diff --git "a/data/track_applied/splits/task9_spatial_patterns_dev.json" "b/data/track_applied/splits/task9_spatial_patterns_dev.json" new file mode 100644--- /dev/null +++ "b/data/track_applied/splits/task9_spatial_patterns_dev.json" @@ -0,0 +1,21082 @@ +[ + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.11639, + "lon": -49.99806, + "name": "Taió" + }, + { + "lat": -25.76972, + "lon": -49.71583, + "name": "Lapa" + }, + { + "lat": -29.51694, + "lon": -50.77778, + "name": "Três Coroas" + }, + { + "lat": -31.76333, + "lon": -52.48389, + "name": "Capão do Leão" + }, + { + "lat": 26.2452, + "lon": 91.52525, + "name": "Hājo" + } + ], + "question": "Which location is the geographic outlier among: Taió, Lapa, Três Coroas, Capão do Leão, Hājo?", + "ground_truth": { + "answer": "Hājo", + "outlier_distance_km": 13188.8, + "second_furthest_km": 3417.2, + "clarity_ratio": 3.86, + "median_distance_km": 3180.6, + "distances_to_centroid": { + "Taió": 3031.8, + "Lapa": 2969.5, + "Três Coroas": 3180.6, + "Capão do Leão": 3417.2, + "Hājo": 13188.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taió: (-27.12°, -50.00°)", + " Lapa: (-25.77°, -49.72°)", + " Três Coroas: (-29.52°, -50.78°)", + " Capão do Leão: (-31.76°, -52.48°)", + " Hājo: (26.25°, 91.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hājo: 13188.8 km from centroid", + " Capão do Leão: 3417.2 km from centroid", + " Três Coroas: 3180.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hājo", + "FINAL ANSWER: Hājo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.28889, + "lon": 36.24167, + "name": "Bonga" + }, + { + "lat": 10.26858, + "lon": 13.26701, + "name": "Mubi" + }, + { + "lat": 7.4824, + "lon": 4.56032, + "name": "Ile-Ife" + }, + { + "lat": -3.63045, + "lon": 39.84992, + "name": "Kilifi" + }, + { + "lat": -1.22361, + "lon": -48.29444, + "name": "Santa Bárbara do Pará" + } + ], + "question": "Which location is the geographic outlier among: Bonga, Mubi, Ile-Ife, Kilifi, Santa Bárbara do Pará?", + "ground_truth": { + "answer": "Santa Bárbara do Pará", + "outlier_distance_km": 6407.1, + "second_furthest_km": 3518.7, + "clarity_ratio": 1.82, + "median_distance_km": 3021.5, + "distances_to_centroid": { + "Bonga": 3021.5, + "Mubi": 829.9, + "Ile-Ife": 633.8, + "Kilifi": 3518.7, + "Santa Bárbara do Pará": 6407.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bonga: (7.29°, 36.24°)", + " Mubi: (10.27°, 13.27°)", + " Ile-Ife: (7.48°, 4.56°)", + " Kilifi: (-3.63°, 39.85°)", + " 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: 6407.1 km from centroid", + " Kilifi: 3518.7 km from centroid", + " Bonga: 3021.5 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": -26.36, + "lon": 28.129, + "name": "Tokoza" + }, + { + "lat": 30.82796, + "lon": 30.53552, + "name": "Ad Dilinjāt" + }, + { + "lat": -26.98023, + "lon": 26.67272, + "name": "Orkney" + }, + { + "lat": 29.84144, + "lon": 31.30084, + "name": "Ḩalwān" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + } + ], + "question": "Which location is the geographic outlier among: Tokoza, Ad Dilinjāt, Orkney, Ḩalwān, Logan City?", + "ground_truth": { + "answer": "Logan City", + "outlier_distance_km": 10695.7, + "second_furthest_km": 4607.2, + "clarity_ratio": 2.32, + "median_distance_km": 4475.4, + "distances_to_centroid": { + "Tokoza": 3700.7, + "Ad Dilinjāt": 4607.2, + "Orkney": 3857.7, + "Ḩalwān": 4475.4, + "Logan City": 10695.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tokoza: (-26.36°, 28.13°)", + " Ad Dilinjāt: (30.83°, 30.54°)", + " Orkney: (-26.98°, 26.67°)", + " Ḩalwān: (29.84°, 31.30°)", + " Logan City: (-27.64°, 153.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Logan City: 10695.7 km from centroid", + " Ad Dilinjāt: 4607.2 km from centroid", + " Ḩalwān: 4475.4 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": 31.32047, + "lon": 109.48416, + "name": "Shanghuang" + }, + { + "lat": 5.02298, + "lon": 118.32897, + "name": "Lahad Datu" + }, + { + "lat": 14.51288, + "lon": 75.80716, + "name": "Harihar" + }, + { + "lat": 25.98546, + "lon": 84.17233, + "name": "Maniar" + }, + { + "lat": 43.77639, + "lon": -79.38028, + "name": "Bayview Village" + } + ], + "question": "Which location is the geographic outlier among: Shanghuang, Lahad Datu, Harihar, Maniar, Bayview Village?", + "ground_truth": { + "answer": "Bayview Village", + "outlier_distance_km": 11484.9, + "second_furthest_km": 6406.2, + "clarity_ratio": 1.79, + "median_distance_km": 4736.3, + "distances_to_centroid": { + "Shanghuang": 4736.3, + "Lahad Datu": 6406.2, + "Harihar": 1825.0, + "Maniar": 2272.1, + "Bayview Village": 11484.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shanghuang: (31.32°, 109.48°)", + " Lahad Datu: (5.02°, 118.33°)", + " Harihar: (14.51°, 75.81°)", + " Maniar: (25.99°, 84.17°)", + " Bayview Village: (43.78°, -79.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bayview Village: 11484.9 km from centroid", + " Lahad Datu: 6406.2 km from centroid", + " Shanghuang: 4736.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bayview Village", + "FINAL ANSWER: Bayview Village" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.7, + "lon": -1.65, + "name": "Assin Foso" + }, + { + "lat": 27.55642, + "lon": 30.81057, + "name": "Dayrūţ" + }, + { + "lat": 29.14816, + "lon": 31.12733, + "name": "Būsh" + }, + { + "lat": -3.21799, + "lon": 40.11692, + "name": "Malindi" + }, + { + "lat": -29.17139, + "lon": -51.51917, + "name": "Bento Gonçalves" + } + ], + "question": "Which location is the geographic outlier among: Assin Foso, Dayrūţ, Būsh, Malindi, Bento Gonçalves?", + "ground_truth": { + "answer": "Bento Gonçalves", + "outlier_distance_km": 7619.7, + "second_furthest_km": 3521.5, + "clarity_ratio": 2.16, + "median_distance_km": 3413.0, + "distances_to_centroid": { + "Assin Foso": 1264.4, + "Dayrūţ": 3267.6, + "Būsh": 3413.0, + "Malindi": 3521.5, + "Bento Gonçalves": 7619.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Assin Foso: (5.70°, -1.65°)", + " Dayrūţ: (27.56°, 30.81°)", + " Būsh: (29.15°, 31.13°)", + " Malindi: (-3.22°, 40.12°)", + " Bento Gonçalves: (-29.17°, -51.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bento Gonçalves: 7619.7 km from centroid", + " Malindi: 3521.5 km from centroid", + " Būsh: 3413.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bento Gonçalves", + "FINAL ANSWER: Bento Gonçalves" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.9535, + "lon": 2.31514, + "name": "Épinay-sur-Seine" + }, + { + "lat": 37.97872, + "lon": -0.68222, + "name": "Torrevieja" + }, + { + "lat": 43.33333, + "lon": -8.31667, + "name": "Oleiros" + }, + { + "lat": 50.10038, + "lon": 8.6295, + "name": "Gallus" + }, + { + "lat": 26.90687, + "lon": -101.42056, + "name": "Monclova" + } + ], + "question": "Which location is the geographic outlier among: Épinay-sur-Seine, Torrevieja, Oleiros, Gallus, Monclova?", + "ground_truth": { + "answer": "Monclova", + "outlier_distance_km": 7399.1, + "second_furthest_km": 2393.1, + "clarity_ratio": 3.09, + "median_distance_km": 1920.0, + "distances_to_centroid": { + "Épinay-sur-Seine": 1920.0, + "Torrevieja": 1684.3, + "Oleiros": 972.6, + "Gallus": 2393.1, + "Monclova": 7399.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Épinay-sur-Seine: (48.95°, 2.32°)", + " Torrevieja: (37.98°, -0.68°)", + " Oleiros: (43.33°, -8.32°)", + " Gallus: (50.10°, 8.63°)", + " Monclova: (26.91°, -101.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Monclova: 7399.1 km from centroid", + " Gallus: 2393.1 km from centroid", + " Épinay-sur-Seine: 1920.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Monclova", + "FINAL ANSWER: Monclova" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": 12.11667, + "lon": 37.78333, + "name": "Ādīs Zemen" + } + ], + "question": "Which location is the geographic outlier among: Lalor, Bairnsdale, Pacific Pines, Wainuiomata, Ādīs Zemen?", + "ground_truth": { + "answer": "Ādīs Zemen", + "outlier_distance_km": 10992.6, + "second_furthest_km": 4260.3, + "clarity_ratio": 2.58, + "median_distance_km": 2136.7, + "distances_to_centroid": { + "Lalor": 1757.9, + "Bairnsdale": 1947.7, + "Pacific Pines": 2136.7, + "Wainuiomata": 4260.3, + "Ādīs Zemen": 10992.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lalor: (-37.67°, 145.02°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Pacific Pines: (-27.94°, 153.31°)", + " Wainuiomata: (-41.27°, 174.95°)", + " Ādīs Zemen: (12.12°, 37.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ādīs Zemen: 10992.6 km from centroid", + " Wainuiomata: 4260.3 km from centroid", + " Pacific Pines: 2136.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ādīs Zemen", + "FINAL ANSWER: Ādīs Zemen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.26954, + "lon": -95.85471, + "name": "Owasso" + }, + { + "lat": 37.93576, + "lon": -122.34775, + "name": "Richmond" + }, + { + "lat": 39.07039, + "lon": -76.54524, + "name": "Severna Park" + }, + { + "lat": 30.41131, + "lon": -88.82781, + "name": "Ocean Springs" + }, + { + "lat": 11.73559, + "lon": 108.3733, + "name": "Đưc Trọng" + } + ], + "question": "Which location is the geographic outlier among: Owasso, Richmond, Severna Park, Ocean Springs, Đưc Trọng?", + "ground_truth": { + "answer": "Đưc Trọng", + "outlier_distance_km": 14935.1, + "second_furthest_km": 6081.3, + "clarity_ratio": 2.46, + "median_distance_km": 3792.3, + "distances_to_centroid": { + "Owasso": 3792.3, + "Richmond": 6081.3, + "Severna Park": 2141.9, + "Ocean Springs": 3217.1, + "Đưc Trọng": 14935.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Owasso: (36.27°, -95.85°)", + " Richmond: (37.94°, -122.35°)", + " Severna Park: (39.07°, -76.55°)", + " Ocean Springs: (30.41°, -88.83°)", + " Đưc Trọng: (11.74°, 108.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Đưc Trọng: 14935.1 km from centroid", + " Richmond: 6081.3 km from centroid", + " Owasso: 3792.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Đưc Trọng", + "FINAL ANSWER: Đưc Trọng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.13014, + "lon": -119.27808, + "name": "Moses Lake" + }, + { + "lat": 25.64205, + "lon": -80.39839, + "name": "Three Lakes" + }, + { + "lat": 25.97205, + "lon": -100.45029, + "name": "Hidalgo" + }, + { + "lat": 42.24087, + "lon": -83.26965, + "name": "Taylor" + }, + { + "lat": 25.19413, + "lon": 32.6771, + "name": "As Sibā‘īyah" + } + ], + "question": "Which location is the geographic outlier among: Moses Lake, Three Lakes, Hidalgo, Taylor, As Sibā‘īyah?", + "ground_truth": { + "answer": "As Sibā‘īyah", + "outlier_distance_km": 9590.8, + "second_furthest_km": 4368.2, + "clarity_ratio": 2.2, + "median_distance_km": 3027.3, + "distances_to_centroid": { + "Moses Lake": 4368.2, + "Three Lakes": 1302.2, + "Hidalgo": 3027.3, + "Taylor": 1524.8, + "As Sibā‘īyah": 9590.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Moses Lake: (47.13°, -119.28°)", + " Three Lakes: (25.64°, -80.40°)", + " Hidalgo: (25.97°, -100.45°)", + " Taylor: (42.24°, -83.27°)", + " As Sibā‘īyah: (25.19°, 32.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " As Sibā‘īyah: 9590.8 km from centroid", + " Moses Lake: 4368.2 km from centroid", + " Hidalgo: 3027.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: As Sibā‘īyah", + "FINAL ANSWER: As Sibā‘īyah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.68921, + "lon": 2.48965, + "name": "Sant Celoni" + }, + { + "lat": 54.53478, + "lon": -1.05606, + "name": "Guisborough" + }, + { + "lat": 53.00974, + "lon": -3.05814, + "name": "Rhosllannerchrugog" + }, + { + "lat": 52.63598, + "lon": 13.20419, + "name": "Hennigsdorf" + }, + { + "lat": -21.76333, + "lon": -52.11556, + "name": "Presidente Epitácio" + } + ], + "question": "Which location is the geographic outlier among: Sant Celoni, Guisborough, Rhosllannerchrugog, Hennigsdorf, Presidente Epitácio?", + "ground_truth": { + "answer": "Presidente Epitácio", + "outlier_distance_km": 7917.5, + "second_furthest_km": 2488.4, + "clarity_ratio": 3.18, + "median_distance_km": 2128.7, + "distances_to_centroid": { + "Sant Celoni": 1111.9, + "Guisborough": 2128.7, + "Rhosllannerchrugog": 1929.8, + "Hennigsdorf": 2488.4, + "Presidente Epitácio": 7917.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sant Celoni: (41.69°, 2.49°)", + " Guisborough: (54.53°, -1.06°)", + " Rhosllannerchrugog: (53.01°, -3.06°)", + " Hennigsdorf: (52.64°, 13.20°)", + " Presidente Epitácio: (-21.76°, -52.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Presidente Epitácio: 7917.5 km from centroid", + " Hennigsdorf: 2488.4 km from centroid", + " Guisborough: 2128.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Presidente Epitácio", + "FINAL ANSWER: Presidente Epitácio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.00176, + "lon": -73.66568, + "name": "Port Chester" + }, + { + "lat": 33.88399, + "lon": -84.51438, + "name": "Smyrna" + }, + { + "lat": 19.26755, + "lon": -99.61925, + "name": "San Francisco Cuaxusco" + }, + { + "lat": 49.22119, + "lon": -122.68965, + "name": "Pitt Meadows" + }, + { + "lat": -23.84852, + "lon": 151.25775, + "name": "Gladstone" + } + ], + "question": "Which location is the geographic outlier among: Port Chester, Smyrna, San Francisco Cuaxusco, Pitt Meadows, Gladstone?", + "ground_truth": { + "answer": "Gladstone", + "outlier_distance_km": 18277.0, + "second_furthest_km": 7085.3, + "clarity_ratio": 2.58, + "median_distance_km": 5551.8, + "distances_to_centroid": { + "Port Chester": 3205.6, + "Smyrna": 3899.1, + "San Francisco Cuaxusco": 5551.8, + "Pitt Meadows": 7085.3, + "Gladstone": 18277.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Port Chester: (41.00°, -73.67°)", + " Smyrna: (33.88°, -84.51°)", + " San Francisco Cuaxusco: (19.27°, -99.62°)", + " Pitt Meadows: (49.22°, -122.69°)", + " Gladstone: (-23.85°, 151.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gladstone: 18277.0 km from centroid", + " Pitt Meadows: 7085.3 km from centroid", + " San Francisco Cuaxusco: 5551.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gladstone", + "FINAL ANSWER: Gladstone" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -19.51361, + "lon": -43.745, + "name": "Jaboticatubas" + }, + { + "lat": -23.53729, + "lon": -46.5666, + "name": "Tatuapé" + }, + { + "lat": -8.48972, + "lon": -36.05944, + "name": "Altinho" + }, + { + "lat": -20.53389, + "lon": -49.31417, + "name": "Nova Granada" + }, + { + "lat": 31.06062, + "lon": 76.30166, + "name": "Bālāchor" + } + ], + "question": "Which location is the geographic outlier among: Jaboticatubas, Tatuapé, Altinho, Nova Granada, Bālāchor?", + "ground_truth": { + "answer": "Bālāchor", + "outlier_distance_km": 11062.7, + "second_furthest_km": 3445.9, + "clarity_ratio": 3.21, + "median_distance_km": 3314.3, + "distances_to_centroid": { + "Jaboticatubas": 2861.9, + "Tatuapé": 3314.3, + "Altinho": 1780.5, + "Nova Granada": 3445.9, + "Bālāchor": 11062.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jaboticatubas: (-19.51°, -43.74°)", + " Tatuapé: (-23.54°, -46.57°)", + " Altinho: (-8.49°, -36.06°)", + " Nova Granada: (-20.53°, -49.31°)", + " Bālāchor: (31.06°, 76.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bālāchor: 11062.7 km from centroid", + " Nova Granada: 3445.9 km from centroid", + " Tatuapé: 3314.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bālāchor", + "FINAL ANSWER: Bālāchor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.80263, + "lon": 44.47491, + "name": "Gorodishche" + }, + { + "lat": 37.08343, + "lon": 15.15332, + "name": "Floridia" + }, + { + "lat": 50.76871, + "lon": 0.28453, + "name": "Eastbourne" + }, + { + "lat": 50.81342, + "lon": 10.2361, + "name": "Bad Salzungen" + }, + { + "lat": 39.5186, + "lon": -104.76136, + "name": "Parker" + } + ], + "question": "Which location is the geographic outlier among: Gorodishche, Floridia, Eastbourne, Bad Salzungen, Parker?", + "ground_truth": { + "answer": "Parker", + "outlier_distance_km": 7529.8, + "second_furthest_km": 3834.3, + "clarity_ratio": 1.96, + "median_distance_km": 2055.1, + "distances_to_centroid": { + "Gorodishche": 3834.3, + "Floridia": 2055.1, + "Eastbourne": 801.3, + "Bad Salzungen": 1404.8, + "Parker": 7529.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gorodishche: (48.80°, 44.47°)", + " Floridia: (37.08°, 15.15°)", + " Eastbourne: (50.77°, 0.28°)", + " Bad Salzungen: (50.81°, 10.24°)", + " Parker: (39.52°, -104.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Parker: 7529.8 km from centroid", + " Gorodishche: 3834.3 km from centroid", + " Floridia: 2055.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Parker", + "FINAL ANSWER: Parker" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -39.06667, + "lon": 174.08333, + "name": "New Plymouth" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": 30.09403, + "lon": 105.71297, + "name": "Baizi" + } + ], + "question": "Which location is the geographic outlier among: New Plymouth, Truganina, Townsville, Hervey Bay, Baizi?", + "ground_truth": { + "answer": "Baizi", + "outlier_distance_km": 6815.6, + "second_furthest_km": 3644.7, + "clarity_ratio": 1.87, + "median_distance_km": 2173.7, + "distances_to_centroid": { + "New Plymouth": 3644.7, + "Truganina": 2173.7, + "Townsville": 236.3, + "Hervey Bay": 1131.7, + "Baizi": 6815.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " New Plymouth: (-39.07°, 174.08°)", + " Truganina: (-37.82°, 144.75°)", + " Townsville: (-19.27°, 146.81°)", + " Hervey Bay: (-25.29°, 152.77°)", + " Baizi: (30.09°, 105.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baizi: 6815.6 km from centroid", + " New Plymouth: 3644.7 km from centroid", + " Truganina: 2173.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Baizi", + "FINAL ANSWER: Baizi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.57076, + "lon": 27.42396, + "name": "Stutterheim" + }, + { + "lat": 7.75537, + "lon": -0.98085, + "name": "Atebubu" + }, + { + "lat": 6.52799, + "lon": 3.35411, + "name": "Mushin" + }, + { + "lat": 7.63527, + "lon": 4.18156, + "name": "Iwo" + }, + { + "lat": -37.80128, + "lon": -73.39616, + "name": "Cañete" + } + ], + "question": "Which location is the geographic outlier among: Stutterheim, Atebubu, Mushin, Iwo, Cañete?", + "ground_truth": { + "answer": "Cañete", + "outlier_distance_km": 7203.8, + "second_furthest_km": 4423.2, + "clarity_ratio": 1.63, + "median_distance_km": 2344.6, + "distances_to_centroid": { + "Stutterheim": 4423.2, + "Atebubu": 2085.1, + "Mushin": 2191.4, + "Iwo": 2344.6, + "Cañete": 7203.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stutterheim: (-32.57°, 27.42°)", + " Atebubu: (7.76°, -0.98°)", + " Mushin: (6.53°, 3.35°)", + " Iwo: (7.64°, 4.18°)", + " Cañete: (-37.80°, -73.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cañete: 7203.8 km from centroid", + " Stutterheim: 4423.2 km from centroid", + " Iwo: 2344.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cañete", + "FINAL ANSWER: Cañete" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.70007, + "lon": -100.52353, + "name": "Piedras Negras" + }, + { + "lat": 19.10059, + "lon": -98.8788, + "name": "Juchitepec" + }, + { + "lat": 36.03452, + "lon": -89.38563, + "name": "Dyersburg" + }, + { + "lat": 30.63269, + "lon": -97.67723, + "name": "Georgetown" + }, + { + "lat": 7.35156, + "lon": 4.18335, + "name": "Apomu" + } + ], + "question": "Which location is the geographic outlier among: Piedras Negras, Juchitepec, Dyersburg, Georgetown, Apomu?", + "ground_truth": { + "answer": "Apomu", + "outlier_distance_km": 8726.5, + "second_furthest_km": 2437.9, + "clarity_ratio": 3.58, + "median_distance_km": 2385.7, + "distances_to_centroid": { + "Piedras Negras": 2437.9, + "Juchitepec": 2385.7, + "Dyersburg": 1793.2, + "Georgetown": 2201.8, + "Apomu": 8726.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Piedras Negras: (28.70°, -100.52°)", + " Juchitepec: (19.10°, -98.88°)", + " Dyersburg: (36.03°, -89.39°)", + " Georgetown: (30.63°, -97.68°)", + " Apomu: (7.35°, 4.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Apomu: 8726.5 km from centroid", + " Piedras Negras: 2437.9 km from centroid", + " Juchitepec: 2385.