°, -87.77°)", + " Coscomatepec de Bravo: (19.07°, -97.05°)", + " Hazel Dell: (45.67°, -122.66°)", + " Coburg: (-37.75°, 144.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coburg: 17824.1 km from centroid", + " Hazel Dell: 7038.5 km from centroid", + " Coscomatepec de Bravo: 5006.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coburg", + "FINAL ANSWER: Coburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.29443, + "lon": 30.52248, + "name": "Muţūbas" + }, + { + "lat": -2.27808, + "lon": 37.81867, + "name": "Makindu" + }, + { + "lat": 0.33474, + "lon": 34.48796, + "name": "Mumias" + }, + { + "lat": -23.88384, + "lon": 29.70557, + "name": "Mankweng" + }, + { + "lat": 34.11612, + "lon": -118.15035, + "name": "South Pasadena" + } + ], + "question": "Which location is the geographic outlier among: Muţūbas, Makindu, Mumias, Mankweng, South Pasadena?", + "ground_truth": { + "answer": "South Pasadena", + "outlier_distance_km": 12254.5, + "second_furthest_km": 4581.3, + "clarity_ratio": 2.67, + "median_distance_km": 4037.7, + "distances_to_centroid": { + "Muţūbas": 3868.1, + "Makindu": 4037.7, + "Mumias": 3603.1, + "Mankweng": 4581.3, + "South Pasadena": 12254.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Muţūbas: (31.29°, 30.52°)", + " Makindu: (-2.28°, 37.82°)", + " Mumias: (0.33°, 34.49°)", + " Mankweng: (-23.88°, 29.71°)", + " South Pasadena: (34.12°, -118.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " South Pasadena: 12254.5 km from centroid", + " Mankweng: 4581.3 km from centroid", + " Makindu: 4037.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: South Pasadena", + "FINAL ANSWER: South Pasadena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.23064, + "lon": 19.36409, + "name": "Kutno" + }, + { + "lat": 41.31429, + "lon": 16.28165, + "name": "Barletta" + }, + { + "lat": 52.08731, + "lon": -0.72218, + "name": "Newport Pagnell" + }, + { + "lat": 50.9466, + "lon": 17.2926, + "name": "Oława" + }, + { + "lat": -36.88012, + "lon": 174.61975, + "name": "Henderson" + } + ], + "question": "Which location is the geographic outlier among: Kutno, Barletta, Newport Pagnell, Oława, Henderson?", + "ground_truth": { + "answer": "Henderson", + "outlier_distance_km": 15381.6, + "second_furthest_km": 4317.7, + "clarity_ratio": 3.56, + "median_distance_km": 3118.6, + "distances_to_centroid": { + "Kutno": 3081.0, + "Barletta": 2780.5, + "Newport Pagnell": 4317.7, + "Oława": 3118.6, + "Henderson": 15381.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kutno: (52.23°, 19.36°)", + " Barletta: (41.31°, 16.28°)", + " Newport Pagnell: (52.09°, -0.72°)", + " Oława: (50.95°, 17.29°)", + " Henderson: (-36.88°, 174.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Henderson: 15381.6 km from centroid", + " Newport Pagnell: 4317.7 km from centroid", + " Oława: 3118.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Henderson", + "FINAL ANSWER: Henderson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.63059, + "lon": -112.33322, + "name": "Surprise" + }, + { + "lat": 30.38575, + "lon": -88.61169, + "name": "Gautier" + }, + { + "lat": 40.5976, + "lon": -73.96514, + "name": "Gravesend" + }, + { + "lat": 40.73593, + "lon": -73.08206, + "name": "Sayville" + }, + { + "lat": -24.95911, + "lon": 31.17025, + "name": "Hlanganani" + } + ], + "question": "Which location is the geographic outlier among: Surprise, Gautier, Gravesend, Sayville, Hlanganani?", + "ground_truth": { + "answer": "Hlanganani", + "outlier_distance_km": 11535.9, + "second_furthest_km": 4840.5, + "clarity_ratio": 2.38, + "median_distance_km": 2586.5, + "distances_to_centroid": { + "Surprise": 4840.5, + "Gautier": 2586.5, + "Gravesend": 2085.7, + "Sayville": 2061.4, + "Hlanganani": 11535.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Surprise: (33.63°, -112.33°)", + " Gautier: (30.39°, -88.61°)", + " Gravesend: (40.60°, -73.97°)", + " Sayville: (40.74°, -73.08°)", + " Hlanganani: (-24.96°, 31.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hlanganani: 11535.9 km from centroid", + " Surprise: 4840.5 km from centroid", + " Gautier: 2586.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hlanganani", + "FINAL ANSWER: Hlanganani" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.36605, + "lon": -121.82718, + "name": "Alum Rock" + }, + { + "lat": 33.70918, + "lon": -117.95367, + "name": "Fountain Valley" + }, + { + "lat": 47.67323, + "lon": -117.23937, + "name": "Spokane Valley" + }, + { + "lat": 19.03689, + "lon": -98.79516, + "name": "Ozumba de Alzate" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + } + ], + "question": "Which location is the geographic outlier among: Alum Rock, Fountain Valley, Spokane Valley, Ozumba de Alzate, Morayfield?", + "ground_truth": { + "answer": "Morayfield", + "outlier_distance_km": 16591.9, + "second_furthest_km": 6044.2, + "clarity_ratio": 2.75, + "median_distance_km": 5736.3, + "distances_to_centroid": { + "Alum Rock": 6044.2, + "Fountain Valley": 5710.5, + "Spokane Valley": 5736.3, + "Ozumba de Alzate": 3983.4, + "Morayfield": 16591.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alum Rock: (37.37°, -121.83°)", + " Fountain Valley: (33.71°, -117.95°)", + " Spokane Valley: (47.67°, -117.24°)", + " Ozumba de Alzate: (19.04°, -98.80°)", + " Morayfield: (-27.11°, 152.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morayfield: 16591.9 km from centroid", + " Alum Rock: 6044.2 km from centroid", + " Spokane Valley: 5736.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morayfield", + "FINAL ANSWER: Morayfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.30638, + "lon": 77.22398, + "name": "Nalloor" + }, + { + "lat": 30.63965, + "lon": 108.23701, + "name": "Longsha" + }, + { + "lat": 28.45179, + "lon": 117.94287, + "name": "Shangrao" + }, + { + "lat": 35.65775, + "lon": 139.77489, + "name": "Kachidoki" + }, + { + "lat": -7.51651, + "lon": -63.03105, + "name": "Humaitá" + } + ], + "question": "Which location is the geographic outlier among: Nalloor, Longsha, Shangrao, Kachidoki, Humaitá?", + "ground_truth": { + "answer": "Humaitá", + "outlier_distance_km": 15415.1, + "second_furthest_km": 6445.3, + "clarity_ratio": 2.39, + "median_distance_km": 4366.5, + "distances_to_centroid": { + "Nalloor": 1208.0, + "Longsha": 3477.3, + "Shangrao": 4366.5, + "Kachidoki": 6445.3, + "Humaitá": 15415.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nalloor: (8.31°, 77.22°)", + " Longsha: (30.64°, 108.24°)", + " Shangrao: (28.45°, 117.94°)", + " Kachidoki: (35.66°, 139.77°)", + " Humaitá: (-7.52°, -63.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Humaitá: 15415.1 km from centroid", + " Kachidoki: 6445.3 km from centroid", + " Shangrao: 4366.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Humaitá", + "FINAL ANSWER: Humaitá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.89585, + "lon": -118.22007, + "name": "Compton" + }, + { + "lat": 42.06954, + "lon": -72.61481, + "name": "Agawam" + }, + { + "lat": 43.61062, + "lon": -72.97261, + "name": "Rutland" + }, + { + "lat": 20.73072, + "lon": -105.28257, + "name": "Mezcales" + }, + { + "lat": 12.98417, + "lon": 37.765, + "name": "Dabat" + } + ], + "question": "Which location is the geographic outlier among: Compton, Agawam, Rutland, Mezcales, Dabat?", + "ground_truth": { + "answer": "Dabat", + "outlier_distance_km": 10573.0, + "second_furthest_km": 4845.9, + "clarity_ratio": 2.18, + "median_distance_km": 4040.1, + "distances_to_centroid": { + "Compton": 4845.9, + "Agawam": 1389.4, + "Rutland": 1556.8, + "Mezcales": 4040.1, + "Dabat": 10573.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Compton: (33.90°, -118.22°)", + " Agawam: (42.07°, -72.61°)", + " Rutland: (43.61°, -72.97°)", + " Mezcales: (20.73°, -105.28°)", + " Dabat: (12.98°, 37.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dabat: 10573.0 km from centroid", + " Compton: 4845.9 km from centroid", + " Mezcales: 4040.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dabat", + "FINAL ANSWER: Dabat" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.71649, + "lon": -73.88125, + "name": "Middle Village" + }, + { + "lat": 41.69864, + "lon": -88.0684, + "name": "Bolingbrook" + }, + { + "lat": 40.85343, + "lon": -73.41151, + "name": "Huntington Station" + }, + { + "lat": 42.36837, + "lon": -83.35271, + "name": "Livonia" + }, + { + "lat": -8.80778, + "lon": -39.82556, + "name": "Santa Maria da Boa Vista" + } + ], + "question": "Which location is the geographic outlier among: Middle Village, Bolingbrook, Huntington Station, Livonia, Santa Maria da Boa Vista?", + "ground_truth": { + "answer": "Santa Maria da Boa Vista", + "outlier_distance_km": 5609.4, + "second_furthest_km": 1853.7, + "clarity_ratio": 3.03, + "median_distance_km": 1599.9, + "distances_to_centroid": { + "Middle Village": 1057.8, + "Bolingbrook": 1853.7, + "Huntington Station": 1066.0, + "Livonia": 1599.9, + "Santa Maria da Boa Vista": 5609.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Middle Village: (40.72°, -73.88°)", + " Bolingbrook: (41.70°, -88.07°)", + " Huntington Station: (40.85°, -73.41°)", + " Livonia: (42.37°, -83.35°)", + " Santa Maria da Boa Vista: (-8.81°, -39.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Maria da Boa Vista: 5609.4 km from centroid", + " Bolingbrook: 1853.7 km from centroid", + " Livonia: 1599.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Maria da Boa Vista", + "FINAL ANSWER: Santa Maria da Boa Vista" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": 46.87386, + "lon": -96.76951, + "name": "Moorhead" + } + ], + "question": "Which location is the geographic outlier among: Canning Vale, Wangaratta, Cranbourne East, Bundoora, Moorhead?", + "ground_truth": { + "answer": "Moorhead", + "outlier_distance_km": 16883.7, + "second_furthest_km": 5653.7, + "clarity_ratio": 2.99, + "median_distance_km": 5579.9, + "distances_to_centroid": { + "Canning Vale": 2835.9, + "Wangaratta": 5653.7, + "Cranbourne East": 5579.9, + "Bundoora": 5554.4, + "Moorhead": 16883.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canning Vale: (-32.06°, 115.92°)", + " Wangaratta: (-36.36°, 146.32°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Bundoora: (-37.70°, 145.06°)", + " Moorhead: (46.87°, -96.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Moorhead: 16883.7 km from centroid", + " Wangaratta: 5653.7 km from centroid", + " Cranbourne East: 5579.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Moorhead", + "FINAL ANSWER: Moorhead" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.7528, + "lon": -100.01708, + "name": "Dodge City" + }, + { + "lat": 44.69949, + "lon": -73.45291, + "name": "Plattsburgh" + }, + { + "lat": 37.08339, + "lon": -88.60005, + "name": "Paducah" + }, + { + "lat": 41.56809, + "lon": -87.72033, + "name": "Country Club Hills" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + } + ], + "question": "Which location is the geographic outlier among: Dodge City, Plattsburgh, Paducah, Country Club Hills, New Plymouth?", + "ground_truth": { + "answer": "New Plymouth", + "outlier_distance_km": 16827.8, + "second_furthest_km": 6230.7, + "clarity_ratio": 2.7, + "median_distance_km": 5228.7, + "distances_to_centroid": { + "Dodge City": 6230.7, + "Plattsburgh": 4115.2, + "Paducah": 5228.7, + "Country Club Hills": 5172.1, + "New Plymouth": 16827.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dodge City: (37.75°, -100.02°)", + " Plattsburgh: (44.70°, -73.45°)", + " Paducah: (37.08°, -88.60°)", + " Country Club Hills: (41.57°, -87.72°)", + " New Plymouth: (-39.07°, 174.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " New Plymouth: 16827.8 km from centroid", + " Dodge City: 6230.7 km from centroid", + " Paducah: 5228.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: New Plymouth", + "FINAL ANSWER: New Plymouth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.20768, + "lon": -1.50332, + "name": "Saint-Sébastien-sur-Loire" + }, + { + "lat": 44.48383, + "lon": 11.01096, + "name": "Vignola" + }, + { + "lat": 59.68333, + "lon": 30.43472, + "name": "Pavlovsk" + }, + { + "lat": 53.59601, + "lon": 19.56849, + "name": "Iława" + }, + { + "lat": 34.86676, + "lon": -92.40432, + "name": "Maumelle" + } + ], + "question": "Which location is the geographic outlier among: Saint-Sébastien-sur-Loire, Vignola, Pavlovsk, Iława, Maumelle?", + "ground_truth": { + "answer": "Maumelle", + "outlier_distance_km": 6929.1, + "second_furthest_km": 2707.3, + "clarity_ratio": 2.56, + "median_distance_km": 1928.9, + "distances_to_centroid": { + "Saint-Sébastien-sur-Loire": 389.8, + "Vignola": 1403.9, + "Pavlovsk": 2707.3, + "Iława": 1928.9, + "Maumelle": 6929.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint-Sébastien-sur-Loire: (47.21°, -1.50°)", + " Vignola: (44.48°, 11.01°)", + " Pavlovsk: (59.68°, 30.43°)", + " Iława: (53.60°, 19.57°)", + " Maumelle: (34.87°, -92.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maumelle: 6929.1 km from centroid", + " Pavlovsk: 2707.3 km from centroid", + " Iława: 1928.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maumelle", + "FINAL ANSWER: Maumelle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.00355, + "lon": -80.97372, + "name": "Wilmington Island" + }, + { + "lat": 41.8317, + "lon": -87.67366, + "name": "McKinley Park" + }, + { + "lat": 40.69455, + "lon": -73.73847, + "name": "Cambria Heights" + }, + { + "lat": 18.30334, + "lon": -99.33376, + "name": "Ciudad de Huitzuco" + }, + { + "lat": 3.24177, + "lon": 101.53296, + "name": "Kampung Setia" + } + ], + "question": "Which location is the geographic outlier among: Wilmington Island, McKinley Park, Cambria Heights, Ciudad de Huitzuco, Kampung Setia?", + "ground_truth": { + "answer": "Kampung Setia", + "outlier_distance_km": 15312.3, + "second_furthest_km": 5316.5, + "clarity_ratio": 2.88, + "median_distance_km": 3934.4, + "distances_to_centroid": { + "Wilmington Island": 3215.7, + "McKinley Park": 3934.4, + "Cambria Heights": 2788.3, + "Ciudad de Huitzuco": 5316.5, + "Kampung Setia": 15312.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wilmington Island: (32.00°, -80.97°)", + " McKinley Park: (41.83°, -87.67°)", + " Cambria Heights: (40.69°, -73.74°)", + " Ciudad de Huitzuco: (18.30°, -99.33°)", + " Kampung Setia: (3.24°, 101.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kampung Setia: 15312.3 km from centroid", + " Ciudad de Huitzuco: 5316.5 km from centroid", + " McKinley Park: 3934.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kampung Setia", + "FINAL ANSWER: Kampung Setia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.92333, + "lon": 4.25, + "name": "Maassluis" + }, + { + "lat": 54.57092, + "lon": 18.38802, + "name": "Rumia" + }, + { + "lat": 50.27875, + "lon": 3.97267, + "name": "Maubeuge" + }, + { + "lat": 53.01907, + "lon": 20.88029, + "name": "Przasnysz" + }, + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + } + ], + "question": "Which location is the geographic outlier among: Maassluis, Rumia, Maubeuge, Przasnysz, Launceston?", + "ground_truth": { + "answer": "Launceston", + "outlier_distance_km": 13808.9, + "second_furthest_km": 3430.2, + "clarity_ratio": 4.03, + "median_distance_km": 3382.4, + "distances_to_centroid": { + "Maassluis": 3430.2, + "Rumia": 2821.3, + "Maubeuge": 3382.4, + "Przasnysz": 2583.6, + "Launceston": 13808.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maassluis: (51.92°, 4.25°)", + " Rumia: (54.57°, 18.39°)", + " Maubeuge: (50.28°, 3.97°)", + " Przasnysz: (53.02°, 20.88°)", + " Launceston: (-41.44°, 147.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Launceston: 13808.9 km from centroid", + " Maassluis: 3430.2 km from centroid", + " Maubeuge: 3382.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Launceston", + "FINAL ANSWER: Launceston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.34103, + "lon": 9.8554, + "name": "Witzenhausen" + }, + { + "lat": 49.74506, + "lon": 21.47252, + "name": "Jasło" + }, + { + "lat": 41.99771, + "lon": 12.61814, + "name": "Tor Lupara" + }, + { + "lat": 48.82586, + "lon": 2.3508, + "name": "Maison Blanche" + }, + { + "lat": 37.72855, + "lon": -122.38107, + "name": "Bayview-Hunters Point" + } + ], + "question": "Which location is the geographic outlier among: Witzenhausen, Jasło, Tor Lupara, Maison Blanche, Bayview-Hunters Point?", + "ground_truth": { + "answer": "Bayview-Hunters Point", + "outlier_distance_km": 8217.5, + "second_furthest_km": 2743.0, + "clarity_ratio": 3.0, + "median_distance_km": 2258.2, + "distances_to_centroid": { + "Witzenhausen": 1927.2, + "Jasło": 2743.0, + "Tor Lupara": 2258.2, + "Maison Blanche": 1358.1, + "Bayview-Hunters Point": 8217.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Witzenhausen: (51.34°, 9.86°)", + " Jasło: (49.75°, 21.47°)", + " Tor Lupara: (42.00°, 12.62°)", + " Maison Blanche: (48.83°, 2.35°)", + " Bayview-Hunters Point: (37.73°, -122.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bayview-Hunters Point: 8217.5 km from centroid", + " Jasło: 2743.0 km from centroid", + " Tor Lupara: 2258.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bayview-Hunters Point", + "FINAL ANSWER: Bayview-Hunters Point" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.97054, + "lon": 37.76117, + "name": "Guder" + }, + { + "lat": -0.15816, + "lon": 35.19645, + "name": "Muhoroni" + }, + { + "lat": -25.77507, + "lon": 29.46482, + "name": "Middelburg" + }, + { + "lat": -26.26786, + "lon": 28.12225, + "name": "Alberton" + }, + { + "lat": 42.28343, + "lon": -71.3495, + "name": "Natick" + } + ], + "question": "Which location is the geographic outlier among: Guder, Muhoroni, Middelburg, Alberton, Natick?", + "ground_truth": { + "answer": "Natick", + "outlier_distance_km": 9462.0, + "second_furthest_km": 3416.0, + "clarity_ratio": 2.77, + "median_distance_km": 3384.0, + "distances_to_centroid": { + "Guder": 3046.0, + "Muhoroni": 2597.2, + "Middelburg": 3416.0, + "Alberton": 3384.0, + "Natick": 9462.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guder: (8.97°, 37.76°)", + " Muhoroni: (-0.16°, 35.20°)", + " Middelburg: (-25.78°, 29.46°)", + " Alberton: (-26.27°, 28.12°)", + " Natick: (42.28°, -71.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Natick: 9462.0 km from centroid", + " Middelburg: 3416.0 km from centroid", + " Alberton: 3384.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Natick", + "FINAL ANSWER: Natick" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.7282, + "lon": 16.65141, + "name": "Dzierżoniów" + }, + { + "lat": 48.07667, + "lon": 8.64409, + "name": "Trossingen" + }, + { + "lat": 51.6717, + "lon": 8.60092, + "name": "Salzkotten" + }, + { + "lat": 52.29917, + "lon": 5.24167, + "name": "Huizen" + }, + { + "lat": -33.73333, + "lon": 151.0, + "name": "Castle Hill" + } + ], + "question": "Which location is the geographic outlier among: Dzierżoniów, Trossingen, Salzkotten, Huizen, Castle Hill?", + "ground_truth": { + "answer": "Castle Hill", + "outlier_distance_km": 13939.2, + "second_furthest_km": 3317.9, + "clarity_ratio": 4.2, + "median_distance_km": 3081.2, + "distances_to_centroid": { + "Dzierżoniów": 2557.1, + "Trossingen": 2906.4, + "Salzkotten": 3081.2, + "Huizen": 3317.9, + "Castle Hill": 13939.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dzierżoniów: (50.73°, 16.65°)", + " Trossingen: (48.08°, 8.64°)", + " Salzkotten: (51.67°, 8.60°)", + " Huizen: (52.30°, 5.24°)", + " Castle Hill: (-33.73°, 151.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castle Hill: 13939.2 km from centroid", + " Huizen: 3317.9 km from centroid", + " Salzkotten: 3081.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castle Hill", + "FINAL ANSWER: Castle Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.5503, + "lon": 84.6801, + "name": "Areraj" + }, + { + "lat": 13.34962, + "lon": 74.70394, + "name": "Malpe" + }, + { + "lat": 33.32351, + "lon": 130.44218, + "name": "Nakatsukuma" + }, + { + "lat": 23.2, + "lon": 77.08333, + "name": "Sehore" + }, + { + "lat": -37.81667, + "lon": 145.2, + "name": "Mitcham" + } + ], + "question": "Which location is the geographic outlier among: Areraj, Malpe, Nakatsukuma, Sehore, Mitcham?", + "ground_truth": { + "answer": "Mitcham", + "outlier_distance_km": 7082.3, + "second_furthest_km": 3725.3, + "clarity_ratio": 1.9, + "median_distance_km": 3012.5, + "distances_to_centroid": { + "Areraj": 2482.6, + "Malpe": 3012.5, + "Nakatsukuma": 3725.3, + "Sehore": 2968.3, + "Mitcham": 7082.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Areraj: (26.55°, 84.68°)", + " Malpe: (13.35°, 74.70°)", + " Nakatsukuma: (33.32°, 130.44°)", + " Sehore: (23.20°, 77.08°)", + " Mitcham: (-37.82°, 145.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mitcham: 7082.3 km from centroid", + " Nakatsukuma: 3725.3 km from centroid", + " Malpe: 3012.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mitcham", + "FINAL ANSWER: Mitcham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": 40.34852, + "lon": -3.61621, + "name": "Casco Histórico de Vallecas" + } + ], + "question": "Which location is the geographic outlier among: Titirangi, Saint Ives, Thornlie, Clayton, Casco Histórico de Vallecas?", + "ground_truth": { + "answer": "Casco Histórico de Vallecas", + "outlier_distance_km": 13972.4, + "second_furthest_km": 5876.2, + "clarity_ratio": 2.38, + "median_distance_km": 3721.0, + "distances_to_centroid": { + "Titirangi": 5876.2, + "Saint Ives": 3721.0, + "Thornlie": 1336.3, + "Clayton": 3383.6, + "Casco Histórico de Vallecas": 13972.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Titirangi: (-36.94°, 174.66°)", + " Saint Ives: (-33.73°, 151.16°)", + " Thornlie: (-32.06°, 115.95°)", + " Clayton: (-37.92°, 145.12°)", + " Casco Histórico de Vallecas: (40.35°, -3.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casco Histórico de Vallecas: 13972.4 km from centroid", + " Titirangi: 5876.2 km from centroid", + " Saint Ives: 3721.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casco Histórico de Vallecas", + "FINAL ANSWER: Casco Histórico de Vallecas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.74582, + "lon": 139.82737, + "name": "Horikiri" + }, + { + "lat": 30.14297, + "lon": 77.25959, + "name": "Sisauli" + }, + { + "lat": 37.3925, + "lon": 126.92694, + "name": "Anyang-si" + }, + { + "lat": 24.02423, + "lon": 81.37831, + "name": "Beohāri" + }, + { + "lat": 40.58038, + "lon": -74.28515, + "name": "Avenel" + } + ], + "question": "Which location is the geographic outlier among: Horikiri, Sisauli, Anyang-si, Beohāri, Avenel?", + "ground_truth": { + "answer": "Avenel", + "outlier_distance_km": 11001.7, + "second_furthest_km": 6230.5, + "clarity_ratio": 1.77, + "median_distance_km": 5074.5, + "distances_to_centroid": { + "Horikiri": 6230.5, + "Sisauli": 766.3, + "Anyang-si": 5074.5, + "Beohāri": 1517.9, + "Avenel": 11001.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Horikiri: (35.75°, 139.83°)", + " Sisauli: (30.14°, 77.26°)", + " Anyang-si: (37.39°, 126.93°)", + " Beohāri: (24.02°, 81.38°)", + " Avenel: (40.58°, -74.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Avenel: 11001.7 km from centroid", + " Horikiri: 6230.5 km from centroid", + " Anyang-si: 5074.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Avenel", + "FINAL ANSWER: Avenel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.38673, + "lon": 0.30367, + "name": "Hartley" + }, + { + "lat": 52.00266, + "lon": 85.89741, + "name": "Mayma" + }, + { + "lat": 61.25757, + "lon": 73.41775, + "name": "Surgut" + }, + { + "lat": 38.10558, + "lon": -1.86343, + "name": "Caravaca" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + } + ], + "question": "Which location is the geographic outlier among: Hartley, Mayma, Surgut, Caravaca, Epping?", + "ground_truth": { + "answer": "Epping", + "outlier_distance_km": 11742.4, + "second_furthest_km": 5568.4, + "clarity_ratio": 2.11, + "median_distance_km": 5196.3, + "distances_to_centroid": { + "Hartley": 5196.3, + "Mayma": 2932.0, + "Surgut": 3273.4, + "Caravaca": 5568.4, + "Epping": 11742.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hartley: (51.39°, 0.30°)", + " Mayma: (52.00°, 85.90°)", + " Surgut: (61.26°, 73.42°)", + " Caravaca: (38.11°, -1.86°)", + " Epping: (-37.65°, 145.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Epping: 11742.4 km from centroid", + " Caravaca: 5568.4 km from centroid", + " Hartley: 5196.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Epping", + "FINAL ANSWER: Epping" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -33.79728, + "lon": 150.7847, + "name": "St Clair" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + }, + { + "lat": 35.58486, + "lon": -80.81007, + "name": "Mooresville" + } + ], + "question": "Which location is the geographic outlier among: Corio, Rotorua, St Clair, Napier, Mooresville?", + "ground_truth": { + "answer": "Mooresville", + "outlier_distance_km": 18030.6, + "second_furthest_km": 6183.9, + "clarity_ratio": 2.92, + "median_distance_km": 6133.5, + "distances_to_centroid": { + "Corio": 3390.6, + "Rotorua": 6133.5, + "St Clair": 3826.0, + "Napier": 6183.9, + "Mooresville": 18030.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Corio: (-38.08°, 144.38°)", + " Rotorua: (-38.14°, 176.25°)", + " St Clair: (-33.80°, 150.78°)", + " Napier: (-39.49°, 176.91°)", + " Mooresville: (35.58°, -80.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mooresville: 18030.6 km from centroid", + " Napier: 6183.9 km from centroid", + " Rotorua: 6133.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mooresville", + "FINAL ANSWER: Mooresville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.63333, + "lon": -58.41667, + "name": "Boedo" + }, + { + "lat": 9.36238, + "lon": -73.60313, + "name": "Chiriguaná" + }, + { + "lat": -22.54417, + "lon": -44.17139, + "name": "Barra Mansa" + }, + { + "lat": -24.15667, + "lon": -54.09694, + "name": "Terra Roxa" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + } + ], + "question": "Which location is the geographic outlier among: Boedo, Chiriguaná, Barra Mansa, Terra Roxa, Melbourne?", + "ground_truth": { + "answer": "Melbourne", + "outlier_distance_km": 13108.3, + "second_furthest_km": 7078.3, + "clarity_ratio": 1.85, + "median_distance_km": 4252.8, + "distances_to_centroid": { + "Boedo": 4252.8, + "Chiriguaná": 7078.3, + "Barra Mansa": 2786.6, + "Terra Roxa": 3785.9, + "Melbourne": 13108.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boedo: (-34.63°, -58.42°)", + " Chiriguaná: (9.36°, -73.60°)", + " Barra Mansa: (-22.54°, -44.17°)", + " Terra Roxa: (-24.16°, -54.10°)", + " Melbourne: (-37.81°, 144.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Melbourne: 13108.3 km from centroid", + " Chiriguaná: 7078.3 km from centroid", + " Boedo: 4252.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Melbourne", + "FINAL ANSWER: Melbourne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.05584, + "lon": 145.90375, + "name": "Burnie" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": 7.55632, + "lon": 3.44107, + "name": "Orita-Eruwa" + } + ], + "question": "Which location is the geographic outlier among: Burnie, Palmerston, Yagoona, Officer, Orita-Eruwa?", + "ground_truth": { + "answer": "Orita-Eruwa", + "outlier_distance_km": 12571.2, + "second_furthest_km": 3640.3, + "clarity_ratio": 3.45, + "median_distance_km": 3437.3, + "distances_to_centroid": { + "Burnie": 3437.3, + "Palmerston": 2059.9, + "Yagoona": 3640.3, + "Officer": 3268.7, + "Orita-Eruwa": 12571.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Burnie: (-41.06°, 145.90°)", + " Palmerston: (-12.49°, 130.98°)", + " Yagoona: (-33.90°, 151.02°)", + " Officer: (-38.06°, 145.41°)", + " Orita-Eruwa: (7.56°, 3.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Orita-Eruwa: 12571.2 km from centroid", + " Yagoona: 3640.3 km from centroid", + " Burnie: 3437.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Orita-Eruwa", + "FINAL ANSWER: Orita-Eruwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.92805, + "lon": 2.39627, + "name": "La Courneuve" + }, + { + "lat": 43.46276, + "lon": 11.88068, + "name": "Arezzo" + }, + { + "lat": 37.49773, + "lon": 13.26676, + "name": "Ribera" + }, + { + "lat": 53.55214, + "lon": 14.57182, + "name": "Police" + }, + { + "lat": 20.73072, + "lon": -105.28257, + "name": "Mezcales" + } + ], + "question": "Which location is the geographic outlier among: La Courneuve, Arezzo, Ribera, Police, Mezcales?", + "ground_truth": { + "answer": "Mezcales", + "outlier_distance_km": 8732.8, + "second_furthest_km": 2470.7, + "clarity_ratio": 3.53, + "median_distance_km": 2255.0, + "distances_to_centroid": { + "La Courneuve": 1482.9, + "Arezzo": 2034.4, + "Ribera": 2255.0, + "Police": 2470.7, + "Mezcales": 8732.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Courneuve: (48.93°, 2.40°)", + " Arezzo: (43.46°, 11.88°)", + " Ribera: (37.50°, 13.27°)", + " Police: (53.55°, 14.57°)", + " Mezcales: (20.73°, -105.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mezcales: 8732.8 km from centroid", + " Police: 2470.7 km from centroid", + " Ribera: 2255.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mezcales", + "FINAL ANSWER: Mezcales" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.32092, + "lon": 6.49412, + "name": "Tönisvorst" + }, + { + "lat": 55.78677, + "lon": 37.80165, + "name": "Izmaylovo" + }, + { + "lat": 39.15, + "lon": -0.43333, + "name": "Alzira" + }, + { + "lat": 43.84171, + "lon": 10.57271, + "name": "Capannori" + }, + { + "lat": 34.80447, + "lon": 136.54645, + "name": "Kawage" + } + ], + "question": "Which location is the geographic outlier among: Tönisvorst, Izmaylovo, Alzira, Capannori, Kawage?", + "ground_truth": { + "answer": "Kawage", + "outlier_distance_km": 7938.2, + "second_furthest_km": 3222.2, + "clarity_ratio": 2.46, + "median_distance_km": 2433.7, + "distances_to_centroid": { + "Tönisvorst": 2433.7, + "Izmaylovo": 1201.9, + "Alzira": 3222.2, + "Capannori": 2187.2, + "Kawage": 7938.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tönisvorst: (51.32°, 6.49°)", + " Izmaylovo: (55.79°, 37.80°)", + " Alzira: (39.15°, -0.43°)", + " Capannori: (43.84°, 10.57°)", + " Kawage: (34.80°, 136.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kawage: 7938.2 km from centroid", + " Alzira: 3222.2 km from centroid", + " Tönisvorst: 2433.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kawage", + "FINAL ANSWER: Kawage" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.54723, + "lon": 29.42412, + "name": "Kokstad" + }, + { + "lat": -33.963, + "lon": 22.46173, + "name": "George" + }, + { + "lat": 25.66477, + "lon": 32.63539, + "name": "Al Bayāḑīyah" + }, + { + "lat": 0.33474, + "lon": 34.48796, + "name": "Mumias" + }, + { + "lat": -19.17222, + "lon": -41.47222, + "name": "Conselheiro Pena" + } + ], + "question": "Which location is the geographic outlier among: Kokstad, George, Al Bayāḑīyah, Mumias, Conselheiro Pena?", + "ground_truth": { + "answer": "Conselheiro Pena", + "outlier_distance_km": 6143.5, + "second_furthest_km": 4533.3, + "clarity_ratio": 1.36, + "median_distance_km": 2591.7, + "distances_to_centroid": { + "Kokstad": 2554.5, + "George": 2591.7, + "Al Bayāḑīyah": 4533.3, + "Mumias": 2477.5, + "Conselheiro Pena": 6143.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kokstad: (-30.55°, 29.42°)", + " George: (-33.96°, 22.46°)", + " Al Bayāḑīyah: (25.66°, 32.64°)", + " Mumias: (0.33°, 34.49°)", + " Conselheiro Pena: (-19.17°, -41.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Conselheiro Pena: 6143.5 km from centroid", + " Al Bayāḑīyah: 4533.3 km from centroid", + " George: 2591.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Conselheiro Pena", + "FINAL ANSWER: Conselheiro Pena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.15611, + "lon": 37.89806, + "name": "Debark’" + }, + { + "lat": 6.86, + "lon": 37.76159, + "name": "Sodo" + }, + { + "lat": 5.96669, + "lon": 8.70632, + "name": "Ikom" + }, + { + "lat": 11.8277, + "lon": 39.59164, + "name": "Weldiya" + }, + { + "lat": -7.28083, + "lon": -35.60444, + "name": "Ingá" + } + ], + "question": "Which location is the geographic outlier among: Debark’, Sodo, Ikom, Weldiya, Ingá?", + "ground_truth": { + "answer": "Ingá", + "outlier_distance_km": 6094.5, + "second_furthest_km": 2489.0, + "clarity_ratio": 2.45, + "median_distance_km": 2350.2, + "distances_to_centroid": { + "Debark’": 2350.2, + "Sodo": 2221.1, + "Ikom": 991.4, + "Weldiya": 2489.0, + "Ingá": 6094.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Debark’: (13.16°, 37.90°)", + " Sodo: (6.86°, 37.76°)", + " Ikom: (5.97°, 8.71°)", + " Weldiya: (11.83°, 39.59°)", + " Ingá: (-7.28°, -35.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ingá: 6094.5 km from centroid", + " Weldiya: 2489.0 km from centroid", + " Debark’: 2350.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ingá", + "FINAL ANSWER: Ingá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -19.30323, + "lon": 146.72531, + "name": "Kirwan" + }, + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": -29.58667, + "lon": -51.37556, + "name": "São Sebastião do Caí" + } + ], + "question": "Which location is the geographic outlier among: Miranda, Kirwan, Mulgrave, Nerang, São Sebastião do Caí?", + "ground_truth": { + "answer": "São Sebastião do Caí", + "outlier_distance_km": 13094.7, + "second_furthest_km": 4295.5, + "clarity_ratio": 3.05, + "median_distance_km": 3975.3, + "distances_to_centroid": { + "Miranda": 3975.3, + "Kirwan": 3970.1, + "Mulgrave": 3439.0, + "Nerang": 4295.5, + "São Sebastião do Caí": 13094.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miranda: (-34.04°, 151.10°)", + " Kirwan: (-19.30°, 146.73°)", + " Mulgrave: (-37.93°, 145.18°)", + " Nerang: (-27.99°, 153.34°)", + " São Sebastião do Caí: (-29.59°, -51.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Sebastião do Caí: 13094.7 km from centroid", + " Nerang: 4295.5 km from centroid", + " Miranda: 3975.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Sebastião do Caí", + "FINAL ANSWER: São Sebastião do Caí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -23.56439, + "lon": -46.61695, + "name": "Cambuci" + } + ], + "question": "Which location is the geographic outlier among: Mascot, Rockingham, Granville, Lidcombe, Cambuci?", + "ground_truth": { + "answer": "Cambuci", + "outlier_distance_km": 13163.3, + "second_furthest_km": 4342.1, + "clarity_ratio": 3.03, + "median_distance_km": 4329.3, + "distances_to_centroid": { + "Mascot": 4342.1, + "Rockingham": 1066.1, + "Granville": 4326.8, + "Lidcombe": 4329.3, + "Cambuci": 13163.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mascot: (-33.93°, 151.19°)", + " Rockingham: (-32.28°, 115.73°)", + " Granville: (-33.84°, 151.01°)", + " Lidcombe: (-33.86°, 151.04°)", + " Cambuci: (-23.56°, -46.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cambuci: 13163.3 km from centroid", + " Mascot: 4342.1 km from centroid", + " Lidcombe: 4329.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cambuci", + "FINAL ANSWER: Cambuci" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.60972, + "lon": -42.53972, + "name": "Rio Pardo de Minas" + }, + { + "lat": -17.89194, + "lon": -39.37194, + "name": "Nova Viçosa" + }, + { + "lat": -1.50583, + "lon": -48.62583, + "name": "Barcarena" + }, + { + "lat": -5.40232, + "lon": -80.74224, + "name": "La Unión" + }, + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + } + ], + "question": "Which location is the geographic outlier among: Rio Pardo de Minas, Nova Viçosa, Barcarena, La Unión, Warragul?", + "ground_truth": { + "answer": "Warragul", + "outlier_distance_km": 13636.6, + "second_furthest_km": 7458.1, + "clarity_ratio": 1.83, + "median_distance_km": 4204.9, + "distances_to_centroid": { + "Rio Pardo de Minas": 3152.7, + "Nova Viçosa": 2808.0, + "Barcarena": 4204.9, + "La Unión": 7458.1, + "Warragul": 13636.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rio Pardo de Minas: (-15.61°, -42.54°)", + " Nova Viçosa: (-17.89°, -39.37°)", + " Barcarena: (-1.51°, -48.63°)", + " La Unión: (-5.40°, -80.74°)", + " Warragul: (-38.16°, 145.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Warragul: 13636.6 km from centroid", + " La Unión: 7458.1 km from centroid", + " Barcarena: 4204.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Warragul", + "FINAL ANSWER: Warragul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.62057, + "lon": -75.09415, + "name": "Natagaima" + }, + { + "lat": -23.62821, + "lon": -46.45395, + "name": "Sao Rafael" + }, + { + "lat": -34.47513, + "lon": -58.75367, + "name": "Tortuguitas" + }, + { + "lat": -16.00528, + "lon": -41.29722, + "name": "Pedra Azul" + }, + { + "lat": 37.75, + "lon": 138.88333, + "name": "Maki" + } + ], + "question": "Which location is the geographic outlier among: Natagaima, Sao Rafael, Tortuguitas, Pedra Azul, Maki?", + "ground_truth": { + "answer": "Maki", + "outlier_distance_km": 15750.4, + "second_furthest_km": 6597.1, + "clarity_ratio": 2.39, + "median_distance_km": 5319.9, + "distances_to_centroid": { + "Natagaima": 6597.1, + "Sao Rafael": 3716.1, + "Tortuguitas": 5319.9, + "Pedra Azul": 2893.0, + "Maki": 15750.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Natagaima: (3.62°, -75.09°)", + " Sao Rafael: (-23.63°, -46.45°)", + " Tortuguitas: (-34.48°, -58.75°)", + " Pedra Azul: (-16.01°, -41.30°)", + " Maki: (37.75°, 138.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maki: 15750.4 km from centroid", + " Natagaima: 6597.1 km from centroid", + " Tortuguitas: 5319.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maki", + "FINAL ANSWER: Maki" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.80917, + "lon": -61.30028, + "name": "Manicoré" + }, + { + "lat": -9.64139, + "lon": -36.22028, + "name": "Boca da Mata" + }, + { + "lat": 9.73586, + "lon": -75.52626, + "name": "San Onofre" + }, + { + "lat": -20.46417, + "lon": -41.41306, + "name": "Muniz Freire" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + } + ], + "question": "Which location is the geographic outlier among: Manicoré, Boca da Mata, San Onofre, Muniz Freire, Clayton?", + "ground_truth": { + "answer": "Clayton", + "outlier_distance_km": 13963.0, + "second_furthest_km": 7255.0, + "clarity_ratio": 1.92, + "median_distance_km": 5255.0, + "distances_to_centroid": { + "Manicoré": 5255.0, + "Boca da Mata": 2462.3, + "San Onofre": 7255.0, + "Muniz Freire": 3050.2, + "Clayton": 13963.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manicoré: (-5.81°, -61.30°)", + " Boca da Mata: (-9.64°, -36.22°)", + " San Onofre: (9.74°, -75.53°)", + " Muniz Freire: (-20.46°, -41.41°)", + " Clayton: (-37.92°, 145.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clayton: 13963.0 km from centroid", + " San Onofre: 7255.0 km from centroid", + " Manicoré: 5255.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clayton", + "FINAL ANSWER: Clayton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.29235, + "lon": -81.53565, + "name": "Shelby" + }, + { + "lat": 39.96578, + "lon": -75.23764, + "name": "Haddington" + }, + { + "lat": 49.68657, + "lon": -124.9936, + "name": "Courtenay" + }, + { + "lat": 42.39593, + "lon": -71.17867, + "name": "Belmont" + }, + { + "lat": -37.81667, + "lon": 145.2, + "name": "Mitcham" + } + ], + "question": "Which location is the geographic outlier among: Shelby, Haddington, Courtenay, Belmont, Mitcham?", + "ground_truth": { + "answer": "Mitcham", + "outlier_distance_km": 18546.3, + "second_furthest_km": 7388.8, + "clarity_ratio": 2.51, + "median_distance_km": 3938.3, + "distances_to_centroid": { + "Shelby": 3938.3, + "Haddington": 3482.8, + "Courtenay": 7388.8, + "Belmont": 3258.9, + "Mitcham": 18546.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shelby: (35.29°, -81.54°)", + " Haddington: (39.97°, -75.24°)", + " Courtenay: (49.69°, -124.99°)", + " Belmont: (42.40°, -71.18°)", + " Mitcham: (-37.82°, 145.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mitcham: 18546.3 km from centroid", + " Courtenay: 7388.8 km from centroid", + " Shelby: 3938.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mitcham", + "FINAL ANSWER: Mitcham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.54333, + "lon": 153.20287, + "name": "Capalaba" + }, + { + "lat": -37.99116, + "lon": 145.17385, + "name": "Keysborough" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + { + "lat": 49.35009, + "lon": 8.13886, + "name": "Neustadt an der Weinstraße" + } + ], + "question": "Which location is the geographic outlier among: Capalaba, Keysborough, Cranbourne West, Hawthorn South, Neustadt an der Weinstraße?", + "ground_truth": { + "answer": "Neustadt an der Weinstraße", + "outlier_distance_km": 13078.2, + "second_furthest_km": 3596.4, + "clarity_ratio": 3.64, + "median_distance_km": 3328.4, + "distances_to_centroid": { + "Capalaba": 3596.4, + "Keysborough": 3315.1, + "Cranbourne West": 3328.4, + "Hawthorn South": 3295.3, + "Neustadt an der Weinstraße": 13078.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Capalaba: (-27.54°, 153.20°)", + " Keysborough: (-37.99°, 145.17°)", + " Cranbourne West: (-38.10°, 145.27°)", + " Hawthorn South: (-37.83°, 145.04°)", + " Neustadt an der Weinstraße: (49.35°, 8.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Neustadt an der Weinstraße: 13078.2 km from centroid", + " Capalaba: 3596.4 km from centroid", + " Cranbourne West: 3328.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Neustadt an der Weinstraße", + "FINAL ANSWER: Neustadt an der Weinstraße" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.79056, + "lon": -49.67167, + "name": "Baião" + }, + { + "lat": -27.77333, + "lon": -54.24, + "name": "Três de Maio" + }, + { + "lat": -1.29389, + "lon": -47.92639, + "name": "Castanhal" + }, + { + "lat": -18.50667, + "lon": -54.76, + "name": "Coxim" + }, + { + "lat": 38.23242, + "lon": -122.63665, + "name": "Petaluma" + } + ], + "question": "Which location is the geographic outlier among: Baião, Três de Maio, Castanhal, Coxim, Petaluma?", + "ground_truth": { + "answer": "Petaluma", + "outlier_distance_km": 7360.4, + "second_furthest_km": 3076.5, + "clarity_ratio": 2.39, + "median_distance_km": 2157.8, + "distances_to_centroid": { + "Baião": 1797.2, + "Três de Maio": 3076.5, + "Castanhal": 1995.6, + "Coxim": 2157.8, + "Petaluma": 7360.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baião: (-2.79°, -49.67°)", + " Três de Maio: (-27.77°, -54.24°)", + " Castanhal: (-1.29°, -47.93°)", + " Coxim: (-18.51°, -54.76°)", + " Petaluma: (38.23°, -122.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Petaluma: 7360.4 km from centroid", + " Três de Maio: 3076.5 km from centroid", + " Coxim: 2157.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Petaluma", + "FINAL ANSWER: Petaluma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": -34.78254, + "lon": 138.61077, + "name": "Parafield Gardens" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -38.14711, + "lon": 144.36069, + "name": "Geelong" + }, + { + "lat": 53.49389, + "lon": -1.29243, + "name": "Mexborough" + } + ], + "question": "Which location is the geographic outlier among: Doreen, Parafield Gardens, Port Macquarie, Geelong, Mexborough?", + "ground_truth": { + "answer": "Mexborough", + "outlier_distance_km": 13370.7, + "second_furthest_km": 4013.7, + "clarity_ratio": 3.33, + "median_distance_km": 3602.9, + "distances_to_centroid": { + "Doreen": 3602.9, + "Parafield Gardens": 2939.6, + "Port Macquarie": 4013.7, + "Geelong": 3574.4, + "Mexborough": 13370.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doreen: (-37.60°, 145.15°)", + " Parafield Gardens: (-34.78°, 138.61°)", + " Port Macquarie: (-31.43°, 152.91°)", + " Geelong: (-38.15°, 144.36°)", + " Mexborough: (53.49°, -1.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mexborough: 13370.7 km from centroid", + " Port Macquarie: 4013.7 km from centroid", + " Doreen: 3602.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mexborough", + "FINAL ANSWER: Mexborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.21866, + "lon": 3.20117, + "name": "Okuta" + }, + { + "lat": -34.09345, + "lon": 21.25725, + "name": "Riversdale" + }, + { + "lat": 8.72851, + "lon": 5.75561, + "name": "Patigi" + }, + { + "lat": -0.33024, + "lon": 35.94445, + "name": "Njoro" + }, + { + "lat": -33.91972, + "lon": 151.07592, + "name": "Lakemba" + } + ], + "question": "Which location is the geographic outlier among: Okuta, Riversdale, Patigi, Njoro, Lakemba?", + "ground_truth": { + "answer": "Lakemba", + "outlier_distance_km": 10965.4, + "second_furthest_km": 4943.6, + "clarity_ratio": 2.22, + "median_distance_km": 4666.6, + "distances_to_centroid": { + "Okuta": 4943.6, + "Riversdale": 3497.5, + "Patigi": 4666.6, + "Njoro": 1365.2, + "Lakemba": 10965.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Okuta: (9.22°, 3.20°)", + " Riversdale: (-34.09°, 21.26°)", + " Patigi: (8.73°, 5.76°)", + " Njoro: (-0.33°, 35.94°)", + " Lakemba: (-33.92°, 151.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lakemba: 10965.4 km from centroid", + " Okuta: 4943.6 km from centroid", + " Patigi: 4666.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lakemba", + "FINAL ANSWER: Lakemba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.76667, + "lon": 100.85, + "name": "Padang Rengas" + }, + { + "lat": 24.51333, + "lon": 117.65556, + "name": "Zhangzhou" + }, + { + "lat": 35.1422, + "lon": 136.8121, + "name": "Haruta" + }, + { + "lat": 38.23333, + "lon": 139.48333, + "name": "Murakami" + }, + { + "lat": -23.50099, + "lon": -46.65744, + "name": "Casa Verde" + } + ], + "question": "Which location is the geographic outlier among: Padang Rengas, Zhangzhou, Haruta, Murakami, Casa Verde?", + "ground_truth": { + "answer": "Casa Verde", + "outlier_distance_km": 15376.8, + "second_furthest_km": 5448.6, + "clarity_ratio": 2.82, + "median_distance_km": 5141.0, + "distances_to_centroid": { + "Padang Rengas": 1736.5, + "Zhangzhou": 3073.4, + "Haruta": 5141.0, + "Murakami": 5448.6, + "Casa Verde": 15376.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Padang Rengas: (4.77°, 100.85°)", + " Zhangzhou: (24.51°, 117.66°)", + " Haruta: (35.14°, 136.81°)", + " Murakami: (38.23°, 139.48°)", + " Casa Verde: (-23.50°, -46.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casa Verde: 15376.8 km from centroid", + " Murakami: 5448.6 km from centroid", + " Haruta: 5141.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casa Verde", + "FINAL ANSWER: Casa Verde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 56.0038, + "lon": 40.33905, + "name": "Raduzhnyy" + }, + { + "lat": 43.10322, + "lon": 5.87816, + "name": "La Seyne-sur-Mer" + }, + { + "lat": 61.04027, + "lon": 30.13915, + "name": "Priozërsk" + }, + { + "lat": 49.56526, + "lon": 9.70816, + "name": "Lauda-Königshofen" + }, + { + "lat": -37.83961, + "lon": 144.94228, + "name": "Port Melbourne" + } + ], + "question": "Which location is the geographic outlier among: Raduzhnyy, La Seyne-sur-Mer, Priozërsk, Lauda-Königshofen, Port Melbourne?", + "ground_truth": { + "answer": "Port Melbourne", + "outlier_distance_km": 12948.6, + "second_furthest_km": 3591.9, + "clarity_ratio": 3.6, + "median_distance_km": 3410.6, + "distances_to_centroid": { + "Raduzhnyy": 2446.4, + "La Seyne-sur-Mer": 3591.9, + "Priozërsk": 3179.4, + "Lauda-Königshofen": 3410.6, + "Port Melbourne": 12948.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Raduzhnyy: (56.00°, 40.34°)", + " La Seyne-sur-Mer: (43.10°, 5.88°)", + " Priozërsk: (61.04°, 30.14°)", + " Lauda-Königshofen: (49.57°, 9.71°)", + " Port Melbourne: (-37.84°, 144.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Melbourne: 12948.6 km from centroid", + " La Seyne-sur-Mer: 3591.9 km from centroid", + " Lauda-Königshofen: 3410.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Melbourne", + "FINAL ANSWER: Port Melbourne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.40659, + "lon": -87.6836, + "name": "Foley" + }, + { + "lat": 27.85591, + "lon": -101.11738, + "name": "Sabinas" + }, + { + "lat": 45.4399, + "lon": -75.66498, + "name": "Vanier" + }, + { + "lat": 15.86275, + "lon": -97.06835, + "name": "Puerto Escondido" + }, + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + } + ], + "question": "Which location is the geographic outlier among: Foley, Sabinas, Vanier, Puerto Escondido, Traralgon?", + "ground_truth": { + "answer": "Traralgon", + "outlier_distance_km": 17405.3, + "second_furthest_km": 6072.0, + "clarity_ratio": 2.87, + "median_distance_km": 5759.7, + "distances_to_centroid": { + "Foley": 4789.8, + "Sabinas": 6072.0, + "Vanier": 4441.5, + "Puerto Escondido": 5759.7, + "Traralgon": 17405.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Foley: (30.41°, -87.68°)", + " Sabinas: (27.86°, -101.12°)", + " Vanier: (45.44°, -75.66°)", + " Puerto Escondido: (15.86°, -97.07°)", + " Traralgon: (-38.20°, 146.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Traralgon: 17405.3 km from centroid", + " Sabinas: 6072.0 km from centroid", + " Puerto Escondido: 5759.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Traralgon", + "FINAL ANSWER: Traralgon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.79404, + "lon": -80.26749, + "name": "The Acreage" + }, + { + "lat": 41.26194, + "lon": -95.86083, + "name": "Council Bluffs" + }, + { + "lat": 42.52509, + "lon": -71.75979, + "name": "Leominster" + }, + { + "lat": 33.74557, + "lon": -117.86783, + "name": "Santa Ana" + }, + { + "lat": 38.13387, + "lon": 85.52992, + "name": "Qiemo" + } + ], + "question": "Which location is the geographic outlier among: The Acreage, Council Bluffs, Leominster, Santa Ana, Qiemo?", + "ground_truth": { + "answer": "Qiemo", + "outlier_distance_km": 10826.3, + "second_furthest_km": 5532.8, + "clarity_ratio": 1.96, + "median_distance_km": 3456.5, + "distances_to_centroid": { + "The Acreage": 2524.3, + "Council Bluffs": 3456.5, + "Leominster": 1502.6, + "Santa Ana": 5532.8, + "Qiemo": 10826.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " The Acreage: (26.79°, -80.27°)", + " Council Bluffs: (41.26°, -95.86°)", + " Leominster: (42.53°, -71.76°)", + " Santa Ana: (33.75°, -117.87°)", + " Qiemo: (38.13°, 85.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qiemo: 10826.3 km from centroid", + " Santa Ana: 5532.8 km from centroid", + " Council Bluffs: 3456.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qiemo", + "FINAL ANSWER: Qiemo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.00861, + "lon": -44.51944, + "name": "Santa Rita de Cássia" + }, + { + "lat": -20.58306, + "lon": -46.92194, + "name": "Cássia" + }, + { + "lat": -2.14092, + "lon": -46.12387, + "name": "Centro Novo do Maranhão" + }, + { + "lat": -20.69639, + "lon": -44.82722, + "name": "Oliveira" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + } + ], + "question": "Which location is the geographic outlier among: Santa Rita de Cássia, Cássia, Centro Novo do Maranhão, Oliveira, Blenheim?", + "ground_truth": { + "answer": "Blenheim", + "outlier_distance_km": 13250.1, + "second_furthest_km": 5189.7, + "clarity_ratio": 2.55, + "median_distance_km": 4717.2, + "distances_to_centroid": { + "Santa Rita de Cássia": 4675.1, + "Cássia": 4717.2, + "Centro Novo do Maranhão": 5189.7, + "Oliveira": 4499.1, + "Blenheim": 13250.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Rita de Cássia: (-11.01°, -44.52°)", + " Cássia: (-20.58°, -46.92°)", + " Centro Novo do Maranhão: (-2.14°, -46.12°)", + " Oliveira: (-20.70°, -44.83°)", + " Blenheim: (-41.52°, 173.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blenheim: 13250.1 km from centroid", + " Centro Novo do Maranhão: 5189.7 km from centroid", + " Cássia: 4717.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blenheim", + "FINAL ANSWER: Blenheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.83982, + "lon": 76.94065, + "name": "Kālka" + }, + { + "lat": 23.33794, + "lon": 75.55931, + "name": "Unhel" + }, + { + "lat": 27.93411, + "lon": 76.85541, + "name": "Tijāra" + }, + { + "lat": 20.84852, + "lon": 86.33729, + "name": "Jājpur" + }, + { + "lat": -25.68991, + "lon": 30.03504, + "name": "Belfast" + } + ], + "question": "Which location is the geographic outlier among: Kālka, Unhel, Tijāra, Jājpur, Belfast?", + "ground_truth": { + "answer": "Belfast", + "outlier_distance_km": 6232.7, + "second_furthest_km": 1911.5, + "clarity_ratio": 3.26, + "median_distance_km": 1885.7, + "distances_to_centroid": { + "Kālka": 1885.7, + "Unhel": 1104.5, + "Tijāra": 1598.9, + "Jājpur": 1911.5, + "Belfast": 6232.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kālka: (30.84°, 76.94°)", + " Unhel: (23.34°, 75.56°)", + " Tijāra: (27.93°, 76.86°)", + " Jājpur: (20.85°, 86.34°)", + " Belfast: (-25.69°, 30.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Belfast: 6232.7 km from centroid", + " Jājpur: 1911.5 km from centroid", + " Kālka: 1885.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Belfast", + "FINAL ANSWER: Belfast" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.67478, + "lon": 10.19069, + "name": "Azare" + }, + { + "lat": 9.32541, + "lon": 9.4352, + "name": "Pankshin" + }, + { + "lat": 9.18059, + "lon": 7.17939, + "name": "Suleja" + }, + { + "lat": 6.71667, + "lon": 37.56667, + "name": "Gasuba" + }, + { + "lat": 30.22055, + "lon": 107.50403, + "name": "Gangjia" + } + ], + "question": "Which location is the geographic outlier among: Azare, Pankshin, Suleja, Gasuba, Gangjia?", + "ground_truth": { + "answer": "Gangjia", + "outlier_distance_km": 7656.0, + "second_furthest_km": 3000.9, + "clarity_ratio": 2.55, + "median_distance_km": 2755.2, + "distances_to_centroid": { + "Azare": 2631.1, + "Pankshin": 2755.2, + "Suleja": 3000.9, + "Gasuba": 823.5, + "Gangjia": 7656.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Azare: (11.67°, 10.19°)", + " Pankshin: (9.33°, 9.44°)", + " Suleja: (9.18°, 7.18°)", + " Gasuba: (6.72°, 37.57°)", + " Gangjia: (30.22°, 107.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gangjia: 7656.0 km from centroid", + " Suleja: 3000.9 km from centroid", + " Pankshin: 2755.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gangjia", + "FINAL ANSWER: Gangjia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": -36.9482, + "lon": 174.87019, + "name": "Otara" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + }, + { + "lat": 43.44775, + "lon": 3.75524, + "name": "Frontignan" + } + ], + "question": "Which location is the geographic outlier among: Coorparoo, Wainuiomata, Otara, Hampton Park, Frontignan?", + "ground_truth": { + "answer": "Frontignan", + "outlier_distance_km": 14454.4, + "second_furthest_km": 4801.7, + "clarity_ratio": 3.01, + "median_distance_km": 4684.3, + "distances_to_centroid": { + "Coorparoo": 2446.8, + "Wainuiomata": 4801.7, + "Otara": 4684.3, + "Hampton Park": 2459.5, + "Frontignan": 14454.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coorparoo: (-27.49°, 153.06°)", + " Wainuiomata: (-41.27°, 174.95°)", + " Otara: (-36.95°, 174.87°)", + " Hampton Park: (-38.03°, 145.25°)", + " Frontignan: (43.45°, 3.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Frontignan: 14454.4 km from centroid", + " Wainuiomata: 4801.7 km from centroid", + " Otara: 4684.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Frontignan", + "FINAL ANSWER: Frontignan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9482, + "lon": 174.87019, + "name": "Otara" + }, + { + "lat": -37.6, + "lon": 144.95, + "name": "Craigieburn" + }, + { + "lat": -36.96807, + "lon": 174.79875, + "name": "Mangere" + }, + { + "lat": -37.69047, + "lon": 144.74172, + "name": "Hillside" + }, + { + "lat": 32.70438, + "lon": 74.86114, + "name": "Jammu Cantonment" + } + ], + "question": "Which location is the geographic outlier among: Otara, Craigieburn, Mangere, Hillside, Jammu Cantonment?", + "ground_truth": { + "answer": "Jammu Cantonment", + "outlier_distance_km": 9522.9, + "second_furthest_km": 3411.1, + "clarity_ratio": 2.79, + "median_distance_km": 3405.7, + "distances_to_centroid": { + "Otara": 3411.1, + "Craigieburn": 1602.7, + "Mangere": 3405.7, + "Hillside": 1610.3, + "Jammu Cantonment": 9522.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Otara: (-36.95°, 174.87°)", + " Craigieburn: (-37.60°, 144.95°)", + " Mangere: (-36.97°, 174.80°)", + " Hillside: (-37.69°, 144.74°)", + " Jammu Cantonment: (32.70°, 74.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jammu Cantonment: 9522.9 km from centroid", + " Otara: 3411.1 km from centroid", + " Mangere: 3405.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jammu Cantonment", + "FINAL ANSWER: Jammu Cantonment" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.56667, + "lon": -46.74222, + "name": "Amarante do Maranhão" + }, + { + "lat": -10.59333, + "lon": -36.94028, + "name": "Japaratuba" + }, + { + "lat": -3.92806, + "lon": -41.70917, + "name": "Piracuruca" + }, + { + "lat": -12.50583, + "lon": -38.99861, + "name": "Conceição da Feira" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + } + ], + "question": "Which location is the geographic outlier among: Amarante do Maranhão, Japaratuba, Piracuruca, Conceição da Feira, Seaford?", + "ground_truth": { + "answer": "Seaford", + "outlier_distance_km": 13367.5, + "second_furthest_km": 4786.5, + "clarity_ratio": 2.79, + "median_distance_km": 4302.0, + "distances_to_centroid": { + "Amarante do Maranhão": 4786.5, + "Japaratuba": 3612.5, + "Piracuruca": 4302.0, + "Conceição da Feira": 3803.9, + "Seaford": 13367.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Amarante do Maranhão: (-5.57°, -46.74°)", + " Japaratuba: (-10.59°, -36.94°)", + " Piracuruca: (-3.93°, -41.71°)", + " Conceição da Feira: (-12.51°, -39.00°)", + " Seaford: (-38.10°, 145.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Seaford: 13367.5 km from centroid", + " Amarante do Maranhão: 4786.5 km from centroid", + " Piracuruca: 4302.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Seaford", + "FINAL ANSWER: Seaford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -37.92845, + "lon": 145.17708, + "name": "Mulgrave" + }, + { + "lat": 51.6, + "lon": -0.11667, + "name": "Wood Green" + } + ], + "question": "Which location is the geographic outlier among: Carlton, Mooroolbark, Maitland, Mulgrave, Wood Green?", + "ground_truth": { + "answer": "Wood Green", + "outlier_distance_km": 13532.6, + "second_furthest_km": 3727.2, + "clarity_ratio": 3.63, + "median_distance_km": 3421.5, + "distances_to_centroid": { + "Carlton": 3395.9, + "Mooroolbark": 3421.5, + "Maitland": 3727.2, + "Mulgrave": 3419.0, + "Wood Green": 13532.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlton: (-37.80°, 144.97°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Maitland: (-32.73°, 151.56°)", + " Mulgrave: (-37.93°, 145.18°)", + " Wood Green: (51.60°, -0.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wood Green: 13532.6 km from centroid", + " Maitland: 3727.2 km from centroid", + " Mooroolbark: 3421.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wood Green", + "FINAL ANSWER: Wood Green" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.90694, + "lon": 174.68704, + "name": "New Lynn" + }, + { + "lat": -32.22099, + "lon": 116.009, + "name": "Byford" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + }, + { + "lat": -34.60251, + "lon": 138.74902, + "name": "Gawler" + }, + { + "lat": 43.29551, + "lon": 5.40055, + "name": "Marseille 05" + } + ], + "question": "Which location is the geographic outlier among: New Lynn, Byford, Cherrybrook, Gawler, Marseille 05?", + "ground_truth": { + "answer": "Marseille 05", + "outlier_distance_km": 13174.9, + "second_furthest_km": 5904.8, + "clarity_ratio": 2.23, + "median_distance_km": 3737.0, + "distances_to_centroid": { + "New Lynn": 5904.8, + "Byford": 1493.4, + "Cherrybrook": 3737.0, + "Gawler": 2757.4, + "Marseille 05": 13174.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " New Lynn: (-36.91°, 174.69°)", + " Byford: (-32.22°, 116.01°)", + " Cherrybrook: (-33.72°, 151.05°)", + " Gawler: (-34.60°, 138.75°)", + " Marseille 05: (43.30°, 5.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marseille 05: 13174.9 km from centroid", + " New Lynn: 5904.8 km from centroid", + " Cherrybrook: 3737.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marseille 05", + "FINAL ANSWER: Marseille 05" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.68394, + "lon": 92.56097, + "name": "Hailākāndi" + }, + { + "lat": 12.979, + "lon": 80.19703, + "name": "Ullagaram" + }, + { + "lat": 38.57167, + "lon": 140.95556, + "name": "Furukawa" + }, + { + "lat": 37.30096, + "lon": 79.60128, + "name": "Kageleke" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + } + ], + "question": "Which location is the geographic outlier among: Hailākāndi, Ullagaram, Furukawa, Kageleke, Timaru?", + "ground_truth": { + "answer": "Timaru", + "outlier_distance_km": 8744.5, + "second_furthest_km": 4201.3, + "clarity_ratio": 2.08, + "median_distance_km": 3892.8, + "distances_to_centroid": { + "Hailākāndi": 2449.1, + "Ullagaram": 3537.4, + "Furukawa": 3892.8, + "Kageleke": 4201.3, + "Timaru": 8744.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hailākāndi: (24.68°, 92.56°)", + " Ullagaram: (12.98°, 80.20°)", + " Furukawa: (38.57°, 140.96°)", + " Kageleke: (37.30°, 79.60°)", + " Timaru: (-44.40°, 171.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Timaru: 8744.5 km from centroid", + " Kageleke: 4201.3 km from centroid", + " Furukawa: 3892.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Timaru", + "FINAL ANSWER: Timaru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.09802, + "lon": -38.486, + "name": "Horizonte" + }, + { + "lat": -9.38861, + "lon": -37.99917, + "name": "Delmiro Gouveia" + }, + { + "lat": -19.82028, + "lon": -40.27333, + "name": "Aracruz" + }, + { + "lat": -13.45287, + "lon": -39.4208, + "name": "Presidente Tancredo Neves" + }, + { + "lat": -7.16778, + "lon": 112.71917, + "name": "Kamal" + } + ], + "question": "Which location is the geographic outlier among: Horizonte, Delmiro Gouveia, Aracruz, Presidente Tancredo Neves, Kamal?", + "ground_truth": { + "answer": "Kamal", + "outlier_distance_km": 13230.8, + "second_furthest_km": 3525.9, + "clarity_ratio": 3.75, + "median_distance_km": 3365.6, + "distances_to_centroid": { + "Horizonte": 3365.6, + "Delmiro Gouveia": 3211.0, + "Aracruz": 3525.9, + "Presidente Tancredo Neves": 3351.7, + "Kamal": 13230.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Horizonte: (-4.10°, -38.49°)", + " Delmiro Gouveia: (-9.39°, -38.00°)", + " Aracruz: (-19.82°, -40.27°)", + " Presidente Tancredo Neves: (-13.45°, -39.42°)", + " Kamal: (-7.17°, 112.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kamal: 13230.8 km from centroid", + " Aracruz: 3525.9 km from centroid", + " Horizonte: 3365.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kamal", + "FINAL ANSWER: Kamal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.38, + "lon": -35.12889, + "name": "Canguaretama" + }, + { + "lat": -13.66667, + "lon": -76.15, + "name": "San Clemente" + }, + { + "lat": -23.08639, + "lon": -46.95056, + "name": "Louveira" + }, + { + "lat": -7.40056, + "lon": -79.57139, + "name": "Pacasmayo" + }, + { + "lat": -2.27808, + "lon": 37.81867, + "name": "Makindu" + } + ], + "question": "Which location is the geographic outlier among: Canguaretama, San Clemente, Louveira, Pacasmayo, Makindu?", + "ground_truth": { + "answer": "Makindu", + "outlier_distance_km": 8629.5, + "second_furthest_km": 4358.0, + "clarity_ratio": 1.98, + "median_distance_km": 3942.2, + "distances_to_centroid": { + "Canguaretama": 709.0, + "San Clemente": 3942.2, + "Louveira": 1576.2, + "Pacasmayo": 4358.0, + "Makindu": 8629.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canguaretama: (-6.38°, -35.13°)", + " San Clemente: (-13.67°, -76.15°)", + " Louveira: (-23.09°, -46.95°)", + " Pacasmayo: (-7.40°, -79.57°)", + " Makindu: (-2.28°, 37.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Makindu: 8629.5 km from centroid", + " Pacasmayo: 4358.0 km from centroid", + " San Clemente: 3942.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Makindu", + "FINAL ANSWER: Makindu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.27097, + "lon": -79.94143, + "name": "Roanoke" + }, + { + "lat": 41.16287, + "lon": -73.86152, + "name": "Ossining" + }, + { + "lat": 44.87552, + "lon": -91.91934, + "name": "Menomonie" + }, + { + "lat": 28.67778, + "lon": -81.32785, + "name": "Casselberry" + }, + { + "lat": 11.08333, + "lon": 36.88333, + "name": "Ādīs K’idamē" + } + ], + "question": "Which location is the geographic outlier among: Roanoke, Ossining, Menomonie, Casselberry, Ādīs K’idamē?", + "ground_truth": { + "answer": "Ādīs K’idamē", + "outlier_distance_km": 9798.8, + "second_furthest_km": 3209.1, + "clarity_ratio": 3.05, + "median_distance_km": 2266.2, + "distances_to_centroid": { + "Roanoke": 2057.7, + "Ossining": 1694.3, + "Menomonie": 3209.1, + "Casselberry": 2266.2, + "Ādīs K’idamē": 9798.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Roanoke: (37.27°, -79.94°)", + " Ossining: (41.16°, -73.86°)", + " Menomonie: (44.88°, -91.92°)", + " Casselberry: (28.68°, -81.33°)", + " Ādīs K’idamē: (11.08°, 36.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ādīs K’idamē: 9798.8 km from centroid", + " Menomonie: 3209.1 km from centroid", + " Casselberry: 2266.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ādīs K’idamē", + "FINAL ANSWER: Ādīs K’idamē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.32485, + "lon": 8.11368, + "name": "Abakaliki" + }, + { + "lat": -0.68393, + "lon": 37.35701, + "name": "Wanguru" + }, + { + "lat": -32.93324, + "lon": 27.77656, + "name": "Mdantsane" + }, + { + "lat": 31.35573, + "lon": 31.68484, + "name": "Kafr Sa‘d" + }, + { + "lat": 15.04741, + "lon": 120.51891, + "name": "Pio" + } + ], + "question": "Which location is the geographic outlier among: Abakaliki, Wanguru, Mdantsane, Kafr Sa‘d, Pio?", + "ground_truth": { + "answer": "Pio", + "outlier_distance_km": 8333.7, + "second_furthest_km": 4475.4, + "clarity_ratio": 1.86, + "median_distance_km": 4104.0, + "distances_to_centroid": { + "Abakaliki": 4104.0, + "Wanguru": 994.8, + "Mdantsane": 4475.4, + "Kafr Sa‘d": 3367.6, + "Pio": 8333.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abakaliki: (6.32°, 8.11°)", + " Wanguru: (-0.68°, 37.36°)", + " Mdantsane: (-32.93°, 27.78°)", + " Kafr Sa‘d: (31.36°, 31.68°)", + " Pio: (15.05°, 120.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pio: 8333.7 km from centroid", + " Mdantsane: 4475.4 km from centroid", + " Abakaliki: 4104.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pio", + "FINAL ANSWER: Pio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.90833, + "lon": 119.87083, + "name": "Palu" + }, + { + "lat": 26.30948, + "lon": 127.77024, + "name": "Chatan" + }, + { + "lat": 35.99251, + "lon": 128.39785, + "name": "Waegwan" + }, + { + "lat": 37.85, + "lon": 140.6, + "name": "Yanagawamachi-saiwaichō" + }, + { + "lat": -32.43289, + "lon": -63.24811, + "name": "Villa Nueva" + } + ], + "question": "Which location is the geographic outlier among: Palu, Chatan, Waegwan, Yanagawamachi-saiwaichō, Villa Nueva?", + "ground_truth": { + "answer": "Villa Nueva", + "outlier_distance_km": 16622.6, + "second_furthest_km": 5612.5, + "clarity_ratio": 2.96, + "median_distance_km": 4522.1, + "distances_to_centroid": { + "Palu": 3587.8, + "Chatan": 4119.7, + "Waegwan": 4522.1, + "Yanagawamachi-saiwaichō": 5612.5, + "Villa Nueva": 16622.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Palu: (-0.91°, 119.87°)", + " Chatan: (26.31°, 127.77°)", + " Waegwan: (35.99°, 128.40°)", + " Yanagawamachi-saiwaichō: (37.85°, 140.60°)", + " Villa Nueva: (-32.43°, -63.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Villa Nueva: 16622.6 km from centroid", + " Yanagawamachi-saiwaichō: 5612.5 km from centroid", + " Waegwan: 4522.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Villa Nueva", + "FINAL ANSWER: Villa Nueva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.7355, + "lon": -94.97743, + "name": "Baytown" + }, + { + "lat": 33.7515, + "lon": -84.74771, + "name": "Douglasville" + }, + { + "lat": 40.84954, + "lon": -73.90569, + "name": "Tremont" + }, + { + "lat": 39.98345, + "lon": -75.18268, + "name": "Strawberry Mansion" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + } + ], + "question": "Which location is the geographic outlier among: Baytown, Douglasville, Tremont, Strawberry Mansion, Gosnells?", + "ground_truth": { + "answer": "Gosnells", + "outlier_distance_km": 17647.6, + "second_furthest_km": 5253.3, + "clarity_ratio": 3.36, + "median_distance_km": 4291.8, + "distances_to_centroid": { + "Baytown": 5253.3, + "Douglasville": 4291.8, + "Tremont": 3572.8, + "Strawberry Mansion": 3632.4, + "Gosnells": 17647.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baytown: (29.74°, -94.98°)", + " Douglasville: (33.75°, -84.75°)", + " Tremont: (40.85°, -73.91°)", + " Strawberry Mansion: (39.98°, -75.18°)", + " Gosnells: (-32.08°, 116.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gosnells: 17647.6 km from centroid", + " Baytown: 5253.3 km from centroid", + " Douglasville: 4291.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gosnells", + "FINAL ANSWER: Gosnells" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.43575, + "lon": 10.3779, + "name": "Geesthacht" + }, + { + "lat": 48.79993, + "lon": 2.33256, + "name": "Arcueil" + }, + { + "lat": 53.3618, + "lon": -2.73406, + "name": "Widnes" + }, + { + "lat": 47.90248, + "lon": 1.90407, + "name": "Orléans" + }, + { + "lat": 5.20087, + "lon": -75.86865, + "name": "Belén de Umbría" + } + ], + "question": "Which location is the geographic outlier among: Geesthacht, Arcueil, Widnes, Orléans, Belén de Umbría?", + "ground_truth": { + "answer": "Belén de Umbría", + "outlier_distance_km": 7407.4, + "second_furthest_km": 2154.4, + "clarity_ratio": 3.44, + "median_distance_km": 1493.5, + "distances_to_centroid": { + "Geesthacht": 2154.4, + "Arcueil": 1416.6, + "Widnes": 1493.5, + "Orléans": 1343.6, + "Belén de Umbría": 7407.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Geesthacht: (53.44°, 10.38°)", + " Arcueil: (48.80°, 2.33°)", + " Widnes: (53.36°, -2.73°)", + " Orléans: (47.90°, 1.90°)", + " Belén de Umbría: (5.20°, -75.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Belén de Umbría: 7407.4 km from centroid", + " Geesthacht: 2154.4 km from centroid", + " Widnes: 1493.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Belén de Umbría", + "FINAL ANSWER: Belén de Umbría" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.98889, + "lon": -39.58056, + "name": "Tejuçuoca" + }, + { + "lat": -20.65028, + "lon": -41.90722, + "name": "Espera Feliz" + }, + { + "lat": -30.58072, + "lon": -59.92962, + "name": "San Javier" + }, + { + "lat": -28.35889, + "lon": -49.29139, + "name": "Orleans" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + } + ], + "question": "Which location is the geographic outlier among: Tejuçuoca, Espera Feliz, San Javier, Orleans, Cabramatta?", + "ground_truth": { + "answer": "Cabramatta", + "outlier_distance_km": 13253.9, + "second_furthest_km": 5163.2, + "clarity_ratio": 2.57, + "median_distance_km": 4149.2, + "distances_to_centroid": { + "Tejuçuoca": 4027.6, + "Espera Feliz": 3504.9, + "San Javier": 5163.2, + "Orleans": 4149.2, + "Cabramatta": 13253.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tejuçuoca: (-3.99°, -39.58°)", + " Espera Feliz: (-20.65°, -41.91°)", + " San Javier: (-30.58°, -59.93°)", + " Orleans: (-28.36°, -49.29°)", + " Cabramatta: (-33.90°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cabramatta: 13253.9 km from centroid", + " San Javier: 5163.2 km from centroid", + " Orleans: 4149.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cabramatta", + "FINAL ANSWER: Cabramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.04325, + "lon": 99.08128, + "name": "Ban Tak" + }, + { + "lat": 21.3153, + "lon": 83.00629, + "name": "Saraipali" + }, + { + "lat": 24.04488, + "lon": 78.96094, + "name": "Banda" + }, + { + "lat": 10.65207, + "lon": 75.99512, + "name": "Punnayūr" + }, + { + "lat": 51.87967, + "lon": -0.41748, + "name": "Luton" + } + ], + "question": "Which location is the geographic outlier among: Ban Tak, Saraipali, Banda, Punnayūr, Luton?", + "ground_truth": { + "answer": "Luton", + "outlier_distance_km": 6341.0, + "second_furthest_km": 3403.4, + "clarity_ratio": 1.86, + "median_distance_km": 1837.7, + "distances_to_centroid": { + "Ban Tak": 3403.4, + "Saraipali": 1653.2, + "Banda": 1181.5, + "Punnayūr": 1837.7, + "Luton": 6341.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ban Tak: (17.04°, 99.08°)", + " Saraipali: (21.32°, 83.01°)", + " Banda: (24.04°, 78.96°)", + " Punnayūr: (10.65°, 76.00°)", + " Luton: (51.88°, -0.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Luton: 6341.0 km from centroid", + " Ban Tak: 3403.4 km from centroid", + " Punnayūr: 1837.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Luton", + "FINAL ANSWER: Luton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.46722, + "lon": -50.65111, + "name": "Irati" + }, + { + "lat": -10.66722, + "lon": -39.49917, + "name": "Cansanção" + }, + { + "lat": 1.93556, + "lon": -76.24056, + "name": "Isnos" + }, + { + "lat": -21.175, + "lon": -43.01778, + "name": "Tocantins" + }, + { + "lat": 51.53813, + "lon": -2.39379, + "name": "Chipping Sodbury" + } + ], + "question": "Which location is the geographic outlier among: Irati, Cansanção, Isnos, Tocantins, Chipping Sodbury?", + "ground_truth": { + "answer": "Chipping Sodbury", + "outlier_distance_km": 6917.8, + "second_furthest_km": 3778.7, + "clarity_ratio": 1.83, + "median_distance_km": 2887.0, + "distances_to_centroid": { + "Irati": 2887.0, + "Cansanção": 1145.3, + "Isnos": 3778.7, + "Tocantins": 2270.4, + "Chipping Sodbury": 6917.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Irati: (-25.47°, -50.65°)", + " Cansanção: (-10.67°, -39.50°)", + " Isnos: (1.94°, -76.24°)", + " Tocantins: (-21.18°, -43.02°)", + " Chipping Sodbury: (51.54°, -2.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chipping Sodbury: 6917.8 km from centroid", + " Isnos: 3778.7 km from centroid", + " Irati: 2887.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chipping Sodbury", + "FINAL ANSWER: Chipping Sodbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.68443, + "lon": 153.05705, + "name": "Buderim" + }, + { + "lat": -37.83382, + "lon": 144.93834, + "name": "City of Port Phillip" + }, + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": 10.46167, + "lon": -74.61621, + "name": "Pivijay" + } + ], + "question": "Which location is the geographic outlier among: Buderim, City of Port Phillip, Banora Point, Alexandra Hills, Pivijay?", + "ground_truth": { + "answer": "Pivijay", + "outlier_distance_km": 18734.6, + "second_furthest_km": 4804.8, + "clarity_ratio": 3.9, + "median_distance_km": 4778.7, + "distances_to_centroid": { + "Buderim": 4768.0, + "City of Port Phillip": 4106.6, + "Banora Point": 4804.8, + "Alexandra Hills": 4778.7, + "Pivijay": 18734.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Buderim: (-26.68°, 153.06°)", + " City of Port Phillip: (-37.83°, 144.94°)", + " Banora Point: (-28.21°, 153.54°)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Pivijay: (10.46°, -74.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pivijay: 18734.6 km from centroid", + " Banora Point: 4804.8 km from centroid", + " Alexandra Hills: 4778.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pivijay", + "FINAL ANSWER: Pivijay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.99364, + "lon": 40.16637, + "name": "Āwash" + }, + { + "lat": 6.71667, + "lon": 37.56667, + "name": "Gasuba" + }, + { + "lat": 3.52661, + "lon": 39.0561, + "name": "Moyale" + }, + { + "lat": -27.36541, + "lon": 29.88175, + "name": "Volksrust" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + } + ], + "question": "Which location is the geographic outlier among: Āwash, Gasuba, Moyale, Volksrust, Sunbury?", + "ground_truth": { + "answer": "Sunbury", + "outlier_distance_km": 9078.0, + "second_furthest_km": 3602.7, + "clarity_ratio": 2.52, + "median_distance_km": 2894.4, + "distances_to_centroid": { + "Āwash": 2844.1, + "Gasuba": 2894.4, + "Moyale": 2554.1, + "Volksrust": 3602.7, + "Sunbury": 9078.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Āwash: (8.99°, 40.17°)", + " Gasuba: (6.72°, 37.57°)", + " Moyale: (3.53°, 39.06°)", + " Volksrust: (-27.37°, 29.88°)", + " Sunbury: (-37.58°, 144.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunbury: 9078.0 km from centroid", + " Volksrust: 3602.7 km from centroid", + " Gasuba: 2894.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunbury", + "FINAL ANSWER: Sunbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.95772, + "lon": 99.90555, + "name": "Tha Yang" + }, + { + "lat": 29.39553, + "lon": 107.53939, + "name": "Baima" + }, + { + "lat": 2.8985, + "lon": 98.5231, + "name": "Tongging" + }, + { + "lat": 10.91667, + "lon": 79.83333, + "name": "Kāraikāl" + }, + { + "lat": 55.82885, + "lon": -4.21376, + "name": "Rutherglen" + } + ], + "question": "Which location is the geographic outlier among: Tha Yang, Baima, Tongging, Kāraikāl, Rutherglen?", + "ground_truth": { + "answer": "Rutherglen", + "outlier_distance_km": 7380.9, + "second_furthest_km": 3230.8, + "clarity_ratio": 2.28, + "median_distance_km": 3207.9, + "distances_to_centroid": { + "Tha Yang": 2705.6, + "Baima": 3207.9, + "Tongging": 3230.8, + "Kāraikāl": 1330.4, + "Rutherglen": 7380.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tha Yang: (12.96°, 99.91°)", + " Baima: (29.40°, 107.54°)", + " Tongging: (2.90°, 98.52°)", + " Kāraikāl: (10.92°, 79.83°)", + " Rutherglen: (55.83°, -4.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rutherglen: 7380.9 km from centroid", + " Tongging: 3230.8 km from centroid", + " Baima: 3207.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rutherglen", + "FINAL ANSWER: Rutherglen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.68212, + "lon": 9.01171, + "name": "Böblingen" + }, + { + "lat": 40.39023, + "lon": -3.72178, + "name": "Opañel" + }, + { + "lat": 59.80083, + "lon": 30.54778, + "name": "Metallostroy" + }, + { + "lat": 55.99456, + "lon": 37.82897, + "name": "Pushkino" + }, + { + "lat": 1.33849, + "lon": -77.5957, + "name": "Samaniego" + } + ], + "question": "Which location is the geographic outlier among: Böblingen, Opañel, Metallostroy, Pushkino, Samaniego?", + "ground_truth": { + "answer": "Samaniego", + "outlier_distance_km": 8809.6, + "second_furthest_km": 3218.5, + "clarity_ratio": 2.74, + "median_distance_km": 2976.6, + "distances_to_centroid": { + "Böblingen": 1129.0, + "Opañel": 264.6, + "Metallostroy": 2976.6, + "Pushkino": 3218.5, + "Samaniego": 8809.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Böblingen: (48.68°, 9.01°)", + " Opañel: (40.39°, -3.72°)", + " Metallostroy: (59.80°, 30.55°)", + " Pushkino: (55.99°, 37.83°)", + " Samaniego: (1.34°, -77.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Samaniego: 8809.6 km from centroid", + " Pushkino: 3218.5 km from centroid", + " Metallostroy: 2976.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Samaniego", + "FINAL ANSWER: Samaniego" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.79634, + "lon": -4.09485, + "name": "Blantyre" + }, + { + "lat": 41.07699, + "lon": 1.17891, + "name": "La Pineda" + }, + { + "lat": 41.3799, + "lon": 2.18971, + "name": "la Barceloneta" + }, + { + "lat": 51.02496, + "lon": 7.65599, + "name": "Bergneustadt" + }, + { + "lat": 34.04529, + "lon": -117.94367, + "name": "Valinda" + } + ], + "question": "Which location is the geographic outlier among: Blantyre, La Pineda, la Barceloneta, Bergneustadt, Valinda?", + "ground_truth": { + "answer": "Valinda", + "outlier_distance_km": 7833.9, + "second_furthest_km": 2319.4, + "clarity_ratio": 3.38, + "median_distance_km": 2008.4, + "distances_to_centroid": { + "Blantyre": 1776.3, + "La Pineda": 1939.6, + "la Barceloneta": 2008.4, + "Bergneustadt": 2319.4, + "Valinda": 7833.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blantyre: (55.80°, -4.09°)", + " La Pineda: (41.08°, 1.18°)", + " la Barceloneta: (41.38°, 2.19°)", + " Bergneustadt: (51.02°, 7.66°)", + " Valinda: (34.05°, -117.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Valinda: 7833.9 km from centroid", + " Bergneustadt: 2319.4 km from centroid", + " la Barceloneta: 2008.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Valinda", + "FINAL ANSWER: Valinda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.95, + "lon": 31.2, + "name": "Abū an Numrus" + }, + { + "lat": 9.02497, + "lon": 38.74689, + "name": "Addis Ababa" + }, + { + "lat": 2.33468, + "lon": 37.99086, + "name": "Marsabit" + }, + { + "lat": 11.52134, + "lon": 13.68952, + "name": "Bama" + }, + { + "lat": 36.20005, + "lon": -86.51861, + "name": "Mount Juliet" + } + ], + "question": "Which location is the geographic outlier among: Abū an Numrus, Addis Ababa, Marsabit, Bama, Mount Juliet?", + "ground_truth": { + "answer": "Mount Juliet", + "outlier_distance_km": 9156.6, + "second_furthest_km": 3790.7, + "clarity_ratio": 2.42, + "median_distance_km": 3561.5, + "distances_to_centroid": { + "Abū an Numrus": 2795.7, + "Addis Ababa": 3561.5, + "Marsabit": 3790.7, + "Bama": 1001.1, + "Mount Juliet": 9156.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abū an Numrus: (29.95°, 31.20°)", + " Addis Ababa: (9.02°, 38.75°)", + " Marsabit: (2.33°, 37.99°)", + " Bama: (11.52°, 13.69°)", + " Mount Juliet: (36.20°, -86.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Juliet: 9156.6 km from centroid", + " Marsabit: 3790.7 km from centroid", + " Addis Ababa: 3561.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Juliet", + "FINAL ANSWER: Mount Juliet" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + }, + { + "lat": -37.78821, + "lon": 175.2902, + "name": "Hamilton East" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": 6.01335, + "lon": -73.67352, + "name": "Vélez" + } + ], + "question": "Which location is the geographic outlier among: Bexley, Ringwood, Hamilton East, Glen Iris, Vélez?", + "ground_truth": { + "answer": "Vélez", + "outlier_distance_km": 17527.3, + "second_furthest_km": 6176.1, + "clarity_ratio": 2.84, + "median_distance_km": 4066.7, + "distances_to_centroid": { + "Bexley": 4066.7, + "Ringwood": 3549.0, + "Hamilton East": 6176.1, + "Glen Iris": 3535.1, + "Vélez": 17527.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexley: (-33.95°, 151.12°)", + " Ringwood: (-37.82°, 145.23°)", + " Hamilton East: (-37.79°, 175.29°)", + " Glen Iris: (-37.87°, 145.07°)", + " Vélez: (6.01°, -73.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vélez: 17527.3 km from centroid", + " Hamilton East: 6176.1 km from centroid", + " Bexley: 4066.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vélez", + "FINAL ANSWER: Vélez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.76983, + "lon": 76.75581, + "name": "Sindhnūr" + }, + { + "lat": 36.01839, + "lon": 139.66034, + "name": "Shiraoka" + }, + { + "lat": 30.32443, + "lon": 78.03392, + "name": "Dehra Dūn" + }, + { + "lat": 35.46028, + "lon": 110.42917, + "name": "Hancheng" + }, + { + "lat": 31.72294, + "lon": -116.57196, + "name": "Rodolfo Sánchez Taboada" + } + ], + "question": "Which location is the geographic outlier among: Sindhnūr, Shiraoka, Dehra Dūn, Hancheng, Rodolfo Sánchez Taboada?", + "ground_truth": { + "answer": "Rodolfo Sánchez Taboada", + "outlier_distance_km": 13140.5, + "second_furthest_km": 7452.3, + "clarity_ratio": 1.76, + "median_distance_km": 4921.0, + "distances_to_centroid": { + "Sindhnūr": 2499.9, + "Shiraoka": 7452.3, + "Dehra Dūn": 1958.1, + "Hancheng": 4921.0, + "Rodolfo Sánchez Taboada": 13140.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sindhnūr: (15.77°, 76.76°)", + " Shiraoka: (36.02°, 139.66°)", + " Dehra Dūn: (30.32°, 78.03°)", + " Hancheng: (35.46°, 110.43°)", + " Rodolfo Sánchez Taboada: (31.72°, -116.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rodolfo Sánchez Taboada: 13140.5 km from centroid", + " Shiraoka: 7452.3 km from centroid", + " Hancheng: 4921.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rodolfo Sánchez Taboada", + "FINAL ANSWER: Rodolfo Sánchez Taboada" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": 41.77976, + "lon": -87.64588, + "name": "Englewood" + } + ], + "question": "Which location is the geographic outlier among: Armidale, Carlton, Southport, Cranbourne East, Englewood?", + "ground_truth": { + "answer": "Englewood", + "outlier_distance_km": 17286.3, + "second_furthest_km": 5362.8, + "clarity_ratio": 3.22, + "median_distance_km": 5200.2, + "distances_to_centroid": { + "Armidale": 5200.2, + "Carlton": 4711.5, + "Southport": 5362.8, + "Cranbourne East": 4748.5, + "Englewood": 17286.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Armidale: (-30.50°, 151.67°)", + " Carlton: (-37.80°, 144.97°)", + " Southport: (-27.97°, 153.40°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Englewood: (41.78°, -87.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Englewood: 17286.3 km from centroid", + " Southport: 5362.8 km from centroid", + " Armidale: 5200.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Englewood", + "FINAL ANSWER: Englewood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.39048, + "lon": -118.57372, + "name": "Stevenson Ranch" + }, + { + "lat": 33.71372, + "lon": -117.76091, + "name": "Northwood" + }, + { + "lat": 38.17492, + "lon": -122.2608, + "name": "American Canyon" + }, + { + "lat": 29.88519, + "lon": -93.94233, + "name": "Port Arthur" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + } + ], + "question": "Which location is the geographic outlier among: Stevenson Ranch, Northwood, American Canyon, Port Arthur, Lalor?", + "ground_truth": { + "answer": "Lalor", + "outlier_distance_km": 16766.8, + "second_furthest_km": 6144.2, + "clarity_ratio": 2.73, + "median_distance_km": 5805.7, + "distances_to_centroid": { + "Stevenson Ranch": 5805.7, + "Northwood": 5729.8, + "American Canyon": 6144.2, + "Port Arthur": 3450.6, + "Lalor": 16766.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stevenson Ranch: (34.39°, -118.57°)", + " Northwood: (33.71°, -117.76°)", + " American Canyon: (38.17°, -122.26°)", + " Port Arthur: (29.89°, -93.94°)", + " Lalor: (-37.67°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lalor: 16766.8 km from centroid", + " American Canyon: 6144.2 km from centroid", + " Stevenson Ranch: 5805.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lalor", + "FINAL ANSWER: Lalor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.09228, + "lon": 7.69399, + "name": "Barriera di Milano" + }, + { + "lat": 48.76476, + "lon": 2.3503, + "name": "Chevilly-Larue" + }, + { + "lat": 37.80626, + "lon": -0.83736, + "name": "San Javier" + }, + { + "lat": 47.54612, + "lon": 9.68431, + "name": "Lindau" + }, + { + "lat": -4.85722, + "lon": -39.57667, + "name": "Madalena" + } + ], + "question": "Which location is the geographic outlier among: Barriera di Milano, Chevilly-Larue, San Javier, Lindau, Madalena?", + "ground_truth": { + "answer": "Madalena", + "outlier_distance_km": 5766.2, + "second_furthest_km": 1817.3, + "clarity_ratio": 3.17, + "median_distance_km": 1634.3, + "distances_to_centroid": { + "Barriera di Milano": 1516.0, + "Chevilly-Larue": 1634.3, + "San Javier": 440.3, + "Lindau": 1817.3, + "Madalena": 5766.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Barriera di Milano: (45.09°, 7.69°)", + " Chevilly-Larue: (48.76°, 2.35°)", + " San Javier: (37.81°, -0.84°)", + " Lindau: (47.55°, 9.68°)", + " Madalena: (-4.86°, -39.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Madalena: 5766.2 km from centroid", + " Lindau: 1817.3 km from centroid", + " Chevilly-Larue: 1634.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Madalena", + "FINAL ANSWER: Madalena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.00954, + "lon": -74.17292, + "name": "Wyckoff" + }, + { + "lat": 41.39676, + "lon": -73.07594, + "name": "Seymour" + }, + { + "lat": 33.42697, + "lon": -117.61199, + "name": "San Clemente" + }, + { + "lat": 40.70038, + "lon": -73.59291, + "name": "Uniondale" + }, + { + "lat": -37.66667, + "lon": 145.06667, + "name": "Mill Park" + } + ], + "question": "Which location is the geographic outlier among: Wyckoff, Seymour, San Clemente, Uniondale, Mill Park?", + "ground_truth": { + "answer": "Mill Park", + "outlier_distance_km": 18429.7, + "second_furthest_km": 7602.1, + "clarity_ratio": 2.42, + "median_distance_km": 3806.5, + "distances_to_centroid": { + "Wyckoff": 3806.5, + "Seymour": 3735.0, + "San Clemente": 7602.1, + "Uniondale": 3749.1, + "Mill Park": 18429.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wyckoff: (41.01°, -74.17°)", + " Seymour: (41.40°, -73.08°)", + " San Clemente: (33.43°, -117.61°)", + " Uniondale: (40.70°, -73.59°)", + " Mill Park: (-37.67°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mill Park: 18429.7 km from centroid", + " San Clemente: 7602.1 km from centroid", + " Wyckoff: 3806.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mill Park", + "FINAL ANSWER: Mill Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.55838, + "lon": -81.56929, + "name": "Collinwood" + }, + { + "lat": 39.934, + "lon": -74.74849, + "name": "Vincentown" + }, + { + "lat": 46.87497, + "lon": -96.90036, + "name": "West Fargo" + }, + { + "lat": 40.05011, + "lon": -75.07184, + "name": "Oxford Circle" + }, + { + "lat": 23.16244, + "lon": 114.27342, + "name": "Luoyang" + } + ], + "question": "Which location is the geographic outlier among: Collinwood, Vincentown, West Fargo, Oxford Circle, Luoyang?", + "ground_truth": { + "answer": "Luoyang", + "outlier_distance_km": 12772.7, + "second_furthest_km": 4438.0, + "clarity_ratio": 2.88, + "median_distance_km": 3296.9, + "distances_to_centroid": { + "Collinwood": 3296.9, + "Vincentown": 2746.8, + "West Fargo": 4438.0, + "Oxford Circle": 2772.7, + "Luoyang": 12772.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Collinwood: (41.56°, -81.57°)", + " Vincentown: (39.93°, -74.75°)", + " West Fargo: (46.87°, -96.90°)", + " Oxford Circle: (40.05°, -75.07°)", + " Luoyang: (23.16°, 114.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Luoyang: 12772.7 km from centroid", + " West Fargo: 4438.0 km from centroid", + " Collinwood: 3296.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Luoyang", + "FINAL ANSWER: Luoyang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.49923, + "lon": 39.63723, + "name": "Dolo" + }, + { + "lat": 7.85868, + "lon": 10.97187, + "name": "Beli" + }, + { + "lat": -29.26737, + "lon": 26.72595, + "name": "Botshabelo" + }, + { + "lat": 11.52134, + "lon": 13.68952, + "name": "Bama" + }, + { + "lat": 34.58277, + "lon": -117.40922, + "name": "Adelanto" + } + ], + "question": "Which location is the geographic outlier among: Dolo, Beli, Botshabelo, Bama, Adelanto?", + "ground_truth": { + "answer": "Adelanto", + "outlier_distance_km": 11499.0, + "second_furthest_km": 5345.2, + "clarity_ratio": 2.15, + "median_distance_km": 4945.7, + "distances_to_centroid": { + "Dolo": 4945.7, + "Beli": 1790.3, + "Botshabelo": 5345.2, + "Bama": 2123.2, + "Adelanto": 11499.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dolo: (13.50°, 39.64°)", + " Beli: (7.86°, 10.97°)", + " Botshabelo: (-29.27°, 26.73°)", + " Bama: (11.52°, 13.69°)", + " Adelanto: (34.58°, -117.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adelanto: 11499.0 km from centroid", + " Botshabelo: 5345.2 km from centroid", + " Dolo: 4945.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adelanto", + "FINAL ANSWER: Adelanto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.02764, + "lon": 79.85425, + "name": "Tharangambadi" + }, + { + "lat": 10.38128, + "lon": 78.82141, + "name": "Pudukkottai" + }, + { + "lat": 16.86968, + "lon": 99.12898, + "name": "Tak" + }, + { + "lat": 29.89029, + "lon": 106.89727, + "name": "Dasheng" + }, + { + "lat": 5.55874, + "lon": 7.63359, + "name": "Bende" + } + ], + "question": "Which location is the geographic outlier among: Tharangambadi, Pudukkottai, Tak, Dasheng, Bende?", + "ground_truth": { + "answer": "Bende", + "outlier_distance_km": 7362.7, + "second_furthest_km": 3717.8, + "clarity_ratio": 1.98, + "median_distance_km": 2647.4, + "distances_to_centroid": { + "Tharangambadi": 715.4, + "Pudukkottai": 677.3, + "Tak": 2647.4, + "Dasheng": 3717.8, + "Bende": 7362.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tharangambadi: (11.03°, 79.85°)", + " Pudukkottai: (10.38°, 78.82°)", + " Tak: (16.87°, 99.13°)", + " Dasheng: (29.89°, 106.90°)", + " Bende: (5.56°, 7.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bende: 7362.7 km from centroid", + " Dasheng: 3717.8 km from centroid", + " Tak: 2647.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bende", + "FINAL ANSWER: Bende" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.1235, + "lon": 18.00762, + "name": "Bydgoszcz" + }, + { + "lat": 53.41667, + "lon": -1.2, + "name": "Maltby" + }, + { + "lat": 51.29652, + "lon": -0.3338, + "name": "Leatherhead" + }, + { + "lat": 51.35478, + "lon": 6.63918, + "name": "Uerdingen" + }, + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + } + ], + "question": "Which location is the geographic outlier among: Bydgoszcz, Maltby, Leatherhead, Uerdingen, Cambridge?", + "ground_truth": { + "answer": "Cambridge", + "outlier_distance_km": 16053.0, + "second_furthest_km": 3834.0, + "clarity_ratio": 4.19, + "median_distance_km": 3712.5, + "distances_to_centroid": { + "Bydgoszcz": 2706.0, + "Maltby": 3834.0, + "Leatherhead": 3712.5, + "Uerdingen": 3256.1, + "Cambridge": 16053.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bydgoszcz: (53.12°, 18.01°)", + " Maltby: (53.42°, -1.20°)", + " Leatherhead: (51.30°, -0.33°)", + " Uerdingen: (51.35°, 6.64°)", + " Cambridge: (-37.88°, 175.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cambridge: 16053.0 km from centroid", + " Maltby: 3834.0 km from centroid", + " Leatherhead: 3712.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cambridge", + "FINAL ANSWER: Cambridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.58508, + "lon": 5.00268, + "name": "Miramas" + }, + { + "lat": 52.46667, + "lon": 13.4, + "name": "Tempelhof" + }, + { + "lat": 53.5, + "lon": -1.45, + "name": "Hoyland Nether" + }, + { + "lat": 53.55, + "lon": 9.93333, + "name": "Altona" + }, + { + "lat": -36.90694, + "lon": 174.68704, + "name": "New Lynn" + } + ], + "question": "Which location is the geographic outlier among: Miramas, Tempelhof, Hoyland Nether, Altona, New Lynn?", + "ground_truth": { + "answer": "New Lynn", + "outlier_distance_km": 15882.1, + "second_furthest_km": 3973.8, + "clarity_ratio": 4.0, + "median_distance_km": 3290.2, + "distances_to_centroid": { + "Miramas": 3255.3, + "Tempelhof": 3030.0, + "Hoyland Nether": 3973.8, + "Altona": 3290.2, + "New Lynn": 15882.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miramas: (43.59°, 5.00°)", + " Tempelhof: (52.47°, 13.40°)", + " Hoyland Nether: (53.50°, -1.45°)", + " Altona: (53.55°, 9.93°)", + " New Lynn: (-36.91°, 174.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " New Lynn: 15882.1 km from centroid", + " Hoyland Nether: 3973.8 km from centroid", + " Altona: 3290.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: New Lynn", + "FINAL ANSWER: New Lynn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.41505, + "lon": -111.54958, + "name": "Apache Junction" + }, + { + "lat": 34.09001, + "lon": -118.36174, + "name": "West Hollywood" + }, + { + "lat": 40.19475, + "lon": -92.58325, + "name": "Kirksville" + }, + { + "lat": 41.60003, + "lon": -87.93811, + "name": "Homer Glen" + }, + { + "lat": 24.41288, + "lon": 76.56719, + "name": "Aklera" + } + ], + "question": "Which location is the geographic outlier among: Apache Junction, West Hollywood, Kirksville, Homer Glen, Aklera?", + "ground_truth": { + "answer": "Aklera", + "outlier_distance_km": 12385.9, + "second_furthest_km": 4678.9, + "clarity_ratio": 2.65, + "median_distance_km": 4092.0, + "distances_to_centroid": { + "Apache Junction": 4092.0, + "West Hollywood": 4678.9, + "Kirksville": 2347.9, + "Homer Glen": 1994.5, + "Aklera": 12385.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Apache Junction: (33.42°, -111.55°)", + " West Hollywood: (34.09°, -118.36°)", + " Kirksville: (40.19°, -92.58°)", + " Homer Glen: (41.60°, -87.94°)", + " Aklera: (24.41°, 76.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aklera: 12385.9 km from centroid", + " West Hollywood: 4678.9 km from centroid", + " Apache Junction: 4092.