[ { "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, "Igaraçu 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": { "Viçosa": 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" ] } ]