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Apomu", + "FINAL ANSWER: Apomu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.86522, + "lon": 25.64421, + "name": "Mafikeng" + }, + { + "lat": 9.59306, + "lon": 41.86611, + "name": "Dire Dawa" + }, + { + "lat": 30.6713, + "lon": 31.58801, + "name": "Hihyā" + }, + { + "lat": -28.28756, + "lon": 26.14996, + "name": "Bultfontein" + }, + { + "lat": 22.07748, + "lon": -102.2714, + "name": "San Francisco de los Romo" + } + ], + "question": "Which location is the geographic outlier among: Mafikeng, Dire Dawa, Hihyā, Bultfontein, San Francisco de los Romo?", + "ground_truth": { + "answer": "San Francisco de los Romo", + "outlier_distance_km": 11670.2, + "second_furthest_km": 4300.7, + "clarity_ratio": 2.71, + "median_distance_km": 4214.1, + "distances_to_centroid": { + "Mafikeng": 3804.1, + "Dire Dawa": 4214.1, + "Hihyā": 4300.7, + "Bultfontein": 4045.1, + "San Francisco de los Romo": 11670.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mafikeng: (-25.87°, 25.64°)", + " Dire Dawa: (9.59°, 41.87°)", + " Hihyā: (30.67°, 31.59°)", + " Bultfontein: (-28.29°, 26.15°)", + " San Francisco de los Romo: (22.08°, -102.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Francisco de los Romo: 11670.2 km from centroid", + " Hihyā: 4300.7 km from centroid", + " Dire Dawa: 4214.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Francisco de los Romo", + "FINAL ANSWER: San Francisco de los Romo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.61012, + "lon": 3.30968, + "name": "Akowonjo" + }, + { + "lat": 27.26881, + "lon": 31.15232, + "name": "Abnūb" + }, + { + "lat": 6.31667, + "lon": 38.26667, + "name": "Wenago" + }, + { + "lat": 8.4541, + "lon": 39.21752, + "name": "Wonji" + }, + { + "lat": 34.02862, + "lon": -117.81034, + "name": "Diamond Bar" + } + ], + "question": "Which location is the geographic outlier among: Akowonjo, Abnūb, Wenago, Wonji, Diamond Bar?", + "ground_truth": { + "answer": "Diamond Bar", + "outlier_distance_km": 11270.4, + "second_furthest_km": 4467.5, + "clarity_ratio": 2.52, + "median_distance_km": 4436.6, + "distances_to_centroid": { + "Akowonjo": 1206.6, + "Abnūb": 3529.2, + "Wenago": 4436.6, + "Wonji": 4467.5, + "Diamond Bar": 11270.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Akowonjo: (6.61°, 3.31°)", + " Abnūb: (27.27°, 31.15°)", + " Wenago: (6.32°, 38.27°)", + " Wonji: (8.45°, 39.22°)", + " Diamond Bar: (34.03°, -117.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Diamond Bar: 11270.4 km from centroid", + " Wonji: 4467.5 km from centroid", + " Wenago: 4436.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Diamond Bar", + "FINAL ANSWER: Diamond Bar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.55475, + "lon": -88.09867, + "name": "Crest Hill" + }, + { + "lat": 43.95977, + "lon": -78.16515, + "name": "Cobourg" + }, + { + "lat": 38.84685, + "lon": -76.92591, + "name": "Suitland-Silver Hill" + }, + { + "lat": 43.37729, + "lon": -73.61317, + "name": "Queensbury" + }, + { + "lat": 10.79115, + "lon": -74.76059, + "name": "Sabanagrande" + } + ], + "question": "Which location is the geographic outlier among: Crest Hill, Cobourg, Suitland-Silver Hill, Queensbury, Sabanagrande?", + "ground_truth": { + "answer": "Sabanagrande", + "outlier_distance_km": 2793.5, + "second_furthest_km": 1069.1, + "clarity_ratio": 2.61, + "median_distance_km": 943.0, + "distances_to_centroid": { + "Crest Hill": 1069.1, + "Cobourg": 917.9, + "Suitland-Silver Hill": 370.2, + "Queensbury": 943.0, + "Sabanagrande": 2793.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Crest Hill: (41.55°, -88.10°)", + " Cobourg: (43.96°, -78.17°)", + " Suitland-Silver Hill: (38.85°, -76.93°)", + " Queensbury: (43.38°, -73.61°)", + " Sabanagrande: (10.79°, -74.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sabanagrande: 2793.5 km from centroid", + " Crest Hill: 1069.1 km from centroid", + " Queensbury: 943.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sabanagrande", + "FINAL ANSWER: Sabanagrande" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.9827, + "lon": 7.45534, + "name": "Enugu-Ezike" + }, + { + "lat": 6.75, + "lon": 38.41667, + "name": "Yirga ‘Alem" + }, + { + "lat": 10.89469, + "lon": -1.09083, + "name": "Navrongo" + }, + { + "lat": 7.11345, + "lon": 6.73866, + "name": "Idah" + }, + { + "lat": 23.6658, + "lon": 86.43166, + "name": "Pāthardih" + } + ], + "question": "Which location is the geographic outlier among: Enugu-Ezike, Yirga ‘Alem, Navrongo, Idah, Pāthardih?", + "ground_truth": { + "answer": "Pāthardih", + "outlier_distance_km": 6356.5, + "second_furthest_km": 3129.6, + "clarity_ratio": 2.03, + "median_distance_km": 2330.8, + "distances_to_centroid": { + "Enugu-Ezike": 2256.8, + "Yirga ‘Alem": 1282.8, + "Navrongo": 3129.6, + "Idah": 2330.8, + "Pāthardih": 6356.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Enugu-Ezike: (6.98°, 7.46°)", + " Yirga ‘Alem: (6.75°, 38.42°)", + " Navrongo: (10.89°, -1.09°)", + " Idah: (7.11°, 6.74°)", + " Pāthardih: (23.67°, 86.43°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pāthardih: 6356.5 km from centroid", + " Navrongo: 3129.6 km from centroid", + " Idah: 2330.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pāthardih", + "FINAL ANSWER: Pāthardih" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.14306, + "lon": -58.44417, + "name": "Itacoatiara" + }, + { + "lat": -17.345, + "lon": -44.94194, + "name": "Pirapora" + }, + { + "lat": -10.6875, + "lon": -37.86167, + "name": "Paripiranga" + }, + { + "lat": -32.0671, + "lon": -60.64267, + "name": "Diamante" + }, + { + "lat": 48.44963, + "lon": -123.50261, + "name": "Langford" + } + ], + "question": "Which location is the geographic outlier among: Itacoatiara, Pirapora, Paripiranga, Diamante, Langford?", + "ground_truth": { + "answer": "Langford", + "outlier_distance_km": 8011.4, + "second_furthest_km": 3269.8, + "clarity_ratio": 2.45, + "median_distance_km": 3122.7, + "distances_to_centroid": { + "Itacoatiara": 737.0, + "Pirapora": 2717.9, + "Paripiranga": 3122.7, + "Diamante": 3269.8, + "Langford": 8011.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itacoatiara: (-3.14°, -58.44°)", + " Pirapora: (-17.34°, -44.94°)", + " Paripiranga: (-10.69°, -37.86°)", + " Diamante: (-32.07°, -60.64°)", + " Langford: (48.45°, -123.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Langford: 8011.4 km from centroid", + " Diamante: 3269.8 km from centroid", + " Paripiranga: 3122.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Langford", + "FINAL ANSWER: Langford" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.2546, + "lon": 20.90844, + "name": "Bemowo" + }, + { + "lat": 48.06212, + "lon": 39.9355, + "name": "Gukovo" + }, + { + "lat": 50.65256, + "lon": 3.18681, + "name": "Hem" + }, + { + "lat": 50.19645, + "lon": 39.56631, + "name": "Rossosh’" + }, + { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + } + ], + "question": "Which location is the geographic outlier among: Bemowo, Gukovo, Hem, Rossosh’, Orange?", + "ground_truth": { + "answer": "Orange", + "outlier_distance_km": 12679.3, + "second_furthest_km": 4250.8, + "clarity_ratio": 2.98, + "median_distance_km": 3144.7, + "distances_to_centroid": { + "Bemowo": 3144.7, + "Gukovo": 1837.4, + "Hem": 4250.8, + "Rossosh’": 2054.1, + "Orange": 12679.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bemowo: (52.25°, 20.91°)", + " Gukovo: (48.06°, 39.94°)", + " Hem: (50.65°, 3.19°)", + " Rossosh’: (50.20°, 39.57°)", + " Orange: (-33.28°, 149.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Orange: 12679.3 km from centroid", + " Hem: 4250.8 km from centroid", + " Bemowo: 3144.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Orange", + "FINAL ANSWER: Orange" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + }, + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -34.78254, + "lon": 138.61077, + "name": "Parafield Gardens" + }, + { + "lat": 33.58699, + "lon": 130.48676, + "name": "Shime" + } + ], + "question": "Which location is the geographic outlier among: Willetton, Hoppers Crossing, Epsom, Parafield Gardens, Shime?", + "ground_truth": { + "answer": "Shime", + "outlier_distance_km": 6235.2, + "second_furthest_km": 3672.9, + "clarity_ratio": 1.7, + "median_distance_km": 2730.3, + "distances_to_centroid": { + "Willetton": 2730.3, + "Hoppers Crossing": 1846.6, + "Epsom": 3672.9, + "Parafield Gardens": 1482.2, + "Shime": 6235.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Willetton: (-32.05°, 115.89°)", + " Hoppers Crossing: (-37.88°, 144.70°)", + " Epsom: (-36.89°, 174.77°)", + " Parafield Gardens: (-34.78°, 138.61°)", + " Shime: (33.59°, 130.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shime: 6235.2 km from centroid", + " Epsom: 3672.9 km from centroid", + " Willetton: 2730.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shime", + "FINAL ANSWER: Shime" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": 41.56667, + "lon": 2.01667, + "name": "Terrassa" + } + ], + "question": "Which location is the geographic outlier among: Canning Vale, Bentleigh East, Ellenbrook, Saint Kilda, Terrassa?", + "ground_truth": { + "answer": "Terrassa", + "outlier_distance_km": 12480.4, + "second_furthest_km": 4375.5, + "clarity_ratio": 2.85, + "median_distance_km": 4367.8, + "distances_to_centroid": { + "Canning Vale": 1774.3, + "Bentleigh East": 4375.5, + "Ellenbrook": 1753.4, + "Saint Kilda": 4367.8, + "Terrassa": 12480.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Canning Vale: (-32.06°, 115.92°)", + " Bentleigh East: (-37.92°, 145.05°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Terrassa: (41.57°, 2.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Terrassa: 12480.4 km from centroid", + " Bentleigh East: 4375.5 km from centroid", + " Saint Kilda: 4367.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Terrassa", + "FINAL ANSWER: Terrassa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.46794, + "lon": 153.02809, + "name": "Brisbane" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": -33.75881, + "lon": 150.99292, + "name": "Baulkham Hills" + }, + { + "lat": 0.28422, + "lon": 34.75229, + "name": "Kakamega" + } + ], + "question": "Which location is the geographic outlier among: Brisbane, Wollongong city centre, Maroubra, Baulkham Hills, Kakamega?", + "ground_truth": { + "answer": "Kakamega", + "outlier_distance_km": 10364.3, + "second_furthest_km": 2471.5, + "clarity_ratio": 4.19, + "median_distance_km": 2390.2, + "distances_to_centroid": { + "Brisbane": 2471.5, + "Wollongong city centre": 2375.4, + "Maroubra": 2390.2, + "Baulkham Hills": 2363.0, + "Kakamega": 10364.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brisbane: (-27.47°, 153.03°)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Maroubra: (-33.95°, 151.23°)", + " Baulkham Hills: (-33.76°, 150.99°)", + " Kakamega: (0.28°, 34.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kakamega: 10364.3 km from centroid", + " Brisbane: 2471.5 km from centroid", + " Maroubra: 2390.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kakamega", + "FINAL ANSWER: Kakamega" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.47856, + "lon": 76.59284, + "name": "Rajpura" + }, + { + "lat": 29.7283, + "lon": 106.63506, + "name": "Jiangbei" + }, + { + "lat": 32.62082, + "lon": 117.06319, + "name": "Datong" + }, + { + "lat": 37.75266, + "lon": 128.87239, + "name": "Gangneung" + }, + { + "lat": 41.86003, + "lon": -87.71839, + "name": "North Lawndale" + } + ], + "question": "Which location is the geographic outlier among: Rajpura, Jiangbei, Datong, Gangneung, North Lawndale?", + "ground_truth": { + "answer": "North Lawndale", + "outlier_distance_km": 11179.9, + "second_furthest_km": 5357.6, + "clarity_ratio": 2.09, + "median_distance_km": 4480.3, + "distances_to_centroid": { + "Rajpura": 897.0, + "Jiangbei": 3628.6, + "Datong": 4480.3, + "Gangneung": 5357.6, + "North Lawndale": 11179.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rajpura: (30.48°, 76.59°)", + " Jiangbei: (29.73°, 106.64°)", + " Datong: (32.62°, 117.06°)", + " Gangneung: (37.75°, 128.87°)", + " North Lawndale: (41.86°, -87.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " North Lawndale: 11179.9 km from centroid", + " Gangneung: 5357.6 km from centroid", + " Datong: 4480.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: North Lawndale", + "FINAL ANSWER: North Lawndale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.9376, + "lon": 75.88657, + "name": "Talwāra" + }, + { + "lat": 30.08167, + "lon": 106.5912, + "name": "Sanhui" + }, + { + "lat": 35.46028, + "lon": 110.42917, + "name": "Hancheng" + }, + { + "lat": 29.65, + "lon": 91.1, + "name": "Lhasa" + }, + { + "lat": -34.91119, + "lon": 138.70735, + "name": "Adelaide Hills" + } + ], + "question": "Which location is the geographic outlier among: Talwāra, Sanhui, Hancheng, Lhasa, Adelaide Hills?", + "ground_truth": { + "answer": "Adelaide Hills", + "outlier_distance_km": 6943.5, + "second_furthest_km": 3235.6, + "clarity_ratio": 2.15, + "median_distance_km": 1978.9, + "distances_to_centroid": { + "Talwāra": 3235.6, + "Sanhui": 1310.5, + "Hancheng": 1978.9, + "Lhasa": 1845.3, + "Adelaide Hills": 6943.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Talwāra: (31.94°, 75.89°)", + " Sanhui: (30.08°, 106.59°)", + " Hancheng: (35.46°, 110.43°)", + " Lhasa: (29.65°, 91.10°)", + " Adelaide Hills: (-34.91°, 138.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adelaide Hills: 6943.5 km from centroid", + " Talwāra: 3235.6 km from centroid", + " Hancheng: 1978.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adelaide Hills", + "FINAL ANSWER: Adelaide Hills" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.58222, + "lon": 46.43333, + "name": "Qorof" + }, + { + "lat": 27.06309, + "lon": 31.34425, + "name": "As Sāḩil" + }, + { + "lat": 28.49456, + "lon": 30.80526, + "name": "Banī Mazār" + }, + { + "lat": -27.65036, + "lon": 27.23488, + "name": "Kroonstad" + }, + { + "lat": -29.16163, + "lon": -67.49934, + "name": "Chilecito" + } + ], + "question": "Which location is the geographic outlier among: Qorof, As Sāḩil, Banī Mazār, Kroonstad, Chilecito?", + "ground_truth": { + "answer": "Chilecito", + "outlier_distance_km": 9208.7, + "second_furthest_km": 3685.5, + "clarity_ratio": 2.5, + "median_distance_km": 3552.2, + "distances_to_centroid": { + "Qorof": 3685.5, + "As Sāḩil": 3452.1, + "Banī Mazār": 3552.2, + "Kroonstad": 3507.0, + "Chilecito": 9208.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Qorof: (6.58°, 46.43°)", + " As Sāḩil: (27.06°, 31.34°)", + " Banī Mazār: (28.49°, 30.81°)", + " Kroonstad: (-27.65°, 27.23°)", + " Chilecito: (-29.16°, -67.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chilecito: 9208.7 km from centroid", + " Qorof: 3685.5 km from centroid", + " Banī Mazār: 3552.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chilecito", + "FINAL ANSWER: Chilecito" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.60333, + "lon": -48.36583, + "name": "Matão" + }, + { + "lat": -19.67722, + "lon": -51.19083, + "name": "Paranaíba" + }, + { + "lat": -21.64611, + "lon": -41.74694, + "name": "São Fidélis" + }, + { + "lat": -13.55222, + "lon": -52.26833, + "name": "Canarana" + }, + { + "lat": 45.48706, + "lon": -122.80371, + "name": "Beaverton" + } + ], + "question": "Which location is the geographic outlier among: Matão, Paranaíba, São Fidélis, Canarana, Beaverton?", + "ground_truth": { + "answer": "Beaverton", + "outlier_distance_km": 8223.1, + "second_furthest_km": 2882.1, + "clarity_ratio": 2.85, + "median_distance_km": 2346.2, + "distances_to_centroid": { + "Matão": 2346.2, + "Paranaíba": 1987.9, + "São Fidélis": 2882.1, + "Canarana": 1456.1, + "Beaverton": 8223.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Matão: (-21.60°, -48.37°)", + " Paranaíba: (-19.68°, -51.19°)", + " São Fidélis: (-21.65°, -41.75°)", + " Canarana: (-13.55°, -52.27°)", + " Beaverton: (45.49°, -122.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Beaverton: 8223.1 km from centroid", + " São Fidélis: 2882.1 km from centroid", + " Matão: 2346.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Beaverton", + "FINAL ANSWER: Beaverton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.19667, + "lon": -46.14, + "name": "Viseu" + }, + { + "lat": -21.26083, + "lon": -50.64278, + "name": "Guararapes" + }, + { + "lat": -20.73139, + "lon": -48.05778, + "name": "Morro Agudo" + }, + { + "lat": -4.44696, + "lon": -49.11556, + "name": "Jacundá" + }, + { + "lat": 28.86504, + "lon": 106.83814, + "name": "Qingnian" + } + ], + "question": "Which location is the geographic outlier among: Viseu, Guararapes, Morro Agudo, Jacundá, Qingnian?", + "ground_truth": { + "answer": "Qingnian", + "outlier_distance_km": 13518.3, + "second_furthest_km": 4081.5, + "clarity_ratio": 3.31, + "median_distance_km": 3813.1, + "distances_to_centroid": { + "Viseu": 3202.5, + "Guararapes": 4081.5, + "Morro Agudo": 3813.1, + "Jacundá": 3515.6, + "Qingnian": 13518.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viseu: (-1.20°, -46.14°)", + " Guararapes: (-21.26°, -50.64°)", + " Morro Agudo: (-20.73°, -48.06°)", + " Jacundá: (-4.45°, -49.12°)", + " Qingnian: (28.87°, 106.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qingnian: 13518.3 km from centroid", + " Guararapes: 4081.5 km from centroid", + " Morro Agudo: 3813.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qingnian", + "FINAL ANSWER: Qingnian" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.15011, + "lon": -79.86635, + "name": "Alliston" + }, + { + "lat": 21.47831, + "lon": -101.21566, + "name": "San Felipe" + }, + { + "lat": 38.85039, + "lon": -77.1297, + "name": "Baileys Crossroads" + }, + { + "lat": 34.89859, + "lon": -117.02282, + "name": "Barstow" + }, + { + "lat": 21.0045, + "lon": 105.7404, + "name": "Vinhomes Smart City" + } + ], + "question": "Which location is the geographic outlier among: Alliston, San Felipe, Baileys Crossroads, Barstow, Vinhomes Smart City?", + "ground_truth": { + "answer": "Vinhomes Smart City", + "outlier_distance_km": 13727.4, + "second_furthest_km": 5763.3, + "clarity_ratio": 2.38, + "median_distance_km": 4803.3, + "distances_to_centroid": { + "Alliston": 2622.0, + "San Felipe": 4803.3, + "Baileys Crossroads": 2227.2, + "Barstow": 5763.3, + "Vinhomes Smart City": 13727.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alliston: (44.15°, -79.87°)", + " San Felipe: (21.48°, -101.22°)", + " Baileys Crossroads: (38.85°, -77.13°)", + " Barstow: (34.90°, -117.02°)", + " Vinhomes Smart City: (21.00°, 105.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vinhomes Smart City: 13727.4 km from centroid", + " Barstow: 5763.3 km from centroid", + " San Felipe: 4803.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vinhomes Smart City", + "FINAL ANSWER: Vinhomes Smart City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.48815, + "lon": 70.07576, + "name": "Bāntva" + }, + { + "lat": 36.05701, + "lon": 103.83987, + "name": "Lanzhou" + }, + { + "lat": 13.69196, + "lon": 100.40691, + "name": "Bang Khae" + }, + { + "lat": 30.81609, + "lon": 108.26216, + "name": "Lihe" + }, + { + "lat": 32.86013, + "lon": -97.36391, + "name": "Saginaw" + } + ], + "question": "Which location is the geographic outlier among: Bāntva, Lanzhou, Bang Khae, Lihe, Saginaw?", + "ground_truth": { + "answer": "Saginaw", + "outlier_distance_km": 12831.9, + "second_furthest_km": 4961.3, + "clarity_ratio": 2.59, + "median_distance_km": 4729.7, + "distances_to_centroid": { + "Bāntva": 1454.6, + "Lanzhou": 4504.8, + "Bang Khae": 4729.7, + "Lihe": 4961.3, + "Saginaw": 12831.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bāntva: (21.49°, 70.08°)", + " Lanzhou: (36.06°, 103.84°)", + " Bang Khae: (13.69°, 100.41°)", + " Lihe: (30.82°, 108.26°)", + " Saginaw: (32.86°, -97.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Saginaw: 12831.9 km from centroid", + " Lihe: 4961.3 km from centroid", + " Bang Khae: 4729.