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aklera", + "FINAL ANSWER: Aklera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.95, + "lon": 151.13333, + "name": "Rockdale" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + }, + { + "lat": -37.73333, + "lon": 145.15, + "name": "Eltham" + }, + { + "lat": -37.73261, + "lon": 144.86504, + "name": "Keilor East" + }, + { + "lat": 43.33904, + "lon": -1.78938, + "name": "Irun" + } + ], + "question": "Which location is the geographic outlier among: Rockdale, Griffith, Eltham, Keilor East, Irun?", + "ground_truth": { + "answer": "Irun", + "outlier_distance_km": 13836.0, + "second_furthest_km": 3686.4, + "clarity_ratio": 3.75, + "median_distance_km": 3342.4, + "distances_to_centroid": { + "Rockdale": 3686.4, + "Griffith": 3255.2, + "Eltham": 3342.4, + "Keilor East": 3320.3, + "Irun": 13836.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rockdale: (-33.95°, 151.13°)", + " Griffith: (-34.29°, 146.05°)", + " Eltham: (-37.73°, 145.15°)", + " Keilor East: (-37.73°, 144.87°)", + " Irun: (43.34°, -1.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Irun: 13836.0 km from centroid", + " Rockdale: 3686.4 km from centroid", + " Eltham: 3342.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Irun", + "FINAL ANSWER: Irun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.37794, + "lon": 1.10467, + "name": "Saint-Étienne-du-Rouvray" + }, + { + "lat": 42.6865, + "lon": -2.94695, + "name": "Miranda de Ebro" + }, + { + "lat": 50.05553, + "lon": 8.80076, + "name": "Heusenstamm" + }, + { + "lat": 48.16783, + "lon": 8.62719, + "name": "Rottweil" + }, + { + "lat": 29.94167, + "lon": 108.08442, + "name": "Xialu" + } + ], + "question": "Which location is the geographic outlier among: Saint-Étienne-du-Rouvray, Miranda de Ebro, Heusenstamm, Rottweil, Xialu?", + "ground_truth": { + "answer": "Xialu", + "outlier_distance_km": 7252.2, + "second_furthest_km": 2232.2, + "clarity_ratio": 3.25, + "median_distance_km": 1887.4, + "distances_to_centroid": { + "Saint-Étienne-du-Rouvray": 1887.4, + "Miranda de Ebro": 2232.2, + "Heusenstamm": 1375.8, + "Rottweil": 1320.6, + "Xialu": 7252.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint-Étienne-du-Rouvray: (49.38°, 1.10°)", + " Miranda de Ebro: (42.69°, -2.95°)", + " Heusenstamm: (50.06°, 8.80°)", + " Rottweil: (48.17°, 8.63°)", + " Xialu: (29.94°, 108.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xialu: 7252.2 km from centroid", + " Miranda de Ebro: 2232.2 km from centroid", + " Saint-Étienne-du-Rouvray: 1887.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xialu", + "FINAL ANSWER: Xialu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.3, + "lon": 36.88333, + "name": "Felege Neway" + }, + { + "lat": 5.43385, + "lon": -2.14295, + "name": "Prestea" + }, + { + "lat": 30.61927, + "lon": 31.46165, + "name": "Al Qanāyāt" + }, + { + "lat": -24.19436, + "lon": 29.00974, + "name": "Mokopane" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + } + ], + "question": "Which location is the geographic outlier among: Felege Neway, Prestea, Al Qanāyāt, Mokopane, Pacific Pines?", + "ground_truth": { + "answer": "Pacific Pines", + "outlier_distance_km": 11236.8, + "second_furthest_km": 5816.7, + "clarity_ratio": 1.93, + "median_distance_km": 4105.6, + "distances_to_centroid": { + "Felege Neway": 1693.8, + "Prestea": 5816.7, + "Al Qanāyāt": 4105.6, + "Mokopane": 3326.1, + "Pacific Pines": 11236.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Felege Neway: (6.30°, 36.88°)", + " Prestea: (5.43°, -2.14°)", + " Al Qanāyāt: (30.62°, 31.46°)", + " Mokopane: (-24.19°, 29.01°)", + " Pacific Pines: (-27.94°, 153.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pacific Pines: 11236.8 km from centroid", + " Prestea: 5816.7 km from centroid", + " Al Qanāyāt: 4105.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pacific Pines", + "FINAL ANSWER: Pacific Pines" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.01759, + "lon": 1.3542, + "name": "Montauban" + }, + { + "lat": 52.41868, + "lon": 13.36723, + "name": "Marienfelde" + }, + { + "lat": 45.05288, + "lon": 7.67979, + "name": "San Salvario" + }, + { + "lat": 50.704, + "lon": 7.054, + "name": "Bonn Hardtberg" + }, + { + "lat": 41.63031, + "lon": -87.85394, + "name": "Orland Park" + } + ], + "question": "Which location is the geographic outlier among: Montauban, Marienfelde, San Salvario, Bonn Hardtberg, Orland Park?", + "ground_truth": { + "answer": "Orland Park", + "outlier_distance_km": 5857.1, + "second_furthest_km": 1900.2, + "clarity_ratio": 3.08, + "median_distance_km": 1506.0, + "distances_to_centroid": { + "Montauban": 1061.2, + "Marienfelde": 1900.2, + "San Salvario": 1506.0, + "Bonn Hardtberg": 1437.5, + "Orland Park": 5857.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Montauban: (44.02°, 1.35°)", + " Marienfelde: (52.42°, 13.37°)", + " San Salvario: (45.05°, 7.68°)", + " Bonn Hardtberg: (50.70°, 7.05°)", + " Orland Park: (41.63°, -87.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Orland Park: 5857.1 km from centroid", + " Marienfelde: 1900.2 km from centroid", + " San Salvario: 1506.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Orland Park", + "FINAL ANSWER: Orland Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.38602, + "lon": 103.02301, + "name": "Dien Bien Phu" + }, + { + "lat": 13.15823, + "lon": 80.30181, + "name": "Tiruvottiyūr" + }, + { + "lat": 32.06167, + "lon": 118.77778, + "name": "Nanjing" + }, + { + "lat": 4.6411, + "lon": 101.1393, + "name": "Bercham" + }, + { + "lat": 43.66228, + "lon": -7.59344, + "name": "Viveiro" + } + ], + "question": "Which location is the geographic outlier among: Dien Bien Phu, Tiruvottiyūr, Nanjing, Bercham, Viveiro?", + "ground_truth": { + "answer": "Viveiro", + "outlier_distance_km": 8015.3, + "second_furthest_km": 4014.0, + "clarity_ratio": 2.0, + "median_distance_km": 3121.9, + "distances_to_centroid": { + "Dien Bien Phu": 2463.8, + "Tiruvottiyūr": 1099.3, + "Nanjing": 4014.0, + "Bercham": 3121.9, + "Viveiro": 8015.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dien Bien Phu: (21.39°, 103.02°)", + " Tiruvottiyūr: (13.16°, 80.30°)", + " Nanjing: (32.06°, 118.78°)", + " Bercham: (4.64°, 101.14°)", + " Viveiro: (43.66°, -7.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viveiro: 8015.3 km from centroid", + " Nanjing: 4014.0 km from centroid", + " Bercham: 3121.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viveiro", + "FINAL ANSWER: Viveiro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.14952, + "lon": 18.84215, + "name": "Łaziska Górne" + }, + { + "lat": 51.55493, + "lon": 7.91403, + "name": "Werl" + }, + { + "lat": 48.84656, + "lon": 2.37439, + "name": "Quinze-Vingts" + }, + { + "lat": 49.23848, + "lon": 9.1018, + "name": "Bad Rappenau" + }, + { + "lat": -22.73083, + "lon": -45.12472, + "name": "Lorena" + } + ], + "question": "Which location is the geographic outlier among: Łaziska Górne, Werl, Quinze-Vingts, Bad Rappenau, Lorena?", + "ground_truth": { + "answer": "Lorena", + "outlier_distance_km": 7938.1, + "second_furthest_km": 2311.3, + "clarity_ratio": 3.43, + "median_distance_km": 1941.6, + "distances_to_centroid": { + "Łaziska Górne": 2311.3, + "Werl": 1941.6, + "Quinze-Vingts": 1525.1, + "Bad Rappenau": 1758.6, + "Lorena": 7938.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Łaziska Górne: (50.15°, 18.84°)", + " Werl: (51.55°, 7.91°)", + " Quinze-Vingts: (48.85°, 2.37°)", + " Bad Rappenau: (49.24°, 9.10°)", + " Lorena: (-22.73°, -45.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lorena: 7938.1 km from centroid", + " Łaziska Górne: 2311.3 km from centroid", + " Werl: 1941.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lorena", + "FINAL ANSWER: Lorena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.23013, + "lon": 115.78128, + "name": "Kwinana" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + }, + { + "lat": -3.22028, + "lon": -45.00361, + "name": "Viana" + } + ], + "question": "Which location is the geographic outlier among: Kwinana, Saint Kilda, Australind, Mount Eden, Viana?", + "ground_truth": { + "answer": "Viana", + "outlier_distance_km": 14958.6, + "second_furthest_km": 6764.9, + "clarity_ratio": 2.21, + "median_distance_km": 4151.6, + "distances_to_centroid": { + "Kwinana": 1446.0, + "Saint Kilda": 4151.6, + "Australind": 1468.7, + "Mount Eden": 6764.9, + "Viana": 14958.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kwinana: (-32.23°, 115.78°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Australind: (-33.28°, 115.72°)", + " Mount Eden: (-36.88°, 174.76°)", + " Viana: (-3.22°, -45.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Viana: 14958.6 km from centroid", + " Mount Eden: 6764.9 km from centroid", + " Saint Kilda: 4151.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Viana", + "FINAL ANSWER: Viana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.33991, + "lon": -2.32676, + "name": "Sunyani" + }, + { + "lat": 30.62914, + "lon": 31.08235, + "name": "Birkat as Sab‘" + }, + { + "lat": 7.53333, + "lon": 39.25, + "name": "Bek’ojī" + }, + { + "lat": 31.12624, + "lon": 31.64313, + "name": "Minyat an Naşr" + }, + { + "lat": -11.73028, + "lon": -40.55528, + "name": "Piritiba" + } + ], + "question": "Which location is the geographic outlier among: Sunyani, Birkat as Sab‘, Bek’ojī, Minyat an Naşr, Piritiba?", + "ground_truth": { + "answer": "Piritiba", + "outlier_distance_km": 6397.3, + "second_furthest_km": 3059.8, + "clarity_ratio": 2.09, + "median_distance_km": 2861.4, + "distances_to_centroid": { + "Sunyani": 1669.7, + "Birkat as Sab‘": 2784.8, + "Bek’ojī": 3059.8, + "Minyat an Naşr": 2861.4, + "Piritiba": 6397.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sunyani: (7.34°, -2.33°)", + " Birkat as Sab‘: (30.63°, 31.08°)", + " Bek’ojī: (7.53°, 39.25°)", + " Minyat an Naşr: (31.13°, 31.64°)", + " Piritiba: (-11.73°, -40.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piritiba: 6397.3 km from centroid", + " Bek’ojī: 3059.8 km from centroid", + " Minyat an Naşr: 2861.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piritiba", + "FINAL ANSWER: Piritiba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.86136, + "lon": -92.62381, + "name": "River Falls" + }, + { + "lat": 37.08339, + "lon": -88.60005, + "name": "Paducah" + }, + { + "lat": 19.25465, + "lon": -99.10356, + "name": "Xochimilco" + }, + { + "lat": 43.90012, + "lon": -78.84957, + "name": "Oshawa" + }, + { + "lat": 11.49984, + "lon": 76.48152, + "name": "Kollivāyal" + } + ], + "question": "Which location is the geographic outlier among: River Falls, Paducah, Xochimilco, Oshawa, Kollivāyal?", + "ground_truth": { + "answer": "Kollivāyal", + "outlier_distance_km": 13106.8, + "second_furthest_km": 4454.1, + "clarity_ratio": 2.94, + "median_distance_km": 3461.1, + "distances_to_centroid": { + "River Falls": 3461.1, + "Paducah": 3002.3, + "Xochimilco": 4454.1, + "Oshawa": 2399.5, + "Kollivāyal": 13106.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " River Falls: (44.86°, -92.62°)", + " Paducah: (37.08°, -88.60°)", + " Xochimilco: (19.25°, -99.10°)", + " Oshawa: (43.90°, -78.85°)", + " Kollivāyal: (11.50°, 76.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kollivāyal: 13106.8 km from centroid", + " Xochimilco: 4454.1 km from centroid", + " River Falls: 3461.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kollivāyal", + "FINAL ANSWER: Kollivāyal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + }, + { + "lat": 23.25999, + "lon": 76.14567, + "name": "Maksi" + } + ], + "question": "Which location is the geographic outlier among: Umina Beach, Granville, Greenvale, Merrylands, Maksi?", + "ground_truth": { + "answer": "Maksi", + "outlier_distance_km": 8174.7, + "second_furthest_km": 1978.7, + "clarity_ratio": 4.13, + "median_distance_km": 1973.6, + "distances_to_centroid": { + "Umina Beach": 1978.7, + "Granville": 1973.6, + "Greenvale": 1875.3, + "Merrylands": 1971.3, + "Maksi": 8174.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Umina Beach: (-33.52°, 151.31°)", + " Granville: (-33.84°, 151.01°)", + " Greenvale: (-37.63°, 144.87°)", + " Merrylands: (-33.83°, 150.98°)", + " Maksi: (23.26°, 76.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maksi: 8174.7 km from centroid", + " Umina Beach: 1978.7 km from centroid", + " Granville: 1973.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maksi", + "FINAL ANSWER: Maksi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.09001, + "lon": -117.89034, + "name": "Covina" + }, + { + "lat": 33.50169, + "lon": -117.66255, + "name": "San Juan Capistrano" + }, + { + "lat": 40.84829, + "lon": -74.58148, + "name": "Randolph" + }, + { + "lat": 38.83039, + "lon": -77.19637, + "name": "Annandale" + }, + { + "lat": 29.68403, + "lon": 106.61486, + "name": "Huixing" + } + ], + "question": "Which location is the geographic outlier among: Covina, San Juan Capistrano, Randolph, Annandale, Huixing?", + "ground_truth": { + "answer": "Huixing", + "outlier_distance_km": 12557.2, + "second_furthest_km": 5551.0, + "clarity_ratio": 2.26, + "median_distance_km": 5548.0, + "distances_to_centroid": { + "Covina": 5548.0, + "San Juan Capistrano": 5551.0, + "Randolph": 1719.2, + "Annandale": 1901.1, + "Huixing": 12557.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Covina: (34.09°, -117.89°)", + " San Juan Capistrano: (33.50°, -117.66°)", + " Randolph: (40.85°, -74.58°)", + " Annandale: (38.83°, -77.20°)", + " Huixing: (29.68°, 106.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huixing: 12557.2 km from centroid", + " San Juan Capistrano: 5551.0 km from centroid", + " Covina: 5548.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huixing", + "FINAL ANSWER: Huixing" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.07127, + "lon": -55.91479, + "name": "Lucas do Rio Verde" + }, + { + "lat": -5.0925, + "lon": -80.1625, + "name": "Chulucanas" + }, + { + "lat": -3.22083, + "lon": -64.80417, + "name": "Alvarães" + }, + { + "lat": -23.10417, + "lon": -55.22583, + "name": "Amambai" + }, + { + "lat": 38.70144, + "lon": -90.14872, + "name": "Granite City" + } + ], + "question": "Which location is the geographic outlier among: Lucas do Rio Verde, Chulucanas, Alvarães, Amambai, Granite City?", + "ground_truth": { + "answer": "Granite City", + "outlier_distance_km": 4920.4, + "second_furthest_km": 2871.8, + "clarity_ratio": 1.71, + "median_distance_km": 1977.9, + "distances_to_centroid": { + "Lucas do Rio Verde": 1977.9, + "Chulucanas": 1287.8, + "Alvarães": 544.8, + "Amambai": 2871.8, + "Granite City": 4920.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lucas do Rio Verde: (-13.07°, -55.91°)", + " Chulucanas: (-5.09°, -80.16°)", + " Alvarães: (-3.22°, -64.80°)", + " Amambai: (-23.10°, -55.23°)", + " Granite City: (38.70°, -90.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Granite City: 4920.4 km from centroid", + " Amambai: 2871.8 km from centroid", + " Lucas do Rio Verde: 1977.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Granite City", + "FINAL ANSWER: Granite City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.25642, + "lon": 9.1444, + "name": "Monserrato" + }, + { + "lat": 43.53692, + "lon": 6.46458, + "name": "Draguignan" + }, + { + "lat": 39.58932, + "lon": 2.61899, + "name": "Son Rapinya" + }, + { + "lat": 52.59319, + "lon": 13.32127, + "name": "Wittenau" + }, + { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + } + ], + "question": "Which location is the geographic outlier among: Monserrato, Draguignan, Son Rapinya, Wittenau, Scarborough?", + "ground_truth": { + "answer": "Scarborough", + "outlier_distance_km": 11322.8, + "second_furthest_km": 2978.6, + "clarity_ratio": 3.8, + "median_distance_km": 2741.8, + "distances_to_centroid": { + "Monserrato": 2208.6, + "Draguignan": 2634.7, + "Son Rapinya": 2741.8, + "Wittenau": 2978.6, + "Scarborough": 11322.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Monserrato: (39.26°, 9.14°)", + " Draguignan: (43.54°, 6.46°)", + " Son Rapinya: (39.59°, 2.62°)", + " Wittenau: (52.59°, 13.32°)", + " Scarborough: (-31.90°, 115.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Scarborough: 11322.8 km from centroid", + " Wittenau: 2978.6 km from centroid", + " Son Rapinya: 2741.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Scarborough", + "FINAL ANSWER: Scarborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.03283, + "lon": -51.23019, + "name": "Porto Alegre" + }, + { + "lat": -5.1875, + "lon": -37.34417, + "name": "Mossoró" + }, + { + "lat": -24.23127, + "lon": -64.86614, + "name": "San Pedro de Jujuy" + }, + { + "lat": -22.31472, + "lon": -49.06056, + "name": "Bauru" + }, + { + "lat": 25.71826, + "lon": 116.74892, + "name": "Liancheng" + } + ], + "question": "Which location is the geographic outlier among: Porto Alegre, Mossoró, San Pedro de Jujuy, Bauru, Liancheng?", + "ground_truth": { + "answer": "Liancheng", + "outlier_distance_km": 14922.2, + "second_furthest_km": 5229.5, + "clarity_ratio": 2.85, + "median_distance_km": 4092.6, + "distances_to_centroid": { + "Porto Alegre": 4092.6, + "Mossoró": 2319.9, + "San Pedro de Jujuy": 5229.5, + "Bauru": 3605.0, + "Liancheng": 14922.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porto Alegre: (-30.03°, -51.23°)", + " Mossoró: (-5.19°, -37.34°)", + " San Pedro de Jujuy: (-24.23°, -64.87°)", + " Bauru: (-22.31°, -49.06°)", + " Liancheng: (25.72°, 116.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Liancheng: 14922.2 km from centroid", + " San Pedro de Jujuy: 5229.5 km from centroid", + " Porto Alegre: 4092.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Liancheng", + "FINAL ANSWER: Liancheng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.96333, + "lon": -35.69167, + "name": "Areia" + }, + { + "lat": -23.59468, + "lon": -46.54359, + "name": "Sao Lucas" + }, + { + "lat": -23.56439, + "lon": -46.61695, + "name": "Cambuci" + }, + { + "lat": -16.96222, + "lon": -49.22806, + "name": "Hidrolândia" + }, + { + "lat": 3.8766, + "lon": 100.9328, + "name": "Hutan Melintang" + } + ], + "question": "Which location is the geographic outlier among: Areia, Sao Lucas, Cambuci, Hidrolândia, Hutan Melintang?", + "ground_truth": { + "answer": "Hutan Melintang", + "outlier_distance_km": 12957.1, + "second_furthest_km": 3643.4, + "clarity_ratio": 3.56, + "median_distance_km": 3466.5, + "distances_to_centroid": { + "Areia": 2329.9, + "Sao Lucas": 3460.0, + "Cambuci": 3466.5, + "Hidrolândia": 3643.4, + "Hutan Melintang": 12957.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Areia: (-6.96°, -35.69°)", + " Sao Lucas: (-23.59°, -46.54°)", + " Cambuci: (-23.56°, -46.62°)", + " Hidrolândia: (-16.96°, -49.23°)", + " Hutan Melintang: (3.88°, 100.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hutan Melintang: 12957.1 km from centroid", + " Hidrolândia: 3643.4 km from centroid", + " Cambuci: 3466.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hutan Melintang", + "FINAL ANSWER: Hutan Melintang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.51314, + "lon": 9.14343, + "name": "Quarto Oggiaro" + }, + { + "lat": 46.06251, + "lon": 6.57497, + "name": "Cluses" + }, + { + "lat": 51.31889, + "lon": -2.20861, + "name": "Trowbridge" + }, + { + "lat": 43.34122, + "lon": 3.21402, + "name": "Béziers" + }, + { + "lat": 6.78611, + "lon": 125.21333, + "name": "Bansalan" + } + ], + "question": "Which location is the geographic outlier among: Quarto Oggiaro, Cluses, Trowbridge, Béziers, Bansalan?", + "ground_truth": { + "answer": "Bansalan", + "outlier_distance_km": 10125.4, + "second_furthest_km": 2762.1, + "clarity_ratio": 3.67, + "median_distance_km": 2169.0, + "distances_to_centroid": { + "Quarto Oggiaro": 1758.7, + "Cluses": 1967.0, + "Trowbridge": 2762.1, + "Béziers": 2169.0, + "Bansalan": 10125.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Quarto Oggiaro: (45.51°, 9.14°)", + " Cluses: (46.06°, 6.57°)", + " Trowbridge: (51.32°, -2.21°)", + " Béziers: (43.34°, 3.21°)", + " Bansalan: (6.79°, 125.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bansalan: 10125.4 km from centroid", + " Trowbridge: 2762.1 km from centroid", + " Béziers: 2169.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bansalan", + "FINAL ANSWER: Bansalan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.805, + "lon": -37.68444, + "name": "Poço Redondo" + }, + { + "lat": -8.41889, + "lon": -37.05389, + "name": "Arcoverde" + }, + { + "lat": -33.67571, + "lon": -65.45783, + "name": "Villa Mercedes" + }, + { + "lat": -33.14091, + "lon": -59.31257, + "name": "Gualeguay" + }, + { + "lat": 31.81667, + "lon": 130.3, + "name": "Sendai" + } + ], + "question": "Which location is the geographic outlier among: Poço Redondo, Arcoverde, Villa Mercedes, Gualeguay, Sendai?", + "ground_truth": { + "answer": "Sendai", + "outlier_distance_km": 15649.0, + "second_furthest_km": 5825.7, + "clarity_ratio": 2.69, + "median_distance_km": 5260.2, + "distances_to_centroid": { + "Poço Redondo": 2610.1, + "Arcoverde": 2556.8, + "Villa Mercedes": 5825.7, + "Gualeguay": 5260.2, + "Sendai": 15649.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Poço Redondo: (-9.80°, -37.68°)", + " Arcoverde: (-8.42°, -37.05°)", + " Villa Mercedes: (-33.68°, -65.46°)", + " Gualeguay: (-33.14°, -59.31°)", + " Sendai: (31.82°, 130.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sendai: 15649.0 km from centroid", + " Villa Mercedes: 5825.7 km from centroid", + " Gualeguay: 5260.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sendai", + "FINAL ANSWER: Sendai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.42172, + "lon": 40.76282, + "name": "Mīlē" + }, + { + "lat": -0.72104, + "lon": 37.15259, + "name": "Murang’a" + }, + { + "lat": 31.20864, + "lon": 31.63528, + "name": "Az Zarqā" + }, + { + "lat": 5.1009, + "lon": 6.81411, + "name": "Elele" + }, + { + "lat": 45.85008, + "lon": -73.76588, + "name": "Saint-Lin-Laurentides" + } + ], + "question": "Which location is the geographic outlier among: Mīlē, Murang’a, Az Zarqā, Elele, Saint-Lin-Laurentides?", + "ground_truth": { + "answer": "Saint-Lin-Laurentides", + "outlier_distance_km": 7951.4, + "second_furthest_km": 3793.3, + "clarity_ratio": 2.1, + "median_distance_km": 3547.5, + "distances_to_centroid": { + "Mīlē": 3547.5, + "Murang’a": 3793.3, + "Az Zarqā": 2713.1, + "Elele": 1509.3, + "Saint-Lin-Laurentides": 7951.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mīlē: (11.42°, 40.76°)", + " Murang’a: (-0.72°, 37.15°)", + " Az Zarqā: (31.21°, 31.64°)", + " Elele: (5.10°, 6.81°)", + " Saint-Lin-Laurentides: (45.85°, -73.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint-Lin-Laurentides: 7951.4 km from centroid", + " Murang’a: 3793.3 km from centroid", + " Mīlē: 3547.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint-Lin-Laurentides", + "FINAL ANSWER: Saint-Lin-Laurentides" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.67768, + "lon": -116.78047, + "name": "Coeur d'Alene" + }, + { + "lat": 35.35014, + "lon": -80.20006, + "name": "Albemarle" + }, + { + "lat": 42.45843, + "lon": -71.06616, + "name": "Melrose" + }, + { + "lat": 36.01562, + "lon": -86.58194, + "name": "La Vergne" + }, + { + "lat": 32.06317, + "lon": 131.48693, + "name": "Shintomi" + } + ], + "question": "Which location is the geographic outlier among: Coeur d'Alene, Albemarle, Melrose, La Vergne, Shintomi?", + "ground_truth": { + "answer": "Shintomi", + "outlier_distance_km": 12134.9, + "second_furthest_km": 5719.0, + "clarity_ratio": 2.12, + "median_distance_km": 3687.5, + "distances_to_centroid": { + "Coeur d'Alene": 5719.0, + "Albemarle": 3159.8, + "Melrose": 2261.5, + "La Vergne": 3687.5, + "Shintomi": 12134.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coeur d'Alene: (47.68°, -116.78°)", + " Albemarle: (35.35°, -80.20°)", + " Melrose: (42.46°, -71.07°)", + " La Vergne: (36.02°, -86.58°)", + " Shintomi: (32.06°, 131.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shintomi: 12134.9 km from centroid", + " Coeur d'Alene: 5719.0 km from centroid", + " La Vergne: 3687.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shintomi", + "FINAL ANSWER: Shintomi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.39022, + "lon": -70.04556, + "name": "Diego de Almagro" + }, + { + "lat": -2.90472, + "lon": -41.77667, + "name": "Parnaíba" + }, + { + "lat": -23.87389, + "lon": -49.80278, + "name": "Wenceslau Braz" + }, + { + "lat": -23.2325, + "lon": -51.66556, + "name": "Astorga" + }, + { + "lat": 51.18459, + "lon": 6.81249, + "name": "Wersten" + } + ], + "question": "Which location is the geographic outlier among: Diego de Almagro, Parnaíba, Wenceslau Braz, Astorga, Wersten?", + "ground_truth": { + "answer": "Wersten", + "outlier_distance_km": 7740.2, + "second_furthest_km": 3866.8, + "clarity_ratio": 2.0, + "median_distance_km": 2308.3, + "distances_to_centroid": { + "Diego de Almagro": 3866.8, + "Parnaíba": 243.7, + "Wenceslau Braz": 2283.4, + "Astorga": 2308.3, + "Wersten": 7740.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Diego de Almagro: (-26.39°, -70.05°)", + " Parnaíba: (-2.90°, -41.78°)", + " Wenceslau Braz: (-23.87°, -49.80°)", + " Astorga: (-23.23°, -51.67°)", + " Wersten: (51.18°, 6.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wersten: 7740.2 km from centroid", + " Diego de Almagro: 3866.8 km from centroid", + " Astorga: 2308.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wersten", + "FINAL ANSWER: Wersten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.33672, + "lon": 15.0499, + "name": "Stargard" + }, + { + "lat": 40.46702, + "lon": -3.70416, + "name": "Valdeacederas" + }, + { + "lat": 53.03333, + "lon": 8.75, + "name": "Stuhr" + }, + { + "lat": 49.99472, + "lon": 8.58361, + "name": "Mörfelden-Walldorf" + }, + { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + } + ], + "question": "Which location is the geographic outlier among: Stargard, Valdeacederas, Stuhr, Mörfelden-Walldorf, Dianella?", + "ground_truth": { + "answer": "Dianella", + "outlier_distance_km": 11616.6, + "second_furthest_km": 3004.1, + "clarity_ratio": 3.87, + "median_distance_km": 2746.3, + "distances_to_centroid": { + "Stargard": 2516.2, + "Valdeacederas": 3004.1, + "Stuhr": 2746.3, + "Mörfelden-Walldorf": 2521.5, + "Dianella": 11616.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stargard: (53.34°, 15.05°)", + " Valdeacederas: (40.47°, -3.70°)", + " Stuhr: (53.03°, 8.75°)", + " Mörfelden-Walldorf: (49.99°, 8.58°)", + " Dianella: (-31.89°, 115.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dianella: 11616.6 km from centroid", + " Valdeacederas: 3004.1 km from centroid", + " Stuhr: 2746.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dianella", + "FINAL ANSWER: Dianella" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + }, + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + { + "lat": 6.61667, + "lon": -1.21667, + "name": "Konongo" + } + ], + "question": "Which location is the geographic outlier among: Broken Hill, Avondale, Paraparaumu, Cambridge, Konongo?", + "ground_truth": { + "answer": "Konongo", + "outlier_distance_km": 14649.1, + "second_furthest_km": 4055.3, + "clarity_ratio": 3.61, + "median_distance_km": 4047.2, + "distances_to_centroid": { + "Broken Hill": 907.2, + "Avondale": 3985.8, + "Paraparaumu": 4047.2, + "Cambridge": 4055.3, + "Konongo": 14649.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Broken Hill: (-31.97°, 141.45°)", + " Avondale: (-36.88°, 174.70°)", + " Paraparaumu: (-40.92°, 175.02°)", + " Cambridge: (-37.88°, 175.44°)", + " Konongo: (6.62°, -1.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Konongo: 14649.1 km from centroid", + " Cambridge: 4055.3 km from centroid", + " Paraparaumu: 4047.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Konongo", + "FINAL ANSWER: Konongo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.76694, + "lon": -44.08667, + "name": "Ribeirão das Neves" + }, + { + "lat": -34.57365, + "lon": -58.44924, + "name": "Colegiales" + }, + { + "lat": -31.44957, + "lon": -60.93153, + "name": "Esperanza" + }, + { + "lat": -5.1275, + "lon": -39.73222, + "name": "Boa Viagem" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + } + ], + "question": "Which location is the geographic outlier among: Ribeirão das Neves, Colegiales, Esperanza, Boa Viagem, Casula?", + "ground_truth": { + "answer": "Casula", + "outlier_distance_km": 13173.3, + "second_furthest_km": 4955.1, + "clarity_ratio": 2.66, + "median_distance_km": 4708.2, + "distances_to_centroid": { + "Ribeirão das Neves": 3496.8, + "Colegiales": 4708.2, + "Esperanza": 4955.1, + "Boa Viagem": 3822.8, + "Casula": 13173.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ribeirão das Neves: (-19.77°, -44.09°)", + " Colegiales: (-34.57°, -58.45°)", + " Esperanza: (-31.45°, -60.93°)", + " Boa Viagem: (-5.13°, -39.73°)", + " Casula: (-33.95°, 150.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casula: 13173.3 km from centroid", + " Esperanza: 4955.1 km from centroid", + " Colegiales: 4708.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casula", + "FINAL ANSWER: Casula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.13817, + "lon": -122.93817, + "name": "Longview" + }, + { + "lat": 44.44888, + "lon": -88.06038, + "name": "De Pere" + }, + { + "lat": 33.13845, + "lon": -95.60107, + "name": "Sulphur Springs" + }, + { + "lat": 28.01769, + "lon": -82.50619, + "name": "Egypt Lake-Leto" + }, + { + "lat": 13.04888, + "lon": 80.11488, + "name": "Poonamalle" + } + ], + "question": "Which location is the geographic outlier among: Longview, De Pere, Sulphur Springs, Egypt Lake-Leto, Poonamalle?", + "ground_truth": { + "answer": "Poonamalle", + "outlier_distance_km": 13495.4, + "second_furthest_km": 5305.1, + "clarity_ratio": 2.54, + "median_distance_km": 3136.7, + "distances_to_centroid": { + "Longview": 5305.1, + "De Pere": 2595.9, + "Sulphur Springs": 3136.7, + "Egypt Lake-Leto": 2055.0, + "Poonamalle": 13495.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Longview: (46.14°, -122.94°)", + " De Pere: (44.45°, -88.06°)", + " Sulphur Springs: (33.14°, -95.60°)", + " Egypt Lake-Leto: (28.02°, -82.51°)", + " Poonamalle: (13.05°, 80.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Poonamalle: 13495.4 km from centroid", + " Longview: 5305.1 km from centroid", + " Sulphur Springs: 3136.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Poonamalle", + "FINAL ANSWER: Poonamalle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.9516, + "lon": 101.843, + "name": "Semenyih" + }, + { + "lat": 36.31275, + "lon": 118.41185, + "name": "Sitou" + }, + { + "lat": 21.32112, + "lon": 70.44078, + "name": "Mendarda" + }, + { + "lat": 36.07254, + "lon": 139.72615, + "name": "Satte" + }, + { + "lat": 1.25744, + "lon": -70.23551, + "name": "Mitú" + } + ], + "question": "Which location is the geographic outlier among: Semenyih, Sitou, Mendarda, Satte, Mitú?", + "ground_truth": { + "answer": "Mitú", + "outlier_distance_km": 15292.8, + "second_furthest_km": 6770.9, + "clarity_ratio": 2.26, + "median_distance_km": 4865.5, + "distances_to_centroid": { + "Semenyih": 3727.2, + "Sitou": 4865.5, + "Mendarda": 255.0, + "Satte": 6770.9, + "Mitú": 15292.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Semenyih: (2.95°, 101.84°)", + " Sitou: (36.31°, 118.41°)", + " Mendarda: (21.32°, 70.44°)", + " Satte: (36.07°, 139.73°)", + " Mitú: (1.26°, -70.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mitú: 15292.8 km from centroid", + " Satte: 6770.9 km from centroid", + " Sitou: 4865.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mitú", + "FINAL ANSWER: Mitú" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.20437, + "lon": 127.75267, + "name": "Yonabaru" + }, + { + "lat": 37.5986, + "lon": 127.1394, + "name": "Guri-si" + }, + { + "lat": 11.02427, + "lon": 77.12565, + "name": "Sulur" + }, + { + "lat": 9.65556, + "lon": 123.85219, + "name": "Tagbilaran City" + }, + { + "lat": 37.26383, + "lon": -122.02301, + "name": "Saratoga" + } + ], + "question": "Which location is the geographic outlier among: Yonabaru, Guri-si, Sulur, Tagbilaran City, Saratoga?", + "ground_truth": { + "answer": "Saratoga", + "outlier_distance_km": 13102.5, + "second_furthest_km": 6242.0, + "clarity_ratio": 2.1, + "median_distance_km": 6076.9, + "distances_to_centroid": { + "Yonabaru": 6076.9, + "Guri-si": 5840.4, + "Sulur": 1841.6, + "Tagbilaran City": 6242.0, + "Saratoga": 13102.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yonabaru: (26.20°, 127.75°)", + " Guri-si: (37.60°, 127.14°)", + " Sulur: (11.02°, 77.13°)", + " Tagbilaran City: (9.66°, 123.85°)", + " Saratoga: (37.26°, -122.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saratoga: 13102.5 km from centroid", + " Tagbilaran City: 6242.0 km from centroid", + " Yonabaru: 6076.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saratoga", + "FINAL ANSWER: Saratoga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.45917, + "lon": -52.82083, + "name": "Não-Me-Toque" + }, + { + "lat": -5.65084, + "lon": -48.11119, + "name": "Araguatins" + }, + { + "lat": -26.30444, + "lon": -48.84556, + "name": "Joinville" + }, + { + "lat": -35.81081, + "lon": -61.89897, + "name": "Pehuajó" + }, + { + "lat": 21.63585, + "lon": 73.04752, + "name": "Sarangpore" + } + ], + "question": "Which location is the geographic outlier among: Não-Me-Toque, Araguatins, Joinville, Pehuajó, Sarangpore?", + "ground_truth": { + "answer": "Sarangpore", + "outlier_distance_km": 11701.8, + "second_furthest_km": 4110.9, + "clarity_ratio": 2.85, + "median_distance_km": 2988.1, + "distances_to_centroid": { + "Não-Me-Toque": 2988.1, + "Araguatins": 2454.1, + "Joinville": 2530.8, + "Pehuajó": 4110.9, + "Sarangpore": 11701.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Não-Me-Toque: (-28.46°, -52.82°)", + " Araguatins: (-5.65°, -48.11°)", + " Joinville: (-26.30°, -48.85°)", + " Pehuajó: (-35.81°, -61.90°)", + " Sarangpore: (21.64°, 73.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sarangpore: 11701.8 km from centroid", + " Pehuajó: 4110.9 km from centroid", + " Não-Me-Toque: 2988.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sarangpore", + "FINAL ANSWER: Sarangpore" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.93366, + "lon": 29.24152, + "name": "Standerton" + }, + { + "lat": 1.01659, + "lon": 39.49122, + "name": "Habaswein" + }, + { + "lat": 6.01277, + "lon": 6.74768, + "name": "Atani" + }, + { + "lat": 14.23333, + "lon": 37.0, + "name": "Abala" + }, + { + "lat": -21.54722, + "lon": -45.7375, + "name": "Paraguaçu" + } + ], + "question": "Which location is the geographic outlier among: Standerton, Habaswein, Atani, Abala, Paraguaçu?", + "ground_truth": { + "answer": "Paraguaçu", + "outlier_distance_km": 6593.9, + "second_furthest_km": 3404.9, + "clarity_ratio": 1.94, + "median_distance_km": 2990.7, + "distances_to_centroid": { + "Standerton": 2923.4, + "Habaswein": 2990.7, + "Atani": 1469.6, + "Abala": 3404.9, + "Paraguaçu": 6593.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Standerton: (-26.93°, 29.24°)", + " Habaswein: (1.02°, 39.49°)", + " Atani: (6.01°, 6.75°)", + " Abala: (14.23°, 37.00°)", + " Paraguaçu: (-21.55°, -45.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paraguaçu: 6593.9 km from centroid", + " Abala: 3404.9 km from centroid", + " Habaswein: 2990.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paraguaçu", + "FINAL ANSWER: Paraguaçu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.37898, + "lon": -3.72617, + "name": "Abrantes" + }, + { + "lat": 49.54033, + "lon": 8.5782, + "name": "Viernheim" + }, + { + "lat": 39.5, + "lon": -0.35, + "name": "Alboraya" + }, + { + "lat": 49.4891, + "lon": 8.46694, + "name": "Mannheim" + }, + { + "lat": 29.73861, + "lon": 107.29477, + "name": "Lidu" + } + ], + "question": "Which location is the geographic outlier among: Abrantes, Viernheim, Alboraya, Mannheim, Lidu?", + "ground_truth": { + "answer": "Lidu", + "outlier_distance_km": 7341.0, + "second_furthest_km": 2324.0, + "clarity_ratio": 3.16, + "median_distance_km": 2067.6, + "distances_to_centroid": { + "Abrantes": 2324.0, + "Viernheim": 1479.2, + "Alboraya": 2067.6, + "Mannheim": 1483.4, + "Lidu": 7341.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abrantes: (40.38°, -3.73°)", + " Viernheim: (49.54°, 8.58°)", + " Alboraya: (39.50°, -0.35°)", + " Mannheim: (49.49°, 8.47°)", + " Lidu: (29.74°, 107.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lidu: 7341.0 km from centroid", + " Abrantes: 2324.0 km from centroid", + " Alboraya: 2067.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lidu", + "FINAL ANSWER: Lidu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.93333, + "lon": 145.23333, + "name": "Rowville" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + }, + { + "lat": -37.95855, + "lon": 176.98545, + "name": "Whakatane" + }, + { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + { + "lat": 31.41648, + "lon": 31.81332, + "name": "Damietta" + } + ], + "question": "Which location is the geographic outlier among: Rowville, Papakura, Whakatane, Eastwood, Damietta?", + "ground_truth": { + "answer": "Damietta", + "outlier_distance_km": 12607.1, + "second_furthest_km": 4218.4, + "clarity_ratio": 2.99, + "median_distance_km": 4022.2, + "distances_to_centroid": { + "Rowville": 1871.9, + "Papakura": 4022.2, + "Whakatane": 4218.4, + "Eastwood": 1891.8, + "Damietta": 12607.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rowville: (-37.93°, 145.23°)", + " Papakura: (-37.06°, 174.94°)", + " Whakatane: (-37.96°, 176.99°)", + " Eastwood: (-33.79°, 151.08°)", + " Damietta: (31.42°, 31.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Damietta: 12607.1 km from centroid", + " Whakatane: 4218.4 km from centroid", + " Papakura: 4022.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Damietta", + "FINAL ANSWER: Damietta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.1137, + "lon": 101.8142, + "name": "Hulu Langat" + }, + { + "lat": 24.22388, + "lon": 92.67869, + "name": "Kolasib" + }, + { + "lat": 10.2708, + "lon": 123.5839, + "name": "Pinamungahan" + }, + { + "lat": 11.26258, + "lon": 75.8796, + "name": "Kuttikkāttūr" + }, + { + "lat": -25.46722, + "lon": -50.65111, + "name": "Irati" + } + ], + "question": "Which location is the geographic outlier among: Hulu Langat, Kolasib, Pinamungahan, Kuttikkāttūr, Irati?", + "ground_truth": { + "answer": "Irati", + "outlier_distance_km": 13165.4, + "second_furthest_km": 6080.2, + "clarity_ratio": 2.17, + "median_distance_km": 3681.7, + "distances_to_centroid": { + "Hulu Langat": 3681.7, + "Kolasib": 3365.4, + "Pinamungahan": 6080.2, + "Kuttikkāttūr": 1080.2, + "Irati": 13165.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hulu Langat: (3.11°, 101.81°)", + " Kolasib: (24.22°, 92.68°)", + " Pinamungahan: (10.27°, 123.58°)", + " Kuttikkāttūr: (11.26°, 75.88°)", + " Irati: (-25.47°, -50.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Irati: 13165.4 km from centroid", + " Pinamungahan: 6080.2 km from centroid", + " Hulu Langat: 3681.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Irati", + "FINAL ANSWER: Irati" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.285, + "lon": -0.746, + "name": "Apam" + }, + { + "lat": 8.53333, + "lon": 34.8, + "name": "Dembī Dolo" + }, + { + "lat": 9.56667, + "lon": 37.1, + "name": "Shambu" + }, + { + "lat": 26.87524, + "lon": 31.32963, + "name": "Al Ghanāyim" + }, + { + "lat": 34.13216, + "lon": -84.30067, + "name": "Milton" + } + ], + "question": "Which location is the geographic outlier among: Apam, Dembī Dolo, Shambu, Al Ghanāyim, Milton?", + "ground_truth": { + "answer": "Milton", + "outlier_distance_km": 8780.4, + "second_furthest_km": 3706.9, + "clarity_ratio": 2.37, + "median_distance_km": 3500.1, + "distances_to_centroid": { + "Apam": 1374.7, + "Dembī Dolo": 3500.1, + "Shambu": 3706.9, + "Al Ghanāyim": 3057.4, + "Milton": 8780.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Apam: (5.29°, -0.75°)", + " Dembī Dolo: (8.53°, 34.80°)", + " Shambu: (9.57°, 37.10°)", + " Al Ghanāyim: (26.88°, 31.33°)", + " Milton: (34.13°, -84.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Milton: 8780.4 km from centroid", + " Shambu: 3706.9 km from centroid", + " Dembī Dolo: 3500.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Milton", + "FINAL ANSWER: Milton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.0021, + "lon": 0.20251, + "name": "Le Mans" + }, + { + "lat": 51.5824, + "lon": -0.09956, + "name": "Harringay" + }, + { + "lat": 37.64442, + "lon": 14.86685, + "name": "Biancavilla" + }, + { + "lat": 45.67574, + "lon": 9.23723, + "name": "Carate Brianza" + }, + { + "lat": 27.06193, + "lon": -101.54891, + "name": "San Buenaventura" + } + ], + "question": "Which location is the geographic outlier among: Le Mans, Harringay, Biancavilla, Carate Brianza, San Buenaventura?", + "ground_truth": { + "answer": "San Buenaventura", + "outlier_distance_km": 7732.0, + "second_furthest_km": 2621.3, + "clarity_ratio": 2.95, + "median_distance_km": 2015.0, + "distances_to_centroid": { + "Le Mans": 1398.0, + "Harringay": 1577.2, + "Biancavilla": 2621.3, + "Carate Brianza": 2015.0, + "San Buenaventura": 7732.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Le Mans: (48.00°, 0.20°)", + " Harringay: (51.58°, -0.10°)", + " Biancavilla: (37.64°, 14.87°)", + " Carate Brianza: (45.68°, 9.24°)", + " San Buenaventura: (27.06°, -101.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Buenaventura: 7732.0 km from centroid", + " Biancavilla: 2621.3 km from centroid", + " Carate Brianza: 2015.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Buenaventura", + "FINAL ANSWER: San Buenaventura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.69863, + "lon": 144.78631, + "name": "Taylors Lakes" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": 9.96453, + "lon": 78.0667, + "name": "Paravai" + } + ], + "question": "Which location is the geographic outlier among: Taylors Lakes, Blacktown, Logan City, Willetton, Paravai?", + "ground_truth": { + "answer": "Paravai", + "outlier_distance_km": 6668.9, + "second_furthest_km": 2480.2, + "clarity_ratio": 2.69, + "median_distance_km": 2411.9, + "distances_to_centroid": { + "Taylors Lakes": 2146.7, + "Blacktown": 2411.9, + "Logan City": 2480.2, + "Willetton": 1513.7, + "Paravai": 6668.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taylors Lakes: (-37.70°, 144.79°)", + " Blacktown: (-33.77°, 150.92°)", + " Logan City: (-27.64°, 153.11°)", + " Willetton: (-32.05°, 115.89°)", + " Paravai: (9.96°, 78.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paravai: 6668.9 km from centroid", + " Logan City: 2480.2 km from centroid", + " Blacktown: 2411.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paravai", + "FINAL ANSWER: Paravai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.94013, + "lon": 7.00605, + "name": "Kalk" + }, + { + "lat": 49.96675, + "lon": 7.8992, + "name": "Bingen am Rhein" + }, + { + "lat": 48.91882, + "lon": 2.25404, + "name": "Colombes" + }, + { + "lat": 44.1391, + "lon": 12.24315, + "name": "Cesena" + }, + { + "lat": 5.02208, + "lon": -74.00481, + "name": "Zipaquirá" + } + ], + "question": "Which location is the geographic outlier among: Kalk, Bingen am Rhein, Colombes, Cesena, Zipaquirá?", + "ground_truth": { + "answer": "Zipaquirá", + "outlier_distance_km": 7534.7, + "second_furthest_km": 1809.4, + "clarity_ratio": 4.16, + "median_distance_km": 1748.7, + "distances_to_centroid": { + "Kalk": 1748.7, + "Bingen am Rhein": 1735.0, + "Colombes": 1345.5, + "Cesena": 1809.4, + "Zipaquirá": 7534.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kalk: (50.94°, 7.01°)", + " Bingen am Rhein: (49.97°, 7.90°)", + " Colombes: (48.92°, 2.25°)", + " Cesena: (44.14°, 12.24°)", + " Zipaquirá: (5.02°, -74.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zipaquirá: 7534.7 km from centroid", + " Cesena: 1809.4 km from centroid", + " Kalk: 1748.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zipaquirá", + "FINAL ANSWER: Zipaquirá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.67144, + "lon": 4.84862, + "name": "Heerhugowaard" + }, + { + "lat": 51.50896, + "lon": -0.3713, + "name": "Southall" + }, + { + "lat": 51.44083, + "lon": 5.47778, + "name": "Eindhoven" + }, + { + "lat": 54.13579, + "lon": -1.52826, + "name": "Ripon" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + } + ], + "question": "Which location is the geographic outlier among: Heerhugowaard, Southall, Eindhoven, Ripon, Cabramatta?", + "ground_truth": { + "answer": "Cabramatta", + "outlier_distance_km": 14522.6, + "second_furthest_km": 3328.1, + "clarity_ratio": 4.36, + "median_distance_km": 3137.5, + "distances_to_centroid": { + "Heerhugowaard": 2879.3, + "Southall": 3137.5, + "Eindhoven": 2771.8, + "Ripon": 3328.1, + "Cabramatta": 14522.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Heerhugowaard: (52.67°, 4.85°)", + " Southall: (51.51°, -0.37°)", + " Eindhoven: (51.44°, 5.48°)", + " Ripon: (54.14°, -1.53°)", + " Cabramatta: (-33.90°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cabramatta: 14522.6 km from centroid", + " Ripon: 3328.1 km from centroid", + " Southall: 3137.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cabramatta", + "FINAL ANSWER: Cabramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.21667, + "lon": 174.91667, + "name": "Lower Hutt" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + }, + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + }, + { + "lat": 53.57416, + "lon": 9.95679, + "name": "Eimsbüttel" + } + ], + "question": "Which location is the geographic outlier among: Lower Hutt, Glenroy, Taylors Hill, New Plymouth, Eimsbüttel?", + "ground_truth": { + "answer": "Eimsbüttel", + "outlier_distance_km": 13772.0, + "second_furthest_km": 4824.1, + "clarity_ratio": 2.85, + "median_distance_km": 4698.3, + "distances_to_centroid": { + "Lower Hutt": 4824.1, + "Glenroy": 2416.4, + "Taylors Hill": 2406.9, + "New Plymouth": 4698.3, + "Eimsbüttel": 13772.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lower Hutt: (-41.22°, 174.92°)", + " Glenroy: (-37.70°, 144.93°)", + " Taylors Hill: (-37.71°, 144.75°)", + " New Plymouth: (-39.07°, 174.08°)", + " Eimsbüttel: (53.57°, 9.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Eimsbüttel: 13772.0 km from centroid", + " Lower Hutt: 4824.1 km from centroid", + " New Plymouth: 4698.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Eimsbüttel", + "FINAL ANSWER: Eimsbüttel" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.11667, + "lon": 8.83333, + "name": "Mühlheim am Main" + }, + { + "lat": 49.74657, + "lon": 8.11513, + "name": "Alzey" + }, + { + "lat": 53.91887, + "lon": 10.69691, + "name": "Bad Schwartau" + }, + { + "lat": 55.83116, + "lon": -3.22608, + "name": "Penicuik" + }, + { + "lat": 30.31269, + "lon": 31.32018, + "name": "Shibīn al Qanāţir" + } + ], + "question": "Which location is the geographic outlier among: Mühlheim am Main, Alzey, Bad Schwartau, Penicuik, Shibīn al Qanāţir?", + "ground_truth": { + "answer": "Shibīn al Qanāţir", + "outlier_distance_km": 2608.2, + "second_furthest_km": 1312.0, + "clarity_ratio": 1.99, + "median_distance_km": 660.5, + "distances_to_centroid": { + "Mühlheim am Main": 290.9, + "Alzey": 295.9, + "Bad Schwartau": 660.5, + "Penicuik": 1312.0, + "Shibīn al Qanāţir": 2608.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mühlheim am Main: (50.12°, 8.83°)", + " Alzey: (49.75°, 8.12°)", + " Bad Schwartau: (53.92°, 10.70°)", + " Penicuik: (55.83°, -3.23°)", + " Shibīn al Qanāţir: (30.31°, 31.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shibīn al Qanāţir: 2608.2 km from centroid", + " Penicuik: 1312.0 km from centroid", + " Bad Schwartau: 660.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shibīn al Qanāţir", + "FINAL ANSWER: Shibīn al Qanāţir" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.6103, + "lon": -117.72533, + "name": "Laguna Woods" + }, + { + "lat": 17.17291, + "lon": -92.33392, + "name": "Yajalón" + }, + { + "lat": 21.35087, + "lon": -97.68656, + "name": "Naranjos" + }, + { + "lat": 33.04623, + "lon": -96.99417, + "name": "Lewisville" + }, + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + } + ], + "question": "Which location is the geographic outlier among: Laguna Woods, Yajalón, Naranjos, Lewisville, Reservoir?", + "ground_truth": { + "answer": "Reservoir", + "outlier_distance_km": 16842.4, + "second_furthest_km": 6952.1, + "clarity_ratio": 2.42, + "median_distance_km": 5039.5, + "distances_to_centroid": { + "Laguna Woods": 6952.1, + "Yajalón": 4342.7, + "Naranjos": 4913.6, + "Lewisville": 5039.5, + "Reservoir": 16842.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Laguna Woods: (33.61°, -117.73°)", + " Yajalón: (17.17°, -92.33°)", + " Naranjos: (21.35°, -97.69°)", + " Lewisville: (33.05°, -96.99°)", + " Reservoir: (-37.72°, 145.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Reservoir: 16842.4 km from centroid", + " Laguna Woods: 6952.1 km from centroid", + " Lewisville: 5039.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Reservoir", + "FINAL ANSWER: Reservoir" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.07538, + "lon": -75.73422, + "name": "Ica" + }, + { + "lat": 2.56799, + "lon": -72.63972, + "name": "San José del Guaviare" + }, + { + "lat": -3.89833, + "lon": -61.37306, + "name": "Beruri" + }, + { + "lat": 2.39341, + "lon": -75.89232, + "name": "La Plata" + }, + { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + } + ], + "question": "Which location is the geographic outlier among: Ica, San José del Guaviare, Beruri, La Plata, Warwick?", + "ground_truth": { + "answer": "Warwick", + "outlier_distance_km": 15958.1, + "second_furthest_km": 5578.9, + "clarity_ratio": 2.86, + "median_distance_km": 5377.0, + "distances_to_centroid": { + "Ica": 5377.0, + "San José del Guaviare": 5231.7, + "Beruri": 3860.3, + "La Plata": 5578.9, + "Warwick": 15958.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ica: (-14.08°, -75.73°)", + " San José del Guaviare: (2.57°, -72.64°)", + " Beruri: (-3.90°, -61.37°)", + " La Plata: (2.39°, -75.89°)", + " Warwick: (-28.22°, 152.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Warwick: 15958.1 km from centroid", + " La Plata: 5578.9 km from centroid", + " Ica: 5377.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Warwick", + "FINAL ANSWER: Warwick" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.35357, + "lon": 7.57883, + "name": "Koblenz" + }, + { + "lat": 51.34948, + "lon": -0.2494, + "name": "Ewell" + }, + { + "lat": 52.00667, + "lon": 4.35556, + "name": "Delft" + }, + { + "lat": 48.89198, + "lon": 2.20675, + "name": "Nanterre" + }, + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + } + ], + "question": "Which location is the geographic outlier among: Koblenz, Ewell, Delft, Nanterre, Springfield Lakes?", + "ground_truth": { + "answer": "Springfield Lakes", + "outlier_distance_km": 14302.5, + "second_furthest_km": 3233.6, + "clarity_ratio": 4.42, + "median_distance_km": 2975.0, + "distances_to_centroid": { + "Koblenz": 2689.6, + "Ewell": 3233.6, + "Delft": 2975.0, + "Nanterre": 2974.2, + "Springfield Lakes": 14302.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Koblenz: (50.35°, 7.58°)", + " Ewell: (51.35°, -0.25°)", + " Delft: (52.01°, 4.36°)", + " Nanterre: (48.89°, 2.21°)", + " Springfield Lakes: (-27.67°, 152.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Springfield Lakes: 14302.5 km from centroid", + " Ewell: 3233.6 km from centroid", + " Delft: 2975.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Springfield Lakes", + "FINAL ANSWER: Springfield Lakes" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.52833, + "lon": -39.07639, + "name": "Barrocas" + }, + { + "lat": 9.7174, + "lon": -75.12023, + "name": "El Carmen de Bolívar" + }, + { + "lat": -26.11139, + "lon": -49.80528, + "name": "Mafra" + }, + { + "lat": -28.81833, + "lon": -52.51028, + "name": "Soledade" + }, + { + "lat": 53.92099, + "lon": 9.51529, + "name": "Itzehoe" + } + ], + "question": "Which location is the geographic outlier among: Barrocas, El Carmen de Bolívar, Mafra, Soledade, Itzehoe?", + "ground_truth": { + "answer": "Itzehoe", + "outlier_distance_km": 7638.7, + "second_furthest_km": 3903.3, + "clarity_ratio": 1.96, + "median_distance_km": 3356.1, + "distances_to_centroid": { + "Barrocas": 1245.9, + "El Carmen de Bolívar": 3903.3, + "Mafra": 2980.1, + "Soledade": 3356.1, + "Itzehoe": 7638.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Barrocas: (-11.53°, -39.08°)", + " El Carmen de Bolívar: (9.72°, -75.12°)", + " Mafra: (-26.11°, -49.81°)", + " Soledade: (-28.82°, -52.51°)", + " Itzehoe: (53.92°, 9.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itzehoe: 7638.7 km from centroid", + " El Carmen de Bolívar: 3903.3 km from centroid", + " Soledade: 3356.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itzehoe", + "FINAL ANSWER: Itzehoe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.81639, + "lon": -45.1925, + "name": "Guaratinguetá" + }, + { + "lat": -1.67417, + "lon": -47.77111, + "name": "São Domingos do Capim" + }, + { + "lat": -33.036, + "lon": -71.62963, + "name": "Valparaíso" + }, + { + "lat": -2.68333, + "lon": -54.64278, + "name": "Mojuí dos Campos" + }, + { + "lat": 37.73987, + "lon": -121.42618, + "name": "Tracy" + } + ], + "question": "Which location is the geographic outlier among: Guaratinguetá, São Domingos do Capim, Valparaíso, Mojuí dos Campos, Tracy?", + "ground_truth": { + "answer": "Tracy", + "outlier_distance_km": 7223.2, + "second_furthest_km": 3198.1, + "clarity_ratio": 2.26, + "median_distance_km": 3194.4, + "distances_to_centroid": { + "Guaratinguetá": 3198.1, + "São Domingos do Capim": 2282.2, + "Valparaíso": 3194.4, + "Mojuí dos Campos": 1510.4, + "Tracy": 7223.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guaratinguetá: (-22.82°, -45.19°)", + " São Domingos do Capim: (-1.67°, -47.77°)", + " Valparaíso: (-33.04°, -71.63°)", + " Mojuí dos Campos: (-2.68°, -54.64°)", + " Tracy: (37.74°, -121.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tracy: 7223.2 km from centroid", + " Guaratinguetá: 3198.1 km from centroid", + " Valparaíso: 3194.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tracy", + "FINAL ANSWER: Tracy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.41209, + "lon": 2.14394, + "name": "Vallcarca" + }, + { + "lat": 50.60982, + "lon": 3.01874, + "name": "Loos" + }, + { + "lat": 53.7426, + "lon": -2.997, + "name": "Lytham St Annes" + }, + { + "lat": 50.5442, + "lon": 9.71792, + "name": "Künzell" + }, + { + "lat": 29.6241, + "lon": -90.7512, + "name": "Bayou Cane" + } + ], + "question": "Which location is the geographic outlier among: Vallcarca, Loos, Lytham St Annes, Künzell, Bayou Cane?", + "ground_truth": { + "answer": "Bayou Cane", + "outlier_distance_km": 6601.8, + "second_furthest_km": 1981.4, + "clarity_ratio": 3.33, + "median_distance_km": 1519.8, + "distances_to_centroid": { + "Vallcarca": 1505.9, + "Loos": 1519.8, + "Lytham St Annes": 1321.9, + "Künzell": 1981.4, + "Bayou Cane": 6601.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vallcarca: (41.41°, 2.14°)", + " Loos: (50.61°, 3.02°)", + " Lytham St Annes: (53.74°, -3.00°)", + " Künzell: (50.54°, 9.72°)", + " Bayou Cane: (29.62°, -90.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bayou Cane: 6601.8 km from centroid", + " Künzell: 1981.4 km from centroid", + " Loos: 1519.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bayou Cane", + "FINAL ANSWER: Bayou Cane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.46159, + "lon": -87.31497, + "name": "Bellview" + }, + { + "lat": 34.80617, + "lon": -106.73336, + "name": "Los Lunas" + }, + { + "lat": 35.44951, + "lon": -97.3967, + "name": "Midwest City" + }, + { + "lat": 16.79151, + "lon": -96.67455, + "name": "Ocotlán de Morelos" + }, + { + "lat": 40.45245, + "lon": -3.70763, + "name": "Bellas Vistas" + } + ], + "question": "Which location is the geographic outlier among: Bellview, Los Lunas, Midwest City, Ocotlán de Morelos, Bellas Vistas?", + "ground_truth": { + "answer": "Bellas Vistas", + "outlier_distance_km": 6587.6, + "second_furthest_km": 2654.6, + "clarity_ratio": 2.48, + "median_distance_km": 2474.1, + "distances_to_centroid": { + "Bellview": 861.7, + "Los Lunas": 2654.6, + "Midwest City": 1812.4, + "Ocotlán de Morelos": 2474.1, + "Bellas Vistas": 6587.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bellview: (30.46°, -87.31°)", + " Los Lunas: (34.81°, -106.73°)", + " Midwest City: (35.45°, -97.40°)", + " Ocotlán de Morelos: (16.79°, -96.67°)", + " Bellas Vistas: (40.45°, -3.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bellas Vistas: 6587.6 km from centroid", + " Los Lunas: 2654.6 km from centroid", + " Ocotlán de Morelos: 2474.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bellas Vistas", + "FINAL ANSWER: Bellas Vistas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.45123, + "lon": 8.60805, + "name": "Igbor" + }, + { + "lat": 4.93422, + "lon": -1.71454, + "name": "Sekondi" + }, + { + "lat": -26.45794, + "lon": 29.46553, + "name": "Bethal" + }, + { + "lat": 30.13806, + "lon": 31.61556, + "name": "El Shorouk" + }, + { + "lat": -32.24295, + "lon": 148.60484, + "name": "Dubbo" + } + ], + "question": "Which location is the geographic outlier among: Igbor, Sekondi, Bethal, El Shorouk, Dubbo?", + "ground_truth": { + "answer": "Dubbo", + "outlier_distance_km": 11242.0, + "second_furthest_km": 5084.1, + "clarity_ratio": 2.21, + "median_distance_km": 4030.2, + "distances_to_centroid": { + "Igbor": 4030.2, + "Sekondi": 5084.1, + "Bethal": 2974.3, + "El Shorouk": 3913.9, + "Dubbo": 11242.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Igbor: (7.45°, 8.61°)", + " Sekondi: (4.93°, -1.71°)", + " Bethal: (-26.46°, 29.47°)", + " El Shorouk: (30.14°, 31.62°)", + " Dubbo: (-32.24°, 148.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dubbo: 11242.0 km from centroid", + " Sekondi: 5084.1 km from centroid", + " Igbor: 4030.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dubbo", + "FINAL ANSWER: Dubbo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.48361, + "lon": -36.15361, + "name": "Cuité" + }, + { + "lat": -24.82361, + "lon": -49.26111, + "name": "Cerro Azul" + }, + { + "lat": -22.45389, + "lon": -43.46889, + "name": "Miguel Pereira" + }, + { + "lat": -3.56222, + "lon": -41.09222, + "name": "Viçosa do Ceará" + }, + { + "lat": 0.90925, + "lon": 108.98463, + "name": "Singkawang" + } + ], + "question": "Which location is the geographic outlier among: Cuité, Cerro Azul, Miguel Pereira, Viçosa do Ceará, Singkawang?", + "ground_truth": { + "answer": "Singkawang", + "outlier_distance_km": 13423.2, + "second_furthest_km": 4179.9, + "clarity_ratio": 3.21, + "median_distance_km": 3542.1, + "distances_to_centroid": { + "Cuité": 2684.1, + "Cerro Azul": 4179.9, + "Miguel Pereira": 3542.1, + "Viçosa do Ceará": 3296.6, + "Singkawang": 13423.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cuité: (-6.48°, -36.15°)", + " Cerro Azul: (-24.82°, -49.26°)", + " Miguel Pereira: (-22.45°, -43.47°)", + " Viçosa do Ceará: (-3.56°, -41.09°)", + " Singkawang: (0.91°, 108.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Singkawang: 13423.2 km from centroid", + " Cerro Azul: 4179.9 km from centroid", + " Miguel Pereira: 3542.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Singkawang", + "FINAL ANSWER: Singkawang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.41502, + "lon": 2.88132, + "name": "Badagry" + }, + { + "lat": -33.36889, + "lon": 19.31095, + "name": "Ceres" + }, + { + "lat": 7.53333, + "lon": 39.25, + "name": "Bek’ojī" + }, + { + "lat": 8.84651, + "lon": 7.87354, + "name": "Keffi" + }, + { + "lat": 23.49276, + "lon": 87.73484, + "name": "Guskhara" + } + ], + "question": "Which location is the geographic outlier among: Badagry, Ceres, Bek’ojī, Keffi, Guskhara?", + "ground_truth": { + "answer": "Guskhara", + "outlier_distance_km": 6478.9, + "second_furthest_km": 4194.7, + "clarity_ratio": 1.54, + "median_distance_km": 3190.2, + "distances_to_centroid": { + "Badagry": 3190.2, + "Ceres": 4194.7, + "Bek’ojī": 1027.8, + "Keffi": 2694.2, + "Guskhara": 6478.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Badagry: (6.42°, 2.88°)", + " Ceres: (-33.37°, 19.31°)", + " Bek’ojī: (7.53°, 39.25°)", + " Keffi: (8.85°, 7.87°)", + " Guskhara: (23.49°, 87.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guskhara: 6478.9 km from centroid", + " Ceres: 4194.7 km from centroid", + " Badagry: 3190.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guskhara", + "FINAL ANSWER: Guskhara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.70552, + "lon": 100.38933, + "name": "Bang Khae Nuea" + }, + { + "lat": 21.03333, + "lon": 105.83333, + "name": "Yên Phụ" + }, + { + "lat": 22.66568, + "lon": 106.25786, + "name": "Cao Bằng" + }, + { + "lat": 34.98419, + "lon": 134.97407, + "name": "Nishiwaki" + }, + { + "lat": -37.89359, + "lon": 145.05534, + "name": "Carnegie" + } + ], + "question": "Which location is the geographic outlier among: Bang Khae Nuea, Yên Phụ, Cao Bằng, Nishiwaki, Carnegie?", + "ground_truth": { + "answer": "Carnegie", + "outlier_distance_km": 6088.7, + "second_furthest_km": 3154.3, + "clarity_ratio": 1.93, + "median_distance_km": 1991.8, + "distances_to_centroid": { + "Bang Khae Nuea": 1991.8, + "Yên Phụ": 1760.0, + "Cao Bằng": 1844.7, + "Nishiwaki": 3154.3, + "Carnegie": 6088.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bang Khae Nuea: (13.71°, 100.39°)", + " Yên Phụ: (21.03°, 105.83°)", + " Cao Bằng: (22.67°, 106.26°)", + " Nishiwaki: (34.98°, 134.97°)", + " Carnegie: (-37.89°, 145.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carnegie: 6088.7 km from centroid", + " Nishiwaki: 3154.3 km from centroid", + " Bang Khae Nuea: 1991.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carnegie", + "FINAL ANSWER: Carnegie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + }, + { + "lat": 41.23756, + "lon": -80.81842, + "name": "Warren" + } + ], + "question": "Which location is the geographic outlier among: Seven Hills, Eight Mile Plains, Lidcombe, Merrylands, Warren?", + "ground_truth": { + "answer": "Warren", + "outlier_distance_km": 17323.9, + "second_furthest_km": 5026.4, + "clarity_ratio": 3.45, + "median_distance_km": 4903.3, + "distances_to_centroid": { + "Seven Hills": 4892.1, + "Eight Mile Plains": 5026.4, + "Lidcombe": 4903.3, + "Merrylands": 4897.6, + "Warren": 17323.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Seven Hills: (-33.78°, 150.93°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " Lidcombe: (-33.86°, 151.04°)", + " Merrylands: (-33.83°, 150.98°)", + " Warren: (41.24°, -80.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Warren: 17323.9 km from centroid", + " Eight Mile Plains: 5026.4 km from centroid", + " Lidcombe: 4903.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Warren", + "FINAL ANSWER: Warren" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.64397, + "lon": -53.60633, + "name": "Cruz Alta" + }, + { + "lat": -8.66667, + "lon": -35.71667, + "name": "Catende" + }, + { + "lat": -5.73333, + "lon": -44.15833, + "name": "Fortuna" + }, + { + "lat": -22.48194, + "lon": -47.45667, + "name": "Cordeirópolis" + }, + { + "lat": 6.42389, + "lon": 124.77833, + "name": "Bañga" + } + ], + "question": "Which location is the geographic outlier among: Cruz Alta, Catende, Fortuna, Cordeirópolis, Bañga?", + "ground_truth": { + "answer": "Bañga", + "outlier_distance_km": 15153.5, + "second_furthest_km": 4767.9, + "clarity_ratio": 3.18, + "median_distance_km": 4014.9, + "distances_to_centroid": { + "Cruz Alta": 4767.9, + "Catende": 2701.0, + "Fortuna": 3678.2, + "Cordeirópolis": 4014.9, + "Bañga": 15153.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cruz Alta: (-28.64°, -53.61°)", + " Catende: (-8.67°, -35.72°)", + " Fortuna: (-5.73°, -44.16°)", + " Cordeirópolis: (-22.48°, -47.46°)", + " Bañga: (6.42°, 124.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bañga: 15153.5 km from centroid", + " Cruz Alta: 4767.9 km from centroid", + " Cordeirópolis: 4014.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bañga", + "FINAL ANSWER: Bañga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.62528, + "lon": 119.71333, + "name": "Cuijiaji" + }, + { + "lat": 18.66206, + "lon": 105.75575, + "name": "Nghi Xuân" + }, + { + "lat": 13.78528, + "lon": 100.66958, + "name": "Bueng Kum" + }, + { + "lat": 30.66134, + "lon": 117.47783, + "name": "Chizhou" + }, + { + "lat": -33.73333, + "lon": 151.0, + "name": "Castle Hill" + } + ], + "question": "Which location is the geographic outlier among: Cuijiaji, Nghi Xuân, Bueng Kum, Chizhou, Castle Hill?", + "ground_truth": { + "answer": "Castle Hill", + "outlier_distance_km": 6226.5, + "second_furthest_km": 2605.9, + "clarity_ratio": 2.39, + "median_distance_km": 1974.3, + "distances_to_centroid": { + "Cuijiaji": 2605.9, + "Nghi Xuân": 1532.5, + "Bueng Kum": 1974.3, + "Chizhou": 1947.2, + "Castle Hill": 6226.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cuijiaji: (36.63°, 119.71°)", + " Nghi Xuân: (18.66°, 105.76°)", + " Bueng Kum: (13.79°, 100.67°)", + " Chizhou: (30.66°, 117.48°)", + " Castle Hill: (-33.73°, 151.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Castle Hill: 6226.5 km from centroid", + " Cuijiaji: 2605.9 km from centroid", + " Bueng Kum: 1974.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Castle Hill", + "FINAL ANSWER: Castle Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.38673, + "lon": 0.30367, + "name": "Hartley" + }, + { + "lat": 51.48333, + "lon": 7.55, + "name": "Aplerbeck" + }, + { + "lat": 52.1653, + "lon": 8.85996, + "name": "Vlotho" + }, + { + "lat": 54.59682, + "lon": -5.92541, + "name": "Belfast" + }, + { + "lat": -23.47544, + "lon": -46.60609, + "name": "Tucuruvi" + } + ], + "question": "Which location is the geographic outlier among: Hartley, Aplerbeck, Vlotho, Belfast, Tucuruvi?", + "ground_truth": { + "answer": "Tucuruvi", + "outlier_distance_km": 7912.4, + "second_furthest_km": 2078.6, + "clarity_ratio": 3.81, + "median_distance_km": 1961.8, + "distances_to_centroid": { + "Hartley": 1680.3, + "Aplerbeck": 1961.8, + "Vlotho": 2078.6, + "Belfast": 1933.2, + "Tucuruvi": 7912.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hartley: (51.39°, 0.30°)", + " Aplerbeck: (51.48°, 7.55°)", + " Vlotho: (52.17°, 8.86°)", + " Belfast: (54.60°, -5.93°)", + " Tucuruvi: (-23.48°, -46.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tucuruvi: 7912.4 km from centroid", + " Vlotho: 2078.6 km from centroid", + " Aplerbeck: 1961.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tucuruvi", + "FINAL ANSWER: Tucuruvi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.55333, + "lon": 76.88972, + "name": "Dhārni" + }, + { + "lat": 8.7498, + "lon": 78.13112, + "name": "Muttayyāpuram" + }, + { + "lat": 36.75541, + "lon": 81.60765, + "name": "Arix" + }, + { + "lat": 12.45795, + "lon": 75.95904, + "name": "Kushālnagar" + }, + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + } + ], + "question": "Which location is the geographic outlier among: Dhārni, Muttayyāpuram, Arix, Kushālnagar, Epsom?", + "ground_truth": { + "answer": "Epsom", + "outlier_distance_km": 9465.9, + "second_furthest_km": 3524.0, + "clarity_ratio": 2.69, + "median_distance_km": 2637.1, + "distances_to_centroid": { + "Dhārni": 2637.1, + "Muttayyāpuram": 2126.1, + "Arix": 3524.0, + "Kushālnagar": 2391.4, + "Epsom": 9465.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dhārni: (21.55°, 76.89°)", + " Muttayyāpuram: (8.75°, 78.13°)", + " Arix: (36.76°, 81.61°)", + " Kushālnagar: (12.46°, 75.96°)", + " Epsom: (-36.89°, 174.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Epsom: 9465.9 km from centroid", + " Arix: 3524.0 km from centroid", + " Dhārni: 2637.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Epsom", + "FINAL ANSWER: Epsom" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.82499, + "lon": -79.29872, + "name": "Milliken" + }, + { + "lat": 32.2504, + "lon": -101.47874, + "name": "Big Spring" + }, + { + "lat": 45.63922, + "lon": -73.82757, + "name": "Sainte-Thérèse" + }, + { + "lat": 34.54002, + "lon": -112.4685, + "name": "Prescott" + }, + { + "lat": 53.11254, + "lon": 6.0989, + "name": "Drachten" + } + ], + "question": "Which location is the geographic outlier among: Milliken, Big Spring, Sainte-Thérèse, Prescott, Drachten?", + "ground_truth": { + "answer": "Drachten", + "outlier_distance_km": 5709.9, + "second_furthest_km": 3577.6, + "clarity_ratio": 1.6, + "median_distance_km": 2792.7, + "distances_to_centroid": { + "Milliken": 618.2, + "Big Spring": 2792.7, + "Sainte-Thérèse": 438.8, + "Prescott": 3577.6, + "Drachten": 5709.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Milliken: (43.82°, -79.30°)", + " Big Spring: (32.25°, -101.48°)", + " Sainte-Thérèse: (45.64°, -73.83°)", + " Prescott: (34.54°, -112.47°)", + " Drachten: (53.11°, 6.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Drachten: 5709.9 km from centroid", + " Prescott: 3577.6 km from centroid", + " Big Spring: 2792.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Drachten", + "FINAL ANSWER: Drachten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.17775, + "lon": -40.66949, + "name": "Crateús" + }, + { + "lat": -17.79806, + "lon": -50.92806, + "name": "Rio Verde" + }, + { + "lat": -6.0, + "lon": -40.28333, + "name": "São João dos Inhamuns" + }, + { + "lat": -6.78889, + "lon": -39.29583, + "name": "Várzea Alegre" + }, + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + } + ], + "question": "Which location is the geographic outlier among: Crateús, Rio Verde, São João dos Inhamuns, Várzea Alegre, Te Atatu South?", + "ground_truth": { + "answer": "Te Atatu South", + "outlier_distance_km": 14265.7, + "second_furthest_km": 5508.7, + "clarity_ratio": 2.59, + "median_distance_km": 4640.9, + "distances_to_centroid": { + "Crateús": 4640.9, + "Rio Verde": 5508.7, + "São João dos Inhamuns": 4575.1, + "Várzea Alegre": 4447.1, + "Te Atatu South": 14265.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Crateús: (-5.18°, -40.67°)", + " Rio Verde: (-17.80°, -50.93°)", + " São João dos Inhamuns: (-6.00°, -40.28°)", + " Várzea Alegre: (-6.79°, -39.30°)", + " Te Atatu South: (-36.86°, 174.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Te Atatu South: 14265.7 km from centroid", + " Rio Verde: 5508.7 km from centroid", + " Crateús: 4640.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Te Atatu South", + "FINAL ANSWER: Te Atatu South" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.95, + "lon": 117.78333, + "name": "Tongling" + }, + { + "lat": 36.23333, + "lon": 137.96667, + "name": "Matsumoto" + }, + { + "lat": 40.76432, + "lon": 120.85327, + "name": "Lianshan" + }, + { + "lat": 20.86481, + "lon": 106.68345, + "name": "Haiphong" + }, + { + "lat": 30.93055, + "lon": 31.69864, + "name": "Awlād Şaqr" + } + ], + "question": "Which location is the geographic outlier among: Tongling, Matsumoto, Lianshan, Haiphong, Awlād Şaqr?", + "ground_truth": { + "answer": "Awlād Şaqr", + "outlier_distance_km": 6632.2, + "second_furthest_km": 3237.6, + "clarity_ratio": 2.05, + "median_distance_km": 1870.1, + "distances_to_centroid": { + "Tongling": 1405.9, + "Matsumoto": 3237.6, + "Lianshan": 1870.1, + "Haiphong": 1285.7, + "Awlād Şaqr": 6632.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tongling: (30.95°, 117.78°)", + " Matsumoto: (36.23°, 137.97°)", + " Lianshan: (40.76°, 120.85°)", + " Haiphong: (20.86°, 106.68°)", + " Awlād Şaqr: (30.93°, 31.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Awlād Şaqr: 6632.2 km from centroid", + " Matsumoto: 3237.6 km from centroid", + " Lianshan: 1870.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Awlād Şaqr", + "FINAL ANSWER: Awlād Şaqr" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.43167, + "lon": -54.05111, + "name": "Paranatinga" + }, + { + "lat": -25.32472, + "lon": -49.31, + "name": "Almirante Tamandaré" + }, + { + "lat": -9.74583, + "lon": -41.88528, + "name": "Sento Sé" + }, + { + "lat": -20.53861, + "lon": -47.40083, + "name": "Franca" + }, + { + "lat": 40.79677, + "lon": -74.48154, + "name": "Morristown" + } + ], + "question": "Which location is the geographic outlier among: Paranatinga, Almirante Tamandaré, Sento Sé, Franca, Morristown?", + "ground_truth": { + "answer": "Morristown", + "outlier_distance_km": 5614.1, + "second_furthest_km": 2209.5, + "clarity_ratio": 2.54, + "median_distance_km": 1758.1, + "distances_to_centroid": { + "Paranatinga": 956.8, + "Almirante Tamandaré": 2209.5, + "Sento Sé": 1342.9, + "Franca": 1758.1, + "Morristown": 5614.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paranatinga: (-14.43°, -54.05°)", + " Almirante Tamandaré: (-25.32°, -49.31°)", + " Sento Sé: (-9.75°, -41.89°)", + " Franca: (-20.54°, -47.40°)", + " Morristown: (40.80°, -74.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morristown: 5614.1 km from centroid", + " Almirante Tamandaré: 2209.5 km from centroid", + " Franca: 1758.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morristown", + "FINAL ANSWER: Morristown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.749, + "lon": -84.38798, + "name": "Atlanta" + }, + { + "lat": 38.88101, + "lon": -77.10428, + "name": "Arlington" + }, + { + "lat": 29.58497, + "lon": -81.20784, + "name": "Palm Coast" + }, + { + "lat": 41.95781, + "lon": -87.76506, + "name": "Portage Park" + }, + { + "lat": 56.22912, + "lon": 51.06098, + "name": "Vyatskiye Polyany" + } + ], + "question": "Which location is the geographic outlier among: Atlanta, Arlington, Palm Coast, Portage Park, Vyatskiye Polyany?", + "ground_truth": { + "answer": "Vyatskiye Polyany", + "outlier_distance_km": 7307.1, + "second_furthest_km": 2667.6, + "clarity_ratio": 2.74, + "median_distance_km": 2617.8, + "distances_to_centroid": { + "Atlanta": 2617.8, + "Arlington": 1822.0, + "Palm Coast": 2576.8, + "Portage Park": 2667.6, + "Vyatskiye Polyany": 7307.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Atlanta: (33.75°, -84.39°)", + " Arlington: (38.88°, -77.10°)", + " Palm Coast: (29.58°, -81.21°)", + " Portage Park: (41.96°, -87.77°)", + " Vyatskiye Polyany: (56.23°, 51.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vyatskiye Polyany: 7307.1 km from centroid", + " Portage Park: 2667.6 km from centroid", + " Atlanta: 2617.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vyatskiye Polyany", + "FINAL ANSWER: Vyatskiye Polyany" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.99456, + "lon": 37.82897, + "name": "Pushkino" + }, + { + "lat": 49.35571, + "lon": 6.1926, + "name": "Yutz" + }, + { + "lat": 49.71754, + "lon": 11.05877, + "name": "Forchheim" + }, + { + "lat": 50.58969, + "lon": 16.81239, + "name": "Ząbkowice Śląskie" + }, + { + "lat": 42.43933, + "lon": -123.33067, + "name": "Grants Pass" + } + ], + "question": "Which location is the geographic outlier among: Pushkino, Yutz, Forchheim, Ząbkowice Śląskie, Grants Pass?", + "ground_truth": { + "answer": "Grants Pass", + "outlier_distance_km": 7885.9, + "second_furthest_km": 3240.9, + "clarity_ratio": 2.43, + "median_distance_km": 1925.0, + "distances_to_centroid": { + "Pushkino": 3240.9, + "Yutz": 1188.4, + "Forchheim": 1531.1, + "Ząbkowice Śląskie": 1925.0, + "Grants Pass": 7885.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pushkino: (55.99°, 37.83°)", + " Yutz: (49.36°, 6.19°)", + " Forchheim: (49.72°, 11.06°)", + " Ząbkowice Śląskie: (50.59°, 16.81°)", + " Grants Pass: (42.44°, -123.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Grants Pass: 7885.9 km from centroid", + " Pushkino: 3240.9 km from centroid", + " Ząbkowice Śląskie: 1925.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Grants Pass", + "FINAL ANSWER: Grants Pass" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.86301, + "lon": 26.89756, + "name": "Koster" + }, + { + "lat": 8.3, + "lon": 38.95, + "name": "‘Alem T’ēna" + }, + { + "lat": -27.97654, + "lon": 27.02423, + "name": "Hennenman" + }, + { + "lat": 5.6658, + "lon": -0.16307, + "name": "Medina Estates" + }, + { + "lat": 37.04339, + "lon": -93.29435, + "name": "Nixa" + } + ], + "question": "Which location is the geographic outlier among: Koster, ‘Alem T’ēna, Hennenman, Medina Estates, Nixa?", + "ground_truth": { + "answer": "Nixa", + "outlier_distance_km": 10327.4, + "second_furthest_km": 4440.2, + "clarity_ratio": 2.33, + "median_distance_km": 4199.7, + "distances_to_centroid": { + "Koster": 4036.4, + "‘Alem T’ēna": 4440.2, + "Hennenman": 4199.7, + "Medina Estates": 693.0, + "Nixa": 10327.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Koster: (-25.86°, 26.90°)", + " ‘Alem T’ēna: (8.30°, 38.95°)", + " Hennenman: (-27.98°, 27.02°)", + " Medina Estates: (5.67°, -0.16°)", + " Nixa: (37.04°, -93.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nixa: 10327.4 km from centroid", + " ‘Alem T’ēna: 4440.2 km from centroid", + " Hennenman: 4199.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nixa", + "FINAL ANSWER: Nixa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.76667, + "lon": 117.78333, + "name": "Liji" + }, + { + "lat": 23.17233, + "lon": 112.28298, + "name": "Lubu" + }, + { + "lat": 14.67333, + "lon": 120.93972, + "name": "Malabon" + }, + { + "lat": 17.03795, + "lon": 81.77597, + "name": "Katheru" + }, + { + "lat": -5.61278, + "lon": -38.76694, + "name": "Jaguaretama" + } + ], + "question": "Which location is the geographic outlier among: Liji, Lubu, Malabon, Katheru, Jaguaretama?", + "ground_truth": { + "answer": "Jaguaretama", + "outlier_distance_km": 13120.1, + "second_furthest_km": 4509.0, + "clarity_ratio": 2.91, + "median_distance_km": 4326.6, + "distances_to_centroid": { + "Liji": 4326.6, + "Lubu": 3567.6, + "Malabon": 4509.0, + "Katheru": 320.0, + "Jaguaretama": 13120.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Liji: (33.77°, 117.78°)", + " Lubu: (23.17°, 112.28°)", + " Malabon: (14.67°, 120.94°)", + " Katheru: (17.04°, 81.78°)", + " Jaguaretama: (-5.61°, -38.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaguaretama: 13120.1 km from centroid", + " Malabon: 4509.0 km from centroid", + " Liji: 4326.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaguaretama", + "FINAL ANSWER: Jaguaretama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.78609, + "lon": -79.33502, + "name": "Pleasant View" + }, + { + "lat": 30.31188, + "lon": -95.45605, + "name": "Conroe" + }, + { + "lat": 45.42067, + "lon": -122.67065, + "name": "Lake Oswego" + }, + { + "lat": 35.26266, + "lon": -77.58164, + "name": "Kinston" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + } + ], + "question": "Which location is the geographic outlier among: Pleasant View, Conroe, Lake Oswego, Kinston, Carlton?", + "ground_truth": { + "answer": "Carlton", + "outlier_distance_km": 18102.7, + "second_furthest_km": 7164.9, + "clarity_ratio": 2.53, + "median_distance_km": 4926.8, + "distances_to_centroid": { + "Pleasant View": 3787.6, + "Conroe": 4926.8, + "Lake Oswego": 7164.9, + "Kinston": 3313.8, + "Carlton": 18102.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pleasant View: (43.79°, -79.34°)", + " Conroe: (30.31°, -95.46°)", + " Lake Oswego: (45.42°, -122.67°)", + " Kinston: (35.26°, -77.58°)", + " Carlton: (-37.80°, 144.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carlton: 18102.7 km from centroid", + " Lake Oswego: 7164.9 km from centroid", + " Conroe: 4926.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carlton", + "FINAL ANSWER: Carlton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.54667, + "lon": -38.71194, + "name": "Santo Amaro" + }, + { + "lat": 7.83389, + "lon": -72.47417, + "name": "Villa del Rosario" + }, + { + "lat": -27.69934, + "lon": -48.53219, + "name": "Ribeirão da Ilha" + }, + { + "lat": -23.62623, + "lon": -46.72828, + "name": "Vila Andrade" + }, + { + "lat": 2.2152, + "lon": 102.2851, + "name": "Kampung Bukit Baharu" + } + ], + "question": "Which location is the geographic outlier among: Santo Amaro, Villa del Rosario, Ribeirão da Ilha, Vila Andrade, Kampung Bukit Baharu?", + "ground_truth": { + "answer": "Kampung Bukit Baharu", + "outlier_distance_km": 13668.8, + "second_furthest_km": 6077.3, + "clarity_ratio": 2.25, + "median_distance_km": 3449.7, + "distances_to_centroid": { + "Santo Amaro": 1956.8, + "Villa del Rosario": 6077.3, + "Ribeirão da Ilha": 3449.7, + "Vila Andrade": 3091.9, + "Kampung Bukit Baharu": 13668.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santo Amaro: (-12.55°, -38.71°)", + " Villa del Rosario: (7.83°, -72.47°)", + " Ribeirão da Ilha: (-27.70°, -48.53°)", + " Vila Andrade: (-23.63°, -46.73°)", + " Kampung Bukit Baharu: (2.22°, 102.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kampung Bukit Baharu: 13668.8 km from centroid", + " Villa del Rosario: 6077.3 km from centroid", + " Ribeirão da Ilha: 3449.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kampung Bukit Baharu", + "FINAL ANSWER: Kampung Bukit Baharu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.16667, + "lon": 145.16667, + "name": "Langwarrin" + }, + { + "lat": -33.80383, + "lon": 150.98768, + "name": "Westmead" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + }, + { + "lat": -38.23291, + "lon": -72.33292, + "name": "Victoria" + } + ], + "question": "Which location is the geographic outlier among: Langwarrin, Westmead, Perth, Albany, Victoria?", + "ground_truth": { + "answer": "Victoria", + "outlier_distance_km": 11656.3, + "second_furthest_km": 5360.3, + "clarity_ratio": 2.17, + "median_distance_km": 4719.5, + "distances_to_centroid": { + "Langwarrin": 4719.5, + "Westmead": 5360.3, + "Perth": 2279.6, + "Albany": 2388.4, + "Victoria": 11656.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Langwarrin: (-38.17°, 145.17°)", + " Westmead: (-33.80°, 150.99°)", + " Perth: (-31.95°, 115.86°)", + " Albany: (-35.03°, 117.88°)", + " Victoria: (-38.23°, -72.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Victoria: 11656.3 km from centroid", + " Westmead: 5360.3 km from centroid", + " Langwarrin: 4719.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Victoria", + "FINAL ANSWER: Victoria" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.095, + "lon": -50.16194, + "name": "Ponta Grossa" + }, + { + "lat": -3.92333, + "lon": -40.88944, + "name": "Ibiapina" + }, + { + "lat": 4.29005, + "lon": -74.81612, + "name": "Flandes" + }, + { + "lat": -1.8, + "lon": -53.48, + "name": "Prainha" + }, + { + "lat": 45.54672, + "lon": 11.5475, + "name": "Vicenza" + } + ], + "question": "Which location is the geographic outlier among: Ponta Grossa, Ibiapina, Flandes, Prainha, Vicenza?", + "ground_truth": { + "answer": "Vicenza", + "outlier_distance_km": 6913.0, + "second_furthest_km": 3688.8, + "clarity_ratio": 1.87, + "median_distance_km": 3344.9, + "distances_to_centroid": { + "Ponta Grossa": 3344.9, + "Ibiapina": 862.4, + "Flandes": 3688.8, + "Prainha": 1463.9, + "Vicenza": 6913.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ponta Grossa: (-25.09°, -50.16°)", + " Ibiapina: (-3.92°, -40.89°)", + " Flandes: (4.29°, -74.82°)", + " Prainha: (-1.80°, -53.48°)", + " Vicenza: (45.55°, 11.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vicenza: 6913.0 km from centroid", + " Flandes: 3688.8 km from centroid", + " Ponta Grossa: 3344.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vicenza", + "FINAL ANSWER: Vicenza" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.82345, + "lon": 2.29025, + "name": "Vanves" + }, + { + "lat": 48.82319, + "lon": 1.9541, + "name": "Plaisir" + }, + { + "lat": 49.71754, + "lon": 11.05877, + "name": "Forchheim" + }, + { + "lat": 37.18856, + "lon": -3.71887, + "name": "Santafé" + }, + { + "lat": -21.03306, + "lon": -44.75806, + "name": "Bom Sucesso" + } + ], + "question": "Which location is the geographic outlier among: Vanves, Plaisir, Forchheim, Santafé, Bom Sucesso?", + "ground_truth": { + "answer": "Bom Sucesso", + "outlier_distance_km": 7218.3, + "second_furthest_km": 2389.3, + "clarity_ratio": 3.02, + "median_distance_km": 1940.4, + "distances_to_centroid": { + "Vanves": 1940.4, + "Plaisir": 1929.8, + "Forchheim": 2389.3, + "Santafé": 565.0, + "Bom Sucesso": 7218.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vanves: (48.82°, 2.29°)", + " Plaisir: (48.82°, 1.95°)", + " Forchheim: (49.72°, 11.06°)", + " Santafé: (37.19°, -3.72°)", + " Bom Sucesso: (-21.03°, -44.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bom Sucesso: 7218.3 km from centroid", + " Forchheim: 2389.3 km from centroid", + " Vanves: 1940.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bom Sucesso", + "FINAL ANSWER: Bom Sucesso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.39015, + "lon": 30.78742, + "name": "Fernie" + }, + { + "lat": 12.45389, + "lon": 4.1975, + "name": "Birnin Kebbi" + }, + { + "lat": 5.80893, + "lon": -0.35026, + "name": "Nsawam" + }, + { + "lat": 30.46597, + "lon": 30.93199, + "name": "Munūf" + }, + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + } + ], + "question": "Which location is the geographic outlier among: Fernie, Birnin Kebbi, Nsawam, Munūf, Brisbane?", + "ground_truth": { + "answer": "Brisbane", + "outlier_distance_km": 11849.4, + "second_furthest_km": 4951.5, + "clarity_ratio": 2.39, + "median_distance_km": 4611.7, + "distances_to_centroid": { + "Fernie": 3141.3, + "Birnin Kebbi": 4611.7, + "Nsawam": 4951.5, + "Munūf": 3754.3, + "Brisbane": 11849.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fernie: (-26.39°, 30.79°)", + " Birnin Kebbi: (12.45°, 4.20°)", + " Nsawam: (5.81°, -0.35°)", + " Munūf: (30.47°, 30.93°)", + " Brisbane: (-27.47°, 153.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brisbane: 11849.4 km from centroid", + " Nsawam: 4951.5 km from centroid", + " Birnin Kebbi: 4611.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brisbane", + "FINAL ANSWER: Brisbane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + }, + { + "lat": -37.75405, + "lon": 145.14864, + "name": "Templestowe" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": 53.8426, + "lon": -1.63754, + "name": "Horsforth" + } + ], + "question": "Which location is the geographic outlier among: Saint Albans, West Pennant Hills, Templestowe, Bairnsdale, Horsforth?", + "ground_truth": { + "answer": "Horsforth", + "outlier_distance_km": 13561.9, + "second_furthest_km": 3730.5, + "clarity_ratio": 3.64, + "median_distance_km": 3620.9, + "distances_to_centroid": { + "Saint Albans": 3400.6, + "West Pennant Hills": 3730.5, + "Templestowe": 3428.1, + "Bairnsdale": 3620.9, + "Horsforth": 13561.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Albans: (-37.73°, 144.80°)", + " West Pennant Hills: (-33.75°, 151.05°)", + " Templestowe: (-37.75°, 145.15°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Horsforth: (53.84°, -1.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Horsforth: 13561.9 km from centroid", + " West Pennant Hills: 3730.5 km from centroid", + " Bairnsdale: 3620.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Horsforth", + "FINAL ANSWER: Horsforth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.56853, + "lon": 42.02388, + "name": "Murom" + }, + { + "lat": 52.73416, + "lon": 4.77682, + "name": "Harenkarspel" + }, + { + "lat": 36.79014, + "lon": 14.7028, + "name": "Scicli" + }, + { + "lat": 41.40269, + "lon": 2.1162, + "name": "Sarrià" + }, + { + "lat": 43.15357, + "lon": -93.20104, + "name": "Mason City" + } + ], + "question": "Which location is the geographic outlier among: Murom, Harenkarspel, Scicli, Sarrià, Mason City?", + "ground_truth": { + "answer": "Mason City", + "outlier_distance_km": 6557.4, + "second_furthest_km": 3460.6, + "clarity_ratio": 1.89, + "median_distance_km": 1989.8, + "distances_to_centroid": { + "Murom": 3460.6, + "Harenkarspel": 1080.9, + "Scicli": 1989.8, + "Sarrià": 818.4, + "Mason City": 6557.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Murom: (55.57°, 42.02°)", + " Harenkarspel: (52.73°, 4.78°)", + " Scicli: (36.79°, 14.70°)", + " Sarrià: (41.40°, 2.12°)", + " Mason City: (43.15°, -93.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mason City: 6557.4 km from centroid", + " Murom: 3460.6 km from centroid", + " Scicli: 1989.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mason City", + "FINAL ANSWER: Mason City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.53472, + "lon": -39.11833, + "name": "Porteiras" + }, + { + "lat": -10.95817, + "lon": -38.79084, + "name": "Tucano" + }, + { + "lat": -23.72576, + "lon": -46.7024, + "name": "Cidade Dutra" + }, + { + "lat": -6.4075, + "lon": -41.74556, + "name": "Valença do Piauí" + }, + { + "lat": 29.2376, + "lon": 30.78944, + "name": "Iţsā" + } + ], + "question": "Which location is the geographic outlier among: Porteiras, Tucano, Cidade Dutra, Valença do Piauí, Iţsā?", + "ground_truth": { + "answer": "Iţsā", + "outlier_distance_km": 7178.7, + "second_furthest_km": 3047.9, + "clarity_ratio": 2.36, + "median_distance_km": 1644.5, + "distances_to_centroid": { + "Porteiras": 1388.9, + "Tucano": 1508.5, + "Cidade Dutra": 3047.9, + "Valença do Piauí": 1644.5, + "Iţsā": 7178.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porteiras: (-7.53°, -39.12°)", + " Tucano: (-10.96°, -38.79°)", + " Cidade Dutra: (-23.73°, -46.70°)", + " Valença do Piauí: (-6.41°, -41.75°)", + " Iţsā: (29.24°, 30.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Iţsā: 7178.7 km from centroid", + " Cidade Dutra: 3047.9 km from centroid", + " Valença do Piauí: 1644.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Iţsā", + "FINAL ANSWER: Iţsā" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.11319, + "lon": 29.04454, + "name": "Siyabuswa" + }, + { + "lat": -25.78842, + "lon": 31.05319, + "name": "Barberton" + }, + { + "lat": -32.77477, + "lon": 26.63376, + "name": "Fort Beaufort" + }, + { + "lat": 9.18059, + "lon": 7.17939, + "name": "Suleja" + }, + { + "lat": 45.43722, + "lon": 40.5704, + "name": "Kropotkin" + } + ], + "question": "Which location is the geographic outlier among: Siyabuswa, Barberton, Fort Beaufort, Suleja, Kropotkin?", + "ground_truth": { + "answer": "Kropotkin", + "outlier_distance_km": 5858.7, + "second_furthest_km": 2998.3, + "clarity_ratio": 1.95, + "median_distance_km": 2748.5, + "distances_to_centroid": { + "Siyabuswa": 2158.4, + "Barberton": 2264.8, + "Fort Beaufort": 2998.3, + "Suleja": 2748.5, + "Kropotkin": 5858.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Siyabuswa: (-25.11°, 29.04°)", + " Barberton: (-25.79°, 31.05°)", + " Fort Beaufort: (-32.77°, 26.63°)", + " Suleja: (9.18°, 7.18°)", + " Kropotkin: (45.44°, 40.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kropotkin: 5858.7 km from centroid", + " Fort Beaufort: 2998.3 km from centroid", + " Suleja: 2748.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kropotkin", + "FINAL ANSWER: Kropotkin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.30472, + "lon": -43.765, + "name": "Carinhanha" + }, + { + "lat": -1.52833, + "lon": -49.21667, + "name": "Muaná" + }, + { + "lat": -15.24889, + "lon": -40.24778, + "name": "Itapetinga" + }, + { + "lat": -23.57595, + "lon": -46.46298, + "name": "Parque Do Carmo" + }, + { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + } + ], + "question": "Which location is the geographic outlier among: Carinhanha, Muaná, Itapetinga, Parque Do Carmo, Papakura?", + "ground_truth": { + "answer": "Papakura", + "outlier_distance_km": 13838.8, + "second_furthest_km": 5582.8, + "clarity_ratio": 2.48, + "median_distance_km": 4742.5, + "distances_to_centroid": { + "Carinhanha": 4580.9, + "Muaná": 5582.8, + "Itapetinga": 4189.6, + "Parque Do Carmo": 4742.5, + "Papakura": 13838.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carinhanha: (-14.30°, -43.77°)", + " Muaná: (-1.53°, -49.22°)", + " Itapetinga: (-15.25°, -40.25°)", + " Parque Do Carmo: (-23.58°, -46.46°)", + " Papakura: (-37.06°, 174.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Papakura: 13838.8 km from centroid", + " Muaná: 5582.8 km from centroid", + " Parque Do Carmo: 4742.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Papakura", + "FINAL ANSWER: Papakura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.12056, + "lon": 17.03761, + "name": "Rejon placu Świętego Macieja" + }, + { + "lat": 48.8162, + "lon": 2.31393, + "name": "Montrouge" + }, + { + "lat": 52.51108, + "lon": 4.67165, + "name": "Heemskerk" + }, + { + "lat": 36.82145, + "lon": 14.95132, + "name": "Rosolini" + }, + { + "lat": -25.44141, + "lon": 27.51114, + "name": "Hartbeestfontein-A" + } + ], + "question": "Which location is the geographic outlier among: Rejon placu Świętego Macieja, Montrouge, Heemskerk, Rosolini, Hartbeestfontein-A?", + "ground_truth": { + "answer": "Hartbeestfontein-A", + "outlier_distance_km": 6645.1, + "second_furthest_km": 2302.3, + "clarity_ratio": 2.89, + "median_distance_km": 2063.6, + "distances_to_centroid": { + "Rejon placu Świętego Macieja": 2063.6, + "Montrouge": 2005.2, + "Heemskerk": 2302.3, + "Rosolini": 475.6, + "Hartbeestfontein-A": 6645.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rejon placu Świętego Macieja: (51.12°, 17.04°)", + " Montrouge: (48.82°, 2.31°)", + " Heemskerk: (52.51°, 4.67°)", + " Rosolini: (36.82°, 14.95°)", + " Hartbeestfontein-A: (-25.44°, 27.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hartbeestfontein-A: 6645.1 km from centroid", + " Heemskerk: 2302.3 km from centroid", + " Rejon placu Świętego Macieja: 2063.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hartbeestfontein-A", + "FINAL ANSWER: Hartbeestfontein-A" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.48921, + "lon": -1.51921, + "name": "Anglet" + }, + { + "lat": 37.13548, + "lon": -3.67029, + "name": "Las Gabias" + }, + { + "lat": 55.71667, + "lon": 37.78333, + "name": "Novokuz’minki" + }, + { + "lat": 52.01667, + "lon": 4.70833, + "name": "Gouda" + }, + { + "lat": -33.14091, + "lon": -59.31257, + "name": "Gualeguay" + } + ], + "question": "Which location is the geographic outlier among: Anglet, Las Gabias, Novokuz’minki, Gouda, Gualeguay?", + "ground_truth": { + "answer": "Gualeguay", + "outlier_distance_km": 9173.9, + "second_furthest_km": 4269.9, + "clarity_ratio": 2.15, + "median_distance_km": 2447.8, + "distances_to_centroid": { + "Anglet": 1407.0, + "Las Gabias": 680.7, + "Novokuz’minki": 4269.9, + "Gouda": 2447.8, + "Gualeguay": 9173.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Anglet: (43.49°, -1.52°)", + " Las Gabias: (37.14°, -3.67°)", + " Novokuz’minki: (55.72°, 37.78°)", + " Gouda: (52.02°, 4.71°)", + " Gualeguay: (-33.14°, -59.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gualeguay: 9173.9 km from centroid", + " Novokuz’minki: 4269.9 km from centroid", + " Gouda: 2447.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gualeguay", + "FINAL ANSWER: Gualeguay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.60556, + "lon": -55.33167, + "name": "Aveiro" + }, + { + "lat": -1.85302, + "lon": -65.57426, + "name": "Maraã" + }, + { + "lat": -22.83917, + "lon": -42.10278, + "name": "São Pedro da Aldeia" + }, + { + "lat": -23.51567, + "lon": -46.49373, + "name": "Ponte Rasa" + }, + { + "lat": -38.18333, + "lon": 145.08333, + "name": "Mount Eliza" + } + ], + "question": "Which location is the geographic outlier among: Aveiro, Maraã, São Pedro da Aldeia, Ponte Rasa, Mount Eliza?", + "ground_truth": { + "answer": "Mount Eliza", + "outlier_distance_km": 13357.8, + "second_furthest_km": 6017.4, + "clarity_ratio": 2.22, + "median_distance_km": 4888.1, + "distances_to_centroid": { + "Aveiro": 4888.1, + "Maraã": 6017.4, + "São Pedro da Aldeia": 3086.7, + "Ponte Rasa": 3539.8, + "Mount Eliza": 13357.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aveiro: (-3.61°, -55.33°)", + " Maraã: (-1.85°, -65.57°)", + " São Pedro da Aldeia: (-22.84°, -42.10°)", + " Ponte Rasa: (-23.52°, -46.49°)", + " Mount Eliza: (-38.18°, 145.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mount Eliza: 13357.8 km from centroid", + " Maraã: 6017.4 km from centroid", + " Aveiro: 4888.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mount Eliza", + "FINAL ANSWER: Mount Eliza" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.51552, + "lon": 31.34629, + "name": "Minyā al Qamḩ" + }, + { + "lat": 11.2471, + "lon": 10.561, + "name": "Kari" + }, + { + "lat": -26.71667, + "lon": 27.1, + "name": "Potchefstroom" + }, + { + "lat": 30.29636, + "lon": 31.74633, + "name": "Al ‘Āshir min Ramaḑān" + }, + { + "lat": 22.39309, + "lon": -97.93857, + "name": "Altamira" + } + ], + "question": "Which location is the geographic outlier among: Minyā al Qamḩ, Kari, Potchefstroom, Al ‘Āshir min Ramaḑān, Altamira?", + "ground_truth": { + "answer": "Altamira", + "outlier_distance_km": 10285.7, + "second_furthest_km": 5316.2, + "clarity_ratio": 1.93, + "median_distance_km": 3697.1, + "distances_to_centroid": { + "Minyā al Qamḩ": 3671.8, + "Kari": 1115.4, + "Potchefstroom": 5316.2, + "Al ‘Āshir min Ramaḑān": 3697.1, + "Altamira": 10285.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Minyā al Qamḩ: (30.52°, 31.35°)", + " Kari: (11.25°, 10.56°)", + " Potchefstroom: (-26.72°, 27.10°)", + " Al ‘Āshir min Ramaḑān: (30.30°, 31.75°)", + " Altamira: (22.39°, -97.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Altamira: 10285.7 km from centroid", + " Potchefstroom: 5316.2 km from centroid", + " Al ‘Āshir min Ramaḑān: 3697.