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Saginaw", + "FINAL ANSWER: Saginaw" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -38.09968, + "lon": 145.17248, + "name": "Carrum Downs" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": 38.55, + "lon": 141.05, + "name": "Kogota" + } + ], + "question": "Which location is the geographic outlier among: Elwood, Ellenbrook, Carrum Downs, Maryborough, Kogota?", + "ground_truth": { + "answer": "Kogota", + "outlier_distance_km": 6394.5, + "second_furthest_km": 2791.8, + "clarity_ratio": 2.29, + "median_distance_km": 2188.2, + "distances_to_centroid": { + "Elwood": 2160.6, + "Ellenbrook": 2791.8, + "Carrum Downs": 2188.2, + "Maryborough": 1499.9, + "Kogota": 6394.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Elwood: (-37.88°, 144.98°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Carrum Downs: (-38.10°, 145.17°)", + " Maryborough: (-25.54°, 152.70°)", + " Kogota: (38.55°, 141.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kogota: 6394.5 km from centroid", + " Ellenbrook: 2791.8 km from centroid", + " Carrum Downs: 2188.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kogota", + "FINAL ANSWER: Kogota" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.699, + "lon": 27.47475, + "name": "Marikana" + }, + { + "lat": 25.90107, + "lon": 32.72392, + "name": "Naqādah" + }, + { + "lat": -30.99766, + "lon": 26.32862, + "name": "Burgersdorp" + }, + { + "lat": 9.11972, + "lon": 4.8236, + "name": "Jebba" + }, + { + "lat": 42.97866, + "lon": -82.40407, + "name": "Sarnia" + } + ], + "question": "Which location is the geographic outlier among: Marikana, Naqādah, Burgersdorp, Jebba, Sarnia?", + "ground_truth": { + "answer": "Sarnia", + "outlier_distance_km": 9212.6, + "second_furthest_km": 4706.2, + "clarity_ratio": 1.96, + "median_distance_km": 4332.1, + "distances_to_centroid": { + "Marikana": 4332.1, + "Naqādah": 4079.4, + "Burgersdorp": 4706.2, + "Jebba": 635.7, + "Sarnia": 9212.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marikana: (-25.70°, 27.47°)", + " Naqādah: (25.90°, 32.72°)", + " Burgersdorp: (-31.00°, 26.33°)", + " Jebba: (9.12°, 4.82°)", + " Sarnia: (42.98°, -82.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sarnia: 9212.6 km from centroid", + " Burgersdorp: 4706.2 km from centroid", + " Marikana: 4332.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sarnia", + "FINAL ANSWER: Sarnia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 56.01141, + "lon": -3.72183, + "name": "Grangemouth" + }, + { + "lat": 41.20036, + "lon": 16.59905, + "name": "Molfetta" + }, + { + "lat": 55.71815, + "lon": 37.47271, + "name": "Davydkovo" + }, + { + "lat": 51.954, + "lon": 7.00481, + "name": "Gescher" + }, + { + "lat": 26.15422, + "lon": 78.7812, + "name": "Seondha" + } + ], + "question": "Which location is the geographic outlier among: Grangemouth, Molfetta, Davydkovo, Gescher, Seondha?", + "ground_truth": { + "answer": "Seondha", + "outlier_distance_km": 5027.9, + "second_furthest_km": 2392.5, + "clarity_ratio": 2.1, + "median_distance_km": 1598.6, + "distances_to_centroid": { + "Grangemouth": 2392.5, + "Molfetta": 1018.4, + "Davydkovo": 1275.1, + "Gescher": 1598.6, + "Seondha": 5027.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Grangemouth: (56.01°, -3.72°)", + " Molfetta: (41.20°, 16.60°)", + " Davydkovo: (55.72°, 37.47°)", + " Gescher: (51.95°, 7.00°)", + " Seondha: (26.15°, 78.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Seondha: 5027.9 km from centroid", + " Grangemouth: 2392.5 km from centroid", + " Gescher: 1598.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Seondha", + "FINAL ANSWER: Seondha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.81353, + "lon": 37.71617, + "name": "Bogorodskoye" + }, + { + "lat": 50.19661, + "lon": 38.11674, + "name": "Valuyki" + }, + { + "lat": 39.88853, + "lon": 4.26583, + "name": "Maó" + }, + { + "lat": 56.5234, + "lon": 52.99431, + "name": "Agryz" + }, + { + "lat": 40.22039, + "lon": -74.01208, + "name": "Asbury Park" + } + ], + "question": "Which location is the geographic outlier among: Bogorodskoye, Valuyki, Maó, Agryz, Asbury Park?", + "ground_truth": { + "answer": "Asbury Park", + "outlier_distance_km": 6518.9, + "second_furthest_km": 2874.5, + "clarity_ratio": 2.27, + "median_distance_km": 1928.1, + "distances_to_centroid": { + "Bogorodskoye": 1928.1, + "Valuyki": 1903.6, + "Maó": 1132.4, + "Agryz": 2874.5, + "Asbury Park": 6518.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bogorodskoye: (55.81°, 37.72°)", + " Valuyki: (50.20°, 38.12°)", + " Maó: (39.89°, 4.27°)", + " Agryz: (56.52°, 52.99°)", + " Asbury Park: (40.22°, -74.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Asbury Park: 6518.9 km from centroid", + " Agryz: 2874.5 km from centroid", + " Bogorodskoye: 1928.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Asbury Park", + "FINAL ANSWER: Asbury Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.00751, + "lon": 119.90851, + "name": "Zhicheng" + }, + { + "lat": 33.5567, + "lon": 131.44506, + "name": "Bungo-Takada-shi" + }, + { + "lat": 21.89764, + "lon": 83.3966, + "name": "Raigarh" + }, + { + "lat": 35.68917, + "lon": 139.83282, + "name": "Ōjima" + }, + { + "lat": 38.70712, + "lon": -121.28106, + "name": "Citrus Heights" + } + ], + "question": "Which location is the geographic outlier among: Zhicheng, Bungo-Takada-shi, Raigarh, Ōjima, Citrus Heights?", + "ground_truth": { + "answer": "Citrus Heights", + "outlier_distance_km": 12037.6, + "second_furthest_km": 6258.5, + "clarity_ratio": 1.92, + "median_distance_km": 5594.4, + "distances_to_centroid": { + "Zhicheng": 4624.8, + "Bungo-Takada-shi": 5594.4, + "Raigarh": 1699.2, + "Ōjima": 6258.5, + "Citrus Heights": 12037.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhicheng: (31.01°, 119.91°)", + " Bungo-Takada-shi: (33.56°, 131.45°)", + " Raigarh: (21.90°, 83.40°)", + " Ōjima: (35.69°, 139.83°)", + " Citrus Heights: (38.71°, -121.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Citrus Heights: 12037.6 km from centroid", + " Ōjima: 6258.5 km from centroid", + " Bungo-Takada-shi: 5594.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Citrus Heights", + "FINAL ANSWER: Citrus Heights" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.27842, + "lon": -93.13379, + "name": "Russellville" + }, + { + "lat": 42.35843, + "lon": -71.12589, + "name": "Allston" + }, + { + "lat": 42.61065, + "lon": -71.23422, + "name": "Tewksbury" + }, + { + "lat": 40.12448, + "lon": -87.63002, + "name": "Danville" + }, + { + "lat": -37.15276, + "lon": -58.48838, + "name": "Ayacucho" + } + ], + "question": "Which location is the geographic outlier among: Russellville, Allston, Tewksbury, Danville, Ayacucho?", + "ground_truth": { + "answer": "Ayacucho", + "outlier_distance_km": 7120.6, + "second_furthest_km": 2051.6, + "clarity_ratio": 3.47, + "median_distance_km": 2026.8, + "distances_to_centroid": { + "Russellville": 2000.3, + "Allston": 2026.8, + "Tewksbury": 2051.6, + "Danville": 2018.5, + "Ayacucho": 7120.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Russellville: (35.28°, -93.13°)", + " Allston: (42.36°, -71.13°)", + " Tewksbury: (42.61°, -71.23°)", + " Danville: (40.12°, -87.63°)", + " Ayacucho: (-37.15°, -58.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ayacucho: 7120.6 km from centroid", + " Tewksbury: 2051.6 km from centroid", + " Allston: 2026.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ayacucho", + "FINAL ANSWER: Ayacucho" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.16667, + "lon": 145.16667, + "name": "Langwarrin" + }, + { + "lat": -37.78828, + "lon": 145.12373, + "name": "Doncaster" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + { + "lat": 40.87363, + "lon": 14.34085, + "name": "Volla" + } + ], + "question": "Which location is the geographic outlier among: Langwarrin, Doncaster, Auburn, Mooroolbark, Volla?", + "ground_truth": { + "answer": "Volla", + "outlier_distance_km": 12843.5, + "second_furthest_km": 3324.5, + "clarity_ratio": 3.86, + "median_distance_km": 3033.8, + "distances_to_centroid": { + "Langwarrin": 3033.8, + "Doncaster": 3009.1, + "Auburn": 3324.5, + "Mooroolbark": 3023.5, + "Volla": 12843.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Langwarrin: (-38.17°, 145.17°)", + " Doncaster: (-37.79°, 145.12°)", + " Auburn: (-33.85°, 151.03°)", + " Mooroolbark: (-37.78°, 145.32°)", + " Volla: (40.87°, 14.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Volla: 12843.5 km from centroid", + " Auburn: 3324.5 km from centroid", + " Langwarrin: 3033.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Volla", + "FINAL ANSWER: Volla" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.63593, + "lon": 141.4448, + "name": "Hitokawame" + }, + { + "lat": 29.86203, + "lon": 106.20288, + "name": "Jiuxian" + }, + { + "lat": 34.30339, + "lon": 135.53322, + "name": "Nakaiburi" + }, + { + "lat": 33.16834, + "lon": 129.72502, + "name": "Sasebo" + }, + { + "lat": 36.73393, + "lon": -3.69072, + "name": "Almuñécar" + } + ], + "question": "Which location is the geographic outlier among: Hitokawame, Jiuxian, Nakaiburi, Sasebo, Almuñécar?", + "ground_truth": { + "answer": "Almuñécar", + "outlier_distance_km": 8941.1, + "second_furthest_km": 3506.9, + "clarity_ratio": 2.55, + "median_distance_km": 3068.9, + "distances_to_centroid": { + "Hitokawame": 3506.9, + "Jiuxian": 697.3, + "Nakaiburi": 3068.9, + "Sasebo": 2567.9, + "Almuñécar": 8941.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hitokawame: (40.64°, 141.44°)", + " Jiuxian: (29.86°, 106.20°)", + " Nakaiburi: (34.30°, 135.53°)", + " Sasebo: (33.17°, 129.73°)", + " Almuñécar: (36.73°, -3.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Almuñécar: 8941.1 km from centroid", + " Hitokawame: 3506.9 km from centroid", + " Nakaiburi: 3068.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Almuñécar", + "FINAL ANSWER: Almuñécar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.73333, + "lon": 145.15, + "name": "Eltham" + }, + { + "lat": -34.03857, + "lon": 151.10005, + "name": "Miranda" + }, + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -6.64167, + "lon": -35.79, + "name": "Cacimba de Dentro" + } + ], + "question": "Which location is the geographic outlier among: Eltham, Miranda, Clayton, Port Macquarie, Cacimba de Dentro?", + "ground_truth": { + "answer": "Cacimba de Dentro", + "outlier_distance_km": 14698.9, + "second_furthest_km": 3931.2, + "clarity_ratio": 3.74, + "median_distance_km": 3734.3, + "distances_to_centroid": { + "Eltham": 3208.4, + "Miranda": 3734.3, + "Clayton": 3207.9, + "Port Macquarie": 3931.2, + "Cacimba de Dentro": 14698.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eltham: (-37.73°, 145.15°)", + " Miranda: (-34.04°, 151.10°)", + " Clayton: (-37.92°, 145.12°)", + " Port Macquarie: (-31.43°, 152.91°)", + " Cacimba de Dentro: (-6.64°, -35.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cacimba de Dentro: 14698.9 km from centroid", + " Port Macquarie: 3931.2 km from centroid", + " Miranda: 3734.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cacimba de Dentro", + "FINAL ANSWER: Cacimba de Dentro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.97083, + "lon": -44.31556, + "name": "Bacabeira" + }, + { + "lat": -28.66056, + "lon": -56.00444, + "name": "São Borja" + }, + { + "lat": -21.12, + "lon": -42.94278, + "name": "Ubá" + }, + { + "lat": -19.17222, + "lon": -41.47222, + "name": "Conselheiro Pena" + }, + { + "lat": -0.50397, + "lon": 36.31845, + "name": "Gilgil" + } + ], + "question": "Which location is the geographic outlier among: Bacabeira, São Borja, Ubá, Conselheiro Pena, Gilgil?", + "ground_truth": { + "answer": "Gilgil", + "outlier_distance_km": 7413.8, + "second_furthest_km": 3133.5, + "clarity_ratio": 2.37, + "median_distance_km": 2053.3, + "distances_to_centroid": { + "Bacabeira": 2053.3, + "São Borja": 3133.5, + "Ubá": 1584.7, + "Conselheiro Pena": 1358.1, + "Gilgil": 7413.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bacabeira: (-2.97°, -44.32°)", + " São Borja: (-28.66°, -56.00°)", + " Ubá: (-21.12°, -42.94°)", + " Conselheiro Pena: (-19.17°, -41.47°)", + " Gilgil: (-0.50°, 36.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gilgil: 7413.8 km from centroid", + " São Borja: 3133.5 km from centroid", + " Bacabeira: 2053.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gilgil", + "FINAL ANSWER: Gilgil" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.23222, + "lon": -39.1925, + "name": "Caridade" + }, + { + "lat": -5.35, + "lon": -40.38333, + "name": "Várzea Alegre" + }, + { + "lat": -25.22, + "lon": -49.34778, + "name": "Itaperuçu" + }, + { + "lat": -23.54889, + "lon": -46.93417, + "name": "Itapevi" + }, + { + "lat": -31.83291, + "lon": 115.7759, + "name": "Duncraig" + } + ], + "question": "Which location is the geographic outlier among: Caridade, Várzea Alegre, Itaperuçu, Itapevi, Duncraig?", + "ground_truth": { + "answer": "Duncraig", + "outlier_distance_km": 12161.8, + "second_furthest_km": 3927.5, + "clarity_ratio": 3.1, + "median_distance_km": 3672.0, + "distances_to_centroid": { + "Caridade": 3330.6, + "Várzea Alegre": 3388.0, + "Itaperuçu": 3927.5, + "Itapevi": 3672.0, + "Duncraig": 12161.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Caridade: (-4.23°, -39.19°)", + " Várzea Alegre: (-5.35°, -40.38°)", + " Itaperuçu: (-25.22°, -49.35°)", + " Itapevi: (-23.55°, -46.93°)", + " Duncraig: (-31.83°, 115.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Duncraig: 12161.8 km from centroid", + " Itaperuçu: 3927.5 km from centroid", + " Itapevi: 3672.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Duncraig", + "FINAL ANSWER: Duncraig" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -37.90561, + "lon": 145.00279, + "name": "Brighton" + }, + { + "lat": 51.90224, + "lon": -0.20256, + "name": "Stevenage" + } + ], + "question": "Which location is the geographic outlier among: Robina, Dunedin, Bairnsdale, Brighton, Stevenage?", + "ground_truth": { + "answer": "Stevenage", + "outlier_distance_km": 13980.8, + "second_furthest_km": 5194.1, + "clarity_ratio": 2.69, + "median_distance_km": 3198.3, + "distances_to_centroid": { + "Robina": 3198.3, + "Dunedin": 5194.1, + "Bairnsdale": 3107.5, + "Brighton": 2927.8, + "Stevenage": 13980.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Robina: (-28.07°, 153.39°)", + " Dunedin: (-45.87°, 170.50°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Brighton: (-37.91°, 145.00°)", + " Stevenage: (51.90°, -0.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stevenage: 13980.8 km from centroid", + " Dunedin: 5194.1 km from centroid", + " Robina: 3198.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stevenage", + "FINAL ANSWER: Stevenage" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + }, + { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + { + "lat": -33.92019, + "lon": 151.22241, + "name": "Kensington" + }, + { + "lat": -24.52611, + "lon": -49.94861, + "name": "Piraí do Sul" + } + ], + "question": "Which location is the geographic outlier among: Albany, Bairnsdale, Rockingham, Kensington, Piraí do Sul?", + "ground_truth": { + "answer": "Piraí do Sul", + "outlier_distance_km": 12724.0, + "second_furthest_km": 5024.4, + "clarity_ratio": 2.53, + "median_distance_km": 4617.3, + "distances_to_centroid": { + "Albany": 1987.1, + "Bairnsdale": 4617.3, + "Rockingham": 1801.7, + "Kensington": 5024.4, + "Piraí do Sul": 12724.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albany: (-35.03°, 117.88°)", + " Bairnsdale: (-37.82°, 147.61°)", + " Rockingham: (-32.28°, 115.73°)", + " Kensington: (-33.92°, 151.22°)", + " Piraí do Sul: (-24.53°, -49.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piraí do Sul: 12724.0 km from centroid", + " Kensington: 5024.4 km from centroid", + " Bairnsdale: 4617.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piraí do Sul", + "FINAL ANSWER: Piraí do Sul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -7.31111, + "lon": -39.30417, + "name": "Barbalha" + }, + { + "lat": -23.56202, + "lon": -46.4913, + "name": "Cidade Lider" + }, + { + "lat": -23.62821, + "lon": -46.45395, + "name": "Sao Rafael" + }, + { + "lat": -23.43389, + "lon": -45.07111, + "name": "Ubatuba" + }, + { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + } + ], + "question": "Which location is the geographic outlier among: Barbalha, Cidade Lider, Sao Rafael, Ubatuba, Southbank?", + "ground_truth": { + "answer": "Southbank", + "outlier_distance_km": 12607.1, + "second_furthest_km": 4072.0, + "clarity_ratio": 3.1, + "median_distance_km": 4067.3, + "distances_to_centroid": { + "Barbalha": 3923.0, + "Cidade Lider": 4072.0, + "Sao Rafael": 4067.3, + "Ubatuba": 3930.3, + "Southbank": 12607.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Barbalha: (-7.31°, -39.30°)", + " Cidade Lider: (-23.56°, -46.49°)", + " Sao Rafael: (-23.63°, -46.45°)", + " Ubatuba: (-23.43°, -45.07°)", + " Southbank: (-37.82°, 144.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Southbank: 12607.1 km from centroid", + " Cidade Lider: 4072.0 km from centroid", + " Sao Rafael: 4067.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Southbank", + "FINAL ANSWER: Southbank" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.99082, + "lon": 7.60177, + "name": "Katsina" + }, + { + "lat": 7.2, + "lon": 38.6, + "name": "Shashamane" + }, + { + "lat": 11.59364, + "lon": 37.39077, + "name": "Bahir Dar" + }, + { + "lat": 30.29636, + "lon": 31.74633, + "name": "Al ‘Āshir min Ramaḑān" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + } + ], + "question": "Which location is the geographic outlier among: Katsina, Shashamane, Bahir Dar, Al ‘Āshir min Ramaḑān, Footscray?", + "ground_truth": { + "answer": "Footscray", + "outlier_distance_km": 10588.5, + "second_furthest_km": 4958.0, + "clarity_ratio": 2.14, + "median_distance_km": 3539.6, + "distances_to_centroid": { + "Katsina": 4958.0, + "Shashamane": 1509.6, + "Bahir Dar": 1777.5, + "Al ‘Āshir min Ramaḑān": 3539.6, + "Footscray": 10588.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Katsina: (12.99°, 7.60°)", + " Shashamane: (7.20°, 38.60°)", + " Bahir Dar: (11.59°, 37.39°)", + " Al ‘Āshir min Ramaḑān: (30.30°, 31.75°)", + " Footscray: (-37.80°, 144.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Footscray: 10588.5 km from centroid", + " Katsina: 4958.0 km from centroid", + " Al ‘Āshir min Ramaḑān: 3539.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Footscray", + "FINAL ANSWER: Footscray" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": -27.61025, + "lon": 153.05388, + "name": "Sunnybank Hills" + }, + { + "lat": -27.19354, + "lon": 153.02631, + "name": "Deception Bay" + }, + { + "lat": 50.99687, + "lon": 8.11062, + "name": "Hilchenbach" + } + ], + "question": "Which location is the geographic outlier among: Hastings, Earlwood, Sunnybank Hills, Deception Bay, Hilchenbach?", + "ground_truth": { + "answer": "Hilchenbach", + "outlier_distance_km": 13443.5, + "second_furthest_km": 5391.5, + "clarity_ratio": 2.49, + "median_distance_km": 3062.1, + "distances_to_centroid": { + "Hastings": 5391.5, + "Earlwood": 3062.1, + "Sunnybank Hills": 2873.4, + "Deception Bay": 2853.2, + "Hilchenbach": 13443.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hastings: (-39.64°, 176.85°)", + " Earlwood: (-33.92°, 151.13°)", + " Sunnybank Hills: (-27.61°, 153.05°)", + " Deception Bay: (-27.19°, 153.03°)", + " Hilchenbach: (51.00°, 8.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hilchenbach: 13443.5 km from centroid", + " Hastings: 5391.5 km from centroid", + " Earlwood: 3062.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hilchenbach", + "FINAL ANSWER: Hilchenbach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.58698, + "lon": -82.91992, + "name": "Clinton Township" + }, + { + "lat": 31.31716, + "lon": -113.53799, + "name": "Puerto Peñasco" + }, + { + "lat": 34.95303, + "lon": -120.43572, + "name": "Santa Maria" + }, + { + "lat": 48.0151, + "lon": -122.06374, + "name": "Lake Stevens" + }, + { + "lat": 27.15092, + "lon": 78.39781, + "name": "Fīrozābād" + } + ], + "question": "Which location is the geographic outlier among: Clinton Township, Puerto Peñasco, Santa Maria, Lake Stevens, Fīrozābād?", + "ground_truth": { + "answer": "Fīrozābād", + "outlier_distance_km": 12263.6, + "second_furthest_km": 4311.9, + "clarity_ratio": 2.84, + "median_distance_km": 4205.4, + "distances_to_centroid": { + "Clinton Township": 1124.8, + "Puerto Peñasco": 3834.5, + "Santa Maria": 4311.9, + "Lake Stevens": 4205.4, + "Fīrozābād": 12263.