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Altamira", + "FINAL ANSWER: Altamira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.45667, + "lon": -47.53028, + "name": "Santa Gertrudes" + }, + { + "lat": -9.58833, + "lon": -67.5325, + "name": "Porto Acre" + }, + { + "lat": -21.18694, + "lon": -43.97583, + "name": "Barroso" + }, + { + "lat": -20.91806, + "lon": -49.44528, + "name": "Bady Bassitt" + }, + { + "lat": 45.46427, + "lon": 9.18951, + "name": "Milan" + } + ], + "question": "Which location is the geographic outlier among: Santa Gertrudes, Porto Acre, Barroso, Bady Bassitt, Milan?", + "ground_truth": { + "answer": "Milan", + "outlier_distance_km": 7481.9, + "second_furthest_km": 3078.5, + "clarity_ratio": 2.43, + "median_distance_km": 2033.5, + "distances_to_centroid": { + "Santa Gertrudes": 2033.5, + "Porto Acre": 3078.5, + "Barroso": 1774.3, + "Bady Bassitt": 1979.4, + "Milan": 7481.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Gertrudes: (-22.46°, -47.53°)", + " Porto Acre: (-9.59°, -67.53°)", + " Barroso: (-21.19°, -43.98°)", + " Bady Bassitt: (-20.92°, -49.45°)", + " Milan: (45.46°, 9.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Milan: 7481.9 km from centroid", + " Porto Acre: 3078.5 km from centroid", + " Santa Gertrudes: 2033.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Milan", + "FINAL ANSWER: Milan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.23013, + "lon": 115.78128, + "name": "Kwinana" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": 39.92595, + "lon": -75.11962, + "name": "Camden" + } + ], + "question": "Which location is the geographic outlier among: Kwinana, Gosnells, Randwick, Armidale, Camden?", + "ground_truth": { + "answer": "Camden", + "outlier_distance_km": 17252.9, + "second_furthest_km": 6157.4, + "clarity_ratio": 2.8, + "median_distance_km": 6117.9, + "distances_to_centroid": { + "Kwinana": 2882.2, + "Gosnells": 2893.1, + "Randwick": 6117.9, + "Armidale": 6157.4, + "Camden": 17252.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kwinana: (-32.23°, 115.78°)", + " Gosnells: (-32.08°, 116.01°)", + " Randwick: (-33.91°, 151.25°)", + " Armidale: (-30.50°, 151.67°)", + " Camden: (39.93°, -75.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camden: 17252.9 km from centroid", + " Armidale: 6157.4 km from centroid", + " Randwick: 6117.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camden", + "FINAL ANSWER: Camden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.76323, + "lon": -121.16384, + "name": "Granite Bay" + }, + { + "lat": 42.50982, + "lon": -70.94949, + "name": "South Peabody" + }, + { + "lat": 40.3934, + "lon": -82.48572, + "name": "Mount Vernon" + }, + { + "lat": 42.04114, + "lon": -87.69006, + "name": "Evanston" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + } + ], + "question": "Which location is the geographic outlier among: Granite Bay, South Peabody, Mount Vernon, Evanston, Te Atatu Peninsula?", + "ground_truth": { + "answer": "Te Atatu Peninsula", + "outlier_distance_km": 16716.8, + "second_furthest_km": 7754.1, + "clarity_ratio": 2.16, + "median_distance_km": 4915.6, + "distances_to_centroid": { + "Granite Bay": 7754.1, + "South Peabody": 3589.2, + "Mount Vernon": 4461.7, + "Evanston": 4915.6, + "Te Atatu Peninsula": 16716.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Granite Bay: (38.76°, -121.16°)", + " South Peabody: (42.51°, -70.95°)", + " Mount Vernon: (40.39°, -82.49°)", + " Evanston: (42.04°, -87.69°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Te Atatu Peninsula: 16716.8 km from centroid", + " Granite Bay: 7754.1 km from centroid", + " Evanston: 4915.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Te Atatu Peninsula", + "FINAL ANSWER: Te Atatu Peninsula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.9133, + "lon": -93.50329, + "name": "Minnetonka" + }, + { + "lat": 42.04177, + "lon": -70.67226, + "name": "Duxbury" + }, + { + "lat": 20.68812, + "lon": -88.19936, + "name": "Valladolid" + }, + { + "lat": 42.36837, + "lon": -83.35271, + "name": "Livonia" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + } + ], + "question": "Which location is the geographic outlier among: Minnetonka, Duxbury, Valladolid, Livonia, Doncaster East?", + "ground_truth": { + "answer": "Doncaster East", + "outlier_distance_km": 18280.7, + "second_furthest_km": 5571.7, + "clarity_ratio": 3.28, + "median_distance_km": 5158.7, + "distances_to_centroid": { + "Minnetonka": 5571.7, + "Duxbury": 3721.2, + "Valladolid": 5158.7, + "Livonia": 4717.6, + "Doncaster East": 18280.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Minnetonka: (44.91°, -93.50°)", + " Duxbury: (42.04°, -70.67°)", + " Valladolid: (20.69°, -88.20°)", + " Livonia: (42.37°, -83.35°)", + " Doncaster East: (-37.79°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doncaster East: 18280.7 km from centroid", + " Minnetonka: 5571.7 km from centroid", + " Valladolid: 5158.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doncaster East", + "FINAL ANSWER: Doncaster East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.81047, + "lon": 102.02881, + "name": "Chaiyaphum" + }, + { + "lat": 34.83056, + "lon": 116.81944, + "name": "Anguo" + }, + { + "lat": 11.10983, + "lon": 77.98883, + "name": "Pottanūr" + }, + { + "lat": 30.80767, + "lon": 108.40846, + "name": "Chenjiaba" + }, + { + "lat": -22.9527, + "lon": -46.54418, + "name": "Bragança Paulista" + } + ], + "question": "Which location is the geographic outlier among: Chaiyaphum, Anguo, Pottanūr, Chenjiaba, Bragança Paulista?", + "ground_truth": { + "answer": "Bragança Paulista", + "outlier_distance_km": 13471.7, + "second_furthest_km": 5067.4, + "clarity_ratio": 2.66, + "median_distance_km": 4184.9, + "distances_to_centroid": { + "Chaiyaphum": 3259.2, + "Anguo": 5067.4, + "Pottanūr": 746.8, + "Chenjiaba": 4184.9, + "Bragança Paulista": 13471.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chaiyaphum: (15.81°, 102.03°)", + " Anguo: (34.83°, 116.82°)", + " Pottanūr: (11.11°, 77.99°)", + " Chenjiaba: (30.81°, 108.41°)", + " Bragança Paulista: (-22.95°, -46.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bragança Paulista: 13471.7 km from centroid", + " Anguo: 5067.4 km from centroid", + " Chenjiaba: 4184.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bragança Paulista", + "FINAL ANSWER: Bragança Paulista" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.04623, + "lon": -96.99417, + "name": "Lewisville" + }, + { + "lat": 33.89807, + "lon": -118.19535, + "name": "East Rancho Dominguez" + }, + { + "lat": 40.03122, + "lon": -75.04434, + "name": "Tacony" + }, + { + "lat": 31.57851, + "lon": -84.15574, + "name": "Albany" + }, + { + "lat": -32.02957, + "lon": -61.22097, + "name": "Gálvez" + } + ], + "question": "Which location is the geographic outlier among: Lewisville, East Rancho Dominguez, Tacony, Albany, Gálvez?", + "ground_truth": { + "answer": "Gálvez", + "outlier_distance_km": 6539.9, + "second_furthest_km": 3349.1, + "clarity_ratio": 1.95, + "median_distance_km": 2375.8, + "distances_to_centroid": { + "Lewisville": 1628.4, + "East Rancho Dominguez": 3349.1, + "Tacony": 2375.8, + "Albany": 1179.8, + "Gálvez": 6539.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lewisville: (33.05°, -96.99°)", + " East Rancho Dominguez: (33.90°, -118.20°)", + " Tacony: (40.03°, -75.04°)", + " Albany: (31.58°, -84.16°)", + " Gálvez: (-32.03°, -61.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gálvez: 6539.9 km from centroid", + " East Rancho Dominguez: 3349.1 km from centroid", + " Tacony: 2375.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gálvez", + "FINAL ANSWER: Gálvez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": 43.64415, + "lon": -79.56985, + "name": "Etobicoke" + } + ], + "question": "Which location is the geographic outlier among: Redbank Plains, Saint Albans, Palm Beach, Caroline Springs, Etobicoke?", + "ground_truth": { + "answer": "Etobicoke", + "outlier_distance_km": 17097.9, + "second_furthest_km": 5242.2, + "clarity_ratio": 3.26, + "median_distance_km": 5181.1, + "distances_to_centroid": { + "Redbank Plains": 5181.1, + "Saint Albans": 4617.0, + "Palm Beach": 5242.2, + "Caroline Springs": 4611.9, + "Etobicoke": 17097.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Redbank Plains: (-27.65°, 152.86°)", + " Saint Albans: (-37.73°, 144.80°)", + " Palm Beach: (-28.12°, 153.47°)", + " Caroline Springs: (-37.74°, 144.74°)", + " Etobicoke: (43.64°, -79.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Etobicoke: 17097.9 km from centroid", + " Palm Beach: 5242.2 km from centroid", + " Redbank Plains: 5181.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Etobicoke", + "FINAL ANSWER: Etobicoke" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.5301, + "lon": -122.03262, + "name": "Issaquah" + }, + { + "lat": 21.36022, + "lon": -157.91838, + "name": "Aliamanu / Salt Lakes / Foster Village" + }, + { + "lat": 46.89028, + "lon": -71.37222, + "name": "La Haute-Saint-Charles" + }, + { + "lat": 49.16667, + "lon": -122.8, + "name": "Fleetwood" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + } + ], + "question": "Which location is the geographic outlier among: Issaquah, Aliamanu / Salt Lakes / Foster Village, La Haute-Saint-Charles, Fleetwood, Lincoln?", + "ground_truth": { + "answer": "Lincoln", + "outlier_distance_km": 14755.0, + "second_furthest_km": 9750.4, + "clarity_ratio": 1.51, + "median_distance_km": 5941.8, + "distances_to_centroid": { + "Issaquah": 5879.8, + "Aliamanu / Salt Lakes / Foster Village": 9750.4, + "La Haute-Saint-Charles": 2572.9, + "Fleetwood": 5941.8, + "Lincoln": 14755.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Issaquah: (47.53°, -122.03°)", + " Aliamanu / Salt Lakes / Foster Village: (21.36°, -157.92°)", + " La Haute-Saint-Charles: (46.89°, -71.37°)", + " Fleetwood: (49.17°, -122.80°)", + " Lincoln: (-36.86°, 174.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lincoln: 14755.0 km from centroid", + " Aliamanu / Salt Lakes / Foster Village: 9750.4 km from centroid", + " Fleetwood: 5941.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lincoln", + "FINAL ANSWER: Lincoln" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.30778, + "lon": -118.44925, + "name": "Sylmar" + }, + { + "lat": 28.66111, + "lon": -81.36562, + "name": "Altamonte Springs" + }, + { + "lat": 38.92567, + "lon": -77.02942, + "name": "Columbia Heights" + }, + { + "lat": 44.59132, + "lon": -75.68705, + "name": "Brockville" + }, + { + "lat": -31.91099, + "lon": 152.45387, + "name": "Taree" + } + ], + "question": "Which location is the geographic outlier among: Sylmar, Altamonte Springs, Columbia Heights, Brockville, Taree?", + "ground_truth": { + "answer": "Taree", + "outlier_distance_km": 18431.2, + "second_furthest_km": 7579.1, + "clarity_ratio": 2.43, + "median_distance_km": 4168.5, + "distances_to_centroid": { + "Sylmar": 7579.1, + "Altamonte Springs": 4168.5, + "Columbia Heights": 3917.7, + "Brockville": 4033.3, + "Taree": 18431.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sylmar: (34.31°, -118.45°)", + " Altamonte Springs: (28.66°, -81.37°)", + " Columbia Heights: (38.93°, -77.03°)", + " Brockville: (44.59°, -75.69°)", + " Taree: (-31.91°, 152.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taree: 18431.2 km from centroid", + " Sylmar: 7579.1 km from centroid", + " Altamonte Springs: 4168.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taree", + "FINAL ANSWER: Taree" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.80066, + "lon": -76.98304, + "name": "Hanover" + }, + { + "lat": 49.06206, + "lon": -122.36008, + "name": "Townline" + }, + { + "lat": 31.84688, + "lon": -81.59595, + "name": "Hinesville" + }, + { + "lat": 41.8317, + "lon": -87.67366, + "name": "McKinley Park" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + } + ], + "question": "Which location is the geographic outlier among: Hanover, Townline, Hinesville, McKinley Park, Sunbury?", + "ground_truth": { + "answer": "Sunbury", + "outlier_distance_km": 18351.9, + "second_furthest_km": 7056.1, + "clarity_ratio": 2.6, + "median_distance_km": 4342.8, + "distances_to_centroid": { + "Hanover": 3416.2, + "Townline": 7056.1, + "Hinesville": 3662.3, + "McKinley Park": 4342.8, + "Sunbury": 18351.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hanover: (39.80°, -76.98°)", + " Townline: (49.06°, -122.36°)", + " Hinesville: (31.85°, -81.60°)", + " McKinley Park: (41.83°, -87.67°)", + " Sunbury: (-37.58°, 144.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunbury: 18351.9 km from centroid", + " Townline: 7056.1 km from centroid", + " McKinley Park: 4342.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunbury", + "FINAL ANSWER: Sunbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.04514, + "lon": 31.31845, + "name": "Abū Tīj" + }, + { + "lat": 26.87524, + "lon": 31.32963, + "name": "Al Ghanāyim" + }, + { + "lat": -1.24627, + "lon": 36.66291, + "name": "Kikuyu" + }, + { + "lat": 6.31667, + "lon": 38.26667, + "name": "Wenago" + }, + { + "lat": -27.02528, + "lon": -48.65444, + "name": "Camboriú" + } + ], + "question": "Which location is the geographic outlier among: Abū Tīj, Al Ghanāyim, Kikuyu, Wenago, Camboriú?", + "ground_truth": { + "answer": "Camboriú", + "outlier_distance_km": 8044.5, + "second_furthest_km": 2705.8, + "clarity_ratio": 2.97, + "median_distance_km": 2690.8, + "distances_to_centroid": { + "Abū Tīj": 2705.8, + "Al Ghanāyim": 2690.8, + "Kikuyu": 2261.1, + "Wenago": 2263.4, + "Camboriú": 8044.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Abū Tīj: (27.05°, 31.32°)", + " Al Ghanāyim: (26.88°, 31.33°)", + " Kikuyu: (-1.25°, 36.66°)", + " Wenago: (6.32°, 38.27°)", + " Camboriú: (-27.03°, -48.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camboriú: 8044.5 km from centroid", + " Abū Tīj: 2705.8 km from centroid", + " Al Ghanāyim: 2690.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camboriú", + "FINAL ANSWER: Camboriú" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -12.28389, + "lon": -40.49389, + "name": "Ruy Barbosa" + }, + { + "lat": -14.05, + "lon": -52.15861, + "name": "Água Boa" + }, + { + "lat": -21.59556, + "lon": -46.88861, + "name": "São José do Rio Pardo" + }, + { + "lat": -23.415, + "lon": -46.035, + "name": "Guararema" + }, + { + "lat": 54.59682, + "lon": -5.92541, + "name": "Belfast" + } + ], + "question": "Which location is the geographic outlier among: Ruy Barbosa, Água Boa, São José do Rio Pardo, Guararema, Belfast?", + "ground_truth": { + "answer": "Belfast", + "outlier_distance_km": 7099.1, + "second_furthest_km": 2381.1, + "clarity_ratio": 2.98, + "median_distance_km": 2231.0, + "distances_to_centroid": { + "Ruy Barbosa": 1022.4, + "Água Boa": 1930.9, + "São José do Rio Pardo": 2231.0, + "Guararema": 2381.1, + "Belfast": 7099.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ruy Barbosa: (-12.28°, -40.49°)", + " Água Boa: (-14.05°, -52.16°)", + " São José do Rio Pardo: (-21.60°, -46.89°)", + " Guararema: (-23.41°, -46.03°)", + " Belfast: (54.60°, -5.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Belfast: 7099.1 km from centroid", + " Guararema: 2381.1 km from centroid", + " São José do Rio Pardo: 2231.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Belfast", + "FINAL ANSWER: Belfast" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.44879, + "lon": -68.52396, + "name": "Rimouski" + }, + { + "lat": 26.00315, + "lon": -80.22394, + "name": "Pembroke Pines" + }, + { + "lat": 40.90399, + "lon": -74.11848, + "name": "Elmwood Park" + }, + { + "lat": 40.22039, + "lon": -74.01208, + "name": "Asbury Park" + }, + { + "lat": 6.75, + "lon": 38.41667, + "name": "Yirga ‘Alem" + } + ], + "question": "Which location is the geographic outlier among: Rimouski, Pembroke Pines, Elmwood Park, Asbury Park, Yirga ‘Alem?", + "ground_truth": { + "answer": "Yirga ‘Alem", + "outlier_distance_km": 9615.5, + "second_furthest_km": 2850.7, + "clarity_ratio": 3.37, + "median_distance_km": 2266.8, + "distances_to_centroid": { + "Rimouski": 2266.8, + "Pembroke Pines": 2850.7, + "Elmwood Park": 2200.4, + "Asbury Park": 2169.3, + "Yirga ‘Alem": 9615.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rimouski: (48.45°, -68.52°)", + " Pembroke Pines: (26.00°, -80.22°)", + " Elmwood Park: (40.90°, -74.12°)", + " Asbury Park: (40.22°, -74.01°)", + " Yirga ‘Alem: (6.75°, 38.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yirga ‘Alem: 9615.5 km from centroid", + " Pembroke Pines: 2850.7 km from centroid", + " Rimouski: 2266.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yirga ‘Alem", + "FINAL ANSWER: Yirga ‘Alem" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.34508, + "lon": -80.14671, + "name": "Boca Del Mar" + }, + { + "lat": 41.31649, + "lon": -73.09316, + "name": "Shelton" + }, + { + "lat": 44.60868, + "lon": -79.42068, + "name": "Orillia" + }, + { + "lat": 38.79345, + "lon": -77.27165, + "name": "Burke" + }, + { + "lat": 22.99376, + "lon": 114.71311, + "name": "Pingshan" + } + ], + "question": "Which location is the geographic outlier among: Boca Del Mar, Shelton, Orillia, Burke, Pingshan?", + "ground_truth": { + "answer": "Pingshan", + "outlier_distance_km": 13016.3, + "second_furthest_km": 4016.6, + "clarity_ratio": 3.24, + "median_distance_km": 3580.6, + "distances_to_centroid": { + "Boca Del Mar": 4016.6, + "Shelton": 3046.4, + "Orillia": 3580.6, + "Burke": 3407.4, + "Pingshan": 13016.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boca Del Mar: (26.35°, -80.15°)", + " Shelton: (41.32°, -73.09°)", + " Orillia: (44.61°, -79.42°)", + " Burke: (38.79°, -77.27°)", + " Pingshan: (22.99°, 114.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pingshan: 13016.3 km from centroid", + " Boca Del Mar: 4016.6 km from centroid", + " Orillia: 3580.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pingshan", + "FINAL ANSWER: Pingshan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.35462, + "lon": 37.58218, + "name": "Isiolo" + }, + { + "lat": 11.52134, + "lon": 13.68952, + "name": "Bama" + }, + { + "lat": -29.53897, + "lon": 31.21439, + "name": "Ballitoville" + }, + { + "lat": -1.06343, + "lon": 34.47313, + "name": "Migori" + }, + { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + } + ], + "question": "Which location is the geographic outlier among: Isiolo, Bama, Ballitoville, Migori, Paralowie?", + "ground_truth": { + "answer": "Paralowie", + "outlier_distance_km": 9105.6, + "second_furthest_km": 4816.7, + "clarity_ratio": 1.89, + "median_distance_km": 2940.5, + "distances_to_centroid": { + "Isiolo": 1936.1, + "Bama": 4816.7, + "Ballitoville": 2940.5, + "Migori": 2127.6, + "Paralowie": 9105.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Isiolo: (0.35°, 37.58°)", + " Bama: (11.52°, 13.69°)", + " Ballitoville: (-29.54°, 31.21°)", + " Migori: (-1.06°, 34.47°)", + " Paralowie: (-34.76°, 138.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paralowie: 9105.6 km from centroid", + " Bama: 4816.7 km from centroid", + " Ballitoville: 2940.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paralowie", + "FINAL ANSWER: Paralowie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.1334, + "lon": -80.26636, + "name": "Brantford" + }, + { + "lat": 34.61834, + "lon": -79.01045, + "name": "Lumberton" + }, + { + "lat": 18.00011, + "lon": -94.5569, + "name": "Minatitlán" + }, + { + "lat": 44.9483, + "lon": -93.34801, + "name": "Saint Louis Park" + }, + { + "lat": -27.54333, + "lon": 153.20287, + "name": "Capalaba" + } + ], + "question": "Which location is the geographic outlier among: Brantford, Lumberton, Minatitlán, Saint Louis Park, Capalaba?", + "ground_truth": { + "answer": "Capalaba", + "outlier_distance_km": 18690.0, + "second_furthest_km": 5805.1, + "clarity_ratio": 3.22, + "median_distance_km": 5493.6, + "distances_to_centroid": { + "Brantford": 4430.4, + "Lumberton": 4114.0, + "Minatitlán": 5805.1, + "Saint Louis Park": 5493.6, + "Capalaba": 18690.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brantford: (43.13°, -80.27°)", + " Lumberton: (34.62°, -79.01°)", + " Minatitlán: (18.00°, -94.56°)", + " Saint Louis Park: (44.95°, -93.35°)", + " Capalaba: (-27.54°, 153.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Capalaba: 18690.0 km from centroid", + " Minatitlán: 5805.1 km from centroid", + " Saint Louis Park: 5493.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Capalaba", + "FINAL ANSWER: Capalaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.68444, + "lon": -42.75028, + "name": "Brejo" + }, + { + "lat": -25.29528, + "lon": -54.09389, + "name": "Medianeira" + }, + { + "lat": 6.17358, + "lon": -75.33621, + "name": "Marinilla" + }, + { + "lat": -14.16417, + "lon": -39.37361, + "name": "Ibirapitanga" + }, + { + "lat": 25.40529, + "lon": 76.07431, + "name": "Kāpren" + } + ], + "question": "Which location is the geographic outlier among: Brejo, Medianeira, Marinilla, Ibirapitanga, Kāpren?", + "ground_truth": { + "answer": "Kāpren", + "outlier_distance_km": 11440.1, + "second_furthest_km": 5438.4, + "clarity_ratio": 2.1, + "median_distance_km": 3858.1, + "distances_to_centroid": { + "Brejo": 1744.9, + "Medianeira": 3858.1, + "Marinilla": 5438.4, + "Ibirapitanga": 1885.5, + "Kāpren": 11440.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brejo: (-3.68°, -42.75°)", + " Medianeira: (-25.30°, -54.09°)", + " Marinilla: (6.17°, -75.34°)", + " Ibirapitanga: (-14.16°, -39.37°)", + " Kāpren: (25.41°, 76.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kāpren: 11440.1 km from centroid", + " Marinilla: 5438.4 km from centroid", + " Medianeira: 3858.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kāpren", + "FINAL ANSWER: Kāpren" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.2481, + "lon": -122.89236, + "name": "Lougheed" + }, + { + "lat": 40.75566, + "lon": -73.88541, + "name": "Jackson Heights" + }, + { + "lat": 19.53159, + "lon": -98.87464, + "name": "Tulantongo" + }, + { + "lat": 39.20705, + "lon": -76.72692, + "name": "West Elkridge" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + } + ], + "question": "Which location is the geographic outlier among: Lougheed, Jackson Heights, Tulantongo, West Elkridge, Hawthorn?", + "ground_truth": { + "answer": "Hawthorn", + "outlier_distance_km": 18007.0, + "second_furthest_km": 7262.5, + "clarity_ratio": 2.48, + "median_distance_km": 5528.9, + "distances_to_centroid": { + "Lougheed": 7262.5, + "Jackson Heights": 3369.0, + "Tulantongo": 5528.9, + "West Elkridge": 3510.0, + "Hawthorn": 18007.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lougheed: (49.25°, -122.89°)", + " Jackson Heights: (40.76°, -73.89°)", + " Tulantongo: (19.53°, -98.87°)", + " West Elkridge: (39.21°, -76.73°)", + " Hawthorn: (-37.82°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hawthorn: 18007.0 km from centroid", + " Lougheed: 7262.5 km from centroid", + " Tulantongo: 5528.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hawthorn", + "FINAL ANSWER: Hawthorn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.8805, + "lon": -62.07503, + "name": "Punta Alta" + }, + { + "lat": -8.58444, + "lon": -35.38667, + "name": "Gameleira" + }, + { + "lat": -15.8981, + "lon": -48.04671, + "name": "Riacho Fundo II" + }, + { + "lat": -34.65072, + "lon": -59.43143, + "name": "Mercedes" + }, + { + "lat": 7.83333, + "lon": 38.23333, + "name": "Ciro" + } + ], + "question": "Which location is the geographic outlier among: Punta Alta, Gameleira, Riacho Fundo II, Mercedes, Ciro?", + "ground_truth": { + "answer": "Ciro", + "outlier_distance_km": 8361.3, + "second_furthest_km": 3613.7, + "clarity_ratio": 2.31, + "median_distance_km": 3172.7, + "distances_to_centroid": { + "Punta Alta": 3613.7, + "Gameleira": 1074.0, + "Riacho Fundo II": 1581.5, + "Mercedes": 3172.7, + "Ciro": 8361.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Punta Alta: (-38.88°, -62.08°)", + " Gameleira: (-8.58°, -35.39°)", + " Riacho Fundo II: (-15.90°, -48.05°)", + " Mercedes: (-34.65°, -59.43°)", + " Ciro: (7.83°, 38.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciro: 8361.3 km from centroid", + " Punta Alta: 3613.7 km from centroid", + " Mercedes: 3172.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciro", + "FINAL ANSWER: Ciro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.12416, + "lon": 12.49639, + "name": "Borna" + }, + { + "lat": 51.42212, + "lon": -0.20805, + "name": "Wimbledon" + }, + { + "lat": 51.80924, + "lon": 8.42841, + "name": "Rietberg" + }, + { + "lat": 37.65896, + "lon": -5.52751, + "name": "Lora del Río" + }, + { + "lat": -39.81422, + "lon": -73.24589, + "name": "Valdivia" + } + ], + "question": "Which location is the geographic outlier among: Borna, Wimbledon, Rietberg, Lora del Río, Valdivia?", + "ground_truth": { + "answer": "Valdivia", + "outlier_distance_km": 10069.8, + "second_furthest_km": 3039.4, + "clarity_ratio": 3.31, + "median_distance_km": 2888.4, + "distances_to_centroid": { + "Borna": 3039.4, + "Wimbledon": 2515.2, + "Rietberg": 2888.4, + "Lora del Río": 978.5, + "Valdivia": 10069.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Borna: (51.12°, 12.50°)", + " Wimbledon: (51.42°, -0.21°)", + " Rietberg: (51.81°, 8.43°)", + " Lora del Río: (37.66°, -5.53°)", + " Valdivia: (-39.81°, -73.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Valdivia: 10069.8 km from centroid", + " Borna: 3039.4 km from centroid", + " Rietberg: 2888.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Valdivia", + "FINAL ANSWER: Valdivia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.54583, + "lon": -47.18333, + "name": "Mairinque" + }, + { + "lat": -25.9466, + "lon": -60.62008, + "name": "Juan José Castelli" + }, + { + "lat": -26.76083, + "lon": -53.1725, + "name": "Maravilha" + }, + { + "lat": -22.54417, + "lon": -44.17139, + "name": "Barra Mansa" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + } + ], + "question": "Which location is the geographic outlier among: Mairinque, Juan José Castelli, Maravilha, Barra Mansa, Melbourne?", + "ground_truth": { + "answer": "Melbourne", + "outlier_distance_km": 12385.7, + "second_furthest_km": 4800.4, + "clarity_ratio": 2.58, + "median_distance_km": 4055.7, + "distances_to_centroid": { + "Mairinque": 3542.7, + "Juan José Castelli": 4800.4, + "Maravilha": 4055.7, + "Barra Mansa": 3274.3, + "Melbourne": 12385.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mairinque: (-23.55°, -47.18°)", + " Juan José Castelli: (-25.95°, -60.62°)", + " Maravilha: (-26.76°, -53.17°)", + " Barra Mansa: (-22.54°, -44.17°)", + " Melbourne: (-37.81°, 144.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Melbourne: 12385.7 km from centroid", + " Juan José Castelli: 4800.4 km from centroid", + " Maravilha: 4055.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Melbourne", + "FINAL ANSWER: Melbourne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + }, + { + "lat": -37.78828, + "lon": 145.12373, + "name": "Doncaster" + }, + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": 52.73371, + "lon": 15.22505, + "name": "Gorzów Wielkopolski" + } + ], + "question": "Which location is the geographic outlier among: Southbank, Doncaster, Newcastle, Otahuhu, Gorzów Wielkopolski?", + "ground_truth": { + "answer": "Gorzów Wielkopolski", + "outlier_distance_km": 13055.7, + "second_furthest_km": 5123.1, + "clarity_ratio": 2.55, + "median_distance_km": 2991.3, + "distances_to_centroid": { + "Southbank": 2800.6, + "Doncaster": 2807.8, + "Newcastle": 2991.3, + "Otahuhu": 5123.1, + "Gorzów Wielkopolski": 13055.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Southbank: (-37.82°, 144.96°)", + " Doncaster: (-37.79°, 145.12°)", + " Newcastle: (-32.93°, 151.78°)", + " Otahuhu: (-36.94°, 174.84°)", + " Gorzów Wielkopolski: (52.73°, 15.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gorzów Wielkopolski: 13055.7 km from centroid", + " Otahuhu: 5123.1 km from centroid", + " Newcastle: 2991.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gorzów Wielkopolski", + "FINAL ANSWER: Gorzów Wielkopolski" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.18341, + "lon": -114.46871, + "name": "Cochrane" + }, + { + "lat": 47.8601, + "lon": -122.2043, + "name": "Mill Creek" + }, + { + "lat": 41.24006, + "lon": -81.44067, + "name": "Hudson" + }, + { + "lat": 37.44882, + "lon": -77.47353, + "name": "Meadowbrook" + }, + { + "lat": 36.2, + "lon": 139.28333, + "name": "Fukayachō" + } + ], + "question": "Which location is the geographic outlier among: Cochrane, Mill Creek, Hudson, Meadowbrook, Fukayachō?", + "ground_truth": { + "answer": "Fukayachō", + "outlier_distance_km": 11167.3, + "second_furthest_km": 5377.4, + "clarity_ratio": 2.08, + "median_distance_km": 4732.0, + "distances_to_centroid": { + "Cochrane": 4732.0, + "Mill Creek": 5377.4, + "Hudson": 2486.0, + "Meadowbrook": 2296.3, + "Fukayachō": 11167.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cochrane: (51.18°, -114.47°)", + " Mill Creek: (47.86°, -122.20°)", + " Hudson: (41.24°, -81.44°)", + " Meadowbrook: (37.45°, -77.47°)", + " Fukayachō: (36.20°, 139.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fukayachō: 11167.3 km from centroid", + " Mill Creek: 5377.4 km from centroid", + " Cochrane: 4732.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fukayachō", + "FINAL ANSWER: Fukayachō" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.39283, + "lon": -3.48194, + "name": "Mejorada del Campo" + }, + { + "lat": 48.80263, + "lon": 44.47491, + "name": "Gorodishche" + }, + { + "lat": 52.44254, + "lon": 13.58228, + "name": "Berlin Köpenick" + }, + { + "lat": 51.57344, + "lon": -0.42341, + "name": "Ruislip" + }, + { + "lat": 22.31038, + "lon": 69.60376, + "name": "Salāya" + } + ], + "question": "Which location is the geographic outlier among: Mejorada del Campo, Gorodishche, Berlin Köpenick, Ruislip, Salāya?", + "ground_truth": { + "answer": "Salāya", + "outlier_distance_km": 4716.6, + "second_furthest_km": 2350.2, + "clarity_ratio": 2.01, + "median_distance_km": 2103.4, + "distances_to_centroid": { + "Mejorada del Campo": 2350.2, + "Gorodishche": 1645.1, + "Berlin Köpenick": 1329.1, + "Ruislip": 2103.4, + "Salāya": 4716.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mejorada del Campo: (40.39°, -3.48°)", + " Gorodishche: (48.80°, 44.47°)", + " Berlin Köpenick: (52.44°, 13.58°)", + " Ruislip: (51.57°, -0.42°)", + " Salāya: (22.31°, 69.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Salāya: 4716.6 km from centroid", + " Mejorada del Campo: 2350.2 km from centroid", + " Ruislip: 2103.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Salāya", + "FINAL ANSWER: Salāya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + }, + { + "lat": -0.50397, + "lon": 36.31845, + "name": "Gilgil" + } + ], + "question": "Which location is the geographic outlier among: Reservoir, Karori, Rotorua, Cessnock, Gilgil?", + "ground_truth": { + "answer": "Gilgil", + "outlier_distance_km": 10979.5, + "second_furthest_km": 3716.1, + "clarity_ratio": 2.95, + "median_distance_km": 3617.2, + "distances_to_centroid": { + "Reservoir": 1139.3, + "Karori": 3617.2, + "Rotorua": 3716.1, + "Cessnock": 1418.7, + "Gilgil": 10979.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reservoir: (-37.72°, 145.00°)", + " Karori: (-41.28°, 174.74°)", + " Rotorua: (-38.14°, 176.25°)", + " Cessnock: (-32.83°, 151.36°)", + " Gilgil: (-0.50°, 36.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gilgil: 10979.5 km from centroid", + " Rotorua: 3716.1 km from centroid", + " Karori: 3617.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gilgil", + "FINAL ANSWER: Gilgil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.52541, + "lon": 102.24591, + "name": "Khon Buri" + }, + { + "lat": 18.6057, + "lon": 84.23546, + "name": "Tekkali" + }, + { + "lat": 6.26812, + "lon": 100.42167, + "name": "Jitra" + }, + { + "lat": 14.19544, + "lon": 79.15896, + "name": "Rāzampeta" + }, + { + "lat": 52.5, + "lon": -2.08333, + "name": "Dudley" + } + ], + "question": "Which location is the geographic outlier among: Khon Buri, Tekkali, Jitra, Rāzampeta, Dudley?", + "ground_truth": { + "answer": "Dudley", + "outlier_distance_km": 7139.1, + "second_furthest_km": 3405.5, + "clarity_ratio": 2.1, + "median_distance_km": 3198.8, + "distances_to_centroid": { + "Khon Buri": 3198.8, + "Tekkali": 1230.4, + "Jitra": 3405.5, + "Rāzampeta": 1031.2, + "Dudley": 7139.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Khon Buri: (14.53°, 102.25°)", + " Tekkali: (18.61°, 84.24°)", + " Jitra: (6.27°, 100.42°)", + " Rāzampeta: (14.20°, 79.16°)", + " Dudley: (52.50°, -2.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dudley: 7139.1 km from centroid", + " Jitra: 3405.5 km from centroid", + " Khon Buri: 3198.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dudley", + "FINAL ANSWER: Dudley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.1653, + "lon": 8.85996, + "name": "Vlotho" + }, + { + "lat": 48.94743, + "lon": 9.43718, + "name": "Backnang" + }, + { + "lat": 52.16772, + "lon": 22.29006, + "name": "Siedlce" + }, + { + "lat": 61.09979, + "lon": 72.60349, + "name": "Nefteyugansk" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + } + ], + "question": "Which location is the geographic outlier among: Vlotho, Backnang, Siedlce, Nefteyugansk, Greystanes?", + "ground_truth": { + "answer": "Greystanes", + "outlier_distance_km": 12789.0, + "second_furthest_km": 3858.7, + "clarity_ratio": 3.31, + "median_distance_km": 3769.6, + "distances_to_centroid": { + "Vlotho": 3858.7, + "Backnang": 3769.6, + "Siedlce": 2984.6, + "Nefteyugansk": 3107.8, + "Greystanes": 12789.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vlotho: (52.17°, 8.86°)", + " Backnang: (48.95°, 9.44°)", + " Siedlce: (52.17°, 22.29°)", + " Nefteyugansk: (61.10°, 72.60°)", + " Greystanes: (-33.82°, 150.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greystanes: 12789.0 km from centroid", + " Vlotho: 3858.7 km from centroid", + " Backnang: 3769.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greystanes", + "FINAL ANSWER: Greystanes" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.98556, + "lon": 47.40393, + "name": "Semender" + }, + { + "lat": 55.62047, + "lon": 37.49338, + "name": "Tyoply Stan" + }, + { + "lat": 49.34737, + "lon": 8.68733, + "name": "Leimen" + }, + { + "lat": 50.53791, + "lon": 12.78522, + "name": "Schwarzenberg" + }, + { + "lat": 34.33833, + "lon": 132.91667, + "name": "Takehara" + } + ], + "question": "Which location is the geographic outlier among: Semender, Tyoply Stan, Leimen, Schwarzenberg, Takehara?", + "ground_truth": { + "answer": "Takehara", + "outlier_distance_km": 6972.9, + "second_furthest_km": 2900.2, + "clarity_ratio": 2.4, + "median_distance_km": 2593.9, + "distances_to_centroid": { + "Semender": 399.7, + "Tyoply Stan": 1237.2, + "Leimen": 2900.2, + "Schwarzenberg": 2593.9, + "Takehara": 6972.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Semender: (42.99°, 47.40°)", + " Tyoply Stan: (55.62°, 37.49°)", + " Leimen: (49.35°, 8.69°)", + " Schwarzenberg: (50.54°, 12.79°)", + " Takehara: (34.34°, 132.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Takehara: 6972.9 km from centroid", + " Leimen: 2900.2 km from centroid", + " Schwarzenberg: 2593.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Takehara", + "FINAL ANSWER: Takehara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.46538, + "lon": -74.33043, + "name": "Sayreville Junction" + }, + { + "lat": 26.52036, + "lon": -81.96398, + "name": "Iona" + }, + { + "lat": 38.81061, + "lon": -90.69985, + "name": "O'Fallon" + }, + { + "lat": 44.87552, + "lon": -91.91934, + "name": "Menomonie" + }, + { + "lat": -25.43321, + "lon": 31.95478, + "name": "Komatipoort" + } + ], + "question": "Which location is the geographic outlier among: Sayreville Junction, Iona, O'Fallon, Menomonie, Komatipoort?", + "ground_truth": { + "answer": "Komatipoort", + "outlier_distance_km": 11483.4, + "second_furthest_km": 3513.8, + "clarity_ratio": 3.27, + "median_distance_km": 3140.7, + "distances_to_centroid": { + "Sayreville Junction": 2093.1, + "Iona": 2064.1, + "O'Fallon": 3140.7, + "Menomonie": 3513.8, + "Komatipoort": 11483.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sayreville Junction: (40.47°, -74.33°)", + " Iona: (26.52°, -81.96°)", + " O'Fallon: (38.81°, -90.70°)", + " Menomonie: (44.88°, -91.92°)", + " Komatipoort: (-25.43°, 31.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Komatipoort: 11483.4 km from centroid", + " Menomonie: 3513.8 km from centroid", + " O'Fallon: 3140.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Komatipoort", + "FINAL ANSWER: Komatipoort" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -33.86667, + "lon": 150.95, + "name": "Fairfield" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": 45.78693, + "lon": 4.9251, + "name": "Vaulx-en-Velin" + } + ], + "question": "Which location is the geographic outlier among: Sunnybank Hills, Maryborough, Fairfield, Blenheim, Vaulx-en-Velin?", + "ground_truth": { + "answer": "Vaulx-en-Velin", + "outlier_distance_km": 13796.5, + "second_furthest_km": 5245.2, + "clarity_ratio": 2.63, + "median_distance_km": 3060.8, + "distances_to_centroid": { + "Sunnybank Hills": 2933.3, + "Maryborough": 2831.0, + "Fairfield": 3060.8, + "Blenheim": 5245.2, + "Vaulx-en-Velin": 13796.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Maryborough: (-25.54°, 152.70°)", + " Fairfield: (-33.87°, 150.95°)", + " Blenheim: (-41.52°, 173.95°)", + " Vaulx-en-Velin: (45.79°, 4.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vaulx-en-Velin: 13796.5 km from centroid", + " Blenheim: 5245.2 km from centroid", + " Fairfield: 3060.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vaulx-en-Velin", + "FINAL ANSWER: Vaulx-en-Velin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.63033, + "lon": 0.00051, + "name": "Chingford" + }, + { + "lat": 42.06622, + "lon": 48.28759, + "name": "Derbent" + }, + { + "lat": 45.74525, + "lon": 4.84197, + "name": "Lyon 07" + }, + { + "lat": 51.88247, + "lon": 17.01225, + "name": "Gostyń" + }, + { + "lat": 14.4996, + "lon": 121.0507, + "name": "Upper Bicutan" + } + ], + "question": "Which location is the geographic outlier among: Chingford, Derbent, Lyon 07, Gostyń, Upper Bicutan?", + "ground_truth": { + "answer": "Upper Bicutan", + "outlier_distance_km": 8358.2, + "second_furthest_km": 3111.3, + "clarity_ratio": 2.69, + "median_distance_km": 2722.8, + "distances_to_centroid": { + "Chingford": 3111.3, + "Derbent": 840.9, + "Lyon 07": 2722.8, + "Gostyń": 2002.1, + "Upper Bicutan": 8358.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chingford: (51.63°, 0.00°)", + " Derbent: (42.07°, 48.29°)", + " Lyon 07: (45.75°, 4.84°)", + " Gostyń: (51.88°, 17.01°)", + " Upper Bicutan: (14.50°, 121.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Upper Bicutan: 8358.2 km from centroid", + " Chingford: 3111.3 km from centroid", + " Lyon 07: 2722.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Upper Bicutan", + "FINAL ANSWER: Upper Bicutan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.66917, + "lon": -42.07611, + "name": "Itaocara" + }, + { + "lat": -16.36314, + "lon": -72.1921, + "name": "El Pedregal" + }, + { + "lat": -26.42528, + "lon": -49.24306, + "name": "Corupá" + }, + { + "lat": 7.06222, + "lon": -73.08644, + "name": "Floridablanca" + }, + { + "lat": 25.07145, + "lon": 73.8798, + "name": "Rājsamand" + } + ], + "question": "Which location is the geographic outlier among: Itaocara, El Pedregal, Corupá, Floridablanca, Rājsamand?", + "ground_truth": { + "answer": "Rājsamand", + "outlier_distance_km": 11963.3, + "second_furthest_km": 4742.4, + "clarity_ratio": 2.52, + "median_distance_km": 4450.1, + "distances_to_centroid": { + "Itaocara": 1976.8, + "El Pedregal": 4450.1, + "Corupá": 2838.2, + "Floridablanca": 4742.4, + "Rājsamand": 11963.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itaocara: (-21.67°, -42.08°)", + " El Pedregal: (-16.36°, -72.19°)", + " Corupá: (-26.43°, -49.24°)", + " Floridablanca: (7.06°, -73.09°)", + " Rājsamand: (25.07°, 73.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rājsamand: 11963.3 km from centroid", + " Floridablanca: 4742.4 km from centroid", + " El Pedregal: 4450.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rājsamand", + "FINAL ANSWER: Rājsamand" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + }, + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + }, + { + "lat": -33.73333, + "lon": 150.93284, + "name": "Glenwood" + }, + { + "lat": 34.93343, + "lon": -95.76971, + "name": "McAlester" + } + ], + "question": "Which location is the geographic outlier among: Malvern East, Alexandra Hills, Mornington, Glenwood, McAlester?", + "ground_truth": { + "answer": "McAlester", + "outlier_distance_km": 17807.6, + "second_furthest_km": 5453.5, + "clarity_ratio": 3.27, + "median_distance_km": 5225.4, + "distances_to_centroid": { + "Malvern East": 4751.6, + "Alexandra Hills": 5453.5, + "Mornington": 4758.6, + "Glenwood": 5225.4, + "McAlester": 17807.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Malvern East: (-37.87°, 145.04°)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Mornington: (-38.22°, 145.04°)", + " Glenwood: (-33.73°, 150.93°)", + " McAlester: (34.93°, -95.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " McAlester: 17807.6 km from centroid", + " Alexandra Hills: 5453.5 km from centroid", + " Glenwood: 5225.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: McAlester", + "FINAL ANSWER: McAlester" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.53791, + "lon": -49.48813, + "name": "Campina Verde" + }, + { + "lat": -17.51944, + "lon": -39.19556, + "name": "Alcobaça" + }, + { + "lat": -20.76361, + "lon": -41.53306, + "name": "Alegre" + }, + { + "lat": -22.63417, + "lon": -54.82222, + "name": "Caarapó" + }, + { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + } + ], + "question": "Which location is the geographic outlier among: Campina Verde, Alcobaça, Alegre, Caarapó, Strathfield?", + "ground_truth": { + "answer": "Strathfield", + "outlier_distance_km": 13284.5, + "second_furthest_km": 4902.4, + "clarity_ratio": 2.71, + "median_distance_km": 4426.8, + "distances_to_centroid": { + "Campina Verde": 4426.8, + "Alcobaça": 3426.4, + "Alegre": 3585.9, + "Caarapó": 4902.4, + "Strathfield": 13284.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Campina Verde: (-19.54°, -49.49°)", + " Alcobaça: (-17.52°, -39.20°)", + " Alegre: (-20.76°, -41.53°)", + " Caarapó: (-22.63°, -54.82°)", + " Strathfield: (-33.88°, 151.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Strathfield: 13284.5 km from centroid", + " Caarapó: 4902.4 km from centroid", + " Campina Verde: 4426.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Strathfield", + "FINAL ANSWER: Strathfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + }, + { + "lat": -37.8318, + "lon": 140.77919, + "name": "Mount Gambier" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -12.13556, + "lon": -38.41917, + "name": "Alagoinhas" + } + ], + "question": "Which location is the geographic outlier among: Morphett Vale, Mount Gambier, Logan City, Highton, Alagoinhas?", + "ground_truth": { + "answer": "Alagoinhas", + "outlier_distance_km": 14072.2, + "second_furthest_km": 4403.9, + "clarity_ratio": 3.2, + "median_distance_km": 3462.4, + "distances_to_centroid": { + "Morphett Vale": 2928.6, + "Mount Gambier": 3150.9, + "Logan City": 4403.9, + "Highton": 3462.4, + "Alagoinhas": 14072.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morphett Vale: (-35.13°, 138.52°)", + " Mount Gambier: (-37.83°, 140.78°)", + " Logan City: (-27.64°, 153.11°)", + " Highton: (-38.17°, 144.31°)", + " Alagoinhas: (-12.14°, -38.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alagoinhas: 14072.2 km from centroid", + " Logan City: 4403.9 km from centroid", + " Highton: 3462.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alagoinhas", + "FINAL ANSWER: Alagoinhas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -34.60251, + "lon": 138.74902, + "name": "Gawler" + }, + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + { + "lat": -38.14711, + "lon": 144.36069, + "name": "Geelong" + }, + { + "lat": 14.55883, + "lon": 121.13285, + "name": "Taytay" + } + ], + "question": "Which location is the geographic outlier among: Cranbourne North, Gawler, Kingsford, Geelong, Taytay?", + "ground_truth": { + "answer": "Taytay", + "outlier_distance_km": 4961.2, + "second_furthest_km": 1423.1, + "clarity_ratio": 3.49, + "median_distance_km": 1403.1, + "distances_to_centroid": { + "Cranbourne North": 1423.1, + "Gawler": 961.7, + "Kingsford": 1379.1, + "Geelong": 1403.1, + "Taytay": 4961.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cranbourne North: (-38.08°, 145.30°)", + " Gawler: (-34.60°, 138.75°)", + " Kingsford: (-33.92°, 151.23°)", + " Geelong: (-38.15°, 144.36°)", + " Taytay: (14.56°, 121.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Taytay: 4961.2 km from centroid", + " Cranbourne North: 1423.1 km from centroid", + " Geelong: 1403.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Taytay", + "FINAL ANSWER: Taytay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.91119, + "lon": 138.70735, + "name": "Adelaide Hills" + }, + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + }, + { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + }, + { + "lat": -36.88041, + "lon": 174.79819, + "name": "Remuera" + }, + { + "lat": 40.85216, + "lon": 14.26811, + "name": "Naples" + } + ], + "question": "Which location is the geographic outlier among: Adelaide Hills, Pascoe Vale, Manukau City, Remuera, Naples?", + "ground_truth": { + "answer": "Naples", + "outlier_distance_km": 13617.4, + "second_furthest_km": 4696.4, + "clarity_ratio": 2.9, + "median_distance_km": 4687.2, + "distances_to_centroid": { + "Adelaide Hills": 1775.7, + "Pascoe Vale": 2366.9, + "Manukau City": 4696.4, + "Remuera": 4687.2, + "Naples": 13617.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adelaide Hills: (-34.91°, 138.71°)", + " Pascoe Vale: (-37.73°, 144.93°)", + " Manukau City: (-36.99°, 174.88°)", + " Remuera: (-36.88��, 174.80°)", + " Naples: (40.85°, 14.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Naples: 13617.4 km from centroid", + " Manukau City: 4696.4 km from centroid", + " Remuera: 4687.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Naples", + "FINAL ANSWER: Naples" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.11626, + "lon": 136.19768, + "name": "Youkaichi" + }, + { + "lat": 30.8115, + "lon": 107.95377, + "name": "Yujia" + }, + { + "lat": 29.24946, + "lon": 106.77663, + "name": "Jielong" + }, + { + "lat": 36.05528, + "lon": 139.31503, + "name": "Ranzan" + }, + { + "lat": 53.45131, + "lon": -2.07943, + "name": "Hyde" + } + ], + "question": "Which location is the geographic outlier among: Youkaichi, Yujia, Jielong, Ranzan, Hyde?", + "ground_truth": { + "answer": "Hyde", + "outlier_distance_km": 7368.6, + "second_furthest_km": 3697.1, + "clarity_ratio": 1.99, + "median_distance_km": 3450.4, + "distances_to_centroid": { + "Youkaichi": 3450.4, + "Yujia": 1170.1, + "Jielong": 1205.5, + "Ranzan": 3697.1, + "Hyde": 7368.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Youkaichi: (35.12°, 136.20°)", + " Yujia: (30.81°, 107.95°)", + " Jielong: (29.25°, 106.78°)", + " Ranzan: (36.06°, 139.32°)", + " Hyde: (53.45°, -2.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hyde: 7368.6 km from centroid", + " Ranzan: 3697.1 km from centroid", + " Youkaichi: 3450.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hyde", + "FINAL ANSWER: Hyde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.79802, + "lon": -93.5269, + "name": "Shakopee" + }, + { + "lat": 43.70444, + "lon": -79.39336, + "name": "Mount Pleasant West" + }, + { + "lat": 41.81892, + "lon": -87.69894, + "name": "Brighton Park" + }, + { + "lat": 43.06057, + "lon": -88.10648, + "name": "Brookfield" + }, + { + "lat": -4.83389, + "lon": -37.78111, + "name": "Jaguaruana" + } + ], + "question": "Which location is the geographic outlier among: Shakopee, Mount Pleasant West, Brighton Park, Brookfield, Jaguaruana?", + "ground_truth": { + "answer": "Jaguaruana", + "outlier_distance_km": 5966.1, + "second_furthest_km": 1857.0, + "clarity_ratio": 3.21, + "median_distance_km": 1400.5, + "distances_to_centroid": { + "Shakopee": 1857.0, + "Mount Pleasant West": 1126.0, + "Brighton Park": 1282.1, + "Brookfield": 1400.5, + "Jaguaruana": 5966.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shakopee: (44.80°, -93.53°)", + " Mount Pleasant West: (43.70°, -79.39°)", + " Brighton Park: (41.82°, -87.70°)", + " Brookfield: (43.06°, -88.11°)", + " Jaguaruana: (-4.83°, -37.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jaguaruana: 5966.1 km from centroid", + " Shakopee: 1857.0 km from centroid", + " Brookfield: 1400.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jaguaruana", + "FINAL ANSWER: Jaguaruana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.56798, + "lon": 10.88565, + "name": "Herzogenaurach" + }, + { + "lat": 52.98947, + "lon": 6.9504, + "name": "Stadskanaal" + }, + { + "lat": 51.56872, + "lon": -0.07334, + "name": "Stamford Hill" + }, + { + "lat": 53.48005, + "lon": -2.14543, + "name": "Droylsden" + }, + { + "lat": 30.62914, + "lon": 31.08235, + "name": "Birkat as Sab‘" + } + ], + "question": "Which location is the geographic outlier among: Herzogenaurach, Stadskanaal, Stamford Hill, Droylsden, Birkat as Sab‘?", + "ground_truth": { + "answer": "Birkat as Sab‘", + "outlier_distance_km": 2646.2, + "second_furthest_km": 1036.5, + "clarity_ratio": 2.55, + "median_distance_km": 805.4, + "distances_to_centroid": { + "Herzogenaurach": 241.9, + "Stadskanaal": 617.7, + "Stamford Hill": 805.4, + "Droylsden": 1036.5, + "Birkat as Sab‘": 2646.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Herzogenaurach: (49.57°, 10.89°)", + " Stadskanaal: (52.99°, 6.95°)", + " Stamford Hill: (51.57°, -0.07°)", + " Droylsden: (53.48°, -2.15°)", + " Birkat as Sab‘: (30.63°, 31.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Birkat as Sab‘: 2646.2 km from centroid", + " Droylsden: 1036.5 km from centroid", + " Stamford Hill: 805.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Birkat as Sab‘", + "FINAL ANSWER: Birkat as Sab‘" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.05861, + "lon": -51.03639, + "name": "Sertanópolis" + }, + { + "lat": -19.72806, + "lon": -50.19556, + "name": "Iturama" + }, + { + "lat": -6.48361, + "lon": -36.15361, + "name": "Cuité" + }, + { + "lat": -15.64713, + "lon": -47.79315, + "name": "Sobradinho" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + } + ], + "question": "Which location is the geographic outlier among: Sertanópolis, Iturama, Cuité, Sobradinho, Willetton?", + "ground_truth": { + "answer": "Willetton", + "outlier_distance_km": 12183.5, + "second_furthest_km": 3865.0, + "clarity_ratio": 3.15, + "median_distance_km": 3800.1, + "distances_to_centroid": { + "Sertanópolis": 3865.0, + "Iturama": 3800.1, + "Cuité": 2804.7, + "Sobradinho": 3616.7, + "Willetton": 12183.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sertanópolis: (-23.06°, -51.04°)", + " Iturama: (-19.73°, -50.20°)", + " Cuité: (-6.48°, -36.15°)", + " Sobradinho: (-15.65°, -47.79°)", + " Willetton: (-32.05°, 115.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Willetton: 12183.5 km from centroid", + " Sertanópolis: 3865.0 km from centroid", + " Iturama: 3800.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Willetton", + "FINAL ANSWER: Willetton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -37.89359, + "lon": 145.05534, + "name": "Carnegie" + }, + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + }, + { + "lat": -22.94564, + "lon": 30.48497, + "name": "Thohoyandou" + } + ], + "question": "Which location is the geographic outlier among: Banora Point, Blacktown, Carnegie, Malvern East, Thohoyandou?", + "ground_truth": { + "answer": "Thohoyandou", + "outlier_distance_km": 9074.6, + "second_furthest_km": 2768.7, + "clarity_ratio": 3.28, + "median_distance_km": 2417.9, + "distances_to_centroid": { + "Banora Point": 2768.7, + "Blacktown": 2417.9, + "Carnegie": 1929.9, + "Malvern East": 1928.3, + "Thohoyandou": 9074.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banora Point: (-28.21°, 153.54°)", + " Blacktown: (-33.77°, 150.92°)", + " Carnegie: (-37.89°, 145.06°)", + " Malvern East: (-37.87°, 145.04°)", + " Thohoyandou: (-22.95°, 30.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thohoyandou: 9074.6 km from centroid", + " Banora Point: 2768.7 km from centroid", + " Blacktown: 2417.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thohoyandou", + "FINAL ANSWER: Thohoyandou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.38333, + "lon": 136.26667, + "name": "Nagahama" + }, + { + "lat": 34.86472, + "lon": 117.55417, + "name": "Zaozhuang" + }, + { + "lat": 18.57506, + "lon": 76.02186, + "name": "Kallam" + }, + { + "lat": 15.35116, + "lon": 121.00393, + "name": "Peñaranda" + }, + { + "lat": 12.63056, + "lon": 39.03472, + "name": "Sek’ot’a" + } + ], + "question": "Which location is the geographic outlier among: Nagahama, Zaozhuang, Kallam, Peñaranda, Sek’ot’a?", + "ground_truth": { + "answer": "Sek’ot’a", + "outlier_distance_km": 6306.0, + "second_furthest_km": 3915.0, + "clarity_ratio": 1.61, + "median_distance_km": 2570.5, + "distances_to_centroid": { + "Nagahama": 3915.0, + "Zaozhuang": 2285.1, + "Kallam": 2338.2, + "Peñaranda": 2570.5, + "Sek’ot’a": 6306.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nagahama: (35.38°, 136.27°)", + " Zaozhuang: (34.86°, 117.55°)", + " Kallam: (18.58°, 76.02°)", + " Peñaranda: (15.35°, 121.00°)", + " Sek’ot’a: (12.63°, 39.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sek’ot’a: 6306.0 km from centroid", + " Nagahama: 3915.0 km from centroid", + " Peñaranda: 2570.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sek’ot’a", + "FINAL ANSWER: Sek’ot’a" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.45171, + "lon": -82.03542, + "name": "Avon" + }, + { + "lat": 19.33273, + "lon": -99.60345, + "name": "San Mateo Otzacatipan" + }, + { + "lat": 26.12231, + "lon": -80.14338, + "name": "Fort Lauderdale" + }, + { + "lat": 40.84538, + "lon": -73.89097, + "name": "East Tremont" + }, + { + "lat": 10.83333, + "lon": 38.26667, + "name": "Mertule Maryam" + } + ], + "question": "Which location is the geographic outlier among: Avon, San Mateo Otzacatipan, Fort Lauderdale, East Tremont, Mertule Maryam?", + "ground_truth": { + "answer": "Mertule Maryam", + "outlier_distance_km": 10197.4, + "second_furthest_km": 4176.3, + "clarity_ratio": 2.44, + "median_distance_km": 2555.0, + "distances_to_centroid": { + "Avon": 2555.0, + "San Mateo Otzacatipan": 4176.3, + "Fort Lauderdale": 2053.8, + "East Tremont": 1965.3, + "Mertule Maryam": 10197.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Avon: (41.45°, -82.04°)", + " San Mateo Otzacatipan: (19.33°, -99.60°)", + " Fort Lauderdale: (26.12°, -80.14°)", + " East Tremont: (40.85°, -73.89°)", + " Mertule Maryam: (10.83°, 38.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mertule Maryam: 10197.4 km from centroid", + " San Mateo Otzacatipan: 4176.3 km from centroid", + " Avon: 2555.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mertule Maryam", + "FINAL ANSWER: Mertule Maryam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.29899, + "lon": 19.94885, + "name": "Zakopane" + }, + { + "lat": 52.19166, + "lon": -1.70734, + "name": "Stratford-upon-Avon" + }, + { + "lat": 51.50949, + "lon": -0.59541, + "name": "Slough" + }, + { + "lat": 53.20271, + "lon": 5.80973, + "name": "Leeuwarden" + }, + { + "lat": 18.40116, + "lon": -93.21406, + "name": "Paraiso" + } + ], + "question": "Which location is the geographic outlier among: Zakopane, Stratford-upon-Avon, Slough, Leeuwarden, Paraiso?", + "ground_truth": { + "answer": "Paraiso", + "outlier_distance_km": 7742.5, + "second_furthest_km": 2588.6, + "clarity_ratio": 2.99, + "median_distance_km": 1700.4, + "distances_to_centroid": { + "Zakopane": 2588.6, + "Stratford-upon-Avon": 1207.8, + "Slough": 1228.2, + "Leeuwarden": 1700.4, + "Paraiso": 7742.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zakopane: (49.30°, 19.95°)", + " Stratford-upon-Avon: (52.19°, -1.71°)", + " Slough: (51.51°, -0.60°)", + " Leeuwarden: (53.20°, 5.81°)", + " Paraiso: (18.40°, -93.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paraiso: 7742.5 km from centroid", + " Zakopane: 2588.6 km from centroid", + " Leeuwarden: 1700.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paraiso", + "FINAL ANSWER: Paraiso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.704, + "lon": 7.054, + "name": "Bonn Hardtberg" + }, + { + "lat": 51.39462, + "lon": 8.57146, + "name": "Brilon" + }, + { + "lat": 48.90683, + "lon": 2.50648, + "name": "Les Pavillons-sous-Bois" + }, + { + "lat": 53.35578, + "lon": -2.86572, + "name": "Hunts Cross" + }, + { + "lat": 30.16688, + "lon": -96.39774, + "name": "Brenham" + } + ], + "question": "Which location is the geographic outlier among: Bonn Hardtberg, Brilon, Les Pavillons-sous-Bois, Hunts Cross, Brenham?", + "ground_truth": { + "answer": "Brenham", + "outlier_distance_km": 6906.3, + "second_furthest_km": 1861.3, + "clarity_ratio": 3.71, + "median_distance_km": 1748.5, + "distances_to_centroid": { + "Bonn Hardtberg": 1748.5, + "Brilon": 1861.3, + "Les Pavillons-sous-Bois": 1410.2, + "Hunts Cross": 1189.1, + "Brenham": 6906.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bonn Hardtberg: (50.70°, 7.05°)", + " Brilon: (51.39°, 8.57°)", + " Les Pavillons-sous-Bois: (48.91°, 2.51°)", + " Hunts Cross: (53.36°, -2.87°)", + " Brenham: (30.17°, -96.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brenham: 6906.3 km from centroid", + " Brilon: 1861.3 km from centroid", + " Bonn Hardtberg: 1748.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brenham", + "FINAL ANSWER: Brenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.54932, + "lon": 0.04867, + "name": "Manor Park" + }, + { + "lat": 43.14806, + "lon": 45.90194, + "name": "Shali" + }, + { + "lat": 51.44083, + "lon": 5.47778, + "name": "Eindhoven" + }, + { + "lat": 49.765, + "lon": 8.65194, + "name": "Seeheim-Jugenheim" + }, + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + } + ], + "question": "Which location is the geographic outlier among: Manor Park, Shali, Eindhoven, Seeheim-Jugenheim, Warragul?", + "ground_truth": { + "answer": "Warragul", + "outlier_distance_km": 13296.7, + "second_furthest_km": 4005.7, + "clarity_ratio": 3.32, + "median_distance_km": 3649.4, + "distances_to_centroid": { + "Manor Park": 4005.7, + "Shali": 1354.4, + "Eindhoven": 3649.4, + "Seeheim-Jugenheim": 3368.9, + "Warragul": 13296.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manor Park: (51.55°, 0.05°)", + " Shali: (43.15°, 45.90°)", + " Eindhoven: (51.44°, 5.48°)", + " Seeheim-Jugenheim: (49.77°, 8.65°)", + " Warragul: (-38.16°, 145.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Warragul: 13296.7 km from centroid", + " Manor Park: 4005.7 km from centroid", + " Eindhoven: 3649.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Warragul", + "FINAL ANSWER: Warragul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.71503, + "lon": 11.65598, + "name": "Bressanone" + }, + { + "lat": 51.37547, + "lon": 7.70281, + "name": "Iserlohn" + }, + { + "lat": 56.80239, + "lon": 59.93774, + "name": "Revda" + }, + { + "lat": 53.86437, + "lon": -1.68743, + "name": "Yeadon" + }, + { + "lat": -32.57076, + "lon": 27.42396, + "name": "Stutterheim" + } + ], + "question": "Which location is the geographic outlier among: Bressanone, Iserlohn, Revda, Yeadon, Stutterheim?", + "ground_truth": { + "answer": "Stutterheim", + "outlier_distance_km": 7569.6, + "second_furthest_km": 3761.9, + "clarity_ratio": 2.01, + "median_distance_km": 2718.6, + "distances_to_centroid": { + "Bressanone": 1495.9, + "Iserlohn": 2085.3, + "Revda": 3761.9, + "Yeadon": 2718.6, + "Stutterheim": 7569.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bressanone: (46.72°, 11.66°)", + " Iserlohn: (51.38°, 7.70°)", + " Revda: (56.80°, 59.94°)", + " Yeadon: (53.86°, -1.69°)", + " Stutterheim: (-32.57°, 27.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stutterheim: 7569.6 km from centroid", + " Revda: 3761.9 km from centroid", + " Yeadon: 2718.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stutterheim", + "FINAL ANSWER: Stutterheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.5186, + "lon": -104.76136, + "name": "Parker" + }, + { + "lat": 38.70144, + "lon": -90.14872, + "name": "Granite City" + }, + { + "lat": 37.10415, + "lon": -113.58412, + "name": "Saint George" + }, + { + "lat": 35.88452, + "lon": -84.15353, + "name": "Farragut" + }, + { + "lat": 53.24488, + "lon": -3.13231, + "name": "Flint" + } + ], + "question": "Which location is the geographic outlier among: Parker, Granite City, Saint George, Farragut, Flint?", + "ground_truth": { + "answer": "Flint", + "outlier_distance_km": 5634.7, + "second_furthest_km": 2985.3, + "clarity_ratio": 1.89, + "median_distance_km": 2172.1, + "distances_to_centroid": { + "Parker": 2172.1, + "Granite City": 969.4, + "Saint George": 2985.3, + "Farragut": 706.5, + "Flint": 5634.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Parker: (39.52°, -104.76°)", + " Granite City: (38.70°, -90.15°)", + " Saint George: (37.10°, -113.58°)", + " Farragut: (35.88°, -84.15°)", + " Flint: (53.24°, -3.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Flint: 5634.7 km from centroid", + " Saint George: 2985.3 km from centroid", + " Parker: 2172.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Flint", + "FINAL ANSWER: Flint" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.43342, + "lon": -2.97657, + "name": "Kirkdale" + }, + { + "lat": 48.76872, + "lon": 2.53474, + "name": "Sucy-en-Brie" + }, + { + "lat": 51.33645, + "lon": 6.55381, + "name": "Krefeld" + }, + { + "lat": 50.62388, + "lon": 7.02942, + "name": "Meckenheim" + }, + { + "lat": 33.93113, + "lon": -117.54866, + "name": "Norco" + } + ], + "question": "Which location is the geographic outlier among: Kirkdale, Sucy-en-Brie, Krefeld, Meckenheim, Norco?", + "ground_truth": { + "answer": "Norco", + "outlier_distance_km": 7747.2, + "second_furthest_km": 2045.9, + "clarity_ratio": 3.79, + "median_distance_km": 2012.3, + "distances_to_centroid": { + "Kirkdale": 1415.9, + "Sucy-en-Brie": 1733.5, + "Krefeld": 2012.3, + "Meckenheim": 2045.9, + "Norco": 7747.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kirkdale: (53.43°, -2.98°)", + " Sucy-en-Brie: (48.77°, 2.53°)", + " Krefeld: (51.34°, 6.55°)", + " Meckenheim: (50.62°, 7.03°)", + " Norco: (33.93°, -117.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Norco: 7747.2 km from centroid", + " Meckenheim: 2045.9 km from centroid", + " Krefeld: 2012.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Norco", + "FINAL ANSWER: Norco" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + { + "lat": -22.74639, + "lon": -50.38694, + "name": "Cândido Mota" + } + ], + "question": "Which location is the geographic outlier among: Masterton, Ashburton, Tauranga, Werribee, Cândido Mota?", + "ground_truth": { + "answer": "Cândido Mota", + "outlier_distance_km": 13381.4, + "second_furthest_km": 4599.6, + "clarity_ratio": 2.91, + "median_distance_km": 4472.9, + "distances_to_centroid": { + "Masterton": 4472.9, + "Ashburton": 4105.6, + "Tauranga": 4599.6, + "Werribee": 1868.4, + "Cândido Mota": 13381.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Masterton: (-40.96°, 175.66°)", + " Ashburton: (-43.90°, 171.73°)", + " Tauranga: (-37.69°, 176.17°)", + " Werribee: (-37.90°, 144.67°)", + " Cândido Mota: (-22.75°, -50.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cândido Mota: 13381.4 km from centroid", + " Tauranga: 4599.6 km from centroid", + " Masterton: 4472.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cândido Mota", + "FINAL ANSWER: Cândido Mota" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 18.6, + "lon": -96.15, + "name": "La Isla" + }, + { + "lat": 42.43933, + "lon": -123.33067, + "name": "Grants Pass" + }, + { + "lat": 33.24428, + "lon": -86.81638, + "name": "Alabaster" + }, + { + "lat": 40.23384, + "lon": -111.65853, + "name": "Provo" + }, + { + "lat": 52.26, + "lon": 4.55694, + "name": "Lisse" + } + ], + "question": "Which location is the geographic outlier among: La Isla, Grants Pass, Alabaster, Provo, Lisse?", + "ground_truth": { + "answer": "Lisse", + "outlier_distance_km": 6647.6, + "second_furthest_km": 3479.8, + "clarity_ratio": 1.91, + "median_distance_km": 2520.4, + "distances_to_centroid": { + "La Isla": 2463.4, + "Grants Pass": 3479.8, + "Alabaster": 591.4, + "Provo": 2520.4, + "Lisse": 6647.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Isla: (18.60°, -96.15°)", + " Grants Pass: (42.44°, -123.33°)", + " Alabaster: (33.24°, -86.82°)", + " Provo: (40.23°, -111.66°)", + " Lisse: (52.26°, 4.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lisse: 6647.6 km from centroid", + " Grants Pass: 3479.8 km from centroid", + " Provo: 2520.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lisse", + "FINAL ANSWER: Lisse" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.65347, + "lon": 73.14811, + "name": "Vāda" + }, + { + "lat": 43.71947, + "lon": 81.86398, + "name": "Samuyuzi" + }, + { + "lat": 35.65583, + "lon": 139.32389, + "name": "Hachiōji" + }, + { + "lat": 29.90536, + "lon": 107.23789, + "name": "Changshouhu" + }, + { + "lat": -36.88041, + "lon": 174.79819, + "name": "Remuera" + } + ], + "question": "Which location is the geographic outlier among: Vāda, Samuyuzi, Hachiōji, Changshouhu, Remuera?", + "ground_truth": { + "answer": "Remuera", + "outlier_distance_km": 8754.7, + "second_furthest_km": 4419.1, + "clarity_ratio": 1.98, + "median_distance_km": 4197.5, + "distances_to_centroid": { + "Vāda": 4419.1, + "Samuyuzi": 4197.5, + "Hachiōji": 3042.5, + "Changshouhu": 1514.8, + "Remuera": 8754.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vāda: (19.65°, 73.15°)", + " Samuyuzi: (43.72°, 81.86°)", + " Hachiōji: (35.66°, 139.32°)", + " Changshouhu: (29.91°, 107.24°)", + " Remuera: (-36.88°, 174.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Remuera: 8754.7 km from centroid", + " Vāda: 4419.1 km from centroid", + " Samuyuzi: 4197.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Remuera", + "FINAL ANSWER: Remuera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.89667, + "lon": -39.02639, + "name": "Canudos" + }, + { + "lat": -7.86806, + "lon": -37.97472, + "name": "Flores" + }, + { + "lat": -5.57667, + "lon": -36.90861, + "name": "Açu" + }, + { + "lat": -37.15276, + "lon": -58.48838, + "name": "Ayacucho" + }, + { + "lat": 34.84184, + "lon": 116.55722, + "name": "Shunhe" + } + ], + "question": "Which location is the geographic outlier among: Canudos, Flores, Açu, Ayacucho, Shunhe?", + "ground_truth": { + "answer": "Shunhe", + "outlier_distance_km": 13727.4, + "second_furthest_km": 5970.1, + "clarity_ratio": 2.3, + "median_distance_km": 3115.0, + "distances_to_centroid": { + "Canudos": 3115.0, + "Flores": 2976.6, + "Açu": 2849.9, + "Ayacucho": 5970.1, + "Shunhe": 13727.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canudos: (-9.90°, -39.03°)", + " Flores: (-7.87°, -37.97°)", + " Açu: (-5.58°, -36.91°)", + " Ayacucho: (-37.15°, -58.49°)", + " Shunhe: (34.84°, 116.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shunhe: 13727.4 km from centroid", + " Ayacucho: 5970.1 km from centroid", + " Canudos: 3115.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shunhe", + "FINAL ANSWER: Shunhe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -41.27078, + "lon": 173.28404, + "name": "Nelson" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + }, + { + "lat": -37.58333, + "lon": 145.03333, + "name": "Wollert" + }, + { + "lat": 23.73267, + "lon": -103.98247, + "name": "Vicente Guerrero" + } + ], + "question": "Which location is the geographic outlier among: Highton, Nelson, Levin, Wollert, Vicente Guerrero?", + "ground_truth": { + "answer": "Vicente Guerrero", + "outlier_distance_km": 16910.0, + "second_furthest_km": 6359.2, + "clarity_ratio": 2.66, + "median_distance_km": 6183.7, + "distances_to_centroid": { + "Highton": 3711.1, + "Nelson": 6183.7, + "Levin": 6359.2, + "Wollert": 3764.8, + "Vicente Guerrero": 16910.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Highton: (-38.17°, 144.31°)", + " Nelson: (-41.27°, 173.28°)", + " Levin: (-40.63°, 175.28°)", + " Wollert: (-37.58°, 145.03°)", + " Vicente Guerrero: (23.73°, -103.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vicente Guerrero: 16910.0 km from centroid", + " Levin: 6359.2 km from centroid", + " Nelson: 6183.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vicente Guerrero", + "FINAL ANSWER: Vicente Guerrero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.84171, + "lon": 10.57271, + "name": "Capannori" + }, + { + "lat": 48.90683, + "lon": 2.50648, + "name": "Les Pavillons-sous-Bois" + }, + { + "lat": 48.96691, + "lon": 2.36104, + "name": "Pierrefitte-sur-Seine" + }, + { + "lat": 51.76109, + "lon": 18.09102, + "name": "Kalisz" + }, + { + "lat": 40.88593, + "lon": -74.04347, + "name": "Hackensack" + } + ], + "question": "Which location is the geographic outlier among: Capannori, Les Pavillons-sous-Bois, Pierrefitte-sur-Seine, Kalisz, Hackensack?", + "ground_truth": { + "answer": "Hackensack", + "outlier_distance_km": 5170.0, + "second_furthest_km": 1962.9, + "clarity_ratio": 2.63, + "median_distance_km": 1493.7, + "distances_to_centroid": { + "Capannori": 1493.7, + "Les Pavillons-sous-Bois": 822.0, + "Pierrefitte-sur-Seine": 813.0, + "Kalisz": 1962.9, + "Hackensack": 5170.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Capannori: (43.84°, 10.57°)", + " Les Pavillons-sous-Bois: (48.91°, 2.51°)", + " Pierrefitte-sur-Seine: (48.97°, 2.36°)", + " Kalisz: (51.76°, 18.09°)", + " Hackensack: (40.89°, -74.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hackensack: 5170.0 km from centroid", + " Kalisz: 1962.9 km from centroid", + " Capannori: 1493.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hackensack", + "FINAL ANSWER: Hackensack" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.14146, + "lon": 11.45599, + "name": "Pasing" + }, + { + "lat": 47.89246, + "lon": 40.07185, + "name": "Krasnyy Sulin" + }, + { + "lat": 42.88052, + "lon": -8.54569, + "name": "Santiago de Compostela" + }, + { + "lat": 53.58374, + "lon": 9.69835, + "name": "Wedel" + }, + { + "lat": 7.84083, + "lon": 125.04444, + "name": "Dologon" + } + ], + "question": "Which location is the geographic outlier among: Pasing, Krasnyy Sulin, Santiago de Compostela, Wedel, Dologon?", + "ground_truth": { + "answer": "Dologon", + "outlier_distance_km": 9405.0, + "second_furthest_km": 3644.6, + "clarity_ratio": 2.58, + "median_distance_km": 2451.8, + "distances_to_centroid": { + "Pasing": 2110.8, + "Krasnyy Sulin": 942.0, + "Santiago de Compostela": 3644.6, + "Wedel": 2451.8, + "Dologon": 9405.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pasing: (48.14°, 11.46°)", + " Krasnyy Sulin: (47.89°, 40.07°)", + " Santiago de Compostela: (42.88°, -8.55°)", + " Wedel: (53.58°, 9.70°)", + " Dologon: (7.84°, 125.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dologon: 9405.0 km from centroid", + " Santiago de Compostela: 3644.6 km from centroid", + " Wedel: 2451.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dologon", + "FINAL ANSWER: Dologon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.01327, + "lon": -71.26084, + "name": "Limache" + }, + { + "lat": 10.77107, + "lon": -73.00314, + "name": "San Juan del Cesar" + }, + { + "lat": -16.3775, + "lon": -39.58028, + "name": "Eunápolis" + }, + { + "lat": -2.97236, + "lon": -45.35126, + "name": "Pedro do Rosário" + }, + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + } + ], + "question": "Which location is the geographic outlier among: Limache, San Juan del Cesar, Eunápolis, Pedro do Rosário, Tauranga?", + "ground_truth": { + "answer": "Tauranga", + "outlier_distance_km": 14019.5, + "second_furthest_km": 7477.3, + "clarity_ratio": 1.87, + "median_distance_km": 6341.7, + "distances_to_centroid": { + "Limache": 6341.7, + "San Juan del Cesar": 7477.3, + "Eunápolis": 3093.1, + "Pedro do Rosário": 4062.1, + "Tauranga": 14019.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Limache: (-33.01°, -71.26°)", + " San Juan del Cesar: (10.77°, -73.00°)", + " Eunápolis: (-16.38°, -39.58°)", + " Pedro do Rosário: (-2.97°, -45.35°)", + " Tauranga: (-37.69°, 176.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tauranga: 14019.5 km from centroid", + " San Juan del Cesar: 7477.3 km from centroid", + " Limache: 6341.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tauranga", + "FINAL ANSWER: Tauranga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -41.31667, + "lon": 173.23333, + "name": "Stoke" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": 6.33732, + "lon": -75.55795, + "name": "Bello" + } + ], + "question": "Which location is the geographic outlier among: Mildura, Stoke, Camberwell, Rotorua, Bello?", + "ground_truth": { + "answer": "Bello", + "outlier_distance_km": 17362.6, + "second_furthest_km": 5899.9, + "clarity_ratio": 2.94, + "median_distance_km": 5593.4, + "distances_to_centroid": { + "Mildura": 2881.1, + "Stoke": 5593.4, + "Camberwell": 3181.9, + "Rotorua": 5899.9, + "Bello": 17362.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mildura: (-34.19°, 142.16°)", + " Stoke: (-41.32°, 173.23°)", + " Camberwell: (-37.84°, 145.07°)", + " Rotorua: (-38.14°, 176.25°)", + " Bello: (6.34°, -75.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bello: 17362.6 km from centroid", + " Rotorua: 5899.9 km from centroid", + " Stoke: 5593.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bello", + "FINAL ANSWER: Bello" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.26917, + "lon": -51.04806, + "name": "Ibiporã" + }, + { + "lat": -6.51056, + "lon": -36.34694, + "name": "Picuí" + }, + { + "lat": -33.03016, + "lon": -60.64045, + "name": "Gobernador Gálvez" + }, + { + "lat": -29.58667, + "lon": -51.37556, + "name": "São Sebastião do Caí" + }, + { + "lat": 27.81641, + "lon": -80.47061, + "name": "Sebastian" + } + ], + "question": "Which location is the geographic outlier among: Ibiporã, Picuí, Gobernador Gálvez, São Sebastião do Caí, Sebastian?", + "ground_truth": { + "answer": "Sebastian", + "outlier_distance_km": 5242.0, + "second_furthest_km": 2286.2, + "clarity_ratio": 2.29, + "median_distance_km": 2264.8, + "distances_to_centroid": { + "Ibiporã": 1263.2, + "Picuí": 2264.8, + "Gobernador Gálvez": 2286.2, + "São Sebastião do Caí": 1913.4, + "Sebastian": 5242.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ibiporã: (-23.27°, -51.05°)", + " Picuí: (-6.51°, -36.35°)", + " Gobernador Gálvez: (-33.03°, -60.64°)", + " São Sebastião do Caí: (-29.59°, -51.38°)", + " Sebastian: (27.82°, -80.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sebastian: 5242.0 km from centroid", + " Gobernador Gálvez: 2286.2 km from centroid", + " Picuí: 2264.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sebastian", + "FINAL ANSWER: Sebastian" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.33565, + "lon": -75.92687, + "name": "Reading" + }, + { + "lat": 18.8106, + "lon": -98.93525, + "name": "Cuautla" + }, + { + "lat": 17.83498, + "lon": -93.38902, + "name": "Huimanguillo" + }, + { + "lat": 36.07264, + "lon": -79.79198, + "name": "Greensboro" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + } + ], + "question": "Which location is the geographic outlier among: Reading, Cuautla, Huimanguillo, Greensboro, Sunbury?", + "ground_truth": { + "answer": "Sunbury", + "outlier_distance_km": 17459.4, + "second_furthest_km": 6185.3, + "clarity_ratio": 2.82, + "median_distance_km": 5612.7, + "distances_to_centroid": { + "Reading": 4413.6, + "Cuautla": 6185.3, + "Huimanguillo": 5612.7, + "Greensboro": 4520.0, + "Sunbury": 17459.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reading: (40.34°, -75.93°)", + " Cuautla: (18.81°, -98.94°)", + " Huimanguillo: (17.83°, -93.39°)", + " Greensboro: (36.07°, -79.79°)", + " Sunbury: (-37.58°, 144.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunbury: 17459.4 km from centroid", + " Cuautla: 6185.3 km from centroid", + " Huimanguillo: 5612.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunbury", + "FINAL ANSWER: Sunbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.96122, + "lon": -77.02748, + "name": "Brightwood" + }, + { + "lat": 33.39678, + "lon": -84.59576, + "name": "Peachtree City" + }, + { + "lat": 40.5142, + "lon": -88.99063, + "name": "Normal" + }, + { + "lat": 22.74678, + "lon": -102.5188, + "name": "Guadalupe" + }, + { + "lat": 19.84505, + "lon": 73.99866, + "name": "Sinnar" + } + ], + "question": "Which location is the geographic outlier among: Brightwood, Peachtree City, Normal, Guadalupe, Sinnar?", + "ground_truth": { + "answer": "Sinnar", + "outlier_distance_km": 12221.5, + "second_furthest_km": 4687.0, + "clarity_ratio": 2.61, + "median_distance_km": 3147.0, + "distances_to_centroid": { + "Brightwood": 2112.7, + "Peachtree City": 2709.1, + "Normal": 3147.0, + "Guadalupe": 4687.0, + "Sinnar": 12221.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brightwood: (38.96°, -77.03°)", + " Peachtree City: (33.40°, -84.60°)", + " Normal: (40.51°, -88.99°)", + " Guadalupe: (22.75°, -102.52°)", + " Sinnar: (19.85°, 74.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sinnar: 12221.5 km from centroid", + " Guadalupe: 4687.0 km from centroid", + " Normal: 3147.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sinnar", + "FINAL ANSWER: Sinnar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.54528, + "lon": -52.98778, + "name": "Ubiratã" + }, + { + "lat": 6.28535, + "lon": -75.33385, + "name": "San Vicente" + }, + { + "lat": -7.71361, + "lon": -66.97639, + "name": "Pauini" + }, + { + "lat": -10.80639, + "lon": -37.17, + "name": "Laranjeiras" + }, + { + "lat": 41.49206, + "lon": 2.36524, + "name": "Premià de Mar" + } + ], + "question": "Which location is the geographic outlier among: Ubiratã, San Vicente, Pauini, Laranjeiras, Premià de Mar?", + "ground_truth": { + "answer": "Premià de Mar", + "outlier_distance_km": 6610.6, + "second_furthest_km": 3305.5, + "clarity_ratio": 2.0, + "median_distance_km": 2932.0, + "distances_to_centroid": { + "Ubiratã": 2932.0, + "San Vicente": 3305.5, + "Pauini": 2515.3, + "Laranjeiras": 1632.4, + "Premià de Mar": 6610.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ubiratã: (-24.55°, -52.99°)", + " San Vicente: (6.29°, -75.33°)", + " Pauini: (-7.71°, -66.98°)", + " Laranjeiras: (-10.81°, -37.17°)", + " Premià de Mar: (41.49°, 2.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Premià de Mar: 6610.6 km from centroid", + " San Vicente: 3305.5 km from centroid", + " Ubiratã: 2932.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Premià de Mar", + "FINAL ANSWER: Premià de Mar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.79808, + "lon": 100.65397, + "name": "Lop Buri" + }, + { + "lat": 21.69482, + "lon": 72.9805, + "name": "Bharūch" + }, + { + "lat": 10.0009, + "lon": 105.75095, + "name": "Cái Răng" + }, + { + "lat": 22.96585, + "lon": 76.05526, + "name": "Dewas" + }, + { + "lat": 5.71417, + "lon": -0.15418, + "name": "Adenta" + } + ], + "question": "Which location is the geographic outlier among: Lop Buri, Bharūch, Cái Răng, Dewas, Adenta?", + "ground_truth": { + "answer": "Adenta", + "outlier_distance_km": 7828.9, + "second_furthest_km": 3803.3, + "clarity_ratio": 2.06, + "median_distance_km": 3177.8, + "distances_to_centroid": { + "Lop Buri": 3177.8, + "Bharūch": 767.8, + "Cái Răng": 3803.3, + "Dewas": 1026.3, + "Adenta": 7828.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lop Buri: (14.80°, 100.65°)", + " Bharūch: (21.69°, 72.98°)", + " Cái Răng: (10.00°, 105.75°)", + " Dewas: (22.97°, 76.06°)", + " Adenta: (5.71°, -0.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adenta: 7828.9 km from centroid", + " Cái Răng: 3803.3 km from centroid", + " Lop Buri: 3177.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adenta", + "FINAL ANSWER: Adenta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.87796, + "lon": -77.00314, + "name": "Capitol Riverfront" + }, + { + "lat": 39.61366, + "lon": -86.10665, + "name": "Greenwood" + }, + { + "lat": 41.6764, + "lon": -91.58045, + "name": "Coralville" + }, + { + "lat": 43.67089, + "lon": -79.52246, + "name": "Edenbridge-Humber Valley" + }, + { + "lat": 54.37648, + "lon": 18.60753, + "name": "Wrzeszcz" + } + ], + "question": "Which location is the geographic outlier among: Capitol Riverfront, Greenwood, Coralville, Edenbridge-Humber Valley, Wrzeszcz?", + "ground_truth": { + "answer": "Wrzeszcz", + "outlier_distance_km": 5733.6, + "second_furthest_km": 2326.0, + "clarity_ratio": 2.47, + "median_distance_km": 1955.4, + "distances_to_centroid": { + "Capitol Riverfront": 1273.5, + "Greenwood": 1955.4, + "Coralville": 2326.0, + "Edenbridge-Humber Valley": 1317.3, + "Wrzeszcz": 5733.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Capitol Riverfront: (38.88°, -77.00°)", + " Greenwood: (39.61°, -86.11°)", + " Coralville: (41.68°, -91.58°)", + " Edenbridge-Humber Valley: (43.67°, -79.52°)", + " Wrzeszcz: (54.38°, 18.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wrzeszcz: 5733.6 km from centroid", + " Coralville: 2326.0 km from centroid", + " Greenwood: 1955.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wrzeszcz", + "FINAL ANSWER: Wrzeszcz" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.46556, + "lon": 12.2375, + "name": "Città di Castello" + }, + { + "lat": 51.3624, + "lon": -0.30427, + "name": "Chessington" + }, + { + "lat": 49.13645, + "lon": 8.91229, + "name": "Eppingen" + }, + { + "lat": 50.34984, + "lon": 18.22606, + "name": "Kędzierzyn-Koźle" + }, + { + "lat": 31.0475, + "lon": 30.85487, + "name": "Qillīn" + } + ], + "question": "Which location is the geographic outlier among: Città di Castello, Chessington, Eppingen, Kędzierzyn-Koźle, Qillīn?", + "ground_truth": { + "answer": "Qillīn", + "outlier_distance_km": 2139.2, + "second_furthest_km": 1265.5, + "clarity_ratio": 1.69, + "median_distance_km": 666.9, + "distances_to_centroid": { + "Città di Castello": 226.5, + "Chessington": 1265.5, + "Eppingen": 592.7, + "Kędzierzyn-Koźle": 666.9, + "Qillīn": 2139.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Città di Castello: (43.47°, 12.24°)", + " Chessington: (51.36°, -0.30°)", + " Eppingen: (49.14°, 8.91°)", + " Kędzierzyn-Koźle: (50.35°, 18.23°)", + " Qillīn: (31.05°, 30.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qillīn: 2139.2 km from centroid", + " Chessington: 1265.5 km from centroid", + " Kędzierzyn-Koźle: 666.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qillīn", + "FINAL ANSWER: Qillīn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.7541, + "lon": 103.2798, + "name": "Kawasan Penempatan Ulu Sungai Benut" + }, + { + "lat": 26.31397, + "lon": 86.58537, + "name": "Nirmāli" + }, + { + "lat": 17.26214, + "lon": 74.17574, + "name": "Malkapur" + }, + { + "lat": 3.7755, + "lon": 98.6832, + "name": "Belawan" + }, + { + "lat": 41.3145, + "lon": -81.83569, + "name": "Strongsville" + } + ], + "question": "Which location is the geographic outlier among: Kawasan Penempatan Ulu Sungai Benut, Nirmāli, Malkapur, Belawan, Strongsville?", + "ground_truth": { + "answer": "Strongsville", + "outlier_distance_km": 12121.7, + "second_furthest_km": 5446.8, + "clarity_ratio": 2.23, + "median_distance_km": 4889.1, + "distances_to_centroid": { + "Kawasan Penempatan Ulu Sungai Benut": 5446.8, + "Nirmāli": 3252.5, + "Malkapur": 1908.3, + "Belawan": 4889.1, + "Strongsville": 12121.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kawasan Penempatan Ulu Sungai Benut: (1.75°, 103.28°)", + " Nirmāli: (26.31°, 86.59°)", + " Malkapur: (17.26°, 74.18°)", + " Belawan: (3.78°, 98.68°)", + " Strongsville: (41.31°, -81.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Strongsville: 12121.7 km from centroid", + " Kawasan Penempatan Ulu Sungai Benut: 5446.8 km from centroid", + " Belawan: 4889.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Strongsville", + "FINAL ANSWER: Strongsville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.62361, + "lon": -37.75667, + "name": "Piranhas" + }, + { + "lat": -13.64136, + "lon": -41.84319, + "name": "Livramento de Nossa Senhora" + }, + { + "lat": -10.16931, + "lon": -54.93439, + "name": "Matupá" + }, + { + "lat": -38.90056, + "lon": -70.06674, + "name": "Zapala" + }, + { + "lat": 6.86, + "lon": 37.76159, + "name": "Sodo" + } + ], + "question": "Which location is the geographic outlier among: Piranhas, Livramento de Nossa Senhora, Matupá, Zapala, Sodo?", + "ground_truth": { + "answer": "Sodo", + "outlier_distance_km": 8161.6, + "second_furthest_km": 4604.2, + "clarity_ratio": 1.77, + "median_distance_km": 2370.4, + "distances_to_centroid": { + "Piranhas": 614.7, + "Livramento de Nossa Senhora": 918.8, + "Matupá": 2370.4, + "Zapala": 4604.2, + "Sodo": 8161.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piranhas: (-9.62°, -37.76°)", + " Livramento de Nossa Senhora: (-13.64°, -41.84°)", + " Matupá: (-10.17°, -54.93°)", + " Zapala: (-38.90°, -70.07°)", + " Sodo: (6.86°, 37.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sodo: 8161.6 km from centroid", + " Zapala: 4604.2 km from centroid", + " Matupá: 2370.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sodo", + "FINAL ANSWER: Sodo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.03312, + "lon": -86.78278, + "name": "Brentwood" + }, + { + "lat": 40.36979, + "lon": -80.63396, + "name": "Steubenville" + }, + { + "lat": 25.62177, + "lon": -80.32477, + "name": "Palmetto Bay" + }, + { + "lat": 43.57036, + "lon": -70.38783, + "name": "West Scarborough" + }, + { + "lat": 14.6377, + "lon": 102.79138, + "name": "Nang Rong" + } + ], + "question": "Which location is the geographic outlier among: Brentwood, Steubenville, Palmetto Bay, West Scarborough, Nang Rong?", + "ground_truth": { + "answer": "Nang Rong", + "outlier_distance_km": 13677.3, + "second_furthest_km": 4018.8, + "clarity_ratio": 3.4, + "median_distance_km": 3680.2, + "distances_to_centroid": { + "Brentwood": 4018.8, + "Steubenville": 3466.8, + "Palmetto Bay": 3680.2, + "West Scarborough": 2703.0, + "Nang Rong": 13677.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brentwood: (36.03°, -86.78°)", + " Steubenville: (40.37°, -80.63°)", + " Palmetto Bay: (25.62°, -80.32°)", + " West Scarborough: (43.57°, -70.39°)", + " Nang Rong: (14.64°, 102.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nang Rong: 13677.3 km from centroid", + " Brentwood: 4018.8 km from centroid", + " Palmetto Bay: 3680.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nang Rong", + "FINAL ANSWER: Nang Rong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -3.38361, + "lon": -57.71861, + "name": "Maués" + } + ], + "question": "Which location is the geographic outlier among: Coogee, Perth, Kensington, Blenheim, Maués?", + "ground_truth": { + "answer": "Maués", + "outlier_distance_km": 16064.5, + "second_furthest_km": 6094.0, + "clarity_ratio": 2.64, + "median_distance_km": 4211.0, + "distances_to_centroid": { + "Coogee": 4211.0, + "Perth": 920.4, + "Kensington": 4208.0, + "Blenheim": 6094.0, + "Maués": 16064.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coogee: (-33.92°, 151.26°)", + " Perth: (-31.95°, 115.86°)", + " Kensington: (-33.92°, 151.22°)", + " Blenheim: (-41.52°, 173.95°)", + " Maués: (-3.38°, -57.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maués: 16064.5 km from centroid", + " Blenheim: 6094.0 km from centroid", + " Coogee: 4211.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maués", + "FINAL ANSWER: Maués" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.98219, + "lon": -70.7104, + "name": "San Francisco de Mostazal" + }, + { + "lat": -12.5275, + "lon": -40.30694, + "name": "Itaberaba" + }, + { + "lat": 7.48971, + "lon": -74.86919, + "name": "Zaragoza" + }, + { + "lat": -21.64611, + "lon": -41.74694, + "name": "São Fidélis" + }, + { + "lat": 50.2584, + "lon": 18.85632, + "name": "Ruda Śląska" + } + ], + "question": "Which location is the geographic outlier among: San Francisco de Mostazal, Itaberaba, Zaragoza, São Fidélis, Ruda Śląska?", + "ground_truth": { + "answer": "Ruda Śląska", + "outlier_distance_km": 8162.3, + "second_furthest_km": 4648.8, + "clarity_ratio": 1.76, + "median_distance_km": 3824.6, + "distances_to_centroid": { + "San Francisco de Mostazal": 4648.8, + "Itaberaba": 1172.4, + "Zaragoza": 3824.6, + "São Fidélis": 2175.5, + "Ruda Śląska": 8162.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Francisco de Mostazal: (-33.98°, -70.71°)", + " Itaberaba: (-12.53°, -40.31°)", + " Zaragoza: (7.49°, -74.87°)", + " São Fidélis: (-21.65°, -41.75°)", + " Ruda Śląska: (50.26°, 18.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ruda Śląska: 8162.3 km from centroid", + " San Francisco de Mostazal: 4648.8 km from centroid", + " Zaragoza: 3824.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ruda Śląska", + "FINAL ANSWER: Ruda Śląska" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.5, + "lon": -3.68333, + "name": "Fuencarral" + }, + { + "lat": 52.7875, + "lon": 6.12083, + "name": "Steenwijk" + }, + { + "lat": 52.04098, + "lon": 4.36981, + "name": "Ypenburg" + }, + { + "lat": 51.1397, + "lon": 7.21583, + "name": "Wermelskirchen" + }, + { + "lat": 25.80722, + "lon": 109.2125, + "name": "Long’e" + } + ], + "question": "Which location is the geographic outlier among: Fuencarral, Steenwijk, Ypenburg, Wermelskirchen, Long’e?", + "ground_truth": { + "answer": "Long’e", + "outlier_distance_km": 7622.0, + "second_furthest_km": 2352.3, + "clarity_ratio": 3.24, + "median_distance_km": 1713.8, + "distances_to_centroid": { + "Fuencarral": 2352.3, + "Steenwijk": 1639.4, + "Ypenburg": 1713.8, + "Wermelskirchen": 1493.9, + "Long’e": 7622.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fuencarral: (40.50°, -3.68°)", + " Steenwijk: (52.79°, 6.12°)", + " Ypenburg: (52.04°, 4.37°)", + " Wermelskirchen: (51.14°, 7.22°)", + " Long’e: (25.81°, 109.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Long’e: 7622.0 km from centroid", + " Fuencarral: 2352.3 km from centroid", + " Ypenburg: 1713.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Long’e", + "FINAL ANSWER: Long’e" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.53811, + "lon": -0.2502, + "name": "Harlesden" + }, + { + "lat": 49.4891, + "lon": 8.46694, + "name": "Mannheim" + }, + { + "lat": 51.94349, + "lon": 7.16809, + "name": "Coesfeld" + }, + { + "lat": 51.41363, + "lon": -0.75054, + "name": "Bracknell" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + } + ], + "question": "Which location is the geographic outlier among: Harlesden, Mannheim, Coesfeld, Bracknell, Coorparoo?", + "ground_truth": { + "answer": "Coorparoo", + "outlier_distance_km": 14297.8, + "second_furthest_km": 3249.6, + "clarity_ratio": 4.4, + "median_distance_km": 3221.9, + "distances_to_centroid": { + "Harlesden": 3221.9, + "Mannheim": 2567.0, + "Coesfeld": 2781.6, + "Bracknell": 3249.6, + "Coorparoo": 14297.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Harlesden: (51.54°, -0.25°)", + " Mannheim: (49.49°, 8.47°)", + " Coesfeld: (51.94°, 7.17°)", + " Bracknell: (51.41°, -0.75°)", + " Coorparoo: (-27.49°, 153.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coorparoo: 14297.8 km from centroid", + " Bracknell: 3249.6 km from centroid", + " Harlesden: 3221.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coorparoo", + "FINAL ANSWER: Coorparoo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + }, + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + }, + { + "lat": -34.75155, + "lon": 149.72086, + "name": "Goulburn" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -23.30528, + "lon": -45.96583, + "name": "Jacareí" + } + ], + "question": "Which location is the geographic outlier among: Malvern East, Hornsby, Goulburn, Ellenbrook, Jacareí?", + "ground_truth": { + "answer": "Jacareí", + "outlier_distance_km": 13018.8, + "second_furthest_km": 4431.9, + "clarity_ratio": 2.94, + "median_distance_km": 4285.5, + "distances_to_centroid": { + "Malvern East": 3828.2, + "Hornsby": 4431.9, + "Goulburn": 4285.5, + "Ellenbrook": 1207.0, + "Jacareí": 13018.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Malvern East: (-37.87°, 145.04°)", + " Hornsby: (-33.70°, 151.10°)", + " Goulburn: (-34.75°, 149.72°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Jacareí: (-23.31°, -45.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jacareí: 13018.8 km from centroid", + " Hornsby: 4431.9 km from centroid", + " Goulburn: 4285.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jacareí", + "FINAL ANSWER: Jacareí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": 29.47091, + "lon": 77.70332, + "name": "Muzaffarnagar" + } + ], + "question": "Which location is the geographic outlier among: Mooroolbark, Mackay, Surfers Paradise, Saint Albans, Muzaffarnagar?", + "ground_truth": { + "answer": "Muzaffarnagar", + "outlier_distance_km": 8098.6, + "second_furthest_km": 2351.4, + "clarity_ratio": 3.44, + "median_distance_km": 2323.9, + "distances_to_centroid": { + "Mooroolbark": 2351.4, + "Mackay": 1591.7, + "Surfers Paradise": 2205.8, + "Saint Albans": 2323.9, + "Muzaffarnagar": 8098.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mooroolbark: (-37.78°, 145.32°)", + " Mackay: (-21.15°, 149.17°)", + " Surfers Paradise: (-28.00°, 153.43°)", + " Saint Albans: (-37.73°, 144.80°)", + " Muzaffarnagar: (29.47°, 77.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Muzaffarnagar: 8098.6 km from centroid", + " Mooroolbark: 2351.4 km from centroid", + " Saint Albans: 2323.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Muzaffarnagar", + "FINAL ANSWER: Muzaffarnagar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -38.14711, + "lon": 144.36069, + "name": "Geelong" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + }, + { + "lat": -33.77271, + "lon": 151.08184, + "name": "Epping" + }, + { + "lat": -22.11639, + "lon": -45.05444, + "name": "São Lourenço" + } + ], + "question": "Which location is the geographic outlier among: Highton, Geelong, Te Atatu Peninsula, Epping, São Lourenço?", + "ground_truth": { + "answer": "São Lourenço", + "outlier_distance_km": 13408.1, + "second_furthest_km": 5430.2, + "clarity_ratio": 2.47, + "median_distance_km": 3419.5, + "distances_to_centroid": { + "Highton": 2768.5, + "Geelong": 2772.8, + "Te Atatu Peninsula": 5430.2, + "Epping": 3419.5, + "São Lourenço": 13408.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Highton: (-38.17°, 144.31°)", + " Geelong: (-38.15°, 144.36°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + " Epping: (-33.77°, 151.08°)", + " São Lourenço: (-22.12°, -45.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Lourenço: 13408.1 km from centroid", + " Te Atatu Peninsula: 5430.2 km from centroid", + " Epping: 3419.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Lourenço", + "FINAL ANSWER: São Lourenço" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.88556, + "lon": -40.12, + "name": "Acaraú" + }, + { + "lat": -3.52278, + "lon": -40.34278, + "name": "Massapê" + }, + { + "lat": -23.05056, + "lon": -50.22889, + "name": "Andirá" + }, + { + "lat": -29.67833, + "lon": -51.13056, + "name": "Novo Hamburgo" + }, + { + "lat": 21.27697, + "lon": -157.81127, + "name": "Diamond Head / Kapahulu / Saint Louis Heights" + } + ], + "question": "Which location is the geographic outlier among: Acaraú, Massapê, Andirá, Novo Hamburgo, Diamond Head / Kapahulu / Saint Louis Heights?", + "ground_truth": { + "answer": "Diamond Head / Kapahulu / Saint Louis Heights", + "outlier_distance_km": 10300.4, + "second_furthest_km": 3121.8, + "clarity_ratio": 3.3, + "median_distance_km": 3084.9, + "distances_to_centroid": { + "Acaraú": 3121.8, + "Massapê": 3084.9, + "Andirá": 2556.6, + "Novo Hamburgo": 3019.9, + "Diamond Head / Kapahulu / Saint Louis Heights": 10300.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Acaraú: (-2.89°, -40.12°)", + " Massapê: (-3.52°, -40.34°)", + " Andirá: (-23.05°, -50.23°)", + " Novo Hamburgo: (-29.68°, -51.13°)", + " Diamond Head / Kapahulu / Saint Louis Heights: (21.28°, -157.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Diamond Head / Kapahulu / Saint Louis Heights: 10300.4 km from centroid", + " Acaraú: 3121.8 km from centroid", + " Massapê: 3084.