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Clinton Township: (42.59°, -82.92°)", + " Puerto Peñasco: (31.32°, -113.54°)", + " Santa Maria: (34.95°, -120.44°)", + " Lake Stevens: (48.02°, -122.06°)", + " Fīrozābād: (27.15°, 78.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fīrozābād: 12263.6 km from centroid", + " Santa Maria: 4311.9 km from centroid", + " Lake Stevens: 4205.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fīrozābād", + "FINAL ANSWER: Fīrozābād" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.18035, + "lon": 14.43494, + "name": "Bautzen" + }, + { + "lat": 49.22045, + "lon": 143.0912, + "name": "Poronaysk" + }, + { + "lat": 50.87197, + "lon": 9.70891, + "name": "Bad Hersfeld" + }, + { + "lat": 45.93778, + "lon": 8.57088, + "name": "Pallanza-Intra-Suna" + }, + { + "lat": 28.26419, + "lon": 78.4056, + "name": "Babrāla" + } + ], + "question": "Which location is the geographic outlier among: Bautzen, Poronaysk, Bad Hersfeld, Pallanza-Intra-Suna, Babrāla?", + "ground_truth": { + "answer": "Poronaysk", + "outlier_distance_km": 6536.7, + "second_furthest_km": 3255.9, + "clarity_ratio": 2.01, + "median_distance_km": 3085.9, + "distances_to_centroid": { + "Bautzen": 2754.4, + "Poronaysk": 6536.7, + "Bad Hersfeld": 3085.9, + "Pallanza-Intra-Suna": 3255.9, + "Babrāla": 3063.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bautzen: (51.18°, 14.43°)", + " Poronaysk: (49.22°, 143.09°)", + " Bad Hersfeld: (50.87°, 9.71°)", + " Pallanza-Intra-Suna: (45.94°, 8.57°)", + " Babrāla: (28.26°, 78.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Poronaysk: 6536.7 km from centroid", + " Pallanza-Intra-Suna: 3255.9 km from centroid", + " Bad Hersfeld: 3085.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Poronaysk", + "FINAL ANSWER: Poronaysk" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.74231, + "lon": -5.16709, + "name": "Ronda" + }, + { + "lat": 48.81451, + "lon": 3.08498, + "name": "Coulommiers" + }, + { + "lat": 51.41387, + "lon": -2.4978, + "name": "Keynsham" + }, + { + "lat": 51.43173, + "lon": -0.45761, + "name": "Ashford" + }, + { + "lat": 10.3121, + "lon": 39.65888, + "name": "Mehal Mēda" + } + ], + "question": "Which location is the geographic outlier among: Ronda, Coulommiers, Keynsham, Ashford, Mehal Mēda?", + "ground_truth": { + "answer": "Mehal Mēda", + "outlier_distance_km": 4596.8, + "second_furthest_km": 1487.8, + "clarity_ratio": 3.09, + "median_distance_km": 1419.3, + "distances_to_centroid": { + "Ronda": 1106.4, + "Coulommiers": 1053.6, + "Keynsham": 1487.8, + "Ashford": 1419.3, + "Mehal Mēda": 4596.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ronda: (36.74°, -5.17°)", + " Coulommiers: (48.81°, 3.08°)", + " Keynsham: (51.41°, -2.50°)", + " Ashford: (51.43°, -0.46°)", + " Mehal Mēda: (10.31°, 39.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mehal Mēda: 4596.8 km from centroid", + " Keynsham: 1487.8 km from centroid", + " Ashford: 1419.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mehal Mēda", + "FINAL ANSWER: Mehal Mēda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.36264, + "lon": 9.68176, + "name": "Crema" + }, + { + "lat": 53.16118, + "lon": 12.48287, + "name": "Wittstock" + }, + { + "lat": 53.22698, + "lon": 8.79528, + "name": "Osterholz-Scharmbeck" + }, + { + "lat": 53.27096, + "lon": 34.32143, + "name": "Bryansk" + }, + { + "lat": 35.50051, + "lon": -119.27178, + "name": "Shafter" + } + ], + "question": "Which location is the geographic outlier among: Crema, Wittstock, Osterholz-Scharmbeck, Bryansk, Shafter?", + "ground_truth": { + "answer": "Shafter", + "outlier_distance_km": 8331.9, + "second_furthest_km": 3174.9, + "clarity_ratio": 2.62, + "median_distance_km": 1726.4, + "distances_to_centroid": { + "Crema": 1585.3, + "Wittstock": 1726.4, + "Osterholz-Scharmbeck": 1487.7, + "Bryansk": 3174.9, + "Shafter": 8331.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Crema: (45.36°, 9.68°)", + " Wittstock: (53.16°, 12.48°)", + " Osterholz-Scharmbeck: (53.23°, 8.80°)", + " Bryansk: (53.27°, 34.32°)", + " Shafter: (35.50°, -119.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shafter: 8331.9 km from centroid", + " Bryansk: 3174.9 km from centroid", + " Wittstock: 1726.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shafter", + "FINAL ANSWER: Shafter" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.95893, + "lon": 8.32695, + "name": "Calabar" + }, + { + "lat": 28.31214, + "lon": 30.71007, + "name": "Samālūţ" + }, + { + "lat": 8.66762, + "lon": 3.39393, + "name": "Saki" + }, + { + "lat": 30.93055, + "lon": 31.69864, + "name": "Awlād Şaqr" + }, + { + "lat": -27.08465, + "lon": 152.9511, + "name": "Caboolture" + } + ], + "question": "Which location is the geographic outlier among: Calabar, Samālūţ, Saki, Awlād Şaqr, Caboolture?", + "ground_truth": { + "answer": "Caboolture", + "outlier_distance_km": 12199.4, + "second_furthest_km": 4613.9, + "clarity_ratio": 2.64, + "median_distance_km": 4117.3, + "distances_to_centroid": { + "Calabar": 4117.3, + "Samālūţ": 2627.4, + "Saki": 4613.9, + "Awlād Şaqr": 2807.0, + "Caboolture": 12199.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Calabar: (4.96°, 8.33°)", + " Samālūţ: (28.31°, 30.71°)", + " Saki: (8.67°, 3.39°)", + " Awlād Şaqr: (30.93°, 31.70°)", + " Caboolture: (-27.08°, 152.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Caboolture: 12199.4 km from centroid", + " Saki: 4613.9 km from centroid", + " Calabar: 4117.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Caboolture", + "FINAL ANSWER: Caboolture" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.56194, + "lon": 120.59833, + "name": "Limay" + }, + { + "lat": 23.6182, + "lon": 91.35596, + "name": "Barjala" + }, + { + "lat": 22.8275, + "lon": 86.21639, + "name": "Mango" + }, + { + "lat": 22.54721, + "lon": 114.13149, + "name": "Luohu District" + }, + { + "lat": -25.87417, + "lon": -50.38278, + "name": "São Mateus do Sul" + } + ], + "question": "Which location is the geographic outlier among: Limay, Barjala, Mango, Luohu District, São Mateus do Sul?", + "ground_truth": { + "answer": "São Mateus do Sul", + "outlier_distance_km": 13828.3, + "second_furthest_km": 5224.5, + "clarity_ratio": 2.65, + "median_distance_km": 4587.0, + "distances_to_centroid": { + "Limay": 5224.5, + "Barjala": 2413.8, + "Mango": 1930.2, + "Luohu District": 4587.0, + "São Mateus do Sul": 13828.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Limay: (14.56°, 120.60°)", + " Barjala: (23.62°, 91.36°)", + " Mango: (22.83°, 86.22°)", + " Luohu District: (22.55°, 114.13°)", + " São Mateus do Sul: (-25.87°, -50.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Mateus do Sul: 13828.3 km from centroid", + " Limay: 5224.5 km from centroid", + " Luohu District: 4587.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Mateus do Sul", + "FINAL ANSWER: São Mateus do Sul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.50463, + "lon": -90.46293, + "name": "Hammond" + }, + { + "lat": 37.68187, + "lon": -121.76801, + "name": "Livermore" + }, + { + "lat": 42.68313, + "lon": -73.77845, + "name": "West Albany" + }, + { + "lat": 40.37637, + "lon": -104.69219, + "name": "Evans" + }, + { + "lat": -9.84139, + "lon": -39.48167, + "name": "Uauá" + } + ], + "question": "Which location is the geographic outlier among: Hammond, Livermore, West Albany, Evans, Uauá?", + "ground_truth": { + "answer": "Uauá", + "outlier_distance_km": 6555.7, + "second_furthest_km": 3469.1, + "clarity_ratio": 1.89, + "median_distance_km": 2170.0, + "distances_to_centroid": { + "Hammond": 494.9, + "Livermore": 3469.1, + "West Albany": 1943.9, + "Evans": 2170.0, + "Uauá": 6555.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hammond: (30.50°, -90.46°)", + " Livermore: (37.68°, -121.77°)", + " West Albany: (42.68°, -73.78°)", + " Evans: (40.38°, -104.69°)", + " Uauá: (-9.84°, -39.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uauá: 6555.7 km from centroid", + " Livermore: 3469.1 km from centroid", + " Evans: 2170.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uauá", + "FINAL ANSWER: Uauá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -39.6381, + "lon": 176.84918, + "name": "Hastings" + }, + { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + { + "lat": -37.83834, + "lon": 144.99149, + "name": "South Yarra" + }, + { + "lat": 51.51312, + "lon": 10.25951, + "name": "Duderstadt" + } + ], + "question": "Which location is the geographic outlier among: Hastings, Palmerston, Lincoln, South Yarra, Duderstadt?", + "ground_truth": { + "answer": "Duderstadt", + "outlier_distance_km": 13188.9, + "second_furthest_km": 5494.4, + "clarity_ratio": 2.4, + "median_distance_km": 5225.9, + "distances_to_centroid": { + "Hastings": 5494.4, + "Palmerston": 469.3, + "Lincoln": 5225.9, + "South Yarra": 3059.1, + "Duderstadt": 13188.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hastings: (-39.64°, 176.85°)", + " Palmerston: (-12.49°, 130.98°)", + " Lincoln: (-36.86°, 174.62°)", + " South Yarra: (-37.84°, 144.99°)", + " Duderstadt: (51.51°, 10.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Duderstadt: 13188.9 km from centroid", + " Hastings: 5494.4 km from centroid", + " Lincoln: 5225.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Duderstadt", + "FINAL ANSWER: Duderstadt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.75918, + "lon": -118.00673, + "name": "Westminster" + }, + { + "lat": 20.68812, + "lon": -88.19936, + "name": "Valladolid" + }, + { + "lat": 20.51853, + "lon": -103.18159, + "name": "El Salto" + }, + { + "lat": 41.62697, + "lon": -88.20395, + "name": "Plainfield" + }, + { + "lat": 54.04649, + "lon": -2.79988, + "name": "Lancaster" + } + ], + "question": "Which location is the geographic outlier among: Westminster, Valladolid, El Salto, Plainfield, Lancaster?", + "ground_truth": { + "answer": "Lancaster", + "outlier_distance_km": 6211.6, + "second_furthest_km": 3478.5, + "clarity_ratio": 1.79, + "median_distance_km": 2727.6, + "distances_to_centroid": { + "Westminster": 3478.5, + "Valladolid": 1694.2, + "El Salto": 2727.6, + "Plainfield": 1096.2, + "Lancaster": 6211.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Westminster: (33.76°, -118.01°)", + " Valladolid: (20.69°, -88.20°)", + " El Salto: (20.52°, -103.18°)", + " Plainfield: (41.63°, -88.20°)", + " Lancaster: (54.05°, -2.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lancaster: 6211.6 km from centroid", + " Westminster: 3478.5 km from centroid", + " El Salto: 2727.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lancaster", + "FINAL ANSWER: Lancaster" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.21286, + "lon": -80.24977, + "name": "Tamarac" + }, + { + "lat": 40.3934, + "lon": -82.48572, + "name": "Mount Vernon" + }, + { + "lat": 48.05176, + "lon": -122.17708, + "name": "Marysville" + }, + { + "lat": 33.37642, + "lon": -117.25115, + "name": "Fallbrook" + }, + { + "lat": -0.27088, + "lon": 36.37917, + "name": "Ol Kalou" + } + ], + "question": "Which location is the geographic outlier among: Tamarac, Mount Vernon, Marysville, Fallbrook, Ol Kalou?", + "ground_truth": { + "answer": "Ol Kalou", + "outlier_distance_km": 11903.5, + "second_furthest_km": 4622.1, + "clarity_ratio": 2.58, + "median_distance_km": 4172.9, + "distances_to_centroid": { + "Tamarac": 789.6, + "Mount Vernon": 1473.0, + "Marysville": 4622.1, + "Fallbrook": 4172.9, + "Ol Kalou": 11903.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tamarac: (26.21°, -80.25°)", + " Mount Vernon: (40.39°, -82.49°)", + " Marysville: (48.05°, -122.18°)", + " Fallbrook: (33.38°, -117.25°)", + " Ol Kalou: (-0.27°, 36.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ol Kalou: 11903.5 km from centroid", + " Marysville: 4622.1 km from centroid", + " Fallbrook: 4172.9 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": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -37.96649, + "lon": 145.2081, + "name": "Dandenong North" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": 41.8092, + "lon": -87.59755, + "name": "Kenwood" + } + ], + "question": "Which location is the geographic outlier among: Maryborough, Wahroonga, Dandenong North, Earlwood, Kenwood?", + "ground_truth": { + "answer": "Kenwood", + "outlier_distance_km": 17185.0, + "second_furthest_km": 5225.6, + "clarity_ratio": 3.29, + "median_distance_km": 5126.4, + "distances_to_centroid": { + "Maryborough": 5225.6, + "Wahroonga": 5122.5, + "Dandenong North": 4698.0, + "Earlwood": 5126.4, + "Kenwood": 17185.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maryborough: (-25.54°, 152.70°)", + " Wahroonga: (-33.72°, 151.12°)", + " Dandenong North: (-37.97°, 145.21°)", + " Earlwood: (-33.92°, 151.13°)", + " Kenwood: (41.81°, -87.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kenwood: 17185.0 km from centroid", + " Maryborough: 5225.6 km from centroid", + " Earlwood: 5126.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kenwood", + "FINAL ANSWER: Kenwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.78613, + "lon": 78.5936, + "name": "Pipri" + }, + { + "lat": 30.96853, + "lon": 74.99106, + "name": "Zira" + }, + { + "lat": 4.2168, + "lon": 100.6996, + "name": "Sitiawan" + }, + { + "lat": 6.02867, + "lon": 100.40691, + "name": "Tokai" + }, + { + "lat": -29.06415, + "lon": 30.59279, + "name": "Greytown" + } + ], + "question": "Which location is the geographic outlier among: Pipri, Zira, Sitiawan, Tokai, Greytown?", + "ground_truth": { + "answer": "Greytown", + "outlier_distance_km": 6355.3, + "second_furthest_km": 2719.6, + "clarity_ratio": 2.34, + "median_distance_km": 2630.2, + "distances_to_centroid": { + "Pipri": 1587.5, + "Zira": 2719.6, + "Sitiawan": 2630.2, + "Tokai": 2581.2, + "Greytown": 6355.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pipri: (20.79°, 78.59°)", + " Zira: (30.97°, 74.99°)", + " Sitiawan: (4.22°, 100.70°)", + " Tokai: (6.03°, 100.41°)", + " Greytown: (-29.06°, 30.59°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greytown: 6355.3 km from centroid", + " Zira: 2719.6 km from centroid", + " Sitiawan: 2630.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greytown", + "FINAL ANSWER: Greytown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.72204, + "lon": 78.32056, + "name": "Pulgaon" + }, + { + "lat": -6.17694, + "lon": 106.94667, + "name": "Utan" + }, + { + "lat": 23.21337, + "lon": 82.20232, + "name": "Manendragarh" + }, + { + "lat": 22.75268, + "lon": 73.14967, + "name": "Dākor" + }, + { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + } + ], + "question": "Which location is the geographic outlier among: Pulgaon, Utan, Manendragarh, Dākor, Cabramatta?", + "ground_truth": { + "answer": "Cabramatta", + "outlier_distance_km": 7034.0, + "second_furthest_km": 3323.9, + "clarity_ratio": 2.12, + "median_distance_km": 2754.4, + "distances_to_centroid": { + "Pulgaon": 2754.4, + "Utan": 1598.1, + "Manendragarh": 2634.5, + "Dākor": 3323.9, + "Cabramatta": 7034.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pulgaon: (20.72°, 78.32°)", + " Utan: (-6.18°, 106.95°)", + " Manendragarh: (23.21°, 82.20°)", + " Dākor: (22.75°, 73.15°)", + " Cabramatta: (-33.90°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cabramatta: 7034.0 km from centroid", + " Dākor: 3323.9 km from centroid", + " Pulgaon: 2754.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cabramatta", + "FINAL ANSWER: Cabramatta" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.86396, + "lon": 82.14103, + "name": "Nawābganj" + }, + { + "lat": 21.01767, + "lon": 75.91042, + "name": "Varangaon" + }, + { + "lat": 29.96207, + "lon": 106.60996, + "name": "Liuyin" + }, + { + "lat": 1.6006, + "lon": 103.6419, + "name": "Taman Senai" + }, + { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + } + ], + "question": "Which location is the geographic outlier among: Nawābganj, Varangaon, Liuyin, Taman Senai, Hurstville?", + "ground_truth": { + "answer": "Hurstville", + "outlier_distance_km": 6905.6, + "second_furthest_km": 3275.0, + "clarity_ratio": 2.11, + "median_distance_km": 3021.3, + "distances_to_centroid": { + "Nawābganj": 3021.3, + "Varangaon": 3275.0, + "Liuyin": 2337.6, + "Taman Senai": 833.8, + "Hurstville": 6905.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nawābganj: (26.86°, 82.14°)", + " Varangaon: (21.02°, 75.91°)", + " Liuyin: (29.96°, 106.61°)", + " Taman Senai: (1.60°, 103.64°)", + " Hurstville: (-33.97°, 151.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hurstville: 6905.6 km from centroid", + " Varangaon: 3275.0 km from centroid", + " Nawābganj: 3021.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hurstville", + "FINAL ANSWER: Hurstville" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.04368, + "lon": 22.22574, + "name": "Groot-Brakrivier" + }, + { + "lat": 7.94783, + "lon": 4.78836, + "name": "Otan Ayegbaju" + }, + { + "lat": 30.136, + "lon": 31.715, + "name": "Badr" + }, + { + "lat": -24.98776, + "lon": 31.2385, + "name": "Mkhuhlu" + }, + { + "lat": 34.4048, + "lon": -103.20523, + "name": "Clovis" + } + ], + "question": "Which location is the geographic outlier among: Groot-Brakrivier, Otan Ayegbaju, Badr, Mkhuhlu, Clovis?", + "ground_truth": { + "answer": "Clovis", + "outlier_distance_km": 10802.6, + "second_furthest_km": 4843.8, + "clarity_ratio": 2.23, + "median_distance_km": 4777.4, + "distances_to_centroid": { + "Groot-Brakrivier": 4843.8, + "Otan Ayegbaju": 1009.4, + "Badr": 4731.3, + "Mkhuhlu": 4777.4, + "Clovis": 10802.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Groot-Brakrivier: (-34.04°, 22.23°)", + " Otan Ayegbaju: (7.95°, 4.79°)", + " Badr: (30.14°, 31.71°)", + " Mkhuhlu: (-24.99°, 31.24°)", + " Clovis: (34.40°, -103.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clovis: 10802.6 km from centroid", + " Groot-Brakrivier: 4843.8 km from centroid", + " Mkhuhlu: 4777.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clovis", + "FINAL ANSWER: Clovis" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.09869, + "lon": -75.91797, + "name": "Binghamton" + }, + { + "lat": 46.28569, + "lon": -119.28446, + "name": "Richland" + }, + { + "lat": 41.13815, + "lon": -73.54346, + "name": "North Stamford" + }, + { + "lat": 29.53885, + "lon": -95.44744, + "name": "Fresno" + }, + { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + } + ], + "question": "Which location is the geographic outlier among: Binghamton, Richland, North Stamford, Fresno, Yagoona?", + "ground_truth": { + "answer": "Yagoona", + "outlier_distance_km": 18368.2, + "second_furthest_km": 7030.9, + "clarity_ratio": 2.61, + "median_distance_km": 5199.4, + "distances_to_centroid": { + "Binghamton": 3586.6, + "Richland": 7030.9, + "North Stamford": 3363.6, + "Fresno": 5199.4, + "Yagoona": 18368.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Binghamton: (42.10°, -75.92°)", + " Richland: (46.29°, -119.28°)", + " North Stamford: (41.14°, -73.54°)", + " Fresno: (29.54°, -95.45°)", + " Yagoona: (-33.90°, 151.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yagoona: 18368.2 km from centroid", + " Richland: 7030.9 km from centroid", + " Fresno: 5199.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yagoona", + "FINAL ANSWER: Yagoona" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.46885, + "lon": 106.62226, + "name": "Đồng Hới" + }, + { + "lat": 12.33042, + "lon": 76.60213, + "name": "Hinakallu" + }, + { + "lat": 21.34222, + "lon": 71.30633, + "name": "Kundla" + }, + { + "lat": 14.04472, + "lon": 121.15861, + "name": "Malvar" + }, + { + "lat": 41.48593, + "lon": -73.05066, + "name": "Naugatuck" + } + ], + "question": "Which location is the geographic outlier among: Đồng Hới, Hinakallu, Kundla, Malvar, Naugatuck?", + "ground_truth": { + "answer": "Naugatuck", + "outlier_distance_km": 11551.7, + "second_furthest_km": 6437.7, + "clarity_ratio": 1.79, + "median_distance_km": 4837.0, + "distances_to_centroid": { + "Đồng Hới": 4837.0, + "Hinakallu": 1979.9, + "Kundla": 1116.1, + "Malvar": 6437.7, + "Naugatuck": 11551.