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Diamond Head / Kapahulu / Saint Louis Heights", + "FINAL ANSWER: Diamond Head / Kapahulu / Saint Louis Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.67806, + "lon": -39.375, + "name": "Itajuípe" + }, + { + "lat": -16.735, + "lon": -43.86167, + "name": "Montes Claros" + }, + { + "lat": -19.96722, + "lon": -43.80417, + "name": "Raposos" + }, + { + "lat": -26.76389, + "lon": -48.67167, + "name": "Balneário Piçarras" + }, + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + } + ], + "question": "Which location is the geographic outlier among: Itajuípe, Montes Claros, Raposos, Balneário Piçarras, Rotorua?", + "ground_truth": { + "answer": "Rotorua", + "outlier_distance_km": 13176.3, + "second_furthest_km": 4901.4, + "clarity_ratio": 2.69, + "median_distance_km": 4634.0, + "distances_to_centroid": { + "Itajuípe": 4245.9, + "Montes Claros": 4634.0, + "Raposos": 4537.4, + "Balneário Piçarras": 4901.4, + "Rotorua": 13176.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itajuípe: (-14.68°, -39.38°)", + " Montes Claros: (-16.73°, -43.86°)", + " Raposos: (-19.97°, -43.80°)", + " Balneário Piçarras: (-26.76°, -48.67°)", + " Rotorua: (-38.14°, 176.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rotorua: 13176.3 km from centroid", + " Balneário Piçarras: 4901.4 km from centroid", + " Montes Claros: 4634.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rotorua", + "FINAL ANSWER: Rotorua" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.33212, + "lon": -99.21118, + "name": "Magdalena Contreras" + }, + { + "lat": 27.80058, + "lon": -97.39638, + "name": "Corpus Christi" + }, + { + "lat": 40.82927, + "lon": -73.90653, + "name": "Morrisania" + }, + { + "lat": 38.02931, + "lon": -78.47668, + "name": "Charlottesville" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + } + ], + "question": "Which location is the geographic outlier among: Magdalena Contreras, Corpus Christi, Morrisania, Charlottesville, Paraparaumu?", + "ground_truth": { + "answer": "Paraparaumu", + "outlier_distance_km": 16117.3, + "second_furthest_km": 6770.5, + "clarity_ratio": 2.38, + "median_distance_km": 6480.8, + "distances_to_centroid": { + "Magdalena Contreras": 6770.5, + "Corpus Christi": 6480.8, + "Morrisania": 4578.2, + "Charlottesville": 4840.5, + "Paraparaumu": 16117.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Magdalena Contreras: (19.33°, -99.21°)", + " Corpus Christi: (27.80°, -97.40°)", + " Morrisania: (40.83°, -73.91°)", + " Charlottesville: (38.03°, -78.48°)", + " Paraparaumu: (-40.92°, 175.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paraparaumu: 16117.3 km from centroid", + " Magdalena Contreras: 6770.5 km from centroid", + " Corpus Christi: 6480.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paraparaumu", + "FINAL ANSWER: Paraparaumu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.90561, + "lon": 145.00279, + "name": "Brighton" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -36.88012, + "lon": 174.61975, + "name": "Henderson" + }, + { + "lat": -27.94402, + "lon": 153.39815, + "name": "Labrador" + }, + { + "lat": -16.575, + "lon": -39.55333, + "name": "Itabela" + } + ], + "question": "Which location is the geographic outlier among: Brighton, Ellenbrook, Henderson, Labrador, Itabela?", + "ground_truth": { + "answer": "Itabela", + "outlier_distance_km": 13868.8, + "second_furthest_km": 5931.2, + "clarity_ratio": 2.34, + "median_distance_km": 4210.3, + "distances_to_centroid": { + "Brighton": 3324.6, + "Ellenbrook": 604.8, + "Henderson": 5931.2, + "Labrador": 4210.3, + "Itabela": 13868.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brighton: (-37.91°, 145.00°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Henderson: (-36.88°, 174.62°)", + " Labrador: (-27.94°, 153.40°)", + " Itabela: (-16.57°, -39.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itabela: 13868.8 km from centroid", + " Henderson: 5931.2 km from centroid", + " Labrador: 4210.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itabela", + "FINAL ANSWER: Itabela" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.83342, + "lon": 14.24751, + "name": "San Ferdinando" + }, + { + "lat": 53.84711, + "lon": -1.78785, + "name": "Baildon" + }, + { + "lat": 40.39023, + "lon": -3.72178, + "name": "Opañel" + }, + { + "lat": 50.36463, + "lon": 8.73859, + "name": "Bad Nauheim" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + } + ], + "question": "Which location is the geographic outlier among: San Ferdinando, Baildon, Opañel, Bad Nauheim, Broken Hill?", + "ground_truth": { + "answer": "Broken Hill", + "outlier_distance_km": 13459.8, + "second_furthest_km": 3714.1, + "clarity_ratio": 3.62, + "median_distance_km": 3362.6, + "distances_to_centroid": { + "San Ferdinando": 1936.9, + "Baildon": 3714.1, + "Opañel": 3362.6, + "Bad Nauheim": 2904.6, + "Broken Hill": 13459.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Ferdinando: (40.83°, 14.25°)", + " Baildon: (53.85°, -1.79°)", + " Opañel: (40.39°, -3.72°)", + " Bad Nauheim: (50.36°, 8.74°)", + " Broken Hill: (-31.97°, 141.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Broken Hill: 13459.8 km from centroid", + " Baildon: 3714.1 km from centroid", + " Opañel: 3362.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Broken Hill", + "FINAL ANSWER: Broken Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 11.19152, + "lon": 40.01675, + "name": "Batī" + }, + { + "lat": -26.53333, + "lon": 29.06667, + "name": "eMbalenhle" + }, + { + "lat": 12.01667, + "lon": 39.63333, + "name": "Robīt" + }, + { + "lat": -26.1466, + "lon": 28.68322, + "name": "Delmas" + }, + { + "lat": 41.82649, + "lon": -72.73009, + "name": "Bloomfield" + } + ], + "question": "Which location is the geographic outlier among: Batī, eMbalenhle, Robīt, Delmas, Bloomfield?", + "ground_truth": { + "answer": "Bloomfield", + "outlier_distance_km": 9465.1, + "second_furthest_km": 3661.1, + "clarity_ratio": 2.59, + "median_distance_km": 3604.6, + "distances_to_centroid": { + "Batī": 3140.1, + "eMbalenhle": 3661.1, + "Robīt": 3126.8, + "Delmas": 3604.6, + "Bloomfield": 9465.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Batī: (11.19°, 40.02°)", + " eMbalenhle: (-26.53°, 29.07°)", + " Robīt: (12.02°, 39.63°)", + " Delmas: (-26.15°, 28.68°)", + " Bloomfield: (41.83°, -72.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bloomfield: 9465.1 km from centroid", + " eMbalenhle: 3661.1 km from centroid", + " Delmas: 3604.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bloomfield", + "FINAL ANSWER: Bloomfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88041, + "lon": 174.79819, + "name": "Remuera" + }, + { + "lat": -33.79728, + "lon": 150.7847, + "name": "St Clair" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + { + "lat": -28.65083, + "lon": -49.21, + "name": "Morro da Fumaça" + } + ], + "question": "Which location is the geographic outlier among: Remuera, St Clair, Pacific Pines, Boronia, Morro da Fumaça?", + "ground_truth": { + "answer": "Morro da Fumaça", + "outlier_distance_km": 12957.4, + "second_furthest_km": 5377.8, + "clarity_ratio": 2.41, + "median_distance_km": 3694.9, + "distances_to_centroid": { + "Remuera": 5377.8, + "St Clair": 3306.2, + "Pacific Pines": 3694.9, + "Boronia": 2783.3, + "Morro da Fumaça": 12957.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Remuera: (-36.88°, 174.80°)", + " St Clair: (-33.80°, 150.78°)", + " Pacific Pines: (-27.94°, 153.31°)", + " Boronia: (-37.87°, 145.28°)", + " Morro da Fumaça: (-28.65°, -49.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morro da Fumaça: 12957.4 km from centroid", + " Remuera: 5377.8 km from centroid", + " Pacific Pines: 3694.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morro da Fumaça", + "FINAL ANSWER: Morro da Fumaça" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.6501, + "lon": -63.91165, + "name": "Río Segundo" + }, + { + "lat": -22.55417, + "lon": -45.78, + "name": "Paraisópolis" + }, + { + "lat": -53.78773, + "lon": -67.70975, + "name": "Río Grande" + }, + { + "lat": -17.08222, + "lon": -40.93583, + "name": "Águas Formosas" + }, + { + "lat": -37.83382, + "lon": 144.93834, + "name": "City of Port Phillip" + } + ], + "question": "Which location is the geographic outlier among: Río Segundo, Paraisópolis, Río Grande, Águas Formosas, City of Port Phillip?", + "ground_truth": { + "answer": "City of Port Phillip", + "outlier_distance_km": 11905.6, + "second_furthest_km": 4757.9, + "clarity_ratio": 2.5, + "median_distance_km": 4595.2, + "distances_to_centroid": { + "Río Segundo": 4595.2, + "Paraisópolis": 3247.5, + "Río Grande": 4757.9, + "Águas Formosas": 3146.1, + "City of Port Phillip": 11905.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Río Segundo: (-31.65°, -63.91°)", + " Paraisópolis: (-22.55°, -45.78°)", + " Río Grande: (-53.79°, -67.71°)", + " Águas Formosas: (-17.08°, -40.94°)", + " City of Port Phillip: (-37.83°, 144.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " City of Port Phillip: 11905.6 km from centroid", + " Río Grande: 4757.9 km from centroid", + " Río Segundo: 4595.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: City of Port Phillip", + "FINAL ANSWER: City of Port Phillip" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.1625, + "lon": 27.8725, + "name": "Roodepoort" + }, + { + "lat": -25.33177, + "lon": 31.01166, + "name": "White River" + }, + { + "lat": 12.17024, + "lon": 6.66412, + "name": "Gusau" + }, + { + "lat": 6.83333, + "lon": 38.08333, + "name": "Bedēsa" + }, + { + "lat": 16.06667, + "lon": 120.68333, + "name": "Guiset East" + } + ], + "question": "Which location is the geographic outlier among: Roodepoort, White River, Gusau, Bedēsa, Guiset East?", + "ground_truth": { + "answer": "Guiset East", + "outlier_distance_km": 8599.9, + "second_furthest_km": 4557.5, + "clarity_ratio": 1.89, + "median_distance_km": 3123.2, + "distances_to_centroid": { + "Roodepoort": 3123.2, + "White River": 2864.2, + "Gusau": 4557.5, + "Bedēsa": 1353.6, + "Guiset East": 8599.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Roodepoort: (-26.16°, 27.87°)", + " White River: (-25.33°, 31.01°)", + " Gusau: (12.17°, 6.66°)", + " Bedēsa: (6.83°, 38.08°)", + " Guiset East: (16.07°, 120.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guiset East: 8599.9 km from centroid", + " Gusau: 4557.5 km from centroid", + " Roodepoort: 3123.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guiset East", + "FINAL ANSWER: Guiset East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.95373, + "lon": -74.19792, + "name": "Toms River" + }, + { + "lat": 49.26305, + "lon": -123.13212, + "name": "Fairview" + }, + { + "lat": 33.8464, + "lon": -118.04673, + "name": "La Palma" + }, + { + "lat": 44.99012, + "lon": -123.02621, + "name": "Keizer" + }, + { + "lat": -24.09306, + "lon": -46.62083, + "name": "Mongaguá" + } + ], + "question": "Which location is the geographic outlier among: Toms River, Fairview, La Palma, Keizer, Mongaguá?", + "ground_truth": { + "answer": "Mongaguá", + "outlier_distance_km": 7975.9, + "second_furthest_km": 3174.5, + "clarity_ratio": 2.51, + "median_distance_km": 2910.2, + "distances_to_centroid": { + "Toms River": 2422.7, + "Fairview": 3174.5, + "La Palma": 2072.1, + "Keizer": 2910.2, + "Mongaguá": 7975.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Toms River: (39.95°, -74.20°)", + " Fairview: (49.26°, -123.13°)", + " La Palma: (33.85°, -118.05°)", + " Keizer: (44.99°, -123.03°)", + " Mongaguá: (-24.09°, -46.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mongaguá: 7975.9 km from centroid", + " Fairview: 3174.5 km from centroid", + " Keizer: 2910.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mongaguá", + "FINAL ANSWER: Mongaguá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.66663, + "lon": -92.97464, + "name": "Austin" + }, + { + "lat": 43.73766, + "lon": -79.34972, + "name": "Banbury-Don Mills" + }, + { + "lat": 35.40888, + "lon": -80.58158, + "name": "Concord" + }, + { + "lat": 43.68417, + "lon": -79.29936, + "name": "East End-Danforth" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + } + ], + "question": "Which location is the geographic outlier among: Austin, Banbury-Don Mills, Concord, East End-Danforth, Blenheim?", + "ground_truth": { + "answer": "Blenheim", + "outlier_distance_km": 17028.0, + "second_furthest_km": 5857.0, + "clarity_ratio": 2.91, + "median_distance_km": 4792.8, + "distances_to_centroid": { + "Austin": 5857.0, + "Banbury-Don Mills": 4767.3, + "Concord": 4792.8, + "East End-Danforth": 4762.3, + "Blenheim": 17028.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Austin: (43.67°, -92.97°)", + " Banbury-Don Mills: (43.74°, -79.35°)", + " Concord: (35.41°, -80.58°)", + " East End-Danforth: (43.68°, -79.30°)", + " Blenheim: (-41.52°, 173.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Blenheim: 17028.0 km from centroid", + " Austin: 5857.0 km from centroid", + " Concord: 4792.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Blenheim", + "FINAL ANSWER: Blenheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -36.96807, + "lon": 174.79875, + "name": "Mangere" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": 59.76831, + "lon": 60.0062, + "name": "Karpinsk" + } + ], + "question": "Which location is the geographic outlier among: Baldivis, Corio, Mangere, South Morang, Karpinsk?", + "ground_truth": { + "answer": "Karpinsk", + "outlier_distance_km": 10474.2, + "second_furthest_km": 5072.1, + "clarity_ratio": 2.07, + "median_distance_km": 2833.7, + "distances_to_centroid": { + "Baldivis": 2094.6, + "Corio": 2830.5, + "Mangere": 5072.1, + "South Morang": 2833.7, + "Karpinsk": 10474.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baldivis: (-32.33°, 115.83°)", + " Corio: (-38.08°, 144.38°)", + " Mangere: (-36.97°, 174.80°)", + " South Morang: (-37.65°, 145.10°)", + " Karpinsk: (59.77°, 60.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karpinsk: 10474.2 km from centroid", + " Mangere: 5072.1 km from centroid", + " South Morang: 2833.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karpinsk", + "FINAL ANSWER: Karpinsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": 5.95996, + "lon": -1.77792, + "name": "Dunkwa" + } + ], + "question": "Which location is the geographic outlier among: Karori, Palmerston, Ballajura, Hervey Bay, Dunkwa?", + "ground_truth": { + "answer": "Dunkwa", + "outlier_distance_km": 12971.6, + "second_furthest_km": 6028.1, + "clarity_ratio": 2.15, + "median_distance_km": 3926.9, + "distances_to_centroid": { + "Karori": 6028.1, + "Palmerston": 1989.3, + "Ballajura": 1214.5, + "Hervey Bay": 3926.9, + "Dunkwa": 12971.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Karori: (-41.28°, 174.74°)", + " Palmerston: (-12.49°, 130.98°)", + " Ballajura: (-31.84°, 115.90°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Dunkwa: (5.96°, -1.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dunkwa: 12971.6 km from centroid", + " Karori: 6028.1 km from centroid", + " Hervey Bay: 3926.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dunkwa", + "FINAL ANSWER: Dunkwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": -38.18333, + "lon": 145.08333, + "name": "Mount Eliza" + }, + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": 55.79479, + "lon": 37.94794, + "name": "Balashikha" + } + ], + "question": "Which location is the geographic outlier among: Morayfield, Altona Meadows, Mount Eliza, Pakenham, Balashikha?", + "ground_truth": { + "answer": "Balashikha", + "outlier_distance_km": 11405.9, + "second_furthest_km": 3054.8, + "clarity_ratio": 3.73, + "median_distance_km": 3053.8, + "distances_to_centroid": { + "Morayfield": 3054.8, + "Altona Meadows": 2996.3, + "Mount Eliza": 3038.3, + "Pakenham": 3053.8, + "Balashikha": 11405.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morayfield: (-27.11°, 152.95°)", + " Altona Meadows: (-37.88°, 144.78°)", + " Mount Eliza: (-38.18°, 145.08°)", + " Pakenham: (-38.07°, 145.47°)", + " Balashikha: (55.79°, 37.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Balashikha: 11405.9 km from centroid", + " Morayfield: 3054.8 km from centroid", + " Pakenham: 3053.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Balashikha", + "FINAL ANSWER: Balashikha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91667, + "lon": 151.03333, + "name": "Bankstown" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -4.44696, + "lon": -49.11556, + "name": "Jacundá" + } + ], + "question": "Which location is the geographic outlier among: Bankstown, Cranbourne East, Rockhampton, Baldivis, Jacundá?", + "ground_truth": { + "answer": "Jacundá", + "outlier_distance_km": 15434.0, + "second_furthest_km": 4805.1, + "clarity_ratio": 3.21, + "median_distance_km": 4676.2, + "distances_to_centroid": { + "Bankstown": 4676.2, + "Cranbourne East": 4168.4, + "Rockhampton": 4805.1, + "Baldivis": 1428.5, + "Jacundá": 15434.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bankstown: (-33.92°, 151.03°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Rockhampton: (-23.38°, 150.51°)", + " Baldivis: (-32.33°, 115.83°)", + " Jacundá: (-4.45°, -49.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jacundá: 15434.0 km from centroid", + " Rockhampton: 4805.1 km from centroid", + " Bankstown: 4676.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jacundá", + "FINAL ANSWER: Jacundá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.95996, + "lon": -1.77792, + "name": "Dunkwa" + }, + { + "lat": 28.34827, + "lon": 28.86936, + "name": "Al Bawīţī" + }, + { + "lat": 10.06069, + "lon": -2.50192, + "name": "Wa" + }, + { + "lat": -30.8063, + "lon": 30.33484, + "name": "Ga-Malakhe" + }, + { + "lat": 8.25, + "lon": 124.4, + "name": "Iligan City" + } + ], + "question": "Which location is the geographic outlier among: Dunkwa, Al Bawīţī, Wa, Ga-Malakhe, Iligan City?", + "ground_truth": { + "answer": "Iligan City", + "outlier_distance_km": 9777.2, + "second_furthest_km": 4276.5, + "clarity_ratio": 2.29, + "median_distance_km": 4171.7, + "distances_to_centroid": { + "Dunkwa": 4171.7, + "Al Bawīţī": 2767.7, + "Wa": 4276.5, + "Ga-Malakhe": 3954.5, + "Iligan City": 9777.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dunkwa: (5.96°, -1.78°)", + " Al Bawīţī: (28.35°, 28.87°)", + " Wa: (10.06°, -2.50°)", + " Ga-Malakhe: (-30.81°, 30.33°)", + " Iligan City: (8.25°, 124.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Iligan City: 9777.2 km from centroid", + " Wa: 4276.5 km from centroid", + " Dunkwa: 4171.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Iligan City", + "FINAL ANSWER: Iligan City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.58412, + "lon": 3.98336, + "name": "Epe" + }, + { + "lat": -0.27088, + "lon": 36.37917, + "name": "Ol Kalou" + }, + { + "lat": -26.37945, + "lon": 28.92112, + "name": "Lebohang" + }, + { + "lat": -1.48256, + "lon": 40.03341, + "name": "Hola" + }, + { + "lat": 48.84232, + "lon": 9.23028, + "name": "Stuttgart Mühlhausen" + } + ], + "question": "Which location is the geographic outlier among: Epe, Ol Kalou, Lebohang, Hola, Stuttgart Mühlhausen?", + "ground_truth": { + "answer": "Stuttgart Mühlhausen", + "outlier_distance_km": 5014.1, + "second_furthest_km": 3584.5, + "clarity_ratio": 1.4, + "median_distance_km": 2184.8, + "distances_to_centroid": { + "Epe": 2184.8, + "Ol Kalou": 1544.3, + "Lebohang": 3584.5, + "Hola": 1970.4, + "Stuttgart Mühlhausen": 5014.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epe: (6.58°, 3.98°)", + " Ol Kalou: (-0.27°, 36.38°)", + " Lebohang: (-26.38°, 28.92°)", + " Hola: (-1.48°, 40.03°)", + " Stuttgart Mühlhausen: (48.84°, 9.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stuttgart Mühlhausen: 5014.1 km from centroid", + " Lebohang: 3584.5 km from centroid", + " Epe: 2184.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stuttgart Mühlhausen", + "FINAL ANSWER: Stuttgart Mühlhausen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.18333, + "lon": 145.08333, + "name": "Mount Eliza" + }, + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + }, + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -25.91849, + "lon": 28.19881, + "name": "Midstream" + } + ], + "question": "Which location is the geographic outlier among: Mount Eliza, Springvale, Altona Meadows, Palmerston, Midstream?", + "ground_truth": { + "answer": "Midstream", + "outlier_distance_km": 8639.7, + "second_furthest_km": 2547.5, + "clarity_ratio": 3.39, + "median_distance_km": 2546.7, + "distances_to_centroid": { + "Mount Eliza": 2546.7, + "Springvale": 2547.5, + "Altona Meadows": 2514.3, + "Palmerston": 2358.8, + "Midstream": 8639.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mount Eliza: (-38.18°, 145.08°)", + " Springvale: (-37.95°, 145.15°)", + " Altona Meadows: (-37.88°, 144.78°)", + " Palmerston: (-12.49°, 130.98°)", + " Midstream: (-25.92°, 28.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Midstream: 8639.7 km from centroid", + " Springvale: 2547.5 km from centroid", + " Mount Eliza: 2546.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Midstream", + "FINAL ANSWER: Midstream" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.78556, + "lon": -0.85139, + "name": "Bolgatanga" + }, + { + "lat": 29.84144, + "lon": 31.30084, + "name": "Ḩalwān" + }, + { + "lat": 12.42417, + "lon": 37.325, + "name": "K’ola Diba" + }, + { + "lat": 11.26667, + "lon": 36.83333, + "name": "Dangila" + }, + { + "lat": -8.43333, + "lon": 114.33333, + "name": "Muncar" + } + ], + "question": "Which location is the geographic outlier among: Bolgatanga, Ḩalwān, K’ola Diba, Dangila, Muncar?", + "ground_truth": { + "answer": "Muncar", + "outlier_distance_km": 8101.1, + "second_furthest_km": 4868.2, + "clarity_ratio": 1.66, + "median_distance_km": 2444.7, + "distances_to_centroid": { + "Bolgatanga": 4868.2, + "Ḩalwān": 2444.7, + "K’ola Diba": 717.0, + "Dangila": 758.6, + "Muncar": 8101.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bolgatanga: (10.79°, -0.85°)", + " Ḩalwān: (29.84°, 31.30°)", + " K’ola Diba: (12.42°, 37.33°)", + " Dangila: (11.27°, 36.83°)", + " Muncar: (-8.43°, 114.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Muncar: 8101.1 km from centroid", + " Bolgatanga: 4868.2 km from centroid", + " Ḩalwān: 2444.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Muncar", + "FINAL ANSWER: Muncar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.81845, + "lon": -77.14331, + "name": "Lincolnia" + }, + { + "lat": 40.20148, + "lon": -77.18887, + "name": "Carlisle" + }, + { + "lat": 42.61065, + "lon": -71.23422, + "name": "Tewksbury" + }, + { + "lat": 35.73319, + "lon": -81.3412, + "name": "Hickory" + }, + { + "lat": 29.85058, + "lon": 115.5525, + "name": "Wuxue" + } + ], + "question": "Which location is the geographic outlier among: Lincolnia, Carlisle, Tewksbury, Hickory, Wuxue?", + "ground_truth": { + "answer": "Wuxue", + "outlier_distance_km": 12051.8, + "second_furthest_km": 3816.5, + "clarity_ratio": 3.16, + "median_distance_km": 3377.7, + "distances_to_centroid": { + "Lincolnia": 3377.7, + "Carlisle": 3358.4, + "Tewksbury": 2846.0, + "Hickory": 3816.5, + "Wuxue": 12051.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lincolnia: (38.82°, -77.14°)", + " Carlisle: (40.20°, -77.19°)", + " Tewksbury: (42.61°, -71.23°)", + " Hickory: (35.73°, -81.34°)", + " Wuxue: (29.85°, 115.55°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wuxue: 12051.8 km from centroid", + " Hickory: 3816.5 km from centroid", + " Lincolnia: 3377.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wuxue", + "FINAL ANSWER: Wuxue" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.9236, + "lon": 22.22706, + "name": "Kraśnik" + }, + { + "lat": 45.04616, + "lon": 38.79491, + "name": "Yelizavetinskaya" + }, + { + "lat": 53.20356, + "lon": 45.19227, + "name": "Zarechnyy" + }, + { + "lat": 37.99384, + "lon": -3.47103, + "name": "Baeza" + }, + { + "lat": 41.34621, + "lon": -73.079, + "name": "Ansonia" + } + ], + "question": "Which location is the geographic outlier among: Kraśnik, Yelizavetinskaya, Zarechnyy, Baeza, Ansonia?", + "ground_truth": { + "answer": "Ansonia", + "outlier_distance_km": 6122.2, + "second_furthest_km": 2916.7, + "clarity_ratio": 2.1, + "median_distance_km": 2549.8, + "distances_to_centroid": { + "Kraśnik": 1333.7, + "Yelizavetinskaya": 2549.8, + "Zarechnyy": 2916.7, + "Baeza": 1156.6, + "Ansonia": 6122.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kraśnik: (50.92°, 22.23°)", + " Yelizavetinskaya: (45.05°, 38.79°)", + " Zarechnyy: (53.20°, 45.19°)", + " Baeza: (37.99°, -3.47°)", + " Ansonia: (41.35°, -73.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ansonia: 6122.2 km from centroid", + " Zarechnyy: 2916.7 km from centroid", + " Yelizavetinskaya: 2549.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ansonia", + "FINAL ANSWER: Ansonia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.75417, + "lon": 105.02472, + "name": "Luomen" + }, + { + "lat": 29.91964, + "lon": 77.30438, + "name": "Nakūr" + }, + { + "lat": 29.39557, + "lon": 108.06579, + "name": "Gaogu" + }, + { + "lat": 15.88109, + "lon": 78.58704, + "name": "Atmakūr" + }, + { + "lat": 52.21, + "lon": 5.96944, + "name": "Apeldoorn" + } + ], + "question": "Which location is the geographic outlier among: Luomen, Nakūr, Gaogu, Atmakūr, Apeldoorn?", + "ground_truth": { + "answer": "Apeldoorn", + "outlier_distance_km": 5835.9, + "second_furthest_km": 3160.8, + "clarity_ratio": 1.85, + "median_distance_km": 2783.5, + "distances_to_centroid": { + "Luomen": 2783.5, + "Nakūr": 355.7, + "Gaogu": 3160.8, + "Atmakūr": 1875.8, + "Apeldoorn": 5835.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Luomen: (34.75°, 105.02°)", + " Nakūr: (29.92°, 77.30°)", + " Gaogu: (29.40°, 108.07°)", + " Atmakūr: (15.88°, 78.59°)", + " Apeldoorn: (52.21°, 5.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Apeldoorn: 5835.9 km from centroid", + " Gaogu: 3160.8 km from centroid", + " Luomen: 2783.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Apeldoorn", + "FINAL ANSWER: Apeldoorn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + { + "lat": -41.28374, + "lon": 174.74141, + "name": "Karori" + }, + { + "lat": -33.73333, + "lon": 150.88333, + "name": "Quakers Hill" + }, + { + "lat": 30.83481, + "lon": 109.50499, + "name": "Fengping" + } + ], + "question": "Which location is the geographic outlier among: Rotorua, Punchbowl, Karori, Quakers Hill, Fengping?", + "ground_truth": { + "answer": "Fengping", + "outlier_distance_km": 7559.7, + "second_furthest_km": 2881.7, + "clarity_ratio": 2.62, + "median_distance_km": 2796.9, + "distances_to_centroid": { + "Rotorua": 2796.9, + "Punchbowl": 1195.6, + "Karori": 2881.7, + "Quakers Hill": 1176.1, + "Fengping": 7559.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rotorua: (-38.14°, 176.25°)", + " Punchbowl: (-33.93°, 151.05°)", + " Karori: (-41.28°, 174.74°)", + " Quakers Hill: (-33.73°, 150.88°)", + " Fengping: (30.83°, 109.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fengping: 7559.7 km from centroid", + " Karori: 2881.7 km from centroid", + " Rotorua: 2796.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fengping", + "FINAL ANSWER: Fengping" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.45777, + "lon": -88.83733, + "name": "Beaver Dam" + }, + { + "lat": 25.94065, + "lon": -80.2456, + "name": "Carol City" + }, + { + "lat": 40.04122, + "lon": -75.12379, + "name": "Olney" + }, + { + "lat": 17.54528, + "lon": -98.57599, + "name": "Tlapa de Comonfort" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + } + ], + "question": "Which location is the geographic outlier among: Beaver Dam, Carol City, Olney, Tlapa de Comonfort, Miranda?", + "ground_truth": { + "answer": "Miranda", + "outlier_distance_km": 18059.1, + "second_furthest_km": 6337.7, + "clarity_ratio": 2.85, + "median_distance_km": 5441.6, + "distances_to_centroid": { + "Beaver Dam": 5441.6, + "Carol City": 4370.8, + "Olney": 4243.9, + "Tlapa de Comonfort": 6337.7, + "Miranda": 18059.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beaver Dam: (43.46°, -88.84°)", + " Carol City: (25.94°, -80.25°)", + " Olney: (40.04°, -75.12°)", + " Tlapa de Comonfort: (17.55°, -98.58°)", + " Miranda: (-34.04°, 151.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Miranda: 18059.1 km from centroid", + " Tlapa de Comonfort: 6337.7 km from centroid", + " Beaver Dam: 5441.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Miranda", + "FINAL ANSWER: Miranda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.72593, + "lon": -73.51429, + "name": "Levittown" + }, + { + "lat": 40.80207, + "lon": -124.16367, + "name": "Eureka" + }, + { + "lat": 33.96807, + "lon": -118.22507, + "name": "Walnut Park" + }, + { + "lat": 40.82649, + "lon": -74.10681, + "name": "Rutherford" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + } + ], + "question": "Which location is the geographic outlier among: Levittown, Eureka, Walnut Park, Rutherford, Wantirna South?", + "ground_truth": { + "answer": "Wantirna South", + "outlier_distance_km": 17940.7, + "second_furthest_km": 7108.2, + "clarity_ratio": 2.52, + "median_distance_km": 6720.6, + "distances_to_centroid": { + "Levittown": 2969.3, + "Eureka": 7108.2, + "Walnut Park": 6720.6, + "Rutherford": 3017.6, + "Wantirna South": 17940.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Levittown: (40.73°, -73.51°)", + " Eureka: (40.80°, -124.16°)", + " Walnut Park: (33.97°, -118.23°)", + " Rutherford: (40.83°, -74.11°)", + " Wantirna South: (-37.88°, 145.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wantirna South: 17940.7 km from centroid", + " Eureka: 7108.2 km from centroid", + " Walnut Park: 6720.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wantirna South", + "FINAL ANSWER: Wantirna South" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.73156, + "lon": -1.6137, + "name": "Tafo" + }, + { + "lat": 26.12242, + "lon": 32.46749, + "name": "Dishnā" + }, + { + "lat": 6.60086, + "lon": 3.48818, + "name": "Ebute Ikorodu" + }, + { + "lat": 7.60039, + "lon": 4.19264, + "name": "Olupona" + }, + { + "lat": 23.25397, + "lon": 69.66928, + "name": "Bhuj" + } + ], + "question": "Which location is the geographic outlier among: Tafo, Dishnā, Ebute Ikorodu, Olupona, Bhuj?", + "ground_truth": { + "answer": "Bhuj", + "outlier_distance_km": 5138.9, + "second_furthest_km": 2668.4, + "clarity_ratio": 1.93, + "median_distance_km": 2150.4, + "distances_to_centroid": { + "Tafo": 2668.4, + "Dishnā": 1752.1, + "Ebute Ikorodu": 2150.4, + "Olupona": 2035.2, + "Bhuj": 5138.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tafo: (6.73°, -1.61°)", + " Dishnā: (26.12°, 32.47°)", + " Ebute Ikorodu: (6.60°, 3.49°)", + " Olupona: (7.60°, 4.19°)", + " Bhuj: (23.25°, 69.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhuj: 5138.9 km from centroid", + " Tafo: 2668.4 km from centroid", + " Ebute Ikorodu: 2150.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhuj", + "FINAL ANSWER: Bhuj" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -28.52423, + "lon": 28.81582, + "name": "Phuthaditjhaba" + } + ], + "question": "Which location is the geographic outlier among: Tamworth, Melbourne, Orange, Glen Iris, Phuthaditjhaba?", + "ground_truth": { + "answer": "Phuthaditjhaba", + "outlier_distance_km": 8712.4, + "second_furthest_km": 2558.5, + "clarity_ratio": 3.41, + "median_distance_km": 2342.8, + "distances_to_centroid": { + "Tamworth": 2558.5, + "Melbourne": 1960.6, + "Orange": 2342.8, + "Glen Iris": 1970.4, + "Phuthaditjhaba": 8712.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tamworth: (-31.09°, 150.93°)", + " Melbourne: (-37.81°, 144.96°)", + " Orange: (-33.28°, 149.10°)", + " Glen Iris: (-37.87°, 145.07°)", + " Phuthaditjhaba: (-28.52°, 28.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Phuthaditjhaba: 8712.4 km from centroid", + " Tamworth: 2558.5 km from centroid", + " Orange: 2342.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Phuthaditjhaba", + "FINAL ANSWER: Phuthaditjhaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.54595, + "lon": -0.57069, + "name": "Ribarroja del Turia" + }, + { + "lat": 45.43854, + "lon": 10.9938, + "name": "Verona" + }, + { + "lat": 40.74574, + "lon": 14.49698, + "name": "Pompei" + }, + { + "lat": 52.37025, + "lon": 5.21413, + "name": "Almere Stad" + }, + { + "lat": 29.6241, + "lon": -90.7512, + "name": "Bayou Cane" + } + ], + "question": "Which location is the geographic outlier among: Ribarroja del Turia, Verona, Pompei, Almere Stad, Bayou Cane?", + "ground_truth": { + "answer": "Bayou Cane", + "outlier_distance_km": 6990.1, + "second_furthest_km": 2222.0, + "clarity_ratio": 3.15, + "median_distance_km": 1907.3, + "distances_to_centroid": { + "Ribarroja del Turia": 1000.3, + "Verona": 1907.3, + "Pompei": 2222.0, + "Almere Stad": 1774.9, + "Bayou Cane": 6990.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ribarroja del Turia: (39.55°, -0.57°)", + " Verona: (45.44°, 10.99°)", + " Pompei: (40.75°, 14.50°)", + " Almere Stad: (52.37°, 5.21°)", + " Bayou Cane: (29.62°, -90.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bayou Cane: 6990.1 km from centroid", + " Pompei: 2222.0 km from centroid", + " Verona: 1907.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bayou Cane", + "FINAL ANSWER: Bayou Cane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.09342, + "lon": 105.73188, + "name": "Thượng Cát" + }, + { + "lat": 26.57927, + "lon": 101.36325, + "name": "Shilongba" + }, + { + "lat": 10.11947, + "lon": 123.27287, + "name": "Guihulñgan" + }, + { + "lat": 39.7, + "lon": 141.15, + "name": "Morioka" + }, + { + "lat": -5.63444, + "lon": -35.42556, + "name": "Ceará-Mirim" + } + ], + "question": "Which location is the geographic outlier among: Thượng Cát, Shilongba, Guihulñgan, Morioka, Ceará-Mirim?", + "ground_truth": { + "answer": "Ceará-Mirim", + "outlier_distance_km": 13644.8, + "second_furthest_km": 5655.3, + "clarity_ratio": 2.41, + "median_distance_km": 3984.8, + "distances_to_centroid": { + "Thượng Cát": 1960.0, + "Shilongba": 1714.1, + "Guihulñgan": 3984.8, + "Morioka": 5655.3, + "Ceará-Mirim": 13644.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thượng Cát: (21.09°, 105.73°)", + " Shilongba: (26.58°, 101.36°)", + " Guihulñgan: (10.12°, 123.27°)", + " Morioka: (39.70°, 141.15°)", + " Ceará-Mirim: (-5.63°, -35.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ceará-Mirim: 13644.8 km from centroid", + " Morioka: 5655.3 km from centroid", + " Guihulñgan: 3984.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ceará-Mirim", + "FINAL ANSWER: Ceará-Mirim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.89174, + "lon": -59.09542, + "name": "Nova Olinda do Norte" + }, + { + "lat": 3.19698, + "lon": -75.64506, + "name": "Planadas" + }, + { + "lat": -26.25028, + "lon": -49.37861, + "name": "São Bento do Sul" + }, + { + "lat": -15.00806, + "lon": -59.95056, + "name": "Vila Bela da Santíssima Trindade" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + } + ], + "question": "Which location is the geographic outlier among: Nova Olinda do Norte, Planadas, São Bento do Sul, Vila Bela da Santíssima Trindade, Canning Vale?", + "ground_truth": { + "answer": "Canning Vale", + "outlier_distance_km": 13388.2, + "second_furthest_km": 5859.5, + "clarity_ratio": 2.28, + "median_distance_km": 3859.9, + "distances_to_centroid": { + "Nova Olinda do Norte": 3859.9, + "Planadas": 5859.5, + "São Bento do Sul": 2774.2, + "Vila Bela da Santíssima Trindade": 3684.1, + "Canning Vale": 13388.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nova Olinda do Norte: (-3.89°, -59.10°)", + " Planadas: (3.20°, -75.65°)", + " São Bento do Sul: (-26.25°, -49.38°)", + " Vila Bela da Santíssima Trindade: (-15.01°, -59.95°)", + " Canning Vale: (-32.06°, 115.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Canning Vale: 13388.2 km from centroid", + " Planadas: 5859.5 km from centroid", + " Nova Olinda do Norte: 3859.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Canning Vale", + "FINAL ANSWER: Canning Vale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.98626, + "lon": -3.92907, + "name": "Ciudad Real" + }, + { + "lat": 52.21167, + "lon": 5.2875, + "name": "Baarn" + }, + { + "lat": 51.5675, + "lon": 5.45972, + "name": "Sint-Oedenrode" + }, + { + "lat": 52.92979, + "lon": -1.12537, + "name": "West Bridgford" + }, + { + "lat": -5.74507, + "lon": -47.36395, + "name": "Governador Edison Lobão" + } + ], + "question": "Which location is the geographic outlier among: Ciudad Real, Baarn, Sint-Oedenrode, West Bridgford, Governador Edison Lobão?", + "ground_truth": { + "answer": "Governador Edison Lobão", + "outlier_distance_km": 6316.1, + "second_furthest_km": 1902.0, + "clarity_ratio": 3.32, + "median_distance_km": 1854.7, + "distances_to_centroid": { + "Ciudad Real": 399.0, + "Baarn": 1902.0, + "Sint-Oedenrode": 1854.7, + "West Bridgford": 1751.6, + "Governador Edison Lobão": 6316.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ciudad Real: (38.99°, -3.93°)", + " Baarn: (52.21°, 5.29°)", + " Sint-Oedenrode: (51.57°, 5.46°)", + " West Bridgford: (52.93°, -1.13°)", + " Governador Edison Lobão: (-5.75°, -47.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Governador Edison Lobão: 6316.1 km from centroid", + " Baarn: 1902.0 km from centroid", + " Sint-Oedenrode: 1854.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Governador Edison Lobão", + "FINAL ANSWER: Governador Edison Lobão" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.31002, + "lon": 30.66275, + "name": "eMuziwezinto" + }, + { + "lat": 9.01667, + "lon": 37.45, + "name": "Gēdo" + }, + { + "lat": 30.90316, + "lon": 29.55276, + "name": "Burj al ‘Arab" + }, + { + "lat": 11.0, + "lon": 36.91667, + "name": "Injibara" + }, + { + "lat": -14.63126, + "lon": -69.44638, + "name": "La Rinconada" + } + ], + "question": "Which location is the geographic outlier among: eMuziwezinto, Gēdo, Burj al ‘Arab, Injibara, La Rinconada?", + "ground_truth": { + "answer": "La Rinconada", + "outlier_distance_km": 9231.9, + "second_furthest_km": 3970.3, + "clarity_ratio": 2.33, + "median_distance_km": 3733.7, + "distances_to_centroid": { + "eMuziwezinto": 3970.3, + "Gēdo": 2839.1, + "Burj al ‘Arab": 3733.7, + "Injibara": 2854.2, + "La Rinconada": 9231.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " eMuziwezinto: (-30.31°, 30.66°)", + " Gēdo: (9.02°, 37.45°)", + " Burj al ‘Arab: (30.90°, 29.55°)", + " Injibara: (11.00°, 36.92°)", + " La Rinconada: (-14.63°, -69.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " La Rinconada: 9231.9 km from centroid", + " eMuziwezinto: 3970.3 km from centroid", + " Burj al ‘Arab: 3733.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: La Rinconada", + "FINAL ANSWER: La Rinconada" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.76194, + "lon": -42.27444, + "name": "Tutóia" + }, + { + "lat": -2.62139, + "lon": -60.94417, + "name": "Novo Airão" + }, + { + "lat": -46.44785, + "lon": -67.52274, + "name": "Caleta Olivia" + }, + { + "lat": 2.39341, + "lon": -75.89232, + "name": "La Plata" + }, + { + "lat": 44.73188, + "lon": 37.76176, + "name": "Novorossiysk" + } + ], + "question": "Which location is the geographic outlier among: Tutóia, Novo Airão, Caleta Olivia, La Plata, Novorossiysk?", + "ground_truth": { + "answer": "Novorossiysk", + "outlier_distance_km": 9257.6, + "second_furthest_km": 5645.5, + "clarity_ratio": 1.64, + "median_distance_km": 3811.0, + "distances_to_centroid": { + "Tutóia": 209.9, + "Novo Airão": 2138.6, + "Caleta Olivia": 5645.5, + "La Plata": 3811.0, + "Novorossiysk": 9257.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tutóia: (-2.76°, -42.27°)", + " Novo Airão: (-2.62°, -60.94°)", + " Caleta Olivia: (-46.45°, -67.52°)", + " La Plata: (2.39°, -75.89°)", + " Novorossiysk: (44.73°, 37.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Novorossiysk: 9257.6 km from centroid", + " Caleta Olivia: 5645.5 km from centroid", + " La Plata: 3811.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Novorossiysk", + "FINAL ANSWER: Novorossiysk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.58333, + "lon": 114.26667, + "name": "Wuhan" + }, + { + "lat": 23.87355, + "lon": 86.1516, + "name": "Gomoh" + }, + { + "lat": 22.58826, + "lon": 88.23544, + "name": "Mahiari" + }, + { + "lat": 19.25395, + "lon": 73.38993, + "name": "Murbād" + }, + { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + } + ], + "question": "Which location is the geographic outlier among: Wuhan, Gomoh, Mahiari, Murbād, Hamilton?", + "ground_truth": { + "answer": "Hamilton", + "outlier_distance_km": 8932.7, + "second_furthest_km": 3739.8, + "clarity_ratio": 2.39, + "median_distance_km": 2625.5, + "distances_to_centroid": { + "Wuhan": 2213.2, + "Gomoh": 2625.5, + "Mahiari": 2370.7, + "Murbād": 3739.8, + "Hamilton": 8932.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wuhan: (30.58°, 114.27°)", + " Gomoh: (23.87°, 86.15°)", + " Mahiari: (22.59°, 88.24°)", + " Murbād: (19.25°, 73.39°)", + " Hamilton: (-37.78°, 175.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hamilton: 8932.7 km from centroid", + " Murbād: 3739.8 km from centroid", + " Gomoh: 2625.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hamilton", + "FINAL ANSWER: Hamilton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + }, + { + "lat": 31.22323, + "lon": -85.39049, + "name": "Dothan" + } + ], + "question": "Which location is the geographic outlier among: Auburn, Corio, Sunnybank Hills, Hornsby, Dothan?", + "ground_truth": { + "answer": "Dothan", + "outlier_distance_km": 18558.5, + "second_furthest_km": 5129.6, + "clarity_ratio": 3.62, + "median_distance_km": 4954.7, + "distances_to_centroid": { + "Auburn": 4950.0, + "Corio": 4436.7, + "Sunnybank Hills": 5129.6, + "Hornsby": 4954.7, + "Dothan": 18558.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auburn: (-33.85°, 151.03°)", + " Corio: (-38.08°, 144.38°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Hornsby: (-33.70°, 151.10°)", + " Dothan: (31.22°, -85.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dothan: 18558.5 km from centroid", + " Sunnybank Hills: 5129.6 km from centroid", + " Hornsby: 4954.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dothan", + "FINAL ANSWER: Dothan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.53811, + "lon": 114.01504, + "name": "Zhuzilin" + }, + { + "lat": 10.48098, + "lon": 79.39939, + "name": "Madukkūr" + }, + { + "lat": 31.9925, + "lon": 116.24722, + "name": "Wuyang" + }, + { + "lat": 34.50561, + "lon": 117.70222, + "name": "Yanzibu" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + } + ], + "question": "Which location is the geographic outlier among: Zhuzilin, Madukkūr, Wuyang, Yanzibu, Griffith?", + "ground_truth": { + "answer": "Griffith", + "outlier_distance_km": 6220.1, + "second_furthest_km": 3848.6, + "clarity_ratio": 1.62, + "median_distance_km": 2405.6, + "distances_to_centroid": { + "Zhuzilin": 1057.9, + "Madukkūr": 3848.6, + "Wuyang": 2112.8, + "Yanzibu": 2405.6, + "Griffith": 6220.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhuzilin: (22.54°, 114.02°)", + " Madukkūr: (10.48°, 79.40°)", + " Wuyang: (31.99°, 116.25°)", + " Yanzibu: (34.51°, 117.70°)", + " Griffith: (-34.29°, 146.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Griffith: 6220.1 km from centroid", + " Madukkūr: 3848.6 km from centroid", + " Yanzibu: 2405.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Griffith", + "FINAL ANSWER: Griffith" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73333, + "lon": 151.0, + "name": "Castle Hill" + }, + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + }, + { + "lat": 11.43522, + "lon": 5.23494, + "name": "Zuru" + } + ], + "question": "Which location is the geographic outlier among: Castle Hill, Randwick, Porirua, Springvale, Zuru?", + "ground_truth": { + "answer": "Zuru", + "outlier_distance_km": 13567.0, + "second_furthest_km": 4736.3, + "clarity_ratio": 2.86, + "median_distance_km": 2574.6, + "distances_to_centroid": { + "Castle Hill": 2548.4, + "Randwick": 2574.6, + "Porirua": 4736.3, + "Springvale": 2198.0, + "Zuru": 13567.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Castle Hill: (-33.73°, 151.00°)", + " Randwick: (-33.91°, 151.25°)", + " Porirua: (-41.13°, 174.85°)", + " Springvale: (-37.95°, 145.15°)", + " Zuru: (11.44°, 5.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zuru: 13567.0 km from centroid", + " Porirua: 4736.3 km from centroid", + " Randwick: 2574.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zuru", + "FINAL ANSWER: Zuru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.71522, + "lon": 15.09019, + "name": "Pachino" + }, + { + "lat": 41.53333, + "lon": 2.08333, + "name": "Sant Quirze del Vallès" + }, + { + "lat": 27.88385, + "lon": -15.72538, + "name": "Mogán" + }, + { + "lat": 52.55632, + "lon": 13.46649, + "name": "Weißensee" + }, + { + "lat": -23.99306, + "lon": -46.25639, + "name": "Guarujá" + } + ], + "question": "Which location is the geographic outlier among: Pachino, Sant Quirze del Vallès, Mogán, Weißensee, Guarujá?", + "ground_truth": { + "answer": "Guarujá", + "outlier_distance_km": 7106.3, + "second_furthest_km": 3286.6, + "clarity_ratio": 2.16, + "median_distance_km": 2284.5, + "distances_to_centroid": { + "Pachino": 2284.5, + "Sant Quirze del Vallès": 1793.0, + "Mogán": 939.2, + "Weißensee": 3286.6, + "Guarujá": 7106.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pachino: (36.72°, 15.09°)", + " Sant Quirze del Vallès: (41.53°, 2.08°)", + " Mogán: (27.88°, -15.73°)", + " Weißensee: (52.56°, 13.47°)", + " Guarujá: (-23.99°, -46.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guarujá: 7106.3 km from centroid", + " Weißensee: 3286.6 km from centroid", + " Pachino: 2284.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guarujá", + "FINAL ANSWER: Guarujá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.23222, + "lon": -39.1925, + "name": "Caridade" + }, + { + "lat": -10.06806, + "lon": -78.15222, + "name": "Huarmey" + }, + { + "lat": -10.00053, + "lon": -42.47975, + "name": "Pilão Arcado" + }, + { + "lat": -27.41444, + "lon": -49.6025, + "name": "Ituporanga" + }, + { + "lat": -40.35636, + "lon": 175.61113, + "name": "Palmerston North" + } + ], + "question": "Which location is the geographic outlier among: Caridade, Huarmey, Pilão Arcado, Ituporanga, Palmerston North?", + "ground_truth": { + "answer": "Palmerston North", + "outlier_distance_km": 13475.5, + "second_furthest_km": 7706.6, + "clarity_ratio": 1.75, + "median_distance_km": 4477.6, + "distances_to_centroid": { + "Caridade": 3860.5, + "Huarmey": 7706.6, + "Pilão Arcado": 3954.2, + "Ituporanga": 4477.6, + "Palmerston North": 13475.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caridade: (-4.23°, -39.19°)", + " Huarmey: (-10.07°, -78.15°)", + " Pilão Arcado: (-10.00°, -42.48°)", + " Ituporanga: (-27.41°, -49.60°)", + " Palmerston North: (-40.36°, 175.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Palmerston North: 13475.5 km from centroid", + " Huarmey: 7706.6 km from centroid", + " Ituporanga: 4477.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Palmerston North", + "FINAL ANSWER: Palmerston North" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.13259, + "lon": 30.64784, + "name": "Disūq" + }, + { + "lat": 31.55582, + "lon": 31.08918, + "name": "Balţīm" + }, + { + "lat": -28.27276, + "lon": 29.12946, + "name": "Harrismith" + }, + { + "lat": 0.49194, + "lon": 35.74303, + "name": "Kabarnet" + }, + { + "lat": -22.21056, + "lon": -49.65611, + "name": "Garça" + } + ], + "question": "Which location is the geographic outlier among: Disūq, Balţīm, Harrismith, Kabarnet, Garça?", + "ground_truth": { + "answer": "Garça", + "outlier_distance_km": 7569.2, + "second_furthest_km": 3727.4, + "clarity_ratio": 2.03, + "median_distance_km": 3621.7, + "distances_to_centroid": { + "Disūq": 3560.0, + "Balţīm": 3621.7, + "Harrismith": 3727.4, + "Kabarnet": 2273.6, + "Garça": 7569.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Disūq: (31.13°, 30.65°)", + " Balţīm: (31.56°, 31.09°)", + " Harrismith: (-28.27°, 29.13°)", + " Kabarnet: (0.49°, 35.74°)", + " Garça: (-22.21°, -49.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Garça: 7569.2 km from centroid", + " Harrismith: 3727.4 km from centroid", + " Balţīm: 3621.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Garça", + "FINAL ANSWER: Garça" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.91333, + "lon": 42.72083, + "name": "Kislovodsk" + }, + { + "lat": 43.30047, + "lon": 5.40563, + "name": "La Blancarde" + }, + { + "lat": 57.91944, + "lon": 59.965, + "name": "Nizhny Tagil" + }, + { + "lat": 50.66667, + "lon": 3.08333, + "name": "Marcq-en-Barœul" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + } + ], + "question": "Which location is the geographic outlier among: Kislovodsk, La Blancarde, Nizhny Tagil, Marcq-en-Barœul, Levin?", + "ground_truth": { + "answer": "Levin", + "outlier_distance_km": 14439.3, + "second_furthest_km": 4919.5, + "clarity_ratio": 2.94, + "median_distance_km": 4714.4, + "distances_to_centroid": { + "Kislovodsk": 1918.7, + "La Blancarde": 4714.4, + "Nizhny Tagil": 2996.6, + "Marcq-en-Barœul": 4919.5, + "Levin": 14439.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kislovodsk: (43.91°, 42.72°)", + " La Blancarde: (43.30°, 5.41°)", + " Nizhny Tagil: (57.92°, 59.97°)", + " Marcq-en-Barœul: (50.67°, 3.08°)", + " Levin: (-40.63°, 175.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Levin: 14439.3 km from centroid", + " Marcq-en-Barœul: 4919.5 km from centroid", + " La Blancarde: 4714.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Levin", + "FINAL ANSWER: Levin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.34006, + "lon": 21.24207, + "name": "Wołomin" + }, + { + "lat": 47.39484, + "lon": 0.70398, + "name": "Tours" + }, + { + "lat": 62.03114, + "lon": 129.72288, + "name": "Yakutsk" + }, + { + "lat": 53.44852, + "lon": -2.35419, + "name": "Urmston" + }, + { + "lat": 24.09082, + "lon": 32.89942, + "name": "Aswān" + } + ], + "question": "Which location is the geographic outlier among: Wołomin, Tours, Yakutsk, Urmston, Aswān?", + "ground_truth": { + "answer": "Yakutsk", + "outlier_distance_km": 5608.5, + "second_furthest_km": 2768.0, + "clarity_ratio": 2.03, + "median_distance_km": 2661.6, + "distances_to_centroid": { + "Wołomin": 1190.1, + "Tours": 2654.6, + "Yakutsk": 5608.5, + "Urmston": 2768.0, + "Aswān": 2661.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wołomin: (52.34°, 21.24°)", + " Tours: (47.39°, 0.70°)", + " Yakutsk: (62.03°, 129.72°)", + " Urmston: (53.45°, -2.35°)", + " Aswān: (24.09°, 32.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yakutsk: 5608.5 km from centroid", + " Urmston: 2768.0 km from centroid", + " Aswān: 2661.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yakutsk", + "FINAL ANSWER: Yakutsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": 21.81295, + "lon": -105.20844, + "name": "Santiago Ixcuintla" + } + ], + "question": "Which location is the geographic outlier among: Cheltenham, Wollongong city centre, Campsie, Lara, Santiago Ixcuintla?", + "ground_truth": { + "answer": "Santiago Ixcuintla", + "outlier_distance_km": 17702.4, + "second_furthest_km": 5271.2, + "clarity_ratio": 3.36, + "median_distance_km": 5248.7, + "distances_to_centroid": { + "Cheltenham": 4728.1, + "Wollongong city centre": 5248.7, + "Campsie": 5271.2, + "Lara": 4672.5, + "Santiago Ixcuintla": 17702.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cheltenham: (-37.97°, 145.05°)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Campsie: (-33.91°, 151.10°)", + " Lara: (-38.02°, 144.41°)", + " Santiago Ixcuintla: (21.81°, -105.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santiago Ixcuintla: 17702.4 km from centroid", + " Campsie: 5271.2 km from centroid", + " Wollongong city centre: 5248.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santiago Ixcuintla", + "FINAL ANSWER: Santiago Ixcuintla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -37.88461, + "lon": 145.29539, + "name": "Ferntree Gully" + }, + { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": 7.20417, + "lon": 124.43972, + "name": "Budta" + } + ], + "question": "Which location is the geographic outlier among: Blacktown, Ferntree Gully, Cairns, Carrum Downs, Budta?", + "ground_truth": { + "answer": "Budta", + "outlier_distance_km": 3965.3, + "second_furthest_km": 1602.6, + "clarity_ratio": 2.47, + "median_distance_km": 1581.1, + "distances_to_centroid": { + "Blacktown": 1379.5, + "Ferntree Gully": 1581.1, + "Cairns": 854.2, + "Carrum Downs": 1602.6, + "Budta": 3965.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blacktown: (-33.77°, 150.92°)", + " Ferntree Gully: (-37.88°, 145.30°)", + " Cairns: (-16.92°, 145.77°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Budta: (7.20°, 124.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Budta: 3965.3 km from centroid", + " Carrum Downs: 1602.6 km from centroid", + " Ferntree Gully: 1581.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Budta", + "FINAL ANSWER: Budta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.40979, + "lon": -2.15761, + "name": "Stockport" + }, + { + "lat": 41.63976, + "lon": 13.34109, + "name": "Frosinone" + }, + { + "lat": 48.8, + "lon": 9.01667, + "name": "Leonberg" + }, + { + "lat": 48.63115, + "lon": 8.07607, + "name": "Achern" + }, + { + "lat": -12.78444, + "lon": -38.40389, + "name": "Simões Filho" + } + ], + "question": "Which location is the geographic outlier among: Stockport, Frosinone, Leonberg, Achern, Simões Filho?", + "ground_truth": { + "answer": "Simões Filho", + "outlier_distance_km": 6628.8, + "second_furthest_km": 1942.7, + "clarity_ratio": 3.41, + "median_distance_km": 1689.6, + "distances_to_centroid": { + "Stockport": 1942.7, + "Frosinone": 1472.1, + "Leonberg": 1689.6, + "Achern": 1634.5, + "Simões Filho": 6628.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stockport: (53.41°, -2.16°)", + " Frosinone: (41.64°, 13.34°)", + " Leonberg: (48.80°, 9.02°)", + " Achern: (48.63°, 8.08°)", + " Simões Filho: (-12.78°, -38.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Simões Filho: 6628.8 km from centroid", + " Stockport: 1942.7 km from centroid", + " Leonberg: 1689.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Simões Filho", + "FINAL ANSWER: Simões Filho" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.98154, + "lon": -81.23621, + "name": "Lexington" + }, + { + "lat": 29.08874, + "lon": -110.96677, + "name": "Hermosillo" + }, + { + "lat": 33.88863, + "lon": -117.81311, + "name": "Yorba Linda" + }, + { + "lat": 35.82348, + "lon": -78.82556, + "name": "Morrisville" + }, + { + "lat": -0.1181, + "lon": -67.08527, + "name": "São Gabriel da Cachoeira" + } + ], + "question": "Which location is the geographic outlier among: Lexington, Hermosillo, Yorba Linda, Morrisville, São Gabriel da Cachoeira?", + "ground_truth": { + "answer": "São Gabriel da Cachoeira", + "outlier_distance_km": 3929.2, + "second_furthest_km": 2677.2, + "clarity_ratio": 1.47, + "median_distance_km": 1963.8, + "distances_to_centroid": { + "Lexington": 1263.3, + "Hermosillo": 1963.8, + "Yorba Linda": 2677.2, + "Morrisville": 1562.7, + "São Gabriel da Cachoeira": 3929.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lexington: (33.98°, -81.24°)", + " Hermosillo: (29.09°, -110.97°)", + " Yorba Linda: (33.89°, -117.81°)", + " Morrisville: (35.82°, -78.83°)", + " São Gabriel da Cachoeira: (-0.12°, -67.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Gabriel da Cachoeira: 3929.2 km from centroid", + " Yorba Linda: 2677.2 km from centroid", + " Hermosillo: 1963.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Gabriel da Cachoeira", + "FINAL ANSWER: São Gabriel da Cachoeira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.75, + "lon": 106.65, + "name": "Chợ Lớn" + }, + { + "lat": 26.92007, + "lon": 71.91631, + "name": "Pokaran" + }, + { + "lat": 16.87639, + "lon": 74.1909, + "name": "Kodoli" + }, + { + "lat": 14.2733, + "lon": 120.7377, + "name": "Maragondon" + }, + { + "lat": -4.83778, + "lon": -80.64556, + "name": "Querecotillo" + } + ], + "question": "Which location is the geographic outlier among: Chợ Lớn, Pokaran, Kodoli, Maragondon, Querecotillo?", + "ground_truth": { + "answer": "Querecotillo", + "outlier_distance_km": 15453.2, + "second_furthest_km": 6702.3, + "clarity_ratio": 2.31, + "median_distance_km": 5231.6, + "distances_to_centroid": { + "Chợ Lớn": 5231.6, + "Pokaran": 2097.6, + "Kodoli": 1738.5, + "Maragondon": 6702.3, + "Querecotillo": 15453.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chợ Lớn: (10.75°, 106.65°)", + " Pokaran: (26.92°, 71.92°)", + " Kodoli: (16.88°, 74.19°)", + " Maragondon: (14.27°, 120.74°)", + " Querecotillo: (-4.84°, -80.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Querecotillo: 15453.2 km from centroid", + " Maragondon: 6702.3 km from centroid", + " Chợ Lớn: 5231.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Querecotillo", + "FINAL ANSWER: Querecotillo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.51353, + "lon": -97.73973, + "name": "Brushy Creek" + }, + { + "lat": 41.91419, + "lon": -88.30869, + "name": "St. Charles" + }, + { + "lat": 28.03947, + "lon": -81.9498, + "name": "Lakeland" + }, + { + "lat": 43.01253, + "lon": -83.68746, + "name": "Flint" + }, + { + "lat": 29.07888, + "lon": 106.262, + "name": "Lishi" + } + ], + "question": "Which location is the geographic outlier among: Brushy Creek, St. Charles, Lakeland, Flint, Lishi?", + "ground_truth": { + "answer": "Lishi", + "outlier_distance_km": 12485.0, + "second_furthest_km": 4540.4, + "clarity_ratio": 2.75, + "median_distance_km": 3492.1, + "distances_to_centroid": { + "Brushy Creek": 4540.4, + "St. Charles": 3492.1, + "Lakeland": 3190.3, + "Flint": 3120.4, + "Lishi": 12485.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brushy Creek: (30.51°, -97.74°)", + " St. Charles: (41.91°, -88.31°)", + " Lakeland: (28.04°, -81.95°)", + " Flint: (43.01°, -83.69°)", + " Lishi: (29.08°, 106.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lishi: 12485.0 km from centroid", + " Brushy Creek: 4540.4 km from centroid", + " St. Charles: 3492.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lishi", + "FINAL ANSWER: Lishi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.18667, + "lon": -35.09194, + "name": "Tibau do Sul" + }, + { + "lat": -20.38389, + "lon": -42.25056, + "name": "Santa Margarida" + }, + { + "lat": -34.61082, + "lon": -58.481, + "name": "Villa Santa Rita" + }, + { + "lat": -34.38333, + "lon": -72.0, + "name": "Pichilemu" + }, + { + "lat": 35.08834, + "lon": 139.05325, + "name": "Atami" + } + ], + "question": "Which location is the geographic outlier among: Tibau do Sul, Santa Margarida, Villa Santa Rita, Pichilemu, Atami?", + "ground_truth": { + "answer": "Atami", + "outlier_distance_km": 16269.7, + "second_furthest_km": 6350.5, + "clarity_ratio": 2.56, + "median_distance_km": 5149.3, + "distances_to_centroid": { + "Tibau do Sul": 2431.5, + "Santa Margarida": 3173.2, + "Villa Santa Rita": 5149.3, + "Pichilemu": 6350.5, + "Atami": 16269.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tibau do Sul: (-6.19°, -35.09°)", + " Santa Margarida: (-20.38°, -42.25°)", + " Villa Santa Rita: (-34.61°, -58.48°)", + " Pichilemu: (-34.38°, -72.00°)", + " Atami: (35.09°, 139.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Atami: 16269.7 km from centroid", + " Pichilemu: 6350.5 km from centroid", + " Villa Santa Rita: 5149.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Atami", + "FINAL ANSWER: Atami" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.25585, + "lon": -69.7863, + "name": "Pozo Almonte" + }, + { + "lat": -20.31833, + "lon": -48.31056, + "name": "Guaíra" + }, + { + "lat": -7.60333, + "lon": -35.23083, + "name": "Aliança" + }, + { + "lat": -21.27472, + "lon": -43.17917, + "name": "Rio Pomba" + }, + { + "lat": 29.64885, + "lon": 94.35509, + "name": "Nyingchi" + } + ], + "question": "Which location is the geographic outlier among: Pozo Almonte, Guaíra, Aliança, Rio Pomba, Nyingchi?", + "ground_truth": { + "answer": "Nyingchi", + "outlier_distance_km": 12834.7, + "second_furthest_km": 5473.2, + "clarity_ratio": 2.35, + "median_distance_km": 3297.4, + "distances_to_centroid": { + "Pozo Almonte": 5473.2, + "Guaíra": 3297.4, + "Aliança": 1631.0, + "Rio Pomba": 2854.0, + "Nyingchi": 12834.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pozo Almonte: (-20.26°, -69.79°)", + " Guaíra: (-20.32°, -48.31°)", + " Aliança: (-7.60°, -35.23°)", + " Rio Pomba: (-21.27°, -43.18°)", + " Nyingchi: (29.65°, 94.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nyingchi: 12834.7 km from centroid", + " Pozo Almonte: 5473.2 km from centroid", + " Guaíra: 3297.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nyingchi", + "FINAL ANSWER: Nyingchi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.56561, + "lon": 36.63569, + "name": "Gutin" + }, + { + "lat": 30.82796, + "lon": 30.53552, + "name": "Ad Dilinjāt" + }, + { + "lat": -26.25, + "lon": 29.26, + "name": "Kriel" + }, + { + "lat": 31.20176, + "lon": 29.91582, + "name": "Alexandria" + }, + { + "lat": 42.37649, + "lon": -71.23561, + "name": "Waltham" + } + ], + "question": "Which location is the geographic outlier among: Gutin, Ad Dilinjāt, Kriel, Alexandria, Waltham?", + "ground_truth": { + "answer": "Waltham", + "outlier_distance_km": 8079.3, + "second_furthest_km": 5253.4, + "clarity_ratio": 1.54, + "median_distance_km": 2903.7, + "distances_to_centroid": { + "Gutin": 2903.7, + "Ad Dilinjāt": 2462.7, + "Kriel": 5253.4, + "Alexandria": 2436.1, + "Waltham": 8079.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gutin: (9.57°, 36.64°)", + " Ad Dilinjāt: (30.83°, 30.54°)", + " Kriel: (-26.25°, 29.26°)", + " Alexandria: (31.20°, 29.92°)", + " Waltham: (42.38°, -71.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Waltham: 8079.3 km from centroid", + " Kriel: 5253.4 km from centroid", + " Gutin: 2903.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Waltham", + "FINAL ANSWER: Waltham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.65817, + "lon": 31.67137, + "name": "Sāqultah" + }, + { + "lat": 28.09193, + "lon": 30.75813, + "name": "Minya" + }, + { + "lat": 27.95243, + "lon": 30.78082, + "name": "Banī ‘Ubayd" + }, + { + "lat": 9.18059, + "lon": 7.17939, + "name": "Suleja" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + } + ], + "question": "Which location is the geographic outlier among: Sāqultah, Minya, Banī ‘Ubayd, Suleja, Maryborough?", + "ground_truth": { + "answer": "Maryborough", + "outlier_distance_km": 11834.4, + "second_furthest_km": 4754.0, + "clarity_ratio": 2.49, + "median_distance_km": 2635.6, + "distances_to_centroid": { + "Sāqultah": 2471.6, + "Minya": 2635.6, + "Banī ‘Ubayd": 2624.9, + "Suleja": 4754.0, + "Maryborough": 11834.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sāqultah: (26.66°, 31.67°)", + " Minya: (28.09°, 30.76°)", + " Banī ‘Ubayd: (27.95°, 30.78°)", + " Suleja: (9.18°, 7.18°)", + " Maryborough: (-25.54°, 152.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maryborough: 11834.4 km from centroid", + " Suleja: 4754.0 km from centroid", + " Minya: 2635.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maryborough", + "FINAL ANSWER: Maryborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + }, + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + { + "lat": 46.71621, + "lon": -122.9543, + "name": "Centralia" + } + ], + "question": "Which location is the geographic outlier among: Southbank, Burwood, Warwick, Yagoona, Centralia?", + "ground_truth": { + "answer": "Centralia", + "outlier_distance_km": 15241.0, + "second_furthest_km": 5892.6, + "clarity_ratio": 2.59, + "median_distance_km": 5816.7, + "distances_to_centroid": { + "Southbank": 5323.4, + "Burwood": 5816.7, + "Warwick": 5892.6, + "Yagoona": 5809.5, + "Centralia": 15241.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Southbank: (-37.82°, 144.96°)", + " Burwood: (-33.88°, 151.10°)", + " Warwick: (-28.22°, 152.03°)", + " Yagoona: (-33.90°, 151.02°)", + " Centralia: (46.72°, -122.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Centralia: 15241.0 km from centroid", + " Warwick: 5892.6 km from centroid", + " Burwood: 5816.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Centralia", + "FINAL ANSWER: Centralia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.0907, + "lon": -80.68618, + "name": "Stallings" + }, + { + "lat": 47.51659, + "lon": -52.78135, + "name": "Mount Pearl" + }, + { + "lat": 33.88168, + "lon": -118.11701, + "name": "Bellflower" + }, + { + "lat": 19.10059, + "lon": -98.8788, + "name": "Juchitepec" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + } + ], + "question": "Which location is the geographic outlier among: Stallings, Mount Pearl, Bellflower, Juchitepec, Bracken Ridge?", + "ground_truth": { + "answer": "Bracken Ridge", + "outlier_distance_km": 18601.7, + "second_furthest_km": 7676.2, + "clarity_ratio": 2.42, + "median_distance_km": 6159.6, + "distances_to_centroid": { + "Stallings": 4263.2, + "Mount Pearl": 3112.4, + "Bellflower": 7676.2, + "Juchitepec": 6159.6, + "Bracken Ridge": 18601.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stallings: (35.09°, -80.69°)", + " Mount Pearl: (47.52°, -52.78°)", + " Bellflower: (33.88°, -118.12°)", + " Juchitepec: (19.10°, -98.88°)", + " Bracken Ridge: (-27.32°, 153.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bracken Ridge: 18601.7 km from centroid", + " Bellflower: 7676.2 km from centroid", + " Juchitepec: 6159.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bracken Ridge", + "FINAL ANSWER: Bracken Ridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.70053, + "lon": 137.52253, + "name": "Kosai" + }, + { + "lat": 22.50321, + "lon": 73.47242, + "name": "Hālol" + }, + { + "lat": 20.28845, + "lon": 72.85029, + "name": "Sarigam INA" + }, + { + "lat": 28.68001, + "lon": 106.75651, + "name": "Anwen" + }, + { + "lat": -31.97365, + "lon": -60.91935, + "name": "Coronda" + } + ], + "question": "Which location is the geographic outlier among: Kosai, Hālol, Sarigam INA, Anwen, Coronda?", + "ground_truth": { + "answer": "Coronda", + "outlier_distance_km": 14328.9, + "second_furthest_km": 7407.7, + "clarity_ratio": 1.93, + "median_distance_km": 4461.2, + "distances_to_centroid": { + "Kosai": 7407.7, + "Hālol": 1164.0, + "Sarigam INA": 950.6, + "Anwen": 4461.2, + "Coronda": 14328.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kosai: (34.70°, 137.52°)", + " Hālol: (22.50°, 73.47°)", + " Sarigam INA: (20.29°, 72.85°)", + " Anwen: (28.68°, 106.76°)", + " Coronda: (-31.97°, -60.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coronda: 14328.9 km from centroid", + " Kosai: 7407.7 km from centroid", + " Anwen: 4461.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coronda", + "FINAL ANSWER: Coronda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.99696, + "lon": 2.73261, + "name": "Montargis" + }, + { + "lat": 44.67552, + "lon": 8.46934, + "name": "Acqui Terme" + }, + { + "lat": 48.81074, + "lon": 2.57363, + "name": "Le Plessis-Trévise" + }, + { + "lat": 51.14648, + "lon": 0.87376, + "name": "Ashford" + }, + { + "lat": -21.66917, + "lon": -42.07611, + "name": "Itaocara" + } + ], + "question": "Which location is the geographic outlier among: Montargis, Acqui Terme, Le Plessis-Trévise, Ashford, Itaocara?", + "ground_truth": { + "answer": "Itaocara", + "outlier_distance_km": 7318.2, + "second_furthest_km": 1953.8, + "clarity_ratio": 3.75, + "median_distance_km": 1756.2, + "distances_to_centroid": { + "Montargis": 1680.1, + "Acqui Terme": 1667.4, + "Le Plessis-Trévise": 1756.2, + "Ashford": 1953.8, + "Itaocara": 7318.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Montargis: (48.00°, 2.73°)", + " Acqui Terme: (44.68°, 8.47°)", + " Le Plessis-Trévise: (48.81°, 2.57°)", + " Ashford: (51.15°, 0.87°)", + " Itaocara: (-21.67°, -42.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itaocara: 7318.2 km from centroid", + " Ashford: 1953.8 km from centroid", + " Le Plessis-Trévise: 1756.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itaocara", + "FINAL ANSWER: Itaocara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.84577, + "lon": -47.88369, + "name": "Lago Sul" + }, + { + "lat": -31.44957, + "lon": -60.93153, + "name": "Esperanza" + }, + { + "lat": -10.66577, + "lon": -76.25309, + "name": "Cerro de Pasco" + }, + { + "lat": -21.75227, + "lon": -41.33044, + "name": "Campos dos Goytacazes" + }, + { + "lat": 7.15181, + "lon": 0.47362, + "name": "Hohoe" + } + ], + "question": "Which location is the geographic outlier among: Lago Sul, Esperanza, Cerro de Pasco, Campos dos Goytacazes, Hohoe?", + "ground_truth": { + "answer": "Hohoe", + "outlier_distance_km": 5581.5, + "second_furthest_km": 3395.8, + "clarity_ratio": 1.64, + "median_distance_km": 2472.6, + "distances_to_centroid": { + "Lago Sul": 325.3, + "Esperanza": 2472.6, + "Cerro de Pasco": 3395.8, + "Campos dos Goytacazes": 902.1, + "Hohoe": 5581.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lago Sul: (-15.85°, -47.88°)", + " Esperanza: (-31.45°, -60.93°)", + " Cerro de Pasco: (-10.67°, -76.25°)", + " Campos dos Goytacazes: (-21.75°, -41.33°)", + " Hohoe: (7.15°, 0.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hohoe: 5581.5 km from centroid", + " Cerro de Pasco: 3395.8 km from centroid", + " Esperanza: 2472.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hohoe", + "FINAL ANSWER: Hohoe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": -41.27078, + "lon": 173.28404, + "name": "Nelson" + }, + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": 55.9076, + "lon": 94.9118, + "name": "Borodino" + } + ], + "question": "Which location is the geographic outlier among: Ballajura, Nelson, Tauranga, Blenheim, Borodino?", + "ground_truth": { + "answer": "Borodino", + "outlier_distance_km": 9671.0, + "second_furthest_km": 3559.0, + "clarity_ratio": 2.72, + "median_distance_km": 3497.8, + "distances_to_centroid": { + "Ballajura": 3387.8, + "Nelson": 3497.8, + "Tauranga": 3496.7, + "Blenheim": 3559.0, + "Borodino": 9671.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ballajura: (-31.84°, 115.90°)", + " Nelson: (-41.27°, 173.28°)", + " Tauranga: (-37.69°, 176.17°)", + " Blenheim: (-41.52°, 173.95°)", + " Borodino: (55.91°, 94.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Borodino: 9671.0 km from centroid", + " Blenheim: 3559.0 km from centroid", + " Nelson: 3497.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Borodino", + "FINAL ANSWER: Borodino" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.98436, + "lon": -43.20285, + "name": "Ipanema" + }, + { + "lat": -10.66577, + "lon": -76.25309, + "name": "Cerro de Pasco" + }, + { + "lat": -8.76194, + "lon": -63.90389, + "name": "Porto Velho" + }, + { + "lat": -39.36708, + "lon": -72.63087, + "name": "Loncoche" + }, + { + "lat": 36.91218, + "lon": 119.5566, + "name": "Buzhuang" + } + ], + "question": "Which location is the geographic outlier among: Ipanema, Cerro de Pasco, Porto Velho, Loncoche, Buzhuang?", + "ground_truth": { + "answer": "Buzhuang", + "outlier_distance_km": 15457.5, + "second_furthest_km": 5618.9, + "clarity_ratio": 2.75, + "median_distance_km": 5363.0, + "distances_to_centroid": { + "Ipanema": 2302.7, + "Cerro de Pasco": 5363.0, + "Porto Velho": 4021.3, + "Loncoche": 5618.9, + "Buzhuang": 15457.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ipanema: (-22.98°, -43.20°)", + " Cerro de Pasco: (-10.67°, -76.25°)", + " Porto Velho: (-8.76°, -63.90°)", + " Loncoche: (-39.37°, -72.63°)", + " Buzhuang: (36.91°, 119.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Buzhuang: 15457.5 km from centroid", + " Loncoche: 5618.9 km from centroid", + " Cerro de Pasco: 5363.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Buzhuang", + "FINAL ANSWER: Buzhuang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.89405, + "lon": 5.67666, + "name": "Sapele" + }, + { + "lat": -0.30037, + "lon": 35.80935, + "name": "Elburgon" + }, + { + "lat": 9.03528, + "lon": 38.66083, + "name": "Burayu" + }, + { + "lat": 9.18059, + "lon": 7.17939, + "name": "Suleja" + }, + { + "lat": -33.8178, + "lon": 151.00348, + "name": "Parramatta" + } + ], + "question": "Which location is the geographic outlier among: Sapele, Elburgon, Burayu, Suleja, Parramatta?", + "ground_truth": { + "answer": "Parramatta", + "outlier_distance_km": 11109.5, + "second_furthest_km": 4744.4, + "clarity_ratio": 2.34, + "median_distance_km": 4654.5, + "distances_to_centroid": { + "Sapele": 4744.4, + "Elburgon": 1331.6, + "Burayu": 1581.7, + "Suleja": 4654.5, + "Parramatta": 11109.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sapele: (5.89°, 5.68°)", + " Elburgon: (-0.30°, 35.81°)", + " Burayu: (9.04°, 38.66°)", + " Suleja: (9.18°, 7.18°)", + " Parramatta: (-33.82°, 151.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Parramatta: 11109.5 km from centroid", + " Sapele: 4744.4 km from centroid", + " Suleja: 4654.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Parramatta", + "FINAL ANSWER: Parramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.7468, + "lon": 106.64903, + "name": "Quận Sáu" + }, + { + "lat": 22.74252, + "lon": 88.37326, + "name": "Titāgarh" + }, + { + "lat": 33.27668, + "lon": 131.15628, + "name": "Tsukawaki" + }, + { + "lat": 40.64581, + "lon": 140.58354, + "name": "Kuroishi" + }, + { + "lat": -43.58333, + "lon": 172.38333, + "name": "Rolleston" + } + ], + "question": "Which location is the geographic outlier among: Quận Sáu, Titāgarh, Tsukawaki, Kuroishi, Rolleston?", + "ground_truth": { + "answer": "Rolleston", + "outlier_distance_km": 7722.1, + "second_furthest_km": 4308.6, + "clarity_ratio": 1.79, + "median_distance_km": 3340.4, + "distances_to_centroid": { + "Quận Sáu": 2315.9, + "Titāgarh": 4308.6, + "Tsukawaki": 2305.6, + "Kuroishi": 3340.4, + "Rolleston": 7722.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Quận Sáu: (10.75°, 106.65°)", + " Titāgarh: (22.74°, 88.37°)", + " Tsukawaki: (33.28°, 131.16°)", + " Kuroishi: (40.65°, 140.58°)", + " Rolleston: (-43.58°, 172.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rolleston: 7722.1 km from centroid", + " Titāgarh: 4308.6 km from centroid", + " Kuroishi: 3340.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rolleston", + "FINAL ANSWER: Rolleston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -41.21667, + "lon": 174.91667, + "name": "Lower Hutt" + }, + { + "lat": -13.48694, + "lon": -39.04389, + "name": "Cairu" + } + ], + "question": "Which location is the geographic outlier among: Mosman, Greenvale, Wellington, Lower Hutt, Cairu?", + "ground_truth": { + "answer": "Cairu", + "outlier_distance_km": 14392.9, + "second_furthest_km": 4736.2, + "clarity_ratio": 3.04, + "median_distance_km": 4723.5, + "distances_to_centroid": { + "Mosman": 2756.5, + "Greenvale": 2170.2, + "Wellington": 4723.5, + "Lower Hutt": 4736.2, + "Cairu": 14392.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mosman: (-33.84°, 151.24°)", + " Greenvale: (-37.63°, 144.87°)", + " Wellington: (-41.29°, 174.78°)", + " Lower Hutt: (-41.22°, 174.92°)", + " Cairu: (-13.49°, -39.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cairu: 14392.9 km from centroid", + " Lower Hutt: 4736.2 km from centroid", + " Wellington: 4723.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cairu", + "FINAL ANSWER: Cairu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.35611, + "lon": -46.87694, + "name": "Cajamar" + }, + { + "lat": -31.42497, + "lon": -62.08404, + "name": "San Francisco" + }, + { + "lat": -27.46784, + "lon": -58.8344, + "name": "Corrientes" + }, + { + "lat": -25.46722, + "lon": -50.65111, + "name": "Irati" + }, + { + "lat": 38.83289, + "lon": -76.95942, + "name": "Hillcrest Heights" + } + ], + "question": "Which location is the geographic outlier among: Cajamar, San Francisco, Corrientes, Irati, Hillcrest Heights?", + "ground_truth": { + "answer": "Hillcrest Heights", + "outlier_distance_km": 6138.0, + "second_furthest_km": 1986.2, + "clarity_ratio": 3.09, + "median_distance_km": 1668.4, + "distances_to_centroid": { + "Cajamar": 1668.4, + "San Francisco": 1986.2, + "Corrientes": 1522.6, + "Irati": 1570.2, + "Hillcrest Heights": 6138.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cajamar: (-23.36°, -46.88°)", + " San Francisco: (-31.42°, -62.08°)", + " Corrientes: (-27.47°, -58.83°)", + " Irati: (-25.47°, -50.65°)", + " Hillcrest Heights: (38.83°, -76.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hillcrest Heights: 6138.0 km from centroid", + " San Francisco: 1986.2 km from centroid", + " Cajamar: 1668.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hillcrest Heights", + "FINAL ANSWER: Hillcrest Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.28333, + "lon": 36.81667, + "name": "Nairobi" + }, + { + "lat": -33.98735, + "lon": 18.49746, + "name": "Lansdowne" + }, + { + "lat": 5.05127, + "lon": 7.9335, + "name": "Uyo" + }, + { + "lat": 11.75618, + "lon": 9.33896, + "name": "Dutse" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + } + ], + "question": "Which location is the geographic outlier among: Nairobi, Lansdowne, Uyo, Dutse, Carrum Downs?", + "ground_truth": { + "answer": "Carrum Downs", + "outlier_distance_km": 10226.7, + "second_furthest_km": 4566.7, + "clarity_ratio": 2.24, + "median_distance_km": 4340.6, + "distances_to_centroid": { + "Nairobi": 1340.3, + "Lansdowne": 3580.3, + "Uyo": 4340.6, + "Dutse": 4566.7, + "Carrum Downs": 10226.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nairobi: (-1.28°, 36.82°)", + " Lansdowne: (-33.99°, 18.50°)", + " Uyo: (5.05°, 7.93°)", + " Dutse: (11.76°, 9.34°)", + " Carrum Downs: (-38.10°, 145.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carrum Downs: 10226.7 km from centroid", + " Dutse: 4566.7 km from centroid", + " Uyo: 4340.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carrum Downs", + "FINAL ANSWER: Carrum Downs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -16.06583, + "lon": -47.97861, + "name": "Valparaíso de Goiás" + }, + { + "lat": -0.16, + "lon": -49.98833, + "name": "Chaves" + }, + { + "lat": -31.34582, + "lon": -64.33849, + "name": "La Calera" + }, + { + "lat": -25.29167, + "lon": -49.22417, + "name": "Colombo" + }, + { + "lat": 26.4775, + "lon": 31.80394, + "name": "Al Minshāh" + } + ], + "question": "Which location is the geographic outlier among: Valparaíso de Goiás, Chaves, La Calera, Colombo, Al Minshāh?", + "ground_truth": { + "answer": "Al Minshāh", + "outlier_distance_km": 8314.4, + "second_furthest_km": 3822.6, + "clarity_ratio": 2.18, + "median_distance_km": 2267.4, + "distances_to_centroid": { + "Valparaíso de Goiás": 1507.1, + "Chaves": 1855.9, + "La Calera": 3822.6, + "Colombo": 2267.4, + "Al Minshāh": 8314.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Valparaíso de Goiás: (-16.07°, -47.98°)", + " Chaves: (-0.16°, -49.99°)", + " La Calera: (-31.35°, -64.34°)", + " Colombo: (-25.29°, -49.22°)", + " Al Minshāh: (26.48°, 31.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Minshāh: 8314.4 km from centroid", + " La Calera: 3822.6 km from centroid", + " Colombo: 2267.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Minshāh", + "FINAL ANSWER: Al Minshāh" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.65825, + "lon": -0.25223, + "name": "Taifa" + }, + { + "lat": 31.21114, + "lon": 31.05119, + "name": "Sīdī Ghāzī" + }, + { + "lat": 31.29443, + "lon": 30.52248, + "name": "Muţūbas" + }, + { + "lat": 27.25738, + "lon": 33.81291, + "name": "Hurghada" + }, + { + "lat": 41.95503, + "lon": -87.94007, + "name": "Bensenville" + } + ], + "question": "Which location is the geographic outlier among: Taifa, Sīdī Ghāzī, Muţūbas, Hurghada, Bensenville?", + "ground_truth": { + "answer": "Bensenville", + "outlier_distance_km": 7961.9, + "second_furthest_km": 3187.8, + "clarity_ratio": 2.5, + "median_distance_km": 2891.5, + "distances_to_centroid": { + "Taifa": 2432.5, + "Sīdī Ghāzī": 2891.5, + "Muţūbas": 2841.4, + "Hurghada": 3187.8, + "Bensenville": 7961.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taifa: (5.66°, -0.25°)", + " Sīdī Ghāzī: (31.21°, 31.05°)", + " Muţūbas: (31.29°, 30.52°)", + " Hurghada: (27.26°, 33.81°)", + " Bensenville: (41.96°, -87.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bensenville: 7961.9 km from centroid", + " Hurghada: 3187.8 km from centroid", + " Sīdī Ghāzī: 2891.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bensenville", + "FINAL ANSWER: Bensenville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.77664, + "lon": 6.08342, + "name": "Aachen" + }, + { + "lat": 53.53333, + "lon": -2.28333, + "name": "Prestwich" + }, + { + "lat": 51.50583, + "lon": -3.57722, + "name": "Bridgend" + }, + { + "lat": 43.67681, + "lon": 4.63031, + "name": "Arles" + }, + { + "lat": 36.42472, + "lon": 114.20472, + "name": "Linshui" + } + ], + "question": "Which location is the geographic outlier among: Aachen, Prestwich, Bridgend, Arles, Linshui?", + "ground_truth": { + "answer": "Linshui", + "outlier_distance_km": 7163.0, + "second_furthest_km": 2028.6, + "clarity_ratio": 3.53, + "median_distance_km": 1967.6, + "distances_to_centroid": { + "Aachen": 1350.3, + "Prestwich": 1967.6, + "Bridgend": 2028.6, + "Arles": 1542.4, + "Linshui": 7163.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aachen: (50.78°, 6.08°)", + " Prestwich: (53.53°, -2.28°)", + " Bridgend: (51.51°, -3.58°)", + " Arles: (43.68°, 4.63°)", + " Linshui: (36.42°, 114.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Linshui: 7163.0 km from centroid", + " Bridgend: 2028.6 km from centroid", + " Prestwich: 1967.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Linshui", + "FINAL ANSWER: Linshui" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.23221, + "lon": 136.89703, + "name": "Amursk" + }, + { + "lat": 50.72048, + "lon": -1.8795, + "name": "Bournemouth" + }, + { + "lat": 48.77413, + "lon": 2.01781, + "name": "Trappes" + }, + { + "lat": 52.21833, + "lon": 6.89583, + "name": "Enschede" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + } + ], + "question": "Which location is the geographic outlier among: Amursk, Bournemouth, Trappes, Enschede, Mackay?", + "ground_truth": { + "answer": "Mackay", + "outlier_distance_km": 11421.4, + "second_furthest_km": 6232.7, + "clarity_ratio": 1.83, + "median_distance_km": 4991.8, + "distances_to_centroid": { + "Amursk": 6232.7, + "Bournemouth": 4991.8, + "Trappes": 4731.6, + "Enschede": 4381.0, + "Mackay": 11421.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Amursk: (50.23°, 136.90°)", + " Bournemouth: (50.72°, -1.88°)", + " Trappes: (48.77°, 2.02°)", + " Enschede: (52.22°, 6.90°)", + " Mackay: (-21.15°, 149.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mackay: 11421.4 km from centroid", + " Amursk: 6232.7 km from centroid", + " Bournemouth: 4991.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mackay", + "FINAL ANSWER: Mackay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.08605, + "lon": -94.10185, + "name": "Beaumont" + }, + { + "lat": 34.97044, + "lon": -78.94531, + "name": "Hope Mills" + }, + { + "lat": 26.46146, + "lon": -80.07282, + "name": "Delray Beach" + }, + { + "lat": 37.99742, + "lon": -121.71245, + "name": "Oakley" + }, + { + "lat": -27.25204, + "lon": 152.99226, + "name": "Kallangur" + } + ], + "question": "Which location is the geographic outlier among: Beaumont, Hope Mills, Delray Beach, Oakley, Kallangur?", + "ground_truth": { + "answer": "Kallangur", + "outlier_distance_km": 18097.0, + "second_furthest_km": 7545.6, + "clarity_ratio": 2.4, + "median_distance_km": 5074.8, + "distances_to_centroid": { + "Beaumont": 5074.8, + "Hope Mills": 3741.6, + "Delray Beach": 3690.8, + "Oakley": 7545.6, + "Kallangur": 18097.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beaumont: (30.09°, -94.10°)", + " Hope Mills: (34.97°, -78.95°)", + " Delray Beach: (26.46°, -80.07°)", + " Oakley: (38.00°, -121.71°)", + " Kallangur: (-27.25°, 152.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kallangur: 18097.0 km from centroid", + " Oakley: 7545.6 km from centroid", + " Beaumont: 5074.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kallangur", + "FINAL ANSWER: Kallangur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.70311, + "lon": 45.19611, + "name": "Leninsk" + }, + { + "lat": 52.83492, + "lon": 13.81951, + "name": "Eberswalde" + }, + { + "lat": 51.47274, + "lon": 58.45155, + "name": "Gay" + }, + { + "lat": 56.11095, + "lon": 47.47755, + "name": "Novocheboksarsk" + }, + { + "lat": -0.45275, + "lon": 39.64601, + "name": "Garissa" + } + ], + "question": "Which location is the geographic outlier among: Leninsk, Eberswalde, Gay, Novocheboksarsk, Garissa?", + "ground_truth": { + "answer": "Garissa", + "outlier_distance_km": 4692.7, + "second_furthest_km": 2366.5, + "clarity_ratio": 1.98, + "median_distance_km": 1714.8, + "distances_to_centroid": { + "Leninsk": 843.9, + "Eberswalde": 2366.5, + "Gay": 1714.8, + "Novocheboksarsk": 1667.1, + "Garissa": 4692.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Leninsk: (48.70°, 45.20°)", + " Eberswalde: (52.83°, 13.82°)", + " Gay: (51.47°, 58.45°)", + " Novocheboksarsk: (56.11°, 47.48°)", + " Garissa: (-0.45°, 39.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Garissa: 4692.7 km from centroid", + " Eberswalde: 2366.5 km from centroid", + " Gay: 1714.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Garissa", + "FINAL ANSWER: Garissa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.89807, + "lon": -118.19535, + "name": "East Rancho Dominguez" + }, + { + "lat": 39.32924, + "lon": -82.10126, + "name": "Athens" + }, + { + "lat": 16.17535, + "lon": -95.19424, + "name": "Salina Cruz" + }, + { + "lat": 19.02492, + "lon": -102.09318, + "name": "Nueva Italia de Ruiz" + }, + { + "lat": 29.05551, + "lon": 108.79636, + "name": "Heishui" + } + ], + "question": "Which location is the geographic outlier among: East Rancho Dominguez, Athens, Salina Cruz, Nueva Italia de Ruiz, Heishui?", + "ground_truth": { + "answer": "Heishui", + "outlier_distance_km": 13565.8, + "second_furthest_km": 5740.9, + "clarity_ratio": 2.36, + "median_distance_km": 4601.6, + "distances_to_centroid": { + "East Rancho Dominguez": 5740.9, + "Athens": 2602.1, + "Salina Cruz": 4045.6, + "Nueva Italia de Ruiz": 4601.6, + "Heishui": 13565.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " East Rancho Dominguez: (33.90°, -118.20°)", + " Athens: (39.33°, -82.10°)", + " Salina Cruz: (16.18°, -95.19°)", + " Nueva Italia de Ruiz: (19.02°, -102.09°)", + " Heishui: (29.06°, 108.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Heishui: 13565.8 km from centroid", + " East Rancho Dominguez: 5740.9 km from centroid", + " Nueva Italia de Ruiz: 4601.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Heishui", + "FINAL ANSWER: Heishui" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": -36.8, + "lon": 174.75, + "name": "North Shore" + }, + { + "lat": -37.97695, + "lon": 145.25866, + "name": "Endeavour Hills" + }, + { + "lat": 50.85974, + "lon": 16.31966, + "name": "Świebodzice" + } + ], + "question": "Which location is the geographic outlier among: Timaru, Wainuiomata, North Shore, Endeavour Hills, Świebodzice?", + "ground_truth": { + "answer": "Świebodzice", + "outlier_distance_km": 13980.4, + "second_furthest_km": 4180.4, + "clarity_ratio": 3.34, + "median_distance_km": 4037.7, + "distances_to_centroid": { + "Timaru": 4037.7, + "Wainuiomata": 4180.4, + "North Shore": 4024.6, + "Endeavour Hills": 1972.5, + "Świebodzice": 13980.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Timaru: (-44.40°, 171.25°)", + " Wainuiomata: (-41.27°, 174.95°)", + " North Shore: (-36.80°, 174.75°)", + " Endeavour Hills: (-37.98°, 145.26°)", + " Świebodzice: (50.86°, 16.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Świebodzice: 13980.4 km from centroid", + " Wainuiomata: 4180.4 km from centroid", + " Timaru: 4037.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Świebodzice", + "FINAL ANSWER: Świebodzice" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.22139, + "lon": -51.30278, + "name": "Regente Feijó" + }, + { + "lat": -23.5475, + "lon": -46.63611, + "name": "São Paulo" + }, + { + "lat": -14.06694, + "lon": -39.64056, + "name": "Ibirataia" + }, + { + "lat": -21.85389, + "lon": -47.47917, + "name": "Porto Ferreira" + }, + { + "lat": 5.91667, + "lon": 102.21667, + "name": "Kampong Pangkal Kalong" + } + ], + "question": "Which location is the geographic outlier among: Regente Feijó, São Paulo, Ibirataia, Porto Ferreira, Kampong Pangkal Kalong?", + "ground_truth": { + "answer": "Kampong Pangkal Kalong", + "outlier_distance_km": 13264.6, + "second_furthest_km": 3733.2, + "clarity_ratio": 3.55, + "median_distance_km": 3337.0, + "distances_to_centroid": { + "Regente Feijó": 3733.2, + "São Paulo": 3282.0, + "Ibirataia": 2484.4, + "Porto Ferreira": 3337.0, + "Kampong Pangkal Kalong": 13264.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Regente Feijó: (-22.22°, -51.30°)", + " São Paulo: (-23.55°, -46.64°)", + " Ibirataia: (-14.07°, -39.64°)", + " Porto Ferreira: (-21.85°, -47.48°)", + " Kampong Pangkal Kalong: (5.92°, 102.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kampong Pangkal Kalong: 13264.6 km from centroid", + " Regente Feijó: 3733.2 km from centroid", + " Porto Ferreira: 3337.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kampong Pangkal Kalong", + "FINAL ANSWER: Kampong Pangkal Kalong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.3596, + "lon": -2.83148, + "name": "Halewood" + }, + { + "lat": 53.95763, + "lon": -1.08271, + "name": "York" + }, + { + "lat": 48.65412, + "lon": 2.39343, + "name": "Grigny" + }, + { + "lat": 52.95929, + "lon": 5.91854, + "name": "Heerenveen" + }, + { + "lat": 35.87291, + "lon": 137.97503, + "name": "Minamiminowa" + } + ], + "question": "Which location is the geographic outlier among: Halewood, York, Grigny, Heerenveen, Minamiminowa?", + "ground_truth": { + "answer": "Minamiminowa", + "outlier_distance_km": 8302.9, + "second_furthest_km": 2218.1, + "clarity_ratio": 3.74, + "median_distance_km": 2104.7, + "distances_to_centroid": { + "Halewood": 2218.1, + "York": 2104.7, + "Grigny": 1900.9, + "Heerenveen": 1633.5, + "Minamiminowa": 8302.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Halewood: (53.36°, -2.83°)", + " York: (53.96°, -1.08°)", + " Grigny: (48.65°, 2.39°)", + " Heerenveen: (52.96°, 5.92°)", + " Minamiminowa: (35.87°, 137.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Minamiminowa: 8302.9 km from centroid", + " Halewood: 2218.1 km from centroid", + " York: 2104.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Minamiminowa", + "FINAL ANSWER: Minamiminowa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.08213, + "lon": 34.72139, + "name": "Mbale" + }, + { + "lat": 5.78917, + "lon": 7.83829, + "name": "Amaigbo" + }, + { + "lat": -34.05515, + "lon": 18.47617, + "name": "Retreat" + }, + { + "lat": 5.76494, + "lon": 38.91006, + "name": "Shakiso" + }, + { + "lat": 40.11496, + "lon": -111.65492, + "name": "Spanish Fork" + } + ], + "question": "Which location is the geographic outlier among: Mbale, Amaigbo, Retreat, Shakiso, Spanish Fork?", + "ground_truth": { + "answer": "Spanish Fork", + "outlier_distance_km": 11372.9, + "second_furthest_km": 4715.5, + "clarity_ratio": 2.41, + "median_distance_km": 4577.6, + "distances_to_centroid": { + "Mbale": 4136.4, + "Amaigbo": 1155.6, + "Retreat": 4715.5, + "Shakiso": 4577.6, + "Spanish Fork": 11372.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mbale: (0.08°, 34.72°)", + " Amaigbo: (5.79°, 7.84°)", + " Retreat: (-34.06°, 18.48°)", + " Shakiso: (5.76°, 38.91°)", + " Spanish Fork: (40.11°, -111.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Spanish Fork: 11372.9 km from centroid", + " Retreat: 4715.5 km from centroid", + " Shakiso: 4577.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Spanish Fork", + "FINAL ANSWER: Spanish Fork" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.73988, + "lon": 78.10534, + "name": "Attimarappatti" + }, + { + "lat": 29.03028, + "lon": 106.97028, + "name": "Conglin" + }, + { + "lat": 44.08436, + "lon": 131.11841, + "name": "Dongning" + }, + { + "lat": 28.28635, + "lon": 117.20656, + "name": "Huayuan" + }, + { + "lat": 52.99826, + "lon": -0.40941, + "name": "Sleaford" + } + ], + "question": "Which location is the geographic outlier among: Attimarappatti, Conglin, Dongning, Huayuan, Sleaford?", + "ground_truth": { + "answer": "Sleaford", + "outlier_distance_km": 6983.3, + "second_furthest_km": 4030.7, + "clarity_ratio": 1.73, + "median_distance_km": 2962.8, + "distances_to_centroid": { + "Attimarappatti": 2796.4, + "Conglin": 1982.6, + "Dongning": 4030.7, + "Huayuan": 2962.8, + "Sleaford": 6983.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Attimarappatti: (8.74°, 78.11°)", + " Conglin: (29.03°, 106.97°)", + " Dongning: (44.08°, 131.12°)", + " Huayuan: (28.29°, 117.21°)", + " Sleaford: (53.00°, -0.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sleaford: 6983.3 km from centroid", + " Dongning: 4030.7 km from centroid", + " Huayuan: 2962.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sleaford", + "FINAL ANSWER: Sleaford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.01714, + "lon": 4.90421, + "name": "Ila Orangun" + }, + { + "lat": 6.03333, + "lon": 37.55, + "name": "Arba Minch" + }, + { + "lat": -23.66607, + "lon": 27.74477, + "name": "Lephalale" + }, + { + "lat": -25.70866, + "lon": 31.51025, + "name": "Schoemansdal" + }, + { + "lat": 27.09978, + "lon": -82.45426, + "name": "Venice" + } + ], + "question": "Which location is the geographic outlier among: Ila Orangun, Arba Minch, Lephalale, Schoemansdal, Venice?", + "ground_truth": { + "answer": "Venice", + "outlier_distance_km": 9725.4, + "second_furthest_km": 3990.5, + "clarity_ratio": 2.44, + "median_distance_km": 3837.7, + "distances_to_centroid": { + "Ila Orangun": 1080.7, + "Arba Minch": 3837.7, + "Lephalale": 3551.8, + "Schoemansdal": 3990.5, + "Venice": 9725.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ila Orangun: (8.02°, 4.90°)", + " Arba Minch: (6.03°, 37.55°)", + " Lephalale: (-23.67°, 27.74°)", + " Schoemansdal: (-25.71°, 31.51°)", + " Venice: (27.10°, -82.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Venice: 9725.4 km from centroid", + " Schoemansdal: 3990.5 km from centroid", + " Arba Minch: 3837.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Venice", + "FINAL ANSWER: Venice" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.07039, + "lon": -76.54524, + "name": "Severna Park" + }, + { + "lat": 42.47926, + "lon": -71.15228, + "name": "Woburn" + }, + { + "lat": 36.20773, + "lon": -119.34734, + "name": "Tulare" + }, + { + "lat": 36.0584, + "lon": -90.49733, + "name": "Paragould" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + } + ], + "question": "Which location is the geographic outlier among: Severna Park, Woburn, Tulare, Paragould, Whangarei?", + "ground_truth": { + "answer": "Whangarei", + "outlier_distance_km": 16752.4, + "second_furthest_km": 7861.3, + "clarity_ratio": 2.13, + "median_distance_km": 5306.6, + "distances_to_centroid": { + "Severna Park": 4118.7, + "Woburn": 3799.3, + "Tulare": 7861.3, + "Paragould": 5306.6, + "Whangarei": 16752.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Severna Park: (39.07°, -76.55°)", + " Woburn: (42.48°, -71.15°)", + " Tulare: (36.21°, -119.35°)", + " Paragould: (36.06°, -90.50°)", + " Whangarei: (-35.73°, 174.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Whangarei: 16752.4 km from centroid", + " Tulare: 7861.3 km from centroid", + " Paragould: 5306.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Whangarei", + "FINAL ANSWER: Whangarei" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.94402, + "lon": 153.39815, + "name": "Labrador" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -27.62329, + "lon": 153.04785, + "name": "Calamvale" + }, + { + "lat": -37.73333, + "lon": 145.15, + "name": "Eltham" + }, + { + "lat": -9.38861, + "lon": -37.99917, + "name": "Delmiro Gouveia" + } + ], + "question": "Which location is the geographic outlier among: Labrador, Greystanes, Calamvale, Eltham, Delmiro Gouveia?", + "ground_truth": { + "answer": "Delmiro Gouveia", + "outlier_distance_km": 14870.1, + "second_furthest_km": 3971.1, + "clarity_ratio": 3.74, + "median_distance_km": 3942.6, + "distances_to_centroid": { + "Labrador": 3971.1, + "Greystanes": 3691.9, + "Calamvale": 3942.6, + "Eltham": 3218.2, + "Delmiro Gouveia": 14870.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Labrador: (-27.94°, 153.40°)", + " Greystanes: (-33.82°, 150.95°)", + " Calamvale: (-27.62°, 153.05°)", + " Eltham: (-37.73°, 145.15°)", + " Delmiro Gouveia: (-9.39°, -38.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Delmiro Gouveia: 14870.1 km from centroid", + " Labrador: 3971.1 km from centroid", + " Calamvale: 3942.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Delmiro Gouveia", + "FINAL ANSWER: Delmiro Gouveia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.16036, + "lon": 105.93403, + "name": "Shanghe" + }, + { + "lat": 30.77967, + "lon": 108.45506, + "name": "Wuqiao" + }, + { + "lat": 5.21667, + "lon": 96.28333, + "name": "Reuleuet" + }, + { + "lat": 47.92038, + "lon": 123.50046, + "name": "Gannan" + }, + { + "lat": -32.90719, + "lon": 17.98997, + "name": "Vredenburg" + } + ], + "question": "Which location is the geographic outlier among: Shanghe, Wuqiao, Reuleuet, Gannan, Vredenburg?", + "ground_truth": { + "answer": "Vredenburg", + "outlier_distance_km": 9425.2, + "second_furthest_km": 4636.1, + "clarity_ratio": 2.03, + "median_distance_km": 2441.3, + "distances_to_centroid": { + "Shanghe": 2210.5, + "Wuqiao": 2441.3, + "Reuleuet": 1381.3, + "Gannan": 4636.1, + "Vredenburg": 9425.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shanghe: (30.16°, 105.93°)", + " Wuqiao: (30.78°, 108.46°)", + " Reuleuet: (5.22°, 96.28°)", + " Gannan: (47.92°, 123.50°)", + " Vredenburg: (-32.91°, 17.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vredenburg: 9425.2 km from centroid", + " Gannan: 4636.1 km from centroid", + " Wuqiao: 2441.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vredenburg", + "FINAL ANSWER: Vredenburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.76952, + "lon": 30.79165, + "name": "Vryheid" + }, + { + "lat": 5.43385, + "lon": -2.14295, + "name": "Prestea" + }, + { + "lat": 7.31667, + "lon": 38.08333, + "name": "K’olīto" + }, + { + "lat": -34.05274, + "lon": 23.3716, + "name": "Plettenberg Bay" + }, + { + "lat": 40.75982, + "lon": -74.4171, + "name": "Madison" + } + ], + "question": "Which location is the geographic outlier among: Vryheid, Prestea, K’olīto, Plettenberg Bay, Madison?", + "ground_truth": { + "answer": "Madison", + "outlier_distance_km": 9085.4, + "second_furthest_km": 4170.3, + "clarity_ratio": 2.18, + "median_distance_km": 4132.2, + "distances_to_centroid": { + "Vryheid": 4132.2, + "Prestea": 983.1, + "K’olīto": 4003.4, + "Plettenberg Bay": 4170.3, + "Madison": 9085.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vryheid: (-27.77°, 30.79°)", + " Prestea: (5.43°, -2.14°)", + " K’olīto: (7.32°, 38.08°)", + " Plettenberg Bay: (-34.05°, 23.37°)", + " Madison: (40.76°, -74.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Madison: 9085.4 km from centroid", + " Plettenberg Bay: 4170.3 km from centroid", + " Vryheid: 4132.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Madison", + "FINAL ANSWER: Madison" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.21787, + "lon": -61.18738, + "name": "Charata" + }, + { + "lat": -26.24333, + "lon": -48.63806, + "name": "São Francisco do Sul" + }, + { + "lat": -3.54306, + "lon": -43.91583, + "name": "Vargem Grande" + }, + { + "lat": -26.56849, + "lon": -54.7579, + "name": "Montecarlo" + }, + { + "lat": 45.53455, + "lon": -73.90168, + "name": "Deux-Montagnes" + } + ], + "question": "Which location is the geographic outlier among: Charata, São Francisco do Sul, Vargem Grande, Montecarlo, Deux-Montagnes?", + "ground_truth": { + "answer": "Deux-Montagnes", + "outlier_distance_km": 6159.1, + "second_furthest_km": 2236.3, + "clarity_ratio": 2.75, + "median_distance_km": 2232.0, + "distances_to_centroid": { + "Charata": 2236.3, + "São Francisco do Sul": 2232.0, + "Vargem Grande": 1461.8, + "Montecarlo": 2116.2, + "Deux-Montagnes": 6159.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Charata: (-27.22°, -61.19°)", + " São Francisco do Sul: (-26.24°, -48.64°)", + " Vargem Grande: (-3.54°, -43.92°)", + " Montecarlo: (-26.57°, -54.76°)", + " Deux-Montagnes: (45.53°, -73.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Deux-Montagnes: 6159.1 km from centroid", + " Charata: 2236.3 km from centroid", + " São Francisco do Sul: 2232.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Deux-Montagnes", + "FINAL ANSWER: Deux-Montagnes" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.49283, + "lon": -46.66916, + "name": "Limão" + }, + { + "lat": -11.56389, + "lon": -39.28278, + "name": "Conceição do Coité" + }, + { + "lat": -23.10417, + "lon": -55.22583, + "name": "Amambai" + }, + { + "lat": -29.40111, + "lon": -51.945, + "name": "Arroio do Meio" + }, + { + "lat": 28.47688, + "lon": -82.52546, + "name": "Spring Hill" + } + ], + "question": "Which location is the geographic outlier among: Limão, Conceição do Coité, Amambai, Arroio do Meio, Spring Hill?", + "ground_truth": { + "answer": "Spring Hill", + "outlier_distance_km": 5362.1, + "second_furthest_km": 1982.8, + "clarity_ratio": 2.7, + "median_distance_km": 1725.5, + "distances_to_centroid": { + "Limão": 1576.5, + "Conceição do Coité": 1725.5, + "Amambai": 1255.1, + "Arroio do Meio": 1982.8, + "Spring Hill": 5362.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Limão: (-23.49°, -46.67°)", + " Conceição do Coité: (-11.56°, -39.28°)", + " Amambai: (-23.10°, -55.23°)", + " Arroio do Meio: (-29.40°, -51.95°)", + " Spring Hill: (28.48°, -82.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Spring Hill: 5362.1 km from centroid", + " Arroio do Meio: 1982.8 km from centroid", + " Conceição do Coité: 1725.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Spring Hill", + "FINAL ANSWER: Spring Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -36.8382, + "lon": 174.61019, + "name": "Massey" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -26.23656, + "lon": 28.36938, + "name": "Brakpan" + } + ], + "question": "Which location is the geographic outlier among: Miranda, Massey, Rochedale South, Carlton, Brakpan?", + "ground_truth": { + "answer": "Brakpan", + "outlier_distance_km": 9501.0, + "second_furthest_km": 4032.9, + "clarity_ratio": 2.36, + "median_distance_km": 2246.2, + "distances_to_centroid": { + "Miranda": 1925.6, + "Massey": 4032.9, + "Rochedale South": 2246.2, + "Carlton": 1444.5, + "Brakpan": 9501.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miranda: (-34.04°, 151.10°)", + " Massey: (-36.84°, 174.61°)", + " Rochedale South: (-27.60°, 153.12°)", + " Carlton: (-37.80°, 144.97°)", + " Brakpan: (-26.24°, 28.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brakpan: 9501.0 km from centroid", + " Massey: 4032.9 km from centroid", + " Rochedale South: 2246.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brakpan", + "FINAL ANSWER: Brakpan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.00029, + "lon": 153.43088, + "name": "Gold Coast" + }, + { + "lat": -33.95, + "lon": 151.13333, + "name": "Rockdale" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": 29.85, + "lon": 31.26667, + "name": "Al Badrashayn" + } + ], + "question": "Which location is the geographic outlier among: Gold Coast, Rockdale, Australind, Forest Lake, Al Badrashayn?", + "ground_truth": { + "answer": "Al Badrashayn", + "outlier_distance_km": 10989.7, + "second_furthest_km": 3470.1, + "clarity_ratio": 3.17, + "median_distance_km": 3444.0, + "distances_to_centroid": { + "Gold Coast": 3470.1, + "Rockdale": 3444.0, + "Australind": 1711.8, + "Forest Lake": 3417.9, + "Al Badrashayn": 10989.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gold Coast: (-28.00°, 153.43°)", + " Rockdale: (-33.95°, 151.13°)", + " Australind: (-33.28°, 115.72°)", + " Forest Lake: (-27.63°, 152.97°)", + " Al Badrashayn: (29.85°, 31.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Badrashayn: 10989.7 km from centroid", + " Gold Coast: 3470.1 km from centroid", + " Rockdale: 3444.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Badrashayn", + "FINAL ANSWER: Al Badrashayn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.53921, + "lon": 78.09843, + "name": "Pālaiyampatti" + }, + { + "lat": 36.98874, + "lon": 119.92224, + "name": "Dazeshan" + }, + { + "lat": 42.81944, + "lon": 141.65222, + "name": "Chitose" + }, + { + "lat": 35.3, + "lon": 135.11667, + "name": "Fukuchiyama" + }, + { + "lat": 2.56799, + "lon": -72.63972, + "name": "San José del Guaviare" + } + ], + "question": "Which location is the geographic outlier among: Pālaiyampatti, Dazeshan, Chitose, Fukuchiyama, San José del Guaviare?", + "ground_truth": { + "answer": "San José del Guaviare", + "outlier_distance_km": 15758.9, + "second_furthest_km": 5820.8, + "clarity_ratio": 2.71, + "median_distance_km": 5293.2, + "distances_to_centroid": { + "Pālaiyampatti": 1785.5, + "Dazeshan": 3936.6, + "Chitose": 5820.8, + "Fukuchiyama": 5293.2, + "San José del Guaviare": 15758.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pālaiyampatti: (9.54°, 78.10°)", + " Dazeshan: (36.99°, 119.92°)", + " Chitose: (42.82°, 141.65°)", + " Fukuchiyama: (35.30°, 135.12°)", + " San José del Guaviare: (2.57°, -72.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San José del Guaviare: 15758.9 km from centroid", + " Chitose: 5820.8 km from centroid", + " Fukuchiyama: 5293.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San José del Guaviare", + "FINAL ANSWER: San José del Guaviare" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.16667, + "lon": -122.91667, + "name": "North Delta" + }, + { + "lat": 40.79343, + "lon": -73.41512, + "name": "Melville" + }, + { + "lat": 45.67207, + "lon": -118.7886, + "name": "Pendleton" + }, + { + "lat": 40.61106, + "lon": -111.89994, + "name": "Midvale" + }, + { + "lat": 13.76693, + "lon": 100.48258, + "name": "Arun Amarin" + } + ], + "question": "Which location is the geographic outlier among: North Delta, Melville, Pendleton, Midvale, Arun Amarin?", + "ground_truth": { + "answer": "Arun Amarin", + "outlier_distance_km": 14070.9, + "second_furthest_km": 4682.5, + "clarity_ratio": 3.0, + "median_distance_km": 4427.4, + "distances_to_centroid": { + "North Delta": 4682.5, + "Melville": 762.3, + "Pendleton": 4427.4, + "Midvale": 3972.3, + "Arun Amarin": 14070.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Delta: (49.17°, -122.92°)", + " Melville: (40.79°, -73.42°)", + " Pendleton: (45.67°, -118.79°)", + " Midvale: (40.61°, -111.90°)", + " Arun Amarin: (13.77°, 100.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arun Amarin: 14070.9 km from centroid", + " North Delta: 4682.5 km from centroid", + " Pendleton: 4427.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arun Amarin", + "FINAL ANSWER: Arun Amarin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.02819, + "lon": 28.44498, + "name": "El Dabaa" + }, + { + "lat": 5.20131, + "lon": 7.98373, + "name": "Itu" + }, + { + "lat": -30.28666, + "lon": 30.75316, + "name": "Scottburgh" + }, + { + "lat": 5.95996, + "lon": -1.77792, + "name": "Dunkwa" + }, + { + "lat": -0.61898, + "lon": 100.11997, + "name": "Pariaman" + } + ], + "question": "Which location is the geographic outlier among: El Dabaa, Itu, Scottburgh, Dunkwa, Pariaman?", + "ground_truth": { + "answer": "Pariaman", + "outlier_distance_km": 7456.9, + "second_furthest_km": 3889.7, + "clarity_ratio": 1.92, + "median_distance_km": 3627.3, + "distances_to_centroid": { + "El Dabaa": 3236.5, + "Itu": 2806.2, + "Scottburgh": 3627.3, + "Dunkwa": 3889.7, + "Pariaman": 7456.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " El Dabaa: (31.03°, 28.44°)", + " Itu: (5.20°, 7.98°)", + " Scottburgh: (-30.29°, 30.75°)", + " Dunkwa: (5.96°, -1.78°)", + " Pariaman: (-0.62°, 100.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pariaman: 7456.9 km from centroid", + " Dunkwa: 3889.7 km from centroid", + " Scottburgh: 3627.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pariaman", + "FINAL ANSWER: Pariaman" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -37.69047, + "lon": 144.74172, + "name": "Hillside" + }, + { + "lat": -37.75819, + "lon": 145.00583, + "name": "Thornbury" + }, + { + "lat": 43.29639, + "lon": -2.98813, + "name": "Barakaldo" + } + ], + "question": "Which location is the geographic outlier among: Melbourne City Centre, Rockingham, Hillside, Thornbury, Barakaldo?", + "ground_truth": { + "answer": "Barakaldo", + "outlier_distance_km": 13345.8, + "second_furthest_km": 3916.7, + "clarity_ratio": 3.41, + "median_distance_km": 3915.6, + "distances_to_centroid": { + "Melbourne City Centre": 3915.6, + "Rockingham": 1453.8, + "Hillside": 3892.3, + "Thornbury": 3916.7, + "Barakaldo": 13345.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Rockingham: (-32.28°, 115.73°)", + " Hillside: (-37.69°, 144.74°)", + " Thornbury: (-37.76°, 145.01°)", + " Barakaldo: (43.30°, -2.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barakaldo: 13345.8 km from centroid", + " Thornbury: 3916.7 km from centroid", + " Melbourne City Centre: 3915.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barakaldo", + "FINAL ANSWER: Barakaldo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.81999, + "lon": 2.29998, + "name": "Malakoff" + }, + { + "lat": 45.57176, + "lon": 9.02681, + "name": "Lainate" + }, + { + "lat": 50.95572, + "lon": 6.63986, + "name": "Bergheim" + }, + { + "lat": 57.41435, + "lon": 56.97157, + "name": "Kungur" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + } + ], + "question": "Which location is the geographic outlier among: Malakoff, Lainate, Bergheim, Kungur, Port Macquarie?", + "ground_truth": { + "answer": "Port Macquarie", + "outlier_distance_km": 13371.2, + "second_furthest_km": 3882.6, + "clarity_ratio": 3.44, + "median_distance_km": 3627.2, + "distances_to_centroid": { + "Malakoff": 3882.6, + "Lainate": 3325.1, + "Bergheim": 3627.2, + "Kungur": 2712.8, + "Port Macquarie": 13371.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Malakoff: (48.82°, 2.30°)", + " Lainate: (45.57°, 9.03°)", + " Bergheim: (50.96°, 6.64°)", + " Kungur: (57.41°, 56.97°)", + " Port Macquarie: (-31.43°, 152.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Macquarie: 13371.2 km from centroid", + " Malakoff: 3882.6 km from centroid", + " Bergheim: 3627.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Macquarie", + "FINAL ANSWER: Port Macquarie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.89972, + "lon": -75.8825, + "name": "La Virginia" + }, + { + "lat": -20.00639, + "lon": -45.97694, + "name": "Bambuí" + }, + { + "lat": -14.30472, + "lon": -43.765, + "name": "Carinhanha" + }, + { + "lat": -11.495, + "lon": -77.20778, + "name": "Huaral" + }, + { + "lat": 47.6895, + "lon": 9.83247, + "name": "Wangen" + } + ], + "question": "Which location is the geographic outlier among: La Virginia, Bambuí, Carinhanha, Huaral, Wangen?", + "ground_truth": { + "answer": "Wangen", + "outlier_distance_km": 7457.9, + "second_furthest_km": 3672.0, + "clarity_ratio": 2.03, + "median_distance_km": 3274.4, + "distances_to_centroid": { + "La Virginia": 3274.4, + "Bambuí": 2376.4, + "Carinhanha": 1769.2, + "Huaral": 3672.0, + "Wangen": 7457.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Virginia: (4.90°, -75.88°)", + " Bambuí: (-20.01°, -45.98°)", + " Carinhanha: (-14.30°, -43.77°)", + " Huaral: (-11.49°, -77.21°)", + " Wangen: (47.69°, 9.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wangen: 7457.9 km from centroid", + " Huaral: 3672.0 km from centroid", + " La Virginia: 3274.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wangen", + "FINAL ANSWER: Wangen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -16.32369, + "lon": -71.58151, + "name": "Cono Norte" + }, + { + "lat": -16.67861, + "lon": -49.25389, + "name": "Goiânia" + }, + { + "lat": -28.71333, + "lon": -49.3, + "name": "Içara" + }, + { + "lat": -28.97111, + "lon": -51.06806, + "name": "São Marcos" + }, + { + "lat": 51.01678, + "lon": -4.20832, + "name": "Bideford" + } + ], + "question": "Which location is the geographic outlier among: Cono Norte, Goiânia, Içara, São Marcos, Bideford?", + "ground_truth": { + "answer": "Bideford", + "outlier_distance_km": 7635.1, + "second_furthest_km": 3024.2, + "clarity_ratio": 2.52, + "median_distance_km": 2421.7, + "distances_to_centroid": { + "Cono Norte": 3024.2, + "Goiânia": 1072.6, + "Içara": 2352.4, + "São Marcos": 2421.7, + "Bideford": 7635.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cono Norte: (-16.32°, -71.58°)", + " Goiânia: (-16.68°, -49.25°)", + " Içara: (-28.71°, -49.30°)", + " São Marcos: (-28.97°, -51.07°)", + " Bideford: (51.02°, -4.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bideford: 7635.1 km from centroid", + " Cono Norte: 3024.2 km from centroid", + " São Marcos: 2421.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bideford", + "FINAL ANSWER: Bideford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + }, + { + "lat": -32.24295, + "lon": 148.60484, + "name": "Dubbo" + }, + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": 45.49818, + "lon": -122.43148, + "name": "Gresham" + } + ], + "question": "Which location is the geographic outlier among: Taylors Hill, Dubbo, Punchbowl, Wollongong city centre, Gresham?", + "ground_truth": { + "answer": "Gresham", + "outlier_distance_km": 15484.9, + "second_furthest_km": 5811.0, + "clarity_ratio": 2.66, + "median_distance_km": 5798.6, + "distances_to_centroid": { + "Taylors Hill": 5287.1, + "Dubbo": 5576.5, + "Punchbowl": 5811.0, + "Wollongong city centre": 5798.6, + "Gresham": 15484.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taylors Hill: (-37.71°, 144.75°)", + " Dubbo: (-32.24°, 148.60°)", + " Punchbowl: (-33.93°, 151.05°)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Gresham: (45.50°, -122.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gresham: 15484.9 km from centroid", + " Punchbowl: 5811.0 km from centroid", + " Wollongong city centre: 5798.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gresham", + "FINAL ANSWER: Gresham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.31517, + "lon": -85.85522, + "name": "Enterprise" + }, + { + "lat": 39.79728, + "lon": -84.31133, + "name": "Trotwood" + }, + { + "lat": 40.60538, + "lon": -73.75513, + "name": "Far Rockaway" + }, + { + "lat": 30.22409, + "lon": -92.01984, + "name": "Lafayette" + }, + { + "lat": 29.033, + "lon": 31.11408, + "name": "Banī Suwayf al Jadīdah" + } + ], + "question": "Which location is the geographic outlier among: Enterprise, Trotwood, Far Rockaway, Lafayette, Banī Suwayf al Jadīdah?", + "ground_truth": { + "answer": "Banī Suwayf al Jadīdah", + "outlier_distance_km": 8420.7, + "second_furthest_km": 2943.3, + "clarity_ratio": 2.86, + "median_distance_km": 2343.5, + "distances_to_centroid": { + "Enterprise": 2343.5, + "Trotwood": 2157.7, + "Far Rockaway": 1333.7, + "Lafayette": 2943.3, + "Banī Suwayf al Jadīdah": 8420.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Enterprise: (31.32°, -85.86°)", + " Trotwood: (39.80°, -84.31°)", + " Far Rockaway: (40.61°, -73.76°)", + " Lafayette: (30.22°, -92.02°)", + " Banī Suwayf al Jadīdah: (29.03°, 31.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Banī Suwayf al Jadīdah: 8420.7 km from centroid", + " Lafayette: 2943.3 km from centroid", + " Enterprise: 2343.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Banī Suwayf al Jadīdah", + "FINAL ANSWER: Banī Suwayf al Jadīdah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.05011, + "lon": -79.46631, + "name": "Newmarket" + }, + { + "lat": 35.70791, + "lon": -79.81364, + "name": "Asheboro" + }, + { + "lat": 28.07389, + "lon": -82.43902, + "name": "University" + }, + { + "lat": 20.87127, + "lon": -101.51683, + "name": "Romita" + }, + { + "lat": 55.44783, + "lon": 78.31907, + "name": "Kuybyshev" + } + ], + "question": "Which location is the geographic outlier among: Newmarket, Asheboro, University, Romita, Kuybyshev?", + "ground_truth": { + "answer": "Kuybyshev", + "outlier_distance_km": 8763.2, + "second_furthest_km": 4988.4, + "clarity_ratio": 1.76, + "median_distance_km": 2916.3, + "distances_to_centroid": { + "Newmarket": 2368.2, + "Asheboro": 2400.7, + "University": 2916.3, + "Romita": 4988.4, + "Kuybyshev": 8763.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newmarket: (44.05°, -79.47°)", + " Asheboro: (35.71°, -79.81°)", + " University: (28.07°, -82.44°)", + " Romita: (20.87°, -101.52°)", + " Kuybyshev: (55.45°, 78.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kuybyshev: 8763.2 km from centroid", + " Romita: 4988.4 km from centroid", + " University: 2916.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kuybyshev", + "FINAL ANSWER: Kuybyshev" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.80083, + "lon": -41.71306, + "name": "Ipanema" + }, + { + "lat": -8.35806, + "lon": -42.24667, + "name": "São João do Piauí" + }, + { + "lat": -37.15276, + "lon": -58.48838, + "name": "Ayacucho" + }, + { + "lat": 2.77717, + "lon": -75.25642, + "name": "Rivera" + }, + { + "lat": -37.62581, + "lon": 144.92555, + "name": "Roxburgh Park" + } + ], + "question": "Which location is the geographic outlier among: Ipanema, São João do Piauí, Ayacucho, Rivera, Roxburgh Park?", + "ground_truth": { + "answer": "Roxburgh Park", + "outlier_distance_km": 13253.8, + "second_furthest_km": 7086.3, + "clarity_ratio": 1.87, + "median_distance_km": 4641.6, + "distances_to_centroid": { + "Ipanema": 2836.1, + "São João do Piauí": 3247.8, + "Ayacucho": 4641.6, + "Rivera": 7086.3, + "Roxburgh Park": 13253.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ipanema: (-19.80°, -41.71°)", + " São João do Piauí: (-8.36°, -42.25°)", + " Ayacucho: (-37.15°, -58.49°)", + " Rivera: (2.78°, -75.26°)", + " Roxburgh Park: (-37.63°, 144.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Roxburgh Park: 13253.8 km from centroid", + " Rivera: 7086.3 km from centroid", + " Ayacucho: 4641.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Roxburgh Park", + "FINAL ANSWER: Roxburgh Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -37.80639, + "lon": 145.03086, + "name": "Kew" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -34.92873, + "lon": 138.60334, + "name": "Adelaide city centre" + }, + { + "lat": 39.62713, + "lon": 16.51368, + "name": "Corigliano Scalo" + } + ], + "question": "Which location is the geographic outlier among: Mildura, Kew, North Melbourne, Adelaide city centre, Corigliano Scalo?", + "ground_truth": { + "answer": "Corigliano Scalo", + "outlier_distance_km": 12389.1, + "second_furthest_km": 3238.4, + "clarity_ratio": 3.83, + "median_distance_km": 3231.3, + "distances_to_centroid": { + "Mildura": 2829.4, + "Kew": 3238.4, + "North Melbourne": 3231.3, + "Adelaide city centre": 2580.1, + "Corigliano Scalo": 12389.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mildura: (-34.19°, 142.16°)", + " Kew: (-37.81°, 145.03°)", + " North Melbourne: (-37.80°, 144.95°)", + " Adelaide city centre: (-34.93°, 138.60°)", + " Corigliano Scalo: (39.63°, 16.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Corigliano Scalo: 12389.1 km from centroid", + " Kew: 3238.4 km from centroid", + " North Melbourne: 3231.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Corigliano Scalo", + "FINAL ANSWER: Corigliano Scalo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": -23.69748, + "lon": 133.88362, + "name": "Alice Springs" + }, + { + "lat": -37.79798, + "lon": 144.94512, + "name": "North Melbourne" + }, + { + "lat": -3.10194, + "lon": -60.025, + "name": "Manaus" + } + ], + "question": "Which location is the geographic outlier among: Bundoora, Shepparton, Alice Springs, North Melbourne, Manaus?", + "ground_truth": { + "answer": "Manaus", + "outlier_distance_km": 16075.0, + "second_furthest_km": 4178.3, + "clarity_ratio": 3.85, + "median_distance_km": 4152.1, + "distances_to_centroid": { + "Bundoora": 4152.1, + "Shepparton": 4178.3, + "Alice Springs": 3231.1, + "North Melbourne": 4142.5, + "Manaus": 16075.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bundoora: (-37.70°, 145.06°)", + " Shepparton: (-36.38°, 145.40°)", + " Alice Springs: (-23.70°, 133.88°)", + " North Melbourne: (-37.80°, 144.95°)", + " Manaus: (-3.10°, -60.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manaus: 16075.0 km from centroid", + " Shepparton: 4178.3 km from centroid", + " Bundoora: 4152.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manaus", + "FINAL ANSWER: Manaus" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.29636, + "lon": 18.91726, + "name": "Świętochłowice" + }, + { + "lat": 55.38752, + "lon": 36.73307, + "name": "Naro-Fominsk" + }, + { + "lat": 51.63388, + "lon": 13.70662, + "name": "Finsterwalde" + }, + { + "lat": 51.45625, + "lon": -0.97113, + "name": "Reading" + }, + { + "lat": -4.14167, + "lon": -40.58222, + "name": "Reriutaba" + } + ], + "question": "Which location is the geographic outlier among: Świętochłowice, Naro-Fominsk, Finsterwalde, Reading, Reriutaba?", + "ground_truth": { + "answer": "Reriutaba", + "outlier_distance_km": 6855.5, + "second_furthest_km": 2779.2, + "clarity_ratio": 2.47, + "median_distance_km": 1467.1, + "distances_to_centroid": { + "Świętochłowice": 1467.1, + "Naro-Fominsk": 2779.2, + "Finsterwalde": 1343.2, + "Reading": 1273.0, + "Reriutaba": 6855.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Świętochłowice: (50.30°, 18.92°)", + " Naro-Fominsk: (55.39°, 36.73°)", + " Finsterwalde: (51.63°, 13.71°)", + " Reading: (51.46°, -0.97°)", + " Reriutaba: (-4.14°, -40.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Reriutaba: 6855.5 km from centroid", + " Naro-Fominsk: 2779.2 km from centroid", + " Świętochłowice: 1467.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Reriutaba", + "FINAL ANSWER: Reriutaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.12056, + "lon": -60.37972, + "name": "Novo Aripuanã" + }, + { + "lat": -24.00306, + "lon": -53.70417, + "name": "Iporã" + }, + { + "lat": -7.31111, + "lon": -39.30417, + "name": "Barbalha" + }, + { + "lat": -31.73271, + "lon": -60.52897, + "name": "Paraná" + }, + { + "lat": 6.12361, + "lon": 102.24333, + "name": "Kota Bharu" + } + ], + "question": "Which location is the geographic outlier among: Novo Aripuanã, Iporã, Barbalha, Paraná, Kota Bharu?", + "ground_truth": { + "answer": "Kota Bharu", + "outlier_distance_km": 13902.9, + "second_furthest_km": 4449.8, + "clarity_ratio": 3.12, + "median_distance_km": 4254.0, + "distances_to_centroid": { + "Novo Aripuanã": 4254.0, + "Iporã": 3544.6, + "Barbalha": 1942.7, + "Paraná": 4449.8, + "Kota Bharu": 13902.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Novo Aripuanã: (-5.12°, -60.38°)", + " Iporã: (-24.00°, -53.70°)", + " Barbalha: (-7.31°, -39.30°)", + " Paraná: (-31.73°, -60.53°)", + " Kota Bharu: (6.12°, 102.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kota Bharu: 13902.9 km from centroid", + " Paraná: 4449.8 km from centroid", + " Novo Aripuanã: 4254.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kota Bharu", + "FINAL ANSWER: Kota Bharu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.62727, + "lon": -90.19789, + "name": "St. Louis" + }, + { + "lat": 33.38067, + "lon": -84.79966, + "name": "Newnan" + }, + { + "lat": 40.7876, + "lon": -73.84597, + "name": "College Point" + }, + { + "lat": 43.80418, + "lon": -79.27528, + "name": "Agincourt North" + }, + { + "lat": 12.42417, + "lon": 37.325, + "name": "K’ola Diba" + } + ], + "question": "Which location is the geographic outlier among: St. Louis, Newnan, College Point, Agincourt North, K’ola Diba?", + "ground_truth": { + "answer": "K’ola Diba", + "outlier_distance_km": 9738.9, + "second_furthest_km": 2908.6, + "clarity_ratio": 3.35, + "median_distance_km": 2461.1, + "distances_to_centroid": { + "St. Louis": 2908.6, + "Newnan": 2461.1, + "College Point": 1586.7, + "Agincourt North": 2131.8, + "K’ola Diba": 9738.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " St. Louis: (38.63°, -90.20°)", + " Newnan: (33.38°, -84.80°)", + " College Point: (40.79°, -73.85°)", + " Agincourt North: (43.80°, -79.28°)", + " K’ola Diba: (12.42°, 37.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " K’ola Diba: 9738.9 km from centroid", + " St. Louis: 2908.6 km from centroid", + " Newnan: 2461.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: K’ola Diba", + "FINAL ANSWER: K’ola Diba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + }, + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -36.86472, + "lon": 174.64768, + "name": "Te Atatu South" + }, + { + "lat": 47.85105, + "lon": 9.0091, + "name": "Stockach" + } + ], + "question": "Which location is the geographic outlier among: Tarneit, Cronulla, Robina, Te Atatu South, Stockach?", + "ground_truth": { + "answer": "Stockach", + "outlier_distance_km": 13508.4, + "second_furthest_km": 5135.5, + "clarity_ratio": 2.63, + "median_distance_km": 3037.2, + "distances_to_centroid": { + "Tarneit": 2839.8, + "Cronulla": 3037.2, + "Robina": 2965.9, + "Te Atatu South": 5135.5, + "Stockach": 13508.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tarneit: (-37.84°, 144.66°)", + " Cronulla: (-34.06°, 151.15°)", + " Robina: (-28.07°, 153.39°)", + " Te Atatu South: (-36.86°, 174.65°)", + " Stockach: (47.85°, 9.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stockach: 13508.4 km from centroid", + " Te Atatu South: 5135.5 km from centroid", + " Cronulla: 3037.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stockach", + "FINAL ANSWER: Stockach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.92774, + "lon": 80.81266, + "name": "Fatehpur" + }, + { + "lat": 10.16707, + "lon": 77.91318, + "name": "Ammainaickanur" + }, + { + "lat": 8.54884, + "lon": 76.91716, + "name": "Sreekaryam" + }, + { + "lat": -2.88333, + "lon": 108.26667, + "name": "Manggar" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + } + ], + "question": "Which location is the geographic outlier among: Fatehpur, Ammainaickanur, Sreekaryam, Manggar, The Gap?", + "ground_truth": { + "answer": "The Gap", + "outlier_distance_km": 6647.0, + "second_furthest_km": 3241.1, + "clarity_ratio": 2.05, + "median_distance_km": 2562.2, + "distances_to_centroid": { + "Fatehpur": 3241.1, + "Ammainaickanur": 2503.9, + "Sreekaryam": 2562.2, + "Manggar": 1177.4, + "The Gap": 6647.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fatehpur: (25.93°, 80.81°)", + " Ammainaickanur: (10.17°, 77.91°)", + " Sreekaryam: (8.55°, 76.92°)", + " Manggar: (-2.88°, 108.27°)", + " The Gap: (-27.44°, 152.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " The Gap: 6647.0 km from centroid", + " Fatehpur: 3241.1 km from centroid", + " Sreekaryam: 2562.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: The Gap", + "FINAL ANSWER: The Gap" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.27808, + "lon": 37.81867, + "name": "Makindu" + }, + { + "lat": 30.72816, + "lon": 31.79697, + "name": "Fāqūs" + }, + { + "lat": 26.12242, + "lon": 32.46749, + "name": "Dishnā" + }, + { + "lat": 9.03528, + "lon": 38.66083, + "name": "Burayu" + }, + { + "lat": 38.97167, + "lon": -95.23525, + "name": "Lawrence" + } + ], + "question": "Which location is the geographic outlier among: Makindu, Fāqūs, Dishnā, Burayu, Lawrence?", + "ground_truth": { + "answer": "Lawrence", + "outlier_distance_km": 9751.9, + "second_furthest_km": 4027.0, + "clarity_ratio": 2.42, + "median_distance_km": 3416.7, + "distances_to_centroid": { + "Makindu": 4027.0, + "Fāqūs": 2535.9, + "Dishnā": 2462.0, + "Burayu": 3416.7, + "Lawrence": 9751.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Makindu: (-2.28°, 37.82°)", + " Fāqūs: (30.73°, 31.80°)", + " Dishnā: (26.12°, 32.47°)", + " Burayu: (9.04°, 38.66°)", + " Lawrence: (38.97°, -95.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lawrence: 9751.9 km from centroid", + " Makindu: 4027.0 km from centroid", + " Burayu: 3416.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lawrence", + "FINAL ANSWER: Lawrence" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.65118, + "lon": -58.62205, + "name": "Morón" + }, + { + "lat": -25.59912, + "lon": -54.57355, + "name": "Puerto Iguazú" + }, + { + "lat": -23.5212, + "lon": -46.67409, + "name": "Barra Funda" + }, + { + "lat": -2.42306, + "lon": -44.10333, + "name": "Raposa" + }, + { + "lat": 31.26531, + "lon": 32.3019, + "name": "Port Said" + } + ], + "question": "Which location is the geographic outlier among: Morón, Puerto Iguazú, Barra Funda, Raposa, Port Said?", + "ground_truth": { + "answer": "Port Said", + "outlier_distance_km": 8503.7, + "second_furthest_km": 3601.5, + "clarity_ratio": 2.36, + "median_distance_km": 2677.4, + "distances_to_centroid": { + "Morón": 3601.5, + "Puerto Iguazú": 2677.4, + "Barra Funda": 1910.6, + "Raposa": 1438.1, + "Port Said": 8503.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morón: (-34.65°, -58.62°)", + " Puerto Iguazú: (-25.60°, -54.57°)", + " Barra Funda: (-23.52°, -46.67°)", + " Raposa: (-2.42°, -44.10°)", + " Port Said: (31.27°, 32.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Said: 8503.7 km from centroid", + " Morón: 3601.5 km from centroid", + " Puerto Iguazú: 2677.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Said", + "FINAL ANSWER: Port Said" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": -38.05916, + "lon": 145.40947, + "name": "Officer" + }, + { + "lat": 16.47771, + "lon": 80.70755, + "name": "Poranki" + } + ], + "question": "Which location is the geographic outlier among: Launceston, Lalor, Clayton, Officer, Poranki?", + "ground_truth": { + "answer": "Poranki", + "outlier_distance_km": 7448.0, + "second_furthest_km": 2013.8, + "clarity_ratio": 3.7, + "median_distance_km": 1650.6, + "distances_to_centroid": { + "Launceston": 2013.8, + "Lalor": 1596.1, + "Clayton": 1620.8, + "Officer": 1650.6, + "Poranki": 7448.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Launceston: (-41.44°, 147.13°)", + " Lalor: (-37.67°, 145.02°)", + " Clayton: (-37.92°, 145.12°)", + " Officer: (-38.06°, 145.41°)", + " Poranki: (16.48°, 80.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Poranki: 7448.0 km from centroid", + " Launceston: 2013.8 km from centroid", + " Officer: 1650.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Poranki", + "FINAL ANSWER: Poranki" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.19551, + "lon": 9.46421, + "name": "Bad Münder am Deister" + }, + { + "lat": 44.21028, + "lon": 43.13528, + "name": "Mineralnye Vody" + }, + { + "lat": 52.4603, + "lon": 4.61048, + "name": "IJmuiden" + }, + { + "lat": 40.42972, + "lon": -3.67975, + "name": "Salamanca" + }, + { + "lat": -4.47, + "lon": -38.90139, + "name": "Capistrano" + } + ], + "question": "Which location is the geographic outlier among: Bad Münder am Deister, Mineralnye Vody, IJmuiden, Salamanca, Capistrano?", + "ground_truth": { + "answer": "Capistrano", + "outlier_distance_km": 6322.4, + "second_furthest_km": 3453.1, + "clarity_ratio": 1.83, + "median_distance_km": 1769.1, + "distances_to_centroid": { + "Bad Münder am Deister": 1769.1, + "Mineralnye Vody": 3453.1, + "IJmuiden": 1728.0, + "Salamanca": 690.4, + "Capistrano": 6322.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bad Münder am Deister: (52.20°, 9.46°)", + " Mineralnye Vody: (44.21°, 43.14°)", + " IJmuiden: (52.46°, 4.61°)", + " Salamanca: (40.43°, -3.68°)", + " Capistrano: (-4.47°, -38.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Capistrano: 6322.4 km from centroid", + " Mineralnye Vody: 3453.1 km from centroid", + " Bad Münder am Deister: 1769.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Capistrano", + "FINAL ANSWER: Capistrano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + }, + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -23.10139, + "lon": -46.72833, + "name": "Jarinu" + } + ], + "question": "Which location is the geographic outlier among: Dandenong North, Dandenong, Wantirna South, Greystanes, Jarinu?", + "ground_truth": { + "answer": "Jarinu", + "outlier_distance_km": 13109.7, + "second_furthest_km": 3932.5, + "clarity_ratio": 3.33, + "median_distance_km": 3353.3, + "distances_to_centroid": { + "Dandenong North": 3351.9, + "Dandenong": 3351.0, + "Wantirna South": 3353.3, + "Greystanes": 3932.5, + "Jarinu": 13109.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dandenong North: (-37.97°, 145.21°)", + " Dandenong: (-37.98°, 145.20°)", + " Wantirna South: (-37.88°, 145.22°)", + " Greystanes: (-33.82°, 150.95°)", + " Jarinu: (-23.10°, -46.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jarinu: 13109.7 km from centroid", + " Greystanes: 3932.5 km from centroid", + " Wantirna South: 3353.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jarinu", + "FINAL ANSWER: Jarinu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.60234, + "lon": -39.49241, + "name": "Teolândia" + }, + { + "lat": -9.07444, + "lon": -44.35861, + "name": "Bom Jesus" + }, + { + "lat": -26.72528, + "lon": -53.51806, + "name": "São Miguel d'Oeste" + }, + { + "lat": -23.72576, + "lon": -46.7024, + "name": "Cidade Dutra" + }, + { + "lat": 47.17176, + "lon": -122.51846, + "name": "Lakewood" + } + ], + "question": "Which location is the geographic outlier among: Teolândia, Bom Jesus, São Miguel d'Oeste, Cidade Dutra, Lakewood?", + "ground_truth": { + "answer": "Lakewood", + "outlier_distance_km": 8333.2, + "second_furthest_km": 2587.9, + "clarity_ratio": 3.22, + "median_distance_km": 2568.0, + "distances_to_centroid": { + "Teolândia": 2568.0, + "Bom Jesus": 1919.9, + "São Miguel d'Oeste": 2533.5, + "Cidade Dutra": 2587.9, + "Lakewood": 8333.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Teolândia: (-13.60°, -39.49°)", + " Bom Jesus: (-9.07°, -44.36°)", + " São Miguel d'Oeste: (-26.73°, -53.52°)", + " Cidade Dutra: (-23.73°, -46.70°)", + " Lakewood: (47.17°, -122.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lakewood: 8333.2 km from centroid", + " Cidade Dutra: 2587.9 km from centroid", + " Teolândia: 2568.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lakewood", + "FINAL ANSWER: Lakewood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.36857, + "lon": -94.97131, + "name": "La Marque" + }, + { + "lat": 43.6367, + "lon": -79.43934, + "name": "South Parkdale" + }, + { + "lat": 47.56494, + "lon": -52.70931, + "name": "St. John's" + }, + { + "lat": 42.32509, + "lon": -72.6412, + "name": "Northampton" + }, + { + "lat": 14.43379, + "lon": 121.02231, + "name": "Banco Filipino Homes" + } + ], + "question": "Which location is the geographic outlier among: La Marque, South Parkdale, St. John's, Northampton, Banco Filipino Homes?", + "ground_truth": { + "answer": "Banco Filipino Homes", + "outlier_distance_km": 13950.9, + "second_furthest_km": 5518.4, + "clarity_ratio": 2.53, + "median_distance_km": 3808.2, + "distances_to_centroid": { + "La Marque": 5518.4, + "South Parkdale": 3808.2, + "St. John's": 1942.4, + "Northampton": 3255.5, + "Banco Filipino Homes": 13950.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Marque: (29.37°, -94.97°)", + " South Parkdale: (43.64°, -79.44°)", + " St. John's: (47.56°, -52.71°)", + " Northampton: (42.33°, -72.64°)", + " Banco Filipino Homes: (14.43°, 121.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Banco Filipino Homes: 13950.9 km from centroid", + " La Marque: 5518.4 km from centroid", + " South Parkdale: 3808.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Banco Filipino Homes", + "FINAL ANSWER: Banco Filipino Homes" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.32711, + "lon": 115.64137, + "name": "Bunbury" + }, + { + "lat": -33.8188, + "lon": 151.1062, + "name": "Ryde" + }, + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": -38.03333, + "lon": 145.3, + "name": "Narre Warren" + }, + { + "lat": 19.66658, + "lon": -99.09477, + "name": "San Pablo de las Salinas" + } + ], + "question": "Which location is the geographic outlier among: Bunbury, Ryde, Altona Meadows, Narre Warren, San Pablo de las Salinas?", + "ground_truth": { + "answer": "San Pablo de las Salinas", + "outlier_distance_km": 18786.3, + "second_furthest_km": 5788.5, + "clarity_ratio": 3.25, + "median_distance_km": 5239.8, + "distances_to_centroid": { + "Bunbury": 2525.0, + "Ryde": 5788.5, + "Altona Meadows": 5194.5, + "Narre Warren": 5239.8, + "San Pablo de las Salinas": 18786.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bunbury: (-33.33°, 115.64°)", + " Ryde: (-33.82°, 151.11°)", + " Altona Meadows: (-37.88°, 144.78°)", + " Narre Warren: (-38.03°, 145.30°)", + " San Pablo de las Salinas: (19.67°, -99.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Pablo de las Salinas: 18786.3 km from centroid", + " Ryde: 5788.5 km from centroid", + " Narre Warren: 5239.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Pablo de las Salinas", + "FINAL ANSWER: San Pablo de las Salinas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + }, + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": 53.08621, + "lon": 21.57566, + "name": "Ostrołęka" + } + ], + "question": "Which location is the geographic outlier among: Springfield Lakes, Mascot, Saint Albans, Carlton, Ostrołęka?", + "ground_truth": { + "answer": "Ostrołęka", + "outlier_distance_km": 12258.4, + "second_furthest_km": 3386.0, + "clarity_ratio": 3.62, + "median_distance_km": 3288.2, + "distances_to_centroid": { + "Springfield Lakes": 3288.2, + "Mascot": 3386.0, + "Saint Albans": 3148.4, + "Carlton": 3164.3, + "Ostrołęka": 12258.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Springfield Lakes: (-27.67°, 152.92°)", + " Mascot: (-33.93°, 151.19°)", + " Saint Albans: (-37.73°, 144.80°)", + " Carlton: (-37.80°, 144.97°)", + " Ostrołęka: (53.09°, 21.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ostrołęka: 12258.4 km from centroid", + " Mascot: 3386.0 km from centroid", + " Springfield Lakes: 3288.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ostrołęka", + "FINAL ANSWER: Ostrołęka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + }, + { + "lat": 40.12448, + "lon": -87.63002, + "name": "Danville" + } + ], + "question": "Which location is the geographic outlier among: Helensvale, Masterton, Broken Hill, Morphett Vale, Danville?", + "ground_truth": { + "answer": "Danville", + "outlier_distance_km": 17422.8, + "second_furthest_km": 7084.6, + "clarity_ratio": 2.46, + "median_distance_km": 5062.4, + "distances_to_centroid": { + "Helensvale": 5062.4, + "Masterton": 7084.6, + "Broken Hill": 3967.9, + "Morphett Vale": 3798.4, + "Danville": 17422.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Helensvale: (-27.92°, 153.33°)", + " Masterton: (-40.96°, 175.66°)", + " Broken Hill: (-31.97°, 141.45°)", + " Morphett Vale: (-35.13°, 138.52°)", + " Danville: (40.12°, -87.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Danville: 17422.8 km from centroid", + " Masterton: 7084.6 km from centroid", + " Helensvale: 5062.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Danville", + "FINAL ANSWER: Danville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.23992, + "lon": 4.6707, + "name": "Annonay" + }, + { + "lat": 28.21154, + "lon": -16.77947, + "name": "Guía de Isora" + }, + { + "lat": 47.32049, + "lon": 40.3847, + "name": "Bagayevskaya" + }, + { + "lat": 56.08616, + "lon": 63.63816, + "name": "Shadrinsk" + }, + { + "lat": -36.12179, + "lon": 146.88809, + "name": "Wodonga" + } + ], + "question": "Which location is the geographic outlier among: Annonay, Guía de Isora, Bagayevskaya, Shadrinsk, Wodonga?", + "ground_truth": { + "answer": "Wodonga", + "outlier_distance_km": 12567.4, + "second_furthest_km": 6243.6, + "clarity_ratio": 2.01, + "median_distance_km": 4221.7, + "distances_to_centroid": { + "Annonay": 4221.7, + "Guía de Isora": 6243.6, + "Bagayevskaya": 2225.9, + "Shadrinsk": 3353.0, + "Wodonga": 12567.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Annonay: (45.24°, 4.67°)", + " Guía de Isora: (28.21°, -16.78°)", + " Bagayevskaya: (47.32°, 40.38°)", + " Shadrinsk: (56.09°, 63.64°)", + " Wodonga: (-36.12°, 146.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wodonga: 12567.4 km from centroid", + " Guía de Isora: 6243.6 km from centroid", + " Annonay: 4221.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wodonga", + "FINAL ANSWER: Wodonga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.43944, + "lon": -39.14833, + "name": "Paraipaba" + }, + { + "lat": -14.06944, + "lon": -42.475, + "name": "Caetité" + }, + { + "lat": 6.15515, + "lon": -75.37371, + "name": "Rionegro" + }, + { + "lat": -3.47222, + "lon": -51.19778, + "name": "Anapu" + }, + { + "lat": 36.63333, + "lon": 139.98333, + "name": "Hōshakuji" + } + ], + "question": "Which location is the geographic outlier among: Paraipaba, Caetité, Rionegro, Anapu, Hōshakuji?", + "ground_truth": { + "answer": "Hōshakuji", + "outlier_distance_km": 14697.9, + "second_furthest_km": 6834.8, + "clarity_ratio": 2.15, + "median_distance_km": 4262.5, + "distances_to_centroid": { + "Paraipaba": 2963.6, + "Caetité": 3783.3, + "Rionegro": 6834.8, + "Anapu": 4262.5, + "Hōshakuji": 14697.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paraipaba: (-3.44°, -39.15°)", + " Caetité: (-14.07°, -42.48°)", + " Rionegro: (6.16°, -75.37°)", + " Anapu: (-3.47°, -51.20°)", + " Hōshakuji: (36.63°, 139.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hōshakuji: 14697.9 km from centroid", + " Rionegro: 6834.8 km from centroid", + " Anapu: 4262.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hōshakuji", + "FINAL ANSWER: Hōshakuji" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.185, + "lon": -48.53278, + "name": "Guapiara" + }, + { + "lat": -12.24861, + "lon": -41.61944, + "name": "Iraquara" + }, + { + "lat": 8.09263, + "lon": -76.72822, + "name": "Turbo" + }, + { + "lat": -28.4602, + "lon": -62.83354, + "name": "Añatuya" + }, + { + "lat": 10.90682, + "lon": 106.7694, + "name": "Dĩ An" + } + ], + "question": "Which location is the geographic outlier among: Guapiara, Iraquara, Turbo, Añatuya, Dĩ An?", + "ground_truth": { + "answer": "Dĩ An", + "outlier_distance_km": 14691.2, + "second_furthest_km": 6086.0, + "clarity_ratio": 2.41, + "median_distance_km": 4530.5, + "distances_to_centroid": { + "Guapiara": 3038.6, + "Iraquara": 1891.3, + "Turbo": 6086.0, + "Añatuya": 4530.5, + "Dĩ An": 14691.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guapiara: (-24.18°, -48.53°)", + " Iraquara: (-12.25°, -41.62°)", + " Turbo: (8.09°, -76.73°)", + " Añatuya: (-28.46°, -62.83°)", + " Dĩ An: (10.91°, 106.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dĩ An: 14691.2 km from centroid", + " Turbo: 6086.0 km from centroid", + " Añatuya: 4530.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dĩ An", + "FINAL ANSWER: Dĩ An" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.67023, + "lon": 74.03469, + "name": "Kodoli" + }, + { + "lat": 29.84431, + "lon": 117.71937, + "name": "Qishan" + }, + { + "lat": 18.58054, + "lon": 99.00745, + "name": "Lamphun" + }, + { + "lat": 23.33664, + "lon": 88.64109, + "name": "Bagulā" + }, + { + "lat": 45.49428, + "lon": -122.86705, + "name": "Aloha" + } + ], + "question": "Which location is the geographic outlier among: Kodoli, Qishan, Lamphun, Bagulā, Aloha?", + "ground_truth": { + "answer": "Aloha", + "outlier_distance_km": 11934.2, + "second_furthest_km": 6410.3, + "clarity_ratio": 1.86, + "median_distance_km": 4949.9, + "distances_to_centroid": { + "Kodoli": 2551.3, + "Qishan": 6410.3, + "Lamphun": 4949.9, + "Bagulā": 3765.9, + "Aloha": 11934.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kodoli: (17.67°, 74.03°)", + " Qishan: (29.84°, 117.72°)", + " Lamphun: (18.58°, 99.01°)", + " Bagulā: (23.34°, 88.64°)", + " Aloha: (45.49°, -122.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aloha: 11934.2 km from centroid", + " Qishan: 6410.3 km from centroid", + " Lamphun: 4949.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aloha", + "FINAL ANSWER: Aloha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.59939, + "lon": 112.8186, + "name": "Bangil" + }, + { + "lat": 22.85095, + "lon": 75.54224, + "name": "Depālpur" + }, + { + "lat": 38.91222, + "lon": 121.60222, + "name": "Dalian" + }, + { + "lat": 23.63134, + "lon": 77.43351, + "name": "Berasia" + }, + { + "lat": -22.50222, + "lon": -48.71139, + "name": "Macatuba" + } + ], + "question": "Which location is the geographic outlier among: Bangil, Depālpur, Dalian, Berasia, Macatuba?", + "ground_truth": { + "answer": "Macatuba", + "outlier_distance_km": 13177.3, + "second_furthest_km": 6137.3, + "clarity_ratio": 2.15, + "median_distance_km": 5402.2, + "distances_to_centroid": { + "Bangil": 5402.2, + "Depālpur": 1550.9, + "Dalian": 6137.3, + "Berasia": 1734.3, + "Macatuba": 13177.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bangil: (-7.60°, 112.82°)", + " Depālpur: (22.85°, 75.54°)", + " Dalian: (38.91°, 121.60°)", + " Berasia: (23.63°, 77.43°)", + " Macatuba: (-22.50°, -48.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Macatuba: 13177.3 km from centroid", + " Dalian: 6137.3 km from centroid", + " Bangil: 5402.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Macatuba", + "FINAL ANSWER: Macatuba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -37.75, + "lon": 145.01667, + "name": "Preston" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + }, + { + "lat": 37.16181, + "lon": -5.92433, + "name": "Los Palacios y Villafranca" + } + ], + "question": "Which location is the geographic outlier among: Porirua, Preston, Rochedale South, Te Atatu Peninsula, Los Palacios y Villafranca?", + "ground_truth": { + "answer": "Los Palacios y Villafranca", + "outlier_distance_km": 15289.2, + "second_furthest_km": 4873.4, + "clarity_ratio": 3.14, + "median_distance_km": 4771.2, + "distances_to_centroid": { + "Porirua": 4873.4, + "Preston": 2436.8, + "Rochedale South": 2601.6, + "Te Atatu Peninsula": 4771.2, + "Los Palacios y Villafranca": 15289.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porirua: (-41.13°, 174.85°)", + " Preston: (-37.75°, 145.02°)", + " Rochedale South: (-27.60°, 153.12°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + " Los Palacios y Villafranca: (37.16°, -5.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Los Palacios y Villafranca: 15289.2 km from centroid", + " Porirua: 4873.4 km from centroid", + " Te Atatu Peninsula: 4771.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Los Palacios y Villafranca", + "FINAL ANSWER: Los Palacios y Villafranca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.7721, + "lon": -78.63861, + "name": "Raleigh" + }, + { + "lat": 34.01279, + "lon": -117.90478, + "name": "South San Jose Hills" + }, + { + "lat": 33.03929, + "lon": -85.03133, + "name": "LaGrange" + }, + { + "lat": 42.37169, + "lon": -88.09008, + "name": "Round Lake Beach" + }, + { + "lat": 36.45556, + "lon": 127.12472, + "name": "Gongju" + } + ], + "question": "Which location is the geographic outlier among: Raleigh, South San Jose Hills, LaGrange, Round Lake Beach, Gongju?", + "ground_truth": { + "answer": "Gongju", + "outlier_distance_km": 11909.1, + "second_furthest_km": 6171.5, + "clarity_ratio": 1.93, + "median_distance_km": 3437.0, + "distances_to_centroid": { + "Raleigh": 2698.4, + "South San Jose Hills": 6171.5, + "LaGrange": 3339.7, + "Round Lake Beach": 3437.0, + "Gongju": 11909.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Raleigh: (35.77°, -78.64°)", + " South San Jose Hills: (34.01°, -117.90°)", + " LaGrange: (33.04°, -85.03°)", + " Round Lake Beach: (42.37°, -88.09°)", + " Gongju: (36.46°, 127.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gongju: 11909.1 km from centroid", + " South San Jose Hills: 6171.5 km from centroid", + " Round Lake Beach: 3437.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gongju", + "FINAL ANSWER: Gongju" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.09989, + "lon": 35.34254, + "name": "Sukhinichi" + }, + { + "lat": 40.59144, + "lon": -4.14738, + "name": "San Lorenzo de El Escorial" + }, + { + "lat": 60.74985, + "lon": 72.85824, + "name": "Pyt-Yakh" + }, + { + "lat": 41.37732, + "lon": 2.08809, + "name": "Esplugues de Llobregat" + }, + { + "lat": 38.49602, + "lon": -121.40884, + "name": "Florin" + } + ], + "question": "Which location is the geographic outlier among: Sukhinichi, San Lorenzo de El Escorial, Pyt-Yakh, Esplugues de Llobregat, Florin?", + "ground_truth": { + "answer": "Florin", + "outlier_distance_km": 8708.5, + "second_furthest_km": 4888.6, + "clarity_ratio": 1.78, + "median_distance_km": 2783.2, + "distances_to_centroid": { + "Sukhinichi": 2783.2, + "San Lorenzo de El Escorial": 724.9, + "Pyt-Yakh": 4888.6, + "Esplugues de Llobregat": 753.0, + "Florin": 8708.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sukhinichi: (54.10°, 35.34°)", + " San Lorenzo de El Escorial: (40.59°, -4.15°)", + " Pyt-Yakh: (60.75°, 72.86°)", + " Esplugues de Llobregat: (41.38°, 2.09°)", + " Florin: (38.50°, -121.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Florin: 8708.5 km from centroid", + " Pyt-Yakh: 4888.6 km from centroid", + " Sukhinichi: 2783.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Florin", + "FINAL ANSWER: Florin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.81201, + "lon": -100.59874, + "name": "García" + }, + { + "lat": 44.30011, + "lon": -79.64964, + "name": "Innisfil" + }, + { + "lat": 41.48477, + "lon": -81.92208, + "name": "Bay Village" + }, + { + "lat": 41.69788, + "lon": -72.72371, + "name": "Newington" + }, + { + "lat": 0.28422, + "lon": 34.75229, + "name": "Kakamega" + } + ], + "question": "Which location is the geographic outlier among: García, Innisfil, Bay Village, Newington, Kakamega?", + "ground_truth": { + "answer": "Kakamega", + "outlier_distance_km": 10448.2, + "second_furthest_km": 3989.2, + "clarity_ratio": 2.62, + "median_distance_km": 2292.8, + "distances_to_centroid": { + "García": 3989.2, + "Innisfil": 2286.3, + "Bay Village": 2292.8, + "Newington": 1666.3, + "Kakamega": 10448.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " García: (25.81°, -100.60°)", + " Innisfil: (44.30°, -79.65°)", + " Bay Village: (41.48°, -81.92°)", + " Newington: (41.70°, -72.72°)", + " Kakamega: (0.28°, 34.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kakamega: 10448.2 km from centroid", + " García: 3989.2 km from centroid", + " Bay Village: 2292.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kakamega", + "FINAL ANSWER: Kakamega" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.821, + "lon": -73.143, + "name": "Ronkonkoma" + }, + { + "lat": 19.10059, + "lon": -98.8788, + "name": "Juchitepec" + }, + { + "lat": 25.6151, + "lon": -80.31061, + "name": "Cutler" + }, + { + "lat": 42.41224, + "lon": -82.18494, + "name": "Chatham" + }, + { + "lat": -15.7907, + "lon": -47.93711, + "name": "Cruzeiro" + } + ], + "question": "Which location is the geographic outlier among: Ronkonkoma, Juchitepec, Cutler, Chatham, Cruzeiro?", + "ground_truth": { + "answer": "Cruzeiro", + "outlier_distance_km": 5265.8, + "second_furthest_km": 2354.7, + "clarity_ratio": 2.24, + "median_distance_km": 2283.7, + "distances_to_centroid": { + "Ronkonkoma": 2068.8, + "Juchitepec": 2354.7, + "Cutler": 525.1, + "Chatham": 2283.7, + "Cruzeiro": 5265.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ronkonkoma: (40.82°, -73.14°)", + " Juchitepec: (19.10°, -98.88°)", + " Cutler: (25.62°, -80.31°)", + " Chatham: (42.41°, -82.18°)", + " Cruzeiro: (-15.79°, -47.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cruzeiro: 5265.8 km from centroid", + " Juchitepec: 2354.7 km from centroid", + " Chatham: 2283.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cruzeiro", + "FINAL ANSWER: Cruzeiro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -36.96807, + "lon": 174.79875, + "name": "Mangere" + }, + { + "lat": 42.07225, + "lon": -87.72284, + "name": "Wilmette" + } + ], + "question": "Which location is the geographic outlier among: Melbourne City Centre, Carlton, Cranbourne North, Mangere, Wilmette?", + "ground_truth": { + "answer": "Wilmette", + "outlier_distance_km": 17482.5, + "second_furthest_km": 6873.8, + "clarity_ratio": 2.54, + "median_distance_km": 4292.4, + "distances_to_centroid": { + "Melbourne City Centre": 4257.4, + "Carlton": 4257.0, + "Cranbourne North": 4292.4, + "Mangere": 6873.8, + "Wilmette": 17482.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Carlton: (-37.80°, 144.97°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Mangere: (-36.97°, 174.80°)", + " Wilmette: (42.07°, -87.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wilmette: 17482.5 km from centroid", + " Mangere: 6873.8 km from centroid", + " Cranbourne North: 4292.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wilmette", + "FINAL ANSWER: Wilmette" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.59468, + "lon": -46.54359, + "name": "Sao Lucas" + }, + { + "lat": -6.82972, + "lon": -35.24722, + "name": "Itapororoca" + }, + { + "lat": -6.64056, + "lon": -79.38917, + "name": "Chongoyape" + }, + { + "lat": -20.33944, + "lon": -47.78056, + "name": "Ituverava" + }, + { + "lat": 51.57917, + "lon": 5.18889, + "name": "Oisterwijk" + } + ], + "question": "Which location is the geographic outlier among: Sao Lucas, Itapororoca, Chongoyape, Ituverava, Oisterwijk?", + "ground_truth": { + "answer": "Oisterwijk", + "outlier_distance_km": 7273.4, + "second_furthest_km": 4327.0, + "clarity_ratio": 1.68, + "median_distance_km": 2571.0, + "distances_to_centroid": { + "Sao Lucas": 2571.0, + "Itapororoca": 877.3, + "Chongoyape": 4327.0, + "Ituverava": 2264.7, + "Oisterwijk": 7273.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sao Lucas: (-23.59°, -46.54°)", + " Itapororoca: (-6.83°, -35.25°)", + " Chongoyape: (-6.64°, -79.39°)", + " Ituverava: (-20.34°, -47.78°)", + " Oisterwijk: (51.58°, 5.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oisterwijk: 7273.4 km from centroid", + " Chongoyape: 4327.0 km from centroid", + " Sao Lucas: 2571.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oisterwijk", + "FINAL ANSWER: Oisterwijk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.15, + "lon": -123.18333, + "name": "Seafair" + }, + { + "lat": 19.64388, + "lon": -99.21598, + "name": "Cuautitlán Izcalli" + }, + { + "lat": 40.8351, + "lon": -73.13122, + "name": "Lake Ronkonkoma" + }, + { + "lat": 32.74596, + "lon": -96.99778, + "name": "Grand Prairie" + }, + { + "lat": 34.33333, + "lon": 136.83333, + "name": "Shima" + } + ], + "question": "Which location is the geographic outlier among: Seafair, Cuautitlán Izcalli, Lake Ronkonkoma, Grand Prairie, Shima?", + "ground_truth": { + "answer": "Shima", + "outlier_distance_km": 12223.4, + "second_furthest_km": 5891.6, + "clarity_ratio": 2.07, + "median_distance_km": 4998.0, + "distances_to_centroid": { + "Seafair": 5891.6, + "Cuautitlán Izcalli": 4998.0, + "Lake Ronkonkoma": 2013.0, + "Grand Prairie": 4197.5, + "Shima": 12223.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Seafair: (49.15°, -123.18°)", + " Cuautitlán Izcalli: (19.64°, -99.22°)", + " Lake Ronkonkoma: (40.84°, -73.13°)", + " Grand Prairie: (32.75°, -97.00°)", + " Shima: (34.33°, 136.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shima: 12223.4 km from centroid", + " Seafair: 5891.6 km from centroid", + " Cuautitlán Izcalli: 4998.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shima", + "FINAL ANSWER: Shima" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91439, + "lon": 151.24895, + "name": "Randwick" + }, + { + "lat": -32.23013, + "lon": 115.78128, + "name": "Kwinana" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": 40.43285, + "lon": -3.70113, + "name": "Trafalgar" + } + ], + "question": "Which location is the geographic outlier among: Randwick, Kwinana, Perth, Mackay, Trafalgar?", + "ground_truth": { + "answer": "Trafalgar", + "outlier_distance_km": 12763.3, + "second_furthest_km": 4972.3, + "clarity_ratio": 2.57, + "median_distance_km": 4612.7, + "distances_to_centroid": { + "Randwick": 4972.3, + "Kwinana": 2096.5, + "Perth": 2074.2, + "Mackay": 4612.7, + "Trafalgar": 12763.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Randwick: (-33.91°, 151.25°)", + " Kwinana: (-32.23°, 115.78°)", + " Perth: (-31.95°, 115.86°)", + " Mackay: (-21.15°, 149.17°)", + " Trafalgar: (40.43°, -3.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Trafalgar: 12763.3 km from centroid", + " Randwick: 4972.3 km from centroid", + " Mackay: 4612.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Trafalgar", + "FINAL ANSWER: Trafalgar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.41885, + "lon": 2.17364, + "name": "el Guinardó" + }, + { + "lat": 55.65333, + "lon": -4.70666, + "name": "Kilwinning" + }, + { + "lat": 40.81249, + "lon": 0.5216, + "name": "Tortosa" + }, + { + "lat": 52.37917, + "lon": 5.78611, + "name": "Nunspeet" + }, + { + "lat": 38.4039, + "lon": -96.18166, + "name": "Emporia" + } + ], + "question": "Which location is the geographic outlier among: el Guinardó, Kilwinning, Tortosa, Nunspeet, Emporia?", + "ground_truth": { + "answer": "Emporia", + "outlier_distance_km": 6210.2, + "second_furthest_km": 1904.9, + "clarity_ratio": 3.26, + "median_distance_km": 1726.1, + "distances_to_centroid": { + "el Guinardó": 1726.1, + "Kilwinning": 1463.7, + "Tortosa": 1628.1, + "Nunspeet": 1904.9, + "Emporia": 6210.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " el Guinardó: (41.42°, 2.17°)", + " Kilwinning: (55.65°, -4.71°)", + " Tortosa: (40.81°, 0.52°)", + " Nunspeet: (52.38°, 5.79°)", + " Emporia: (38.40°, -96.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Emporia: 6210.2 km from centroid", + " Nunspeet: 1904.9 km from centroid", + " el Guinardó: 1726.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Emporia", + "FINAL ANSWER: Emporia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.97263, + "lon": -71.32474, + "name": "North Attleborough Center" + }, + { + "lat": 43.23418, + "lon": -86.24839, + "name": "Muskegon" + }, + { + "lat": 29.703, + "lon": -98.12445, + "name": "New Braunfels" + }, + { + "lat": 44.78941, + "lon": -93.60218, + "name": "Chaska" + }, + { + "lat": -14.72028, + "lon": -56.3275, + "name": "Nobres" + } + ], + "question": "Which location is the geographic outlier among: North Attleborough Center, Muskegon, New Braunfels, Chaska, Nobres?", + "ground_truth": { + "answer": "Nobres", + "outlier_distance_km": 5543.2, + "second_furthest_km": 2071.8, + "clarity_ratio": 2.68, + "median_distance_km": 1691.3, + "distances_to_centroid": { + "North Attleborough Center": 1691.3, + "Muskegon": 1647.9, + "New Braunfels": 1648.0, + "Chaska": 2071.8, + "Nobres": 5543.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Attleborough Center: (41.97°, -71.32°)", + " Muskegon: (43.23°, -86.25°)", + " New Braunfels: (29.70°, -98.12°)", + " Chaska: (44.79°, -93.60°)", + " Nobres: (-14.72°, -56.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nobres: 5543.2 km from centroid", + " Chaska: 2071.8 km from centroid", + " North Attleborough Center: 1691.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nobres", + "FINAL ANSWER: Nobres" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.22961, + "lon": 8.91612, + "name": "Porta Westfalica" + }, + { + "lat": 41.40392, + "lon": 2.20413, + "name": "el Poblenou" + }, + { + "lat": 52.13129, + "lon": 11.63189, + "name": "Magdeburg" + }, + { + "lat": 53.86437, + "lon": -1.68743, + "name": "Yeadon" + }, + { + "lat": 41.10172, + "lon": -80.76452, + "name": "Austintown" + } + ], + "question": "Which location is the geographic outlier among: Porta Westfalica, el Poblenou, Magdeburg, Yeadon, Austintown?", + "ground_truth": { + "answer": "Austintown", + "outlier_distance_km": 5318.9, + "second_furthest_km": 1728.9, + "clarity_ratio": 3.08, + "median_distance_km": 1546.5, + "distances_to_centroid": { + "Porta Westfalica": 1546.5, + "el Poblenou": 1341.5, + "Magdeburg": 1728.9, + "Yeadon": 956.9, + "Austintown": 5318.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porta Westfalica: (52.23°, 8.92°)", + " el Poblenou: (41.40°, 2.20°)", + " Magdeburg: (52.13°, 11.63°)", + " Yeadon: (53.86°, -1.69°)", + " Austintown: (41.10°, -80.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Austintown: 5318.9 km from centroid", + " Magdeburg: 1728.9 km from centroid", + " Porta Westfalica: 1546.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Austintown", + "FINAL ANSWER: Austintown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.59407, + "lon": 9.47302, + "name": "Hansestadt Stade" + }, + { + "lat": 49.02542, + "lon": 2.21691, + "name": "Taverny" + }, + { + "lat": 53.16167, + "lon": 6.76111, + "name": "Hoogezand" + }, + { + "lat": 51.5861, + "lon": -0.55543, + "name": "Gerrards Cross" + }, + { + "lat": 29.56444, + "lon": -104.41639, + "name": "Manuel Ojinaga" + } + ], + "question": "Which location is the geographic outlier among: Hansestadt Stade, Taverny, Hoogezand, Gerrards Cross, Manuel Ojinaga?", + "ground_truth": { + "answer": "Manuel Ojinaga", + "outlier_distance_km": 7435.9, + "second_furthest_km": 2001.7, + "clarity_ratio": 3.71, + "median_distance_km": 1816.2, + "distances_to_centroid": { + "Hansestadt Stade": 2001.7, + "Taverny": 1454.0, + "Hoogezand": 1816.2, + "Gerrards Cross": 1293.2, + "Manuel Ojinaga": 7435.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hansestadt Stade: (53.59°, 9.47°)", + " Taverny: (49.03°, 2.22°)", + " Hoogezand: (53.16°, 6.76°)", + " Gerrards Cross: (51.59°, -0.56°)", + " Manuel Ojinaga: (29.56°, -104.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manuel Ojinaga: 7435.9 km from centroid", + " Hansestadt Stade: 2001.7 km from centroid", + " Hoogezand: 1816.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manuel Ojinaga", + "FINAL ANSWER: Manuel Ojinaga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.75, + "lon": 39.15, + "name": "Sagurē" + }, + { + "lat": -25.976, + "lon": 28.118, + "name": "Midrand" + }, + { + "lat": 6.54584, + "lon": -0.76264, + "name": "Nkawkaw" + }, + { + "lat": 9.56561, + "lon": 36.63569, + "name": "Gutin" + }, + { + "lat": 36.41528, + "lon": 128.16056, + "name": "Sangju" + } + ], + "question": "Which location is the geographic outlier among: Sagurē, Midrand, Nkawkaw, Gutin, Sangju?", + "ground_truth": { + "answer": "Sangju", + "outlier_distance_km": 8831.9, + "second_furthest_km": 5191.0, + "clarity_ratio": 1.7, + "median_distance_km": 4143.6, + "distances_to_centroid": { + "Sagurē": 790.4, + "Midrand": 4143.6, + "Nkawkaw": 5191.0, + "Gutin": 1101.0, + "Sangju": 8831.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sagurē: (7.75°, 39.15°)", + " Midrand: (-25.98°, 28.12°)", + " Nkawkaw: (6.55°, -0.76°)", + " Gutin: (9.57°, 36.64°)", + " Sangju: (36.42°, 128.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sangju: 8831.9 km from centroid", + " Nkawkaw: 5191.0 km from centroid", + " Midrand: 4143.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sangju", + "FINAL ANSWER: Sangju" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.95996, + "lon": -1.77792, + "name": "Dunkwa" + }, + { + "lat": 9.88333, + "lon": 38.26667, + "name": "Dayē" + }, + { + "lat": 30.55258, + "lon": 31.00904, + "name": "Shibīn al Kawm" + }, + { + "lat": 31.55371, + "lon": 25.15793, + "name": "As Sallūm" + }, + { + "lat": 38.96872, + "lon": -77.3411, + "name": "Reston" + } + ], + "question": "Which location is the geographic outlier among: Dunkwa, Dayē, Shibīn al Kawm, As Sallūm, Reston?", + "ground_truth": { + "answer": "Reston", + "outlier_distance_km": 7602.7, + "second_furthest_km": 4025.0, + "clarity_ratio": 1.89, + "median_distance_km": 2873.4, + "distances_to_centroid": { + "Dunkwa": 2005.6, + "Dayē": 4025.0, + "Shibīn al Kawm": 2873.4, + "As Sallūm": 2355.8, + "Reston": 7602.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dunkwa: (5.96°, -1.78°)", + " Dayē: (9.88°, 38.27°)", + " Shibīn al Kawm: (30.55°, 31.01°)", + " As Sallūm: (31.55°, 25.16°)", + " Reston: (38.97°, -77.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Reston: 7602.7 km from centroid", + " Dayē: 4025.0 km from centroid", + " Shibīn al Kawm: 2873.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Reston", + "FINAL ANSWER: Reston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.58481, + "lon": -46.40084, + "name": "Cidade Tiradentes" + }, + { + "lat": -11.52472, + "lon": -61.01278, + "name": "Espigão dOeste" + }, + { + "lat": -6.85472, + "lon": -35.49, + "name": "Guarabira" + }, + { + "lat": -8.66361, + "lon": -36.32, + "name": "Lajedo" + }, + { + "lat": 19.62749, + "lon": -103.41752, + "name": "Zapotiltic" + } + ], + "question": "Which location is the geographic outlier among: Cidade Tiradentes, Espigão dOeste, Guarabira, Lajedo, Zapotiltic?", + "ground_truth": { + "answer": "Zapotiltic", + "outlier_distance_km": 5878.6, + "second_furthest_km": 2325.1, + "clarity_ratio": 2.53, + "median_distance_km": 2244.6, + "distances_to_centroid": { + "Cidade Tiradentes": 2215.8, + "Espigão dOeste": 770.1, + "Guarabira": 2325.1, + "Lajedo": 2244.6, + "Zapotiltic": 5878.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cidade Tiradentes: (-23.58°, -46.40°)", + " Espigão dOeste: (-11.52°, -61.01°)", + " Guarabira: (-6.85°, -35.49°)", + " Lajedo: (-8.66°, -36.32°)", + " Zapotiltic: (19.63°, -103.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zapotiltic: 5878.6 km from centroid", + " Guarabira: 2325.1 km from centroid", + " Lajedo: 2244.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zapotiltic", + "FINAL ANSWER: Zapotiltic" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.66124, + "lon": -0.90169, + "name": "Almozara" + }, + { + "lat": 48.89317, + "lon": 2.10371, + "name": "Le Pecq" + }, + { + "lat": 48.9193, + "lon": 2.54305, + "name": "Livry-Gargan" + }, + { + "lat": 45.54672, + "lon": 11.5475, + "name": "Vicenza" + }, + { + "lat": 6.3, + "lon": 36.88333, + "name": "Felege Neway" + } + ], + "question": "Which location is the geographic outlier among: Almozara, Le Pecq, Livry-Gargan, Vicenza, Felege Neway?", + "ground_truth": { + "answer": "Felege Neway", + "outlier_distance_km": 4441.3, + "second_furthest_km": 1357.2, + "clarity_ratio": 3.27, + "median_distance_km": 1342.8, + "distances_to_centroid": { + "Almozara": 1036.4, + "Le Pecq": 1357.2, + "Livry-Gargan": 1342.8, + "Vicenza": 815.0, + "Felege Neway": 4441.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Almozara: (41.66°, -0.90°)", + " Le Pecq: (48.89°, 2.10°)", + " Livry-Gargan: (48.92°, 2.54°)", + " Vicenza: (45.55°, 11.55°)", + " Felege Neway: (6.30°, 36.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Felege Neway: 4441.3 km from centroid", + " Le Pecq: 1357.2 km from centroid", + " Livry-Gargan: 1342.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Felege Neway", + "FINAL ANSWER: Felege Neway" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -37.99116, + "lon": 145.17385, + "name": "Keysborough" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": 51.51473, + "lon": 81.20613, + "name": "Rubtsovsk" + } + ], + "question": "Which location is the geographic outlier among: Armidale, Keysborough, Shepparton, Saint Kilda, Rubtsovsk?", + "ground_truth": { + "answer": "Rubtsovsk", + "outlier_distance_km": 9273.9, + "second_furthest_km": 2462.9, + "clarity_ratio": 3.77, + "median_distance_km": 2442.6, + "distances_to_centroid": { + "Armidale": 2269.1, + "Keysborough": 2462.9, + "Shepparton": 2320.5, + "Saint Kilda": 2442.6, + "Rubtsovsk": 9273.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Armidale: (-30.50°, 151.67°)", + " Keysborough: (-37.99°, 145.17°)", + " Shepparton: (-36.38°, 145.40°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Rubtsovsk: (51.51°, 81.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rubtsovsk: 9273.9 km from centroid", + " Keysborough: 2462.9 km from centroid", + " Saint Kilda: 2442.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rubtsovsk", + "FINAL ANSWER: Rubtsovsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.9128, + "lon": 30.29019, + "name": "Ḩawsh ‘Īsá" + }, + { + "lat": -1.08083, + "lon": 35.87111, + "name": "Narok" + }, + { + "lat": -33.78664, + "lon": 20.12106, + "name": "Montagu" + }, + { + "lat": 3.11988, + "lon": 35.59642, + "name": "Lodwar" + }, + { + "lat": -27.08819, + "lon": -61.08217, + "name": "Las Breñas" + } + ], + "question": "Which location is the geographic outlier among: Ḩawsh ‘Īsá, Narok, Montagu, Lodwar, Las Breñas?", + "ground_truth": { + "answer": "Las Breñas", + "outlier_distance_km": 8067.6, + "second_furthest_km": 4492.8, + "clarity_ratio": 1.8, + "median_distance_km": 3241.8, + "distances_to_centroid": { + "Ḩawsh ‘Īsá": 4492.8, + "Narok": 2678.7, + "Montagu": 3241.8, + "Lodwar": 2777.1, + "Las Breñas": 8067.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ḩawsh ‘Īsá: (30.91°, 30.29°)", + " Narok: (-1.08°, 35.87°)", + " Montagu: (-33.79°, 20.12°)", + " Lodwar: (3.12°, 35.60°)", + " Las Breñas: (-27.09°, -61.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Las Breñas: 8067.6 km from centroid", + " Ḩawsh ‘Īsá: 4492.8 km from centroid", + " Montagu: 3241.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Las Breñas", + "FINAL ANSWER: Las Breñas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.80938, + "lon": -79.22344, + "name": "Malvern" + }, + { + "lat": 45.42067, + "lon": -122.67065, + "name": "Lake Oswego" + }, + { + "lat": 43.79572, + "lon": -79.31408, + "name": "L'Amoreaux" + }, + { + "lat": 35.86815, + "lon": -83.56184, + "name": "Sevierville" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + } + ], + "question": "Which location is the geographic outlier among: Malvern, Lake Oswego, L'Amoreaux, Sevierville, Doncaster East?", + "ground_truth": { + "answer": "Doncaster East", + "outlier_distance_km": 18472.3, + "second_furthest_km": 7122.0, + "clarity_ratio": 2.59, + "median_distance_km": 3896.6, + "distances_to_centroid": { + "Malvern": 3721.1, + "Lake Oswego": 7122.0, + "L'Amoreaux": 3727.4, + "Sevierville": 3896.6, + "Doncaster East": 18472.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Malvern: (43.81°, -79.22°)", + " Lake Oswego: (45.42°, -122.67°)", + " L'Amoreaux: (43.80°, -79.31°)", + " Sevierville: (35.87°, -83.56°)", + " Doncaster East: (-37.79°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Doncaster East: 18472.3 km from centroid", + " Lake Oswego: 7122.0 km from centroid", + " Sevierville: 3896.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Doncaster East", + "FINAL ANSWER: Doncaster East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.00288, + "lon": -84.14464, + "name": "Duluth" + }, + { + "lat": 42.96083, + "lon": -89.46984, + "name": "Fitchburg" + }, + { + "lat": 40.6976, + "lon": -74.2632, + "name": "Union" + }, + { + "lat": 41.79586, + "lon": -87.97562, + "name": "Westmont" + }, + { + "lat": -34.75155, + "lon": 149.72086, + "name": "Goulburn" + } + ], + "question": "Which location is the geographic outlier among: Duluth, Fitchburg, Union, Westmont, Goulburn?", + "ground_truth": { + "answer": "Goulburn", + "outlier_distance_km": 18735.8, + "second_furthest_km": 5123.5, + "clarity_ratio": 3.66, + "median_distance_km": 4988.9, + "distances_to_centroid": { + "Duluth": 4611.6, + "Fitchburg": 5123.5, + "Union": 3840.7, + "Westmont": 4988.9, + "Goulburn": 18735.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Duluth: (34.00°, -84.14°)", + " Fitchburg: (42.96°, -89.47°)", + " Union: (40.70°, -74.26°)", + " Westmont: (41.80°, -87.98°)", + " Goulburn: (-34.75°, 149.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Goulburn: 18735.8 km from centroid", + " Fitchburg: 5123.5 km from centroid", + " Westmont: 4988.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Goulburn", + "FINAL ANSWER: Goulburn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.68747, + "lon": 77.28558, + "name": "Bābarpur" + }, + { + "lat": 9.88151, + "lon": 78.07306, + "name": "Tirupparangunram" + }, + { + "lat": 35.27651, + "lon": 139.57733, + "name": "Hayama" + }, + { + "lat": 3.3285, + "lon": 99.1625, + "name": "Tebingtinggi" + }, + { + "lat": 36.0397, + "lon": -114.98194, + "name": "Henderson" + } + ], + "question": "Which location is the geographic outlier among: Bābarpur, Tirupparangunram, Hayama, Tebingtinggi, Henderson?", + "ground_truth": { + "answer": "Henderson", + "outlier_distance_km": 13418.6, + "second_furthest_km": 8037.5, + "clarity_ratio": 1.67, + "median_distance_km": 5134.4, + "distances_to_centroid": { + "Bābarpur": 2249.7, + "Tirupparangunram": 2760.3, + "Hayama": 8037.5, + "Tebingtinggi": 5134.4, + "Henderson": 13418.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bābarpur: (28.69°, 77.29°)", + " Tirupparangunram: (9.88°, 78.07°)", + " Hayama: (35.28°, 139.58°)", + " Tebingtinggi: (3.33°, 99.16°)", + " Henderson: (36.04°, -114.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Henderson: 13418.6 km from centroid", + " Hayama: 8037.5 km from centroid", + " Tebingtinggi: 5134.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Henderson", + "FINAL ANSWER: Henderson" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.97083, + "lon": -44.31556, + "name": "Bacabeira" + }, + { + "lat": -26.02267, + "lon": -54.61356, + "name": "Puerto Esperanza" + }, + { + "lat": -11.38333, + "lon": -37.65778, + "name": "Umbaúba" + }, + { + "lat": -29.59111, + "lon": -51.16056, + "name": "Ivoti" + }, + { + "lat": 27.71809, + "lon": -82.35176, + "name": "Sun City Center" + } + ], + "question": "Which location is the geographic outlier among: Bacabeira, Puerto Esperanza, Umbaúba, Ivoti, Sun City Center?", + "ground_truth": { + "answer": "Sun City Center", + "outlier_distance_km": 5046.0, + "second_furthest_km": 2369.6, + "clarity_ratio": 2.13, + "median_distance_km": 1955.0, + "distances_to_centroid": { + "Bacabeira": 1234.1, + "Puerto Esperanza": 1955.0, + "Umbaúba": 1821.2, + "Ivoti": 2369.6, + "Sun City Center": 5046.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bacabeira: (-2.97°, -44.32°)", + " Puerto Esperanza: (-26.02°, -54.61°)", + " Umbaúba: (-11.38°, -37.66°)", + " Ivoti: (-29.59°, -51.16°)", + " Sun City Center: (27.72°, -82.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sun City Center: 5046.0 km from centroid", + " Ivoti: 2369.6 km from centroid", + " Puerto Esperanza: 1955.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sun City Center", + "FINAL ANSWER: Sun City Center" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.52532, + "lon": 76.20611, + "name": "Akalkot" + }, + { + "lat": 16.05662, + "lon": 75.94773, + "name": "Amīngarh" + }, + { + "lat": 11.28333, + "lon": 106.13333, + "name": "Phú Khương" + }, + { + "lat": -8.36667, + "lon": 114.15, + "name": "Genteng" + }, + { + "lat": -14.79909, + "lon": -39.03228, + "name": "Ilhéus" + } + ], + "question": "Which location is the geographic outlier among: Akalkot, Amīngarh, Phú Khương, Genteng, Ilhéus?", + "ground_truth": { + "answer": "Ilhéus", + "outlier_distance_km": 11818.4, + "second_furthest_km": 5450.2, + "clarity_ratio": 2.17, + "median_distance_km": 4409.8, + "distances_to_centroid": { + "Akalkot": 1796.0, + "Amīngarh": 1649.8, + "Phú Khương": 4409.8, + "Genteng": 5450.2, + "Ilhéus": 11818.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Akalkot: (17.53°, 76.21°)", + " Amīngarh: (16.06°, 75.95°)", + " Phú Khương: (11.28°, 106.13°)", + " Genteng: (-8.37°, 114.15°)", + " Ilhéus: (-14.80°, -39.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ilhéus: 11818.4 km from centroid", + " Genteng: 5450.2 km from centroid", + " Phú Khương: 4409.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ilhéus", + "FINAL ANSWER: Ilhéus" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.54846, + "lon": -2.00455, + "name": "Saddleworth" + }, + { + "lat": 50.9466, + "lon": 17.2926, + "name": "Oława" + }, + { + "lat": 52.4603, + "lon": 4.61048, + "name": "IJmuiden" + }, + { + "lat": 50.44767, + "lon": 23.41616, + "name": "Tomaszów Lubelski" + }, + { + "lat": 6.04639, + "lon": -75.90705, + "name": "Concordia" + } + ], + "question": "Which location is the geographic outlier among: Saddleworth, Oława, IJmuiden, Tomaszów Lubelski, Concordia?", + "ground_truth": { + "answer": "Concordia", + "outlier_distance_km": 7873.5, + "second_furthest_km": 2425.4, + "clarity_ratio": 3.25, + "median_distance_km": 2018.8, + "distances_to_centroid": { + "Saddleworth": 1252.4, + "Oława": 2018.8, + "IJmuiden": 1366.9, + "Tomaszów Lubelski": 2425.4, + "Concordia": 7873.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saddleworth: (53.55°, -2.00°)", + " Oława: (50.95°, 17.29°)", + " IJmuiden: (52.46°, 4.61°)", + " Tomaszów Lubelski: (50.45°, 23.42°)", + " Concordia: (6.05°, -75.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Concordia: 7873.5 km from centroid", + " Tomaszów Lubelski: 2425.4 km from centroid", + " Oława: 2018.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Concordia", + "FINAL ANSWER: Concordia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": 43.42896, + "lon": 39.92391, + "name": "Adler" + } + ], + "question": "Which location is the geographic outlier among: Carlton, Saint Kilda, Kingsford, Hervey Bay, Adler?", + "ground_truth": { + "answer": "Adler", + "outlier_distance_km": 11146.7, + "second_furthest_km": 2983.7, + "clarity_ratio": 3.74, + "median_distance_km": 2804.6, + "distances_to_centroid": { + "Carlton": 2798.3, + "Saint Kilda": 2804.6, + "Kingsford": 2983.7, + "Hervey Bay": 2789.1, + "Adler": 11146.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carlton: (-37.80°, 144.97°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Kingsford: (-33.92°, 151.23°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Adler: (43.43°, 39.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adler: 11146.7 km from centroid", + " Kingsford: 2983.7 km from centroid", + " Saint Kilda: 2804.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adler", + "FINAL ANSWER: Adler" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.80917, + "lon": -61.30028, + "name": "Manicoré" + }, + { + "lat": -30.18111, + "lon": -50.20556, + "name": "Cidreira" + }, + { + "lat": -5.30972, + "lon": -38.92056, + "name": "Banabuiú" + }, + { + "lat": -22.4625, + "lon": -42.65306, + "name": "Cachoeiras de Macacu" + }, + { + "lat": 6.58333, + "lon": 38.33333, + "name": "Ch’iko" + } + ], + "question": "Which location is the geographic outlier among: Manicoré, Cidreira, Banabuiú, Cachoeiras de Macacu, Ch’iko?", + "ground_truth": { + "answer": "Ch’iko", + "outlier_distance_km": 7920.8, + "second_furthest_km": 3392.6, + "clarity_ratio": 2.33, + "median_distance_km": 2880.0, + "distances_to_centroid": { + "Manicoré": 3392.6, + "Cidreira": 2880.0, + "Banabuiú": 1110.1, + "Cachoeiras de Macacu": 1745.4, + "Ch’iko": 7920.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Manicoré: (-5.81°, -61.30°)", + " Cidreira: (-30.18°, -50.21°)", + " Banabuiú: (-5.31°, -38.92°)", + " Cachoeiras de Macacu: (-22.46°, -42.65°)", + " Ch’iko: (6.58°, 38.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ch’iko: 7920.8 km from centroid", + " Manicoré: 3392.6 km from centroid", + " Cidreira: 2880.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ch’iko", + "FINAL ANSWER: Ch’iko" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.30225, + "lon": 27.08395, + "name": "Zastron" + }, + { + "lat": 6.71897, + "lon": -1.61188, + "name": "New Tafo" + }, + { + "lat": -0.49887, + "lon": 37.28031, + "name": "Kerugoya" + }, + { + "lat": 30.13806, + "lon": 31.61556, + "name": "El Shorouk" + }, + { + "lat": -37.0182, + "lon": 174.88019, + "name": "Manurewa" + } + ], + "question": "Which location is the geographic outlier among: Zastron, New Tafo, Kerugoya, El Shorouk, Manurewa?", + "ground_truth": { + "answer": "Manurewa", + "outlier_distance_km": 12246.6, + "second_furthest_km": 6318.9, + "clarity_ratio": 1.94, + "median_distance_km": 4684.1, + "distances_to_centroid": { + "Zastron": 3873.5, + "New Tafo": 6318.9, + "Kerugoya": 1944.4, + "El Shorouk": 4684.1, + "Manurewa": 12246.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zastron: (-30.30°, 27.08°)", + " New Tafo: (6.72°, -1.61°)", + " Kerugoya: (-0.50°, 37.28°)", + " El Shorouk: (30.14°, 31.62°)", + " Manurewa: (-37.02°, 174.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manurewa: 12246.6 km from centroid", + " New Tafo: 6318.9 km from centroid", + " El Shorouk: 4684.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manurewa", + "FINAL ANSWER: Manurewa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 46.25917, + "lon": 5.65727, + "name": "Oyonnax" + }, + { + "lat": 44.88515, + "lon": 11.06902, + "name": "Mirandola" + }, + { + "lat": 55.8, + "lon": 37.45, + "name": "Shchukino" + }, + { + "lat": 50.79646, + "lon": 19.12409, + "name": "Częstochowa" + }, + { + "lat": -9.74833, + "lon": -37.43667, + "name": "Pão de Açúcar" + } + ], + "question": "Which location is the geographic outlier among: Oyonnax, Mirandola, Shchukino, Częstochowa, Pão de Açúcar?", + "ground_truth": { + "answer": "Pão de Açúcar", + "outlier_distance_km": 7015.2, + "second_furthest_km": 3027.3, + "clarity_ratio": 2.32, + "median_distance_km": 1744.8, + "distances_to_centroid": { + "Oyonnax": 971.1, + "Mirandola": 873.0, + "Shchukino": 3027.3, + "Częstochowa": 1744.8, + "Pão de Açúcar": 7015.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oyonnax: (46.26°, 5.66°)", + " Mirandola: (44.89°, 11.07°)", + " Shchukino: (55.80°, 37.45°)", + " Częstochowa: (50.80°, 19.12°)", + " Pão de Açúcar: (-9.75°, -37.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pão de Açúcar: 7015.2 km from centroid", + " Shchukino: 3027.3 km from centroid", + " Częstochowa: 1744.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pão de Açúcar", + "FINAL ANSWER: Pão de Açúcar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + }, + { + "lat": -7.65694, + "lon": -35.32667, + "name": "Vicência" + } + ], + "question": "Which location is the geographic outlier among: Mosman, Sunshine West, Saint Ives, Wantirna South, Vicência?", + "ground_truth": { + "answer": "Vicência", + "outlier_distance_km": 14511.2, + "second_furthest_km": 3753.2, + "clarity_ratio": 3.87, + "median_distance_km": 3746.9, + "distances_to_centroid": { + "Mosman": 3753.2, + "Sunshine West": 3174.6, + "Saint Ives": 3746.9, + "Wantirna South": 3210.6, + "Vicência": 14511.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mosman: (-33.84°, 151.24°)", + " Sunshine West: (-37.79°, 144.82°)", + " Saint Ives: (-33.73°, 151.16°)", + " Wantirna South: (-37.88°, 145.22°)", + " Vicência: (-7.66°, -35.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vicência: 14511.2 km from centroid", + " Mosman: 3753.2 km from centroid", + " Saint Ives: 3746.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vicência", + "FINAL ANSWER: Vicência" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": -34.60251, + "lon": 138.74902, + "name": "Gawler" + }, + { + "lat": -33.86785, + "lon": 151.20732, + "name": "Sydney" + }, + { + "lat": 26.08657, + "lon": 32.42265, + "name": "Al Waqf" + } + ], + "question": "Which location is the geographic outlier among: Blacktown, Bundoora, Gawler, Sydney, Al Waqf?", + "ground_truth": { + "answer": "Al Waqf", + "outlier_distance_km": 11214.0, + "second_furthest_km": 2951.9, + "clarity_ratio": 3.8, + "median_distance_km": 2922.9, + "distances_to_centroid": { + "Blacktown": 2922.9, + "Bundoora": 2630.0, + "Gawler": 1969.0, + "Sydney": 2951.9, + "Al Waqf": 11214.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blacktown: (-33.77°, 150.92°)", + " Bundoora: (-37.70°, 145.06°)", + " Gawler: (-34.60°, 138.75°)", + " Sydney: (-33.87°, 151.21°)", + " Al Waqf: (26.09°, 32.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Waqf: 11214.0 km from centroid", + " Sydney: 2951.9 km from centroid", + " Blacktown: 2922.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Waqf", + "FINAL ANSWER: Al Waqf" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.31667, + "lon": -38.23333, + "name": "Itapicuru" + }, + { + "lat": -13.74389, + "lon": -39.48667, + "name": "Gandu" + }, + { + "lat": -28.06111, + "lon": -50.93833, + "name": "Estrela" + }, + { + "lat": -27.49417, + "lon": -48.65556, + "name": "Biguaçu" + }, + { + "lat": 52.5, + "lon": -2.08333, + "name": "Dudley" + } + ], + "question": "Which location is the geographic outlier among: Itapicuru, Gandu, Estrela, Biguaçu, Dudley?", + "ground_truth": { + "answer": "Dudley", + "outlier_distance_km": 7205.8, + "second_furthest_km": 2958.1, + "clarity_ratio": 2.44, + "median_distance_km": 2782.0, + "distances_to_centroid": { + "Itapicuru": 683.9, + "Gandu": 985.6, + "Estrela": 2958.1, + "Biguaçu": 2782.0, + "Dudley": 7205.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itapicuru: (-11.32°, -38.23°)", + " Gandu: (-13.74°, -39.49°)", + " Estrela: (-28.06°, -50.94°)", + " Biguaçu: (-27.49°, -48.66°)", + " Dudley: (52.50°, -2.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dudley: 7205.8 km from centroid", + " Estrela: 2958.1 km from centroid", + " Biguaçu: 2782.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dudley", + "FINAL ANSWER: Dudley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -6.98111, + "lon": -34.83389, + "name": "Cabedelo" + }, + { + "lat": 10.32944, + "lon": -75.41137, + "name": "Turbaco" + }, + { + "lat": -31.39195, + "lon": -58.01706, + "name": "Concordia" + }, + { + "lat": -14.63126, + "lon": -69.44638, + "name": "La Rinconada" + }, + { + "lat": 8.4902, + "lon": 77.0374, + "name": "Malayinkeezhu" + } + ], + "question": "Which location is the geographic outlier among: Cabedelo, Turbaco, Concordia, La Rinconada, Malayinkeezhu?", + "ground_truth": { + "answer": "Malayinkeezhu", + "outlier_distance_km": 12218.2, + "second_furthest_km": 5157.8, + "clarity_ratio": 2.37, + "median_distance_km": 4161.5, + "distances_to_centroid": { + "Cabedelo": 298.4, + "Turbaco": 5157.8, + "Concordia": 3831.5, + "La Rinconada": 4161.5, + "Malayinkeezhu": 12218.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cabedelo: (-6.98°, -34.83°)", + " Turbaco: (10.33°, -75.41°)", + " Concordia: (-31.39°, -58.02°)", + " La Rinconada: (-14.63°, -69.45°)", + " Malayinkeezhu: (8.49°, 77.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Malayinkeezhu: 12218.2 km from centroid", + " Turbaco: 5157.8 km from centroid", + " La Rinconada: 4161.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Malayinkeezhu", + "FINAL ANSWER: Malayinkeezhu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.46139, + "lon": -40.18944, + "name": "Senhor do Bonfim" + }, + { + "lat": -22.24556, + "lon": -43.70028, + "name": "Valença" + }, + { + "lat": -16.83056, + "lon": -49.53194, + "name": "Guapó" + }, + { + "lat": -16.58197, + "lon": -39.78117, + "name": "Guaratinga" + }, + { + "lat": -38.65333, + "lon": 178.00417, + "name": "Gisborne" + } + ], + "question": "Which location is the geographic outlier among: Senhor do Bonfim, Valença, Guapó, Guaratinga, Gisborne?", + "ground_truth": { + "answer": "Gisborne", + "outlier_distance_km": 13379.8, + "second_furthest_km": 5310.9, + "clarity_ratio": 2.52, + "median_distance_km": 4602.7, + "distances_to_centroid": { + "Senhor do Bonfim": 4542.2, + "Valença": 4602.7, + "Guapó": 5310.9, + "Guaratinga": 4305.7, + "Gisborne": 13379.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Senhor do Bonfim: (-10.46°, -40.19°)", + " Valença: (-22.25°, -43.70°)", + " Guapó: (-16.83°, -49.53°)", + " Guaratinga: (-16.58°, -39.78°)", + " Gisborne: (-38.65°, 178.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gisborne: 13379.8 km from centroid", + " Guapó: 5310.9 km from centroid", + " Valença: 4602.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gisborne", + "FINAL ANSWER: Gisborne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.63461, + "lon": -52.2754, + "name": "Erechim" + }, + { + "lat": -22.95972, + "lon": -44.04056, + "name": "Mangaratiba" + }, + { + "lat": -22.90556, + "lon": -47.06083, + "name": "Campinas" + }, + { + "lat": -1.81361, + "lon": -49.79528, + "name": "Curralinho" + }, + { + "lat": -33.86785, + "lon": 151.20732, + "name": "Sydney" + } + ], + "question": "Which location is the geographic outlier among: Erechim, Mangaratiba, Campinas, Curralinho, Sydney?", + "ground_truth": { + "answer": "Sydney", + "outlier_distance_km": 13455.3, + "second_furthest_km": 4998.5, + "clarity_ratio": 2.69, + "median_distance_km": 4455.7, + "distances_to_centroid": { + "Erechim": 4455.7, + "Mangaratiba": 3658.0, + "Campinas": 3966.4, + "Curralinho": 4998.5, + "Sydney": 13455.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Erechim: (-27.63°, -52.28°)", + " Mangaratiba: (-22.96°, -44.04°)", + " Campinas: (-22.91°, -47.06°)", + " Curralinho: (-1.81°, -49.80°)", + " Sydney: (-33.87°, 151.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sydney: 13455.3 km from centroid", + " Curralinho: 4998.5 km from centroid", + " Erechim: 4455.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sydney", + "FINAL ANSWER: Sydney" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -20.72523, + "lon": 139.49727, + "name": "Mount Isa" + }, + { + "lat": -38.15912, + "lon": 145.93118, + "name": "Warragul" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": 26.55695, + "lon": 31.69478, + "name": "Sohag" + } + ], + "question": "Which location is the geographic outlier among: Reservoir, Mount Isa, Warragul, Dunedin, Sohag?", + "ground_truth": { + "answer": "Sohag", + "outlier_distance_km": 11586.1, + "second_furthest_km": 4670.2, + "clarity_ratio": 2.48, + "median_distance_km": 2483.6, + "distances_to_centroid": { + "Reservoir": 2388.8, + "Mount Isa": 1364.9, + "Warragul": 2483.6, + "Dunedin": 4670.2, + "Sohag": 11586.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reservoir: (-37.72°, 145.00°)", + " Mount Isa: (-20.73°, 139.50°)", + " Warragul: (-38.16°, 145.93°)", + " Dunedin: (-45.87°, 170.50°)", + " Sohag: (26.56°, 31.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sohag: 11586.1 km from centroid", + " Dunedin: 4670.2 km from centroid", + " Warragul: 2483.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sohag", + "FINAL ANSWER: Sohag" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + }, + { + "lat": 32.64541, + "lon": -85.37828, + "name": "Opelika" + } + ], + "question": "Which location is the geographic outlier among: Australind, Hampton Park, Glenroy, Ballajura, Opelika?", + "ground_truth": { + "answer": "Opelika", + "outlier_distance_km": 18593.3, + "second_furthest_km": 5783.0, + "clarity_ratio": 3.22, + "median_distance_km": 5754.6, + "distances_to_centroid": { + "Australind": 3075.7, + "Hampton Park": 5783.0, + "Glenroy": 5754.6, + "Ballajura": 3047.4, + "Opelika": 18593.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Australind: (-33.28°, 115.72°)", + " Hampton Park: (-38.03°, 145.25°)", + " Glenroy: (-37.70°, 144.93°)", + " Ballajura: (-31.84°, 115.90°)", + " Opelika: (32.65°, -85.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Opelika: 18593.3 km from centroid", + " Hampton Park: 5783.0 km from centroid", + " Glenroy: 5754.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Opelika", + "FINAL ANSWER: Opelika" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + }, + { + "lat": -1.4275, + "lon": 36.6865, + "name": "Kiserian" + } + ], + "question": "Which location is the geographic outlier among: Maitland, South Morang, Miranda, Doncaster East, Kiserian?", + "ground_truth": { + "answer": "Kiserian", + "outlier_distance_km": 9856.4, + "second_furthest_km": 2484.4, + "clarity_ratio": 3.97, + "median_distance_km": 2455.4, + "distances_to_centroid": { + "Maitland": 2484.4, + "South Morang": 2036.3, + "Miranda": 2455.4, + "Doncaster East": 2046.4, + "Kiserian": 9856.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maitland: (-32.73°, 151.56°)", + " South Morang: (-37.65°, 145.10°)", + " Miranda: (-34.04°, 151.10°)", + " Doncaster East: (-37.79°, 145.15°)", + " Kiserian: (-1.43°, 36.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kiserian: 9856.4 km from centroid", + " Maitland: 2484.4 km from centroid", + " Miranda: 2455.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kiserian", + "FINAL ANSWER: Kiserian" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.63143, + "lon": -46.62072, + "name": "Cursino" + }, + { + "lat": 10.79408, + "lon": -74.9164, + "name": "Baranoa" + }, + { + "lat": -12.58946, + "lon": -69.19948, + "name": "Puerto Maldonado" + }, + { + "lat": -10.66577, + "lon": -76.25309, + "name": "Cerro de Pasco" + }, + { + "lat": 54.75263, + "lon": 58.20137, + "name": "Katav-Ivanovsk" + } + ], + "question": "Which location is the geographic outlier among: Cursino, Baranoa, Puerto Maldonado, Cerro de Pasco, Katav-Ivanovsk?", + "ground_truth": { + "answer": "Katav-Ivanovsk", + "outlier_distance_km": 10303.5, + "second_furthest_km": 4140.3, + "clarity_ratio": 2.49, + "median_distance_km": 3737.6, + "distances_to_centroid": { + "Cursino": 3088.0, + "Baranoa": 3737.6, + "Puerto Maldonado": 3533.3, + "Cerro de Pasco": 4140.3, + "Katav-Ivanovsk": 10303.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cursino: (-23.63°, -46.62°)", + " Baranoa: (10.79°, -74.92°)", + " Puerto Maldonado: (-12.59°, -69.20°)", + " Cerro de Pasco: (-10.67°, -76.25°)", + " Katav-Ivanovsk: (54.75°, 58.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Katav-Ivanovsk: 10303.5 km from centroid", + " Cerro de Pasco: 4140.3 km from centroid", + " Baranoa: 3737.