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Đồng Hới: (17.47°, 106.62°)", + " Hinakallu: (12.33°, 76.60°)", + " Kundla: (21.34°, 71.31°)", + " Malvar: (14.04°, 121.16°)", + " Naugatuck: (41.49°, -73.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Naugatuck: 11551.7 km from centroid", + " Malvar: 6437.7 km from centroid", + " Đồng Hới: 4837.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Naugatuck", + "FINAL ANSWER: Naugatuck" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.79836, + "lon": 73.34297, + "name": "Deshnoke" + }, + { + "lat": 24.51379, + "lon": 86.64576, + "name": "Jasidih" + }, + { + "lat": 23.8507, + "lon": 72.12963, + "name": "Pātan" + }, + { + "lat": 14.15093, + "lon": 79.8521, + "name": "Gūdūr" + }, + { + "lat": 48.83584, + "lon": 2.64241, + "name": "Marne La Vallée" + } + ], + "question": "Which location is the geographic outlier among: Deshnoke, Jasidih, Pātan, Gūdūr, Marne La Vallée?", + "ground_truth": { + "answer": "Marne La Vallée", + "outlier_distance_km": 5582.6, + "second_furthest_km": 2392.1, + "clarity_ratio": 2.33, + "median_distance_km": 2319.1, + "distances_to_centroid": { + "Deshnoke": 1024.5, + "Jasidih": 2392.1, + "Pātan": 1021.7, + "Gūdūr": 2319.1, + "Marne La Vallée": 5582.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Deshnoke: (27.80°, 73.34°)", + " Jasidih: (24.51°, 86.65°)", + " Pātan: (23.85°, 72.13°)", + " Gūdūr: (14.15°, 79.85°)", + " Marne La Vallée: (48.84°, 2.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Marne La Vallée: 5582.6 km from centroid", + " Jasidih: 2392.1 km from centroid", + " Gūdūr: 2319.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Marne La Vallée", + "FINAL ANSWER: Marne La Vallée" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.54518, + "lon": 0.18769, + "name": "Montivilliers" + }, + { + "lat": 42.81483, + "lon": -1.64898, + "name": "Primer Ensanche" + }, + { + "lat": 53.17477, + "lon": 5.42244, + "name": "Harlingen" + }, + { + "lat": 47.29221, + "lon": -2.36395, + "name": "La Baule-Escoublac" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + } + ], + "question": "Which location is the geographic outlier among: Montivilliers, Primer Ensanche, Harlingen, La Baule-Escoublac, Maroubra?", + "ground_truth": { + "answer": "Maroubra", + "outlier_distance_km": 14547.2, + "second_furthest_km": 3273.0, + "clarity_ratio": 4.44, + "median_distance_km": 3199.1, + "distances_to_centroid": { + "Montivilliers": 3199.1, + "Primer Ensanche": 3078.7, + "Harlingen": 3115.8, + "La Baule-Escoublac": 3273.0, + "Maroubra": 14547.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Montivilliers: (49.55°, 0.19°)", + " Primer Ensanche: (42.81°, -1.65°)", + " Harlingen: (53.17°, 5.42°)", + " La Baule-Escoublac: (47.29°, -2.36°)", + " Maroubra: (-33.95°, 151.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maroubra: 14547.2 km from centroid", + " La Baule-Escoublac: 3273.0 km from centroid", + " Montivilliers: 3199.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maroubra", + "FINAL ANSWER: Maroubra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.74278, + "lon": 111.29556, + "name": "Shangmei" + }, + { + "lat": 3.24177, + "lon": 101.53296, + "name": "Kampung Setia" + }, + { + "lat": 29.53284, + "lon": 108.42504, + "name": "Yushan" + }, + { + "lat": 2.6579, + "lon": 101.5629, + "name": "Tanjung Sepat" + }, + { + "lat": 6.09392, + "lon": -0.83599, + "name": "Kade" + } + ], + "question": "Which location is the geographic outlier among: Shangmei, Kampung Setia, Yushan, Tanjung Sepat, Kade?", + "ground_truth": { + "answer": "Kade", + "outlier_distance_km": 9333.1, + "second_furthest_km": 3182.8, + "clarity_ratio": 2.93, + "median_distance_km": 3022.2, + "distances_to_centroid": { + "Shangmei": 3182.8, + "Kampung Setia": 2220.8, + "Yushan": 3022.2, + "Tanjung Sepat": 2259.6, + "Kade": 9333.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shangmei: (27.74°, 111.30°)", + " Kampung Setia: (3.24°, 101.53°)", + " Yushan: (29.53°, 108.43°)", + " Tanjung Sepat: (2.66°, 101.56°)", + " Kade: (6.09°, -0.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kade: 9333.1 km from centroid", + " Shangmei: 3182.8 km from centroid", + " Yushan: 3022.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kade", + "FINAL ANSWER: Kade" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + }, + { + "lat": -37.79086, + "lon": 145.09386, + "name": "Balwyn North" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -41.31667, + "lon": 173.23333, + "name": "Stoke" + }, + { + "lat": 41.18389, + "lon": -96.03113, + "name": "La Vista" + } + ], + "question": "Which location is the geographic outlier among: Napier, Balwyn North, Broken Hill, Stoke, La Vista?", + "ground_truth": { + "answer": "La Vista", + "outlier_distance_km": 16896.5, + "second_furthest_km": 6699.8, + "clarity_ratio": 2.52, + "median_distance_km": 6377.5, + "distances_to_centroid": { + "Napier": 6699.8, + "Balwyn North": 3945.5, + "Broken Hill": 3472.2, + "Stoke": 6377.5, + "La Vista": 16896.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Napier: (-39.49°, 176.91°)", + " Balwyn North: (-37.79°, 145.09°)", + " Broken Hill: (-31.97°, 141.45°)", + " Stoke: (-41.32°, 173.23°)", + " La Vista: (41.18°, -96.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " La Vista: 16896.5 km from centroid", + " Napier: 6699.8 km from centroid", + " Stoke: 6377.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: La Vista", + "FINAL ANSWER: La Vista" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.86163, + "lon": 31.91809, + "name": "Al Ḩusaynīyah" + }, + { + "lat": 31.28837, + "lon": 31.67719, + "name": "Mīt Abū Ghālib" + }, + { + "lat": 5.75279, + "lon": 45.64603, + "name": "Kahandhale" + }, + { + "lat": -22.34881, + "lon": 30.04074, + "name": "Musina" + }, + { + "lat": 20.68812, + "lon": -88.19936, + "name": "Valladolid" + } + ], + "question": "Which location is the geographic outlier among: Al Ḩusaynīyah, Mīt Abū Ghālib, Kahandhale, Musina, Valladolid?", + "ground_truth": { + "answer": "Valladolid", + "outlier_distance_km": 10341.0, + "second_furthest_km": 4509.6, + "clarity_ratio": 2.29, + "median_distance_km": 3969.3, + "distances_to_centroid": { + "Al Ḩusaynīyah": 2961.4, + "Mīt Abū Ghālib": 2971.8, + "Kahandhale": 3969.3, + "Musina": 4509.6, + "Valladolid": 10341.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Al Ḩusaynīyah: (30.86°, 31.92°)", + " Mīt Abū Ghālib: (31.29°, 31.68°)", + " Kahandhale: (5.75°, 45.65°)", + " Musina: (-22.35°, 30.04°)", + " Valladolid: (20.69°, -88.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Valladolid: 10341.0 km from centroid", + " Musina: 4509.6 km from centroid", + " Kahandhale: 3969.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Valladolid", + "FINAL ANSWER: Valladolid" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.90802, + "lon": 77.51524, + "name": "Bidar" + }, + { + "lat": 29.21399, + "lon": 78.95693, + "name": "Kashipur" + }, + { + "lat": 31.91667, + "lon": 131.41667, + "name": "Miyazaki" + }, + { + "lat": 26.48333, + "lon": 107.91667, + "name": "Zhouxi" + }, + { + "lat": -22.51278, + "lon": -44.00056, + "name": "Pinheiral" + } + ], + "question": "Which location is the geographic outlier among: Bidar, Kashipur, Miyazaki, Zhouxi, Pinheiral?", + "ground_truth": { + "answer": "Pinheiral", + "outlier_distance_km": 13157.9, + "second_furthest_km": 6337.5, + "clarity_ratio": 2.08, + "median_distance_km": 4020.5, + "distances_to_centroid": { + "Bidar": 773.4, + "Kashipur": 1654.4, + "Miyazaki": 6337.5, + "Zhouxi": 4020.5, + "Pinheiral": 13157.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bidar: (17.91°, 77.52°)", + " Kashipur: (29.21°, 78.96°)", + " Miyazaki: (31.92°, 131.42°)", + " Zhouxi: (26.48°, 107.92°)", + " Pinheiral: (-22.51°, -44.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pinheiral: 13157.9 km from centroid", + " Miyazaki: 6337.5 km from centroid", + " Zhouxi: 4020.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pinheiral", + "FINAL ANSWER: Pinheiral" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.65622, + "lon": 76.82093, + "name": "Zerakpur" + }, + { + "lat": 28.02849, + "lon": 74.47442, + "name": "Rājaldesar" + }, + { + "lat": 21.03433, + "lon": 106.77049, + "name": "Thành Phố Uông Bí" + }, + { + "lat": 34.2, + "lon": 118.48333, + "name": "Shiji" + }, + { + "lat": -26.25, + "lon": 28.4, + "name": "Springs" + } + ], + "question": "Which location is the geographic outlier among: Zerakpur, Rājaldesar, Thành Phố Uông Bí, Shiji, Springs?", + "ground_truth": { + "answer": "Springs", + "outlier_distance_km": 7480.7, + "second_furthest_km": 4151.8, + "clarity_ratio": 1.8, + "median_distance_km": 2730.6, + "distances_to_centroid": { + "Zerakpur": 1518.9, + "Rājaldesar": 1343.9, + "Thành Phố Uông Bí": 2730.6, + "Shiji": 4151.8, + "Springs": 7480.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zerakpur: (30.66°, 76.82°)", + " Rājaldesar: (28.03°, 74.47°)", + " Thành Phố Uông Bí: (21.03°, 106.77°)", + " Shiji: (34.20°, 118.48°)", + " Springs: (-26.25°, 28.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Springs: 7480.7 km from centroid", + " Shiji: 4151.8 km from centroid", + " Thành Phố Uông Bí: 2730.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Springs", + "FINAL ANSWER: Springs" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -37.66667, + "lon": 145.06667, + "name": "Mill Park" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -37.0393, + "lon": 174.92815, + "name": "Takanini" + }, + { + "lat": 41.557, + "lon": -83.62716, + "name": "Perrysburg" + } + ], + "question": "Which location is the geographic outlier among: Broken Hill, Mill Park, Helensvale, Takanini, Perrysburg?", + "ground_truth": { + "answer": "Perrysburg", + "outlier_distance_km": 17297.1, + "second_furthest_km": 6911.8, + "clarity_ratio": 2.5, + "median_distance_km": 4891.8, + "distances_to_centroid": { + "Broken Hill": 3817.9, + "Mill Park": 4314.4, + "Helensvale": 4891.8, + "Takanini": 6911.8, + "Perrysburg": 17297.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Broken Hill: (-31.97°, 141.45°)", + " Mill Park: (-37.67°, 145.07°)", + " Helensvale: (-27.92°, 153.33°)", + " Takanini: (-37.04°, 174.93°)", + " Perrysburg: (41.56°, -83.63°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Perrysburg: 17297.1 km from centroid", + " Takanini: 6911.8 km from centroid", + " Helensvale: 4891.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Perrysburg", + "FINAL ANSWER: Perrysburg" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.02492, + "lon": -102.09318, + "name": "Nueva Italia de Ruiz" + }, + { + "lat": 38.9556, + "lon": -90.18678, + "name": "Godfrey" + }, + { + "lat": 19.71288, + "lon": -98.96895, + "name": "Tecámac" + }, + { + "lat": 19.61387, + "lon": -98.9364, + "name": "Tepexpan" + }, + { + "lat": 9.86667, + "lon": 76.5, + "name": "Piravam" + } + ], + "question": "Which location is the geographic outlier among: Nueva Italia de Ruiz, Godfrey, Tecámac, Tepexpan, Piravam?", + "ground_truth": { + "answer": "Piravam", + "outlier_distance_km": 14366.0, + "second_furthest_km": 4104.5, + "clarity_ratio": 3.5, + "median_distance_km": 3768.5, + "distances_to_centroid": { + "Nueva Italia de Ruiz": 4104.5, + "Godfrey": 3257.4, + "Tecámac": 3768.5, + "Tepexpan": 3766.9, + "Piravam": 14366.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nueva Italia de Ruiz: (19.02°, -102.09°)", + " Godfrey: (38.96°, -90.19°)", + " Tecámac: (19.71°, -98.97°)", + " Tepexpan: (19.61°, -98.94°)", + " Piravam: (9.87°, 76.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Piravam: 14366.0 km from centroid", + " Nueva Italia de Ruiz: 4104.5 km from centroid", + " Tecámac: 3768.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Piravam", + "FINAL ANSWER: Piravam" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -30.50123, + "lon": 151.66553, + "name": "Armidale" + }, + { + "lat": -27.35364, + "lon": 152.96848, + "name": "Albany Creek" + }, + { + "lat": 53.6851, + "lon": -1.83878, + "name": "Elland" + } + ], + "question": "Which location is the geographic outlier among: Altona Meadows, Ellenbrook, Armidale, Albany Creek, Elland?", + "ground_truth": { + "answer": "Elland", + "outlier_distance_km": 12933.4, + "second_furthest_km": 4383.2, + "clarity_ratio": 2.95, + "median_distance_km": 4335.6, + "distances_to_centroid": { + "Altona Meadows": 4065.7, + "Ellenbrook": 1919.4, + "Armidale": 4335.6, + "Albany Creek": 4383.2, + "Elland": 12933.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Altona Meadows: (-37.88°, 144.78°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Armidale: (-30.50°, 151.67°)", + " Albany Creek: (-27.35°, 152.97°)", + " Elland: (53.69°, -1.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Elland: 12933.4 km from centroid", + " Albany Creek: 4383.2 km from centroid", + " Armidale: 4335.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Elland", + "FINAL ANSWER: Elland" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": 43.16547, + "lon": -77.70066, + "name": "Gates-North Gates" + } + ], + "question": "Which location is the geographic outlier among: Liverpool, Sunshine West, Caroline Springs, Alexandra Hills, Gates-North Gates?", + "ground_truth": { + "answer": "Gates-North Gates", + "outlier_distance_km": 17300.4, + "second_furthest_km": 5173.0, + "clarity_ratio": 3.34, + "median_distance_km": 4995.3, + "distances_to_centroid": { + "Liverpool": 4995.3, + "Sunshine West": 4541.4, + "Caroline Springs": 4533.1, + "Alexandra Hills": 5173.0, + "Gates-North Gates": 17300.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Liverpool: (-33.92°, 150.93°)", + " Sunshine West: (-37.79°, 144.82°)", + " Caroline Springs: (-37.74°, 144.74°)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Gates-North Gates: (43.17°, -77.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gates-North Gates: 17300.4 km from centroid", + " Alexandra Hills: 5173.0 km from centroid", + " Liverpool: 4995.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gates-North Gates", + "FINAL ANSWER: Gates-North Gates" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.0233, + "lon": -1.48119, + "name": "Belper" + }, + { + "lat": 43.31083, + "lon": 3.47583, + "name": "Agde" + }, + { + "lat": 40.61747, + "lon": 15.05693, + "name": "Eboli" + }, + { + "lat": 51.57344, + "lon": -0.42341, + "name": "Ruislip" + }, + { + "lat": 9.5, + "lon": 35.5, + "name": "Nejo" + } + ], + "question": "Which location is the geographic outlier among: Belper, Agde, Eboli, Ruislip, Nejo?", + "ground_truth": { + "answer": "Nejo", + "outlier_distance_km": 4168.3, + "second_furthest_km": 1744.8, + "clarity_ratio": 2.39, + "median_distance_km": 1572.3, + "distances_to_centroid": { + "Belper": 1744.8, + "Agde": 710.4, + "Eboli": 409.6, + "Ruislip": 1572.3, + "Nejo": 4168.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Belper: (53.02°, -1.48°)", + " Agde: (43.31°, 3.48°)", + " Eboli: (40.62°, 15.06°)", + " Ruislip: (51.57°, -0.42°)", + " Nejo: (9.50°, 35.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nejo: 4168.3 km from centroid", + " Belper: 1744.8 km from centroid", + " Ruislip: 1572.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nejo", + "FINAL ANSWER: Nejo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.92298, + "lon": 14.30935, + "name": "Afragola" + }, + { + "lat": 53.92527, + "lon": -3.01085, + "name": "Fleetwood" + }, + { + "lat": 44.01759, + "lon": 1.3542, + "name": "Montauban" + }, + { + "lat": 53.65917, + "lon": 10.08472, + "name": "Poppenbüttel" + }, + { + "lat": -20.7725, + "lon": -49.71417, + "name": "Monte Aprazível" + } + ], + "question": "Which location is the geographic outlier among: Afragola, Fleetwood, Montauban, Poppenbüttel, Monte Aprazível?", + "ground_truth": { + "answer": "Monte Aprazível", + "outlier_distance_km": 7714.7, + "second_furthest_km": 2466.3, + "clarity_ratio": 3.13, + "median_distance_km": 2184.6, + "distances_to_centroid": { + "Afragola": 1877.3, + "Fleetwood": 2184.6, + "Montauban": 1221.2, + "Poppenbüttel": 2466.3, + "Monte Aprazível": 7714.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Afragola: (40.92°, 14.31°)", + " Fleetwood: (53.93°, -3.01°)", + " Montauban: (44.02°, 1.35°)", + " Poppenbüttel: (53.66°, 10.08°)", + " Monte Aprazível: (-20.77°, -49.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Monte Aprazível: 7714.7 km from centroid", + " Poppenbüttel: 2466.3 km from centroid", + " Fleetwood: 2184.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Monte Aprazível", + "FINAL ANSWER: Monte Aprazível" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.12442, + "lon": 5.92836, + "name": "Toulon" + }, + { + "lat": 45.07873, + "lon": 7.56735, + "name": "Collegno" + }, + { + "lat": 47.39484, + "lon": 0.70398, + "name": "Tours" + }, + { + "lat": 48.60974, + "lon": 42.8569, + "name": "Surovikino" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + } + ], + "question": "Which location is the geographic outlier among: Toulon, Collegno, Tours, Surovikino, Mangere East?", + "ground_truth": { + "answer": "Mangere East", + "outlier_distance_km": 15205.0, + "second_furthest_km": 4370.6, + "clarity_ratio": 3.48, + "median_distance_km": 3885.2, + "distances_to_centroid": { + "Toulon": 3885.2, + "Collegno": 3800.7, + "Tours": 4370.6, + "Surovikino": 2151.6, + "Mangere East": 15205.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Toulon: (43.12°, 5.93°)", + " Collegno: (45.08°, 7.57°)", + " Tours: (47.39°, 0.70°)", + " Surovikino: (48.61°, 42.86°)", + " Mangere East: (-36.97°, 174.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mangere East: 15205.0 km from centroid", + " Tours: 4370.6 km from centroid", + " Toulon: 3885.2 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": 5.92583, + "lon": -75.67056, + "name": "Fredonia" + }, + { + "lat": -23.02972, + "lon": -46.97528, + "name": "Vinhedo" + }, + { + "lat": -25.9466, + "lon": -60.62008, + "name": "Juan José Castelli" + }, + { + "lat": -34.71247, + "lon": -71.0434, + "name": "Chimbarongo" + }, + { + "lat": 34.87724, + "lon": 135.6651, + "name": "Minase" + } + ], + "question": "Which location is the geographic outlier among: Fredonia, Vinhedo, Juan José Castelli, Chimbarongo, Minase?", + "ground_truth": { + "answer": "Minase", + "outlier_distance_km": 16415.4, + "second_furthest_km": 5979.9, + "clarity_ratio": 2.75, + "median_distance_km": 5616.0, + "distances_to_centroid": { + "Fredonia": 5979.9, + "Vinhedo": 2953.2, + "Juan José Castelli": 4344.4, + "Chimbarongo": 5616.0, + "Minase": 16415.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fredonia: (5.93°, -75.67°)", + " Vinhedo: (-23.03°, -46.98°)", + " Juan José Castelli: (-25.95°, -60.62°)", + " Chimbarongo: (-34.71°, -71.04°)", + " Minase: (34.88°, 135.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Minase: 16415.4 km from centroid", + " Fredonia: 5979.9 km from centroid", + " Chimbarongo: 5616.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Minase", + "FINAL ANSWER: Minase" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 59.71417, + "lon": 30.39642, + "name": "Pushkin" + }, + { + "lat": 50.53439, + "lon": 36.68462, + "name": "Razumnoye" + }, + { + "lat": 40.94477, + "lon": 14.3714, + "name": "Acerra" + }, + { + "lat": 52.27333, + "lon": 5.16111, + "name": "Bussum" + }, + { + "lat": -26.255, + "lon": -53.63972, + "name": "Dionísio Cerqueira" + } + ], + "question": "Which location is the geographic outlier among: Pushkin, Razumnoye, Acerra, Bussum, Dionísio Cerqueira?", + "ground_truth": { + "answer": "Dionísio Cerqueira", + "outlier_distance_km": 9329.6, + "second_furthest_km": 3197.7, + "clarity_ratio": 2.92, + "median_distance_km": 2935.4, + "distances_to_centroid": { + "Pushkin": 3197.7, + "Razumnoye": 2935.4, + "Acerra": 913.7, + "Bussum": 1875.0, + "Dionísio Cerqueira": 9329.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pushkin: (59.71°, 30.40°)", + " Razumnoye: (50.53°, 36.68°)", + " Acerra: (40.94°, 14.37°)", + " Bussum: (52.27°, 5.16°)", + " Dionísio Cerqueira: (-26.25°, -53.