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Katav-Ivanovsk", + "FINAL ANSWER: Katav-Ivanovsk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.50259, + "lon": -84.95105, + "name": "Calhoun" + }, + { + "lat": 42.65837, + "lon": -83.14993, + "name": "Rochester Hills" + }, + { + "lat": 38.04668, + "lon": -97.34504, + "name": "Newton" + }, + { + "lat": 33.74585, + "lon": -117.82617, + "name": "Tustin" + }, + { + "lat": -17.08222, + "lon": -40.93583, + "name": "Águas Formosas" + } + ], + "question": "Which location is the geographic outlier among: Calhoun, Rochester Hills, Newton, Tustin, Águas Formosas?", + "ground_truth": { + "answer": "Águas Formosas", + "outlier_distance_km": 6770.4, + "second_furthest_km": 3263.3, + "clarity_ratio": 2.07, + "median_distance_km": 1817.2, + "distances_to_centroid": { + "Calhoun": 903.9, + "Rochester Hills": 1817.2, + "Newton": 1748.2, + "Tustin": 3263.3, + "Águas Formosas": 6770.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Calhoun: (34.50°, -84.95°)", + " Rochester Hills: (42.66°, -83.15°)", + " Newton: (38.05°, -97.35°)", + " Tustin: (33.75°, -117.83°)", + " Águas Formosas: (-17.08°, -40.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Águas Formosas: 6770.4 km from centroid", + " Tustin: 3263.3 km from centroid", + " Rochester Hills: 1817.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Águas Formosas", + "FINAL ANSWER: Águas Formosas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.53782, + "lon": 0.71433, + "name": "Southend-on-Sea" + }, + { + "lat": 55.99003, + "lon": 40.02052, + "name": "Sobinka" + }, + { + "lat": 45.35781, + "lon": 9.3236, + "name": "Melegnano" + }, + { + "lat": 52.56395, + "lon": 13.33552, + "name": "Reinickendorf" + }, + { + "lat": 10.26858, + "lon": 13.26701, + "name": "Mubi" + } + ], + "question": "Which location is the geographic outlier among: Southend-on-Sea, Sobinka, Melegnano, Reinickendorf, Mubi?", + "ground_truth": { + "answer": "Mubi", + "outlier_distance_km": 3661.0, + "second_furthest_km": 2261.4, + "clarity_ratio": 1.62, + "median_distance_km": 1439.1, + "distances_to_centroid": { + "Southend-on-Sea": 1439.1, + "Sobinka": 2261.4, + "Melegnano": 538.0, + "Reinickendorf": 1057.9, + "Mubi": 3661.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Southend-on-Sea: (51.54°, 0.71°)", + " Sobinka: (55.99°, 40.02°)", + " Melegnano: (45.36°, 9.32°)", + " Reinickendorf: (52.56°, 13.34°)", + " Mubi: (10.27°, 13.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mubi: 3661.0 km from centroid", + " Sobinka: 2261.4 km from centroid", + " Southend-on-Sea: 1439.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mubi", + "FINAL ANSWER: Mubi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.55728, + "lon": -0.1864, + "name": "Osu" + }, + { + "lat": -26.1625, + "lon": 27.8725, + "name": "Roodepoort" + }, + { + "lat": 8.15, + "lon": 39.35, + "name": "Huruta" + }, + { + "lat": 6.01962, + "lon": 6.91729, + "name": "Nnewi" + }, + { + "lat": 37.03333, + "lon": 137.85, + "name": "Itoigawa" + } + ], + "question": "Which location is the geographic outlier among: Osu, Roodepoort, Huruta, Nnewi, Itoigawa?", + "ground_truth": { + "answer": "Itoigawa", + "outlier_distance_km": 10082.2, + "second_furthest_km": 4705.7, + "clarity_ratio": 2.14, + "median_distance_km": 3918.3, + "distances_to_centroid": { + "Osu": 4705.7, + "Roodepoort": 3915.1, + "Huruta": 401.6, + "Nnewi": 3918.3, + "Itoigawa": 10082.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Osu: (5.56°, -0.19°)", + " Roodepoort: (-26.16°, 27.87°)", + " Huruta: (8.15°, 39.35°)", + " Nnewi: (6.02°, 6.92°)", + " Itoigawa: (37.03°, 137.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itoigawa: 10082.2 km from centroid", + " Osu: 4705.7 km from centroid", + " Nnewi: 3918.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itoigawa", + "FINAL ANSWER: Itoigawa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.6725, + "lon": -61.19361, + "name": "Pimenta Bueno" + }, + { + "lat": -15.56833, + "lon": -40.42306, + "name": "Macarani" + }, + { + "lat": -15.53722, + "lon": -47.33444, + "name": "Formosa" + }, + { + "lat": -37.84638, + "lon": -58.25549, + "name": "Balcarce" + }, + { + "lat": 30.6798, + "lon": 30.94364, + "name": "Talā" + } + ], + "question": "Which location is the geographic outlier among: Pimenta Bueno, Macarani, Formosa, Balcarce, Talā?", + "ground_truth": { + "answer": "Talā", + "outlier_distance_km": 8375.7, + "second_furthest_km": 3857.0, + "clarity_ratio": 2.17, + "median_distance_km": 2838.3, + "distances_to_centroid": { + "Pimenta Bueno": 2838.3, + "Macarani": 836.0, + "Formosa": 1447.6, + "Balcarce": 3857.0, + "Talā": 8375.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pimenta Bueno: (-11.67°, -61.19°)", + " Macarani: (-15.57°, -40.42°)", + " Formosa: (-15.54°, -47.33°)", + " Balcarce: (-37.85°, -58.26°)", + " Talā: (30.68°, 30.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Talā: 8375.7 km from centroid", + " Balcarce: 3857.0 km from centroid", + " Pimenta Bueno: 2838.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Talā", + "FINAL ANSWER: Talā" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.13874, + "lon": 176.24516, + "name": "Rotorua" + }, + { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + }, + { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + }, + { + "lat": -38.68333, + "lon": 176.08333, + "name": "Taupo" + }, + { + "lat": 30.65622, + "lon": 76.82093, + "name": "Zerakpur" + } + ], + "question": "Which location is the geographic outlier among: Rotorua, Cronulla, Hawthorn, Taupo, Zerakpur?", + "ground_truth": { + "answer": "Zerakpur", + "outlier_distance_km": 9446.6, + "second_furthest_km": 3370.1, + "clarity_ratio": 2.8, + "median_distance_km": 3362.5, + "distances_to_centroid": { + "Rotorua": 3362.5, + "Cronulla": 1303.9, + "Hawthorn": 1580.1, + "Taupo": 3370.1, + "Zerakpur": 9446.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rotorua: (-38.14°, 176.25°)", + " Cronulla: (-34.06°, 151.15°)", + " Hawthorn: (-37.82°, 145.04°)", + " Taupo: (-38.68°, 176.08°)", + " Zerakpur: (30.66°, 76.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zerakpur: 9446.6 km from centroid", + " Taupo: 3370.1 km from centroid", + " Rotorua: 3362.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zerakpur", + "FINAL ANSWER: Zerakpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.98776, + "lon": 31.2385, + "name": "Mkhuhlu" + }, + { + "lat": -26.76566, + "lon": 26.42024, + "name": "Hartbeesfontein" + }, + { + "lat": -29.56822, + "lon": 30.18618, + "name": "Mpophomeni" + }, + { + "lat": -26.33172, + "lon": 26.32065, + "name": "Coligny" + }, + { + "lat": -18.47552, + "lon": -70.30058, + "name": "Arica" + } + ], + "question": "Which location is the geographic outlier among: Mkhuhlu, Hartbeesfontein, Mpophomeni, Coligny, Arica?", + "ground_truth": { + "answer": "Arica", + "outlier_distance_km": 8081.8, + "second_furthest_km": 2259.5, + "clarity_ratio": 3.58, + "median_distance_km": 2165.0, + "distances_to_centroid": { + "Mkhuhlu": 2259.5, + "Hartbeesfontein": 1770.6, + "Mpophomeni": 2165.0, + "Coligny": 1760.0, + "Arica": 8081.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mkhuhlu: (-24.99°, 31.24°)", + " Hartbeesfontein: (-26.77°, 26.42°)", + " Mpophomeni: (-29.57°, 30.19°)", + " Coligny: (-26.33°, 26.32°)", + " Arica: (-18.48°, -70.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arica: 8081.8 km from centroid", + " Mkhuhlu: 2259.5 km from centroid", + " Mpophomeni: 2165.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arica", + "FINAL ANSWER: Arica" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.43099, + "lon": 9.11093, + "name": "Corsico" + }, + { + "lat": 45.53329, + "lon": 9.22585, + "name": "Sesto San Giovanni" + }, + { + "lat": 48.99004, + "lon": 2.25804, + "name": "Ermont" + }, + { + "lat": 51.3502, + "lon": 8.28332, + "name": "Meschede" + }, + { + "lat": 37.66243, + "lon": -121.87468, + "name": "Pleasanton" + } + ], + "question": "Which location is the geographic outlier among: Corsico, Sesto San Giovanni, Ermont, Meschede, Pleasanton?", + "ground_truth": { + "answer": "Pleasanton", + "outlier_distance_km": 7991.1, + "second_furthest_km": 2151.5, + "clarity_ratio": 3.71, + "median_distance_km": 2144.9, + "distances_to_centroid": { + "Corsico": 2144.9, + "Sesto San Giovanni": 2151.5, + "Ermont": 1604.3, + "Meschede": 2058.8, + "Pleasanton": 7991.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Corsico: (45.43°, 9.11°)", + " Sesto San Giovanni: (45.53°, 9.23°)", + " Ermont: (48.99°, 2.26°)", + " Meschede: (51.35°, 8.28°)", + " Pleasanton: (37.66°, -121.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pleasanton: 7991.1 km from centroid", + " Sesto San Giovanni: 2151.5 km from centroid", + " Corsico: 2144.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pleasanton", + "FINAL ANSWER: Pleasanton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.01167, + "lon": 17.9442, + "name": "Saldanha" + }, + { + "lat": -1.85238, + "lon": 36.77683, + "name": "Kajiado" + }, + { + "lat": 7.85, + "lon": 36.65, + "name": "Āgaro" + }, + { + "lat": 12.11451, + "lon": 12.8262, + "name": "Magumeri" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + } + ], + "question": "Which location is the geographic outlier among: Saldanha, Kajiado, Āgaro, Magumeri, Dandenong North?", + "ground_truth": { + "answer": "Dandenong North", + "outlier_distance_km": 9746.7, + "second_furthest_km": 4807.7, + "clarity_ratio": 2.03, + "median_distance_km": 4104.9, + "distances_to_centroid": { + "Saldanha": 4104.9, + "Kajiado": 1741.9, + "Āgaro": 2518.2, + "Magumeri": 4807.7, + "Dandenong North": 9746.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saldanha: (-33.01°, 17.94°)", + " Kajiado: (-1.85°, 36.78°)", + " Āgaro: (7.85°, 36.65°)", + " Magumeri: (12.11°, 12.83°)", + " Dandenong North: (-37.97°, 145.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dandenong North: 9746.7 km from centroid", + " Magumeri: 4807.7 km from centroid", + " Saldanha: 4104.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dandenong North", + "FINAL ANSWER: Dandenong North" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.90222, + "lon": -40.84111, + "name": "Camocim" + }, + { + "lat": -31.4933, + "lon": -68.53838, + "name": "Villa Paula de Sarmiento" + }, + { + "lat": -15.56833, + "lon": -40.42306, + "name": "Macarani" + }, + { + "lat": -12.59694, + "lon": -52.19972, + "name": "Querência" + }, + { + "lat": 20.90686, + "lon": -103.9769, + "name": "Magdalena" + } + ], + "question": "Which location is the geographic outlier among: Camocim, Villa Paula de Sarmiento, Macarani, Querência, Magdalena?", + "ground_truth": { + "answer": "Magdalena", + "outlier_distance_km": 5692.4, + "second_furthest_km": 2685.4, + "clarity_ratio": 2.12, + "median_distance_km": 2396.7, + "distances_to_centroid": { + "Camocim": 2331.0, + "Villa Paula de Sarmiento": 2685.4, + "Macarani": 2396.7, + "Querência": 1091.8, + "Magdalena": 5692.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Camocim: (-2.90°, -40.84°)", + " Villa Paula de Sarmiento: (-31.49°, -68.54°)", + " Macarani: (-15.57°, -40.42°)", + " Querência: (-12.60°, -52.20°)", + " Magdalena: (20.91°, -103.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Magdalena: 5692.4 km from centroid", + " Villa Paula de Sarmiento: 2685.4 km from centroid", + " Macarani: 2396.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Magdalena", + "FINAL ANSWER: Magdalena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.8707, + "lon": -47.96892, + "name": "Núcleo Bandeirante" + }, + { + "lat": -11.48472, + "lon": -37.93278, + "name": "Rio Real" + }, + { + "lat": -31.89706, + "lon": -61.85993, + "name": "San Jorge" + }, + { + "lat": -14.43167, + "lon": -54.05111, + "name": "Paranatinga" + }, + { + "lat": -43.58333, + "lon": 172.38333, + "name": "Rolleston" + } + ], + "question": "Which location is the geographic outlier among: Núcleo Bandeirante, Rio Real, San Jorge, Paranatinga, Rolleston?", + "ground_truth": { + "answer": "Rolleston", + "outlier_distance_km": 12558.8, + "second_furthest_km": 5531.9, + "clarity_ratio": 2.27, + "median_distance_km": 5140.5, + "distances_to_centroid": { + "Núcleo Bandeirante": 4470.5, + "Rio Real": 3639.0, + "San Jorge": 5531.9, + "Paranatinga": 5140.5, + "Rolleston": 12558.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Núcleo Bandeirante: (-15.87°, -47.97°)", + " Rio Real: (-11.48°, -37.93°)", + " San Jorge: (-31.90°, -61.86°)", + " Paranatinga: (-14.43°, -54.05°)", + " Rolleston: (-43.58°, 172.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rolleston: 12558.8 km from centroid", + " San Jorge: 5531.9 km from centroid", + " Paranatinga: 5140.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rolleston", + "FINAL ANSWER: Rolleston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.98898, + "lon": -90.01259, + "name": "Southaven" + }, + { + "lat": 38.84685, + "lon": -76.92591, + "name": "Suitland-Silver Hill" + }, + { + "lat": 40.81232, + "lon": -73.07844, + "name": "Holbrook" + }, + { + "lat": 41.92111, + "lon": -71.435, + "name": "Lincoln" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + } + ], + "question": "Which location is the geographic outlier among: Southaven, Suitland-Silver Hill, Holbrook, Lincoln, Perth?", + "ground_truth": { + "answer": "Perth", + "outlier_distance_km": 17453.9, + "second_furthest_km": 4975.2, + "clarity_ratio": 3.51, + "median_distance_km": 3856.2, + "distances_to_centroid": { + "Southaven": 4975.2, + "Suitland-Silver Hill": 3856.2, + "Holbrook": 3598.1, + "Lincoln": 3512.9, + "Perth": 17453.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Southaven: (34.99°, -90.01°)", + " Suitland-Silver Hill: (38.85°, -76.93°)", + " Holbrook: (40.81°, -73.08°)", + " Lincoln: (41.92°, -71.44°)", + " Perth: (-31.95°, 115.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perth: 17453.9 km from centroid", + " Southaven: 4975.2 km from centroid", + " Suitland-Silver Hill: 3856.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perth", + "FINAL ANSWER: Perth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.93409, + "lon": 109.7311, + "name": "Tonggu" + }, + { + "lat": 0.79065, + "lon": 127.38424, + "name": "Ternate" + }, + { + "lat": 14.35451, + "lon": 108.00759, + "name": "Kon Tum" + }, + { + "lat": 36.26333, + "lon": 119.19389, + "name": "Guanzhuang" + }, + { + "lat": 53.4115, + "lon": -2.83935, + "name": "Huyton" + } + ], + "question": "Which location is the geographic outlier among: Tonggu, Ternate, Kon Tum, Guanzhuang, Huyton?", + "ground_truth": { + "answer": "Huyton", + "outlier_distance_km": 7939.5, + "second_furthest_km": 4753.6, + "clarity_ratio": 1.67, + "median_distance_km": 2727.4, + "distances_to_centroid": { + "Tonggu": 1744.3, + "Ternate": 4753.6, + "Kon Tum": 2162.3, + "Guanzhuang": 2727.4, + "Huyton": 7939.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tonggu: (30.93°, 109.73°)", + " Ternate: (0.79°, 127.38°)", + " Kon Tum: (14.35°, 108.01°)", + " Guanzhuang: (36.26°, 119.19°)", + " Huyton: (53.41°, -2.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huyton: 7939.5 km from centroid", + " Ternate: 4753.6 km from centroid", + " Guanzhuang: 2727.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huyton", + "FINAL ANSWER: Huyton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.50153, + "lon": 3.35808, + "name": "Surulere" + }, + { + "lat": -26.41663, + "lon": 29.08668, + "name": "Kinross" + }, + { + "lat": -26.55, + "lon": 29.16667, + "name": "Secunda" + }, + { + "lat": 5.20913, + "lon": -1.06058, + "name": "Saltpond" + }, + { + "lat": -33.72197, + "lon": 151.04607, + "name": "Cherrybrook" + } + ], + "question": "Which location is the geographic outlier among: Surulere, Kinross, Secunda, Saltpond, Cherrybrook?", + "ground_truth": { + "answer": "Cherrybrook", + "outlier_distance_km": 10737.3, + "second_furthest_km": 5281.0, + "clarity_ratio": 2.03, + "median_distance_km": 4914.3, + "distances_to_centroid": { + "Surulere": 4914.3, + "Kinross": 1870.1, + "Secunda": 1873.6, + "Saltpond": 5281.0, + "Cherrybrook": 10737.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Surulere: (6.50°, 3.36°)", + " Kinross: (-26.42°, 29.09°)", + " Secunda: (-26.55°, 29.17°)", + " Saltpond: (5.21°, -1.06°)", + " Cherrybrook: (-33.72°, 151.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cherrybrook: 10737.3 km from centroid", + " Saltpond: 5281.0 km from centroid", + " Surulere: 4914.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cherrybrook", + "FINAL ANSWER: Cherrybrook" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -37.95855, + "lon": 176.98545, + "name": "Whakatane" + }, + { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -10.49167, + "lon": -37.19333, + "name": "Nossa Senhora das Dores" + } + ], + "question": "Which location is the geographic outlier among: Broken Hill, Whakatane, Mount Martha, Mildura, Nossa Senhora das Dores?", + "ground_truth": { + "answer": "Nossa Senhora das Dores", + "outlier_distance_km": 14490.0, + "second_furthest_km": 5764.3, + "clarity_ratio": 2.51, + "median_distance_km": 2982.4, + "distances_to_centroid": { + "Broken Hill": 2636.3, + "Whakatane": 5764.3, + "Mount Martha": 2982.4, + "Mildura": 2695.3, + "Nossa Senhora das Dores": 14490.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Broken Hill: (-31.97°, 141.45°)", + " Whakatane: (-37.96°, 176.99°)", + " Mount Martha: (-38.27°, 145.02°)", + " Mildura: (-34.19°, 142.16°)", + " Nossa Senhora das Dores: (-10.49°, -37.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nossa Senhora das Dores: 14490.0 km from centroid", + " Whakatane: 5764.3 km from centroid", + " Mount Martha: 2982.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nossa Senhora das Dores", + "FINAL ANSWER: Nossa Senhora das Dores" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.52472, + "lon": -49.14083, + "name": "Uruaçu" + }, + { + "lat": -8.08965, + "lon": -78.9602, + "name": "Laredo" + }, + { + "lat": 2.19593, + "lon": -75.62777, + "name": "Garzón" + }, + { + "lat": -25.46722, + "lon": -50.65111, + "name": "Irati" + }, + { + "lat": -37.89359, + "lon": 145.05534, + "name": "Carnegie" + } + ], + "question": "Which location is the geographic outlier among: Uruaçu, Laredo, Garzón, Irati, Carnegie?", + "ground_truth": { + "answer": "Carnegie", + "outlier_distance_km": 13786.5, + "second_furthest_km": 6262.4, + "clarity_ratio": 2.2, + "median_distance_km": 6254.7, + "distances_to_centroid": { + "Uruaçu": 2928.9, + "Laredo": 6254.7, + "Garzón": 6262.4, + "Irati": 3131.3, + "Carnegie": 13786.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Uruaçu: (-14.52°, -49.14°)", + " Laredo: (-8.09°, -78.96°)", + " Garzón: (2.20°, -75.63°)", + " Irati: (-25.47°, -50.65°)", + " Carnegie: (-37.89°, 145.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Carnegie: 13786.5 km from centroid", + " Garzón: 6262.4 km from centroid", + " Laredo: 6254.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Carnegie", + "FINAL ANSWER: Carnegie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.21667, + "lon": 138.61667, + "name": "Fujinomiya" + }, + { + "lat": 36.78444, + "lon": 119.94639, + "name": "Pingdu" + }, + { + "lat": 20.94099, + "lon": 106.33302, + "name": "Hải Dương" + }, + { + "lat": 36.9918, + "lon": 120.20412, + "name": "Jiudian" + }, + { + "lat": 51.64316, + "lon": -0.36053, + "name": "Bushey" + } + ], + "question": "Which location is the geographic outlier among: Fujinomiya, Pingdu, Hải Dương, Jiudian, Bushey?", + "ground_truth": { + "answer": "Bushey", + "outlier_distance_km": 7380.2, + "second_furthest_km": 3732.2, + "clarity_ratio": 1.98, + "median_distance_km": 2070.8, + "distances_to_centroid": { + "Fujinomiya": 3732.2, + "Pingdu": 2050.1, + "Hải Dương": 1936.9, + "Jiudian": 2070.8, + "Bushey": 7380.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fujinomiya: (35.22°, 138.62°)", + " Pingdu: (36.78°, 119.95°)", + " Hải Dương: (20.94°, 106.33°)", + " Jiudian: (36.99°, 120.20°)", + " Bushey: (51.64°, -0.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bushey: 7380.2 km from centroid", + " Fujinomiya: 3732.2 km from centroid", + " Jiudian: 2070.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bushey", + "FINAL ANSWER: Bushey" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.44665, + "lon": 6.55194, + "name": "Neukirchen-Vluyn" + }, + { + "lat": 51.1221, + "lon": 13.11027, + "name": "Döbeln" + }, + { + "lat": 53.47095, + "lon": 8.64584, + "name": "Loxstedt" + }, + { + "lat": 49.40133, + "lon": 7.16424, + "name": "Ottweiler" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + } + ], + "question": "Which location is the geographic outlier among: Neukirchen-Vluyn, Döbeln, Loxstedt, Ottweiler, Gosnells?", + "ground_truth": { + "answer": "Gosnells", + "outlier_distance_km": 11617.5, + "second_furthest_km": 2690.9, + "clarity_ratio": 4.32, + "median_distance_km": 2660.6, + "distances_to_centroid": { + "Neukirchen-Vluyn": 2660.6, + "Döbeln": 2291.3, + "Loxstedt": 2690.9, + "Ottweiler": 2498.0, + "Gosnells": 11617.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Neukirchen-Vluyn: (51.45°, 6.55°)", + " Döbeln: (51.12°, 13.11°)", + " Loxstedt: (53.47°, 8.65°)", + " Ottweiler: (49.40°, 7.16°)", + " Gosnells: (-32.08°, 116.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gosnells: 11617.5 km from centroid", + " Loxstedt: 2690.9 km from centroid", + " Neukirchen-Vluyn: 2660.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gosnells", + "FINAL ANSWER: Gosnells" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.9355, + "lon": -97.96125, + "name": "Zacatlán" + }, + { + "lat": 43.57036, + "lon": -70.38783, + "name": "West Scarborough" + }, + { + "lat": 32.45821, + "lon": -83.73157, + "name": "Perry" + }, + { + "lat": 32.68589, + "lon": -117.18309, + "name": "Coronado" + }, + { + "lat": 0.17124, + "lon": 34.59466, + "name": "Khwisero" + } + ], + "question": "Which location is the geographic outlier among: Zacatlán, West Scarborough, Perry, Coronado, Khwisero?", + "ground_truth": { + "answer": "Khwisero", + "outlier_distance_km": 11152.1, + "second_furthest_km": 4891.8, + "clarity_ratio": 2.28, + "median_distance_km": 3236.8, + "distances_to_centroid": { + "Zacatlán": 3236.8, + "West Scarborough": 2004.5, + "Perry": 1790.7, + "Coronado": 4891.8, + "Khwisero": 11152.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zacatlán: (19.94°, -97.96°)", + " West Scarborough: (43.57°, -70.39°)", + " Perry: (32.46°, -83.73°)", + " Coronado: (32.69°, -117.18°)", + " Khwisero: (0.17°, 34.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Khwisero: 11152.1 km from centroid", + " Coronado: 4891.8 km from centroid", + " Zacatlán: 3236.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Khwisero", + "FINAL ANSWER: Khwisero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.69993, + "lon": 2.84565, + "name": "Lloret de Mar" + }, + { + "lat": 51.12637, + "lon": 15.91979, + "name": "Złotoryja" + }, + { + "lat": 41.11758, + "lon": 16.48421, + "name": "Ruvo di Puglia" + }, + { + "lat": 54.33424, + "lon": 18.19735, + "name": "Kartuzy" + }, + { + "lat": 6.75, + "lon": 38.41667, + "name": "Yirga ‘Alem" + } + ], + "question": "Which location is the geographic outlier among: Lloret de Mar, Złotoryja, Ruvo di Puglia, Kartuzy, Yirga ‘Alem?", + "ground_truth": { + "answer": "Yirga ‘Alem", + "outlier_distance_km": 4111.1, + "second_furthest_km": 1704.5, + "clarity_ratio": 2.41, + "median_distance_km": 1361.3, + "distances_to_centroid": { + "Lloret de Mar": 1347.4, + "Złotoryja": 1361.3, + "Ruvo di Puglia": 284.6, + "Kartuzy": 1704.5, + "Yirga ‘Alem": 4111.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lloret de Mar: (41.70°, 2.85°)", + " Złotoryja: (51.13°, 15.92°)", + " Ruvo di Puglia: (41.12°, 16.48°)", + " Kartuzy: (54.33°, 18.20°)", + " Yirga ‘Alem: (6.75°, 38.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yirga ‘Alem: 4111.1 km from centroid", + " Kartuzy: 1704.5 km from centroid", + " Złotoryja: 1361.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yirga ‘Alem", + "FINAL ANSWER: Yirga ‘Alem" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.23806, + "lon": -51.07833, + "name": "Porto União" + }, + { + "lat": 4.43139, + "lon": -61.14639, + "name": "Pacaraima" + }, + { + "lat": -7.94083, + "lon": -34.87306, + "name": "Paulista" + }, + { + "lat": -14.63126, + "lon": -69.44638, + "name": "La Rinconada" + }, + { + "lat": 1.72837, + "lon": 128.00948, + "name": "Tobelo" + } + ], + "question": "Which location is the geographic outlier among: Porto União, Pacaraima, Paulista, La Rinconada, Tobelo?", + "ground_truth": { + "answer": "Tobelo", + "outlier_distance_km": 16146.3, + "second_furthest_km": 5665.4, + "clarity_ratio": 2.85, + "median_distance_km": 5027.6, + "distances_to_centroid": { + "Porto União": 4031.7, + "Pacaraima": 5027.6, + "Paulista": 1890.1, + "La Rinconada": 5665.4, + "Tobelo": 16146.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Porto União: (-26.24°, -51.08°)", + " Pacaraima: (4.43°, -61.15°)", + " Paulista: (-7.94°, -34.87°)", + " La Rinconada: (-14.63°, -69.45°)", + " Tobelo: (1.73°, 128.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tobelo: 16146.3 km from centroid", + " La Rinconada: 5665.4 km from centroid", + " Pacaraima: 5027.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tobelo", + "FINAL ANSWER: Tobelo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 23.83605, + "lon": 91.27939, + "name": "Agartala" + }, + { + "lat": 27.7, + "lon": 74.46667, + "name": "Sūjāngarh" + }, + { + "lat": 15.80202, + "lon": 74.48012, + "name": "Piranvādi" + }, + { + "lat": 13.66744, + "lon": 100.64206, + "name": "Bang Na" + }, + { + "lat": -18.16583, + "lon": -47.94639, + "name": "Catalão" + } + ], + "question": "Which location is the geographic outlier among: Agartala, Sūjāngarh, Piranvādi, Bang Na, Catalão?", + "ground_truth": { + "answer": "Catalão", + "outlier_distance_km": 12161.7, + "second_furthest_km": 4550.6, + "clarity_ratio": 2.67, + "median_distance_km": 3662.4, + "distances_to_centroid": { + "Agartala": 3662.4, + "Sūjāngarh": 2357.1, + "Piranvādi": 1750.4, + "Bang Na": 4550.6, + "Catalão": 12161.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Agartala: (23.84°, 91.28°)", + " Sūjāngarh: (27.70°, 74.47°)", + " Piranvādi: (15.80°, 74.48°)", + " Bang Na: (13.67°, 100.64°)", + " Catalão: (-18.17°, -47.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Catalão: 12161.7 km from centroid", + " Bang Na: 4550.6 km from centroid", + " Agartala: 3662.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Catalão", + "FINAL ANSWER: Catalão" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": 38.44957, + "lon": -78.86892, + "name": "Harrisonburg" + } + ], + "question": "Which location is the geographic outlier among: Coorparoo, Saint Albans, Hastings, Epping, Harrisonburg?", + "ground_truth": { + "answer": "Harrisonburg", + "outlier_distance_km": 17941.0, + "second_furthest_km": 6756.4, + "clarity_ratio": 2.66, + "median_distance_km": 4589.7, + "distances_to_centroid": { + "Coorparoo": 4589.7, + "Saint Albans": 3984.3, + "Hastings": 6756.4, + "Epping": 4001.0, + "Harrisonburg": 17941.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coorparoo: (-27.49°, 153.06°)", + " Saint Albans: (-37.73°, 144.80°)", + " Hastings: (-39.64°, 176.85°)", + " Epping: (-37.65°, 145.03°)", + " Harrisonburg: (38.45°, -78.87°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Harrisonburg: 17941.0 km from centroid", + " Hastings: 6756.4 km from centroid", + " Coorparoo: 4589.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Harrisonburg", + "FINAL ANSWER: Harrisonburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.43332, + "lon": -99.19919, + "name": "Polanco" + }, + { + "lat": 43.97478, + "lon": -75.91076, + "name": "Watertown" + }, + { + "lat": 40.79593, + "lon": -74.31487, + "name": "Livingston" + }, + { + "lat": 19.70186, + "lon": -99.14485, + "name": "Melchor Ocampo" + }, + { + "lat": 30.53766, + "lon": 31.67875, + "name": "Abū Ḩammād" + } + ], + "question": "Which location is the geographic outlier among: Polanco, Watertown, Livingston, Melchor Ocampo, Abū Ḩammād?", + "ground_truth": { + "answer": "Abū Ḩammād", + "outlier_distance_km": 8752.7, + "second_furthest_km": 3803.7, + "clarity_ratio": 2.3, + "median_distance_km": 3785.3, + "distances_to_centroid": { + "Polanco": 3803.7, + "Watertown": 1823.6, + "Livingston": 1475.9, + "Melchor Ocampo": 3785.3, + "Abū Ḩammād": 8752.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Polanco: (19.43°, -99.20°)", + " Watertown: (43.97°, -75.91°)", + " Livingston: (40.80°, -74.31°)", + " Melchor Ocampo: (19.70°, -99.14°)", + " Abū Ḩammād: (30.54°, 31.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Abū Ḩammād: 8752.7 km from centroid", + " Polanco: 3803.7 km from centroid", + " Melchor Ocampo: 3785.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Abū Ḩammād", + "FINAL ANSWER: Abū Ḩammād" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + { + "lat": -9.16972, + "lon": -36.67972, + "name": "Bom Conselho" + } + ], + "question": "Which location is the geographic outlier among: Upper Coomera, Maroubra, Mackay, Corio, Bom Conselho?", + "ground_truth": { + "answer": "Bom Conselho", + "outlier_distance_km": 14858.6, + "second_furthest_km": 4050.5, + "clarity_ratio": 3.67, + "median_distance_km": 3828.9, + "distances_to_centroid": { + "Upper Coomera": 4050.5, + "Maroubra": 3828.9, + "Mackay": 3785.4, + "Corio": 3286.6, + "Bom Conselho": 14858.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Upper Coomera: (-27.88°, 153.29°)", + " Maroubra: (-33.95°, 151.23°)", + " Mackay: (-21.15°, 149.17°)", + " Corio: (-38.08°, 144.38°)", + " Bom Conselho: (-9.17°, -36.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bom Conselho: 14858.6 km from centroid", + " Upper Coomera: 4050.5 km from centroid", + " Maroubra: 3828.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bom Conselho", + "FINAL ANSWER: Bom Conselho" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.80463, + "lon": 13.53292, + "name": "Monfalcone" + }, + { + "lat": 53.86893, + "lon": 10.68729, + "name": "Lübeck" + }, + { + "lat": 51.66931, + "lon": -4.04163, + "name": "Gorseinon" + }, + { + "lat": 62.26537, + "lon": 74.47906, + "name": "Kogalym" + }, + { + "lat": -8.44869, + "lon": 115.60621, + "name": "Amlapura city" + } + ], + "question": "Which location is the geographic outlier among: Monfalcone, Lübeck, Gorseinon, Kogalym, Amlapura city?", + "ground_truth": { + "answer": "Amlapura city", + "outlier_distance_km": 9274.5, + "second_furthest_km": 3660.8, + "clarity_ratio": 2.53, + "median_distance_km": 3188.2, + "distances_to_centroid": { + "Monfalcone": 2350.3, + "Lübeck": 2723.6, + "Gorseinon": 3660.8, + "Kogalym": 3188.2, + "Amlapura city": 9274.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Monfalcone: (45.80°, 13.53°)", + " Lübeck: (53.87°, 10.69°)", + " Gorseinon: (51.67°, -4.04°)", + " Kogalym: (62.27°, 74.48°)", + " Amlapura city: (-8.45°, 115.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amlapura city: 9274.5 km from centroid", + " Gorseinon: 3660.8 km from centroid", + " Kogalym: 3188.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amlapura city", + "FINAL ANSWER: Amlapura city" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.89611, + "lon": -51.37944, + "name": "Andradina" + }, + { + "lat": -29.58028, + "lon": -51.08528, + "name": "Dois Irmãos" + }, + { + "lat": -1.9175, + "lon": -55.51806, + "name": "Óbidos" + }, + { + "lat": -22.42556, + "lon": -45.45278, + "name": "Itajubá" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + } + ], + "question": "Which location is the geographic outlier among: Andradina, Dois Irmãos, Óbidos, Itajubá, Granville?", + "ground_truth": { + "answer": "Granville", + "outlier_distance_km": 13532.3, + "second_furthest_km": 5342.8, + "clarity_ratio": 2.53, + "median_distance_km": 4224.7, + "distances_to_centroid": { + "Andradina": 4224.7, + "Dois Irmãos": 4140.3, + "Óbidos": 5342.8, + "Itajubá": 3595.7, + "Granville": 13532.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Andradina: (-20.90°, -51.38°)", + " Dois Irmãos: (-29.58°, -51.09°)", + " Óbidos: (-1.92°, -55.52°)", + " Itajubá: (-22.43°, -45.45°)", + " Granville: (-33.84°, 151.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Granville: 13532.3 km from centroid", + " Óbidos: 5342.8 km from centroid", + " Andradina: 4224.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Granville", + "FINAL ANSWER: Granville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.82346, + "lon": 150.94607, + "name": "Greystanes" + }, + { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -2.12583, + "lon": -45.88528, + "name": "Governador Nunes Freire" + } + ], + "question": "Which location is the geographic outlier among: Greystanes, Redbank Plains, Sunnybank Hills, Caulfield North, Governador Nunes Freire?", + "ground_truth": { + "answer": "Governador Nunes Freire", + "outlier_distance_km": 16049.3, + "second_furthest_km": 4142.3, + "clarity_ratio": 3.87, + "median_distance_km": 4122.8, + "distances_to_centroid": { + "Greystanes": 3911.1, + "Redbank Plains": 4122.8, + "Sunnybank Hills": 4142.3, + "Caulfield North": 3440.9, + "Governador Nunes Freire": 16049.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Greystanes: (-33.82°, 150.95°)", + " Redbank Plains: (-27.65°, 152.86°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Caulfield North: (-37.87°, 145.02°)", + " Governador Nunes Freire: (-2.13°, -45.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Governador Nunes Freire: 16049.3 km from centroid", + " Sunnybank Hills: 4142.3 km from centroid", + " Redbank Plains: 4122.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Governador Nunes Freire", + "FINAL ANSWER: Governador Nunes Freire" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.43573, + "lon": -75.20289, + "name": "Ibagué" + }, + { + "lat": -33.22795, + "lon": -60.32994, + "name": "Villa Constitución" + }, + { + "lat": -18.08639, + "lon": -39.55083, + "name": "Mucuri" + }, + { + "lat": -12.28389, + "lon": -40.49389, + "name": "Ruy Barbosa" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + } + ], + "question": "Which location is the geographic outlier among: Ibagué, Villa Constitución, Mucuri, Ruy Barbosa, Armidale?", + "ground_truth": { + "answer": "Armidale", + "outlier_distance_km": 14378.2, + "second_furthest_km": 7278.6, + "clarity_ratio": 1.98, + "median_distance_km": 5014.6, + "distances_to_centroid": { + "Ibagué": 7278.6, + "Villa Constitución": 5014.6, + "Mucuri": 2828.2, + "Ruy Barbosa": 3037.0, + "Armidale": 14378.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ibagué: (4.44°, -75.20°)", + " Villa Constitución: (-33.23°, -60.33°)", + " Mucuri: (-18.09°, -39.55°)", + " Ruy Barbosa: (-12.28°, -40.49°)", + " Armidale: (-30.50°, 151.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Armidale: 14378.2 km from centroid", + " Ibagué: 7278.6 km from centroid", + " Villa Constitución: 5014.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Armidale", + "FINAL ANSWER: Armidale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.77644, + "lon": 2.29026, + "name": "Sceaux" + }, + { + "lat": 55.13333, + "lon": -6.66667, + "name": "Coleraine" + }, + { + "lat": 52.51108, + "lon": 4.67165, + "name": "Heemskerk" + }, + { + "lat": 51.57835, + "lon": -0.33208, + "name": "Harrow" + }, + { + "lat": -15.8981, + "lon": -48.04671, + "name": "Riacho Fundo II" + } + ], + "question": "Which location is the geographic outlier among: Sceaux, Coleraine, Heemskerk, Harrow, Riacho Fundo II?", + "ground_truth": { + "answer": "Riacho Fundo II", + "outlier_distance_km": 7245.7, + "second_furthest_km": 1915.1, + "clarity_ratio": 3.78, + "median_distance_km": 1871.5, + "distances_to_centroid": { + "Sceaux": 1494.8, + "Coleraine": 1871.5, + "Heemskerk": 1915.1, + "Harrow": 1632.1, + "Riacho Fundo II": 7245.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sceaux: (48.78°, 2.29°)", + " Coleraine: (55.13°, -6.67°)", + " Heemskerk: (52.51°, 4.67°)", + " Harrow: (51.58°, -0.33°)", + " Riacho Fundo II: (-15.90°, -48.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Riacho Fundo II: 7245.7 km from centroid", + " Heemskerk: 1915.1 km from centroid", + " Coleraine: 1871.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Riacho Fundo II", + "FINAL ANSWER: Riacho Fundo II" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.96215, + "lon": -122.34553, + "name": "San Pablo" + }, + { + "lat": 32.95949, + "lon": -117.11531, + "name": "Rancho Penasquitos" + }, + { + "lat": 41.65394, + "lon": -81.45039, + "name": "Eastlake" + }, + { + "lat": 40.57733, + "lon": -74.2282, + "name": "Carteret" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + } + ], + "question": "Which location is the geographic outlier among: San Pablo, Rancho Penasquitos, Eastlake, Carteret, Bendigo?", + "ground_truth": { + "answer": "Bendigo", + "outlier_distance_km": 17975.0, + "second_furthest_km": 6927.6, + "clarity_ratio": 2.59, + "median_distance_km": 6546.9, + "distances_to_centroid": { + "San Pablo": 6927.6, + "Rancho Penasquitos": 6546.9, + "Eastlake": 3543.7, + "Carteret": 2957.6, + "Bendigo": 17975.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Pablo: (37.96°, -122.35°)", + " Rancho Penasquitos: (32.96°, -117.12°)", + " Eastlake: (41.65°, -81.45°)", + " Carteret: (40.58°, -74.23°)", + " Bendigo: (-36.76°, 144.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bendigo: 17975.0 km from centroid", + " San Pablo: 6927.6 km from centroid", + " Rancho Penasquitos: 6546.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bendigo", + "FINAL ANSWER: Bendigo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.5422, + "lon": -5.0826, + "name": "Écija" + }, + { + "lat": 45.52081, + "lon": 9.7544, + "name": "Romano di Lombardia" + }, + { + "lat": 48.52961, + "lon": 12.16179, + "name": "Landshut" + }, + { + "lat": 54.51889, + "lon": 18.53188, + "name": "Gdynia" + }, + { + "lat": 33.6835, + "lon": -78.99837, + "name": "Socastee" + } + ], + "question": "Which location is the geographic outlier among: Écija, Romano di Lombardia, Landshut, Gdynia, Socastee?", + "ground_truth": { + "answer": "Socastee", + "outlier_distance_km": 6009.4, + "second_furthest_km": 2279.6, + "clarity_ratio": 2.64, + "median_distance_km": 1678.6, + "distances_to_centroid": { + "Écija": 776.5, + "Romano di Lombardia": 1466.7, + "Landshut": 1678.6, + "Gdynia": 2279.6, + "Socastee": 6009.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Écija: (37.54°, -5.08°)", + " Romano di Lombardia: (45.52°, 9.75°)", + " Landshut: (48.53°, 12.16°)", + " Gdynia: (54.52°, 18.53°)", + " Socastee: (33.68°, -79.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Socastee: 6009.4 km from centroid", + " Gdynia: 2279.6 km from centroid", + " Landshut: 1678.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Socastee", + "FINAL ANSWER: Socastee" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75, + "lon": 144.96667, + "name": "Coburg" + }, + { + "lat": -41.28664, + "lon": 174.77557, + "name": "Wellington" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -0.5, + "lon": 34.4, + "name": "Awendo" + } + ], + "question": "Which location is the geographic outlier among: Coburg, Wellington, Lidcombe, Whangarei, Awendo?", + "ground_truth": { + "answer": "Awendo", + "outlier_distance_km": 11087.0, + "second_furthest_km": 3704.2, + "clarity_ratio": 2.99, + "median_distance_km": 3628.1, + "distances_to_centroid": { + "Coburg": 1214.5, + "Wellington": 3704.2, + "Lidcombe": 1497.1, + "Whangarei": 3628.1, + "Awendo": 11087.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coburg: (-37.75°, 144.97°)", + " Wellington: (-41.29°, 174.78°)", + " Lidcombe: (-33.86°, 151.04°)", + " Whangarei: (-35.73°, 174.32°)", + " Awendo: (-0.50°, 34.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Awendo: 11087.0 km from centroid", + " Wellington: 3704.2 km from centroid", + " Whangarei: 3628.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Awendo", + "FINAL ANSWER: Awendo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + }, + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + }, + { + "lat": -14.28361, + "lon": -39.84278, + "name": "Itagibá" + } + ], + "question": "Which location is the geographic outlier among: Frankston South, Highton, Te Atatu Peninsula, Merrylands, Itagibá?", + "ground_truth": { + "answer": "Itagibá", + "outlier_distance_km": 14190.3, + "second_furthest_km": 5394.3, + "clarity_ratio": 2.63, + "median_distance_km": 3337.0, + "distances_to_centroid": { + "Frankston South": 2798.0, + "Highton": 2726.2, + "Te Atatu Peninsula": 5394.3, + "Merrylands": 3337.0, + "Itagibá": 14190.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frankston South: (-38.17°, 145.14°)", + " Highton: (-38.17°, 144.31°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + " Merrylands: (-33.83°, 150.98°)", + " Itagibá: (-14.28°, -39.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itagibá: 14190.3 km from centroid", + " Te Atatu Peninsula: 5394.3 km from centroid", + " Merrylands: 3337.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itagibá", + "FINAL ANSWER: Itagibá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.55083, + "lon": -0.51875, + "name": "Salaga" + }, + { + "lat": 25.99845, + "lon": 32.81808, + "name": "Qifţ" + }, + { + "lat": 8.74921, + "lon": 4.13113, + "name": "Igbeti" + }, + { + "lat": -30.29831, + "lon": 29.93772, + "name": "Clydesdale" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + } + ], + "question": "Which location is the geographic outlier among: Salaga, Qifţ, Igbeti, Clydesdale, Port Macquarie?", + "ground_truth": { + "answer": "Port Macquarie", + "outlier_distance_km": 11580.9, + "second_furthest_km": 5104.7, + "clarity_ratio": 2.27, + "median_distance_km": 4615.8, + "distances_to_centroid": { + "Salaga": 5104.7, + "Qifţ": 3508.3, + "Igbeti": 4615.8, + "Clydesdale": 3300.8, + "Port Macquarie": 11580.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Salaga: (8.55°, -0.52°)", + " Qifţ: (26.00°, 32.82°)", + " Igbeti: (8.75°, 4.13°)", + " Clydesdale: (-30.30°, 29.94°)", + " Port Macquarie: (-31.43°, 152.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Macquarie: 11580.9 km from centroid", + " Salaga: 5104.7 km from centroid", + " Igbeti: 4615.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Macquarie", + "FINAL ANSWER: Port Macquarie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -43.58333, + "lon": 172.38333, + "name": "Rolleston" + }, + { + "lat": -37.0393, + "lon": 174.92815, + "name": "Takanini" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": 43.56775, + "lon": 3.90279, + "name": "Lattes" + } + ], + "question": "Which location is the geographic outlier among: Dandenong North, Rolleston, Takanini, Melbourne, Lattes?", + "ground_truth": { + "answer": "Lattes", + "outlier_distance_km": 14450.9, + "second_furthest_km": 4727.1, + "clarity_ratio": 3.06, + "median_distance_km": 4653.6, + "distances_to_centroid": { + "Dandenong North": 2353.5, + "Rolleston": 4653.6, + "Takanini": 4727.1, + "Melbourne": 2326.1, + "Lattes": 14450.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dandenong North: (-37.97°, 145.21°)", + " Rolleston: (-43.58°, 172.38°)", + " Takanini: (-37.04°, 174.93°)", + " Melbourne: (-37.81°, 144.96°)", + " Lattes: (43.57°, 3.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lattes: 14450.9 km from centroid", + " Takanini: 4727.1 km from centroid", + " Rolleston: 4653.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lattes", + "FINAL ANSWER: Lattes" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.11139, + "lon": -37.12306, + "name": "Águas Belas" + }, + { + "lat": -17.28556, + "lon": -42.73, + "name": "Turmalina" + }, + { + "lat": -38.37694, + "lon": -60.27563, + "name": "Tres Arroyos" + }, + { + "lat": -14.77139, + "lon": -42.655, + "name": "Urandi" + }, + { + "lat": -38.04369, + "lon": 145.2923, + "name": "Narre Warren South" + } + ], + "question": "Which location is the geographic outlier among: Águas Belas, Turmalina, Tres Arroyos, Urandi, Narre Warren South?", + "ground_truth": { + "answer": "Narre Warren South", + "outlier_distance_km": 12603.7, + "second_furthest_km": 5221.3, + "clarity_ratio": 2.41, + "median_distance_km": 3808.0, + "distances_to_centroid": { + "Águas Belas": 3532.2, + "Turmalina": 3727.0, + "Tres Arroyos": 5221.3, + "Urandi": 3808.0, + "Narre Warren South": 12603.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Águas Belas: (-9.11°, -37.12°)", + " Turmalina: (-17.29°, -42.73°)", + " Tres Arroyos: (-38.38°, -60.28°)", + " Urandi: (-14.77°, -42.66°)", + " Narre Warren South: (-38.04°, 145.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Narre Warren South: 12603.7 km from centroid", + " Tres Arroyos: 5221.3 km from centroid", + " Urandi: 3808.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Narre Warren South", + "FINAL ANSWER: Narre Warren South" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + { + "lat": -38.02388, + "lon": 144.40617, + "name": "Lara" + }, + { + "lat": -37.70988, + "lon": 144.75483, + "name": "Taylors Hill" + }, + { + "lat": -27.24179, + "lon": 27.57422, + "name": "Koppies" + } + ], + "question": "Which location is the geographic outlier among: Kingsford, Mernda, Lara, Taylors Hill, Koppies?", + "ground_truth": { + "answer": "Koppies", + "outlier_distance_km": 8738.5, + "second_furthest_km": 2618.4, + "clarity_ratio": 3.34, + "median_distance_km": 2033.4, + "distances_to_centroid": { + "Kingsford": 2618.4, + "Mernda": 2033.4, + "Lara": 1975.0, + "Taylors Hill": 2003.9, + "Koppies": 8738.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kingsford: (-33.92°, 151.23°)", + " Mernda: (-37.60°, 145.10°)", + " Lara: (-38.02°, 144.41°)", + " Taylors Hill: (-37.71°, 144.75°)", + " Koppies: (-27.24°, 27.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Koppies: 8738.5 km from centroid", + " Kingsford: 2618.4 km from centroid", + " Mernda: 2033.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Koppies", + "FINAL ANSWER: Koppies" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.32, + "lon": -36.57944, + "name": "Neópolis" + }, + { + "lat": -23.44077, + "lon": -46.73774, + "name": "Jaraguá" + }, + { + "lat": -27.21787, + "lon": -61.18738, + "name": "Charata" + }, + { + "lat": -6.96333, + "lon": -35.69167, + "name": "Areia" + }, + { + "lat": 14.40076, + "lon": 37.93399, + "name": "Sheraro" + } + ], + "question": "Which location is the geographic outlier among: Neópolis, Jaraguá, Charata, Areia, Sheraro?", + "ground_truth": { + "answer": "Sheraro", + "outlier_distance_km": 7831.1, + "second_furthest_km": 3882.4, + "clarity_ratio": 2.02, + "median_distance_km": 2399.9, + "distances_to_centroid": { + "Neópolis": 889.5, + "Jaraguá": 2399.9, + "Charata": 3882.4, + "Areia": 897.7, + "Sheraro": 7831.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Neópolis: (-10.32°, -36.58°)", + " Jaraguá: (-23.44°, -46.74°)", + " Charata: (-27.22°, -61.19°)", + " Areia: (-6.96°, -35.69°)", + " Sheraro: (14.40°, 37.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sheraro: 7831.1 km from centroid", + " Charata: 3882.4 km from centroid", + " Jaraguá: 2399.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sheraro", + "FINAL ANSWER: Sheraro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.71464, + "lon": -49.53152, + "name": "São Sebastião da Boa Vista" + }, + { + "lat": -28.57617, + "lon": -70.75938, + "name": "Vallenar" + }, + { + "lat": -21.41972, + "lon": -50.0775, + "name": "Penápolis" + }, + { + "lat": -8.90167, + "lon": -37.82389, + "name": "Inajá" + }, + { + "lat": 41.47309, + "lon": -87.06114, + "name": "Valparaiso" + } + ], + "question": "Which location is the geographic outlier among: São Sebastião da Boa Vista, Vallenar, Penápolis, Inajá, Valparaiso?", + "ground_truth": { + "answer": "Valparaiso", + "outlier_distance_km": 5780.9, + "second_furthest_km": 3017.4, + "clarity_ratio": 1.92, + "median_distance_km": 2411.7, + "distances_to_centroid": { + "São Sebastião da Boa Vista": 1083.0, + "Vallenar": 3017.4, + "Penápolis": 2183.1, + "Inajá": 2411.7, + "Valparaiso": 5780.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Sebastião da Boa Vista: (-1.71°, -49.53°)", + " Vallenar: (-28.58°, -70.76°)", + " Penápolis: (-21.42°, -50.08°)", + " Inajá: (-8.90°, -37.82°)", + " Valparaiso: (41.47°, -87.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Valparaiso: 5780.9 km from centroid", + " Vallenar: 3017.4 km from centroid", + " Inajá: 2411.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Valparaiso", + "FINAL ANSWER: Valparaiso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.6, + "lon": 145.15, + "name": "Doreen" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": 53.55, + "lon": 9.93333, + "name": "Altona" + } + ], + "question": "Which location is the geographic outlier among: Doreen, Camberwell, Doncaster East, Townsville, Altona?", + "ground_truth": { + "answer": "Altona", + "outlier_distance_km": 12630.4, + "second_furthest_km": 3583.5, + "clarity_ratio": 3.52, + "median_distance_km": 3581.4, + "distances_to_centroid": { + "Doreen": 3571.4, + "Camberwell": 3581.4, + "Doncaster East": 3583.5, + "Townsville": 3030.9, + "Altona": 12630.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doreen: (-37.60°, 145.15°)", + " Camberwell: (-37.84°, 145.07°)", + " Doncaster East: (-37.79°, 145.15°)", + " Townsville: (-19.27°, 146.81°)", + " Altona: (53.55°, 9.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Altona: 12630.4 km from centroid", + " Doncaster East: 3583.5 km from centroid", + " Camberwell: 3581.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Altona", + "FINAL ANSWER: Altona" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.00166, + "lon": 13.6488, + "name": "Freital" + }, + { + "lat": 48.98994, + "lon": 2.1699, + "name": "Herblay-sur-Seine" + }, + { + "lat": 50.95753, + "lon": 6.93611, + "name": "Neuehrenfeld" + }, + { + "lat": 55.58183, + "lon": 38.91994, + "name": "Kurovskoye" + }, + { + "lat": 28.91154, + "lon": 79.52009, + "name": "Kichha" + } + ], + "question": "Which location is the geographic outlier among: Freital, Herblay-sur-Seine, Neuehrenfeld, Kurovskoye, Kichha?", + "ground_truth": { + "answer": "Kichha", + "outlier_distance_km": 4822.9, + "second_furthest_km": 1940.0, + "clarity_ratio": 2.49, + "median_distance_km": 1605.5, + "distances_to_centroid": { + "Freital": 1146.5, + "Herblay-sur-Seine": 1940.0, + "Neuehrenfeld": 1605.5, + "Kurovskoye": 1198.2, + "Kichha": 4822.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Freital: (51.00°, 13.65°)", + " Herblay-sur-Seine: (48.99°, 2.17°)", + " Neuehrenfeld: (50.96°, 6.94°)", + " Kurovskoye: (55.58°, 38.92°)", + " Kichha: (28.91°, 79.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kichha: 4822.9 km from centroid", + " Herblay-sur-Seine: 1940.0 km from centroid", + " Neuehrenfeld: 1605.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kichha", + "FINAL ANSWER: Kichha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.9482, + "lon": 174.87019, + "name": "Otara" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -38.04369, + "lon": 145.2923, + "name": "Narre Warren South" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": 25.75871, + "lon": -80.39839, + "name": "Tamiami" + } + ], + "question": "Which location is the geographic outlier among: Otara, Wheelers Hill, Narre Warren South, Maryborough, Tamiami?", + "ground_truth": { + "answer": "Tamiami", + "outlier_distance_km": 19134.6, + "second_furthest_km": 6562.6, + "clarity_ratio": 2.92, + "median_distance_km": 4578.1, + "distances_to_centroid": { + "Otara": 6562.6, + "Wheelers Hill": 3965.6, + "Narre Warren South": 3978.8, + "Maryborough": 4578.1, + "Tamiami": 19134.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Otara: (-36.95°, 174.87°)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Narre Warren South: (-38.04°, 145.29°)", + " Maryborough: (-25.54°, 152.70°)", + " Tamiami: (25.76°, -80.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tamiami: 19134.6 km from centroid", + " Otara: 6562.6 km from centroid", + " Maryborough: 4578.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tamiami", + "FINAL ANSWER: Tamiami" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + { + "lat": -33.9681, + "lon": 151.13564, + "name": "Kogarah" + }, + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + }, + { + "lat": 56.03715, + "lon": 93.12684, + "name": "Berëzovka" + } + ], + "question": "Which location is the geographic outlier among: Frankston South, Lalor, Kogarah, Surfers Paradise, Berëzovka?", + "ground_truth": { + "answer": "Berëzovka", + "outlier_distance_km": 9053.5, + "second_furthest_km": 2535.7, + "clarity_ratio": 3.57, + "median_distance_km": 2479.8, + "distances_to_centroid": { + "Frankston South": 2535.7, + "Lalor": 2479.8, + "Kogarah": 2382.1, + "Surfers Paradise": 2080.6, + "Berëzovka": 9053.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frankston South: (-38.17°, 145.14°)", + " Lalor: (-37.67°, 145.02°)", + " Kogarah: (-33.97°, 151.14°)", + " Surfers Paradise: (-28.00°, 153.43°)", + " Berëzovka: (56.04°, 93.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Berëzovka: 9053.5 km from centroid", + " Frankston South: 2535.7 km from centroid", + " Lalor: 2479.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Berëzovka", + "FINAL ANSWER: Berëzovka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.48543, + "lon": 105.7629, + "name": "Shuanglu" + }, + { + "lat": 36.11667, + "lon": 139.6, + "name": "Kazo" + }, + { + "lat": 35.7275, + "lon": 116.49611, + "name": "Wenshang" + }, + { + "lat": 35.98411, + "lon": 140.00929, + "name": "Tsukubamirai" + }, + { + "lat": 51.77655, + "lon": 0.11158, + "name": "Harlow" + } + ], + "question": "Which location is the geographic outlier among: Shuanglu, Kazo, Wenshang, Tsukubamirai, Harlow?", + "ground_truth": { + "answer": "Harlow", + "outlier_distance_km": 7424.4, + "second_furthest_km": 3501.9, + "clarity_ratio": 2.12, + "median_distance_km": 3462.5, + "distances_to_centroid": { + "Shuanglu": 1050.8, + "Kazo": 3462.5, + "Wenshang": 1450.9, + "Tsukubamirai": 3501.9, + "Harlow": 7424.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shuanglu: (29.49°, 105.76°)", + " Kazo: (36.12°, 139.60°)", + " Wenshang: (35.73°, 116.50°)", + " Tsukubamirai: (35.98°, 140.01°)", + " Harlow: (51.78°, 0.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Harlow: 7424.4 km from centroid", + " Tsukubamirai: 3501.9 km from centroid", + " Kazo: 3462.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Harlow", + "FINAL ANSWER: Harlow" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -30.30225, + "lon": 27.08395, + "name": "Zastron" + }, + { + "lat": -28.31971, + "lon": 27.62082, + "name": "Senekal" + }, + { + "lat": -26.39015, + "lon": 30.78742, + "name": "Fernie" + }, + { + "lat": -27.00805, + "lon": 27.3646, + "name": "Vredefort" + }, + { + "lat": 41.03522, + "lon": -111.93855, + "name": "Kaysville" + } + ], + "question": "Which location is the geographic outlier among: Zastron, Senekal, Fernie, Vredefort, Kaysville?", + "ground_truth": { + "answer": "Kaysville", + "outlier_distance_km": 12884.6, + "second_furthest_km": 3455.6, + "clarity_ratio": 3.73, + "median_distance_km": 3282.5, + "distances_to_centroid": { + "Zastron": 3282.5, + "Senekal": 3235.7, + "Fernie": 3455.6, + "Vredefort": 3156.9, + "Kaysville": 12884.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zastron: (-30.30°, 27.08°)", + " Senekal: (-28.32°, 27.62°)", + " Fernie: (-26.39°, 30.79°)", + " Vredefort: (-27.01°, 27.36°)", + " Kaysville: (41.04°, -111.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kaysville: 12884.6 km from centroid", + " Fernie: 3455.6 km from centroid", + " Zastron: 3282.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kaysville", + "FINAL ANSWER: Kaysville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.63417, + "lon": -54.82222, + "name": "Caarapó" + }, + { + "lat": -5.7925, + "lon": -37.55667, + "name": "Caraúbas" + }, + { + "lat": -28.71333, + "lon": -49.3, + "name": "Içara" + }, + { + "lat": -21.61, + "lon": -45.56528, + "name": "Elói Mendes" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + } + ], + "question": "Which location is the geographic outlier among: Caarapó, Caraúbas, Içara, Elói Mendes, Epping?", + "ground_truth": { + "answer": "Epping", + "outlier_distance_km": 12694.3, + "second_furthest_km": 4728.4, + "clarity_ratio": 2.68, + "median_distance_km": 4108.2, + "distances_to_centroid": { + "Caarapó": 4728.4, + "Caraúbas": 3673.6, + "Içara": 4108.2, + "Elói Mendes": 3809.4, + "Epping": 12694.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caarapó: (-22.63°, -54.82°)", + " Caraúbas: (-5.79°, -37.56°)", + " Içara: (-28.71°, -49.30°)", + " Elói Mendes: (-21.61°, -45.57°)", + " Epping: (-37.65°, 145.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Epping: 12694.3 km from centroid", + " Caarapó: 4728.4 km from centroid", + " Içara: 4108.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Epping", + "FINAL ANSWER: Epping" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.94647, + "lon": 136.18498, + "name": "Sabae" + }, + { + "lat": 30.78783, + "lon": 75.47391, + "name": "Jagraon" + }, + { + "lat": 44.7598, + "lon": 129.67826, + "name": "Chaihe" + }, + { + "lat": 1.4484, + "lon": 103.5873, + "name": "Gelang Patah" + }, + { + "lat": 5.65396, + "lon": 0.0264, + "name": "Tema New Town" + } + ], + "question": "Which location is the geographic outlier among: Sabae, Jagraon, Chaihe, Gelang Patah, Tema New Town?", + "ground_truth": { + "answer": "Tema New Town", + "outlier_distance_km": 9649.9, + "second_furthest_km": 4702.2, + "clarity_ratio": 2.05, + "median_distance_km": 4346.4, + "distances_to_centroid": { + "Sabae": 4702.2, + "Jagraon": 1548.3, + "Chaihe": 4346.4, + "Gelang Patah": 2933.4, + "Tema New Town": 9649.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sabae: (35.95°, 136.18°)", + " Jagraon: (30.79°, 75.47°)", + " Chaihe: (44.76°, 129.68°)", + " Gelang Patah: (1.45°, 103.59°)", + " Tema New Town: (5.65°, 0.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tema New Town: 9649.9 km from centroid", + " Sabae: 4702.2 km from centroid", + " Chaihe: 4346.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tema New Town", + "FINAL ANSWER: Tema New Town" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.10809, + "lon": -56.53253, + "name": "Bela Vista" + }, + { + "lat": -3.96333, + "lon": -45.65833, + "name": "Santa Luzia" + }, + { + "lat": -8.62306, + "lon": -37.15583, + "name": "Buíque" + }, + { + "lat": -22.04897, + "lon": -63.69075, + "name": "Profesor Salvador Mazza" + }, + { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + } + ], + "question": "Which location is the geographic outlier among: Bela Vista, Santa Luzia, Buíque, Profesor Salvador Mazza, Granville?", + "ground_truth": { + "answer": "Granville", + "outlier_distance_km": 13911.0, + "second_furthest_km": 5554.8, + "clarity_ratio": 2.5, + "median_distance_km": 4819.1, + "distances_to_centroid": { + "Bela Vista": 4819.1, + "Santa Luzia": 4144.4, + "Buíque": 3075.4, + "Profesor Salvador Mazza": 5554.8, + "Granville": 13911.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bela Vista: (-22.11°, -56.53°)", + " Santa Luzia: (-3.96°, -45.66°)", + " Buíque: (-8.62°, -37.16°)", + " Profesor Salvador Mazza: (-22.05°, -63.69°)", + " Granville: (-33.84°, 151.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Granville: 13911.0 km from centroid", + " Profesor Salvador Mazza: 5554.8 km from centroid", + " Bela Vista: 4819.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Granville", + "FINAL ANSWER: Granville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.49417, + "lon": -48.65556, + "name": "Biguaçu" + }, + { + "lat": -4.25528, + "lon": -43.94056, + "name": "Timbiras" + }, + { + "lat": -22.72306, + "lon": -44.13556, + "name": "Rio Claro" + }, + { + "lat": -5.12056, + "lon": -60.37972, + "name": "Novo Aripuanã" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + } + ], + "question": "Which location is the geographic outlier among: Biguaçu, Timbiras, Rio Claro, Novo Aripuanã, Earlwood?", + "ground_truth": { + "answer": "Earlwood", + "outlier_distance_km": 13803.2, + "second_furthest_km": 5747.1, + "clarity_ratio": 2.4, + "median_distance_km": 4134.1, + "distances_to_centroid": { + "Biguaçu": 4134.1, + "Timbiras": 4100.1, + "Rio Claro": 3653.0, + "Novo Aripuanã": 5747.1, + "Earlwood": 13803.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Biguaçu: (-27.49°, -48.66°)", + " Timbiras: (-4.26°, -43.94°)", + " Rio Claro: (-22.72°, -44.14°)", + " Novo Aripuanã: (-5.12°, -60.38°)", + " Earlwood: (-33.92°, 151.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Earlwood: 13803.2 km from centroid", + " Novo Aripuanã: 5747.1 km from centroid", + " Biguaçu: 4134.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Earlwood", + "FINAL ANSWER: Earlwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.61692, + "lon": 27.99471, + "name": "Ga-Rankuwa" + }, + { + "lat": -33.64651, + "lon": 19.44852, + "name": "Worcester" + }, + { + "lat": 8.3, + "lon": 35.58333, + "name": "Metu" + }, + { + "lat": 14.40076, + "lon": 37.93399, + "name": "Sheraro" + }, + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + } + ], + "question": "Which location is the geographic outlier among: Ga-Rankuwa, Worcester, Metu, Sheraro, Lilydale?", + "ground_truth": { + "answer": "Lilydale", + "outlier_distance_km": 9182.2, + "second_furthest_km": 3985.4, + "clarity_ratio": 2.3, + "median_distance_km": 3664.6, + "distances_to_centroid": { + "Ga-Rankuwa": 2887.3, + "Worcester": 3985.4, + "Metu": 3229.8, + "Sheraro": 3664.6, + "Lilydale": 9182.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ga-Rankuwa: (-25.62°, 27.99°)", + " Worcester: (-33.65°, 19.45°)", + " Metu: (8.30°, 35.58°)", + " Sheraro: (14.40°, 37.93°)", + " Lilydale: (-37.75°, 145.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lilydale: 9182.2 km from centroid", + " Worcester: 3985.4 km from centroid", + " Sheraro: 3664.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lilydale", + "FINAL ANSWER: Lilydale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.55122, + "lon": 6.23589, + "name": "Okene" + }, + { + "lat": 31.24193, + "lon": 30.94504, + "name": "Ar Riyāḑ" + }, + { + "lat": -23.88782, + "lon": 30.28708, + "name": "Nkowakowa" + }, + { + "lat": 29.61972, + "lon": 31.2575, + "name": "Al ‘Ayyāţ" + }, + { + "lat": -37.97695, + "lon": 145.25866, + "name": "Endeavour Hills" + } + ], + "question": "Which location is the geographic outlier among: Okene, Ar Riyāḑ, Nkowakowa, Al ‘Ayyāţ, Endeavour Hills?", + "ground_truth": { + "answer": "Endeavour Hills", + "outlier_distance_km": 10663.3, + "second_furthest_km": 4766.1, + "clarity_ratio": 2.24, + "median_distance_km": 3821.2, + "distances_to_centroid": { + "Okene": 4766.1, + "Ar Riyāḑ": 3821.2, + "Nkowakowa": 3442.2, + "Al ‘Ayyāţ": 3654.0, + "Endeavour Hills": 10663.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Okene: (7.55°, 6.24°)", + " Ar Riyāḑ: (31.24°, 30.95°)", + " Nkowakowa: (-23.89°, 30.29°)", + " Al ‘Ayyāţ: (29.62°, 31.26°)", + " Endeavour Hills: (-37.98°, 145.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Endeavour Hills: 10663.3 km from centroid", + " Okene: 4766.1 km from centroid", + " Ar Riyāḑ: 3821.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Endeavour Hills", + "FINAL ANSWER: Endeavour Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.76672, + "lon": -79.39909, + "name": "Willowdale" + }, + { + "lat": 33.9526, + "lon": -84.54993, + "name": "Marietta" + }, + { + "lat": 49.17917, + "lon": -122.86667, + "name": "Whalley" + }, + { + "lat": 32.68589, + "lon": -117.18309, + "name": "Coronado" + }, + { + "lat": -30.74137, + "lon": 30.45499, + "name": "Port Shepstone" + } + ], + "question": "Which location is the geographic outlier among: Willowdale, Marietta, Whalley, Coronado, Port Shepstone?", + "ground_truth": { + "answer": "Port Shepstone", + "outlier_distance_km": 12802.0, + "second_furthest_km": 4870.9, + "clarity_ratio": 2.63, + "median_distance_km": 4164.9, + "distances_to_centroid": { + "Willowdale": 2045.7, + "Marietta": 1313.5, + "Whalley": 4870.9, + "Coronado": 4164.9, + "Port Shepstone": 12802.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Willowdale: (43.77°, -79.40°)", + " Marietta: (33.95°, -84.55°)", + " Whalley: (49.18°, -122.87°)", + " Coronado: (32.69°, -117.18°)", + " Port Shepstone: (-30.74°, 30.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Shepstone: 12802.0 km from centroid", + " Whalley: 4870.9 km from centroid", + " Coronado: 4164.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Shepstone", + "FINAL ANSWER: Port Shepstone" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.40232, + "lon": -80.74224, + "name": "La Unión" + }, + { + "lat": -33.13044, + "lon": -64.35272, + "name": "Río Cuarto" + }, + { + "lat": -2.99, + "lon": -65.10833, + "name": "Uarini" + }, + { + "lat": -27.49362, + "lon": -64.85972, + "name": "Termas de Río Hondo" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + } + ], + "question": "Which location is the geographic outlier among: La Unión, Río Cuarto, Uarini, Termas de Río Hondo, Sunnybank Hills?", + "ground_truth": { + "answer": "Sunnybank Hills", + "outlier_distance_km": 14788.9, + "second_furthest_km": 6283.1, + "clarity_ratio": 2.35, + "median_distance_km": 4778.8, + "distances_to_centroid": { + "La Unión": 6283.1, + "Río Cuarto": 4239.3, + "Uarini": 4778.8, + "Termas de Río Hondo": 4207.9, + "Sunnybank Hills": 14788.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Unión: (-5.40°, -80.74°)", + " Río Cuarto: (-33.13°, -64.35°)", + " Uarini: (-2.99°, -65.11°)", + " Termas de Río Hondo: (-27.49°, -64.86°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunnybank Hills: 14788.9 km from centroid", + " La Unión: 6283.1 km from centroid", + " Uarini: 4778.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunnybank Hills", + "FINAL ANSWER: Sunnybank Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.25585, + "lon": -69.7863, + "name": "Pozo Almonte" + }, + { + "lat": -19.96778, + "lon": -44.19833, + "name": "Betim" + }, + { + "lat": -10.24111, + "lon": -76.64556, + "name": "Yanacancha" + }, + { + "lat": -1.93556, + "lon": -50.82111, + "name": "Portel" + }, + { + "lat": 45.78095, + "lon": -122.53343, + "name": "Battle Ground" + } + ], + "question": "Which location is the geographic outlier among: Pozo Almonte, Betim, Yanacancha, Portel, Battle Ground?", + "ground_truth": { + "answer": "Battle Ground", + "outlier_distance_km": 7147.0, + "second_furthest_km": 3736.6, + "clarity_ratio": 1.91, + "median_distance_km": 2443.5, + "distances_to_centroid": { + "Pozo Almonte": 2130.4, + "Betim": 3736.6, + "Yanacancha": 1078.9, + "Portel": 2443.5, + "Battle Ground": 7147.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pozo Almonte: (-20.26°, -69.79°)", + " Betim: (-19.97°, -44.20°)", + " Yanacancha: (-10.24°, -76.65°)", + " Portel: (-1.94°, -50.82°)", + " Battle Ground: (45.78°, -122.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Battle Ground: 7147.0 km from centroid", + " Betim: 3736.6 km from centroid", + " Portel: 2443.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Battle Ground", + "FINAL ANSWER: Battle Ground" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.99111, + "lon": -1.53397, + "name": "Wallsend" + }, + { + "lat": 39.89158, + "lon": -5.54064, + "name": "Navalmoral de la Mata" + }, + { + "lat": 40.78931, + "lon": 14.36806, + "name": "Torre del Greco" + }, + { + "lat": 55.71667, + "lon": 37.41667, + "name": "Bol’shaya Setun’" + }, + { + "lat": 8.05627, + "lon": -1.73058, + "name": "Kintampo" + } + ], + "question": "Which location is the geographic outlier among: Wallsend, Navalmoral de la Mata, Torre del Greco, Bol’shaya Setun’, Kintampo?", + "ground_truth": { + "answer": "Kintampo", + "outlier_distance_km": 3685.6, + "second_furthest_km": 2745.9, + "clarity_ratio": 1.34, + "median_distance_km": 1839.6, + "distances_to_centroid": { + "Wallsend": 1839.6, + "Navalmoral de la Mata": 1204.8, + "Torre del Greco": 499.3, + "Bol’shaya Setun’": 2745.9, + "Kintampo": 3685.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wallsend: (54.99°, -1.53°)", + " Navalmoral de la Mata: (39.89°, -5.54°)", + " Torre del Greco: (40.79°, 14.37°)", + " Bol’shaya Setun’: (55.72°, 37.42°)", + " Kintampo: (8.06°, -1.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kintampo: 3685.6 km from centroid", + " Bol’shaya Setun’: 2745.9 km from centroid", + " Wallsend: 1839.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kintampo", + "FINAL ANSWER: Kintampo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.14095, + "lon": 28.15247, + "name": "Edenvale" + }, + { + "lat": -29.81292, + "lon": 30.63646, + "name": "Mpumalanga" + }, + { + "lat": 29.03556, + "lon": 31.11792, + "name": "New Bani Sewif City" + }, + { + "lat": 10.89469, + "lon": -1.09083, + "name": "Navrongo" + }, + { + "lat": 21.28298, + "lon": -89.66416, + "name": "Progreso" + } + ], + "question": "Which location is the geographic outlier among: Edenvale, Mpumalanga, New Bani Sewif City, Navrongo, Progreso?", + "ground_truth": { + "answer": "Progreso", + "outlier_distance_km": 9912.7, + "second_furthest_km": 4738.0, + "clarity_ratio": 2.09, + "median_distance_km": 4546.9, + "distances_to_centroid": { + "Edenvale": 4286.9, + "Mpumalanga": 4738.0, + "New Bani Sewif City": 4546.9, + "Navrongo": 1099.2, + "Progreso": 9912.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Edenvale: (-26.14°, 28.15°)", + " Mpumalanga: (-29.81°, 30.64°)", + " New Bani Sewif City: (29.04°, 31.12°)", + " Navrongo: (10.89°, -1.09°)", + " Progreso: (21.28°, -89.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Progreso: 9912.7 km from centroid", + " Mpumalanga: 4738.0 km from centroid", + " New Bani Sewif City: 4546.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Progreso", + "FINAL ANSWER: Progreso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + { + "lat": -38.03333, + "lon": 145.35, + "name": "Berwick" + }, + { + "lat": -6.85472, + "lon": -35.49, + "name": "Guarabira" + } + ], + "question": "Which location is the geographic outlier among: Whanganui, Dandenong North, Tarneit, Berwick, Guarabira?", + "ground_truth": { + "answer": "Guarabira", + "outlier_distance_km": 14667.8, + "second_furthest_km": 5371.8, + "clarity_ratio": 2.73, + "median_distance_km": 2829.2, + "distances_to_centroid": { + "Whanganui": 5371.8, + "Dandenong North": 2816.3, + "Tarneit": 2767.2, + "Berwick": 2829.2, + "Guarabira": 14667.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Whanganui: (-39.93°, 175.05°)", + " Dandenong North: (-37.97°, 145.21°)", + " Tarneit: (-37.84°, 144.66°)", + " Berwick: (-38.03°, 145.35°)", + " Guarabira: (-6.85°, -35.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guarabira: 14667.8 km from centroid", + " Whanganui: 5371.8 km from centroid", + " Berwick: 2829.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guarabira", + "FINAL ANSWER: Guarabira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.06944, + "lon": -42.475, + "name": "Caetité" + }, + { + "lat": -18.99111, + "lon": -50.54361, + "name": "São Simão" + }, + { + "lat": -15.88231, + "lon": -48.10428, + "name": "Samambaia" + }, + { + "lat": -21.92194, + "lon": -50.73389, + "name": "Bastos" + }, + { + "lat": 42.17476, + "lon": -8.50398, + "name": "Ponteareas" + } + ], + "question": "Which location is the geographic outlier among: Caetité, São Simão, Samambaia, Bastos, Ponteareas?", + "ground_truth": { + "answer": "Ponteareas", + "outlier_distance_km": 6211.9, + "second_furthest_km": 2133.8, + "clarity_ratio": 2.91, + "median_distance_km": 1859.7, + "distances_to_centroid": { + "Caetité": 963.0, + "São Simão": 1859.7, + "Samambaia": 1428.2, + "Bastos": 2133.8, + "Ponteareas": 6211.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caetité: (-14.07°, -42.48°)", + " São Simão: (-18.99°, -50.54°)", + " Samambaia: (-15.88°, -48.10°)", + " Bastos: (-21.92°, -50.73°)", + " Ponteareas: (42.17°, -8.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ponteareas: 6211.9 km from centroid", + " Bastos: 2133.8 km from centroid", + " São Simão: 1859.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ponteareas", + "FINAL ANSWER: Ponteareas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + }, + { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + { + "lat": -37.8, + "lon": 145.28333, + "name": "Croydon" + }, + { + "lat": 37.29111, + "lon": 127.00889, + "name": "Suwon" + } + ], + "question": "Which location is the geographic outlier among: Caulfield North, Te Atatu Peninsula, Palm Beach, Croydon, Suwon?", + "ground_truth": { + "answer": "Suwon", + "outlier_distance_km": 6847.3, + "second_furthest_km": 3056.4, + "clarity_ratio": 2.24, + "median_distance_km": 1952.8, + "distances_to_centroid": { + "Caulfield North": 1952.8, + "Te Atatu Peninsula": 3056.4, + "Palm Beach": 939.3, + "Croydon": 1939.9, + "Suwon": 6847.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caulfield North: (-37.87°, 145.02°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + " Palm Beach: (-28.12°, 153.47°)", + " Croydon: (-37.80°, 145.28°)", + " Suwon: (37.29°, 127.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Suwon: 6847.3 km from centroid", + " Te Atatu Peninsula: 3056.4 km from centroid", + " Caulfield North: 1952.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Suwon", + "FINAL ANSWER: Suwon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.54778, + "lon": -54.58806, + "name": "Foz do Iguaçu" + }, + { + "lat": -16.43389, + "lon": -41.00333, + "name": "Jequitinhonha" + }, + { + "lat": -21.64611, + "lon": -41.74694, + "name": "São Fidélis" + }, + { + "lat": -23.60926, + "lon": -46.62304, + "name": "Bosque Saúde" + }, + { + "lat": -33.90034, + "lon": 151.05563, + "name": "Greenacre" + } + ], + "question": "Which location is the geographic outlier among: Foz do Iguaçu, Jequitinhonha, São Fidélis, Bosque Saúde, Greenacre?", + "ground_truth": { + "answer": "Greenacre", + "outlier_distance_km": 13132.8, + "second_furthest_km": 4817.9, + "clarity_ratio": 2.73, + "median_distance_km": 4056.5, + "distances_to_centroid": { + "Foz do Iguaçu": 4817.9, + "Jequitinhonha": 3681.9, + "São Fidélis": 3603.2, + "Bosque Saúde": 4056.5, + "Greenacre": 13132.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Foz do Iguaçu: (-25.55°, -54.59°)", + " Jequitinhonha: (-16.43°, -41.00°)", + " São Fidélis: (-21.65°, -41.75°)", + " Bosque Saúde: (-23.61°, -46.62°)", + " Greenacre: (-33.90°, 151.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greenacre: 13132.8 km from centroid", + " Foz do Iguaçu: 4817.9 km from centroid", + " Bosque Saúde: 4056.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greenacre", + "FINAL ANSWER: Greenacre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.17705, + "lon": -122.18651, + "name": "Bonney Lake" + }, + { + "lat": 42.08507, + "lon": -76.05381, + "name": "Vestal" + }, + { + "lat": 47.61038, + "lon": -122.20068, + "name": "Bellevue" + }, + { + "lat": 39.18361, + "lon": -96.57167, + "name": "Manhattan" + }, + { + "lat": -14.06944, + "lon": -42.475, + "name": "Caetité" + } + ], + "question": "Which location is the geographic outlier among: Bonney Lake, Vestal, Bellevue, Manhattan, Caetité?", + "ground_truth": { + "answer": "Caetité", + "outlier_distance_km": 7368.3, + "second_furthest_km": 3055.5, + "clarity_ratio": 2.41, + "median_distance_km": 3036.3, + "distances_to_centroid": { + "Bonney Lake": 3036.3, + "Vestal": 1763.5, + "Bellevue": 3055.5, + "Manhattan": 864.1, + "Caetité": 7368.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bonney Lake: (47.18°, -122.19°)", + " Vestal: (42.09°, -76.05°)", + " Bellevue: (47.61°, -122.20°)", + " Manhattan: (39.18°, -96.57°)", + " Caetité: (-14.07°, -42.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caetité: 7368.3 km from centroid", + " Bellevue: 3055.5 km from centroid", + " Bonney Lake: 3036.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caetité", + "FINAL ANSWER: Caetité" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -36.8382, + "lon": 174.61019, + "name": "Massey" + }, + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + }, + { + "lat": 53.18478, + "lon": -3.02578, + "name": "Hawarden" + } + ], + "question": "Which location is the geographic outlier among: Robina, Bairnsdale, Massey, Southbank, Hawarden?", + "ground_truth": { + "answer": "Hawarden", + "outlier_distance_km": 13954.7, + "second_furthest_km": 5420.1, + "clarity_ratio": 2.57, + "median_distance_km": 3271.3, + "distances_to_centroid": { + "Robina": 3271.3, + "Bairnsdale": 3260.0, + "Massey": 5420.1, + "Southbank": 3080.2, + "Hawarden": 13954.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Massey: (-36.84°, 174.61°)", + " Southbank: (-37.82°, 144.96°)", + " Hawarden: (53.18°, -3.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hawarden: 13954.7 km from centroid", + " Massey: 5420.1 km from centroid", + " Robina: 3271.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hawarden", + "FINAL ANSWER: Hawarden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.51667, + "lon": 140.08333, + "name": "Ichihara" + }, + { + "lat": 25.03889, + "lon": 102.71833, + "name": "Kunming" + }, + { + "lat": 8.65417, + "lon": 124.75556, + "name": "Jasaan" + }, + { + "lat": 29.32431, + "lon": 107.76056, + "name": "Wulong" + }, + { + "lat": 39.60678, + "lon": -75.83327, + "name": "Elkton" + } + ], + "question": "Which location is the geographic outlier among: Ichihara, Kunming, Jasaan, Wulong, Elkton?", + "ground_truth": { + "answer": "Elkton", + "outlier_distance_km": 12127.4, + "second_furthest_km": 5682.3, + "clarity_ratio": 2.13, + "median_distance_km": 5150.4, + "distances_to_centroid": { + "Ichihara": 5682.3, + "Kunming": 2289.1, + "Jasaan": 5150.4, + "Wulong": 2723.6, + "Elkton": 12127.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ichihara: (35.52°, 140.08°)", + " Kunming: (25.04°, 102.72°)", + " Jasaan: (8.65°, 124.76°)", + " Wulong: (29.32°, 107.76°)", + " Elkton: (39.61°, -75.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Elkton: 12127.4 km from centroid", + " Ichihara: 5682.3 km from centroid", + " Jasaan: 5150.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Elkton", + "FINAL ANSWER: Elkton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": -33.91972, + "lon": 151.07592, + "name": "Lakemba" + }, + { + "lat": -33.98735, + "lon": 18.49746, + "name": "Lansdowne" + } + ], + "question": "Which location is the geographic outlier among: Glen Iris, Australind, Caroline Springs, Lakemba, Lansdowne?", + "ground_truth": { + "answer": "Lansdowne", + "outlier_distance_km": 8419.4, + "second_furthest_km": 3284.4, + "clarity_ratio": 2.56, + "median_distance_km": 2684.8, + "distances_to_centroid": { + "Glen Iris": 2684.8, + "Australind": 239.9, + "Caroline Springs": 2656.6, + "Lakemba": 3284.4, + "Lansdowne": 8419.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Iris: (-37.87°, 145.07°)", + " Australind: (-33.28°, 115.72°)", + " Caroline Springs: (-37.74°, 144.74°)", + " Lakemba: (-33.92°, 151.08°)", + " Lansdowne: (-33.99°, 18.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lansdowne: 8419.4 km from centroid", + " Lakemba: 3284.4 km from centroid", + " Glen Iris: 2684.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lansdowne", + "FINAL ANSWER: Lansdowne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -38.07758, + "lon": 145.29871, + "name": "Cranbourne North" + }, + { + "lat": -38.38176, + "lon": 142.48799, + "name": "Warrnambool" + }, + { + "lat": -6.70111, + "lon": -79.90611, + "name": "Lambayeque" + } + ], + "question": "Which location is the geographic outlier among: Saint Kilda, Elwood, Cranbourne North, Warrnambool, Lambayeque?", + "ground_truth": { + "answer": "Lambayeque", + "outlier_distance_km": 15735.6, + "second_furthest_km": 4184.8, + "clarity_ratio": 3.76, + "median_distance_km": 4159.0, + "distances_to_centroid": { + "Saint Kilda": 4159.0, + "Elwood": 4158.9, + "Cranbourne North": 4184.8, + "Warrnambool": 3937.7, + "Lambayeque": 15735.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint Kilda: (-37.87°, 144.98°)", + " Elwood: (-37.88°, 144.98°)", + " Cranbourne North: (-38.08°, 145.30°)", + " Warrnambool: (-38.38°, 142.49°)", + " Lambayeque: (-6.70°, -79.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lambayeque: 15735.6 km from centroid", + " Cranbourne North: 4184.8 km from centroid", + " Saint Kilda: 4159.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lambayeque", + "FINAL ANSWER: Lambayeque" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.86667, + "lon": 2.71667, + "name": "Lagny-sur-Marne" + }, + { + "lat": 53.05963, + "lon": 14.28154, + "name": "Schwedt (Oder)" + }, + { + "lat": 52.76033, + "lon": 32.23905, + "name": "Klintsy" + }, + { + "lat": 52.89855, + "lon": -1.27136, + "name": "Long Eaton" + }, + { + "lat": 5.86006, + "lon": -0.6635, + "name": "Asamankese" + } + ], + "question": "Which location is the geographic outlier among: Lagny-sur-Marne, Schwedt (Oder), Klintsy, Long Eaton, Asamankese?", + "ground_truth": { + "answer": "Asamankese", + "outlier_distance_km": 4214.7, + "second_furthest_km": 2025.2, + "clarity_ratio": 2.08, + "median_distance_km": 1386.5, + "distances_to_centroid": { + "Lagny-sur-Marne": 862.6, + "Schwedt (Oder)": 1207.2, + "Klintsy": 2025.2, + "Long Eaton": 1386.5, + "Asamankese": 4214.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lagny-sur-Marne: (48.87°, 2.72°)", + " Schwedt (Oder): (53.06°, 14.28°)", + " Klintsy: (52.76°, 32.24°)", + " Long Eaton: (52.90°, -1.27°)", + " Asamankese: (5.86°, -0.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Asamankese: 4214.7 km from centroid", + " Klintsy: 2025.2 km from centroid", + " Long Eaton: 1386.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Asamankese", + "FINAL ANSWER: Asamankese" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.40056, + "lon": -79.57139, + "name": "Pacasmayo" + }, + { + "lat": 5.06692, + "lon": -74.59499, + "name": "Guaduas" + }, + { + "lat": -24.4875, + "lon": -47.84361, + "name": "Registro" + }, + { + "lat": 3.23114, + "lon": -76.41668, + "name": "Puerto Tejada" + }, + { + "lat": -28.41789, + "lon": 32.18483, + "name": "Mtubatuba" + } + ], + "question": "Which location is the geographic outlier among: Pacasmayo, Guaduas, Registro, Puerto Tejada, Mtubatuba?", + "ground_truth": { + "answer": "Mtubatuba", + "outlier_distance_km": 8628.4, + "second_furthest_km": 3368.1, + "clarity_ratio": 2.56, + "median_distance_km": 3346.5, + "distances_to_centroid": { + "Pacasmayo": 3346.5, + "Guaduas": 3291.8, + "Registro": 1573.3, + "Puerto Tejada": 3368.1, + "Mtubatuba": 8628.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacasmayo: (-7.40°, -79.57°)", + " Guaduas: (5.07°, -74.59°)", + " Registro: (-24.49°, -47.84°)", + " Puerto Tejada: (3.23°, -76.42°)", + " Mtubatuba: (-28.42°, 32.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mtubatuba: 8628.4 km from centroid", + " Puerto Tejada: 3368.1 km from centroid", + " Pacasmayo: 3346.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mtubatuba", + "FINAL ANSWER: Mtubatuba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.28417, + "lon": -48.12667, + "name": "Brotas" + }, + { + "lat": -6.60667, + "lon": -39.06222, + "name": "Cedro" + }, + { + "lat": -6.24316, + "lon": -42.84544, + "name": "Amarante" + }, + { + "lat": -7.50528, + "lon": -35.31833, + "name": "Timbaúba" + }, + { + "lat": 7.61667, + "lon": 39.5, + "name": "Gobēsa" + } + ], + "question": "Which location is the geographic outlier among: Brotas, Cedro, Amarante, Timbaúba, Gobēsa?", + "ground_truth": { + "answer": "Gobēsa", + "outlier_distance_km": 7352.9, + "second_furthest_km": 2989.5, + "clarity_ratio": 2.46, + "median_distance_km": 1954.0, + "distances_to_centroid": { + "Brotas": 2989.5, + "Cedro": 1534.4, + "Amarante": 1954.0, + "Timbaúba": 1120.7, + "Gobēsa": 7352.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brotas: (-22.28°, -48.13°)", + " Cedro: (-6.61°, -39.06°)", + " Amarante: (-6.24°, -42.85°)", + " Timbaúba: (-7.51°, -35.32°)", + " Gobēsa: (7.62°, 39.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gobēsa: 7352.9 km from centroid", + " Brotas: 2989.5 km from centroid", + " Amarante: 1954.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gobēsa", + "FINAL ANSWER: Gobēsa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + { + "lat": -27.96724, + "lon": 153.39796, + "name": "Southport" + }, + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + }, + { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + { + "lat": 55.7, + "lon": 37.75, + "name": "Novyye Kuz’minki" + } + ], + "question": "Which location is the geographic outlier among: Whangarei, Southport, Doncaster East, Glen Iris, Novyye Kuz’minki?", + "ground_truth": { + "answer": "Novyye Kuz’minki", + "outlier_distance_km": 11747.3, + "second_furthest_km": 4747.8, + "clarity_ratio": 2.47, + "median_distance_km": 2716.1, + "distances_to_centroid": { + "Whangarei": 4747.8, + "Southport": 2601.4, + "Doncaster East": 2712.8, + "Glen Iris": 2716.1, + "Novyye Kuz’minki": 11747.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Whangarei: (-35.73°, 174.32°)", + " Southport: (-27.97°, 153.40°)", + " Doncaster East: (-37.79°, 145.15°)", + " Glen Iris: (-37.87°, 145.07°)", + " Novyye Kuz’minki: (55.70°, 37.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Novyye Kuz’minki: 11747.3 km from centroid", + " Whangarei: 4747.8 km from centroid", + " Glen Iris: 2716.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Novyye Kuz’minki", + "FINAL ANSWER: Novyye Kuz’minki" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.44775, + "lon": -8.68594, + "name": "Poio" + }, + { + "lat": 47.82672, + "lon": 10.0205, + "name": "Leutkirch" + }, + { + "lat": 49.34737, + "lon": 8.68733, + "name": "Leimen" + }, + { + "lat": 40.91494, + "lon": 14.79103, + "name": "Avellino" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + } + ], + "question": "Which location is the geographic outlier among: Poio, Leutkirch, Leimen, Avellino, Casula?", + "ground_truth": { + "answer": "Casula", + "outlier_distance_km": 14010.4, + "second_furthest_km": 4156.6, + "clarity_ratio": 3.37, + "median_distance_km": 3152.8, + "distances_to_centroid": { + "Poio": 4156.6, + "Leutkirch": 2975.7, + "Leimen": 3152.8, + "Avellino": 2246.9, + "Casula": 14010.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Poio: (42.45°, -8.69°)", + " Leutkirch: (47.83°, 10.02°)", + " Leimen: (49.35°, 8.69°)", + " Avellino: (40.91°, 14.79°)", + " Casula: (-33.95°, 150.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casula: 14010.4 km from centroid", + " Poio: 4156.6 km from centroid", + " Leimen: 3152.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casula", + "FINAL ANSWER: Casula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.01858, + "lon": -101.2591, + "name": "Guanajuato" + }, + { + "lat": 37.26804, + "lon": -77.40726, + "name": "Colonial Heights" + }, + { + "lat": 28.33287, + "lon": -81.64738, + "name": "Four Corners" + }, + { + "lat": 34.14806, + "lon": -117.99895, + "name": "Monrovia" + }, + { + "lat": 22.09901, + "lon": 82.2664, + "name": "Deori" + } + ], + "question": "Which location is the geographic outlier among: Guanajuato, Colonial Heights, Four Corners, Monrovia, Deori?", + "ground_truth": { + "answer": "Deori", + "outlier_distance_km": 13028.8, + "second_furthest_km": 5540.6, + "clarity_ratio": 2.35, + "median_distance_km": 4304.8, + "distances_to_centroid": { + "Guanajuato": 4304.8, + "Colonial Heights": 1949.4, + "Four Corners": 2190.6, + "Monrovia": 5540.6, + "Deori": 13028.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guanajuato: (21.02°, -101.26°)", + " Colonial Heights: (37.27°, -77.41°)", + " Four Corners: (28.33°, -81.65°)", + " Monrovia: (34.15°, -118.00°)", + " Deori: (22.10°, 82.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Deori: 13028.8 km from centroid", + " Monrovia: 5540.6 km from centroid", + " Guanajuato: 4304.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Deori", + "FINAL ANSWER: Deori" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.34772, + "lon": -120.60908, + "name": "Atwater" + }, + { + "lat": 37.74786, + "lon": -84.29465, + "name": "Richmond" + }, + { + "lat": 41.30815, + "lon": -72.92816, + "name": "New Haven" + }, + { + "lat": 19.42155, + "lon": -98.95038, + "name": "Santa María Chimalhuacán" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + } + ], + "question": "Which location is the geographic outlier among: Atwater, Richmond, New Haven, Santa María Chimalhuacán, Camberwell?", + "ground_truth": { + "answer": "Camberwell", + "outlier_distance_km": 17705.6, + "second_furthest_km": 7340.2, + "clarity_ratio": 2.41, + "median_distance_km": 5490.6, + "distances_to_centroid": { + "Atwater": 7340.2, + "Richmond": 4176.6, + "New Haven": 3483.1, + "Santa María Chimalhuacán": 5490.6, + "Camberwell": 17705.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Atwater: (37.35°, -120.61°)", + " Richmond: (37.75°, -84.29°)", + " New Haven: (41.31°, -72.93°)", + " Santa María Chimalhuacán: (19.42°, -98.95°)", + " Camberwell: (-37.84°, 145.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camberwell: 17705.6 km from centroid", + " Atwater: 7340.2 km from centroid", + " Santa María Chimalhuacán: 5490.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camberwell", + "FINAL ANSWER: Camberwell" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.95977, + "lon": -78.16515, + "name": "Cobourg" + }, + { + "lat": 33.51623, + "lon": -90.17953, + "name": "Greenwood" + }, + { + "lat": 29.77606, + "lon": -95.11465, + "name": "Channelview" + }, + { + "lat": 36.02506, + "lon": -86.77917, + "name": "Brentwood Estates" + }, + { + "lat": 57.00816, + "lon": 61.46344, + "name": "Asbest" + } + ], + "question": "Which location is the geographic outlier among: Cobourg, Greenwood, Channelview, Brentwood Estates, Asbest?", + "ground_truth": { + "answer": "Asbest", + "outlier_distance_km": 7822.2, + "second_furthest_km": 3563.0, + "clarity_ratio": 2.2, + "median_distance_km": 2959.9, + "distances_to_centroid": { + "Cobourg": 1736.3, + "Greenwood": 2959.9, + "Channelview": 3563.0, + "Brentwood Estates": 2569.2, + "Asbest": 7822.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cobourg: (43.96°, -78.17°)", + " Greenwood: (33.52°, -90.18°)", + " Channelview: (29.78°, -95.11°)", + " Brentwood Estates: (36.03°, -86.78°)", + " Asbest: (57.01°, 61.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Asbest: 7822.2 km from centroid", + " Channelview: 3563.0 km from centroid", + " Greenwood: 2959.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Asbest", + "FINAL ANSWER: Asbest" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.5392, + "lon": 103.8092, + "name": "Johor Jaya" + }, + { + "lat": 23.33033, + "lon": 77.7811, + "name": "Raisen" + }, + { + "lat": 19.03681, + "lon": 73.01582, + "name": "Navi Mumbai" + }, + { + "lat": 20.14183, + "lon": 78.31333, + "name": "Ghātanji" + }, + { + "lat": -32.90719, + "lon": 17.98997, + "name": "Vredenburg" + } + ], + "question": "Which location is the geographic outlier among: Johor Jaya, Raisen, Navi Mumbai, Ghātanji, Vredenburg?", + "ground_truth": { + "answer": "Vredenburg", + "outlier_distance_km": 7014.6, + "second_furthest_km": 3765.6, + "clarity_ratio": 1.86, + "median_distance_km": 2068.3, + "distances_to_centroid": { + "Johor Jaya": 3765.6, + "Raisen": 2068.3, + "Navi Mumbai": 1456.9, + "Ghātanji": 1778.8, + "Vredenburg": 7014.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Johor Jaya: (1.54°, 103.81°)", + " Raisen: (23.33°, 77.78°)", + " Navi Mumbai: (19.04°, 73.02°)", + " Ghātanji: (20.14°, 78.31°)", + " Vredenburg: (-32.91°, 17.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vredenburg: 7014.6 km from centroid", + " Johor Jaya: 3765.6 km from centroid", + " Raisen: 2068.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vredenburg", + "FINAL ANSWER: Vredenburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.05, + "lon": 2.1, + "name": "Pontoise" + }, + { + "lat": 45.92136, + "lon": 8.55183, + "name": "Verbania" + }, + { + "lat": 52.88157, + "lon": -1.48681, + "name": "Sinfin" + }, + { + "lat": 41.5908, + "lon": 12.82808, + "name": "Cisterna di Latina" + }, + { + "lat": 40.34872, + "lon": -74.65905, + "name": "Princeton" + } + ], + "question": "Which location is the geographic outlier among: Pontoise, Verbania, Sinfin, Cisterna di Latina, Princeton?", + "ground_truth": { + "answer": "Princeton", + "outlier_distance_km": 5097.7, + "second_furthest_km": 1929.8, + "clarity_ratio": 2.64, + "median_distance_km": 1472.2, + "distances_to_centroid": { + "Pontoise": 1007.8, + "Verbania": 1472.2, + "Sinfin": 1008.8, + "Cisterna di Latina": 1929.8, + "Princeton": 5097.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pontoise: (49.05°, 2.10°)", + " Verbania: (45.92°, 8.55°)", + " Sinfin: (52.88°, -1.49°)", + " Cisterna di Latina: (41.59°, 12.83°)", + " Princeton: (40.35°, -74.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Princeton: 5097.7 km from centroid", + " Cisterna di Latina: 1929.8 km from centroid", + " Verbania: 1472.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Princeton", + "FINAL ANSWER: Princeton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.95775, + "lon": 27.26543, + "name": "Northam" + }, + { + "lat": 26.76866, + "lon": 31.50198, + "name": "Ţahţā" + }, + { + "lat": 5.70773, + "lon": 6.43402, + "name": "Kwale" + }, + { + "lat": -0.36774, + "lon": 35.28314, + "name": "Kericho" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + } + ], + "question": "Which location is the geographic outlier among: Northam, Ţahţā, Kwale, Kericho, Pacific Pines?", + "ground_truth": { + "answer": "Pacific Pines", + "outlier_distance_km": 11015.5, + "second_furthest_km": 5042.9, + "clarity_ratio": 2.18, + "median_distance_km": 4014.0, + "distances_to_centroid": { + "Northam": 3413.5, + "Ţahţā": 4014.0, + "Kwale": 5042.9, + "Kericho": 1770.2, + "Pacific Pines": 11015.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Northam: (-24.96°, 27.27°)", + " Ţahţā: (26.77°, 31.50°)", + " Kwale: (5.71°, 6.43°)", + " Kericho: (-0.37°, 35.28°)", + " Pacific Pines: (-27.94°, 153.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pacific Pines: 11015.5 km from centroid", + " Kwale: 5042.9 km from centroid", + " Ţahţā: 4014.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pacific Pines", + "FINAL ANSWER: Pacific Pines" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.56853, + "lon": 42.02388, + "name": "Murom" + }, + { + "lat": 52.56667, + "lon": -1.81667, + "name": "Sutton Coldfield" + }, + { + "lat": 39.3635, + "lon": -0.45949, + "name": "Picassent" + }, + { + "lat": 55.75, + "lon": 37.56667, + "name": "Dorogomilovo" + }, + { + "lat": 49.84692, + "lon": -99.95306, + "name": "Brandon" + } + ], + "question": "Which location is the geographic outlier among: Murom, Sutton Coldfield, Picassent, Dorogomilovo, Brandon?", + "ground_truth": { + "answer": "Brandon", + "outlier_distance_km": 6281.3, + "second_furthest_km": 3095.9, + "clarity_ratio": 2.03, + "median_distance_km": 2816.2, + "distances_to_centroid": { + "Murom": 3095.9, + "Sutton Coldfield": 286.3, + "Picassent": 1291.3, + "Dorogomilovo": 2816.2, + "Brandon": 6281.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Murom: (55.57°, 42.02°)", + " Sutton Coldfield: (52.57°, -1.82°)", + " Picassent: (39.36°, -0.46°)", + " Dorogomilovo: (55.75°, 37.57°)", + " Brandon: (49.85°, -99.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Brandon: 6281.3 km from centroid", + " Murom: 3095.9 km from centroid", + " Dorogomilovo: 2816.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Brandon", + "FINAL ANSWER: Brandon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -37.73333, + "lon": 144.93333, + "name": "Pascoe Vale" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": 33.04083, + "lon": 108.23639, + "name": "Shiquan" + } + ], + "question": "Which location is the geographic outlier among: Wheelers Hill, Burwood, Pascoe Vale, Auburn, Shiquan?", + "ground_truth": { + "answer": "Shiquan", + "outlier_distance_km": 6998.0, + "second_furthest_km": 1826.8, + "clarity_ratio": 3.83, + "median_distance_km": 1802.8, + "distances_to_centroid": { + "Wheelers Hill": 1826.8, + "Burwood": 1698.8, + "Pascoe Vale": 1802.8, + "Auburn": 1691.9, + "Shiquan": 6998.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Burwood: (-33.88°, 151.10°)", + " Pascoe Vale: (-37.73°, 144.93°)", + " Auburn: (-33.85°, 151.03°)", + " Shiquan: (33.04°, 108.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shiquan: 6998.0 km from centroid", + " Wheelers Hill: 1826.8 km from centroid", + " Pascoe Vale: 1802.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shiquan", + "FINAL ANSWER: Shiquan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.0941, + "lon": 28.00123, + "name": "Randburg" + }, + { + "lat": 9.79399, + "lon": 8.86397, + "name": "Bukuru" + }, + { + "lat": -27.76952, + "lon": 30.79165, + "name": "Vryheid" + }, + { + "lat": -1.28316, + "lon": 36.84725, + "name": "Pumwani" + }, + { + "lat": -27.35364, + "lon": 152.96848, + "name": "Albany Creek" + } + ], + "question": "Which location is the geographic outlier among: Randburg, Bukuru, Vryheid, Pumwani, Albany Creek?", + "ground_truth": { + "answer": "Albany Creek", + "outlier_distance_km": 10362.3, + "second_furthest_km": 5423.0, + "clarity_ratio": 1.91, + "median_distance_km": 2759.1, + "distances_to_centroid": { + "Randburg": 2759.1, + "Bukuru": 5423.0, + "Vryheid": 2595.5, + "Pumwani": 2182.5, + "Albany Creek": 10362.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Randburg: (-26.09°, 28.00°)", + " Bukuru: (9.79°, 8.86°)", + " Vryheid: (-27.77°, 30.79°)", + " Pumwani: (-1.28°, 36.85°)", + " Albany Creek: (-27.35°, 152.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Albany Creek: 10362.3 km from centroid", + " Bukuru: 5423.0 km from centroid", + " Randburg: 2759.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Albany Creek", + "FINAL ANSWER: Albany Creek" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.02681, + "lon": 74.71487, + "name": "Ārangaon" + }, + { + "lat": 14.9127, + "lon": 120.56659, + "name": "Santa Cruz" + }, + { + "lat": 34.06153, + "lon": 108.62905, + "name": "Yuxia" + }, + { + "lat": 34.38889, + "lon": 118.05, + "name": "Chenlou" + }, + { + "lat": 19.60833, + "lon": -99.16944, + "name": "Buenavista" + } + ], + "question": "Which location is the geographic outlier among: Ārangaon, Santa Cruz, Yuxia, Chenlou, Buenavista?", + "ground_truth": { + "answer": "Buenavista", + "outlier_distance_km": 14814.0, + "second_furthest_km": 5921.3, + "clarity_ratio": 2.5, + "median_distance_km": 5239.8, + "distances_to_centroid": { + "Ārangaon": 1206.7, + "Santa Cruz": 5921.3, + "Yuxia": 4374.1, + "Chenlou": 5239.8, + "Buenavista": 14814.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ārangaon: (19.03°, 74.71°)", + " Santa Cruz: (14.91°, 120.57°)", + " Yuxia: (34.06°, 108.63°)", + " Chenlou: (34.39°, 118.05°)", + " Buenavista: (19.61°, -99.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Buenavista: 14814.0 km from centroid", + " Santa Cruz: 5921.3 km from centroid", + " Chenlou: 5239.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Buenavista", + "FINAL ANSWER: Buenavista" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.33962, + "lon": 12.37129, + "name": "Leipzig" + }, + { + "lat": 52.47774, + "lon": 10.5511, + "name": "Gifhorn" + }, + { + "lat": 51.17343, + "lon": 7.0845, + "name": "Solingen" + }, + { + "lat": 50.25077, + "lon": 3.92143, + "name": "Hautmont" + }, + { + "lat": 9.6, + "lon": 37.83333, + "name": "Kachīsī" + } + ], + "question": "Which location is the geographic outlier among: Leipzig, Gifhorn, Solingen, Hautmont, Kachīsī?", + "ground_truth": { + "answer": "Kachīsī", + "outlier_distance_km": 4354.2, + "second_furthest_km": 1134.0, + "clarity_ratio": 3.84, + "median_distance_km": 1094.6, + "distances_to_centroid": { + "Leipzig": 942.7, + "Gifhorn": 1094.6, + "Solingen": 1064.4, + "Hautmont": 1134.0, + "Kachīsī": 4354.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Leipzig: (51.34°, 12.37°)", + " Gifhorn: (52.48°, 10.55°)", + " Solingen: (51.17°, 7.08°)", + " Hautmont: (50.25°, 3.92°)", + " Kachīsī: (9.60°, 37.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kachīsī: 4354.2 km from centroid", + " Hautmont: 1134.0 km from centroid", + " Gifhorn: 1094.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kachīsī", + "FINAL ANSWER: Kachīsī" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.958, + "lon": -76.911, + "name": "East Riverdale" + }, + { + "lat": 38.25424, + "lon": -85.75941, + "name": "Louisville" + }, + { + "lat": 24.44676, + "lon": -104.12336, + "name": "Guadalupe Victoria" + }, + { + "lat": 44.8408, + "lon": -93.29828, + "name": "Bloomington" + }, + { + "lat": 35.95694, + "lon": 139.38889, + "name": "Sakado" + } + ], + "question": "Which location is the geographic outlier among: East Riverdale, Louisville, Guadalupe Victoria, Bloomington, Sakado?", + "ground_truth": { + "answer": "Sakado", + "outlier_distance_km": 11951.0, + "second_furthest_km": 5809.7, + "clarity_ratio": 2.06, + "median_distance_km": 4182.4, + "distances_to_centroid": { + "East Riverdale": 2879.7, + "Louisville": 3651.9, + "Guadalupe Victoria": 5809.7, + "Bloomington": 4182.4, + "Sakado": 11951.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " East Riverdale: (38.96°, -76.91°)", + " Louisville: (38.25°, -85.76°)", + " Guadalupe Victoria: (24.45°, -104.12°)", + " Bloomington: (44.84°, -93.30°)", + " Sakado: (35.96°, 139.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sakado: 11951.0 km from centroid", + " Guadalupe Victoria: 5809.7 km from centroid", + " Bloomington: 4182.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sakado", + "FINAL ANSWER: Sakado" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.09571, + "lon": -54.89344, + "name": "Aristóbulo del Valle" + }, + { + "lat": -31.33139, + "lon": -54.10694, + "name": "Bagé" + }, + { + "lat": 4.96531, + "lon": -73.91301, + "name": "Tocancipá" + }, + { + "lat": -25.42861, + "lon": -48.71194, + "name": "Antonina" + }, + { + "lat": 51.88083, + "lon": 5.28889, + "name": "Geldermalsen" + } + ], + "question": "Which location is the geographic outlier among: Aristóbulo del Valle, Bagé, Tocancipá, Antonina, Geldermalsen?", + "ground_truth": { + "answer": "Geldermalsen", + "outlier_distance_km": 7956.7, + "second_furthest_km": 3383.3, + "clarity_ratio": 2.35, + "median_distance_km": 3027.1, + "distances_to_centroid": { + "Aristóbulo del Valle": 2618.9, + "Bagé": 3027.1, + "Tocancipá": 3383.3, + "Antonina": 2256.9, + "Geldermalsen": 7956.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aristóbulo del Valle: (-27.10°, -54.89°)", + " Bagé: (-31.33°, -54.11°)", + " Tocancipá: (4.97°, -73.91°)", + " Antonina: (-25.43°, -48.71°)", + " Geldermalsen: (51.88°, 5.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Geldermalsen: 7956.7 km from centroid", + " Tocancipá: 3383.3 km from centroid", + " Bagé: 3027.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Geldermalsen", + "FINAL ANSWER: Geldermalsen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.96115, + "lon": 2.06882, + "name": "Achères" + }, + { + "lat": 55.32058, + "lon": 42.17402, + "name": "Vyksa" + }, + { + "lat": 60.0122, + "lon": 30.20897, + "name": "Untolovo" + }, + { + "lat": 51.90224, + "lon": -0.20256, + "name": "Stevenage" + }, + { + "lat": 10.92611, + "lon": 78.0941, + "name": "Tāndoni" + } + ], + "question": "Which location is the geographic outlier among: Achères, Vyksa, Untolovo, Stevenage, Tāndoni?", + "ground_truth": { + "answer": "Tāndoni", + "outlier_distance_km": 5912.0, + "second_furthest_km": 2344.7, + "clarity_ratio": 2.52, + "median_distance_km": 2168.4, + "distances_to_centroid": { + "Achères": 2168.4, + "Vyksa": 1374.5, + "Untolovo": 1622.2, + "Stevenage": 2344.7, + "Tāndoni": 5912.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Achères: (48.96°, 2.07°)", + " Vyksa: (55.32°, 42.17°)", + " Untolovo: (60.01°, 30.21°)", + " Stevenage: (51.90°, -0.20°)", + " Tāndoni: (10.93°, 78.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tāndoni: 5912.0 km from centroid", + " Stevenage: 2344.7 km from centroid", + " Achères: 2168.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tāndoni", + "FINAL ANSWER: Tāndoni" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.08033, + "lon": 37.47202, + "name": "Emali" + }, + { + "lat": 31.18352, + "lon": 30.52448, + "name": "Al Maḩmūdīyah" + }, + { + "lat": 30.15293, + "lon": 31.31501, + "name": "Al Khuşūş" + }, + { + "lat": 6.14978, + "lon": 6.78569, + "name": "Onitsha" + }, + { + "lat": 14.75778, + "lon": 120.94833, + "name": "Marilao" + } + ], + "question": "Which location is the geographic outlier among: Emali, Al Maḩmūdīyah, Al Khuşūş, Onitsha, Marilao?", + "ground_truth": { + "answer": "Marilao", + "outlier_distance_km": 8050.0, + "second_furthest_km": 4346.7, + "clarity_ratio": 1.85, + "median_distance_km": 2261.6, + "distances_to_centroid": { + "Emali": 2194.8, + "Al Maḩmūdīyah": 2261.6, + "Al Khuşūş": 2127.3, + "Onitsha": 4346.7, + "Marilao": 8050.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Emali: (-2.08°, 37.47°)", + " Al Maḩmūdīyah: (31.18°, 30.52°)", + " Al Khuşūş: (30.15°, 31.32°)", + " Onitsha: (6.15°, 6.79°)", + " Marilao: (14.76°, 120.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marilao: 8050.0 km from centroid", + " Onitsha: 4346.7 km from centroid", + " Al Maḩmūdīyah: 2261.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marilao", + "FINAL ANSWER: Marilao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.02414, + "lon": 1.15082, + "name": "Évreux" + }, + { + "lat": 40.73542, + "lon": 8.56771, + "name": "Monte Rosello" + }, + { + "lat": 48.87363, + "lon": 2.35197, + "name": "Porte Saint-Denis" + }, + { + "lat": 48.6511, + "lon": 2.41406, + "name": "Ris-Orangis" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + } + ], + "question": "Which location is the geographic outlier among: Évreux, Monte Rosello, Porte Saint-Denis, Ris-Orangis, Glenferrie?", + "ground_truth": { + "answer": "Glenferrie", + "outlier_distance_km": 13908.8, + "second_furthest_km": 3351.5, + "clarity_ratio": 4.15, + "median_distance_km": 3266.5, + "distances_to_centroid": { + "Évreux": 3351.5, + "Monte Rosello": 2425.8, + "Porte Saint-Denis": 3266.5, + "Ris-Orangis": 3250.5, + "Glenferrie": 13908.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Évreux: (49.02°, 1.15°)", + " Monte Rosello: (40.74°, 8.57°)", + " Porte Saint-Denis: (48.87°, 2.35°)", + " Ris-Orangis: (48.65°, 2.41°)", + " Glenferrie: (-37.83°, 145.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glenferrie: 13908.8 km from centroid", + " Évreux: 3351.5 km from centroid", + " Porte Saint-Denis: 3266.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glenferrie", + "FINAL ANSWER: Glenferrie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.92617, + "lon": -60.04852, + "name": "Machagai" + }, + { + "lat": -23.66778, + "lon": -46.46139, + "name": "Mauá" + }, + { + "lat": -22.88717, + "lon": -42.02622, + "name": "Cabo Frio" + }, + { + "lat": -22.15214, + "lon": -42.92335, + "name": "São José do Vale do Rio Preto" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + } + ], + "question": "Which location is the geographic outlier among: Machagai, Mauá, Cabo Frio, São José do Vale do Rio Preto, Glenroy?", + "ground_truth": { + "answer": "Glenroy", + "outlier_distance_km": 12369.7, + "second_furthest_km": 5001.0, + "clarity_ratio": 2.47, + "median_distance_km": 3741.3, + "distances_to_centroid": { + "Machagai": 5001.0, + "Mauá": 3741.3, + "Cabo Frio": 3321.1, + "São José do Vale do Rio Preto": 3430.9, + "Glenroy": 12369.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Machagai: (-26.93°, -60.05°)", + " Mauá: (-23.67°, -46.46°)", + " Cabo Frio: (-22.89°, -42.03°)", + " São José do Vale do Rio Preto: (-22.15°, -42.92°)", + " Glenroy: (-37.70°, 144.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glenroy: 12369.7 km from centroid", + " Machagai: 5001.0 km from centroid", + " Mauá: 3741.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glenroy", + "FINAL ANSWER: Glenroy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.22361, + "lon": -48.29444, + "name": "Santa Bárbara do Pará" + }, + { + "lat": -28.21344, + "lon": -49.16383, + "name": "São José" + }, + { + "lat": -26.8089, + "lon": -55.02147, + "name": "Puerto Rico" + }, + { + "lat": -14.52972, + "lon": -40.36528, + "name": "Poções" + }, + { + "lat": 20.85396, + "lon": 79.32466, + "name": "Umred" + } + ], + "question": "Which location is the geographic outlier among: Santa Bárbara do Pará, São José, Puerto Rico, Poções, Umred?", + "ground_truth": { + "answer": "Umred", + "outlier_distance_km": 11640.5, + "second_furthest_km": 3870.8, + "clarity_ratio": 3.01, + "median_distance_km": 3425.5, + "distances_to_centroid": { + "Santa Bárbara do Pará": 2991.9, + "São José": 3425.5, + "Puerto Rico": 3870.8, + "Poções": 1983.6, + "Umred": 11640.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Bárbara do Pará: (-1.22°, -48.29°)", + " São José: (-28.21°, -49.16°)", + " Puerto Rico: (-26.81°, -55.02°)", + " Poções: (-14.53°, -40.37°)", + " Umred: (20.85°, 79.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Umred: 11640.5 km from centroid", + " Puerto Rico: 3870.8 km from centroid", + " São José: 3425.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Umred", + "FINAL ANSWER: Umred" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.52591, + "lon": 5.75342, + "name": "Ikare" + }, + { + "lat": -25.33177, + "lon": 31.01166, + "name": "White River" + }, + { + "lat": 8.81667, + "lon": 40.51667, + "name": "Gelemso" + }, + { + "lat": -26.31905, + "lon": 27.6486, + "name": "Westonaria" + }, + { + "lat": 35.31947, + "lon": 139.1096, + "name": "Minamiashigara" + } + ], + "question": "Which location is the geographic outlier among: Ikare, White River, Gelemso, Westonaria, Minamiashigara?", + "ground_truth": { + "answer": "Minamiashigara", + "outlier_distance_km": 10034.8, + "second_furthest_km": 4845.9, + "clarity_ratio": 2.07, + "median_distance_km": 3701.8, + "distances_to_centroid": { + "Ikare": 4845.9, + "White River": 3404.6, + "Gelemso": 1343.1, + "Westonaria": 3701.8, + "Minamiashigara": 10034.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ikare: (7.53°, 5.75°)", + " White River: (-25.33°, 31.01°)", + " Gelemso: (8.82°, 40.52°)", + " Westonaria: (-26.32°, 27.65°)", + " Minamiashigara: (35.32°, 139.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Minamiashigara: 10034.8 km from centroid", + " Ikare: 4845.9 km from centroid", + " Westonaria: 3701.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Minamiashigara", + "FINAL ANSWER: Minamiashigara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.68806, + "lon": 111.42944, + "name": "Lengshuijiang" + }, + { + "lat": -6.8976, + "lon": 112.0649, + "name": "Tuban" + }, + { + "lat": 34.16297, + "lon": 132.22, + "name": "Iwakuni" + }, + { + "lat": 33.95182, + "lon": 105.29247, + "name": "Shili" + }, + { + "lat": -25.48251, + "lon": 29.02763, + "name": "Verena" + } + ], + "question": "Which location is the geographic outlier among: Lengshuijiang, Tuban, Iwakuni, Shili, Verena?", + "ground_truth": { + "answer": "Verena", + "outlier_distance_km": 8585.0, + "second_furthest_km": 4195.8, + "clarity_ratio": 2.05, + "median_distance_km": 2674.8, + "distances_to_centroid": { + "Lengshuijiang": 2174.6, + "Tuban": 2674.8, + "Iwakuni": 4195.8, + "Shili": 2477.0, + "Verena": 8585.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lengshuijiang: (27.69°, 111.43°)", + " Tuban: (-6.90°, 112.06°)", + " Iwakuni: (34.16°, 132.22°)", + " Shili: (33.95°, 105.29°)", + " Verena: (-25.48°, 29.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Verena: 8585.0 km from centroid", + " Iwakuni: 4195.8 km from centroid", + " Tuban: 2674.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Verena", + "FINAL ANSWER: Verena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.9825, + "lon": -75.60361, + "name": "Chinchiná" + }, + { + "lat": -20.36333, + "lon": -40.65917, + "name": "Domingos Martins" + }, + { + "lat": -26.33639, + "lon": -49.90639, + "name": "Itaiópolis" + }, + { + "lat": -26.90778, + "lon": -48.66194, + "name": "Itajaí" + }, + { + "lat": 28.72655, + "lon": 77.06689, + "name": "Begampur" + } + ], + "question": "Which location is the geographic outlier among: Chinchiná, Domingos Martins, Itaiópolis, Itajaí, Begampur?", + "ground_truth": { + "answer": "Begampur", + "outlier_distance_km": 11854.9, + "second_furthest_km": 5520.9, + "clarity_ratio": 2.15, + "median_distance_km": 3120.6, + "distances_to_centroid": { + "Chinchiná": 5520.9, + "Domingos Martins": 1970.5, + "Itaiópolis": 3120.6, + "Itajaí": 3062.6, + "Begampur": 11854.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chinchiná: (4.98°, -75.60°)", + " Domingos Martins: (-20.36°, -40.66°)", + " Itaiópolis: (-26.34°, -49.91°)", + " Itajaí: (-26.91°, -48.66°)", + " Begampur: (28.73°, 77.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Begampur: 11854.9 km from centroid", + " Chinchiná: 5520.9 km from centroid", + " Itaiópolis: 3120.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Begampur", + "FINAL ANSWER: Begampur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.96572, + "lon": 10.56111, + "name": "Uelzen" + }, + { + "lat": 45.55301, + "lon": 9.29907, + "name": "Brugherio" + }, + { + "lat": 52.14, + "lon": 5.58472, + "name": "Barneveld" + }, + { + "lat": 45.44207, + "lon": 9.09445, + "name": "Cesano Boscone" + }, + { + "lat": 20.52353, + "lon": -100.8157, + "name": "Celaya" + } + ], + "question": "Which location is the geographic outlier among: Uelzen, Brugherio, Barneveld, Cesano Boscone, Celaya?", + "ground_truth": { + "answer": "Celaya", + "outlier_distance_km": 8268.7, + "second_furthest_km": 2052.2, + "clarity_ratio": 4.03, + "median_distance_km": 1801.6, + "distances_to_centroid": { + "Uelzen": 2052.2, + "Brugherio": 1801.6, + "Barneveld": 1708.3, + "Cesano Boscone": 1785.7, + "Celaya": 8268.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Uelzen: (52.97°, 10.56°)", + " Brugherio: (45.55°, 9.30°)", + " Barneveld: (52.14°, 5.58°)", + " Cesano Boscone: (45.44°, 9.09°)", + " Celaya: (20.52°, -100.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Celaya: 8268.7 km from centroid", + " Uelzen: 2052.2 km from centroid", + " Brugherio: 1801.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Celaya", + "FINAL ANSWER: Celaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.80787, + "lon": -97.77956, + "name": "Ciudad de Huajuapan de León" + }, + { + "lat": 43.65751, + "lon": -79.38572, + "name": "Bay Street Corridor" + }, + { + "lat": 41.18454, + "lon": -73.13317, + "name": "Stratford" + }, + { + "lat": 42.03417, + "lon": -91.59768, + "name": "Marion" + }, + { + "lat": 33.11358, + "lon": 130.00292, + "name": "Ureshinomachi-shimojuku" + } + ], + "question": "Which location is the geographic outlier among: Ciudad de Huajuapan de León, Bay Street Corridor, Stratford, Marion, Ureshinomachi-shimojuku?", + "ground_truth": { + "answer": "Ureshinomachi-shimojuku", + "outlier_distance_km": 12337.9, + "second_furthest_km": 5766.0, + "clarity_ratio": 2.14, + "median_distance_km": 4266.2, + "distances_to_centroid": { + "Ciudad de Huajuapan de León": 5766.0, + "Bay Street Corridor": 3265.8, + "Stratford": 2737.7, + "Marion": 4266.2, + "Ureshinomachi-shimojuku": 12337.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ciudad de Huajuapan de León: (17.81°, -97.78°)", + " Bay Street Corridor: (43.66°, -79.39°)", + " Stratford: (41.18°, -73.13°)", + " Marion: (42.03°, -91.60°)", + " Ureshinomachi-shimojuku: (33.11°, 130.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ureshinomachi-shimojuku: 12337.9 km from centroid", + " Ciudad de Huajuapan de León: 5766.0 km from centroid", + " Marion: 4266.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ureshinomachi-shimojuku", + "FINAL ANSWER: Ureshinomachi-shimojuku" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.77271, + "lon": 151.08184, + "name": "Epping" + }, + { + "lat": -33.94185, + "lon": 150.8717, + "name": "Prestons" + }, + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -34.91119, + "lon": 138.70735, + "name": "Adelaide Hills" + }, + { + "lat": -3.29972, + "lon": -60.62056, + "name": "Manacapuru" + } + ], + "question": "Which location is the geographic outlier among: Epping, Prestons, Melbourne, Adelaide Hills, Manacapuru?", + "ground_truth": { + "answer": "Manacapuru", + "outlier_distance_km": 16134.8, + "second_furthest_km": 4379.6, + "clarity_ratio": 3.68, + "median_distance_km": 4358.5, + "distances_to_centroid": { + "Epping": 4379.6, + "Prestons": 4358.5, + "Melbourne": 3817.9, + "Adelaide Hills": 3241.2, + "Manacapuru": 16134.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epping: (-33.77°, 151.08°)", + " Prestons: (-33.94°, 150.87°)", + " Melbourne: (-37.81°, 144.96°)", + " Adelaide Hills: (-34.91°, 138.71°)", + " Manacapuru: (-3.30°, -60.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Manacapuru: 16134.8 km from centroid", + " Epping: 4379.6 km from centroid", + " Prestons: 4358.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Manacapuru", + "FINAL ANSWER: Manacapuru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.37028, + "lon": -40.21333, + "name": "Pinheiros" + }, + { + "lat": -4.27611, + "lon": -55.98361, + "name": "Itaituba" + }, + { + "lat": -23.54476, + "lon": -46.64105, + "name": "Republica" + }, + { + "lat": -22.45389, + "lon": -43.46889, + "name": "Miguel Pereira" + }, + { + "lat": 38.86484, + "lon": -77.18787, + "name": "West Falls Church" + } + ], + "question": "Which location is the geographic outlier among: Pinheiros, Itaituba, Republica, Miguel Pereira, West Falls Church?", + "ground_truth": { + "answer": "West Falls Church", + "outlier_distance_km": 5585.8, + "second_furthest_km": 2084.9, + "clarity_ratio": 2.68, + "median_distance_km": 2060.4, + "distances_to_centroid": { + "Pinheiros": 1933.6, + "Itaituba": 408.9, + "Republica": 2060.4, + "Miguel Pereira": 2084.9, + "West Falls Church": 5585.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pinheiros: (-18.37°, -40.21°)", + " Itaituba: (-4.28°, -55.98°)", + " Republica: (-23.54°, -46.64°)", + " Miguel Pereira: (-22.45°, -43.47°)", + " West Falls Church: (38.86°, -77.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Falls Church: 5585.8 km from centroid", + " Miguel Pereira: 2084.9 km from centroid", + " Republica: 2060.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Falls Church", + "FINAL ANSWER: West Falls Church" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.20011, + "lon": -90.57093, + "name": "Clarksdale" + }, + { + "lat": 49.25, + "lon": -122.88333, + "name": "Cariboo" + }, + { + "lat": 19.60833, + "lon": -99.16944, + "name": "Buenavista" + }, + { + "lat": 45.56995, + "lon": -73.692, + "name": "Laval" + }, + { + "lat": 46.56459, + "lon": 3.33243, + "name": "Moulins" + } + ], + "question": "Which location is the geographic outlier among: Clarksdale, Cariboo, Buenavista, Laval, Moulins?", + "ground_truth": { + "answer": "Moulins", + "outlier_distance_km": 6291.6, + "second_furthest_km": 3797.9, + "clarity_ratio": 1.66, + "median_distance_km": 3058.1, + "distances_to_centroid": { + "Clarksdale": 1356.3, + "Cariboo": 3797.9, + "Buenavista": 3058.1, + "Laval": 764.4, + "Moulins": 6291.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Clarksdale: (34.20°, -90.57°)", + " Cariboo: (49.25°, -122.88°)", + " Buenavista: (19.61°, -99.17°)", + " Laval: (45.57°, -73.69°)", + " Moulins: (46.56°, 3.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Moulins: 6291.6 km from centroid", + " Cariboo: 3797.9 km from centroid", + " Buenavista: 3058.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Moulins", + "FINAL ANSWER: Moulins" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.65737, + "lon": -70.2589, + "name": "Portland" + }, + { + "lat": 36.72836, + "lon": -76.58496, + "name": "Suffolk" + }, + { + "lat": 28.01888, + "lon": -82.11469, + "name": "Plant City" + }, + { + "lat": 34.41333, + "lon": -119.86097, + "name": "Isla Vista" + }, + { + "lat": -23.51, + "lon": -46.41566, + "name": "Vila Curuca" + } + ], + "question": "Which location is the geographic outlier among: Portland, Suffolk, Plant City, Isla Vista, Vila Curuca?", + "ground_truth": { + "answer": "Vila Curuca", + "outlier_distance_km": 6336.3, + "second_furthest_km": 4103.7, + "clarity_ratio": 1.54, + "median_distance_km": 2342.9, + "distances_to_centroid": { + "Portland": 2342.9, + "Suffolk": 1450.0, + "Plant City": 554.7, + "Isla Vista": 4103.7, + "Vila Curuca": 6336.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Portland: (43.66°, -70.26°)", + " Suffolk: (36.73°, -76.58°)", + " Plant City: (28.02°, -82.11°)", + " Isla Vista: (34.41°, -119.86°)", + " Vila Curuca: (-23.51°, -46.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vila Curuca: 6336.3 km from centroid", + " Isla Vista: 4103.7 km from centroid", + " Portland: 2342.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vila Curuca", + "FINAL ANSWER: Vila Curuca" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.89, + "lon": 4.74028, + "name": "Julianadorp" + }, + { + "lat": 51.965, + "lon": 6.28889, + "name": "Doetinchem" + }, + { + "lat": 49.58333, + "lon": 3.0, + "name": "Noyon" + }, + { + "lat": 42.95488, + "lon": 12.70268, + "name": "Foligno" + }, + { + "lat": 9.56561, + "lon": 36.63569, + "name": "Gutin" + } + ], + "question": "Which location is the geographic outlier among: Julianadorp, Doetinchem, Noyon, Foligno, Gutin?", + "ground_truth": { + "answer": "Gutin", + "outlier_distance_km": 4247.3, + "second_furthest_km": 1410.3, + "clarity_ratio": 3.01, + "median_distance_km": 1271.4, + "distances_to_centroid": { + "Julianadorp": 1410.3, + "Doetinchem": 1271.4, + "Noyon": 1180.5, + "Foligno": 173.8, + "Gutin": 4247.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Julianadorp: (52.89°, 4.74°)", + " Doetinchem: (51.97°, 6.29°)", + " Noyon: (49.58°, 3.00°)", + " Foligno: (42.95°, 12.70°)", + " Gutin: (9.57°, 36.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gutin: 4247.3 km from centroid", + " Julianadorp: 1410.3 km from centroid", + " Doetinchem: 1271.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gutin", + "FINAL ANSWER: Gutin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.17719, + "lon": -1.56412, + "name": "Ashington" + }, + { + "lat": 54.9981, + "lon": -7.30934, + "name": "Derry" + }, + { + "lat": 52.56395, + "lon": 13.33552, + "name": "Reinickendorf" + }, + { + "lat": 28.61052, + "lon": -13.92912, + "name": "La Oliva" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + } + ], + "question": "Which location is the geographic outlier among: Ashington, Derry, Reinickendorf, La Oliva, Nerang?", + "ground_truth": { + "answer": "Nerang", + "outlier_distance_km": 14728.5, + "second_furthest_km": 4083.1, + "clarity_ratio": 3.61, + "median_distance_km": 3742.0, + "distances_to_centroid": { + "Ashington": 3436.5, + "Derry": 3742.0, + "Reinickendorf": 2535.1, + "La Oliva": 4083.1, + "Nerang": 14728.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ashington: (55.18°, -1.56°)", + " Derry: (55.00°, -7.31°)", + " Reinickendorf: (52.56°, 13.34°)", + " La Oliva: (28.61°, -13.93°)", + " Nerang: (-27.99°, 153.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nerang: 14728.5 km from centroid", + " La Oliva: 4083.1 km from centroid", + " Derry: 3742.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nerang", + "FINAL ANSWER: Nerang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.46996, + "lon": 72.9521, + "name": "Tarsadi" + }, + { + "lat": 24.00139, + "lon": 97.86499, + "name": "Mengmao" + }, + { + "lat": 31.18975, + "lon": 108.41461, + "name": "Fengle" + }, + { + "lat": 22.77019, + "lon": 112.95776, + "name": "Shaping" + }, + { + "lat": 4.4516, + "lon": 7.17074, + "name": "Bonny" + } + ], + "question": "Which location is the geographic outlier among: Tarsadi, Mengmao, Fengle, Shaping, Bonny?", + "ground_truth": { + "answer": "Bonny", + "outlier_distance_km": 8034.9, + "second_furthest_km": 3416.7, + "clarity_ratio": 2.35, + "median_distance_km": 3067.4, + "distances_to_centroid": { + "Tarsadi": 721.8, + "Mengmao": 1882.9, + "Fengle": 3067.4, + "Shaping": 3416.7, + "Bonny": 8034.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tarsadi: (21.47°, 72.95°)", + " Mengmao: (24.00°, 97.86°)", + " Fengle: (31.19°, 108.41°)", + " Shaping: (22.77°, 112.96°)", + " Bonny: (4.45°, 7.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bonny: 8034.9 km from centroid", + " Shaping: 3416.7 km from centroid", + " Fengle: 3067.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bonny", + "FINAL ANSWER: Bonny" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.70004, + "lon": 9.2089, + "name": "Giussano" + }, + { + "lat": 43.71032, + "lon": -1.05366, + "name": "Dax" + }, + { + "lat": 43.61692, + "lon": 4.00739, + "name": "Mauguio" + }, + { + "lat": 56.48989, + "lon": 43.60114, + "name": "Novaya Balakhna" + }, + { + "lat": 6.92471, + "lon": 37.65263, + "name": "Gununo" + } + ], + "question": "Which location is the geographic outlier among: Giussano, Dax, Mauguio, Novaya Balakhna, Gununo?", + "ground_truth": { + "answer": "Gununo", + "outlier_distance_km": 4068.4, + "second_furthest_km": 2638.0, + "clarity_ratio": 1.54, + "median_distance_km": 1710.9, + "distances_to_centroid": { + "Giussano": 1053.0, + "Dax": 1710.9, + "Mauguio": 1312.1, + "Novaya Balakhna": 2638.0, + "Gununo": 4068.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Giussano: (45.70°, 9.21°)", + " Dax: (43.71°, -1.05°)", + " Mauguio: (43.62°, 4.01°)", + " Novaya Balakhna: (56.49°, 43.60°)", + " Gununo: (6.92°, 37.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gununo: 4068.4 km from centroid", + " Novaya Balakhna: 2638.0 km from centroid", + " Dax: 1710.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gununo", + "FINAL ANSWER: Gununo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + }, + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + }, + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": -5.1075, + "lon": -36.32028, + "name": "Guamaré" + } + ], + "question": "Which location is the geographic outlier among: Hurstville, Brisbane, Umina Beach, Hervey Bay, Guamaré?", + "ground_truth": { + "answer": "Guamaré", + "outlier_distance_km": 15401.3, + "second_furthest_km": 3849.8, + "clarity_ratio": 4.0, + "median_distance_km": 3847.7, + "distances_to_centroid": { + "Hurstville": 3667.0, + "Brisbane": 3847.7, + "Umina Beach": 3681.9, + "Hervey Bay": 3849.8, + "Guamaré": 15401.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hurstville: (-33.97°, 151.10°)", + " Brisbane: (-27.47°, 153.03°)", + " Umina Beach: (-33.52°, 151.31°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Guamaré: (-5.11°, -36.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guamaré: 15401.3 km from centroid", + " Hervey Bay: 3849.8 km from centroid", + " Brisbane: 3847.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guamaré", + "FINAL ANSWER: Guamaré" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.3, + "lon": 139.11667, + "name": "Tamamura" + }, + { + "lat": 36.84666, + "lon": 136.98355, + "name": "Himi" + }, + { + "lat": 21.15421, + "lon": 72.96141, + "name": "Chalthan" + }, + { + "lat": 43.35, + "lon": 142.38333, + "name": "Shimo-furano" + }, + { + "lat": 47.84965, + "lon": 12.06696, + "name": "Kolbermoor" + } + ], + "question": "Which location is the geographic outlier among: Tamamura, Himi, Chalthan, Shimo-furano, Kolbermoor?", + "ground_truth": { + "answer": "Kolbermoor", + "outlier_distance_km": 6962.5, + "second_furthest_km": 3567.9, + "clarity_ratio": 1.95, + "median_distance_km": 3402.3, + "distances_to_centroid": { + "Tamamura": 3402.3, + "Himi": 3203.2, + "Chalthan": 3206.1, + "Shimo-furano": 3567.9, + "Kolbermoor": 6962.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tamamura: (36.30°, 139.12°)", + " Himi: (36.85°, 136.98°)", + " Chalthan: (21.15°, 72.96°)", + " Shimo-furano: (43.35°, 142.38°)", + " Kolbermoor: (47.85°, 12.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kolbermoor: 6962.5 km from centroid", + " Shimo-furano: 3567.9 km from centroid", + " Tamamura: 3402.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kolbermoor", + "FINAL ANSWER: Kolbermoor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.55038, + "lon": 85.80249, + "name": "Chāībāsa" + }, + { + "lat": 20.74238, + "lon": 78.5871, + "name": "Sindi" + }, + { + "lat": 1.511, + "lon": 103.8198, + "name": "Taman Permas Jaya" + }, + { + "lat": 30.96187, + "lon": 108.24327, + "name": "Nanmen" + }, + { + "lat": 40.66689, + "lon": -111.88799, + "name": "Murray" + } + ], + "question": "Which location is the geographic outlier among: Chāībāsa, Sindi, Taman Permas Jaya, Nanmen, Murray?", + "ground_truth": { + "answer": "Murray", + "outlier_distance_km": 12732.1, + "second_furthest_km": 5991.5, + "clarity_ratio": 2.13, + "median_distance_km": 5487.5, + "distances_to_centroid": { + "Chāībāsa": 3362.2, + "Sindi": 2658.3, + "Taman Permas Jaya": 5991.5, + "Nanmen": 5487.5, + "Murray": 12732.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chāībāsa: (22.55°, 85.80°)", + " Sindi: (20.74°, 78.59°)", + " Taman Permas Jaya: (1.51°, 103.82°)", + " Nanmen: (30.96°, 108.24°)", + " Murray: (40.67°, -111.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Murray: 12732.1 km from centroid", + " Taman Permas Jaya: 5991.5 km from centroid", + " Nanmen: 5487.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Murray", + "FINAL ANSWER: Murray" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.0632, + "lon": -1.34222, + "name": "Banbury" + }, + { + "lat": 45.04248, + "lon": 7.6276, + "name": "Mirafiori Nord" + }, + { + "lat": 54.77676, + "lon": -1.57566, + "name": "Durham" + }, + { + "lat": 53.41392, + "lon": -2.90889, + "name": "Old Swan" + }, + { + "lat": 29.68817, + "lon": 106.58852, + "name": "Cuiyun" + } + ], + "question": "Which location is the geographic outlier among: Banbury, Mirafiori Nord, Durham, Old Swan, Cuiyun?", + "ground_truth": { + "answer": "Cuiyun", + "outlier_distance_km": 7282.8, + "second_furthest_km": 1877.8, + "clarity_ratio": 3.88, + "median_distance_km": 1834.3, + "distances_to_centroid": { + "Banbury": 1745.5, + "Mirafiori Nord": 1104.8, + "Durham": 1834.3, + "Old Swan": 1877.8, + "Cuiyun": 7282.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banbury: (52.06°, -1.34°)", + " Mirafiori Nord: (45.04°, 7.63°)", + " Durham: (54.78°, -1.58°)", + " Old Swan: (53.41°, -2.91°)", + " Cuiyun: (29.69°, 106.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cuiyun: 7282.8 km from centroid", + " Old Swan: 1877.8 km from centroid", + " Durham: 1834.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cuiyun", + "FINAL ANSWER: Cuiyun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.18555, + "lon": 73.45288, + "name": "Sādri" + }, + { + "lat": 34.7, + "lon": 137.85, + "name": "Iwata" + }, + { + "lat": 30.74485, + "lon": 107.81977, + "name": "Hexing" + }, + { + "lat": 34.50065, + "lon": 135.60211, + "name": "Tondabayashichō" + }, + { + "lat": -34.09345, + "lon": 21.25725, + "name": "Riversdale" + } + ], + "question": "Which location is the geographic outlier among: Sādri, Iwata, Hexing, Tondabayashichō, Riversdale?", + "ground_truth": { + "answer": "Riversdale", + "outlier_distance_km": 9736.8, + "second_furthest_km": 4582.7, + "clarity_ratio": 2.12, + "median_distance_km": 4377.3, + "distances_to_centroid": { + "Sādri": 2373.0, + "Iwata": 4582.7, + "Hexing": 1887.8, + "Tondabayashichō": 4377.3, + "Riversdale": 9736.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sādri: (25.19°, 73.45°)", + " Iwata: (34.70°, 137.85°)", + " Hexing: (30.74°, 107.82°)", + " Tondabayashichō: (34.50°, 135.60°)", + " Riversdale: (-34.09°, 21.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Riversdale: 9736.8 km from centroid", + " Iwata: 4582.7 km from centroid", + " Tondabayashichō: 4377.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Riversdale", + "FINAL ANSWER: Riversdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.6025, + "lon": -121.37854, + "name": "Arden-Arcade" + }, + { + "lat": 40.94871, + "lon": -73.73263, + "name": "Mamaroneck" + }, + { + "lat": 32.56645, + "lon": -115.35387, + "name": "Puebla" + }, + { + "lat": 35.44951, + "lon": -97.3967, + "name": "Midwest City" + }, + { + "lat": 39.96348, + "lon": -4.83076, + "name": "Talavera de la Reina" + } + ], + "question": "Which location is the geographic outlier among: Arden-Arcade, Mamaroneck, Puebla, Midwest City, Talavera de la Reina?", + "ground_truth": { + "answer": "Talavera de la Reina", + "outlier_distance_km": 6519.8, + "second_furthest_km": 3377.4, + "clarity_ratio": 1.93, + "median_distance_km": 3022.0, + "distances_to_centroid": { + "Arden-Arcade": 3377.4, + "Mamaroneck": 849.1, + "Puebla": 3022.0, + "Midwest City": 1346.5, + "Talavera de la Reina": 6519.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arden-Arcade: (38.60°, -121.38°)", + " Mamaroneck: (40.95°, -73.73°)", + " Puebla: (32.57°, -115.35°)", + " Midwest City: (35.45°, -97.40°)", + " Talavera de la Reina: (39.96°, -4.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Talavera de la Reina: 6519.8 km from centroid", + " Arden-Arcade: 3377.4 km from centroid", + " Puebla: 3022.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Talavera de la Reina", + "FINAL ANSWER: Talavera de la Reina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.33568, + "lon": 1.41797, + "name": "Ramsgate" + }, + { + "lat": 41.89184, + "lon": 48.41247, + "name": "Belidzhi" + }, + { + "lat": 43.66141, + "lon": 10.63067, + "name": "Pontedera" + }, + { + "lat": 50.72374, + "lon": 2.53729, + "name": "Hazebrouck" + }, + { + "lat": 8.56102, + "lon": 77.97214, + "name": "Nazareth" + } + ], + "question": "Which location is the geographic outlier among: Ramsgate, Belidzhi, Pontedera, Hazebrouck, Nazareth?", + "ground_truth": { + "answer": "Nazareth", + "outlier_distance_km": 5996.9, + "second_furthest_km": 2468.2, + "clarity_ratio": 2.43, + "median_distance_km": 2369.8, + "distances_to_centroid": { + "Ramsgate": 2468.2, + "Belidzhi": 1729.1, + "Pontedera": 1540.8, + "Hazebrouck": 2369.8, + "Nazareth": 5996.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ramsgate: (51.34°, 1.42°)", + " Belidzhi: (41.89°, 48.41°)", + " Pontedera: (43.66°, 10.63°)", + " Hazebrouck: (50.72°, 2.54°)", + " Nazareth: (8.56°, 77.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nazareth: 5996.9 km from centroid", + " Ramsgate: 2468.2 km from centroid", + " Hazebrouck: 2369.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nazareth", + "FINAL ANSWER: Nazareth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.94611, + "lon": -60.41806, + "name": "Rorainópolis" + }, + { + "lat": -21.13556, + "lon": -44.26167, + "name": "São João del Rei" + }, + { + "lat": -27.11639, + "lon": -49.99806, + "name": "Taió" + }, + { + "lat": -3.57972, + "lon": -59.13056, + "name": "Autazes" + }, + { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + } + ], + "question": "Which location is the geographic outlier among: Rorainópolis, São João del Rei, Taió, Autazes, Greensborough?", + "ground_truth": { + "answer": "Greensborough", + "outlier_distance_km": 13467.1, + "second_furthest_km": 5512.5, + "clarity_ratio": 2.44, + "median_distance_km": 5185.4, + "distances_to_centroid": { + "Rorainópolis": 5512.5, + "São João del Rei": 3218.1, + "Taió": 3855.5, + "Autazes": 5185.4, + "Greensborough": 13467.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rorainópolis: (0.95°, -60.42°)", + " São João del Rei: (-21.14°, -44.26°)", + " Taió: (-27.12°, -50.00°)", + " Autazes: (-3.58°, -59.13°)", + " Greensborough: (-37.70°, 145.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greensborough: 13467.1 km from centroid", + " Rorainópolis: 5512.5 km from centroid", + " Autazes: 5185.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greensborough", + "FINAL ANSWER: Greensborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 0.20387, + "lon": 35.105, + "name": "Kapsabet" + }, + { + "lat": -24.7, + "lon": 28.4, + "name": "Modimolle" + }, + { + "lat": -28.33523, + "lon": 31.41617, + "name": "Ulundi" + }, + { + "lat": 27.04514, + "lon": 31.31845, + "name": "Abū Tīj" + }, + { + "lat": 34.06862, + "lon": -117.93895, + "name": "West Covina" + } + ], + "question": "Which location is the geographic outlier among: Kapsabet, Modimolle, Ulundi, Abū Tīj, West Covina?", + "ground_truth": { + "answer": "West Covina", + "outlier_distance_km": 12579.3, + "second_furthest_km": 4603.7, + "clarity_ratio": 2.73, + "median_distance_km": 4238.1, + "distances_to_centroid": { + "Kapsabet": 3721.8, + "Modimolle": 4111.1, + "Ulundi": 4603.7, + "Abū Tīj": 4238.1, + "West Covina": 12579.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kapsabet: (0.20°, 35.10°)", + " Modimolle: (-24.70°, 28.40°)", + " Ulundi: (-28.34°, 31.42°)", + " Abū Tīj: (27.05°, 31.32°)", + " West Covina: (34.07°, -117.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " West Covina: 12579.3 km from centroid", + " Ulundi: 4603.7 km from centroid", + " Abū Tīj: 4238.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: West Covina", + "FINAL ANSWER: West Covina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.13556, + "lon": -44.26167, + "name": "São João del Rei" + }, + { + "lat": -27.16944, + "lon": -53.71222, + "name": "Itapiranga" + }, + { + "lat": -5.40232, + "lon": -80.74224, + "name": "La Unión" + }, + { + "lat": -29.65056, + "lon": -50.78056, + "name": "Taquara" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + } + ], + "question": "Which location is the geographic outlier among: São João del Rei, Itapiranga, La Unión, Taquara, Saint Kilda?", + "ground_truth": { + "answer": "Saint Kilda", + "outlier_distance_km": 12853.9, + "second_furthest_km": 7112.9, + "clarity_ratio": 1.81, + "median_distance_km": 3689.2, + "distances_to_centroid": { + "São João del Rei": 2823.4, + "Itapiranga": 3689.2, + "La Unión": 7112.9, + "Taquara": 3399.0, + "Saint Kilda": 12853.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São João del Rei: (-21.14°, -44.26°)", + " Itapiranga: (-27.17°, -53.71°)", + " La Unión: (-5.40°, -80.74°)", + " Taquara: (-29.65°, -50.78°)", + " Saint Kilda: (-37.87°, 144.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Kilda: 12853.9 km from centroid", + " La Unión: 7112.9 km from centroid", + " Itapiranga: 3689.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Kilda", + "FINAL ANSWER: Saint Kilda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.72855, + "lon": -122.38107, + "name": "Bayview-Hunters Point" + }, + { + "lat": 39.02756, + "lon": -84.72411, + "name": "Burlington" + }, + { + "lat": 22.62795, + "lon": -101.71417, + "name": "Salinas de Hidalgo" + }, + { + "lat": 38.90372, + "lon": -77.00598, + "name": "NoMa" + }, + { + "lat": 30.3708, + "lon": 113.44294, + "name": "Xiantao" + } + ], + "question": "Which location is the geographic outlier among: Bayview-Hunters Point, Burlington, Salinas de Hidalgo, NoMa, Xiantao?", + "ground_truth": { + "answer": "Xiantao", + "outlier_distance_km": 12775.1, + "second_furthest_km": 6009.0, + "clarity_ratio": 2.13, + "median_distance_km": 4748.7, + "distances_to_centroid": { + "Bayview-Hunters Point": 6009.0, + "Burlington": 2757.7, + "Salinas de Hidalgo": 4748.7, + "NoMa": 2092.7, + "Xiantao": 12775.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bayview-Hunters Point: (37.73°, -122.38°)", + " Burlington: (39.03°, -84.72°)", + " Salinas de Hidalgo: (22.63°, -101.71°)", + " NoMa: (38.90°, -77.01°)", + " Xiantao: (30.37°, 113.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Xiantao: 12775.1 km from centroid", + " Bayview-Hunters Point: 6009.0 km from centroid", + " Salinas de Hidalgo: 4748.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Xiantao", + "FINAL ANSWER: Xiantao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.66917, + "lon": -42.07611, + "name": "Itaocara" + }, + { + "lat": -22.50917, + "lon": -48.55778, + "name": "Igaraçu do Tietê" + }, + { + "lat": -3.79833, + "lon": -40.26056, + "name": "Forquilha" + }, + { + "lat": -15.84003, + "lon": -70.02198, + "name": "Puno" + }, + { + "lat": 13.69157, + "lon": 99.92982, + "name": "Bang Phae" + } + ], + "question": "Which location is the geographic outlier among: Itaocara, Igaraçu do Tietê, Forquilha, Puno, Bang Phae?", + "ground_truth": { + "answer": "Bang Phae", + "outlier_distance_km": 13502.1, + "second_furthest_km": 5426.5, + "clarity_ratio": 2.49, + "median_distance_km": 3321.2, + "distances_to_centroid": { + "Itaocara": 2669.3, + "Igaraçu do Tietê": 3321.2, + "Forquilha": 2319.2, + "Puno": 5426.5, + "Bang Phae": 13502.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itaocara: (-21.67°, -42.08°)", + " Igaraçu do Tietê: (-22.51°, -48.56°)", + " Forquilha: (-3.80°, -40.26°)", + " Puno: (-15.84°, -70.02°)", + " Bang Phae: (13.69°, 99.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bang Phae: 13502.1 km from centroid", + " Puno: 5426.5 km from centroid", + " Igaraçu do Tietê: 3321.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bang Phae", + "FINAL ANSWER: Bang Phae" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.05761, + "lon": 109.59088, + "name": "Baidi" + }, + { + "lat": 8.56688, + "lon": 76.99129, + "name": "Kidarakulam" + }, + { + "lat": 35.52336, + "lon": 119.51009, + "name": "Heshan" + }, + { + "lat": -7.54595, + "lon": 112.23307, + "name": "Jombang" + }, + { + "lat": 38.36067, + "lon": -75.59937, + "name": "Salisbury" + } + ], + "question": "Which location is the geographic outlier among: Baidi, Kidarakulam, Heshan, Jombang, Salisbury?", + "ground_truth": { + "answer": "Salisbury", + "outlier_distance_km": 12409.8, + "second_furthest_km": 5739.7, + "clarity_ratio": 2.16, + "median_distance_km": 5174.0, + "distances_to_centroid": { + "Baidi": 4216.4, + "Kidarakulam": 1670.5, + "Heshan": 5174.0, + "Jombang": 5739.7, + "Salisbury": 12409.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baidi: (31.06°, 109.59°)", + " Kidarakulam: (8.57°, 76.99°)", + " Heshan: (35.52°, 119.51°)", + " Jombang: (-7.55°, 112.23°)", + " Salisbury: (38.36°, -75.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Salisbury: 12409.8 km from centroid", + " Jombang: 5739.7 km from centroid", + " Heshan: 5174.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Salisbury", + "FINAL ANSWER: Salisbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.17146, + "lon": 7.00525, + "name": "Enugu-Ukwu" + }, + { + "lat": 11.19152, + "lon": 40.01675, + "name": "Batī" + }, + { + "lat": 7.09316, + "lon": 4.83528, + "name": "Ondo" + }, + { + "lat": 10.95627, + "lon": 36.50456, + "name": "Chagni" + }, + { + "lat": -36.8, + "lon": 174.75, + "name": "North Shore" + } + ], + "question": "Which location is the geographic outlier among: Enugu-Ukwu, Batī, Ondo, Chagni, North Shore?", + "ground_truth": { + "answer": "North Shore", + "outlier_distance_km": 12789.6, + "second_furthest_km": 5363.0, + "clarity_ratio": 2.38, + "median_distance_km": 5113.1, + "distances_to_centroid": { + "Enugu-Ukwu": 5113.1, + "Batī": 1888.5, + "Ondo": 5363.0, + "Chagni": 2175.8, + "North Shore": 12789.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Enugu-Ukwu: (6.17°, 7.01°)", + " Batī: (11.19°, 40.02°)", + " Ondo: (7.09°, 4.84°)", + " Chagni: (10.96°, 36.50°)", + " North Shore: (-36.80°, 174.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " North Shore: 12789.6 km from centroid", + " Ondo: 5363.0 km from centroid", + " Enugu-Ukwu: 5113.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: North Shore", + "FINAL ANSWER: North Shore" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.55, + "lon": 37.48333, + "name": "Dembech’a" + }, + { + "lat": 10.16756, + "lon": 12.73684, + "name": "Gombi" + }, + { + "lat": 9.92849, + "lon": 8.89212, + "name": "Jos" + }, + { + "lat": 29.85, + "lon": 31.26667, + "name": "Al Badrashayn" + }, + { + "lat": -27.25204, + "lon": 152.99226, + "name": "Kallangur" + } + ], + "question": "Which location is the geographic outlier among: Dembech’a, Gombi, Jos, Al Badrashayn, Kallangur?", + "ground_truth": { + "answer": "Kallangur", + "outlier_distance_km": 11758.5, + "second_furthest_km": 4390.0, + "clarity_ratio": 2.68, + "median_distance_km": 3970.3, + "distances_to_centroid": { + "Dembech’a": 1304.3, + "Gombi": 3970.3, + "Jos": 4390.0, + "Al Badrashayn": 3157.6, + "Kallangur": 11758.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dembech’a: (10.55°, 37.48°)", + " Gombi: (10.17°, 12.74°)", + " Jos: (9.93°, 8.89°)", + " Al Badrashayn: (29.85°, 31.27°)", + " Kallangur: (-27.25°, 152.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kallangur: 11758.5 km from centroid", + " Jos: 4390.0 km from centroid", + " Gombi: 3970.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kallangur", + "FINAL ANSWER: Kallangur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.84853, + "lon": 174.76349, + "name": "Auckland" + }, + { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + }, + { + "lat": -37.91806, + "lon": 145.03544, + "name": "Bentleigh" + }, + { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + { + "lat": 37.15222, + "lon": 127.07056, + "name": "Osan" + } + ], + "question": "Which location is the geographic outlier among: Auckland, Greensborough, Bentleigh, Mosman, Osan?", + "ground_truth": { + "answer": "Osan", + "outlier_distance_km": 6937.4, + "second_furthest_km": 3016.6, + "clarity_ratio": 2.3, + "median_distance_km": 1821.8, + "distances_to_centroid": { + "Auckland": 3016.6, + "Greensborough": 1797.3, + "Bentleigh": 1821.8, + "Mosman": 1359.2, + "Osan": 6937.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auckland: (-36.85°, 174.76°)", + " Greensborough: (-37.70°, 145.10°)", + " Bentleigh: (-37.92°, 145.04°)", + " Mosman: (-33.84°, 151.24°)", + " Osan: (37.15°, 127.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Osan: 6937.4 km from centroid", + " Auckland: 3016.6 km from centroid", + " Bentleigh: 1821.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Osan", + "FINAL ANSWER: Osan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.76, + "lon": -40.81639, + "name": "Frecheirinha" + }, + { + "lat": -3.92333, + "lon": -40.88944, + "name": "Ibiapina" + }, + { + "lat": -23.59245, + "lon": -46.78561, + "name": "Raposo Tavares" + }, + { + "lat": 6.01335, + "lon": -73.67352, + "name": "Vélez" + }, + { + "lat": 53.25243, + "lon": 14.48831, + "name": "Gryfino" + } + ], + "question": "Which location is the geographic outlier among: Frecheirinha, Ibiapina, Raposo Tavares, Vélez, Gryfino?", + "ground_truth": { + "answer": "Gryfino", + "outlier_distance_km": 7072.6, + "second_furthest_km": 3997.3, + "clarity_ratio": 1.77, + "median_distance_km": 3397.5, + "distances_to_centroid": { + "Frecheirinha": 1102.5, + "Ibiapina": 1122.3, + "Raposo Tavares": 3397.5, + "Vélez": 3997.3, + "Gryfino": 7072.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Frecheirinha: (-3.76°, -40.82°)", + " Ibiapina: (-3.92°, -40.89°)", + " Raposo Tavares: (-23.59°, -46.79°)", + " Vélez: (6.01°, -73.67°)", + " Gryfino: (53.25°, 14.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gryfino: 7072.6 km from centroid", + " Vélez: 3997.3 km from centroid", + " Raposo Tavares: 3397.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gryfino", + "FINAL ANSWER: Gryfino" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + }, + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -37.97695, + "lon": 145.25866, + "name": "Endeavour Hills" + }, + { + "lat": -37.62581, + "lon": 144.92555, + "name": "Roxburgh Park" + }, + { + "lat": 35.4868, + "lon": -80.86007, + "name": "Cornelius" + } + ], + "question": "Which location is the geographic outlier among: Lilydale, Caulfield North, Endeavour Hills, Roxburgh Park, Cornelius?", + "ground_truth": { + "answer": "Cornelius", + "outlier_distance_km": 18640.9, + "second_furthest_km": 4594.3, + "clarity_ratio": 4.06, + "median_distance_km": 4589.6, + "distances_to_centroid": { + "Lilydale": 4594.3, + "Caulfield North": 4567.8, + "Endeavour Hills": 4589.6, + "Roxburgh Park": 4555.5, + "Cornelius": 18640.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lilydale: (-37.75°, 145.35°)", + " Caulfield North: (-37.87°, 145.02°)", + " Endeavour Hills: (-37.98°, 145.26°)", + " Roxburgh Park: (-37.63°, 144.93°)", + " Cornelius: (35.49°, -80.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cornelius: 18640.9 km from centroid", + " Lilydale: 4594.3 km from centroid", + " Endeavour Hills: 4589.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cornelius", + "FINAL ANSWER: Cornelius" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.26778, + "lon": 87.24855, + "name": "Dumka" + }, + { + "lat": 16.33685, + "lon": 74.96768, + "name": "Mudalgi" + }, + { + "lat": 27.19395, + "lon": 95.31929, + "name": "Nāmrup" + }, + { + "lat": 23.80366, + "lon": 72.39101, + "name": "Unjha" + }, + { + "lat": 2.77717, + "lon": -75.25642, + "name": "Rivera" + } + ], + "question": "Which location is the geographic outlier among: Dumka, Mudalgi, Nāmrup, Unjha, Rivera?", + "ground_truth": { + "answer": "Rivera", + "outlier_distance_km": 13659.9, + "second_furthest_km": 4611.1, + "clarity_ratio": 2.96, + "median_distance_km": 3792.0, + "distances_to_centroid": { + "Dumka": 3792.0, + "Mudalgi": 2560.8, + "Nāmrup": 4611.1, + "Unjha": 2286.2, + "Rivera": 13659.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dumka: (24.27°, 87.25°)", + " Mudalgi: (16.34°, 74.97°)", + " Nāmrup: (27.19°, 95.32°)", + " Unjha: (23.80°, 72.39°)", + " Rivera: (2.78°, -75.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rivera: 13659.9 km from centroid", + " Nāmrup: 4611.1 km from centroid", + " Dumka: 3792.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rivera", + "FINAL ANSWER: Rivera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.01636, + "lon": 76.34168, + "name": "Kakkanad" + }, + { + "lat": 14.31812, + "lon": 120.76609, + "name": "Naic" + }, + { + "lat": 28.9629, + "lon": 106.92844, + "name": "Wansheng" + }, + { + "lat": 10.1624, + "lon": 123.7076, + "name": "San Fernando" + }, + { + "lat": -3.54281, + "lon": -45.60852, + "name": "Bom Jardim" + } + ], + "question": "Which location is the geographic outlier among: Kakkanad, Naic, Wansheng, San Fernando, Bom Jardim?", + "ground_truth": { + "answer": "Bom Jardim", + "outlier_distance_km": 13571.8, + "second_furthest_km": 5157.4, + "clarity_ratio": 2.63, + "median_distance_km": 4801.0, + "distances_to_centroid": { + "Kakkanad": 218.9, + "Naic": 4801.0, + "Wansheng": 3677.6, + "San Fernando": 5157.4, + "Bom Jardim": 13571.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kakkanad: (10.02°, 76.34°)", + " Naic: (14.32°, 120.77°)", + " Wansheng: (28.96°, 106.93°)", + " San Fernando: (10.16°, 123.71°)", + " Bom Jardim: (-3.54°, -45.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bom Jardim: 13571.8 km from centroid", + " San Fernando: 5157.4 km from centroid", + " Naic: 4801.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bom Jardim", + "FINAL ANSWER: Bom Jardim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.62581, + "lon": 144.92555, + "name": "Roxburgh Park" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + }, + { + "lat": -33.9681, + "lon": 151.13564, + "name": "Kogarah" + }, + { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + { + "lat": -28.61961, + "lon": 28.20966, + "name": "Fouriesburg" + } + ], + "question": "Which location is the geographic outlier among: Roxburgh Park, Bracken Ridge, Kogarah, Caulfield North, Fouriesburg?", + "ground_truth": { + "answer": "Fouriesburg", + "outlier_distance_km": 8846.1, + "second_furthest_km": 2809.7, + "clarity_ratio": 3.15, + "median_distance_km": 2467.3, + "distances_to_centroid": { + "Roxburgh Park": 1918.7, + "Bracken Ridge": 2809.7, + "Kogarah": 2467.3, + "Caulfield North": 1931.9, + "Fouriesburg": 8846.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Roxburgh Park: (-37.63°, 144.93°)", + " Bracken Ridge: (-27.32°, 153.03°)", + " Kogarah: (-33.97°, 151.14°)", + " Caulfield North: (-37.87°, 145.02°)", + " Fouriesburg: (-28.62°, 28.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fouriesburg: 8846.1 km from centroid", + " Bracken Ridge: 2809.7 km from centroid", + " Kogarah: 2467.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fouriesburg", + "FINAL ANSWER: Fouriesburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.10149, + "lon": -84.51938, + "name": "Woodstock" + }, + { + "lat": 47.38093, + "lon": -122.23484, + "name": "Kent" + }, + { + "lat": 37.8227, + "lon": -121.27661, + "name": "Lathrop" + }, + { + "lat": 34.14778, + "lon": -119.19511, + "name": "Port Hueneme" + }, + { + "lat": 6.8485, + "lon": 3.64633, + "name": "Shagamu" + } + ], + "question": "Which location is the geographic outlier among: Woodstock, Kent, Lathrop, Port Hueneme, Shagamu?", + "ground_truth": { + "answer": "Shagamu", + "outlier_distance_km": 9825.2, + "second_furthest_km": 3297.3, + "clarity_ratio": 2.98, + "median_distance_km": 3020.2, + "distances_to_centroid": { + "Woodstock": 452.0, + "Kent": 3297.3, + "Lathrop": 3020.2, + "Port Hueneme": 2838.0, + "Shagamu": 9825.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Woodstock: (34.10°, -84.52°)", + " Kent: (47.38°, -122.23°)", + " Lathrop: (37.82°, -121.28°)", + " Port Hueneme: (34.15°, -119.20°)", + " Shagamu: (6.85°, 3.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shagamu: 9825.2 km from centroid", + " Kent: 3297.3 km from centroid", + " Lathrop: 3020.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shagamu", + "FINAL ANSWER: Shagamu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.83333, + "lon": 150.98333, + "name": "Merrylands" + }, + { + "lat": -43.30437, + "lon": 172.58356, + "name": "Rangiora" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + }, + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + { + "lat": 5.65396, + "lon": 0.0264, + "name": "Tema New Town" + } + ], + "question": "Which location is the geographic outlier among: Merrylands, Rangiora, Perth, Maroochydore, Tema New Town?", + "ground_truth": { + "answer": "Tema New Town", + "outlier_distance_km": 13122.8, + "second_furthest_km": 5203.5, + "clarity_ratio": 2.52, + "median_distance_km": 3436.9, + "distances_to_centroid": { + "Merrylands": 3232.7, + "Rangiora": 5203.5, + "Perth": 708.2, + "Maroochydore": 3436.9, + "Tema New Town": 13122.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Merrylands: (-33.83°, 150.98°)", + " Rangiora: (-43.30°, 172.58°)", + " Perth: (-31.95°, 115.86°)", + " Maroochydore: (-26.66°, 153.10°)", + " Tema New Town: (5.65°, 0.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tema New Town: 13122.8 km from centroid", + " Rangiora: 5203.5 km from centroid", + " Maroochydore: 3436.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tema New Town", + "FINAL ANSWER: Tema New Town" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.70365, + "lon": -89.40731, + "name": "Washington" + }, + { + "lat": 38.77261, + "lon": -77.22109, + "name": "West Springfield" + }, + { + "lat": 38.88584, + "lon": -94.53301, + "name": "Grandview" + }, + { + "lat": 22.74678, + "lon": -102.5188, + "name": "Guadalupe" + }, + { + "lat": -4.23116, + "lon": -69.93858, + "name": "Tabatinga" + } + ], + "question": "Which location is the geographic outlier among: Washington, West Springfield, Grandview, Guadalupe, Tabatinga?", + "ground_truth": { + "answer": "Tabatinga", + "outlier_distance_km": 3949.4, + "second_furthest_km": 1670.6, + "clarity_ratio": 2.36, + "median_distance_km": 1543.9, + "distances_to_centroid": { + "Washington": 1502.3, + "West Springfield": 1543.9, + "Grandview": 1470.6, + "Guadalupe": 1670.6, + "Tabatinga": 3949.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Washington: (40.70°, -89.41°)", + " West Springfield: (38.77°, -77.22°)", + " Grandview: (38.89°, -94.53°)", + " Guadalupe: (22.75°, -102.52°)", + " Tabatinga: (-4.23°, -69.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tabatinga: 3949.4 km from centroid", + " Guadalupe: 1670.6 km from centroid", + " West Springfield: 1543.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tabatinga", + "FINAL ANSWER: Tabatinga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.00611, + "lon": -35.69722, + "name": "Cumaru" + }, + { + "lat": -26.14944, + "lon": -53.02611, + "name": "Marmeleiro" + }, + { + "lat": 2.43986, + "lon": -60.91146, + "name": "Mucajaí" + }, + { + "lat": -14.52972, + "lon": -40.36528, + "name": "Poções" + }, + { + "lat": 52.09237, + "lon": -1.94887, + "name": "Evesham" + } + ], + "question": "Which location is the geographic outlier among: Cumaru, Marmeleiro, Mucajaí, Poções, Evesham?", + "ground_truth": { + "answer": "Evesham", + "outlier_distance_km": 6596.0, + "second_furthest_km": 3420.0, + "clarity_ratio": 1.93, + "median_distance_km": 2507.0, + "distances_to_centroid": { + "Cumaru": 1063.1, + "Marmeleiro": 3420.0, + "Mucajaí": 2507.0, + "Poções": 1759.2, + "Evesham": 6596.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cumaru: (-8.01°, -35.70°)", + " Marmeleiro: (-26.15°, -53.03°)", + " Mucajaí: (2.44°, -60.91°)", + " Poções: (-14.53°, -40.37°)", + " Evesham: (52.09°, -1.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Evesham: 6596.0 km from centroid", + " Marmeleiro: 3420.0 km from centroid", + " Mucajaí: 2507.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Evesham", + "FINAL ANSWER: Evesham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.85, + "lon": 31.26667, + "name": "Al Badrashayn" + }, + { + "lat": -26.26781, + "lon": 27.85849, + "name": "Soweto" + }, + { + "lat": -26.93366, + "lon": 29.24152, + "name": "Standerton" + }, + { + "lat": 6.09408, + "lon": -0.25913, + "name": "Koforidua" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + } + ], + "question": "Which location is the geographic outlier among: Al Badrashayn, Soweto, Standerton, Koforidua, Levin?", + "ground_truth": { + "answer": "Levin", + "outlier_distance_km": 11748.2, + "second_furthest_km": 6176.0, + "clarity_ratio": 1.9, + "median_distance_km": 5145.9, + "distances_to_centroid": { + "Al Badrashayn": 5145.9, + "Soweto": 3069.3, + "Standerton": 2984.7, + "Koforidua": 6176.0, + "Levin": 11748.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Badrashayn: (29.85°, 31.27°)", + " Soweto: (-26.27°, 27.86°)", + " Standerton: (-26.93°, 29.24°)", + " Koforidua: (6.09°, -0.26°)", + " Levin: (-40.63°, 175.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Levin: 11748.2 km from centroid", + " Koforidua: 6176.0 km from centroid", + " Al Badrashayn: 5145.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Levin", + "FINAL ANSWER: Levin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 59.70056, + "lon": 30.78472, + "name": "Nikol’skoye" + }, + { + "lat": 51.37, + "lon": 6.16806, + "name": "Venlo" + }, + { + "lat": 28.92313, + "lon": -13.66579, + "name": "Puerto del Carmen" + }, + { + "lat": 28.31122, + "lon": -16.41276, + "name": "Güimar" + }, + { + "lat": 33.59259, + "lon": -84.67294, + "name": "South Fulton" + } + ], + "question": "Which location is the geographic outlier among: Nikol’skoye, Venlo, Puerto del Carmen, Güimar, South Fulton?", + "ground_truth": { + "answer": "South Fulton", + "outlier_distance_km": 6029.0, + "second_furthest_km": 3830.2, + "clarity_ratio": 1.57, + "median_distance_km": 2066.2, + "distances_to_centroid": { + "Nikol’skoye": 3830.2, + "Venlo": 2066.2, + "Puerto del Carmen": 1285.5, + "Güimar": 1344.2, + "South Fulton": 6029.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nikol’skoye: (59.70°, 30.78°)", + " Venlo: (51.37°, 6.17°)", + " Puerto del Carmen: (28.92°, -13.67°)", + " Güimar: (28.31°, -16.41°)", + " South Fulton: (33.59°, -84.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " South Fulton: 6029.0 km from centroid", + " Nikol’skoye: 3830.2 km from centroid", + " Venlo: 2066.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: South Fulton", + "FINAL ANSWER: South Fulton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.42497, + "lon": -62.08404, + "name": "San Francisco" + }, + { + "lat": -5.68167, + "lon": -43.09333, + "name": "Parnarama" + }, + { + "lat": -17.81361, + "lon": -50.59694, + "name": "Santa Helena de Goiás" + }, + { + "lat": -35.4232, + "lon": -71.64974, + "name": "Talca" + }, + { + "lat": 27.29393, + "lon": -80.35033, + "name": "Port Saint Lucie" + } + ], + "question": "Which location is the geographic outlier among: San Francisco, Parnarama, Santa Helena de Goiás, Talca, Port Saint Lucie?", + "ground_truth": { + "answer": "Port Saint Lucie", + "outlier_distance_km": 4878.5, + "second_furthest_km": 2731.9, + "clarity_ratio": 1.79, + "median_distance_km": 2166.8, + "distances_to_centroid": { + "San Francisco": 2092.8, + "Parnarama": 2166.8, + "Santa Helena de Goiás": 1309.9, + "Talca": 2731.9, + "Port Saint Lucie": 4878.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Francisco: (-31.42°, -62.08°)", + " Parnarama: (-5.68°, -43.09°)", + " Santa Helena de Goiás: (-17.81°, -50.60°)", + " Talca: (-35.42°, -71.65°)", + " Port Saint Lucie: (27.29°, -80.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Port Saint Lucie: 4878.5 km from centroid", + " Talca: 2731.9 km from centroid", + " Parnarama: 2166.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Port Saint Lucie", + "FINAL ANSWER: Port Saint Lucie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.17103, + "lon": 18.9041, + "name": "Mikołów" + }, + { + "lat": 51.14987, + "lon": 11.80979, + "name": "Naumburg" + }, + { + "lat": 52.43854, + "lon": 4.82643, + "name": "Zaandam" + }, + { + "lat": 51.29652, + "lon": -0.3338, + "name": "Leatherhead" + }, + { + "lat": 42.28308, + "lon": -87.95313, + "name": "Libertyville" + } + ], + "question": "Which location is the geographic outlier among: Mikołów, Naumburg, Zaandam, Leatherhead, Libertyville?", + "ground_truth": { + "answer": "Libertyville", + "outlier_distance_km": 5777.8, + "second_furthest_km": 2100.8, + "clarity_ratio": 2.75, + "median_distance_km": 1592.5, + "distances_to_centroid": { + "Mikołów": 2100.8, + "Naumburg": 1592.5, + "Zaandam": 1124.0, + "Leatherhead": 751.6, + "Libertyville": 5777.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mikołów: (50.17°, 18.90°)", + " Naumburg: (51.15°, 11.81°)", + " Zaandam: (52.44°, 4.83°)", + " Leatherhead: (51.30°, -0.33°)", + " Libertyville: (42.28°, -87.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Libertyville: 5777.8 km from centroid", + " Mikołów: 2100.8 km from centroid", + " Naumburg: 1592.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Libertyville", + "FINAL ANSWER: Libertyville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -37.58333, + "lon": 145.03333, + "name": "Wollert" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": -43.58333, + "lon": 172.38333, + "name": "Rolleston" + }, + { + "lat": 27.06309, + "lon": 31.34425, + "name": "As Sāḩil" + } + ], + "question": "Which location is the geographic outlier among: Bairnsdale, Wollert, Carrum Downs, Rolleston, As Sāḩil?", + "ground_truth": { + "answer": "As Sāḩil", + "outlier_distance_km": 11925.6, + "second_furthest_km": 4408.5, + "clarity_ratio": 2.71, + "median_distance_km": 2238.6, + "distances_to_centroid": { + "Bairnsdale": 2238.6, + "Wollert": 2032.9, + "Carrum Downs": 2075.8, + "Rolleston": 4408.5, + "As Sāḩil": 11925.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bairnsdale: (-37.82°, 147.61°)", + " Wollert: (-37.58°, 145.03°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Rolleston: (-43.58°, 172.38°)", + " As Sāḩil: (27.06°, 31.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " As Sāḩil: 11925.6 km from centroid", + " Rolleston: 4408.5 km from centroid", + " Bairnsdale: 2238.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: As Sāḩil", + "FINAL ANSWER: As Sāḩil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.74115, + "lon": -87.61255, + "name": "Chatham" + }, + { + "lat": 44.64024, + "lon": -93.14355, + "name": "Farmington" + }, + { + "lat": 33.78391, + "lon": -116.95864, + "name": "San Jacinto" + }, + { + "lat": 19.28279, + "lon": -99.5929, + "name": "San Jerónimo" + }, + { + "lat": 57.2145, + "lon": 41.92555, + "name": "Vichuga" + } + ], + "question": "Which location is the geographic outlier among: Chatham, Farmington, San Jacinto, San Jerónimo, Vichuga?", + "ground_truth": { + "answer": "Vichuga", + "outlier_distance_km": 7598.4, + "second_furthest_km": 4100.1, + "clarity_ratio": 1.85, + "median_distance_km": 3524.8, + "distances_to_centroid": { + "Chatham": 1420.5, + "Farmington": 1910.0, + "San Jacinto": 4100.1, + "San Jerónimo": 3524.8, + "Vichuga": 7598.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chatham: (41.74°, -87.61°)", + " Farmington: (44.64°, -93.14°)", + " San Jacinto: (33.78°, -116.96°)", + " San Jerónimo: (19.28°, -99.59°)", + " Vichuga: (57.21°, 41.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vichuga: 7598.4 km from centroid", + " San Jacinto: 4100.1 km from centroid", + " San Jerónimo: 3524.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vichuga", + "FINAL ANSWER: Vichuga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 32.84069, + "lon": -83.6324, + "name": "Macon" + }, + { + "lat": 28.55778, + "lon": -81.4534, + "name": "Pine Hills" + }, + { + "lat": 29.70523, + "lon": -95.12382, + "name": "Deer Park" + }, + { + "lat": 39.28844, + "lon": -77.20387, + "name": "Damascus" + }, + { + "lat": -26.85213, + "lon": 26.66672, + "name": "Klerksdorp" + } + ], + "question": "Which location is the geographic outlier among: Macon, Pine Hills, Deer Park, Damascus, Klerksdorp?", + "ground_truth": { + "answer": "Klerksdorp", + "outlier_distance_km": 10918.4, + "second_furthest_km": 3451.4, + "clarity_ratio": 3.16, + "median_distance_km": 2516.0, + "distances_to_centroid": { + "Macon": 2515.4, + "Pine Hills": 2133.8, + "Deer Park": 3451.4, + "Damascus": 2516.0, + "Klerksdorp": 10918.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macon: (32.84°, -83.63°)", + " Pine Hills: (28.56°, -81.45°)", + " Deer Park: (29.71°, -95.12°)", + " Damascus: (39.29°, -77.20°)", + " Klerksdorp: (-26.85°, 26.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Klerksdorp: 10918.4 km from centroid", + " Deer Park: 3451.4 km from centroid", + " Damascus: 2516.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Klerksdorp", + "FINAL ANSWER: Klerksdorp" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 59.2239, + "lon": 39.88398, + "name": "Vologda" + }, + { + "lat": 46.98956, + "lon": 3.159, + "name": "Nevers" + }, + { + "lat": 51.75, + "lon": -2.2, + "name": "Stroud" + }, + { + "lat": 45.16031, + "lon": 10.79784, + "name": "Mantova" + }, + { + "lat": 15.18636, + "lon": 100.12353, + "name": "Chai Nat" + } + ], + "question": "Which location is the geographic outlier among: Vologda, Nevers, Stroud, Mantova, Chai Nat?", + "ground_truth": { + "answer": "Chai Nat", + "outlier_distance_km": 7230.1, + "second_furthest_km": 2570.7, + "clarity_ratio": 2.81, + "median_distance_km": 2146.7, + "distances_to_centroid": { + "Vologda": 1847.9, + "Nevers": 2146.7, + "Stroud": 2570.7, + "Mantova": 1558.3, + "Chai Nat": 7230.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vologda: (59.22°, 39.88°)", + " Nevers: (46.99°, 3.16°)", + " Stroud: (51.75°, -2.20°)", + " Mantova: (45.16°, 10.80°)", + " Chai Nat: (15.19°, 100.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chai Nat: 7230.1 km from centroid", + " Stroud: 2570.7 km from centroid", + " Nevers: 2146.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chai Nat", + "FINAL ANSWER: Chai Nat" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.85677, + "lon": -74.12848, + "name": "Passaic" + }, + { + "lat": 20.06417, + "lon": -98.71722, + "name": "La Providencia Siglo XXI" + }, + { + "lat": 38.98872, + "lon": -76.98136, + "name": "Langley Park" + }, + { + "lat": 40.8351, + "lon": -73.13122, + "name": "Lake Ronkonkoma" + }, + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + } + ], + "question": "Which location is the geographic outlier among: Passaic, La Providencia Siglo XXI, Langley Park, Lake Ronkonkoma, Banora Point?", + "ground_truth": { + "answer": "Banora Point", + "outlier_distance_km": 19036.5, + "second_furthest_km": 6669.1, + "clarity_ratio": 2.85, + "median_distance_km": 4456.5, + "distances_to_centroid": { + "Passaic": 4269.2, + "La Providencia Siglo XXI": 6669.1, + "Langley Park": 4456.5, + "Lake Ronkonkoma": 4188.1, + "Banora Point": 19036.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Passaic: (40.86°, -74.13°)", + " La Providencia Siglo XXI: (20.06°, -98.72°)", + " Langley Park: (38.99°, -76.98°)", + " Lake Ronkonkoma: (40.84°, -73.13°)", + " Banora Point: (-28.21°, 153.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Banora Point: 19036.5 km from centroid", + " La Providencia Siglo XXI: 6669.1 km from centroid", + " Langley Park: 4456.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Banora Point", + "FINAL ANSWER: Banora Point" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.62917, + "lon": -43.89806, + "name": "Piraí" + }, + { + "lat": -7.51651, + "lon": -63.03105, + "name": "Humaitá" + }, + { + "lat": -35.84667, + "lon": -71.59308, + "name": "Linares" + }, + { + "lat": -26.34067, + "lon": -60.43207, + "name": "Tres Isletas" + }, + { + "lat": 53.86437, + "lon": -1.68743, + "name": "Yeadon" + } + ], + "question": "Which location is the geographic outlier among: Piraí, Humaitá, Linares, Tres Isletas, Yeadon?", + "ground_truth": { + "answer": "Yeadon", + "outlier_distance_km": 8102.5, + "second_furthest_km": 3934.8, + "clarity_ratio": 2.06, + "median_distance_km": 2447.6, + "distances_to_centroid": { + "Piraí": 1721.3, + "Humaitá": 1642.6, + "Linares": 3934.8, + "Tres Isletas": 2447.6, + "Yeadon": 8102.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piraí: (-22.63°, -43.90°)", + " Humaitá: (-7.52°, -63.03°)", + " Linares: (-35.85°, -71.59°)", + " Tres Isletas: (-26.34°, -60.43°)", + " Yeadon: (53.86°, -1.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yeadon: 8102.5 km from centroid", + " Linares: 3934.8 km from centroid", + " Tres Isletas: 2447.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yeadon", + "FINAL ANSWER: Yeadon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.67037, + "lon": -71.30201, + "name": "Dracut" + }, + { + "lat": 39.34589, + "lon": -84.5605, + "name": "Fairfield" + }, + { + "lat": 17.55602, + "lon": -92.94788, + "name": "Teapa" + }, + { + "lat": 43.2134, + "lon": -77.57972, + "name": "Irondequoit" + }, + { + "lat": -31.66833, + "lon": 18.50119, + "name": "Vredendal" + } + ], + "question": "Which location is the geographic outlier among: Dracut, Fairfield, Teapa, Irondequoit, Vredendal?", + "ground_truth": { + "answer": "Vredendal", + "outlier_distance_km": 10408.0, + "second_furthest_km": 3314.9, + "clarity_ratio": 3.14, + "median_distance_km": 2890.2, + "distances_to_centroid": { + "Dracut": 2445.7, + "Fairfield": 2890.2, + "Teapa": 3314.9, + "Irondequoit": 2761.8, + "Vredendal": 10408.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dracut: (42.67°, -71.30°)", + " Fairfield: (39.35°, -84.56°)", + " Teapa: (17.56°, -92.95°)", + " Irondequoit: (43.21°, -77.58°)", + " Vredendal: (-31.67°, 18.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vredendal: 10408.0 km from centroid", + " Teapa: 3314.9 km from centroid", + " Fairfield: 2890.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vredendal", + "FINAL ANSWER: Vredendal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.30995, + "lon": 30.8418, + "name": "Al Fayyum" + }, + { + "lat": 26.27845, + "lon": 32.05608, + "name": "Dār as Salām" + }, + { + "lat": 12.01667, + "lon": 39.63333, + "name": "Robīt" + }, + { + "lat": -27.03026, + "lon": 28.60061, + "name": "Villiers" + }, + { + "lat": 49.13298, + "lon": -122.30258, + "name": "Mission" + } + ], + "question": "Which location is the geographic outlier among: Al Fayyum, Dār as Salām, Robīt, Villiers, Mission?", + "ground_truth": { + "answer": "Mission", + "outlier_distance_km": 10746.7, + "second_furthest_km": 5777.8, + "clarity_ratio": 1.86, + "median_distance_km": 4113.3, + "distances_to_centroid": { + "Al Fayyum": 3208.7, + "Dār as Salām": 3246.2, + "Robīt": 4113.3, + "Villiers": 5777.8, + "Mission": 10746.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Fayyum: (29.31°, 30.84°)", + " Dār as Salām: (26.28°, 32.06°)", + " Robīt: (12.02°, 39.63°)", + " Villiers: (-27.03°, 28.60°)", + " Mission: (49.13°, -122.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mission: 10746.7 km from centroid", + " Villiers: 5777.8 km from centroid", + " Robīt: 4113.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mission", + "FINAL ANSWER: Mission" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.43293, + "lon": -123.48591, + "name": "Colwood" + }, + { + "lat": 40.5976, + "lon": -73.96514, + "name": "Gravesend" + }, + { + "lat": 40.73482, + "lon": -73.79347, + "name": "Fresh Meadows" + }, + { + "lat": 41.67304, + "lon": -93.69772, + "name": "Johnston" + }, + { + "lat": -38.65333, + "lon": 178.00417, + "name": "Gisborne" + } + ], + "question": "Which location is the geographic outlier among: Colwood, Gravesend, Fresh Meadows, Johnston, Gisborne?", + "ground_truth": { + "answer": "Gisborne", + "outlier_distance_km": 16464.9, + "second_furthest_km": 7559.3, + "clarity_ratio": 2.18, + "median_distance_km": 5348.1, + "distances_to_centroid": { + "Colwood": 7559.3, + "Gravesend": 3696.4, + "Fresh Meadows": 3685.9, + "Johnston": 5348.1, + "Gisborne": 16464.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Colwood: (48.43°, -123.49°)", + " Gravesend: (40.60°, -73.97°)", + " Fresh Meadows: (40.73°, -73.79°)", + " Johnston: (41.67°, -93.70°)", + " Gisborne: (-38.65°, 178.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gisborne: 16464.9 km from centroid", + " Colwood: 7559.3 km from centroid", + " Johnston: 5348.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gisborne", + "FINAL ANSWER: Gisborne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 56.65317, + "lon": 66.30048, + "name": "Yalutorovsk" + }, + { + "lat": 53.89218, + "lon": 11.45563, + "name": "Wismar" + }, + { + "lat": 52.48142, + "lon": -1.89983, + "name": "Birmingham" + }, + { + "lat": 54.53333, + "lon": -1.3, + "name": "Thornaby-on-Tees" + }, + { + "lat": 46.67686, + "lon": 131.13273, + "name": "Shuangyashan" + } + ], + "question": "Which location is the geographic outlier among: Yalutorovsk, Wismar, Birmingham, Thornaby-on-Tees, Shuangyashan?", + "ground_truth": { + "answer": "Shuangyashan", + "outlier_distance_km": 6066.6, + "second_furthest_km": 2858.8, + "clarity_ratio": 2.12, + "median_distance_km": 2757.9, + "distances_to_centroid": { + "Yalutorovsk": 1658.9, + "Wismar": 1958.2, + "Birmingham": 2858.8, + "Thornaby-on-Tees": 2757.9, + "Shuangyashan": 6066.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Yalutorovsk: (56.65°, 66.30°)", + " Wismar: (53.89°, 11.46°)", + " Birmingham: (52.48°, -1.90°)", + " Thornaby-on-Tees: (54.53°, -1.30°)", + " Shuangyashan: (46.68°, 131.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shuangyashan: 6066.6 km from centroid", + " Birmingham: 2858.8 km from centroid", + " Thornaby-on-Tees: 2757.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shuangyashan", + "FINAL ANSWER: Shuangyashan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.51908, + "lon": 6.32363, + "name": "Geldern" + }, + { + "lat": 50.81342, + "lon": 10.2361, + "name": "Bad Salzungen" + }, + { + "lat": 51.59056, + "lon": 19.13278, + "name": "Łask" + }, + { + "lat": 53.04063, + "lon": 16.45629, + "name": "Trzcianka" + }, + { + "lat": 9.21866, + "lon": 3.20117, + "name": "Okuta" + } + ], + "question": "Which location is the geographic outlier among: Geldern, Bad Salzungen, Łask, Trzcianka, Okuta?", + "ground_truth": { + "answer": "Okuta", + "outlier_distance_km": 3859.0, + "second_furthest_km": 1160.3, + "clarity_ratio": 3.33, + "median_distance_km": 1108.0, + "distances_to_centroid": { + "Geldern": 987.4, + "Bad Salzungen": 844.9, + "Łask": 1108.0, + "Trzcianka": 1160.3, + "Okuta": 3859.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Geldern: (51.52°, 6.32°)", + " Bad Salzungen: (50.81°, 10.24°)", + " Łask: (51.59°, 19.13°)", + " Trzcianka: (53.04°, 16.46°)", + " Okuta: (9.22°, 3.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Okuta: 3859.0 km from centroid", + " Trzcianka: 1160.3 km from centroid", + " Łask: 1108.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Okuta", + "FINAL ANSWER: Okuta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.89155, + "lon": -4.77275, + "name": "Córdoba" + }, + { + "lat": 51.06931, + "lon": -1.79569, + "name": "Salisbury" + }, + { + "lat": 51.69917, + "lon": 5.30417, + "name": "'s-Hertogenbosch" + }, + { + "lat": 42.66085, + "lon": -8.11285, + "name": "Lalín" + }, + { + "lat": 10.06522, + "lon": 105.55863, + "name": "Thới Lai" + } + ], + "question": "Which location is the geographic outlier among: Córdoba, Salisbury, 's-Hertogenbosch, Lalín, Thới Lai?", + "ground_truth": { + "answer": "Thới Lai", + "outlier_distance_km": 8993.3, + "second_furthest_km": 2338.1, + "clarity_ratio": 3.85, + "median_distance_km": 2141.8, + "distances_to_centroid": { + "Córdoba": 2091.4, + "Salisbury": 2141.8, + "'s-Hertogenbosch": 1806.9, + "Lalín": 2338.1, + "Thới Lai": 8993.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Córdoba: (37.89°, -4.77°)", + " Salisbury: (51.07°, -1.80°)", + " 's-Hertogenbosch: (51.70°, 5.30°)", + " Lalín: (42.66°, -8.11°)", + " Thới Lai: (10.07°, 105.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thới Lai: 8993.3 km from centroid", + " Lalín: 2338.1 km from centroid", + " Salisbury: 2141.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thới Lai", + "FINAL ANSWER: Thới Lai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.91588, + "lon": 27.56957, + "name": "Hlohlolwane" + }, + { + "lat": -26.152, + "lon": 26.15968, + "name": "Lichtenburg" + }, + { + "lat": 31.5084, + "lon": 31.84106, + "name": "‘Izbat al Burj" + }, + { + "lat": -28.23078, + "lon": 28.30707, + "name": "Bethlehem" + }, + { + "lat": 33.03929, + "lon": -85.03133, + "name": "LaGrange" + } + ], + "question": "Which location is the geographic outlier among: Hlohlolwane, Lichtenburg, ‘Izbat al Burj, Bethlehem, LaGrange?", + "ground_truth": { + "answer": "LaGrange", + "outlier_distance_km": 10309.3, + "second_furthest_km": 4794.1, + "clarity_ratio": 2.15, + "median_distance_km": 3623.0, + "distances_to_centroid": { + "Hlohlolwane": 3623.0, + "Lichtenburg": 3305.3, + "‘Izbat al Burj": 4794.1, + "Bethlehem": 3619.0, + "LaGrange": 10309.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hlohlolwane: (-28.92°, 27.57°)", + " Lichtenburg: (-26.15°, 26.16°)", + " ‘Izbat al Burj: (31.51°, 31.84°)", + " Bethlehem: (-28.23°, 28.31°)", + " LaGrange: (33.04°, -85.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " LaGrange: 10309.3 km from centroid", + " ‘Izbat al Burj: 4794.1 km from centroid", + " Hlohlolwane: 3623.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: LaGrange", + "FINAL ANSWER: LaGrange" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.0847, + "lon": -1.35093, + "name": "Elmina" + }, + { + "lat": 25.87198, + "lon": 32.75585, + "name": "Jarājūs" + }, + { + "lat": -2.08033, + "lon": 37.47202, + "name": "Emali" + }, + { + "lat": 3.15106, + "lon": 41.18577, + "name": "Lafey" + }, + { + "lat": -34.64966, + "lon": -58.38341, + "name": "Barracas" + } + ], + "question": "Which location is the geographic outlier among: Elmina, Jarājūs, Emali, Lafey, Barracas?", + "ground_truth": { + "answer": "Barracas", + "outlier_distance_km": 8041.2, + "second_furthest_km": 3795.5, + "clarity_ratio": 2.12, + "median_distance_km": 3453.1, + "distances_to_centroid": { + "Elmina": 1440.0, + "Jarājūs": 3795.5, + "Emali": 3021.5, + "Lafey": 3453.1, + "Barracas": 8041.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Elmina: (5.08°, -1.35°)", + " Jarājūs: (25.87°, 32.76°)", + " Emali: (-2.08°, 37.47°)", + " Lafey: (3.15°, 41.19°)", + " Barracas: (-34.65°, -58.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barracas: 8041.2 km from centroid", + " Jarājūs: 3795.5 km from centroid", + " Lafey: 3453.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barracas", + "FINAL ANSWER: Barracas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": -33.80383, + "lon": 150.98768, + "name": "Westmead" + }, + { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": 19.77557, + "lon": -98.57471, + "name": "Ciudad Sahagun" + } + ], + "question": "Which location is the geographic outlier among: Maitland, Westmead, Papatoetoe, Thornlie, Ciudad Sahagun?", + "ground_truth": { + "answer": "Ciudad Sahagun", + "outlier_distance_km": 18164.0, + "second_furthest_km": 7276.8, + "clarity_ratio": 2.5, + "median_distance_km": 5223.0, + "distances_to_centroid": { + "Maitland": 5223.0, + "Westmead": 5166.7, + "Papatoetoe": 7276.8, + "Thornlie": 1942.0, + "Ciudad Sahagun": 18164.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maitland: (-32.73°, 151.56°)", + " Westmead: (-33.80°, 150.99°)", + " Papatoetoe: (-36.97°, 174.84°)", + " Thornlie: (-32.06°, 115.95°)", + " Ciudad Sahagun: (19.78°, -98.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciudad Sahagun: 18164.0 km from centroid", + " Papatoetoe: 7276.8 km from centroid", + " Maitland: 5223.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciudad Sahagun", + "FINAL ANSWER: Ciudad Sahagun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.45917, + "lon": -76.46333, + "name": "Uchiza" + }, + { + "lat": -2.55778, + "lon": -47.495, + "name": "Ipixuna do Pará" + }, + { + "lat": -22.05944, + "lon": -46.97861, + "name": "Aguaí" + }, + { + "lat": -14.16417, + "lon": -39.37361, + "name": "Ibirapitanga" + }, + { + "lat": 55.59525, + "lon": 37.05235, + "name": "Krasnoznamensk" + } + ], + "question": "Which location is the geographic outlier among: Uchiza, Ipixuna do Pará, Aguaí, Ibirapitanga, Krasnoznamensk?", + "ground_truth": { + "answer": "Krasnoznamensk", + "outlier_distance_km": 8715.8, + "second_furthest_km": 4769.5, + "clarity_ratio": 1.83, + "median_distance_km": 2958.7, + "distances_to_centroid": { + "Uchiza": 4769.5, + "Ipixuna do Pará": 1503.2, + "Aguaí": 2958.7, + "Ibirapitanga": 1836.0, + "Krasnoznamensk": 8715.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Uchiza: (-8.46°, -76.46°)", + " Ipixuna do Pará: (-2.56°, -47.49°)", + " Aguaí: (-22.06°, -46.98°)", + " Ibirapitanga: (-14.16°, -39.37°)", + " Krasnoznamensk: (55.60°, 37.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Krasnoznamensk: 8715.8 km from centroid", + " Uchiza: 4769.5 km from centroid", + " Aguaí: 2958.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Krasnoznamensk", + "FINAL ANSWER: Krasnoznamensk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.35982, + "lon": 5.33421, + "name": "Marseille 16" + }, + { + "lat": 39.64167, + "lon": -0.23889, + "name": "Grao de Murviedro" + }, + { + "lat": 45.13097, + "lon": 42.02703, + "name": "Mikhaylovsk" + }, + { + "lat": 44.1901, + "lon": 42.6595, + "name": "Suvorovskaya" + }, + { + "lat": -6.06778, + "lon": -35.33222, + "name": "Monte Alegre" + } + ], + "question": "Which location is the geographic outlier among: Marseille 16, Grao de Murviedro, Mikhaylovsk, Suvorovskaya, Monte Alegre?", + "ground_truth": { + "answer": "Monte Alegre", + "outlier_distance_km": 6543.0, + "second_furthest_km": 2988.5, + "clarity_ratio": 2.19, + "median_distance_km": 2965.9, + "distances_to_centroid": { + "Marseille 16": 1223.4, + "Grao de Murviedro": 1221.5, + "Mikhaylovsk": 2965.9, + "Suvorovskaya": 2988.5, + "Monte Alegre": 6543.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marseille 16: (43.36°, 5.33°)", + " Grao de Murviedro: (39.64°, -0.24°)", + " Mikhaylovsk: (45.13°, 42.03°)", + " Suvorovskaya: (44.19°, 42.66°)", + " Monte Alegre: (-6.07°, -35.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Monte Alegre: 6543.0 km from centroid", + " Suvorovskaya: 2988.5 km from centroid", + " Mikhaylovsk: 2965.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Monte Alegre", + "FINAL ANSWER: Monte Alegre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -26.02667, + "lon": -48.855, + "name": "Garuva" + }, + { + "lat": -23.62808, + "lon": -46.66791, + "name": "Campo Belo" + }, + { + "lat": -22.52667, + "lon": -43.73278, + "name": "Mendes" + }, + { + "lat": -7.33561, + "lon": -47.46218, + "name": "Carolina" + }, + { + "lat": -31.95224, + "lon": 115.8614, + "name": "Perth" + } + ], + "question": "Which location is the geographic outlier among: Garuva, Campo Belo, Mendes, Carolina, Perth?", + "ground_truth": { + "answer": "Perth", + "outlier_distance_km": 11976.9, + "second_furthest_km": 3932.0, + "clarity_ratio": 3.05, + "median_distance_km": 3533.0, + "distances_to_centroid": { + "Garuva": 3533.0, + "Campo Belo": 3323.4, + "Mendes": 3033.9, + "Carolina": 3932.0, + "Perth": 11976.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Garuva: (-26.03°, -48.85°)", + " Campo Belo: (-23.63°, -46.67°)", + " Mendes: (-22.53°, -43.73°)", + " Carolina: (-7.34°, -47.46°)", + " Perth: (-31.95°, 115.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perth: 11976.9 km from centroid", + " Carolina: 3932.0 km from centroid", + " Garuva: 3533.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perth", + "FINAL ANSWER: Perth" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.45568, + "lon": -0.461, + "name": "Alaquàs" + }, + { + "lat": 67.58355, + "lon": 63.79399, + "name": "Vorgashor" + }, + { + "lat": 53.48462, + "lon": 10.22904, + "name": "Bergedorf" + }, + { + "lat": 56.33169, + "lon": 36.7292, + "name": "Klin" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + } + ], + "question": "Which location is the geographic outlier among: Alaquàs, Vorgashor, Bergedorf, Klin, Te Atatu Peninsula?", + "ground_truth": { + "answer": "Te Atatu Peninsula", + "outlier_distance_km": 14541.2, + "second_furthest_km": 4981.0, + "clarity_ratio": 2.92, + "median_distance_km": 4076.2, + "distances_to_centroid": { + "Alaquàs": 4981.0, + "Vorgashor": 3538.0, + "Bergedorf": 4076.2, + "Klin": 2724.2, + "Te Atatu Peninsula": 14541.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alaquàs: (39.46°, -0.46°)", + " Vorgashor: (67.58°, 63.79°)", + " Bergedorf: (53.48°, 10.23°)", + " Klin: (56.33°, 36.73°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Te Atatu Peninsula: 14541.2 km from centroid", + " Alaquàs: 4981.0 km from centroid", + " Bergedorf: 4076.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Te Atatu Peninsula", + "FINAL ANSWER: Te Atatu Peninsula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": -43.53333, + "lon": 172.63333, + "name": "Christchurch" + }, + { + "lat": -33.32711, + "lon": 115.64137, + "name": "Bunbury" + }, + { + "lat": 33.93807, + "lon": -118.35258, + "name": "Lennox" + } + ], + "question": "Which location is the geographic outlier among: Burwood, Willetton, Christchurch, Bunbury, Lennox?", + "ground_truth": { + "answer": "Lennox", + "outlier_distance_km": 17158.0, + "second_furthest_km": 7991.3, + "clarity_ratio": 2.15, + "median_distance_km": 6311.4, + "distances_to_centroid": { + "Burwood": 6311.4, + "Willetton": 3036.9, + "Christchurch": 7991.3, + "Bunbury": 3054.6, + "Lennox": 17158.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Burwood: (-33.88°, 151.10°)", + " Willetton: (-32.05°, 115.89°)", + " Christchurch: (-43.53°, 172.63°)", + " Bunbury: (-33.33��, 115.64°)", + " Lennox: (33.94°, -118.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lennox: 17158.0 km from centroid", + " Christchurch: 7991.3 km from centroid", + " Burwood: 6311.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lennox", + "FINAL ANSWER: Lennox" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": 50.07139, + "lon": 8.85123, + "name": "Obertshausen" + } + ], + "question": "Which location is the geographic outlier among: Blacktown, Masterton, Thornlie, Earlwood, Obertshausen?", + "ground_truth": { + "answer": "Obertshausen", + "outlier_distance_km": 13078.9, + "second_furthest_km": 5795.6, + "clarity_ratio": 2.26, + "median_distance_km": 3507.3, + "distances_to_centroid": { + "Blacktown": 3483.0, + "Masterton": 5795.6, + "Thornlie": 1614.9, + "Earlwood": 3507.3, + "Obertshausen": 13078.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blacktown: (-33.77°, 150.92°)", + " Masterton: (-40.96°, 175.66°)", + " Thornlie: (-32.06°, 115.95°)", + " Earlwood: (-33.92°, 151.13°)", + " Obertshausen: (50.07°, 8.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Obertshausen: 13078.9 km from centroid", + " Masterton: 5795.6 km from centroid", + " Earlwood: 3507.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Obertshausen", + "FINAL ANSWER: Obertshausen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.95753, + "lon": -88.0809, + "name": "Bloomingdale" + }, + { + "lat": 43.42528, + "lon": -88.18343, + "name": "West Bend" + }, + { + "lat": 39.80276, + "lon": -105.08748, + "name": "Arvada" + }, + { + "lat": 38.90844, + "lon": -77.04414, + "name": "Dupont Circle" + }, + { + "lat": -31.43722, + "lon": -68.52556, + "name": "Albardón" + } + ], + "question": "Which location is the geographic outlier among: Bloomingdale, West Bend, Arvada, Dupont Circle, Albardón?", + "ground_truth": { + "answer": "Albardón", + "outlier_distance_km": 6689.5, + "second_furthest_km": 2344.5, + "clarity_ratio": 2.85, + "median_distance_km": 1895.4, + "distances_to_centroid": { + "Bloomingdale": 1732.9, + "West Bend": 1895.4, + "Arvada": 2344.5, + "Dupont Circle": 1580.3, + "Albardón": 6689.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bloomingdale: (41.96°, -88.08°)", + " West Bend: (43.43°, -88.18°)", + " Arvada: (39.80°, -105.09°)", + " Dupont Circle: (38.91°, -77.04°)", + " Albardón: (-31.44°, -68.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Albardón: 6689.5 km from centroid", + " Arvada: 2344.5 km from centroid", + " West Bend: 1895.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Albardón", + "FINAL ANSWER: Albardón" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.05962, + "lon": 60.64125, + "name": "Kartaly" + }, + { + "lat": 50.78351, + "lon": -1.09071, + "name": "Southsea" + }, + { + "lat": 43.24622, + "lon": 5.39788, + "name": "Mazargues" + }, + { + "lat": 50.41342, + "lon": 36.92537, + "name": "Shebekino" + }, + { + "lat": 8.96727, + "lon": 76.54188, + "name": "Chavara" + } + ], + "question": "Which location is the geographic outlier among: Kartaly, Southsea, Mazargues, Shebekino, Chavara?", + "ground_truth": { + "answer": "Chavara", + "outlier_distance_km": 5379.8, + "second_furthest_km": 2991.3, + "clarity_ratio": 1.8, + "median_distance_km": 2487.7, + "distances_to_centroid": { + "Kartaly": 2276.7, + "Southsea": 2991.3, + "Mazargues": 2487.7, + "Shebekino": 1018.5, + "Chavara": 5379.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kartaly: (53.06°, 60.64°)", + " Southsea: (50.78°, -1.09°)", + " Mazargues: (43.25°, 5.40°)", + " Shebekino: (50.41°, 36.93°)", + " Chavara: (8.97°, 76.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chavara: 5379.8 km from centroid", + " Southsea: 2991.3 km from centroid", + " Mazargues: 2487.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chavara", + "FINAL ANSWER: Chavara" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.64801, + "lon": -93.36827, + "name": "Albert Lea" + }, + { + "lat": 32.32341, + "lon": -110.9951, + "name": "Casas Adobes" + }, + { + "lat": 37.13179, + "lon": -80.57645, + "name": "Radford" + }, + { + "lat": 33.98168, + "lon": -118.22507, + "name": "Huntington Park" + }, + { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + } + ], + "question": "Which location is the geographic outlier among: Albert Lea, Casas Adobes, Radford, Huntington Park, Paralowie?", + "ground_truth": { + "answer": "Paralowie", + "outlier_distance_km": 18248.1, + "second_furthest_km": 6421.5, + "clarity_ratio": 2.84, + "median_distance_km": 5769.9, + "distances_to_centroid": { + "Albert Lea": 4382.9, + "Casas Adobes": 5769.9, + "Radford": 3110.2, + "Huntington Park": 6421.5, + "Paralowie": 18248.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albert Lea: (43.65°, -93.37°)", + " Casas Adobes: (32.32°, -111.00°)", + " Radford: (37.13°, -80.58°)", + " Huntington Park: (33.98°, -118.23°)", + " Paralowie: (-34.76°, 138.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paralowie: 18248.1 km from centroid", + " Huntington Park: 6421.5 km from centroid", + " Casas Adobes: 5769.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paralowie", + "FINAL ANSWER: Paralowie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.81144, + "lon": -89.95316, + "name": "Edwardsville" + }, + { + "lat": 42.13919, + "lon": -87.92896, + "name": "Wheeling" + }, + { + "lat": 38.25424, + "lon": -85.75941, + "name": "Louisville" + }, + { + "lat": 40.57455, + "lon": -74.30209, + "name": "Colonia" + }, + { + "lat": -8.87556, + "lon": -36.36667, + "name": "São João" + } + ], + "question": "Which location is the geographic outlier among: Edwardsville, Wheeling, Louisville, Colonia, São João?", + "ground_truth": { + "answer": "São João", + "outlier_distance_km": 5980.0, + "second_furthest_km": 1768.9, + "clarity_ratio": 3.38, + "median_distance_km": 1679.7, + "distances_to_centroid": { + "Edwardsville": 1679.7, + "Wheeling": 1768.9, + "Louisville": 1343.5, + "Colonia": 1156.8, + "São João": 5980.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Edwardsville: (38.81°, -89.95°)", + " Wheeling: (42.14°, -87.93°)", + " Louisville: (38.25°, -85.76°)", + " Colonia: (40.57°, -74.30°)", + " São João: (-8.88°, -36.