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dionísio Cerqueira: 9329.6 km from centroid", + " Pushkin: 3197.7 km from centroid", + " Razumnoye: 2935.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dionísio Cerqueira", + "FINAL ANSWER: Dionísio Cerqueira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.72943, + "lon": -104.83192, + "name": "Aurora" + }, + { + "lat": 37.70215, + "lon": -121.93579, + "name": "Dublin" + }, + { + "lat": 29.56884, + "lon": -97.96473, + "name": "Seguin" + }, + { + "lat": 25.77288, + "lon": -80.34783, + "name": "Fountainebleau" + }, + { + "lat": 9.29482, + "lon": 5.05412, + "name": "Mokwa" + } + ], + "question": "Which location is the geographic outlier among: Aurora, Dublin, Seguin, Fountainebleau, Mokwa?", + "ground_truth": { + "answer": "Mokwa", + "outlier_distance_km": 9037.9, + "second_furthest_km": 4006.4, + "clarity_ratio": 2.26, + "median_distance_km": 2597.3, + "distances_to_centroid": { + "Aurora": 2597.3, + "Dublin": 4006.4, + "Seguin": 1749.7, + "Fountainebleau": 295.6, + "Mokwa": 9037.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aurora: (39.73°, -104.83°)", + " Dublin: (37.70°, -121.94°)", + " Seguin: (29.57°, -97.96°)", + " Fountainebleau: (25.77°, -80.35°)", + " Mokwa: (9.29°, 5.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mokwa: 9037.9 km from centroid", + " Dublin: 4006.4 km from centroid", + " Aurora: 2597.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mokwa", + "FINAL ANSWER: Mokwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 48.78583, + "lon": 44.77973, + "name": "Volzhsky" + }, + { + "lat": 44.93553, + "lon": 10.51898, + "name": "Viadana" + }, + { + "lat": 44.1072, + "lon": 42.97798, + "name": "Lermontov" + }, + { + "lat": 43.29551, + "lon": 5.40055, + "name": "Marseille 05" + }, + { + "lat": -4.16694, + "lon": -40.7475, + "name": "Guaraciaba do Norte" + } + ], + "question": "Which location is the geographic outlier among: Volzhsky, Viadana, Lermontov, Marseille 05, Guaraciaba do Norte?", + "ground_truth": { + "answer": "Guaraciaba do Norte", + "outlier_distance_km": 7080.5, + "second_furthest_km": 3013.3, + "clarity_ratio": 2.35, + "median_distance_km": 2754.0, + "distances_to_centroid": { + "Volzhsky": 3013.3, + "Viadana": 1075.6, + "Lermontov": 2754.0, + "Marseille 05": 1073.4, + "Guaraciaba do Norte": 7080.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Volzhsky: (48.79°, 44.78°)", + " Viadana: (44.94°, 10.52°)", + " Lermontov: (44.11°, 42.98°)", + " Marseille 05: (43.30°, 5.40°)", + " Guaraciaba do Norte: (-4.17°, -40.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guaraciaba do Norte: 7080.5 km from centroid", + " Volzhsky: 3013.3 km from centroid", + " Lermontov: 2754.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guaraciaba do Norte", + "FINAL ANSWER: Guaraciaba do Norte" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.07417, + "lon": -41.12389, + "name": "Afonso Cláudio" + }, + { + "lat": -4.45528, + "lon": -43.88556, + "name": "Codó" + }, + { + "lat": -23.53361, + "lon": -46.40866, + "name": "Lajeado" + }, + { + "lat": -2.24444, + "lon": -49.49583, + "name": "Cametá" + }, + { + "lat": 52.30066, + "lon": 7.15763, + "name": "Bad Bentheim" + } + ], + "question": "Which location is the geographic outlier among: Afonso Cláudio, Codó, Lajeado, Cametá, Bad Bentheim?", + "ground_truth": { + "answer": "Bad Bentheim", + "outlier_distance_km": 6958.0, + "second_furthest_km": 2944.1, + "clarity_ratio": 2.36, + "median_distance_km": 2379.9, + "distances_to_centroid": { + "Afonso Cláudio": 2379.9, + "Codó": 1149.4, + "Lajeado": 2944.1, + "Cametá": 1665.3, + "Bad Bentheim": 6958.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Afonso Cláudio: (-20.07°, -41.12°)", + " Codó: (-4.46°, -43.89°)", + " Lajeado: (-23.53°, -46.41°)", + " Cametá: (-2.24°, -49.50°)", + " Bad Bentheim: (52.30°, 7.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bad Bentheim: 6958.0 km from centroid", + " Lajeado: 2944.1 km from centroid", + " Afonso Cláudio: 2379.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bad Bentheim", + "FINAL ANSWER: Bad Bentheim" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": 44.26193, + "lon": -88.41538, + "name": "Appleton" + } + ], + "question": "Which location is the geographic outlier among: Wangaratta, Greenvale, Seaford, The Gap, Appleton?", + "ground_truth": { + "answer": "Appleton", + "outlier_distance_km": 17100.8, + "second_furthest_km": 5432.4, + "clarity_ratio": 3.15, + "median_distance_km": 4878.6, + "distances_to_centroid": { + "Wangaratta": 4878.6, + "Greenvale": 4780.7, + "Seaford": 4815.2, + "The Gap": 5432.4, + "Appleton": 17100.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wangaratta: (-36.36°, 146.32°)", + " Greenvale: (-37.63°, 144.87°)", + " Seaford: (-38.10°, 145.13°)", + " The Gap: (-27.44°, 152.94°)", + " Appleton: (44.26°, -88.42°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Appleton: 17100.8 km from centroid", + " The Gap: 5432.4 km from centroid", + " Wangaratta: 4878.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Appleton", + "FINAL ANSWER: Appleton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.90232, + "lon": 145.01734, + "name": "Brighton East" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + { + "lat": -27.94402, + "lon": 153.39815, + "name": "Labrador" + }, + { + "lat": -24.81811, + "lon": 27.29659, + "name": "Amandelbult" + } + ], + "question": "Which location is the geographic outlier among: Brighton East, Campsie, Landsdale, Labrador, Amandelbult?", + "ground_truth": { + "answer": "Amandelbult", + "outlier_distance_km": 8717.3, + "second_furthest_km": 3376.6, + "clarity_ratio": 2.58, + "median_distance_km": 3052.2, + "distances_to_centroid": { + "Brighton East": 2523.7, + "Campsie": 3052.2, + "Landsdale": 259.8, + "Labrador": 3376.6, + "Amandelbult": 8717.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brighton East: (-37.90°, 145.02°)", + " Campsie: (-33.91°, 151.10°)", + " Landsdale: (-31.81°, 115.87°)", + " Labrador: (-27.94°, 153.40°)", + " Amandelbult: (-24.82°, 27.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amandelbult: 8717.3 km from centroid", + " Labrador: 3376.6 km from centroid", + " Campsie: 3052.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amandelbult", + "FINAL ANSWER: Amandelbult" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.12, + "lon": -42.94278, + "name": "Ubá" + }, + { + "lat": -11.23333, + "lon": -38.48333, + "name": "Nova Soure" + }, + { + "lat": -11.255, + "lon": -57.51972, + "name": "Juara" + }, + { + "lat": -18.57889, + "lon": -46.51806, + "name": "Patos de Minas" + }, + { + "lat": 13.79284, + "lon": 100.58298, + "name": "Khetsamsenok" + } + ], + "question": "Which location is the geographic outlier among: Ubá, Nova Soure, Juara, Patos de Minas, Khetsamsenok?", + "ground_truth": { + "answer": "Khetsamsenok", + "outlier_distance_km": 13219.1, + "second_furthest_km": 4433.3, + "clarity_ratio": 2.98, + "median_distance_km": 3330.0, + "distances_to_centroid": { + "Ubá": 3053.9, + "Nova Soure": 2357.6, + "Juara": 4433.3, + "Patos de Minas": 3330.0, + "Khetsamsenok": 13219.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ubá: (-21.12°, -42.94°)", + " Nova Soure: (-11.23°, -38.48°)", + " Juara: (-11.26°, -57.52°)", + " Patos de Minas: (-18.58°, -46.52°)", + " Khetsamsenok: (13.79°, 100.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Khetsamsenok: 13219.1 km from centroid", + " Juara: 4433.3 km from centroid", + " Patos de Minas: 3330.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Khetsamsenok", + "FINAL ANSWER: Khetsamsenok" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.93553, + "lon": 10.51898, + "name": "Viadana" + }, + { + "lat": 44.40478, + "lon": 8.94439, + "name": "Genoa" + }, + { + "lat": 40.87363, + "lon": 14.34085, + "name": "Volla" + }, + { + "lat": 49.71754, + "lon": 11.05877, + "name": "Forchheim" + }, + { + "lat": 26.97982, + "lon": 84.85065, + "name": "Raxaul" + } + ], + "question": "Which location is the geographic outlier among: Viadana, Genoa, Volla, Forchheim, Raxaul?", + "ground_truth": { + "answer": "Raxaul", + "outlier_distance_km": 5539.5, + "second_furthest_km": 1479.4, + "clarity_ratio": 3.74, + "median_distance_km": 1422.1, + "distances_to_centroid": { + "Viadana": 1309.6, + "Genoa": 1422.1, + "Volla": 972.7, + "Forchheim": 1479.4, + "Raxaul": 5539.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Viadana: (44.94°, 10.52°)", + " Genoa: (44.40°, 8.94°)", + " Volla: (40.87°, 14.34°)", + " Forchheim: (49.72°, 11.06°)", + " Raxaul: (26.98°, 84.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Raxaul: 5539.5 km from centroid", + " Forchheim: 1479.4 km from centroid", + " Genoa: 1422.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Raxaul", + "FINAL ANSWER: Raxaul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.48742, + "lon": 28.97918, + "name": "Mūţ" + }, + { + "lat": -27.1974, + "lon": 25.98311, + "name": "Wolmaransstad" + }, + { + "lat": 5.71044, + "lon": 6.80936, + "name": "Oguta" + }, + { + "lat": 11.66667, + "lon": 38.8, + "name": "Filakit" + }, + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + } + ], + "question": "Which location is the geographic outlier among: Mūţ, Wolmaransstad, Oguta, Filakit, Pakenham?", + "ground_truth": { + "answer": "Pakenham", + "outlier_distance_km": 10246.4, + "second_furthest_km": 4842.5, + "clarity_ratio": 2.12, + "median_distance_km": 3983.8, + "distances_to_centroid": { + "Mūţ": 3983.8, + "Wolmaransstad": 3527.9, + "Oguta": 4842.5, + "Filakit": 2132.9, + "Pakenham": 10246.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mūţ: (25.49°, 28.98°)", + " Wolmaransstad: (-27.20°, 25.98°)", + " Oguta: (5.71°, 6.81°)", + " Filakit: (11.67°, 38.80°)", + " Pakenham: (-38.07°, 145.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pakenham: 10246.4 km from centroid", + " Oguta: 4842.5 km from centroid", + " Mūţ: 3983.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pakenham", + "FINAL ANSWER: Pakenham" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + }, + { + "lat": -44.39672, + "lon": 171.25364, + "name": "Timaru" + }, + { + "lat": 52.22843, + "lon": 17.27617, + "name": "Środa Wielkopolska" + } + ], + "question": "Which location is the geographic outlier among: Nerang, Werribee, Paralowie, Timaru, Środa Wielkopolska?", + "ground_truth": { + "answer": "Środa Wielkopolska", + "outlier_distance_km": 12830.1, + "second_furthest_km": 5144.5, + "clarity_ratio": 2.49, + "median_distance_km": 3066.4, + "distances_to_centroid": { + "Nerang": 3066.4, + "Werribee": 2872.4, + "Paralowie": 2245.1, + "Timaru": 5144.5, + "Środa Wielkopolska": 12830.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nerang: (-27.99°, 153.34°)", + " Werribee: (-37.90°, 144.67°)", + " Paralowie: (-34.76°, 138.61°)", + " Timaru: (-44.40°, 171.25°)", + " Środa Wielkopolska: (52.23°, 17.28°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Środa Wielkopolska: 12830.1 km from centroid", + " Timaru: 5144.5 km from centroid", + " Nerang: 3066.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Środa Wielkopolska", + "FINAL ANSWER: Środa Wielkopolska" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.66689, + "lon": -111.88799, + "name": "Murray" + }, + { + "lat": 23.38359, + "lon": -105.37084, + "name": "Pueblo Nuevo" + }, + { + "lat": 45.47723, + "lon": -75.70164, + "name": "Gatineau" + }, + { + "lat": 40.60816, + "lon": -74.27765, + "name": "Rahway" + }, + { + "lat": 29.074, + "lon": 80.11139, + "name": "Tanakpur" + } + ], + "question": "Which location is the geographic outlier among: Murray, Pueblo Nuevo, Gatineau, Rahway, Tanakpur?", + "ground_truth": { + "answer": "Tanakpur", + "outlier_distance_km": 11539.3, + "second_furthest_km": 4786.6, + "clarity_ratio": 2.41, + "median_distance_km": 4709.8, + "distances_to_centroid": { + "Murray": 4709.8, + "Pueblo Nuevo": 4786.6, + "Gatineau": 1870.3, + "Rahway": 1561.5, + "Tanakpur": 11539.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Murray: (40.67°, -111.89°)", + " Pueblo Nuevo: (23.38°, -105.37°)", + " Gatineau: (45.48°, -75.70°)", + " Rahway: (40.61°, -74.28°)", + " Tanakpur: (29.07°, 80.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tanakpur: 11539.3 km from centroid", + " Pueblo Nuevo: 4786.6 km from centroid", + " Murray: 4709.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tanakpur", + "FINAL ANSWER: Tanakpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.70647, + "lon": 119.1603, + "name": "Changli" + }, + { + "lat": 29.2947, + "lon": 117.20789, + "name": "Jingdezhen" + }, + { + "lat": 11.30975, + "lon": 75.94995, + "name": "Pūlakkōd" + }, + { + "lat": 15.82887, + "lon": 78.03602, + "name": "Kurnool" + }, + { + "lat": 32.59644, + "lon": -114.70968, + "name": "Somerton" + } + ], + "question": "Which location is the geographic outlier among: Changli, Jingdezhen, Pūlakkōd, Kurnool, Somerton?", + "ground_truth": { + "answer": "Somerton", + "outlier_distance_km": 13438.9, + "second_furthest_km": 6062.6, + "clarity_ratio": 2.22, + "median_distance_km": 6058.2, + "distances_to_centroid": { + "Changli": 6058.2, + "Jingdezhen": 6062.6, + "Pūlakkōd": 2712.3, + "Kurnool": 2618.6, + "Somerton": 13438.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Changli: (39.71°, 119.16°)", + " Jingdezhen: (29.29°, 117.21°)", + " Pūlakkōd: (11.31°, 75.95°)", + " Kurnool: (15.83°, 78.04°)", + " Somerton: (32.60°, -114.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Somerton: 13438.9 km from centroid", + " Jingdezhen: 6062.6 km from centroid", + " Changli: 6058.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Somerton", + "FINAL ANSWER: Somerton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.75333, + "lon": -37.33972, + "name": "Tupanatinga" + }, + { + "lat": -22.77944, + "lon": -46.59056, + "name": "Pinhalzinho" + }, + { + "lat": -18.47333, + "lon": -47.20028, + "name": "Coromandel" + }, + { + "lat": -3.10056, + "lon": -45.03361, + "name": "Matinha" + }, + { + "lat": 29.69106, + "lon": -95.2091, + "name": "Pasadena" + } + ], + "question": "Which location is the geographic outlier among: Tupanatinga, Pinhalzinho, Coromandel, Matinha, Pasadena?", + "ground_truth": { + "answer": "Pasadena", + "outlier_distance_km": 5798.4, + "second_furthest_km": 2175.1, + "clarity_ratio": 2.67, + "median_distance_km": 1923.6, + "distances_to_centroid": { + "Tupanatinga": 1923.6, + "Pinhalzinho": 2175.1, + "Coromandel": 1715.2, + "Matinha": 1040.1, + "Pasadena": 5798.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tupanatinga: (-8.75°, -37.34°)", + " Pinhalzinho: (-22.78°, -46.59°)", + " Coromandel: (-18.47°, -47.20°)", + " Matinha: (-3.10°, -45.03°)", + " Pasadena: (29.69°, -95.21°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pasadena: 5798.4 km from centroid", + " Pinhalzinho: 2175.1 km from centroid", + " Tupanatinga: 1923.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pasadena", + "FINAL ANSWER: Pasadena" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.84861, + "lon": -1.83857, + "name": "Bingley" + }, + { + "lat": 49.21088, + "lon": -0.30653, + "name": "Hérouville-Saint-Clair" + }, + { + "lat": 44.09973, + "lon": 3.07848, + "name": "Millau" + }, + { + "lat": 50.0888, + "lon": 9.06455, + "name": "Alzenau in Unterfranken" + }, + { + "lat": -0.97357, + "lon": -62.9269, + "name": "Barcelos" + } + ], + "question": "Which location is the geographic outlier among: Bingley, Hérouville-Saint-Clair, Millau, Alzenau in Unterfranken, Barcelos?", + "ground_truth": { + "answer": "Barcelos", + "outlier_distance_km": 6945.9, + "second_furthest_km": 1955.9, + "clarity_ratio": 3.55, + "median_distance_km": 1752.1, + "distances_to_centroid": { + "Bingley": 1752.1, + "Hérouville-Saint-Clair": 1374.4, + "Millau": 1254.1, + "Alzenau in Unterfranken": 1955.9, + "Barcelos": 6945.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bingley: (53.85°, -1.84°)", + " Hérouville-Saint-Clair: (49.21°, -0.31°)", + " Millau: (44.10°, 3.08°)", + " Alzenau in Unterfranken: (50.09°, 9.06°)", + " Barcelos: (-0.97°, -62.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barcelos: 6945.9 km from centroid", + " Alzenau in Unterfranken: 1955.9 km from centroid", + " Bingley: 1752.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barcelos", + "FINAL ANSWER: Barcelos" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.38119, + "lon": -99.13685, + "name": "Colonia Nativitas" + }, + { + "lat": 38.62456, + "lon": -76.93914, + "name": "Waldorf" + }, + { + "lat": 34.59593, + "lon": -92.48905, + "name": "Bryant" + }, + { + "lat": 42.10009, + "lon": -82.73312, + "name": "Kingsville" + }, + { + "lat": -20.44222, + "lon": -54.86028, + "name": "Terenos" + } + ], + "question": "Which location is the geographic outlier among: Colonia Nativitas, Waldorf, Bryant, Kingsville, Terenos?", + "ground_truth": { + "answer": "Terenos", + "outlier_distance_km": 5599.6, + "second_furthest_km": 2144.8, + "clarity_ratio": 2.61, + "median_distance_km": 1895.6, + "distances_to_centroid": { + "Colonia Nativitas": 1895.6, + "Waldorf": 1800.6, + "Bryant": 1703.3, + "Kingsville": 2144.8, + "Terenos": 5599.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Colonia Nativitas: (19.38°, -99.14°)", + " Waldorf: (38.62°, -76.94°)", + " Bryant: (34.60°, -92.49°)", + " Kingsville: (42.10°, -82.73°)", + " Terenos: (-20.44°, -54.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Terenos: 5599.6 km from centroid", + " Kingsville: 2144.8 km from centroid", + " Colonia Nativitas: 1895.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Terenos", + "FINAL ANSWER: Terenos" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 15.6653, + "lon": 120.6406, + "name": "Ramos" + }, + { + "lat": 18.6057, + "lon": 84.23546, + "name": "Tekkali" + }, + { + "lat": 23.65063, + "lon": 85.00744, + "name": "Khalāri" + }, + { + "lat": 15.11481, + "lon": 104.32938, + "name": "Si Sa Ket" + }, + { + "lat": 41.62697, + "lon": -88.20395, + "name": "Plainfield" + } + ], + "question": "Which location is the geographic outlier among: Ramos, Tekkali, Khalāri, Si Sa Ket, Plainfield?", + "ground_truth": { + "answer": "Plainfield", + "outlier_distance_km": 12175.4, + "second_furthest_km": 6250.7, + "clarity_ratio": 1.95, + "median_distance_km": 4599.7, + "distances_to_centroid": { + "Ramos": 6250.7, + "Tekkali": 2439.8, + "Khalāri": 2429.9, + "Si Sa Ket": 4599.7, + "Plainfield": 12175.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ramos: (15.67°, 120.64°)", + " Tekkali: (18.61°, 84.24°)", + " Khalāri: (23.65°, 85.01°)", + " Si Sa Ket: (15.11°, 104.33°)", + " Plainfield: (41.63°, -88.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Plainfield: 12175.4 km from centroid", + " Ramos: 6250.7 km from centroid", + " Si Sa Ket: 4599.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Plainfield", + "FINAL ANSWER: Plainfield" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.15194, + "lon": -42.41944, + "name": "Bom Jardim" + }, + { + "lat": -23.21003, + "lon": -64.09965, + "name": "Embarcación" + }, + { + "lat": -23.11694, + "lon": -46.55028, + "name": "Atibaia" + }, + { + "lat": -14.79909, + "lon": -39.03228, + "name": "Ilhéus" + }, + { + "lat": 15.39585, + "lon": 73.81568, + "name": "Vasco da Gama" + } + ], + "question": "Which location is the geographic outlier among: Bom Jardim, Embarcación, Atibaia, Ilhéus, Vasco da Gama?", + "ground_truth": { + "answer": "Vasco da Gama", + "outlier_distance_km": 11187.9, + "second_furthest_km": 4384.1, + "clarity_ratio": 2.55, + "median_distance_km": 2633.9, + "distances_to_centroid": { + "Bom Jardim": 2199.8, + "Embarcación": 4384.1, + "Atibaia": 2633.9, + "Ilhéus": 1662.7, + "Vasco da Gama": 11187.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bom Jardim: (-22.15°, -42.42°)", + " Embarcación: (-23.21°, -64.10°)", + " Atibaia: (-23.12°, -46.55°)", + " Ilhéus: (-14.80°, -39.03°)", + " Vasco da Gama: (15.40°, 73.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vasco da Gama: 11187.9 km from centroid", + " Embarcación: 4384.1 km from centroid", + " Atibaia: 2633.