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São João: 5980.0 km from centroid", + " Wheeling: 1768.9 km from centroid", + " Edwardsville: 1679.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São João", + "FINAL ANSWER: São João" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": 48.68333, + "lon": 2.13333, + "name": "Gif-sur-Yvette" + } + ], + "question": "Which location is the geographic outlier among: Glenroy, Sunbury, Levin, Blenheim, Gif-sur-Yvette?", + "ground_truth": { + "answer": "Gif-sur-Yvette", + "outlier_distance_km": 14426.9, + "second_furthest_km": 4873.8, + "clarity_ratio": 2.96, + "median_distance_km": 4785.6, + "distances_to_centroid": { + "Glenroy": 2391.1, + "Sunbury": 2368.5, + "Levin": 4873.8, + "Blenheim": 4785.6, + "Gif-sur-Yvette": 14426.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenroy: (-37.70°, 144.93°)", + " Sunbury: (-37.58°, 144.73°)", + " Levin: (-40.63°, 175.28°)", + " Blenheim: (-41.52°, 173.95°)", + " Gif-sur-Yvette: (48.68°, 2.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gif-sur-Yvette: 14426.9 km from centroid", + " Levin: 4873.8 km from centroid", + " Blenheim: 4785.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gif-sur-Yvette", + "FINAL ANSWER: Gif-sur-Yvette" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.91002, + "lon": 3.66557, + "name": "Iperu" + }, + { + "lat": 9.56667, + "lon": 37.1, + "name": "Shambu" + }, + { + "lat": 9.50619, + "lon": 42.60938, + "name": "Chinahsen" + }, + { + "lat": 12.55, + "lon": 37.06667, + "name": "Āykel" + }, + { + "lat": -27.48306, + "lon": -50.12194, + "name": "Otacílio Costa" + } + ], + "question": "Which location is the geographic outlier among: Iperu, Shambu, Chinahsen, Āykel, Otacílio Costa?", + "ground_truth": { + "answer": "Otacílio Costa", + "outlier_distance_km": 7605.0, + "second_furthest_km": 3257.6, + "clarity_ratio": 2.33, + "median_distance_km": 2781.4, + "distances_to_centroid": { + "Iperu": 1265.2, + "Shambu": 2674.2, + "Chinahsen": 3257.6, + "Āykel": 2781.4, + "Otacílio Costa": 7605.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Iperu: (6.91°, 3.67°)", + " Shambu: (9.57°, 37.10°)", + " Chinahsen: (9.51°, 42.61°)", + " Āykel: (12.55°, 37.07°)", + " Otacílio Costa: (-27.48°, -50.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Otacílio Costa: 7605.0 km from centroid", + " Chinahsen: 3257.6 km from centroid", + " Āykel: 2781.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Otacílio Costa", + "FINAL ANSWER: Otacílio Costa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.74593, + "lon": -80.3045, + "name": "Coral Terrace" + }, + { + "lat": 20.70137, + "lon": -103.97461, + "name": "Ahualulco de Mercado" + }, + { + "lat": 35.75118, + "lon": -86.93, + "name": "Spring Hill" + }, + { + "lat": 40.80677, + "lon": -74.18542, + "name": "Bloomfield" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + } + ], + "question": "Which location is the geographic outlier among: Coral Terrace, Ahualulco de Mercado, Spring Hill, Bloomfield, Napier?", + "ground_truth": { + "answer": "Napier", + "outlier_distance_km": 16120.9, + "second_furthest_km": 7358.3, + "clarity_ratio": 2.19, + "median_distance_km": 5639.2, + "distances_to_centroid": { + "Coral Terrace": 4909.2, + "Ahualulco de Mercado": 7358.3, + "Spring Hill": 5639.2, + "Bloomfield": 4707.7, + "Napier": 16120.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coral Terrace: (25.75°, -80.30°)", + " Ahualulco de Mercado: (20.70°, -103.97°)", + " Spring Hill: (35.75°, -86.93°)", + " Bloomfield: (40.81°, -74.19°)", + " Napier: (-39.49°, 176.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Napier: 16120.9 km from centroid", + " Ahualulco de Mercado: 7358.3 km from centroid", + " Spring Hill: 5639.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Napier", + "FINAL ANSWER: Napier" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.77019, + "lon": 100.68531, + "name": "Saphan Sung" + }, + { + "lat": 35.25048, + "lon": 136.91201, + "name": "Toyoyama" + }, + { + "lat": -7.75, + "lon": 110.49417, + "name": "Candi Prambanan" + }, + { + "lat": 13.66314, + "lon": 100.38781, + "name": "Ban Khlong Bang Phran" + }, + { + "lat": 49.49991, + "lon": -115.76879, + "name": "Cranbrook" + } + ], + "question": "Which location is the geographic outlier among: Saphan Sung, Toyoyama, Candi Prambanan, Ban Khlong Bang Phran, Cranbrook?", + "ground_truth": { + "answer": "Cranbrook", + "outlier_distance_km": 12185.1, + "second_furthest_km": 6947.3, + "clarity_ratio": 1.75, + "median_distance_km": 5760.0, + "distances_to_centroid": { + "Saphan Sung": 3701.9, + "Toyoyama": 6947.3, + "Candi Prambanan": 5760.0, + "Ban Khlong Bang Phran": 3674.7, + "Cranbrook": 12185.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saphan Sung: (13.77°, 100.69°)", + " Toyoyama: (35.25°, 136.91°)", + " Candi Prambanan: (-7.75°, 110.49°)", + " Ban Khlong Bang Phran: (13.66°, 100.39°)", + " Cranbrook: (49.50°, -115.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cranbrook: 12185.1 km from centroid", + " Toyoyama: 6947.3 km from centroid", + " Candi Prambanan: 5760.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cranbrook", + "FINAL ANSWER: Cranbrook" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 16.65363, + "lon": 81.7455, + "name": "Penugonda" + }, + { + "lat": 20.99585, + "lon": 78.22914, + "name": "Ārvi" + }, + { + "lat": 12.75975, + "lon": 75.20169, + "name": "Puttūr" + }, + { + "lat": 22.74747, + "lon": 77.72736, + "name": "Narmadapuram" + }, + { + "lat": -31.84062, + "lon": 115.89549, + "name": "Ballajura" + } + ], + "question": "Which location is the geographic outlier among: Penugonda, Ārvi, Puttūr, Narmadapuram, Ballajura?", + "ground_truth": { + "answer": "Ballajura", + "outlier_distance_km": 5489.0, + "second_furthest_km": 1824.8, + "clarity_ratio": 3.01, + "median_distance_km": 1630.2, + "distances_to_centroid": { + "Penugonda": 1029.6, + "Ārvi": 1630.2, + "Puttūr": 1257.6, + "Narmadapuram": 1824.8, + "Ballajura": 5489.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Penugonda: (16.65°, 81.75°)", + " Ārvi: (21.00°, 78.23°)", + " Puttūr: (12.76°, 75.20°)", + " Narmadapuram: (22.75°, 77.73°)", + " Ballajura: (-31.84°, 115.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ballajura: 5489.0 km from centroid", + " Narmadapuram: 1824.8 km from centroid", + " Ārvi: 1630.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ballajura", + "FINAL ANSWER: Ballajura" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.75389, + "lon": -42.88194, + "name": "Viçosa" + }, + { + "lat": -23.11, + "lon": -50.3675, + "name": "Bandeirantes" + }, + { + "lat": -32.74976, + "lon": -70.72584, + "name": "San Felipe" + }, + { + "lat": -40.33494, + "lon": -72.95564, + "name": "Río Bueno" + }, + { + "lat": 23.73267, + "lon": -103.98247, + "name": "Vicente Guerrero" + } + ], + "question": "Which location is the geographic outlier among: Viçosa, Bandeirantes, San Felipe, Río Bueno, Vicente Guerrero?", + "ground_truth": { + "answer": "Vicente Guerrero", + "outlier_distance_km": 6105.7, + "second_furthest_km": 2656.4, + "clarity_ratio": 2.3, + "median_distance_km": 2454.8, + "distances_to_centroid": { + "Viçosa": 2656.4, + "Bandeirantes": 1914.8, + "San Felipe": 1589.0, + "Río Bueno": 2454.8, + "Vicente Guerrero": 6105.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viçosa: (-20.75°, -42.88°)", + " Bandeirantes: (-23.11°, -50.37°)", + " San Felipe: (-32.75°, -70.73°)", + " Río Bueno: (-40.33°, -72.96°)", + " Vicente Guerrero: (23.73°, -103.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vicente Guerrero: 6105.7 km from centroid", + " Viçosa: 2656.4 km from centroid", + " Río Bueno: 2454.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vicente Guerrero", + "FINAL ANSWER: Vicente Guerrero" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 56.56317, + "lon": -2.58736, + "name": "Arbroath" + }, + { + "lat": 49.3, + "lon": 6.93333, + "name": "Riegelsberg" + }, + { + "lat": 48.12279, + "lon": -1.20983, + "name": "Vitré" + }, + { + "lat": 50.84286, + "lon": -0.21608, + "name": "Portslade" + }, + { + "lat": -37.87397, + "lon": 145.04253, + "name": "Malvern East" + } + ], + "question": "Which location is the geographic outlier among: Arbroath, Riegelsberg, Vitré, Portslade, Malvern East?", + "ground_truth": { + "answer": "Malvern East", + "outlier_distance_km": 14277.0, + "second_furthest_km": 3551.0, + "clarity_ratio": 4.02, + "median_distance_km": 3096.2, + "distances_to_centroid": { + "Arbroath": 3551.0, + "Riegelsberg": 2571.0, + "Vitré": 3037.2, + "Portslade": 3096.2, + "Malvern East": 14277.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arbroath: (56.56°, -2.59°)", + " Riegelsberg: (49.30°, 6.93°)", + " Vitré: (48.12°, -1.21°)", + " Portslade: (50.84°, -0.22°)", + " Malvern East: (-37.87°, 145.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Malvern East: 14277.0 km from centroid", + " Arbroath: 3551.0 km from centroid", + " Portslade: 3096.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Malvern East", + "FINAL ANSWER: Malvern East" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.70244, + "lon": 151.09931, + "name": "Hornsby" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + }, + { + "lat": -32.06003, + "lon": 115.955, + "name": "Thornlie" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": 50.5107, + "lon": 18.30056, + "name": "Strzelce Opolskie" + } + ], + "question": "Which location is the geographic outlier among: Hornsby, Ringwood, Thornlie, Logan City, Strzelce Opolskie?", + "ground_truth": { + "answer": "Strzelce Opolskie", + "outlier_distance_km": 11976.8, + "second_furthest_km": 3949.2, + "clarity_ratio": 3.03, + "median_distance_km": 3946.8, + "distances_to_centroid": { + "Hornsby": 3949.2, + "Ringwood": 3684.6, + "Thornlie": 1771.8, + "Logan City": 3946.8, + "Strzelce Opolskie": 11976.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hornsby: (-33.70°, 151.10°)", + " Ringwood: (-37.82°, 145.23°)", + " Thornlie: (-32.06°, 115.95°)", + " Logan City: (-27.64°, 153.11°)", + " Strzelce Opolskie: (50.51°, 18.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Strzelce Opolskie: 11976.8 km from centroid", + " Hornsby: 3949.2 km from centroid", + " Logan City: 3946.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Strzelce Opolskie", + "FINAL ANSWER: Strzelce Opolskie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.9626, + "lon": -76.72774, + "name": "York" + }, + { + "lat": 38.44957, + "lon": -78.86892, + "name": "Harrisonburg" + }, + { + "lat": 40.69365, + "lon": -89.58899, + "name": "Peoria" + }, + { + "lat": 42.09869, + "lon": -75.91797, + "name": "Binghamton" + }, + { + "lat": -16.02511, + "lon": -48.07121, + "name": "Gama" + } + ], + "question": "Which location is the geographic outlier among: York, Harrisonburg, Peoria, Binghamton, Gama?", + "ground_truth": { + "answer": "Gama", + "outlier_distance_km": 5724.1, + "second_furthest_km": 1929.9, + "clarity_ratio": 2.97, + "median_distance_km": 1464.6, + "distances_to_centroid": { + "York": 1243.4, + "Harrisonburg": 1145.1, + "Peoria": 1929.9, + "Binghamton": 1464.6, + "Gama": 5724.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " York: (39.96°, -76.73°)", + " Harrisonburg: (38.45°, -78.87°)", + " Peoria: (40.69°, -89.59°)", + " Binghamton: (42.10°, -75.92°)", + " Gama: (-16.03°, -48.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gama: 5724.1 km from centroid", + " Peoria: 1929.9 km from centroid", + " Binghamton: 1464.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gama", + "FINAL ANSWER: Gama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + }, + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": 54.94377, + "lon": 41.40341, + "name": "Kasimov" + } + ], + "question": "Which location is the geographic outlier among: Punchbowl, Dandenong, Frankston East, Maroubra, Kasimov?", + "ground_truth": { + "answer": "Kasimov", + "outlier_distance_km": 11332.9, + "second_furthest_km": 3018.0, + "clarity_ratio": 3.76, + "median_distance_km": 3002.3, + "distances_to_centroid": { + "Punchbowl": 3002.3, + "Dandenong": 2869.0, + "Frankston East": 2877.1, + "Maroubra": 3018.0, + "Kasimov": 11332.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Punchbowl: (-33.93°, 151.05°)", + " Dandenong: (-37.98°, 145.20°)", + " Frankston East: (-38.13°, 145.13°)", + " Maroubra: (-33.95°, 151.23°)", + " Kasimov: (54.94°, 41.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kasimov: 11332.9 km from centroid", + " Maroubra: 3018.0 km from centroid", + " Punchbowl: 3002.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kasimov", + "FINAL ANSWER: Kasimov" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.88075, + "lon": 2.35513, + "name": "Saint-Vincent de Paul" + }, + { + "lat": 45.74123, + "lon": 3.19643, + "name": "Cournon-d'Auvergne" + }, + { + "lat": 40.05594, + "lon": 17.99088, + "name": "Gallipoli" + }, + { + "lat": 51.87598, + "lon": 36.90535, + "name": "Shchigry" + }, + { + "lat": 42.48587, + "lon": -83.1052, + "name": "Madison Heights" + } + ], + "question": "Which location is the geographic outlier among: Saint-Vincent de Paul, Cournon-d'Auvergne, Gallipoli, Shchigry, Madison Heights?", + "ground_truth": { + "answer": "Madison Heights", + "outlier_distance_km": 6017.7, + "second_furthest_km": 3062.5, + "clarity_ratio": 1.96, + "median_distance_km": 1934.1, + "distances_to_centroid": { + "Saint-Vincent de Paul": 620.9, + "Cournon-d'Auvergne": 599.2, + "Gallipoli": 1934.1, + "Shchigry": 3062.5, + "Madison Heights": 6017.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saint-Vincent de Paul: (48.88°, 2.36°)", + " Cournon-d'Auvergne: (45.74°, 3.20°)", + " Gallipoli: (40.06°, 17.99°)", + " Shchigry: (51.88°, 36.91°)", + " Madison Heights: (42.49°, -83.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Madison Heights: 6017.7 km from centroid", + " Shchigry: 3062.5 km from centroid", + " Gallipoli: 1934.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Madison Heights", + "FINAL ANSWER: Madison Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.85455, + "lon": -84.21714, + "name": "Tucker" + }, + { + "lat": 19.41687, + "lon": -98.90202, + "name": "Chicoloapan" + }, + { + "lat": 18.15514, + "lon": -94.39289, + "name": "Allende" + }, + { + "lat": 23.63138, + "lon": -103.64134, + "name": "Sombrerete" + }, + { + "lat": 51.80924, + "lon": 8.42841, + "name": "Rietberg" + } + ], + "question": "Which location is the geographic outlier among: Tucker, Chicoloapan, Allende, Sombrerete, Rietberg?", + "ground_truth": { + "answer": "Rietberg", + "outlier_distance_km": 7023.6, + "second_furthest_km": 2956.7, + "clarity_ratio": 2.38, + "median_distance_km": 2696.1, + "distances_to_centroid": { + "Tucker": 1042.0, + "Chicoloapan": 2696.1, + "Allende": 2368.2, + "Sombrerete": 2956.7, + "Rietberg": 7023.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tucker: (33.85°, -84.22°)", + " Chicoloapan: (19.42°, -98.90°)", + " Allende: (18.16°, -94.39°)", + " Sombrerete: (23.63°, -103.64°)", + " Rietberg: (51.81°, 8.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rietberg: 7023.6 km from centroid", + " Sombrerete: 2956.7 km from centroid", + " Chicoloapan: 2696.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rietberg", + "FINAL ANSWER: Rietberg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.18972, + "lon": -46.98028, + "name": "Monte Santo de Minas" + }, + { + "lat": -8.94111, + "lon": -72.79167, + "name": "Marechal Thaumaturgo" + }, + { + "lat": -3.22028, + "lon": -45.00361, + "name": "Viana" + }, + { + "lat": -34.18082, + "lon": -70.64933, + "name": "Machalí" + }, + { + "lat": -33.88374, + "lon": 151.21282, + "name": "Surry Hills" + } + ], + "question": "Which location is the geographic outlier among: Monte Santo de Minas, Marechal Thaumaturgo, Viana, Machalí, Surry Hills?", + "ground_truth": { + "answer": "Surry Hills", + "outlier_distance_km": 13860.5, + "second_furthest_km": 6122.5, + "clarity_ratio": 2.26, + "median_distance_km": 5474.6, + "distances_to_centroid": { + "Monte Santo de Minas": 3131.0, + "Marechal Thaumaturgo": 6122.5, + "Viana": 3593.3, + "Machalí": 5474.6, + "Surry Hills": 13860.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Monte Santo de Minas: (-21.19°, -46.98°)", + " Marechal Thaumaturgo: (-8.94°, -72.79°)", + " Viana: (-3.22°, -45.00°)", + " Machalí: (-34.18°, -70.65°)", + " Surry Hills: (-33.88°, 151.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Surry Hills: 13860.5 km from centroid", + " Marechal Thaumaturgo: 6122.5 km from centroid", + " Machalí: 5474.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Surry Hills", + "FINAL ANSWER: Surry Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.318, + "lon": 76.65165, + "name": "Challakere" + }, + { + "lat": 29.3501, + "lon": 77.5516, + "name": "Shāhpur" + }, + { + "lat": 37.29875, + "lon": 79.83031, + "name": "Ying’awati" + }, + { + "lat": 13.77019, + "lon": 100.68531, + "name": "Saphan Sung" + }, + { + "lat": -37.98333, + "lon": 145.2, + "name": "Dandenong" + } + ], + "question": "Which location is the geographic outlier among: Challakere, Shāhpur, Ying’awati, Saphan Sung, Dandenong?", + "ground_truth": { + "answer": "Dandenong", + "outlier_distance_km": 7499.0, + "second_furthest_km": 3305.5, + "clarity_ratio": 2.27, + "median_distance_km": 2766.1, + "distances_to_centroid": { + "Challakere": 2121.0, + "Shāhpur": 2766.1, + "Ying’awati": 3305.5, + "Saphan Sung": 576.8, + "Dandenong": 7499.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Challakere: (14.32°, 76.65°)", + " Shāhpur: (29.35°, 77.55°)", + " Ying’awati: (37.30°, 79.83°)", + " Saphan Sung: (13.77°, 100.69°)", + " Dandenong: (-37.98°, 145.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dandenong: 7499.0 km from centroid", + " Ying’awati: 3305.5 km from centroid", + " Shāhpur: 2766.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dandenong", + "FINAL ANSWER: Dandenong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.69926, + "lon": -86.74833, + "name": "Madison" + }, + { + "lat": 31.87149, + "lon": -116.60071, + "name": "Ensenada" + }, + { + "lat": 37.52021, + "lon": -122.2758, + "name": "Belmont" + }, + { + "lat": 39.28844, + "lon": -77.20387, + "name": "Damascus" + }, + { + "lat": -20.42833, + "lon": -47.82417, + "name": "Guará" + } + ], + "question": "Which location is the geographic outlier among: Madison, Ensenada, Belmont, Damascus, Guará?", + "ground_truth": { + "answer": "Guará", + "outlier_distance_km": 6781.9, + "second_furthest_km": 3360.5, + "clarity_ratio": 2.02, + "median_distance_km": 2708.5, + "distances_to_centroid": { + "Madison": 1170.4, + "Ensenada": 2708.5, + "Belmont": 3360.5, + "Damascus": 2034.6, + "Guará": 6781.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Madison: (34.70°, -86.75°)", + " Ensenada: (31.87°, -116.60°)", + " Belmont: (37.52°, -122.28°)", + " Damascus: (39.29°, -77.20°)", + " Guará: (-20.43°, -47.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guará: 6781.9 km from centroid", + " Belmont: 3360.5 km from centroid", + " Ensenada: 2708.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guará", + "FINAL ANSWER: Guará" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.87822, + "lon": 14.14352, + "name": "Quarto" + }, + { + "lat": 41.38125, + "lon": 2.11744, + "name": "la Maternitat i Sant Ramon" + }, + { + "lat": 48.79947, + "lon": 9.79809, + "name": "Schwäbisch Gmünd" + }, + { + "lat": 50.94159, + "lon": -2.63211, + "name": "Yeovil" + }, + { + "lat": -4.25667, + "lon": -43.01278, + "name": "Coelho Neto" + } + ], + "question": "Which location is the geographic outlier among: Quarto, la Maternitat i Sant Ramon, Schwäbisch Gmünd, Yeovil, Coelho Neto?", + "ground_truth": { + "answer": "Coelho Neto", + "outlier_distance_km": 6014.2, + "second_furthest_km": 1850.9, + "clarity_ratio": 3.25, + "median_distance_km": 1714.7, + "distances_to_centroid": { + "Quarto": 1681.6, + "la Maternitat i Sant Ramon": 834.2, + "Schwäbisch Gmünd": 1850.9, + "Yeovil": 1714.7, + "Coelho Neto": 6014.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Quarto: (40.88°, 14.14°)", + " la Maternitat i Sant Ramon: (41.38°, 2.12°)", + " Schwäbisch Gmünd: (48.80°, 9.80°)", + " Yeovil: (50.94°, -2.63°)", + " Coelho Neto: (-4.26°, -43.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coelho Neto: 6014.2 km from centroid", + " Schwäbisch Gmünd: 1850.9 km from centroid", + " Yeovil: 1714.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coelho Neto", + "FINAL ANSWER: Coelho Neto" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.74981, + "lon": 144.9109, + "name": "Essendon" + }, + { + "lat": -37.96944, + "lon": 145.04806, + "name": "Cheltenham" + }, + { + "lat": -37.83382, + "lon": 144.93834, + "name": "City of Port Phillip" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": 7.84855, + "lon": 4.32981, + "name": "Inisa" + } + ], + "question": "Which location is the geographic outlier among: Essendon, Cheltenham, City of Port Phillip, Blacktown, Inisa?", + "ground_truth": { + "answer": "Inisa", + "outlier_distance_km": 12739.5, + "second_furthest_km": 3193.2, + "clarity_ratio": 3.99, + "median_distance_km": 2746.2, + "distances_to_centroid": { + "Essendon": 2727.9, + "Cheltenham": 2746.2, + "City of Port Phillip": 2732.7, + "Blacktown": 3193.2, + "Inisa": 12739.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Essendon: (-37.75°, 144.91°)", + " Cheltenham: (-37.97°, 145.05°)", + " City of Port Phillip: (-37.83°, 144.94°)", + " Blacktown: (-33.77°, 150.92°)", + " Inisa: (7.85°, 4.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Inisa: 12739.5 km from centroid", + " Blacktown: 3193.2 km from centroid", + " Cheltenham: 2746.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Inisa", + "FINAL ANSWER: Inisa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.35573, + "lon": 31.68484, + "name": "Kafr Sa‘d" + }, + { + "lat": -32.33083, + "lon": 28.14981, + "name": "Butterworth" + }, + { + "lat": 8.83784, + "lon": 3.75628, + "name": "Igboho" + }, + { + "lat": 27.3126, + "lon": 30.96987, + "name": "Manfalūţ" + }, + { + "lat": -33.95, + "lon": 151.13333, + "name": "Rockdale" + } + ], + "question": "Which location is the geographic outlier among: Kafr Sa‘d, Butterworth, Igboho, Manfalūţ, Rockdale?", + "ground_truth": { + "answer": "Rockdale", + "outlier_distance_km": 11126.8, + "second_furthest_km": 5114.8, + "clarity_ratio": 2.18, + "median_distance_km": 4239.8, + "distances_to_centroid": { + "Kafr Sa‘d": 3917.3, + "Butterworth": 4239.8, + "Igboho": 5114.8, + "Manfalūţ": 3580.7, + "Rockdale": 11126.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kafr Sa‘d: (31.36°, 31.68°)", + " Butterworth: (-32.33°, 28.15°)", + " Igboho: (8.84°, 3.76°)", + " Manfalūţ: (27.31°, 30.97°)", + " Rockdale: (-33.95°, 151.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rockdale: 11126.8 km from centroid", + " Igboho: 5114.8 km from centroid", + " Butterworth: 4239.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rockdale", + "FINAL ANSWER: Rockdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + }, + { + "lat": -38.03333, + "lon": 145.3, + "name": "Narre Warren" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": -37.73261, + "lon": 144.86504, + "name": "Keilor East" + }, + { + "lat": 39.34788, + "lon": -76.76997, + "name": "Milford Mill" + } + ], + "question": "Which location is the geographic outlier among: Paraparaumu, Narre Warren, Morayfield, Keilor East, Milford Mill?", + "ground_truth": { + "answer": "Milford Mill", + "outlier_distance_km": 17907.0, + "second_furthest_km": 6581.0, + "clarity_ratio": 2.72, + "median_distance_km": 4567.4, + "distances_to_centroid": { + "Paraparaumu": 6581.0, + "Narre Warren": 4023.0, + "Morayfield": 4567.4, + "Keilor East": 3976.5, + "Milford Mill": 17907.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paraparaumu: (-40.92°, 175.02°)", + " Narre Warren: (-38.03°, 145.30°)", + " Morayfield: (-27.11°, 152.95°)", + " Keilor East: (-37.73°, 144.87°)", + " Milford Mill: (39.35°, -76.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Milford Mill: 17907.0 km from centroid", + " Paraparaumu: 6581.0 km from centroid", + " Morayfield: 4567.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Milford Mill", + "FINAL ANSWER: Milford Mill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -9.40472, + "lon": -35.50722, + "name": "Barra de Santo Antônio" + }, + { + "lat": -11.72917, + "lon": -49.06861, + "name": "Gurupi" + }, + { + "lat": -12.05354, + "lon": -77.09802, + "name": "Carmen De La Legua Reynoso" + }, + { + "lat": 8.75081, + "lon": -75.87823, + "name": "Montería" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + } + ], + "question": "Which location is the geographic outlier among: Barra de Santo Antônio, Gurupi, Carmen De La Legua Reynoso, Montería, Sunbury?", + "ground_truth": { + "answer": "Sunbury", + "outlier_distance_km": 14190.3, + "second_furthest_km": 6755.0, + "clarity_ratio": 2.1, + "median_distance_km": 6347.2, + "distances_to_centroid": { + "Barra de Santo Antônio": 1879.2, + "Gurupi": 3316.0, + "Carmen De La Legua Reynoso": 6347.2, + "Montería": 6755.0, + "Sunbury": 14190.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Barra de Santo Antônio: (-9.40°, -35.51°)", + " Gurupi: (-11.73°, -49.07°)", + " Carmen De La Legua Reynoso: (-12.05°, -77.10°)", + " Montería: (8.75°, -75.88°)", + " Sunbury: (-37.58°, 144.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunbury: 14190.3 km from centroid", + " Montería: 6755.0 km from centroid", + " Carmen De La Legua Reynoso: 6347.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sunbury", + "FINAL ANSWER: Sunbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.61106, + "lon": -111.89994, + "name": "Midvale" + }, + { + "lat": 26.56285, + "lon": -81.94953, + "name": "Cape Coral" + }, + { + "lat": 26.61708, + "lon": -80.07231, + "name": "Lake Worth Beach" + }, + { + "lat": 41.76204, + "lon": -72.74204, + "name": "West Hartford" + }, + { + "lat": -38.37694, + "lon": -60.27563, + "name": "Tres Arroyos" + } + ], + "question": "Which location is the geographic outlier among: Midvale, Cape Coral, Lake Worth Beach, West Hartford, Tres Arroyos?", + "ground_truth": { + "answer": "Tres Arroyos", + "outlier_distance_km": 6795.5, + "second_furthest_km": 3731.3, + "clarity_ratio": 1.82, + "median_distance_km": 2613.4, + "distances_to_centroid": { + "Midvale": 3731.3, + "Cape Coral": 794.6, + "Lake Worth Beach": 809.8, + "West Hartford": 2613.4, + "Tres Arroyos": 6795.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Midvale: (40.61°, -111.90°)", + " Cape Coral: (26.56°, -81.95°)", + " Lake Worth Beach: (26.62°, -80.07°)", + " West Hartford: (41.76°, -72.74°)", + " Tres Arroyos: (-38.38°, -60.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tres Arroyos: 6795.5 km from centroid", + " Midvale: 3731.3 km from centroid", + " West Hartford: 2613.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tres Arroyos", + "FINAL ANSWER: Tres Arroyos" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.70802, + "lon": 101.41614, + "name": "Pak Chong" + }, + { + "lat": 29.57007, + "lon": 107.04542, + "name": "Dashun" + }, + { + "lat": 21.72288, + "lon": 104.9113, + "name": "Yên Bái" + }, + { + "lat": 33.5594, + "lon": 75.23222, + "name": "Dooru Verinag" + }, + { + "lat": 51.55269, + "lon": 0.60983, + "name": "Hadleigh" + } + ], + "question": "Which location is the geographic outlier among: Pak Chong, Dashun, Yên Bái, Dooru Verinag, Hadleigh?", + "ground_truth": { + "answer": "Hadleigh", + "outlier_distance_km": 6576.0, + "second_furthest_km": 2962.6, + "clarity_ratio": 2.22, + "median_distance_km": 2857.5, + "distances_to_centroid": { + "Pak Chong": 2962.6, + "Dashun": 2808.3, + "Yên Bái": 2857.5, + "Dooru Verinag": 445.4, + "Hadleigh": 6576.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pak Chong: (14.71°, 101.42°)", + " Dashun: (29.57°, 107.05°)", + " Yên Bái: (21.72°, 104.91°)", + " Dooru Verinag: (33.56°, 75.23°)", + " Hadleigh: (51.55°, 0.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hadleigh: 6576.0 km from centroid", + " Pak Chong: 2962.6 km from centroid", + " Yên Bái: 2857.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hadleigh", + "FINAL ANSWER: Hadleigh" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.43099, + "lon": 9.11093, + "name": "Corsico" + }, + { + "lat": 27.91855, + "lon": -15.43433, + "name": "Ingenio" + }, + { + "lat": 49.4891, + "lon": 8.46694, + "name": "Mannheim" + }, + { + "lat": 51.0455, + "lon": 13.66108, + "name": "Gorbitz" + }, + { + "lat": -15.74333, + "lon": -43.02833, + "name": "Porteirinha" + } + ], + "question": "Which location is the geographic outlier among: Corsico, Ingenio, Mannheim, Gorbitz, Porteirinha?", + "ground_truth": { + "answer": "Porteirinha", + "outlier_distance_km": 6618.9, + "second_furthest_km": 2667.3, + "clarity_ratio": 2.48, + "median_distance_km": 2299.3, + "distances_to_centroid": { + "Corsico": 1983.1, + "Ingenio": 1048.1, + "Mannheim": 2299.3, + "Gorbitz": 2667.3, + "Porteirinha": 6618.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Corsico: (45.43°, 9.11°)", + " Ingenio: (27.92°, -15.43°)", + " Mannheim: (49.49°, 8.47°)", + " Gorbitz: (51.05°, 13.66°)", + " Porteirinha: (-15.74°, -43.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Porteirinha: 6618.9 km from centroid", + " Gorbitz: 2667.3 km from centroid", + " Mannheim: 2299.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Porteirinha", + "FINAL ANSWER: Porteirinha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.80229, + "lon": 84.50311, + "name": "Bettiah" + }, + { + "lat": -7.51417, + "lon": 109.29417, + "name": "Banyumas" + }, + { + "lat": 29.33773, + "lon": 105.89237, + "name": "Nandajie" + }, + { + "lat": 22.86643, + "lon": 88.40113, + "name": "Bhātpāra" + }, + { + "lat": -15.10222, + "lon": -44.09194, + "name": "Itacarambi" + } + ], + "question": "Which location is the geographic outlier among: Bettiah, Banyumas, Nandajie, Bhātpāra, Itacarambi?", + "ground_truth": { + "answer": "Itacarambi", + "outlier_distance_km": 12763.8, + "second_furthest_km": 4943.1, + "clarity_ratio": 2.58, + "median_distance_km": 4330.5, + "distances_to_centroid": { + "Bettiah": 2383.2, + "Banyumas": 4943.1, + "Nandajie": 4330.5, + "Bhātpāra": 2445.2, + "Itacarambi": 12763.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bettiah: (26.80°, 84.50°)", + " Banyumas: (-7.51°, 109.29°)", + " Nandajie: (29.34°, 105.89°)", + " Bhātpāra: (22.87°, 88.40°)", + " Itacarambi: (-15.10°, -44.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itacarambi: 12763.8 km from centroid", + " Banyumas: 4943.1 km from centroid", + " Nandajie: 4330.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itacarambi", + "FINAL ANSWER: Itacarambi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.70976, + "lon": 107.64455, + "name": "Qingyang" + }, + { + "lat": 2.94761, + "lon": 101.84695, + "name": "Seminyih" + }, + { + "lat": 9.5162, + "lon": 123.158, + "name": "Tanjay" + }, + { + "lat": 30.76835, + "lon": 108.48439, + "name": "Changling" + }, + { + "lat": -28.87097, + "lon": 31.89961, + "name": "eSikhaleni" + } + ], + "question": "Which location is the geographic outlier among: Qingyang, Seminyih, Tanjay, Changling, eSikhaleni?", + "ground_truth": { + "answer": "eSikhaleni", + "outlier_distance_km": 7989.6, + "second_furthest_km": 3146.5, + "clarity_ratio": 2.54, + "median_distance_km": 3128.3, + "distances_to_centroid": { + "Qingyang": 3146.5, + "Seminyih": 1120.9, + "Tanjay": 3128.3, + "Changling": 2717.4, + "eSikhaleni": 7989.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Qingyang: (35.71°, 107.64°)", + " Seminyih: (2.95°, 101.85°)", + " Tanjay: (9.52°, 123.16°)", + " Changling: (30.77°, 108.48°)", + " eSikhaleni: (-28.87°, 31.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " eSikhaleni: 7989.6 km from centroid", + " Qingyang: 3146.5 km from centroid", + " Tanjay: 3128.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: eSikhaleni", + "FINAL ANSWER: eSikhaleni" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.48165, + "lon": 7.21648, + "name": "Bochum" + }, + { + "lat": 51.87819, + "lon": 0.55292, + "name": "Braintree" + }, + { + "lat": 43.22597, + "lon": 44.77323, + "name": "Nazran" + }, + { + "lat": 38.96667, + "lon": -0.18333, + "name": "Gandia" + }, + { + "lat": -15.10222, + "lon": -44.09194, + "name": "Itacarambi" + } + ], + "question": "Which location is the geographic outlier among: Bochum, Braintree, Nazran, Gandia, Itacarambi?", + "ground_truth": { + "answer": "Itacarambi", + "outlier_distance_km": 7302.6, + "second_furthest_km": 3833.8, + "clarity_ratio": 1.9, + "median_distance_km": 1985.0, + "distances_to_centroid": { + "Bochum": 1985.0, + "Braintree": 1979.9, + "Nazran": 3833.8, + "Gandia": 566.5, + "Itacarambi": 7302.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bochum: (51.48°, 7.22°)", + " Braintree: (51.88°, 0.55°)", + " Nazran: (43.23°, 44.77°)", + " Gandia: (38.97°, -0.18°)", + " Itacarambi: (-15.10°, -44.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itacarambi: 7302.6 km from centroid", + " Nazran: 3833.8 km from centroid", + " Bochum: 1985.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itacarambi", + "FINAL ANSWER: Itacarambi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.53614, + "lon": 105.66685, + "name": "Zhuxi" + }, + { + "lat": 11.36523, + "lon": 77.76235, + "name": "Pallipalayam" + }, + { + "lat": 28.6057, + "lon": 77.31901, + "name": "Dalūpura" + }, + { + "lat": 36.85609, + "lon": 136.9885, + "name": "Himimachi" + }, + { + "lat": 3.40671, + "lon": -76.34819, + "name": "Candelaria" + } + ], + "question": "Which location is the geographic outlier among: Zhuxi, Pallipalayam, Dalūpura, Himimachi, Candelaria?", + "ground_truth": { + "answer": "Candelaria", + "outlier_distance_km": 14889.7, + "second_furthest_km": 7070.8, + "clarity_ratio": 2.11, + "median_distance_km": 4207.8, + "distances_to_centroid": { + "Zhuxi": 4207.8, + "Pallipalayam": 1855.1, + "Dalūpura": 1503.9, + "Himimachi": 7070.8, + "Candelaria": 14889.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhuxi: (29.54°, 105.67°)", + " Pallipalayam: (11.37°, 77.76°)", + " Dalūpura: (28.61°, 77.32°)", + " Himimachi: (36.86°, 136.99°)", + " Candelaria: (3.41°, -76.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Candelaria: 14889.7 km from centroid", + " Himimachi: 7070.8 km from centroid", + " Zhuxi: 4207.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Candelaria", + "FINAL ANSWER: Candelaria" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.4837, + "lon": -46.41309, + "name": "Jardim Helena" + }, + { + "lat": -23.02639, + "lon": -45.55528, + "name": "Taubaté" + }, + { + "lat": -10.90889, + "lon": -37.03861, + "name": "Barra dos Coqueiros" + }, + { + "lat": -7.85583, + "lon": -35.58833, + "name": "João Alfredo" + }, + { + "lat": 40.75566, + "lon": -73.58763, + "name": "Westbury" + } + ], + "question": "Which location is the geographic outlier among: Jardim Helena, Taubaté, Barra dos Coqueiros, João Alfredo, Westbury?", + "ground_truth": { + "answer": "Westbury", + "outlier_distance_km": 5724.0, + "second_furthest_km": 2070.1, + "clarity_ratio": 2.77, + "median_distance_km": 2027.5, + "distances_to_centroid": { + "Jardim Helena": 2070.1, + "Taubaté": 2027.5, + "Barra dos Coqueiros": 1344.2, + "João Alfredo": 1371.1, + "Westbury": 5724.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jardim Helena: (-23.48°, -46.41°)", + " Taubaté: (-23.03°, -45.56°)", + " Barra dos Coqueiros: (-10.91°, -37.04°)", + " João Alfredo: (-7.86°, -35.59°)", + " Westbury: (40.76°, -73.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Westbury: 5724.0 km from centroid", + " Jardim Helena: 2070.1 km from centroid", + " Taubaté: 2027.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Westbury", + "FINAL ANSWER: Westbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.10809, + "lon": -56.53253, + "name": "Bela Vista" + }, + { + "lat": -8.23833, + "lon": -35.46167, + "name": "Chã Grande" + }, + { + "lat": -39.81422, + "lon": -73.24589, + "name": "Valdivia" + }, + { + "lat": -12.60139, + "lon": -38.96576, + "name": "Cachoeira" + }, + { + "lat": 15.2921, + "lon": 120.65498, + "name": "San Vicente" + } + ], + "question": "Which location is the geographic outlier among: Bela Vista, Chã Grande, Valdivia, Cachoeira, San Vicente?", + "ground_truth": { + "answer": "San Vicente", + "outlier_distance_km": 15425.9, + "second_furthest_km": 6210.9, + "clarity_ratio": 2.48, + "median_distance_km": 4310.3, + "distances_to_centroid": { + "Bela Vista": 4310.3, + "Chã Grande": 2128.4, + "Valdivia": 6210.9, + "Cachoeira": 2412.0, + "San Vicente": 15425.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bela Vista: (-22.11°, -56.53°)", + " Chã Grande: (-8.24°, -35.46°)", + " Valdivia: (-39.81°, -73.25°)", + " Cachoeira: (-12.60°, -38.97°)", + " San Vicente: (15.29°, 120.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Vicente: 15425.9 km from centroid", + " Valdivia: 6210.9 km from centroid", + " Bela Vista: 4310.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Vicente", + "FINAL ANSWER: San Vicente" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.27846, + "lon": 106.23157, + "name": "Degan" + }, + { + "lat": 34.43333, + "lon": 132.46667, + "name": "Gion" + }, + { + "lat": 29.32104, + "lon": 77.27101, + "name": "Kāndhla" + }, + { + "lat": 41.18806, + "lon": 122.04944, + "name": "Panshan" + }, + { + "lat": -4.22583, + "lon": -38.73056, + "name": "Redenção" + } + ], + "question": "Which location is the geographic outlier among: Degan, Gion, Kāndhla, Panshan, Redenção?", + "ground_truth": { + "answer": "Redenção", + "outlier_distance_km": 13061.6, + "second_furthest_km": 5085.0, + "clarity_ratio": 2.57, + "median_distance_km": 4206.7, + "distances_to_centroid": { + "Degan": 2617.9, + "Gion": 5085.0, + "Kāndhla": 448.7, + "Panshan": 4206.7, + "Redenção": 13061.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Degan: (29.28°, 106.23°)", + " Gion: (34.43°, 132.47°)", + " Kāndhla: (29.32°, 77.27°)", + " Panshan: (41.19°, 122.05°)", + " Redenção: (-4.23°, -38.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Redenção: 13061.6 km from centroid", + " Gion: 5085.0 km from centroid", + " Panshan: 4206.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Redenção", + "FINAL ANSWER: Redenção" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.70522, + "lon": 2.39147, + "name": "Athis-Mons" + }, + { + "lat": 46.34015, + "lon": 2.60254, + "name": "Montluçon" + }, + { + "lat": 51.95917, + "lon": 5.56806, + "name": "Rhenen" + }, + { + "lat": 50.31542, + "lon": 19.07824, + "name": "Czeladź" + }, + { + "lat": 28.94386, + "lon": 106.88194, + "name": "Nantong" + } + ], + "question": "Which location is the geographic outlier among: Athis-Mons, Montluçon, Rhenen, Czeladź, Nantong?", + "ground_truth": { + "answer": "Nantong", + "outlier_distance_km": 6996.9, + "second_furthest_km": 1919.5, + "clarity_ratio": 3.65, + "median_distance_km": 1911.1, + "distances_to_centroid": { + "Athis-Mons": 1919.5, + "Montluçon": 1911.1, + "Rhenen": 1754.7, + "Czeladź": 832.6, + "Nantong": 6996.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Athis-Mons: (48.71°, 2.39°)", + " Montluçon: (46.34°, 2.60°)", + " Rhenen: (51.96°, 5.57°)", + " Czeladź: (50.32°, 19.08°)", + " Nantong: (28.94°, 106.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nantong: 6996.9 km from centroid", + " Athis-Mons: 1919.5 km from centroid", + " Montluçon: 1911.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nantong", + "FINAL ANSWER: Nantong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.58301, + "lon": 19.35048, + "name": "Gansbaai" + }, + { + "lat": 7.15181, + "lon": 0.47362, + "name": "Hohoe" + }, + { + "lat": -25.86301, + "lon": 26.89756, + "name": "Koster" + }, + { + "lat": 9.23478, + "lon": 40.75593, + "name": "Mī’ēso" + }, + { + "lat": 43.52785, + "lon": -71.47035, + "name": "Laconia" + } + ], + "question": "Which location is the geographic outlier among: Gansbaai, Hohoe, Koster, Mī’ēso, Laconia?", + "ground_truth": { + "answer": "Laconia", + "outlier_distance_km": 8787.2, + "second_furthest_km": 4285.2, + "clarity_ratio": 2.05, + "median_distance_km": 4185.3, + "distances_to_centroid": { + "Gansbaai": 4185.3, + "Hohoe": 861.9, + "Koster": 3828.8, + "Mī’ēso": 4285.2, + "Laconia": 8787.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gansbaai: (-34.58°, 19.35°)", + " Hohoe: (7.15°, 0.47°)", + " Koster: (-25.86°, 26.90°)", + " Mī’ēso: (9.23°, 40.76°)", + " Laconia: (43.53°, -71.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Laconia: 8787.2 km from centroid", + " Mī’ēso: 4285.2 km from centroid", + " Gansbaai: 4185.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Laconia", + "FINAL ANSWER: Laconia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.66267, + "lon": -58.69819, + "name": "San Antonio de Padua" + }, + { + "lat": -20.97194, + "lon": -46.11889, + "name": "Carmo do Rio Claro" + }, + { + "lat": -28.05, + "lon": -56.03333, + "name": "Gobernador Virasora" + }, + { + "lat": -5.115, + "lon": -36.63444, + "name": "Macau" + }, + { + "lat": -19.30323, + "lon": 146.72531, + "name": "Kirwan" + } + ], + "question": "Which location is the geographic outlier among: San Antonio de Padua, Carmo do Rio Claro, Gobernador Virasora, Macau, Kirwan?", + "ground_truth": { + "answer": "Kirwan", + "outlier_distance_km": 14816.0, + "second_furthest_km": 4925.3, + "clarity_ratio": 3.01, + "median_distance_km": 4658.1, + "distances_to_centroid": { + "San Antonio de Padua": 4925.3, + "Carmo do Rio Claro": 3718.6, + "Gobernador Virasora": 4658.1, + "Macau": 3391.4, + "Kirwan": 14816.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Antonio de Padua: (-34.66°, -58.70°)", + " Carmo do Rio Claro: (-20.97°, -46.12°)", + " Gobernador Virasora: (-28.05°, -56.03°)", + " Macau: (-5.12°, -36.63°)", + " Kirwan: (-19.30°, 146.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kirwan: 14816.0 km from centroid", + " San Antonio de Padua: 4925.3 km from centroid", + " Gobernador Virasora: 4658.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kirwan", + "FINAL ANSWER: Kirwan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -17.74431, + "lon": -48.62789, + "name": "Caldas Novas" + }, + { + "lat": -22.22917, + "lon": -50.89306, + "name": "Rancharia" + }, + { + "lat": -21.87611, + "lon": -51.84389, + "name": "Presidente Venceslau" + }, + { + "lat": -6.17972, + "lon": -43.78361, + "name": "Passagem Franca" + }, + { + "lat": 6.76051, + "lon": -1.59402, + "name": "Ahwiaa" + } + ], + "question": "Which location is the geographic outlier among: Caldas Novas, Rancharia, Presidente Venceslau, Passagem Franca, Ahwiaa?", + "ground_truth": { + "answer": "Ahwiaa", + "outlier_distance_km": 4678.5, + "second_furthest_km": 1703.9, + "clarity_ratio": 2.75, + "median_distance_km": 1651.7, + "distances_to_centroid": { + "Caldas Novas": 1168.3, + "Rancharia": 1651.7, + "Presidente Venceslau": 1703.9, + "Passagem Franca": 832.4, + "Ahwiaa": 4678.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caldas Novas: (-17.74°, -48.63°)", + " Rancharia: (-22.23°, -50.89°)", + " Presidente Venceslau: (-21.88°, -51.84°)", + " Passagem Franca: (-6.18°, -43.78°)", + " Ahwiaa: (6.76°, -1.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ahwiaa: 4678.5 km from centroid", + " Presidente Venceslau: 1703.9 km from centroid", + " Rancharia: 1651.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ahwiaa", + "FINAL ANSWER: Ahwiaa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.8025, + "lon": -49.61, + "name": "Cafelândia" + }, + { + "lat": -5.13472, + "lon": -49.32667, + "name": "Itupiranga" + }, + { + "lat": -9.66, + "lon": -37.78944, + "name": "Canindé de São Francisco" + }, + { + "lat": -22.56472, + "lon": -47.40167, + "name": "Limeira" + }, + { + "lat": 31.3529, + "lon": 27.23725, + "name": "Marsá Maţrūḩ" + } + ], + "question": "Which location is the geographic outlier among: Cafelândia, Itupiranga, Canindé de São Francisco, Limeira, Marsá Maţrūḩ?", + "ground_truth": { + "answer": "Marsá Maţrūḩ", + "outlier_distance_km": 7439.8, + "second_furthest_km": 2666.2, + "clarity_ratio": 2.79, + "median_distance_km": 2556.2, + "distances_to_centroid": { + "Cafelândia": 2666.2, + "Itupiranga": 1987.6, + "Canindé de São Francisco": 840.7, + "Limeira": 2556.2, + "Marsá Maţrūḩ": 7439.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cafelândia: (-21.80°, -49.61°)", + " Itupiranga: (-5.13°, -49.33°)", + " Canindé de São Francisco: (-9.66°, -37.79°)", + " Limeira: (-22.56°, -47.40°)", + " Marsá Maţrūḩ: (31.35°, 27.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marsá Maţrūḩ: 7439.8 km from centroid", + " Cafelândia: 2666.2 km from centroid", + " Limeira: 2556.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marsá Maţrūḩ", + "FINAL ANSWER: Marsá Maţrūḩ" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -17.13806, + "lon": -49.98806, + "name": "Indiara" + }, + { + "lat": -2.51389, + "lon": -66.09167, + "name": "Fonte Boa" + }, + { + "lat": -7.33561, + "lon": -47.46218, + "name": "Carolina" + }, + { + "lat": -19.93408, + "lon": -40.40473, + "name": "Fundão" + }, + { + "lat": -33.8188, + "lon": 151.1062, + "name": "Ryde" + } + ], + "question": "Which location is the geographic outlier among: Indiara, Fonte Boa, Carolina, Fundão, Ryde?", + "ground_truth": { + "answer": "Ryde", + "outlier_distance_km": 14129.3, + "second_furthest_km": 6256.0, + "clarity_ratio": 2.26, + "median_distance_km": 4194.0, + "distances_to_centroid": { + "Indiara": 4194.0, + "Fonte Boa": 6256.0, + "Carolina": 4127.1, + "Fundão": 3178.3, + "Ryde": 14129.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Indiara: (-17.14°, -49.99°)", + " Fonte Boa: (-2.51°, -66.09°)", + " Carolina: (-7.34°, -47.46°)", + " Fundão: (-19.93°, -40.40°)", + " Ryde: (-33.82°, 151.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ryde: 14129.3 km from centroid", + " Fonte Boa: 6256.0 km from centroid", + " Indiara: 4194.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ryde", + "FINAL ANSWER: Ryde" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.45984, + "lon": 12.63338, + "name": "Eilenburg" + }, + { + "lat": 50.05912, + "lon": 22.49408, + "name": "Przeworsk" + }, + { + "lat": 48.90702, + "lon": 6.05635, + "name": "Pont-à-Mousson" + }, + { + "lat": 49.97524, + "lon": 19.82869, + "name": "Skawina" + }, + { + "lat": -22.42313, + "lon": -42.96612, + "name": "São Pedro" + } + ], + "question": "Which location is the geographic outlier among: Eilenburg, Przeworsk, Pont-à-Mousson, Skawina, São Pedro?", + "ground_truth": { + "answer": "São Pedro", + "outlier_distance_km": 8101.9, + "second_furthest_km": 2214.3, + "clarity_ratio": 3.66, + "median_distance_km": 2066.4, + "distances_to_centroid": { + "Eilenburg": 1904.7, + "Przeworsk": 2214.3, + "Pont-à-Mousson": 1493.6, + "Skawina": 2066.4, + "São Pedro": 8101.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eilenburg: (51.46°, 12.63°)", + " Przeworsk: (50.06°, 22.49°)", + " Pont-à-Mousson: (48.91°, 6.06°)", + " Skawina: (49.98°, 19.83°)", + " São Pedro: (-22.42°, -42.97°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Pedro: 8101.9 km from centroid", + " Przeworsk: 2214.3 km from centroid", + " Skawina: 2066.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Pedro", + "FINAL ANSWER: São Pedro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": -37.8, + "lon": 145.28333, + "name": "Croydon" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + }, + { + "lat": -25.44141, + "lon": 27.51114, + "name": "Hartbeestfontein-A" + } + ], + "question": "Which location is the geographic outlier among: Launceston, Pacific Pines, Croydon, Bendigo, Hartbeestfontein-A?", + "ground_truth": { + "answer": "Hartbeestfontein-A", + "outlier_distance_km": 8976.3, + "second_furthest_km": 2908.6, + "clarity_ratio": 3.09, + "median_distance_km": 2234.7, + "distances_to_centroid": { + "Launceston": 2234.7, + "Pacific Pines": 2908.6, + "Croydon": 2006.1, + "Bendigo": 1908.1, + "Hartbeestfontein-A": 8976.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Launceston: (-41.44°, 147.13°)", + " Pacific Pines: (-27.94°, 153.31°)", + " Croydon: (-37.80°, 145.28°)", + " Bendigo: (-36.76°, 144.28°)", + " Hartbeestfontein-A: (-25.44°, 27.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hartbeestfontein-A: 8976.3 km from centroid", + " Pacific Pines: 2908.6 km from centroid", + " Launceston: 2234.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hartbeestfontein-A", + "FINAL ANSWER: Hartbeestfontein-A" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73261, + "lon": 144.86504, + "name": "Keilor East" + }, + { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": 53.01532, + "lon": 39.14458, + "name": "Lebedyan’" + } + ], + "question": "Which location is the geographic outlier among: Keilor East, Frankston East, Wheelers Hill, Morayfield, Lebedyan’?", + "ground_truth": { + "answer": "Lebedyan’", + "outlier_distance_km": 11318.1, + "second_furthest_km": 3011.7, + "clarity_ratio": 3.76, + "median_distance_km": 2981.2, + "distances_to_centroid": { + "Keilor East": 2933.2, + "Frankston East": 2981.2, + "Wheelers Hill": 2966.2, + "Morayfield": 3011.7, + "Lebedyan’": 11318.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Keilor East: (-37.73°, 144.87°)", + " Frankston East: (-38.13°, 145.13°)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Morayfield: (-27.11°, 152.95°)", + " Lebedyan’: (53.02°, 39.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lebedyan’: 11318.1 km from centroid", + " Morayfield: 3011.7 km from centroid", + " Frankston East: 2981.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lebedyan’", + "FINAL ANSWER: Lebedyan’" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.61523, + "lon": 84.50208, + "name": "Simdega" + }, + { + "lat": 8.69264, + "lon": 76.79332, + "name": "Kīlattingal" + }, + { + "lat": 13.78126, + "lon": 100.64506, + "name": "Khlong Chan" + }, + { + "lat": 36.25449, + "lon": 140.37962, + "name": "Omitama" + }, + { + "lat": 50.45008, + "lon": -104.6178, + "name": "Regina" + } + ], + "question": "Which location is the geographic outlier among: Simdega, Kīlattingal, Khlong Chan, Omitama, Regina?", + "ground_truth": { + "answer": "Regina", + "outlier_distance_km": 11332.9, + "second_furthest_km": 7540.7, + "clarity_ratio": 1.5, + "median_distance_km": 4492.7, + "distances_to_centroid": { + "Simdega": 2555.9, + "Kīlattingal": 2677.4, + "Khlong Chan": 4492.7, + "Omitama": 7540.7, + "Regina": 11332.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Simdega: (22.62°, 84.50°)", + " Kīlattingal: (8.69°, 76.79°)", + " Khlong Chan: (13.78°, 100.65°)", + " Omitama: (36.25°, 140.38°)", + " Regina: (50.45°, -104.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Regina: 11332.9 km from centroid", + " Omitama: 7540.7 km from centroid", + " Khlong Chan: 4492.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Regina", + "FINAL ANSWER: Regina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.9725, + "lon": 6.71944, + "name": "Winterswijk" + }, + { + "lat": 40.46525, + "lon": -3.7173, + "name": "Valdezarza" + }, + { + "lat": 54.9876, + "lon": -1.74415, + "name": "Newburn" + }, + { + "lat": 43.29664, + "lon": 5.37034, + "name": "Marseille 02" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + } + ], + "question": "Which location is the geographic outlier among: Winterswijk, Valdezarza, Newburn, Marseille 02, Casula?", + "ground_truth": { + "answer": "Casula", + "outlier_distance_km": 14417.9, + "second_furthest_km": 3701.6, + "clarity_ratio": 3.9, + "median_distance_km": 3305.1, + "distances_to_centroid": { + "Winterswijk": 3051.3, + "Valdezarza": 3305.1, + "Newburn": 3701.6, + "Marseille 02": 2648.8, + "Casula": 14417.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Winterswijk: (51.97°, 6.72°)", + " Valdezarza: (40.47°, -3.72°)", + " Newburn: (54.99°, -1.74°)", + " Marseille 02: (43.30°, 5.37°)", + " Casula: (-33.95°, 150.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casula: 14417.9 km from centroid", + " Newburn: 3701.6 km from centroid", + " Valdezarza: 3305.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casula", + "FINAL ANSWER: Casula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.00423, + "lon": 107.69074, + "name": "Gia Nghĩa" + }, + { + "lat": 2.6579, + "lon": 101.5629, + "name": "Tanjung Sepat" + }, + { + "lat": 34.73333, + "lon": 135.56667, + "name": "Moriguchi" + }, + { + "lat": 30.79834, + "lon": 108.37089, + "name": "Jiuchi" + }, + { + "lat": -2.90222, + "lon": -40.84111, + "name": "Camocim" + } + ], + "question": "Which location is the geographic outlier among: Gia Nghĩa, Tanjung Sepat, Moriguchi, Jiuchi, Camocim?", + "ground_truth": { + "answer": "Camocim", + "outlier_distance_km": 13658.0, + "second_furthest_km": 5686.0, + "clarity_ratio": 2.4, + "median_distance_km": 3136.9, + "distances_to_centroid": { + "Gia Nghĩa": 2749.5, + "Tanjung Sepat": 2530.0, + "Moriguchi": 5686.0, + "Jiuchi": 3136.9, + "Camocim": 13658.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gia Nghĩa: (12.00°, 107.69°)", + " Tanjung Sepat: (2.66°, 101.56°)", + " Moriguchi: (34.73°, 135.57°)", + " Jiuchi: (30.80°, 108.37°)", + " Camocim: (-2.90°, -40.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Camocim: 13658.0 km from centroid", + " Moriguchi: 5686.0 km from centroid", + " Jiuchi: 3136.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Camocim", + "FINAL ANSWER: Camocim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 62.20406, + "lon": 34.26932, + "name": "Kondopoga" + }, + { + "lat": 53.20356, + "lon": 45.19227, + "name": "Zarechnyy" + }, + { + "lat": 55.0522, + "lon": 74.5787, + "name": "Kalachinsk" + }, + { + "lat": 52.19166, + "lon": -1.70734, + "name": "Stratford-upon-Avon" + }, + { + "lat": -13.01944, + "lon": -42.69861, + "name": "Macaúbas" + } + ], + "question": "Which location is the geographic outlier among: Kondopoga, Zarechnyy, Kalachinsk, Stratford-upon-Avon, Macaúbas?", + "ground_truth": { + "answer": "Macaúbas", + "outlier_distance_km": 8983.1, + "second_furthest_km": 4033.1, + "clarity_ratio": 2.23, + "median_distance_km": 2397.8, + "distances_to_centroid": { + "Kondopoga": 2397.8, + "Zarechnyy": 2133.4, + "Kalachinsk": 4033.1, + "Stratford-upon-Avon": 2108.4, + "Macaúbas": 8983.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kondopoga: (62.20°, 34.27°)", + " Zarechnyy: (53.20°, 45.19°)", + " Kalachinsk: (55.05°, 74.58°)", + " Stratford-upon-Avon: (52.19°, -1.71°)", + " Macaúbas: (-13.02°, -42.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Macaúbas: 8983.1 km from centroid", + " Kalachinsk: 4033.1 km from centroid", + " Kondopoga: 2397.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Macaúbas", + "FINAL ANSWER: Macaúbas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.34772, + "lon": -120.60908, + "name": "Atwater" + }, + { + "lat": 42.00833, + "lon": -91.64407, + "name": "Cedar Rapids" + }, + { + "lat": 41.31649, + "lon": -73.09316, + "name": "Shelton" + }, + { + "lat": 42.86947, + "lon": -85.64475, + "name": "Kentwood" + }, + { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + } + ], + "question": "Which location is the geographic outlier among: Atwater, Cedar Rapids, Shelton, Kentwood, Mascot?", + "ground_truth": { + "answer": "Mascot", + "outlier_distance_km": 18307.9, + "second_furthest_km": 7173.6, + "clarity_ratio": 2.55, + "median_distance_km": 4676.7, + "distances_to_centroid": { + "Atwater": 7173.6, + "Cedar Rapids": 4676.7, + "Shelton": 3171.1, + "Kentwood": 4208.0, + "Mascot": 18307.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Atwater: (37.35°, -120.61°)", + " Cedar Rapids: (42.01°, -91.64°)", + " Shelton: (41.32°, -73.09°)", + " Kentwood: (42.87°, -85.64°)", + " Mascot: (-33.93°, 151.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mascot: 18307.9 km from centroid", + " Atwater: 7173.6 km from centroid", + " Cedar Rapids: 4676.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mascot", + "FINAL ANSWER: Mascot" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.55555, + "lon": -103.37587, + "name": "Tuxpan" + }, + { + "lat": 45.59456, + "lon": -121.17868, + "name": "The Dalles" + }, + { + "lat": 30.46159, + "lon": -87.31497, + "name": "Bellview" + }, + { + "lat": 25.0321, + "lon": -111.66256, + "name": "Ciudad Constitución" + }, + { + "lat": 9.60776, + "lon": 8.39043, + "name": "Kagoro" + } + ], + "question": "Which location is the geographic outlier among: Tuxpan, The Dalles, Bellview, Ciudad Constitución, Kagoro?", + "ground_truth": { + "answer": "Kagoro", + "outlier_distance_km": 9680.2, + "second_furthest_km": 4012.9, + "clarity_ratio": 2.41, + "median_distance_km": 2869.3, + "distances_to_centroid": { + "Tuxpan": 2204.0, + "The Dalles": 4012.9, + "Bellview": 645.5, + "Ciudad Constitución": 2869.3, + "Kagoro": 9680.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tuxpan: (19.56°, -103.38°)", + " The Dalles: (45.59°, -121.18°)", + " Bellview: (30.46°, -87.31°)", + " Ciudad Constitución: (25.03°, -111.66°)", + " Kagoro: (9.61°, 8.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kagoro: 9680.2 km from centroid", + " The Dalles: 4012.9 km from centroid", + " Ciudad Constitución: 2869.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kagoro", + "FINAL ANSWER: Kagoro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": 28.94386, + "lon": 106.88194, + "name": "Nantong" + } + ], + "question": "Which location is the geographic outlier among: Mooroolbark, Miranda, Bendigo, Footscray, Nantong?", + "ground_truth": { + "answer": "Nantong", + "outlier_distance_km": 6740.5, + "second_furthest_km": 1717.0, + "clarity_ratio": 3.93, + "median_distance_km": 1704.2, + "distances_to_centroid": { + "Mooroolbark": 1717.0, + "Miranda": 1696.0, + "Bendigo": 1576.2, + "Footscray": 1704.2, + "Nantong": 6740.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mooroolbark: (-37.78°, 145.32°)", + " Miranda: (-34.04°, 151.10°)", + " Bendigo: (-36.76°, 144.28°)", + " Footscray: (-37.80°, 144.90°)", + " Nantong: (28.94°, 106.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nantong: 6740.5 km from centroid", + " Mooroolbark: 1717.0 km from centroid", + " Footscray: 1704.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nantong", + "FINAL ANSWER: Nantong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.94944, + "lon": -48.47917, + "name": "Bebedouro" + }, + { + "lat": -7.56056, + "lon": -35.0025, + "name": "Goiana" + }, + { + "lat": -34.09584, + "lon": -59.02423, + "name": "Zárate" + }, + { + "lat": 8.27515, + "lon": -76.37641, + "name": "San Pedro de Urabá" + }, + { + "lat": 28.50254, + "lon": 77.23117, + "name": "Deoli" + } + ], + "question": "Which location is the geographic outlier among: Bebedouro, Goiana, Zárate, San Pedro de Urabá, Deoli?", + "ground_truth": { + "answer": "Deoli", + "outlier_distance_km": 11800.8, + "second_furthest_km": 5533.6, + "clarity_ratio": 2.13, + "median_distance_km": 4510.6, + "distances_to_centroid": { + "Bebedouro": 2793.9, + "Goiana": 783.9, + "Zárate": 4510.6, + "San Pedro de Urabá": 5533.6, + "Deoli": 11800.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bebedouro: (-20.95°, -48.48°)", + " Goiana: (-7.56°, -35.00°)", + " Zárate: (-34.10°, -59.02°)", + " San Pedro de Urabá: (8.28°, -76.38°)", + " Deoli: (28.50°, 77.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Deoli: 11800.8 km from centroid", + " San Pedro de Urabá: 5533.6 km from centroid", + " Zárate: 4510.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Deoli", + "FINAL ANSWER: Deoli" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.93312, + "lon": 28.01213, + "name": "Diepsloot" + }, + { + "lat": 7.85, + "lon": 36.65, + "name": "Āgaro" + }, + { + "lat": 30.13806, + "lon": 31.61556, + "name": "El Shorouk" + }, + { + "lat": -30.28666, + "lon": 30.75316, + "name": "Scottburgh" + }, + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + } + ], + "question": "Which location is the geographic outlier among: Diepsloot, Āgaro, El Shorouk, Scottburgh, Bexley?", + "ground_truth": { + "answer": "Bexley", + "outlier_distance_km": 9860.0, + "second_furthest_km": 5191.7, + "clarity_ratio": 1.9, + "median_distance_km": 3389.4, + "distances_to_centroid": { + "Diepsloot": 3375.8, + "Āgaro": 2923.7, + "El Shorouk": 5191.7, + "Scottburgh": 3389.4, + "Bexley": 9860.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Diepsloot: (-25.93°, 28.01°)", + " Āgaro: (7.85°, 36.65°)", + " El Shorouk: (30.14°, 31.62°)", + " Scottburgh: (-30.29°, 30.75°)", + " Bexley: (-33.95°, 151.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bexley: 9860.0 km from centroid", + " El Shorouk: 5191.7 km from centroid", + " Scottburgh: 3389.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bexley", + "FINAL ANSWER: Bexley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.45978, + "lon": 38.44358, + "name": "Beloozyorskiy" + }, + { + "lat": 51.96236, + "lon": 7.62571, + "name": "Münster" + }, + { + "lat": 40.43533, + "lon": -3.6251, + "name": "Simancas" + }, + { + "lat": 48.99712, + "lon": 2.28249, + "name": "Eaubonne" + }, + { + "lat": 15.31771, + "lon": 78.22669, + "name": "Banganapalle" + } + ], + "question": "Which location is the geographic outlier among: Beloozyorskiy, Münster, Simancas, Eaubonne, Banganapalle?", + "ground_truth": { + "answer": "Banganapalle", + "outlier_distance_km": 5905.4, + "second_furthest_km": 2351.8, + "clarity_ratio": 2.51, + "median_distance_km": 1870.6, + "distances_to_centroid": { + "Beloozyorskiy": 1759.7, + "Münster": 1655.8, + "Simancas": 2351.8, + "Eaubonne": 1870.6, + "Banganapalle": 5905.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beloozyorskiy: (55.46°, 38.44°)", + " Münster: (51.96°, 7.63°)", + " Simancas: (40.44°, -3.63°)", + " Eaubonne: (49.00°, 2.28°)", + " Banganapalle: (15.32°, 78.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Banganapalle: 5905.4 km from centroid", + " Simancas: 2351.8 km from centroid", + " Eaubonne: 1870.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Banganapalle", + "FINAL ANSWER: Banganapalle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.76667, + "lon": 145.0, + "name": "Northcote" + }, + { + "lat": -38.03333, + "lon": 145.25, + "name": "Hampton Park" + }, + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + { + "lat": -37.83382, + "lon": 144.93834, + "name": "City of Port Phillip" + }, + { + "lat": -19.81, + "lon": -43.17361, + "name": "João Monlevade" + } + ], + "question": "Which location is the geographic outlier among: Northcote, Hampton Park, Traralgon, City of Port Phillip, João Monlevade?", + "ground_truth": { + "answer": "João Monlevade", + "outlier_distance_km": 13253.0, + "second_furthest_km": 3482.4, + "clarity_ratio": 3.81, + "median_distance_km": 3371.4, + "distances_to_centroid": { + "Northcote": 3352.0, + "Hampton Park": 3371.4, + "Traralgon": 3482.4, + "City of Port Phillip": 3345.9, + "João Monlevade": 13253.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Northcote: (-37.77°, 145.00°)", + " Hampton Park: (-38.03°, 145.25°)", + " Traralgon: (-38.20°, 146.54°)", + " City of Port Phillip: (-37.83°, 144.94°)", + " João Monlevade: (-19.81°, -43.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " João Monlevade: 13253.0 km from centroid", + " Traralgon: 3482.4 km from centroid", + " Hampton Park: 3371.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: João Monlevade", + "FINAL ANSWER: João Monlevade" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -16.44194, + "lon": -51.11778, + "name": "Iporá" + }, + { + "lat": -10.34472, + "lon": -39.83556, + "name": "Andorinha" + }, + { + "lat": -27.11639, + "lon": -49.99806, + "name": "Taió" + }, + { + "lat": -0.62099, + "lon": -47.35422, + "name": "Salinópolis" + }, + { + "lat": 40.29081, + "lon": 141.31334, + "name": "Ninohe" + } + ], + "question": "Which location is the geographic outlier among: Iporá, Andorinha, Taió, Salinópolis, Ninohe?", + "ground_truth": { + "answer": "Ninohe", + "outlier_distance_km": 14917.0, + "second_furthest_km": 5088.7, + "clarity_ratio": 2.93, + "median_distance_km": 4802.7, + "distances_to_centroid": { + "Iporá": 4802.7, + "Andorinha": 3460.9, + "Taió": 5088.7, + "Salinópolis": 4225.5, + "Ninohe": 14917.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Iporá: (-16.44°, -51.12°)", + " Andorinha: (-10.34°, -39.84°)", + " Taió: (-27.12°, -50.00°)", + " Salinópolis: (-0.62°, -47.35°)", + " Ninohe: (40.29°, 141.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ninohe: 14917.0 km from centroid", + " Taió: 5088.7 km from centroid", + " Iporá: 4802.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ninohe", + "FINAL ANSWER: Ninohe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.87995, + "lon": 76.002, + "name": "Naduvattam" + }, + { + "lat": 34.93806, + "lon": 105.8775, + "name": "Zhongshan" + }, + { + "lat": 20.79393, + "lon": 70.70216, + "name": "Kodīnar" + }, + { + "lat": 23.1912, + "lon": 82.16265, + "name": "Khongapani" + }, + { + "lat": 25.90232, + "lon": -80.25033, + "name": "Opa-locka" + } + ], + "question": "Which location is the geographic outlier among: Naduvattam, Zhongshan, Kodīnar, Khongapani, Opa-locka?", + "ground_truth": { + "answer": "Opa-locka", + "outlier_distance_km": 12440.2, + "second_furthest_km": 5435.0, + "clarity_ratio": 2.29, + "median_distance_km": 3189.8, + "distances_to_centroid": { + "Naduvattam": 2989.8, + "Zhongshan": 5435.0, + "Kodīnar": 2057.1, + "Khongapani": 3189.8, + "Opa-locka": 12440.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Naduvattam: (10.88°, 76.00°)", + " Zhongshan: (34.94°, 105.88°)", + " Kodīnar: (20.79°, 70.70°)", + " Khongapani: (23.19°, 82.16°)", + " Opa-locka: (25.90°, -80.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Opa-locka: 12440.2 km from centroid", + " Zhongshan: 5435.0 km from centroid", + " Khongapani: 3189.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Opa-locka", + "FINAL ANSWER: Opa-locka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": 1.7471, + "lon": 40.05732, + "name": "Wajir" + } + ], + "question": "Which location is the geographic outlier among: Wainuiomata, Mooroolbark, Hastings, Carrum Downs, Wajir?", + "ground_truth": { + "answer": "Wajir", + "outlier_distance_km": 10718.6, + "second_furthest_km": 3753.3, + "clarity_ratio": 2.86, + "median_distance_km": 3605.5, + "distances_to_centroid": { + "Wainuiomata": 3605.5, + "Mooroolbark": 1106.4, + "Hastings": 3753.3, + "Carrum Downs": 1120.2, + "Wajir": 10718.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wainuiomata: (-41.27°, 174.95°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Hastings: (-39.64°, 176.85°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Wajir: (1.75°, 40.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wajir: 10718.6 km from centroid", + " Hastings: 3753.3 km from centroid", + " Wainuiomata: 3605.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wajir", + "FINAL ANSWER: Wajir" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.67616, + "lon": -102.58803, + "name": "Villa Hidalgo" + }, + { + "lat": 35.62246, + "lon": -117.6709, + "name": "Ridgecrest" + }, + { + "lat": 37.04308, + "lon": -100.921, + "name": "Liberal" + }, + { + "lat": 42.24177, + "lon": -71.16616, + "name": "Dedham" + }, + { + "lat": 16.82481, + "lon": 100.25858, + "name": "Phitsanulok" + } + ], + "question": "Which location is the geographic outlier among: Villa Hidalgo, Ridgecrest, Liberal, Dedham, Phitsanulok?", + "ground_truth": { + "answer": "Phitsanulok", + "outlier_distance_km": 14261.2, + "second_furthest_km": 5460.8, + "clarity_ratio": 2.61, + "median_distance_km": 4490.5, + "distances_to_centroid": { + "Villa Hidalgo": 4490.5, + "Ridgecrest": 5460.8, + "Liberal": 3954.5, + "Dedham": 1714.2, + "Phitsanulok": 14261.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Villa Hidalgo: (21.68°, -102.59°)", + " Ridgecrest: (35.62°, -117.67°)", + " Liberal: (37.04°, -100.92°)", + " Dedham: (42.24°, -71.17°)", + " Phitsanulok: (16.82°, 100.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Phitsanulok: 14261.2 km from centroid", + " Ridgecrest: 5460.8 km from centroid", + " Villa Hidalgo: 4490.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Phitsanulok", + "FINAL ANSWER: Phitsanulok" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.82166, + "lon": -1.2886, + "name": "Kidlington" + }, + { + "lat": 51.29472, + "lon": 7.67337, + "name": "Altena" + }, + { + "lat": 49.58333, + "lon": 3.0, + "name": "Noyon" + }, + { + "lat": 49.44287, + "lon": 11.86267, + "name": "Amberg" + }, + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + } + ], + "question": "Which location is the geographic outlier among: Kidlington, Altena, Noyon, Amberg, Southbank?", + "ground_truth": { + "answer": "Southbank", + "outlier_distance_km": 13936.4, + "second_furthest_km": 3482.5, + "clarity_ratio": 4.0, + "median_distance_km": 3104.5, + "distances_to_centroid": { + "Kidlington": 3482.5, + "Altena": 2913.2, + "Noyon": 3104.5, + "Amberg": 2551.9, + "Southbank": 13936.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kidlington: (51.82°, -1.29°)", + " Altena: (51.29°, 7.67°)", + " Noyon: (49.58°, 3.00°)", + " Amberg: (49.44°, 11.86°)", + " Southbank: (-37.82°, 144.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Southbank: 13936.4 km from centroid", + " Kidlington: 3482.5 km from centroid", + " Noyon: 3104.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Southbank", + "FINAL ANSWER: Southbank" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.68219, + "lon": 100.50603, + "name": "Rat Burana" + }, + { + "lat": 34.88333, + "lon": 136.58333, + "name": "Suzuka" + }, + { + "lat": 38.42738, + "lon": 141.21487, + "name": "Yamoto" + }, + { + "lat": 25.53852, + "lon": 87.57044, + "name": "Katihar" + }, + { + "lat": 42.57509, + "lon": -70.93005, + "name": "Danvers" + } + ], + "question": "Which location is the geographic outlier among: Rat Burana, Suzuka, Yamoto, Katihar, Danvers?", + "ground_truth": { + "answer": "Danvers", + "outlier_distance_km": 11273.5, + "second_furthest_km": 5639.5, + "clarity_ratio": 2.0, + "median_distance_km": 5317.2, + "distances_to_centroid": { + "Rat Burana": 2923.8, + "Suzuka": 5317.2, + "Yamoto": 5639.5, + "Katihar": 1037.6, + "Danvers": 11273.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rat Burana: (13.68°, 100.51°)", + " Suzuka: (34.88°, 136.58°)", + " Yamoto: (38.43°, 141.21°)", + " Katihar: (25.54°, 87.57°)", + " Danvers: (42.58°, -70.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Danvers: 11273.5 km from centroid", + " Yamoto: 5639.5 km from centroid", + " Suzuka: 5317.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Danvers", + "FINAL ANSWER: Danvers" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.04422, + "lon": -82.23593, + "name": "North Port" + }, + { + "lat": 32.74255, + "lon": -117.03142, + "name": "Lemon Grove" + }, + { + "lat": 20.44997, + "lon": -101.53073, + "name": "Abasolo" + }, + { + "lat": 17.64344, + "lon": -101.55212, + "name": "Ixtapa-Zihuatanejo" + }, + { + "lat": -6.41972, + "lon": 107.45583, + "name": "Cikampek" + } + ], + "question": "Which location is the geographic outlier among: North Port, Lemon Grove, Abasolo, Ixtapa-Zihuatanejo, Cikampek?", + "ground_truth": { + "answer": "Cikampek", + "outlier_distance_km": 18039.1, + "second_furthest_km": 5968.6, + "clarity_ratio": 3.02, + "median_distance_km": 4493.2, + "distances_to_centroid": { + "North Port": 2571.5, + "Lemon Grove": 5968.6, + "Abasolo": 4457.9, + "Ixtapa-Zihuatanejo": 4493.2, + "Cikampek": 18039.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Port: (27.04°, -82.24°)", + " Lemon Grove: (32.74°, -117.03°)", + " Abasolo: (20.45°, -101.53°)", + " Ixtapa-Zihuatanejo: (17.64°, -101.55°)", + " Cikampek: (-6.42°, 107.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cikampek: 18039.1 km from centroid", + " Lemon Grove: 5968.6 km from centroid", + " Ixtapa-Zihuatanejo: 4493.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cikampek", + "FINAL ANSWER: Cikampek" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.03483, + "lon": -76.90747, + "name": "Beltsville" + }, + { + "lat": 41.4501, + "lon": -71.4495, + "name": "Narragansett" + }, + { + "lat": 39.75554, + "lon": -105.2211, + "name": "Golden" + }, + { + "lat": 48.4277, + "lon": -123.36104, + "name": "Victoria-Downtown" + }, + { + "lat": 27.04514, + "lon": 31.31845, + "name": "Abū Tīj" + } + ], + "question": "Which location is the geographic outlier among: Beltsville, Narragansett, Golden, Victoria-Downtown, Abū Tīj?", + "ground_truth": { + "answer": "Abū Tīj", + "outlier_distance_km": 8972.0, + "second_furthest_km": 4378.1, + "clarity_ratio": 2.05, + "median_distance_km": 3079.0, + "distances_to_centroid": { + "Beltsville": 671.7, + "Narragansett": 323.6, + "Golden": 3079.0, + "Victoria-Downtown": 4378.1, + "Abū Tīj": 8972.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Beltsville: (39.03°, -76.91°)", + " Narragansett: (41.45°, -71.45°)", + " Golden: (39.76°, -105.22°)", + " Victoria-Downtown: (48.43°, -123.36°)", + " Abū Tīj: (27.05°, 31.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Abū Tīj: 8972.0 km from centroid", + " Victoria-Downtown: 4378.1 km from centroid", + " Golden: 3079.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Abū Tīj", + "FINAL ANSWER: Abū Tīj" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.37032, + "lon": -112.58378, + "name": "Buckeye" + }, + { + "lat": 40.03122, + "lon": -75.04434, + "name": "Tacony" + }, + { + "lat": 40.65788, + "lon": -73.83625, + "name": "Howard Beach" + }, + { + "lat": 33.976, + "lon": -118.06909, + "name": "West Whittier-Los Nietos" + }, + { + "lat": 7.15109, + "lon": 35.81703, + "name": "Wacha" + } + ], + "question": "Which location is the geographic outlier among: Buckeye, Tacony, Howard Beach, West Whittier-Los Nietos, Wacha?", + "ground_truth": { + "answer": "Wacha", + "outlier_distance_km": 10963.9, + "second_furthest_km": 4592.6, + "clarity_ratio": 2.39, + "median_distance_km": 4102.7, + "distances_to_centroid": { + "Buckeye": 4102.7, + "Tacony": 1150.4, + "Howard Beach": 1163.5, + "West Whittier-Los Nietos": 4592.6, + "Wacha": 10963.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Buckeye: (33.37°, -112.58°)", + " Tacony: (40.03°, -75.04°)", + " Howard Beach: (40.66°, -73.84°)", + " West Whittier-Los Nietos: (33.98°, -118.07°)", + " Wacha: (7.15°, 35.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wacha: 10963.9 km from centroid", + " West Whittier-Los Nietos: 4592.6 km from centroid", + " Buckeye: 4102.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wacha", + "FINAL ANSWER: Wacha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.88775, + "lon": 115.9099, + "name": "Morley" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": -27.94402, + "lon": 153.39815, + "name": "Labrador" + }, + { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + }, + { + "lat": -12.06866, + "lon": -75.21027, + "name": "Huancayo" + } + ], + "question": "Which location is the geographic outlier among: Morley, Footscray, Labrador, Dianella, Huancayo?", + "ground_truth": { + "answer": "Huancayo", + "outlier_distance_km": 15284.7, + "second_furthest_km": 6047.6, + "clarity_ratio": 2.53, + "median_distance_km": 5064.6, + "distances_to_centroid": { + "Morley": 2425.9, + "Footscray": 5064.6, + "Labrador": 6047.6, + "Dianella": 2422.3, + "Huancayo": 15284.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morley: (-31.89°, 115.91°)", + " Footscray: (-37.80°, 144.90°)", + " Labrador: (-27.94°, 153.40°)", + " Dianella: (-31.89°, 115.87°)", + " Huancayo: (-12.07°, -75.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Huancayo: 15284.7 km from centroid", + " Labrador: 6047.6 km from centroid", + " Footscray: 5064.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Huancayo", + "FINAL ANSWER: Huancayo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.28195, + "lon": -118.43897, + "name": "San Fernando" + }, + { + "lat": 29.56357, + "lon": -95.28605, + "name": "Pearland" + }, + { + "lat": 45.26678, + "lon": -72.14909, + "name": "Magog" + }, + { + "lat": 25.27673, + "lon": -100.01442, + "name": "Ciudad de Allende" + }, + { + "lat": -24.65028, + "lon": -50.85056, + "name": "Reserva" + } + ], + "question": "Which location is the geographic outlier among: San Fernando, Pearland, Magog, Ciudad de Allende, Reserva?", + "ground_truth": { + "answer": "Reserva", + "outlier_distance_km": 6510.2, + "second_furthest_km": 3325.7, + "clarity_ratio": 1.96, + "median_distance_km": 2938.8, + "distances_to_centroid": { + "San Fernando": 3325.7, + "Pearland": 1160.8, + "Magog": 2938.8, + "Ciudad de Allende": 1341.9, + "Reserva": 6510.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Fernando: (34.28°, -118.44°)", + " Pearland: (29.56°, -95.29°)", + " Magog: (45.27°, -72.15°)", + " Ciudad de Allende: (25.28°, -100.01°)", + " Reserva: (-24.65°, -50.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Reserva: 6510.2 km from centroid", + " San Fernando: 3325.7 km from centroid", + " Magog: 2938.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Reserva", + "FINAL ANSWER: Reserva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.18539, + "lon": 6.44172, + "name": "Mönchengladbach" + }, + { + "lat": 48.60603, + "lon": 2.48757, + "name": "Corbeil-Essonnes" + }, + { + "lat": 55.88753, + "lon": 60.75478, + "name": "Kasli" + }, + { + "lat": 53.42324, + "lon": -3.06497, + "name": "Wallasey" + }, + { + "lat": -36.84103, + "lon": 174.65223, + "name": "Te Atatu Peninsula" + } + ], + "question": "Which location is the geographic outlier among: Mönchengladbach, Corbeil-Essonnes, Kasli, Wallasey, Te Atatu Peninsula?", + "ground_truth": { + "answer": "Te Atatu Peninsula", + "outlier_distance_km": 15228.5, + "second_furthest_km": 4493.6, + "clarity_ratio": 3.39, + "median_distance_km": 4049.1, + "distances_to_centroid": { + "Mönchengladbach": 3814.8, + "Corbeil-Essonnes": 4049.1, + "Kasli": 2567.8, + "Wallasey": 4493.6, + "Te Atatu Peninsula": 15228.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mönchengladbach: (51.19°, 6.44°)", + " Corbeil-Essonnes: (48.61°, 2.49°)", + " Kasli: (55.89°, 60.75°)", + " Wallasey: (53.42°, -3.06°)", + " Te Atatu Peninsula: (-36.84°, 174.65°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Te Atatu Peninsula: 15228.5 km from centroid", + " Wallasey: 4493.6 km from centroid", + " Corbeil-Essonnes: 4049.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Te Atatu Peninsula", + "FINAL ANSWER: Te Atatu Peninsula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.07418, + "lon": -82.47176, + "name": "Lake Magdalene" + }, + { + "lat": 49.21392, + "lon": -122.93992, + "name": "Edmonds" + }, + { + "lat": 33.88168, + "lon": -118.11701, + "name": "Bellflower" + }, + { + "lat": 29.97854, + "lon": -90.16396, + "name": "Metairie Terrace" + }, + { + "lat": 8.5688, + "lon": 78.09091, + "name": "Arumuganeri" + } + ], + "question": "Which location is the geographic outlier among: Lake Magdalene, Edmonds, Bellflower, Metairie Terrace, Arumuganeri?", + "ground_truth": { + "answer": "Arumuganeri", + "outlier_distance_km": 14344.2, + "second_furthest_km": 5103.7, + "clarity_ratio": 2.81, + "median_distance_km": 4784.6, + "distances_to_centroid": { + "Lake Magdalene": 1506.1, + "Edmonds": 5103.7, + "Bellflower": 4784.6, + "Metairie Terrace": 2216.1, + "Arumuganeri": 14344.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lake Magdalene: (28.07°, -82.47°)", + " Edmonds: (49.21°, -122.94°)", + " Bellflower: (33.88°, -118.12°)", + " Metairie Terrace: (29.98°, -90.16°)", + " Arumuganeri: (8.57°, 78.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arumuganeri: 14344.2 km from centroid", + " Edmonds: 5103.7 km from centroid", + " Bellflower: 4784.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arumuganeri", + "FINAL ANSWER: Arumuganeri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.14535, + "lon": -85.8583, + "name": "Pleasure Ridge Park" + }, + { + "lat": 42.5001, + "lon": -70.85783, + "name": "Marblehead" + }, + { + "lat": 40.66094, + "lon": -73.92014, + "name": "Brownsville" + }, + { + "lat": 30.21309, + "lon": -93.2044, + "name": "Lake Charles" + }, + { + "lat": -13.22861, + "lon": -39.50472, + "name": "Mutuípe" + } + ], + "question": "Which location is the geographic outlier among: Pleasure Ridge Park, Marblehead, Brownsville, Lake Charles, Mutuípe?", + "ground_truth": { + "answer": "Mutuípe", + "outlier_distance_km": 5783.0, + "second_furthest_km": 2015.6, + "clarity_ratio": 2.87, + "median_distance_km": 1692.5, + "distances_to_centroid": { + "Pleasure Ridge Park": 1692.5, + "Marblehead": 1658.4, + "Brownsville": 1450.4, + "Lake Charles": 2015.6, + "Mutuípe": 5783.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pleasure Ridge Park: (38.15°, -85.86°)", + " Marblehead: (42.50°, -70.86°)", + " Brownsville: (40.66°, -73.92°)", + " Lake Charles: (30.21°, -93.20°)", + " Mutuípe: (-13.23°, -39.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mutuípe: 5783.0 km from centroid", + " Lake Charles: 2015.6 km from centroid", + " Pleasure Ridge Park: 1692.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mutuípe", + "FINAL ANSWER: Mutuípe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.99306, + "lon": 31.41605, + "name": "Al Badārī" + }, + { + "lat": 29.03556, + "lon": 31.11792, + "name": "New Bani Sewif City" + }, + { + "lat": 10.45, + "lon": 38.2, + "name": "Bichena" + }, + { + "lat": 6.6584, + "lon": 8.79923, + "name": "Ogoja" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + } + ], + "question": "Which location is the geographic outlier among: Al Badārī, New Bani Sewif City, Bichena, Ogoja, Cabramatta?", + "ground_truth": { + "answer": "Cabramatta", + "outlier_distance_km": 11306.8, + "second_furthest_km": 4775.4, + "clarity_ratio": 2.37, + "median_distance_km": 3219.6, + "distances_to_centroid": { + "Al Badārī": 3046.6, + "New Bani Sewif City": 3219.6, + "Bichena": 1552.2, + "Ogoja": 4775.4, + "Cabramatta": 11306.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Badārī: (26.99°, 31.42°)", + " New Bani Sewif City: (29.04°, 31.12°)", + " Bichena: (10.45°, 38.20°)", + " Ogoja: (6.66°, 8.80°)", + " Cabramatta: (-33.90°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cabramatta: 11306.8 km from centroid", + " Ogoja: 4775.4 km from centroid", + " New Bani Sewif City: 3219.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cabramatta", + "FINAL ANSWER: Cabramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.12996, + "lon": -81.76815, + "name": "Lakeside" + }, + { + "lat": 42.28343, + "lon": -71.06894, + "name": "Ashmont" + }, + { + "lat": 24.02032, + "lon": -104.65756, + "name": "Victoria de Durango" + }, + { + "lat": 33.70918, + "lon": -117.95367, + "name": "Fountain Valley" + }, + { + "lat": -33.72976, + "lon": 151.15977, + "name": "Saint Ives" + } + ], + "question": "Which location is the geographic outlier among: Lakeside, Ashmont, Victoria de Durango, Fountain Valley, Saint Ives?", + "ground_truth": { + "answer": "Saint Ives", + "outlier_distance_km": 17758.1, + "second_furthest_km": 7305.0, + "clarity_ratio": 2.43, + "median_distance_km": 6158.1, + "distances_to_centroid": { + "Lakeside": 3898.9, + "Ashmont": 3550.5, + "Victoria de Durango": 6158.1, + "Fountain Valley": 7305.0, + "Saint Ives": 17758.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lakeside: (30.13°, -81.77°)", + " Ashmont: (42.28°, -71.07°)", + " Victoria de Durango: (24.02°, -104.66°)", + " Fountain Valley: (33.71°, -117.95°)", + " Saint Ives: (-33.73°, 151.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saint Ives: 17758.1 km from centroid", + " Fountain Valley: 7305.0 km from centroid", + " Victoria de Durango: 6158.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saint Ives", + "FINAL ANSWER: Saint Ives" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.8162, + "lon": 2.31393, + "name": "Montrouge" + }, + { + "lat": 53.38333, + "lon": -2.11667, + "name": "Hazel Grove" + }, + { + "lat": 50.80901, + "lon": 7.14968, + "name": "Troisdorf" + }, + { + "lat": 51.38132, + "lon": 1.38617, + "name": "Margate" + }, + { + "lat": 19.28287, + "lon": -98.19609, + "name": "La Magdalena Tlaltelulco" + } + ], + "question": "Which location is the geographic outlier among: Montrouge, Hazel Grove, Troisdorf, Margate, La Magdalena Tlaltelulco?", + "ground_truth": { + "answer": "La Magdalena Tlaltelulco", + "outlier_distance_km": 7761.0, + "second_furthest_km": 1978.1, + "clarity_ratio": 3.92, + "median_distance_km": 1605.5, + "distances_to_centroid": { + "Montrouge": 1598.9, + "Hazel Grove": 1493.0, + "Troisdorf": 1978.1, + "Margate": 1605.5, + "La Magdalena Tlaltelulco": 7761.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Montrouge: (48.82°, 2.31°)", + " Hazel Grove: (53.38°, -2.12°)", + " Troisdorf: (50.81°, 7.15°)", + " Margate: (51.38°, 1.39°)", + " La Magdalena Tlaltelulco: (19.28°, -98.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " La Magdalena Tlaltelulco: 7761.0 km from centroid", + " Troisdorf: 1978.1 km from centroid", + " Margate: 1605.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: La Magdalena Tlaltelulco", + "FINAL ANSWER: La Magdalena Tlaltelulco" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.71368, + "lon": -82.59933, + "name": "Lancaster" + }, + { + "lat": 20.88205, + "lon": -103.83599, + "name": "Tequila" + }, + { + "lat": 26.28729, + "lon": -98.31335, + "name": "Alton" + }, + { + "lat": 38.79289, + "lon": -77.49749, + "name": "Sudley" + }, + { + "lat": -32.78749, + "lon": 26.8344, + "name": "Alice" + } + ], + "question": "Which location is the geographic outlier among: Lancaster, Tequila, Alton, Sudley, Alice?", + "ground_truth": { + "answer": "Alice", + "outlier_distance_km": 11466.2, + "second_furthest_km": 3847.3, + "clarity_ratio": 2.98, + "median_distance_km": 3313.1, + "distances_to_centroid": { + "Lancaster": 2782.2, + "Tequila": 3847.3, + "Alton": 3313.1, + "Sudley": 2462.5, + "Alice": 11466.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lancaster: (39.71°, -82.60°)", + " Tequila: (20.88°, -103.84°)", + " Alton: (26.29°, -98.31°)", + " Sudley: (38.79°, -77.50°)", + " Alice: (-32.79°, 26.83°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alice: 11466.2 km from centroid", + " Tequila: 3847.3 km from centroid", + " Alton: 3313.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alice", + "FINAL ANSWER: Alice" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.01122, + "lon": 13.82029, + "name": "Leuben" + }, + { + "lat": 41.41109, + "lon": 2.2026, + "name": "Provenals del Poblenou" + }, + { + "lat": 49.4925, + "lon": 9.77361, + "name": "Bad Mergentheim" + }, + { + "lat": 41.76337, + "lon": 12.33078, + "name": "Acilia-Castel Fusano-Ostia Antica" + }, + { + "lat": 0.67028, + "lon": 35.50806, + "name": "Iten" + } + ], + "question": "Which location is the geographic outlier among: Leuben, Provenals del Poblenou, Bad Mergentheim, Acilia-Castel Fusano-Ostia Antica, Iten?", + "ground_truth": { + "answer": "Iten", + "outlier_distance_km": 4556.9, + "second_furthest_km": 1574.1, + "clarity_ratio": 2.89, + "median_distance_km": 1459.1, + "distances_to_centroid": { + "Leuben": 1574.1, + "Provenals del Poblenou": 1190.8, + "Bad Mergentheim": 1459.1, + "Acilia-Castel Fusano-Ostia Antica": 581.8, + "Iten": 4556.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Leuben: (51.01°, 13.82°)", + " Provenals del Poblenou: (41.41°, 2.20°)", + " Bad Mergentheim: (49.49°, 9.77°)", + " Acilia-Castel Fusano-Ostia Antica: (41.76°, 12.33°)", + " Iten: (0.67°, 35.51°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Iten: 4556.9 km from centroid", + " Leuben: 1574.1 km from centroid", + " Bad Mergentheim: 1459.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Iten", + "FINAL ANSWER: Iten" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.31667, + "lon": 136.28333, + "name": "Maibara" + }, + { + "lat": 29.79712, + "lon": 107.45755, + "name": "Qingxi" + }, + { + "lat": 28.94472, + "lon": 106.71056, + "name": "Sanjiang" + }, + { + "lat": 36.19944, + "lon": 139.49465, + "name": "Ōwa" + }, + { + "lat": 40.63205, + "lon": -73.71263, + "name": "Woodmere" + } + ], + "question": "Which location is the geographic outlier among: Maibara, Qingxi, Sanjiang, Ōwa, Woodmere?", + "ground_truth": { + "answer": "Woodmere", + "outlier_distance_km": 11368.1, + "second_furthest_km": 5043.4, + "clarity_ratio": 2.25, + "median_distance_km": 4787.8, + "distances_to_centroid": { + "Maibara": 4787.8, + "Qingxi": 2328.8, + "Sanjiang": 2292.3, + "Ōwa": 5043.4, + "Woodmere": 11368.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maibara: (35.32°, 136.28°)", + " Qingxi: (29.80°, 107.46°)", + " Sanjiang: (28.94°, 106.71°)", + " Ōwa: (36.20°, 139.49°)", + " Woodmere: (40.63°, -73.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Woodmere: 11368.1 km from centroid", + " Ōwa: 5043.4 km from centroid", + " Maibara: 4787.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Woodmere", + "FINAL ANSWER: Woodmere" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.13159, + "lon": 33.79844, + "name": "Arīsh" + }, + { + "lat": 6.55504, + "lon": 3.34363, + "name": "Oshodi" + }, + { + "lat": -27.66606, + "lon": 28.13132, + "name": "Mamafubedu" + }, + { + "lat": 12.59371, + "lon": 6.58648, + "name": "Kaura Namoda" + }, + { + "lat": 37.88687, + "lon": -122.29775, + "name": "Albany" + } + ], + "question": "Which location is the geographic outlier among: Arīsh, Oshodi, Mamafubedu, Kaura Namoda, Albany?", + "ground_truth": { + "answer": "Albany", + "outlier_distance_km": 11050.5, + "second_furthest_km": 6041.8, + "clarity_ratio": 1.83, + "median_distance_km": 4963.2, + "distances_to_centroid": { + "Arīsh": 4963.2, + "Oshodi": 1596.9, + "Mamafubedu": 6041.8, + "Kaura Namoda": 1811.7, + "Albany": 11050.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arīsh: (31.13°, 33.80°)", + " Oshodi: (6.56°, 3.34°)", + " Mamafubedu: (-27.67°, 28.13°)", + " Kaura Namoda: (12.59°, 6.59°)", + " Albany: (37.89°, -122.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Albany: 11050.5 km from centroid", + " Mamafubedu: 6041.8 km from centroid", + " Arīsh: 4963.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Albany", + "FINAL ANSWER: Albany" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.19354, + "lon": 153.02631, + "name": "Deception Bay" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": -34.92873, + "lon": 138.60334, + "name": "Adelaide city centre" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -10.50333, + "lon": -37.05278, + "name": "Capela" + } + ], + "question": "Which location is the geographic outlier among: Deception Bay, Caroline Springs, Adelaide city centre, Dandenong North, Capela?", + "ground_truth": { + "answer": "Capela", + "outlier_distance_km": 14249.5, + "second_furthest_km": 4297.4, + "clarity_ratio": 3.32, + "median_distance_km": 3454.6, + "distances_to_centroid": { + "Deception Bay": 4297.4, + "Caroline Springs": 3411.4, + "Adelaide city centre": 2841.1, + "Dandenong North": 3454.6, + "Capela": 14249.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deception Bay: (-27.19°, 153.03°)", + " Caroline Springs: (-37.74°, 144.74°)", + " Adelaide city centre: (-34.93°, 138.60°)", + " Dandenong North: (-37.97°, 145.21°)", + " Capela: (-10.50°, -37.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Capela: 14249.5 km from centroid", + " Deception Bay: 4297.4 km from centroid", + " Dandenong North: 3454.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Capela", + "FINAL ANSWER: Capela" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.68907, + "lon": 14.52036, + "name": "Gragnano" + }, + { + "lat": 51.56733, + "lon": -0.13415, + "name": "Archway" + }, + { + "lat": 48.35157, + "lon": -1.19961, + "name": "Fougères" + }, + { + "lat": 51.88264, + "lon": 4.54937, + "name": "Groot IJsselmonde" + }, + { + "lat": 9.96115, + "lon": 78.13715, + "name": "Nāyanakulam" + } + ], + "question": "Which location is the geographic outlier among: Gragnano, Archway, Fougères, Groot IJsselmonde, Nāyanakulam?", + "ground_truth": { + "answer": "Nāyanakulam", + "outlier_distance_km": 6682.5, + "second_furthest_km": 1923.3, + "clarity_ratio": 3.47, + "median_distance_km": 1831.0, + "distances_to_centroid": { + "Gragnano": 393.6, + "Archway": 1923.3, + "Fougères": 1831.0, + "Groot IJsselmonde": 1688.5, + "Nāyanakulam": 6682.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gragnano: (40.69°, 14.52°)", + " Archway: (51.57°, -0.13°)", + " Fougères: (48.35°, -1.20°)", + " Groot IJsselmonde: (51.88°, 4.55°)", + " Nāyanakulam: (9.96°, 78.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nāyanakulam: 6682.5 km from centroid", + " Archway: 1923.3 km from centroid", + " Fougères: 1831.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nāyanakulam", + "FINAL ANSWER: Nāyanakulam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.26239, + "lon": 80.16809, + "name": "Khanapuram Haveli" + }, + { + "lat": 15.11481, + "lon": 104.32938, + "name": "Si Sa Ket" + }, + { + "lat": 10.22776, + "lon": 78.22969, + "name": "Natham" + }, + { + "lat": 22.15627, + "lon": 107.97953, + "name": "Shangsi" + }, + { + "lat": -32.93324, + "lon": 27.77656, + "name": "Mdantsane" + } + ], + "question": "Which location is the geographic outlier among: Khanapuram Haveli, Si Sa Ket, Natham, Shangsi, Mdantsane?", + "ground_truth": { + "answer": "Mdantsane", + "outlier_distance_km": 7003.9, + "second_furthest_km": 3505.8, + "clarity_ratio": 2.0, + "median_distance_km": 2858.1, + "distances_to_centroid": { + "Khanapuram Haveli": 1212.8, + "Si Sa Ket": 2858.1, + "Natham": 458.8, + "Shangsi": 3505.8, + "Mdantsane": 7003.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Khanapuram Haveli: (17.26°, 80.17°)", + " Si Sa Ket: (15.11°, 104.33°)", + " Natham: (10.23°, 78.23°)", + " Shangsi: (22.16°, 107.98°)", + " Mdantsane: (-32.93°, 27.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mdantsane: 7003.9 km from centroid", + " Shangsi: 3505.8 km from centroid", + " Si Sa Ket: 2858.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mdantsane", + "FINAL ANSWER: Mdantsane" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.11316, + "lon": -70.81199, + "name": "Hanover" + }, + { + "lat": 16.73006, + "lon": -92.63825, + "name": "San Cristóbal de las Casas" + }, + { + "lat": 39.11656, + "lon": -121.63913, + "name": "South Yuba City" + }, + { + "lat": 49.22119, + "lon": -122.68965, + "name": "Pitt Meadows" + }, + { + "lat": 3.35528, + "lon": 40.22278, + "name": "Takaba" + } + ], + "question": "Which location is the geographic outlier among: Hanover, San Cristóbal de las Casas, South Yuba City, Pitt Meadows, Takaba?", + "ground_truth": { + "answer": "Takaba", + "outlier_distance_km": 12070.9, + "second_furthest_km": 4612.2, + "clarity_ratio": 2.62, + "median_distance_km": 4463.4, + "distances_to_centroid": { + "Hanover": 1356.6, + "San Cristóbal de las Casas": 2447.2, + "South Yuba City": 4463.4, + "Pitt Meadows": 4612.2, + "Takaba": 12070.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hanover: (42.11°, -70.81°)", + " San Cristóbal de las Casas: (16.73°, -92.64°)", + " South Yuba City: (39.12°, -121.64°)", + " Pitt Meadows: (49.22°, -122.69°)", + " Takaba: (3.36°, 40.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Takaba: 12070.9 km from centroid", + " Pitt Meadows: 4612.2 km from centroid", + " South Yuba City: 4463.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Takaba", + "FINAL ANSWER: Takaba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.94402, + "lon": 153.39815, + "name": "Labrador" + }, + { + "lat": -37.2, + "lon": 174.95, + "name": "Pukekohe East" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + { + "lat": -23.69339, + "lon": 30.14002, + "name": "Duiwelskloof" + } + ], + "question": "Which location is the geographic outlier among: Labrador, Pukekohe East, Cranbourne West, Coorparoo, Duiwelskloof?", + "ground_truth": { + "answer": "Duiwelskloof", + "outlier_distance_km": 9667.6, + "second_furthest_km": 4041.1, + "clarity_ratio": 2.39, + "median_distance_km": 2155.7, + "distances_to_centroid": { + "Labrador": 2155.7, + "Pukekohe East": 4041.1, + "Cranbourne West": 1503.0, + "Coorparoo": 2136.0, + "Duiwelskloof": 9667.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Labrador: (-27.94°, 153.40°)", + " Pukekohe East: (-37.20°, 174.95°)", + " Cranbourne West: (-38.10°, 145.27°)", + " Coorparoo: (-27.49°, 153.06°)", + " Duiwelskloof: (-23.69°, 30.14°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Duiwelskloof: 9667.6 km from centroid", + " Pukekohe East: 4041.1 km from centroid", + " Labrador: 2155.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Duiwelskloof", + "FINAL ANSWER: Duiwelskloof" + ] + } +] \ No newline at end of file