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vasco da Gama", + "FINAL ANSWER: Vasco da Gama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.32729, + "lon": -96.9253, + "name": "Shawnee" + }, + { + "lat": 39.70838, + "lon": -91.35848, + "name": "Hannibal" + }, + { + "lat": 20.93482, + "lon": -89.55871, + "name": "Kanasín" + }, + { + "lat": 42.3876, + "lon": -71.0995, + "name": "Somerville" + }, + { + "lat": 45.04616, + "lon": 38.79491, + "name": "Yelizavetinskaya" + } + ], + "question": "Which location is the geographic outlier among: Shawnee, Hannibal, Kanasín, Somerville, Yelizavetinskaya?", + "ground_truth": { + "answer": "Yelizavetinskaya", + "outlier_distance_km": 7957.0, + "second_furthest_km": 3184.4, + "clarity_ratio": 2.5, + "median_distance_km": 3125.3, + "distances_to_centroid": { + "Shawnee": 3125.3, + "Hannibal": 2573.5, + "Kanasín": 3184.4, + "Somerville": 1002.8, + "Yelizavetinskaya": 7957.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shawnee: (35.33°, -96.93°)", + " Hannibal: (39.71°, -91.36°)", + " Kanasín: (20.93°, -89.56°)", + " Somerville: (42.39°, -71.10°)", + " Yelizavetinskaya: (45.05°, 38.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yelizavetinskaya: 7957.0 km from centroid", + " Kanasín: 3184.4 km from centroid", + " Shawnee: 3125.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yelizavetinskaya", + "FINAL ANSWER: Yelizavetinskaya" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.83333, + "lon": 4.13333, + "name": "Hellevoetsluis" + }, + { + "lat": 51.44227, + "lon": -2.85786, + "name": "Clevedon" + }, + { + "lat": 52.25443, + "lon": 21.03472, + "name": "Praga Północ" + }, + { + "lat": 37.28287, + "lon": -5.92088, + "name": "Dos Hermanas" + }, + { + "lat": 38.49602, + "lon": -121.40884, + "name": "Florin" + } + ], + "question": "Which location is the geographic outlier among: Hellevoetsluis, Clevedon, Praga Północ, Dos Hermanas, Florin?", + "ground_truth": { + "answer": "Florin", + "outlier_distance_km": 7715.8, + "second_furthest_km": 3076.8, + "clarity_ratio": 2.51, + "median_distance_km": 1922.5, + "distances_to_centroid": { + "Hellevoetsluis": 1922.5, + "Clevedon": 1442.3, + "Praga Północ": 3076.8, + "Dos Hermanas": 1595.8, + "Florin": 7715.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hellevoetsluis: (51.83°, 4.13°)", + " Clevedon: (51.44°, -2.86°)", + " Praga Północ: (52.25°, 21.03°)", + " Dos Hermanas: (37.28°, -5.92°)", + " Florin: (38.50°, -121.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Florin: 7715.8 km from centroid", + " Praga Północ: 3076.8 km from centroid", + " Hellevoetsluis: 1922.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Florin", + "FINAL ANSWER: Florin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.91667, + "lon": 145.11667, + "name": "Clayton" + }, + { + "lat": -33.88333, + "lon": 151.1, + "name": "Burwood" + }, + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -41.26667, + "lon": 174.95, + "name": "Wainuiomata" + }, + { + "lat": 8.87443, + "lon": -75.62028, + "name": "Ciénaga de Oro" + } + ], + "question": "Which location is the geographic outlier among: Clayton, Burwood, Elwood, Wainuiomata, Ciénaga de Oro?", + "ground_truth": { + "answer": "Ciénaga de Oro", + "outlier_distance_km": 17807.6, + "second_furthest_km": 6113.8, + "clarity_ratio": 2.91, + "median_distance_km": 4106.7, + "distances_to_centroid": { + "Clayton": 3577.0, + "Burwood": 4106.7, + "Elwood": 3564.9, + "Wainuiomata": 6113.8, + "Ciénaga de Oro": 17807.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Clayton: (-37.92°, 145.12°)", + " Burwood: (-33.88°, 151.10°)", + " Elwood: (-37.88°, 144.98°)", + " Wainuiomata: (-41.27°, 174.95°)", + " Ciénaga de Oro: (8.87°, -75.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ciénaga de Oro: 17807.6 km from centroid", + " Wainuiomata: 6113.8 km from centroid", + " Burwood: 4106.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ciénaga de Oro", + "FINAL ANSWER: Ciénaga de Oro" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.21977, + "lon": 7.6273, + "name": "Lüdenscheid" + }, + { + "lat": 57.47908, + "lon": -4.22398, + "name": "Inverness" + }, + { + "lat": 52.52437, + "lon": 13.41053, + "name": "Berlin" + }, + { + "lat": 42.88052, + "lon": -8.54569, + "name": "Santiago de Compostela" + }, + { + "lat": -32.94433, + "lon": 28.01496, + "name": "Gonubie" + } + ], + "question": "Which location is the geographic outlier among: Lüdenscheid, Inverness, Berlin, Santiago de Compostela, Gonubie?", + "ground_truth": { + "answer": "Gonubie", + "outlier_distance_km": 7778.0, + "second_furthest_km": 2724.9, + "clarity_ratio": 2.85, + "median_distance_km": 2092.1, + "distances_to_centroid": { + "Lüdenscheid": 1889.2, + "Inverness": 2724.9, + "Berlin": 2092.1, + "Santiago de Compostela": 1672.7, + "Gonubie": 7778.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lüdenscheid: (51.22°, 7.63°)", + " Inverness: (57.48°, -4.22°)", + " Berlin: (52.52°, 13.41°)", + " Santiago de Compostela: (42.88°, -8.55°)", + " Gonubie: (-32.94°, 28.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gonubie: 7778.0 km from centroid", + " Inverness: 2724.9 km from centroid", + " Berlin: 2092.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gonubie", + "FINAL ANSWER: Gonubie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -15.86126, + "lon": -38.87982, + "name": "Belmonte" + }, + { + "lat": -4.1725, + "lon": -38.46056, + "name": "Pacajus" + }, + { + "lat": -8.80972, + "lon": -63.69556, + "name": "Candeias do Jamari" + }, + { + "lat": -16.56167, + "lon": -41.50333, + "name": "Itaobim" + }, + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + } + ], + "question": "Which location is the geographic outlier among: Belmonte, Pacajus, Candeias do Jamari, Itaobim, Lilydale?", + "ground_truth": { + "answer": "Lilydale", + "outlier_distance_km": 13332.6, + "second_furthest_km": 6145.2, + "clarity_ratio": 2.17, + "median_distance_km": 3656.6, + "distances_to_centroid": { + "Belmonte": 3354.3, + "Pacajus": 3656.6, + "Candeias do Jamari": 6145.2, + "Itaobim": 3625.6, + "Lilydale": 13332.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Belmonte: (-15.86°, -38.88°)", + " Pacajus: (-4.17°, -38.46°)", + " Candeias do Jamari: (-8.81°, -63.70°)", + " Itaobim: (-16.56°, -41.50°)", + " Lilydale: (-37.75°, 145.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lilydale: 13332.6 km from centroid", + " Candeias do Jamari: 6145.2 km from centroid", + " Pacajus: 3656.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lilydale", + "FINAL ANSWER: Lilydale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.16694, + "lon": -40.7475, + "name": "Guaraciaba do Norte" + }, + { + "lat": -29.44806, + "lon": -50.58361, + "name": "São Francisco de Paula" + }, + { + "lat": 3.54625, + "lon": -73.70687, + "name": "Granada" + }, + { + "lat": -23.21472, + "lon": -47.52389, + "name": "Porto Feliz" + }, + { + "lat": 5.52491, + "lon": 7.49461, + "name": "Umuahia" + } + ], + "question": "Which location is the geographic outlier among: Guaraciaba do Norte, São Francisco de Paula, Granada, Porto Feliz, Umuahia?", + "ground_truth": { + "answer": "Umuahia", + "outlier_distance_km": 5629.9, + "second_furthest_km": 3904.0, + "clarity_ratio": 1.44, + "median_distance_km": 2426.2, + "distances_to_centroid": { + "Guaraciaba do Norte": 599.5, + "São Francisco de Paula": 2426.2, + "Granada": 3904.0, + "Porto Feliz": 1669.6, + "Umuahia": 5629.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guaraciaba do Norte: (-4.17°, -40.75°)", + " São Francisco de Paula: (-29.45°, -50.58°)", + " Granada: (3.55°, -73.71°)", + " Porto Feliz: (-23.21°, -47.52°)", + " Umuahia: (5.52°, 7.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Umuahia: 5629.9 km from centroid", + " Granada: 3904.0 km from centroid", + " São Francisco de Paula: 2426.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Umuahia", + "FINAL ANSWER: Umuahia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.65105, + "lon": 7.82089, + "name": "Schopfheim" + }, + { + "lat": 39.1218, + "lon": -0.44812, + "name": "Carcaixent" + }, + { + "lat": 43.31117, + "lon": -0.35583, + "name": "Pau" + }, + { + "lat": 43.29695, + "lon": 5.38107, + "name": "Marseille" + }, + { + "lat": -13.85875, + "lon": -40.08512, + "name": "Jequié" + } + ], + "question": "Which location is the geographic outlier among: Schopfheim, Carcaixent, Pau, Marseille, Jequié?", + "ground_truth": { + "answer": "Jequié", + "outlier_distance_km": 6279.9, + "second_furthest_km": 2083.5, + "clarity_ratio": 3.01, + "median_distance_km": 1587.6, + "distances_to_centroid": { + "Schopfheim": 2083.5, + "Carcaixent": 924.9, + "Pau": 1347.3, + "Marseille": 1587.6, + "Jequié": 6279.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Schopfheim: (47.65°, 7.82°)", + " Carcaixent: (39.12°, -0.45°)", + " Pau: (43.31°, -0.36°)", + " Marseille: (43.30°, 5.38°)", + " Jequié: (-13.86°, -40.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jequié: 6279.9 km from centroid", + " Schopfheim: 2083.5 km from centroid", + " Marseille: 1587.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jequié", + "FINAL ANSWER: Jequié" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.33437, + "lon": -71.10845, + "name": "Mission Hill" + }, + { + "lat": 20.03085, + "lon": -100.72194, + "name": "Acámbaro" + }, + { + "lat": 17.55602, + "lon": -92.94788, + "name": "Teapa" + }, + { + "lat": 39.77978, + "lon": -84.1241, + "name": "Riverside" + }, + { + "lat": 46.53168, + "lon": 125.1038, + "name": "Longfeng" + } + ], + "question": "Which location is the geographic outlier among: Mission Hill, Acámbaro, Teapa, Riverside, Longfeng?", + "ground_truth": { + "answer": "Longfeng", + "outlier_distance_km": 11086.1, + "second_furthest_km": 5685.1, + "clarity_ratio": 1.95, + "median_distance_km": 5094.5, + "distances_to_centroid": { + "Mission Hill": 2512.9, + "Acámbaro": 5685.1, + "Teapa": 5094.5, + "Riverside": 3562.5, + "Longfeng": 11086.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mission Hill: (42.33°, -71.11°)", + " Acámbaro: (20.03°, -100.72°)", + " Teapa: (17.56°, -92.95°)", + " Riverside: (39.78°, -84.12°)", + " Longfeng: (46.53°, 125.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Longfeng: 11086.1 km from centroid", + " Acámbaro: 5685.1 km from centroid", + " Teapa: 5094.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Longfeng", + "FINAL ANSWER: Longfeng" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.115, + "lon": -36.63444, + "name": "Macau" + }, + { + "lat": -15.60972, + "lon": -42.53972, + "name": "Rio Pardo de Minas" + }, + { + "lat": -3.74611, + "lon": -39.78333, + "name": "Irauçuba" + }, + { + "lat": -10.685, + "lon": -37.42528, + "name": "Itabaiana" + }, + { + "lat": 21.86764, + "lon": 75.96391, + "name": "Bhikangaon" + } + ], + "question": "Which location is the geographic outlier among: Macau, Rio Pardo de Minas, Irauçuba, Itabaiana, Bhikangaon?", + "ground_truth": { + "answer": "Bhikangaon", + "outlier_distance_km": 10328.7, + "second_furthest_km": 3235.3, + "clarity_ratio": 3.19, + "median_distance_km": 2633.8, + "distances_to_centroid": { + "Macau": 2296.0, + "Rio Pardo de Minas": 3235.3, + "Irauçuba": 2633.8, + "Itabaiana": 2518.3, + "Bhikangaon": 10328.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macau: (-5.12°, -36.63°)", + " Rio Pardo de Minas: (-15.61°, -42.54°)", + " Irauçuba: (-3.75°, -39.78°)", + " Itabaiana: (-10.69°, -37.43°)", + " Bhikangaon: (21.87°, 75.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhikangaon: 10328.7 km from centroid", + " Rio Pardo de Minas: 3235.3 km from centroid", + " Irauçuba: 2633.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhikangaon", + "FINAL ANSWER: Bhikangaon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.48513, + "lon": 9.14644, + "name": "Bremervörde" + }, + { + "lat": 40.42386, + "lon": -3.53261, + "name": "San Fernando de Henares" + }, + { + "lat": 53.3618, + "lon": -2.73406, + "name": "Widnes" + }, + { + "lat": 51.46171, + "lon": 8.84949, + "name": "Marsberg" + }, + { + "lat": 42.316, + "lon": -82.884, + "name": "Tecumseh" + } + ], + "question": "Which location is the geographic outlier among: Bremervörde, San Fernando de Henares, Widnes, Marsberg, Tecumseh?", + "ground_truth": { + "answer": "Tecumseh", + "outlier_distance_km": 5232.1, + "second_furthest_km": 1733.4, + "clarity_ratio": 3.02, + "median_distance_km": 1686.8, + "distances_to_centroid": { + "Bremervörde": 1733.4, + "San Fernando de Henares": 1211.9, + "Widnes": 988.8, + "Marsberg": 1686.8, + "Tecumseh": 5232.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bremervörde: (53.49°, 9.15°)", + " San Fernando de Henares: (40.42°, -3.53°)", + " Widnes: (53.36°, -2.73°)", + " Marsberg: (51.46°, 8.85°)", + " Tecumseh: (42.32°, -82.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tecumseh: 5232.1 km from centroid", + " Bremervörde: 1733.4 km from centroid", + " Marsberg: 1686.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tecumseh", + "FINAL ANSWER: Tecumseh" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 31.27133, + "lon": 30.78617, + "name": "Sīdī Sālim" + }, + { + "lat": 6.68848, + "lon": -1.62443, + "name": "Kumasi" + }, + { + "lat": 7.52591, + "lon": 5.75342, + "name": "Ikare" + }, + { + "lat": -33.75562, + "lon": 25.40074, + "name": "Kariega" + }, + { + "lat": 8.45611, + "lon": 125.78417, + "name": "Talacogon" + } + ], + "question": "Which location is the geographic outlier among: Sīdī Sālim, Kumasi, Ikare, Kariega, Talacogon?", + "ground_truth": { + "answer": "Talacogon", + "outlier_distance_km": 9784.0, + "second_furthest_km": 4381.9, + "clarity_ratio": 2.23, + "median_distance_km": 4309.3, + "distances_to_centroid": { + "Sīdī Sālim": 3102.2, + "Kumasi": 4309.3, + "Ikare": 3501.7, + "Kariega": 4381.9, + "Talacogon": 9784.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sīdī Sālim: (31.27°, 30.79°)", + " Kumasi: (6.69°, -1.62°)", + " Ikare: (7.53°, 5.75°)", + " Kariega: (-33.76°, 25.40°)", + " Talacogon: (8.46°, 125.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Talacogon: 9784.0 km from centroid", + " Kariega: 4381.9 km from centroid", + " Kumasi: 4309.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Talacogon", + "FINAL ANSWER: Talacogon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.46289, + "lon": 78.81191, + "name": "Chemmumiahpet" + }, + { + "lat": 38.98082, + "lon": 106.3892, + "name": "Shizuishan" + }, + { + "lat": 13.53671, + "lon": 99.81712, + "name": "Ratchaburi" + }, + { + "lat": 14.15093, + "lon": 79.8521, + "name": "Gūdūr" + }, + { + "lat": 6.01277, + "lon": 6.74768, + "name": "Atani" + } + ], + "question": "Which location is the geographic outlier among: Chemmumiahpet, Shizuishan, Ratchaburi, Gūdūr, Atani?", + "ground_truth": { + "answer": "Atani", + "outlier_distance_km": 7432.1, + "second_furthest_km": 3916.4, + "clarity_ratio": 1.9, + "median_distance_km": 2763.7, + "distances_to_centroid": { + "Chemmumiahpet": 582.2, + "Shizuishan": 3916.4, + "Ratchaburi": 2763.7, + "Gūdūr": 694.7, + "Atani": 7432.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chemmumiahpet: (14.46°, 78.81°)", + " Shizuishan: (38.98°, 106.39°)", + " Ratchaburi: (13.54°, 99.82°)", + " Gūdūr: (14.15°, 79.85°)", + " Atani: (6.01°, 6.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Atani: 7432.1 km from centroid", + " Shizuishan: 3916.4 km from centroid", + " Ratchaburi: 2763.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Atani", + "FINAL ANSWER: Atani" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + }, + { + "lat": 30.58333, + "lon": 114.26667, + "name": "Wuhan" + } + ], + "question": "Which location is the geographic outlier among: Reservoir, Baldivis, Truganina, Wheelers Hill, Wuhan?", + "ground_truth": { + "answer": "Wuhan", + "outlier_distance_km": 6288.5, + "second_furthest_km": 2019.1, + "clarity_ratio": 3.11, + "median_distance_km": 1993.2, + "distances_to_centroid": { + "Reservoir": 1993.2, + "Baldivis": 1977.9, + "Truganina": 1988.4, + "Wheelers Hill": 2019.1, + "Wuhan": 6288.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Reservoir: (-37.72°, 145.00°)", + " Baldivis: (-32.33°, 115.83°)", + " Truganina: (-37.82°, 144.75°)", + " Wheelers Hill: (-37.90°, 145.18°)", + " Wuhan: (30.58°, 114.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wuhan: 6288.5 km from centroid", + " Wheelers Hill: 2019.1 km from centroid", + " Reservoir: 1993.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wuhan", + "FINAL ANSWER: Wuhan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.29917, + "lon": -46.8025, + "name": "Guaranésia" + }, + { + "lat": -9.33806, + "lon": -38.25472, + "name": "Glória" + }, + { + "lat": -9.01222, + "lon": -35.2225, + "name": "Maragogi" + }, + { + "lat": -23.485, + "lon": -51.79167, + "name": "Marialva" + }, + { + "lat": 10.06069, + "lon": -2.50192, + "name": "Wa" + } + ], + "question": "Which location is the geographic outlier among: Guaranésia, Glória, Maragogi, Marialva, Wa?", + "ground_truth": { + "answer": "Wa", + "outlier_distance_km": 4258.3, + "second_furthest_km": 2290.8, + "clarity_ratio": 1.86, + "median_distance_km": 1737.9, + "distances_to_centroid": { + "Guaranésia": 1737.9, + "Glória": 392.4, + "Maragogi": 181.4, + "Marialva": 2290.8, + "Wa": 4258.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guaranésia: (-21.30°, -46.80°)", + " Glória: (-9.34°, -38.25°)", + " Maragogi: (-9.01°, -35.22°)", + " Marialva: (-23.48°, -51.79°)", + " Wa: (10.06°, -2.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wa: 4258.3 km from centroid", + " Marialva: 2290.8 km from centroid", + " Guaranésia: 1737.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wa", + "FINAL ANSWER: Wa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.58679, + "lon": 39.12111, + "name": "Mojo" + }, + { + "lat": -32.83483, + "lon": 27.21742, + "name": "Dimbaza" + }, + { + "lat": -27.66606, + "lon": 28.13132, + "name": "Mamafubedu" + }, + { + "lat": 8.27338, + "lon": 5.83526, + "name": "Isanlu-Itedoijowa" + }, + { + "lat": 47.64454, + "lon": -122.69487, + "name": "Silverdale" + } + ], + "question": "Which location is the geographic outlier among: Mojo, Dimbaza, Mamafubedu, Isanlu-Itedoijowa, Silverdale?", + "ground_truth": { + "answer": "Silverdale", + "outlier_distance_km": 12003.5, + "second_furthest_km": 5002.3, + "clarity_ratio": 2.4, + "median_distance_km": 4904.1, + "distances_to_centroid": { + "Mojo": 4904.1, + "Dimbaza": 5002.3, + "Mamafubedu": 4704.8, + "Isanlu-Itedoijowa": 1412.6, + "Silverdale": 12003.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mojo: (8.59°, 39.12°)", + " Dimbaza: (-32.83°, 27.22°)", + " Mamafubedu: (-27.67°, 28.13°)", + " Isanlu-Itedoijowa: (8.27°, 5.84°)", + " Silverdale: (47.64°, -122.69°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Silverdale: 12003.5 km from centroid", + " Dimbaza: 5002.3 km from centroid", + " Mojo: 4904.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Silverdale", + "FINAL ANSWER: Silverdale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.89738, + "lon": 8.84613, + "name": "Dieburg" + }, + { + "lat": 51.99244, + "lon": -2.1601, + "name": "Tewkesbury" + }, + { + "lat": 50.85162, + "lon": -1.17929, + "name": "Fareham" + }, + { + "lat": 42.02896, + "lon": 13.42641, + "name": "Avezzano" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + } + ], + "question": "Which location is the geographic outlier among: Dieburg, Tewkesbury, Fareham, Avezzano, Paraparaumu?", + "ground_truth": { + "answer": "Paraparaumu", + "outlier_distance_km": 15957.1, + "second_furthest_km": 4070.9, + "clarity_ratio": 3.92, + "median_distance_km": 3965.3, + "distances_to_centroid": { + "Dieburg": 3273.0, + "Tewkesbury": 4070.9, + "Fareham": 3965.3, + "Avezzano": 2578.1, + "Paraparaumu": 15957.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dieburg: (49.90°, 8.85°)", + " Tewkesbury: (51.99°, -2.16°)", + " Fareham: (50.85°, -1.18°)", + " Avezzano: (42.03°, 13.43°)", + " Paraparaumu: (-40.92°, 175.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paraparaumu: 15957.1 km from centroid", + " Tewkesbury: 4070.9 km from centroid", + " Fareham: 3965.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paraparaumu", + "FINAL ANSWER: Paraparaumu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.0925, + "lon": -80.1625, + "name": "Chulucanas" + }, + { + "lat": -21.46583, + "lon": -54.38389, + "name": "Nova Alvorada do Sul" + }, + { + "lat": -1.36139, + "lon": -48.24472, + "name": "Benevides" + }, + { + "lat": 3.93135, + "lon": -76.48481, + "name": "Darien" + }, + { + "lat": 43.5283, + "lon": 5.44973, + "name": "Aix-en-Provence" + } + ], + "question": "Which location is the geographic outlier among: Chulucanas, Nova Alvorada do Sul, Benevides, Darien, Aix-en-Provence?", + "ground_truth": { + "answer": "Aix-en-Provence", + "outlier_distance_km": 7039.6, + "second_furthest_km": 3415.2, + "clarity_ratio": 2.06, + "median_distance_km": 2853.1, + "distances_to_centroid": { + "Chulucanas": 3415.2, + "Nova Alvorada do Sul": 2848.8, + "Benevides": 649.4, + "Darien": 2853.1, + "Aix-en-Provence": 7039.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chulucanas: (-5.09°, -80.16°)", + " Nova Alvorada do Sul: (-21.47°, -54.38°)", + " Benevides: (-1.36°, -48.24°)", + " Darien: (3.93°, -76.48°)", + " Aix-en-Provence: (43.53°, 5.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Aix-en-Provence: 7039.6 km from centroid", + " Chulucanas: 3415.2 km from centroid", + " Darien: 2853.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Aix-en-Provence", + "FINAL ANSWER: Aix-en-Provence" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.4399, + "lon": -75.66498, + "name": "Vanier" + }, + { + "lat": 33.91371, + "lon": -98.49339, + "name": "Wichita Falls" + }, + { + "lat": 30.43937, + "lon": -97.62, + "name": "Pflugerville" + }, + { + "lat": 44.35012, + "lon": -78.73286, + "name": "Lindsay" + }, + { + "lat": 23.25469, + "lon": 77.40289, + "name": "Bhopal" + } + ], + "question": "Which location is the geographic outlier among: Vanier, Wichita Falls, Pflugerville, Lindsay, Bhopal?", + "ground_truth": { + "answer": "Bhopal", + "outlier_distance_km": 11760.6, + "second_furthest_km": 4019.0, + "clarity_ratio": 2.93, + "median_distance_km": 3981.4, + "distances_to_centroid": { + "Vanier": 2087.0, + "Wichita Falls": 3981.4, + "Pflugerville": 4019.0, + "Lindsay": 2269.2, + "Bhopal": 11760.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vanier: (45.44°, -75.66°)", + " Wichita Falls: (33.91°, -98.49°)", + " Pflugerville: (30.44°, -97.62°)", + " Lindsay: (44.35°, -78.73°)", + " Bhopal: (23.25°, 77.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bhopal: 11760.6 km from centroid", + " Pflugerville: 4019.0 km from centroid", + " Wichita Falls: 3981.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bhopal", + "FINAL ANSWER: Bhopal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 1.66711, + "lon": 101.44316, + "name": "Dumai" + }, + { + "lat": 14.40599, + "lon": 121.02222, + "name": "Ayala Alabang" + }, + { + "lat": 10.93487, + "lon": 78.41251, + "name": "Kulittalai" + }, + { + "lat": 10.0477, + "lon": 78.74719, + "name": "Sankarapatti" + }, + { + "lat": -6.77008, + "lon": -79.85495, + "name": "Chiclayo" + } + ], + "question": "Which location is the geographic outlier among: Dumai, Ayala Alabang, Kulittalai, Sankarapatti, Chiclayo?", + "ground_truth": { + "answer": "Chiclayo", + "outlier_distance_km": 15574.5, + "second_furthest_km": 6729.0, + "clarity_ratio": 2.31, + "median_distance_km": 4627.1, + "distances_to_centroid": { + "Dumai": 4627.1, + "Ayala Alabang": 6729.0, + "Kulittalai": 2100.4, + "Sankarapatti": 2115.5, + "Chiclayo": 15574.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dumai: (1.67°, 101.44°)", + " Ayala Alabang: (14.41°, 121.02°)", + " Kulittalai: (10.93°, 78.41°)", + " Sankarapatti: (10.05°, 78.75°)", + " Chiclayo: (-6.77°, -79.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chiclayo: 15574.5 km from centroid", + " Ayala Alabang: 6729.0 km from centroid", + " Dumai: 4627.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chiclayo", + "FINAL ANSWER: Chiclayo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.59786, + "lon": 8.4725, + "name": "Lampertheim" + }, + { + "lat": 52.16442, + "lon": 10.54095, + "name": "Wolfenbüttel" + }, + { + "lat": 52.44628, + "lon": 10.0064, + "name": "Burgdorf" + }, + { + "lat": 44.40854, + "lon": 0.70415, + "name": "Villeneuve-sur-Lot" + }, + { + "lat": -8.75222, + "lon": -67.39778, + "name": "Boca do Acre" + } + ], + "question": "Which location is the geographic outlier among: Lampertheim, Wolfenbüttel, Burgdorf, Villeneuve-sur-Lot, Boca do Acre?", + "ground_truth": { + "answer": "Boca do Acre", + "outlier_distance_km": 8082.7, + "second_furthest_km": 2110.8, + "clarity_ratio": 3.83, + "median_distance_km": 2104.8, + "distances_to_centroid": { + "Lampertheim": 1815.4, + "Wolfenbüttel": 2110.8, + "Burgdorf": 2104.8, + "Villeneuve-sur-Lot": 992.7, + "Boca do Acre": 8082.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lampertheim: (49.60°, 8.47°)", + " Wolfenbüttel: (52.16°, 10.54°)", + " Burgdorf: (52.45°, 10.01°)", + " Villeneuve-sur-Lot: (44.41°, 0.70°)", + " Boca do Acre: (-8.75°, -67.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Boca do Acre: 8082.7 km from centroid", + " Wolfenbüttel: 2110.8 km from centroid", + " Burgdorf: 2104.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Boca do Acre", + "FINAL ANSWER: Boca do Acre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.4115, + "lon": 40.79281, + "name": "Mostovskoy" + }, + { + "lat": 37.14386, + "lon": -3.62534, + "name": "Armilla" + }, + { + "lat": 60.70763, + "lon": 28.75283, + "name": "Vyborg" + }, + { + "lat": 60.13044, + "lon": 64.78896, + "name": "Uray" + }, + { + "lat": 17.02921, + "lon": -96.70094, + "name": "San Antonio de la Cal" + } + ], + "question": "Which location is the geographic outlier among: Mostovskoy, Armilla, Vyborg, Uray, San Antonio de la Cal?", + "ground_truth": { + "answer": "San Antonio de la Cal", + "outlier_distance_km": 9739.2, + "second_furthest_km": 4190.2, + "clarity_ratio": 2.32, + "median_distance_km": 2693.1, + "distances_to_centroid": { + "Mostovskoy": 2693.1, + "Armilla": 1155.4, + "Vyborg": 2369.4, + "Uray": 4190.2, + "San Antonio de la Cal": 9739.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mostovskoy: (44.41°, 40.79°)", + " Armilla: (37.14°, -3.63°)", + " Vyborg: (60.71°, 28.75°)", + " Uray: (60.13°, 64.79°)", + " San Antonio de la Cal: (17.03°, -96.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Antonio de la Cal: 9739.2 km from centroid", + " Uray: 4190.2 km from centroid", + " Mostovskoy: 2693.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: San Antonio de la Cal", + "FINAL ANSWER: San Antonio de la Cal" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.15203, + "lon": 39.02335, + "name": "Sendafa" + }, + { + "lat": -28.31971, + "lon": 27.62082, + "name": "Senekal" + }, + { + "lat": -25.99636, + "lon": 28.2268, + "name": "Thembisa" + }, + { + "lat": 28.34827, + "lon": 28.86936, + "name": "Al Bawīţī" + }, + { + "lat": 34.86676, + "lon": -92.40432, + "name": "Maumelle" + } + ], + "question": "Which location is the geographic outlier among: Sendafa, Senekal, Thembisa, Al Bawīţī, Maumelle?", + "ground_truth": { + "answer": "Maumelle", + "outlier_distance_km": 10565.5, + "second_furthest_km": 4221.6, + "clarity_ratio": 2.5, + "median_distance_km": 4053.3, + "distances_to_centroid": { + "Sendafa": 3669.8, + "Senekal": 4221.6, + "Thembisa": 4053.3, + "Al Bawīţī": 3644.8, + "Maumelle": 10565.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sendafa: (9.15°, 39.02°)", + " Senekal: (-28.32°, 27.62°)", + " Thembisa: (-26.00°, 28.23°)", + " Al Bawīţī: (28.35°, 28.87°)", + " Maumelle: (34.87°, -92.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maumelle: 10565.5 km from centroid", + " Senekal: 4221.6 km from centroid", + " Thembisa: 4053.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maumelle", + "FINAL ANSWER: Maumelle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.10317, + "lon": 78.17159, + "name": "Sārni" + }, + { + "lat": 33.59811, + "lon": 131.1883, + "name": "Nakatsu" + }, + { + "lat": 20.28961, + "lon": 83.15233, + "name": "Titlāgarh" + }, + { + "lat": 33.63611, + "lon": 116.97889, + "name": "Suzhou" + }, + { + "lat": -26.49155, + "lon": 29.22878, + "name": "Trichardt" + } + ], + "question": "Which location is the geographic outlier among: Sārni, Nakatsu, Titlāgarh, Suzhou, Trichardt?", + "ground_truth": { + "answer": "Trichardt", + "outlier_distance_km": 7930.6, + "second_furthest_km": 4720.8, + "clarity_ratio": 1.68, + "median_distance_km": 3478.1, + "distances_to_centroid": { + "Sārni": 1173.8, + "Nakatsu": 4720.8, + "Titlāgarh": 632.7, + "Suzhou": 3478.1, + "Trichardt": 7930.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sārni: (22.10°, 78.17°)", + " Nakatsu: (33.60°, 131.19°)", + " Titlāgarh: (20.29°, 83.15°)", + " Suzhou: (33.64°, 116.98°)", + " Trichardt: (-26.49°, 29.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Trichardt: 7930.6 km from centroid", + " Nakatsu: 4720.8 km from centroid", + " Suzhou: 3478.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Trichardt", + "FINAL ANSWER: Trichardt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.75819, + "lon": 145.00583, + "name": "Thornbury" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + }, + { + "lat": -37.78821, + "lon": 175.2902, + "name": "Hamilton East" + }, + { + "lat": 40.32234, + "lon": -3.86496, + "name": "Móstoles" + } + ], + "question": "Which location is the geographic outlier among: Thornbury, Ashburton, Bracken Ridge, Hamilton East, Móstoles?", + "ground_truth": { + "answer": "Móstoles", + "outlier_distance_km": 15048.5, + "second_furthest_km": 4848.1, + "clarity_ratio": 3.1, + "median_distance_km": 4711.2, + "distances_to_centroid": { + "Thornbury": 2438.4, + "Ashburton": 4711.2, + "Bracken Ridge": 2595.3, + "Hamilton East": 4848.1, + "Móstoles": 15048.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Thornbury: (-37.76°, 145.01°)", + " Ashburton: (-43.90°, 171.73°)", + " Bracken Ridge: (-27.32°, 153.03°)", + " Hamilton East: (-37.79°, 175.29°)", + " Móstoles: (40.32°, -3.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Móstoles: 15048.5 km from centroid", + " Hamilton East: 4848.1 km from centroid", + " Ashburton: 4711.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Móstoles", + "FINAL ANSWER: Móstoles" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.76952, + "lon": 30.79165, + "name": "Vryheid" + }, + { + "lat": 31.18352, + "lon": 30.52448, + "name": "Al Maḩmūdīyah" + }, + { + "lat": 8.9, + "lon": 39.91667, + "name": "Metahāra" + }, + { + "lat": 30.29735, + "lon": 30.97641, + "name": "Ashmūn" + }, + { + "lat": 40.57762, + "lon": 17.03812, + "name": "Palagiano" + } + ], + "question": "Which location is the geographic outlier among: Vryheid, Al Maḩmūdīyah, Metahāra, Ashmūn, Palagiano?", + "ground_truth": { + "answer": "Vryheid", + "outlier_distance_km": 4938.9, + "second_furthest_km": 2933.5, + "clarity_ratio": 1.68, + "median_distance_km": 1618.9, + "distances_to_centroid": { + "Vryheid": 4938.9, + "Al Maḩmūdīyah": 1618.9, + "Metahāra": 1389.2, + "Ashmūn": 1523.2, + "Palagiano": 2933.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vryheid: (-27.77°, 30.79°)", + " Al Maḩmūdīyah: (31.18°, 30.52°)", + " Metahāra: (8.90°, 39.92°)", + " Ashmūn: (30.30°, 30.98°)", + " Palagiano: (40.58°, 17.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vryheid: 4938.9 km from centroid", + " Palagiano: 2933.5 km from centroid", + " Al Maḩmūdīyah: 1618.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vryheid", + "FINAL ANSWER: Vryheid" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.7282, + "lon": 16.65141, + "name": "Dzierżoniów" + }, + { + "lat": 51.77714, + "lon": -3.20792, + "name": "Ebbw Vale" + }, + { + "lat": 57.25483, + "lon": 60.09052, + "name": "Novoural’sk" + }, + { + "lat": 41.41209, + "lon": 2.14394, + "name": "Vallcarca" + }, + { + "lat": -1.69405, + "lon": 40.17015, + "name": "Masalani" + } + ], + "question": "Which location is the geographic outlier among: Dzierżoniów, Ebbw Vale, Novoural’sk, Vallcarca, Masalani?", + "ground_truth": { + "answer": "Masalani", + "outlier_distance_km": 4937.7, + "second_furthest_km": 3268.9, + "clarity_ratio": 1.51, + "median_distance_km": 2412.6, + "distances_to_centroid": { + "Dzierżoniów": 1306.7, + "Ebbw Vale": 2412.6, + "Novoural’sk": 3268.9, + "Vallcarca": 1777.3, + "Masalani": 4937.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dzierżoniów: (50.73°, 16.65°)", + " Ebbw Vale: (51.78°, -3.21°)", + " Novoural’sk: (57.25°, 60.09°)", + " Vallcarca: (41.41°, 2.14°)", + " Masalani: (-1.69°, 40.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Masalani: 4937.7 km from centroid", + " Novoural’sk: 3268.9 km from centroid", + " Ebbw Vale: 2412.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Masalani", + "FINAL ANSWER: Masalani" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -2.04278, + "lon": -45.95917, + "name": "Maraca��umé" + }, + { + "lat": -5.7925, + "lon": -37.55667, + "name": "Caraúbas" + }, + { + "lat": -19.49583, + "lon": -41.06389, + "name": "Aimorés" + }, + { + "lat": -22.98436, + "lon": -43.20285, + "name": "Ipanema" + }, + { + "lat": 33.96529, + "lon": -118.15146, + "name": "Bell Gardens" + } + ], + "question": "Which location is the geographic outlier among: Maracaçumé, Caraúbas, Aimorés, Ipanema, Bell Gardens?", + "ground_truth": { + "answer": "Bell Gardens", + "outlier_distance_km": 7592.8, + "second_furthest_km": 2659.2, + "clarity_ratio": 2.86, + "median_distance_km": 2514.0, + "distances_to_centroid": { + "Maracaçumé": 1254.5, + "Caraúbas": 2193.7, + "Aimorés": 2514.0, + "Ipanema": 2659.2, + "Bell Gardens": 7592.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maracaçumé: (-2.04°, -45.96°)", + " Caraúbas: (-5.79°, -37.56°)", + " Aimorés: (-19.50°, -41.06°)", + " Ipanema: (-22.98°, -43.20°)", + " Bell Gardens: (33.97°, -118.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bell Gardens: 7592.8 km from centroid", + " Ipanema: 2659.2 km from centroid", + " Aimorés: 2514.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bell Gardens", + "FINAL ANSWER: Bell Gardens" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.38176, + "lon": 142.48799, + "name": "Warrnambool" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -33.71816, + "lon": 151.11561, + "name": "Wahroonga" + }, + { + "lat": -38.1, + "lon": 145.13333, + "name": "Seaford" + }, + { + "lat": -2.51389, + "lon": -66.09167, + "name": "Fonte Boa" + } + ], + "question": "Which location is the geographic outlier among: Warrnambool, Sunshine West, Wahroonga, Seaford, Fonte Boa?", + "ground_truth": { + "answer": "Fonte Boa", + "outlier_distance_km": 16223.4, + "second_furthest_km": 4473.8, + "clarity_ratio": 3.63, + "median_distance_km": 3901.9, + "distances_to_centroid": { + "Warrnambool": 3671.8, + "Sunshine West": 3873.9, + "Wahroonga": 4473.8, + "Seaford": 3901.9, + "Fonte Boa": 16223.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Warrnambool: (-38.38°, 142.49°)", + " Sunshine West: (-37.79°, 144.82°)", + " Wahroonga: (-33.72°, 151.12°)", + " Seaford: (-38.10°, 145.13°)", + " Fonte Boa: (-2.51°, -66.09°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Fonte Boa: 16223.4 km from centroid", + " Wahroonga: 4473.8 km from centroid", + " Seaford: 3901.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Fonte Boa", + "FINAL ANSWER: Fonte Boa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.43333, + "lon": 116.98333, + "name": "Huangji" + }, + { + "lat": 28.50228, + "lon": 109.26661, + "name": "Hong’an" + }, + { + "lat": 10.88266, + "lon": 78.70456, + "name": "Bhikshāndārkovil" + }, + { + "lat": 21.93458, + "lon": 86.72852, + "name": "Baripāda" + }, + { + "lat": 49.38417, + "lon": 8.3775, + "name": "Schifferstadt" + } + ], + "question": "Which location is the geographic outlier among: Huangji, Hong’an, Bhikshāndārkovil, Baripāda, Schifferstadt?", + "ground_truth": { + "answer": "Schifferstadt", + "outlier_distance_km": 6315.0, + "second_furthest_km": 3528.0, + "clarity_ratio": 1.79, + "median_distance_km": 2844.8, + "distances_to_centroid": { + "Huangji": 3528.0, + "Hong’an": 2844.8, + "Bhikshāndārkovil": 2022.2, + "Baripāda": 1037.1, + "Schifferstadt": 6315.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Huangji: (34.43°, 116.98°)", + " Hong’an: (28.50°, 109.27°)", + " Bhikshāndārkovil: (10.88°, 78.70°)", + " Baripāda: (21.93°, 86.73°)", + " Schifferstadt: (49.38°, 8.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Schifferstadt: 6315.0 km from centroid", + " Huangji: 3528.0 km from centroid", + " Hong’an: 2844.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Schifferstadt", + "FINAL ANSWER: Schifferstadt" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + { + "lat": -36.88012, + "lon": 174.61975, + "name": "Henderson" + }, + { + "lat": -28.77897, + "lon": 114.61459, + "name": "Geraldton" + }, + { + "lat": -33.86785, + "lon": 151.20732, + "name": "Sydney" + }, + { + "lat": 5.89258, + "lon": 7.93534, + "name": "Afikpo" + } + ], + "question": "Which location is the geographic outlier among: Cambridge, Henderson, Geraldton, Sydney, Afikpo?", + "ground_truth": { + "answer": "Afikpo", + "outlier_distance_km": 12966.6, + "second_furthest_km": 4882.3, + "clarity_ratio": 2.66, + "median_distance_km": 4810.5, + "distances_to_centroid": { + "Cambridge": 4882.3, + "Henderson": 4810.5, + "Geraldton": 1037.4, + "Sydney": 2670.7, + "Afikpo": 12966.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cambridge: (-37.88°, 175.44°)", + " Henderson: (-36.88°, 174.62°)", + " Geraldton: (-28.78°, 114.61°)", + " Sydney: (-33.87°, 151.21°)", + " Afikpo: (5.89°, 7.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Afikpo: 12966.6 km from centroid", + " Cambridge: 4882.3 km from centroid", + " Henderson: 4810.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Afikpo", + "FINAL ANSWER: Afikpo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.58547, + "lon": -2.12296, + "name": "Wolverhampton" + }, + { + "lat": 53.48095, + "lon": -2.23743, + "name": "Manchester" + }, + { + "lat": 53.63738, + "lon": 9.91973, + "name": "Schnelsen" + }, + { + "lat": 51.51355, + "lon": -0.3229, + "name": "West Ealing" + }, + { + "lat": 33.50094, + "lon": -86.75221, + "name": "Mountain Brook" + } + ], + "question": "Which location is the geographic outlier among: Wolverhampton, Manchester, Schnelsen, West Ealing, Mountain Brook?", + "ground_truth": { + "answer": "Mountain Brook", + "outlier_distance_km": 5911.9, + "second_furthest_km": 1884.6, + "clarity_ratio": 3.14, + "median_distance_km": 1169.5, + "distances_to_centroid": { + "Wolverhampton": 1074.1, + "Manchester": 1099.4, + "Schnelsen": 1884.6, + "West Ealing": 1169.5, + "Mountain Brook": 5911.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wolverhampton: (52.59°, -2.12°)", + " Manchester: (53.48°, -2.24°)", + " Schnelsen: (53.64°, 9.92°)", + " West Ealing: (51.51°, -0.32°)", + " Mountain Brook: (33.50°, -86.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mountain Brook: 5911.9 km from centroid", + " Schnelsen: 1884.6 km from centroid", + " West Ealing: 1169.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mountain Brook", + "FINAL ANSWER: Mountain Brook" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.1654, + "lon": -70.35486, + "name": "Feijó" + }, + { + "lat": -33.68909, + "lon": -71.21528, + "name": "Melipilla" + }, + { + "lat": -5.50361, + "lon": -41.32333, + "name": "São Miguel do Tapuio" + }, + { + "lat": -21.78083, + "lon": -45.965, + "name": "Poço Fundo" + }, + { + "lat": -28.77897, + "lon": 114.61459, + "name": "Geraldton" + } + ], + "question": "Which location is the geographic outlier among: Feijó, Melipilla, São Miguel do Tapuio, Poço Fundo, Geraldton?", + "ground_truth": { + "answer": "Geraldton", + "outlier_distance_km": 12960.7, + "second_furthest_km": 5264.5, + "clarity_ratio": 2.46, + "median_distance_km": 5007.1, + "distances_to_centroid": { + "Feijó": 5264.5, + "Melipilla": 5007.1, + "São Miguel do Tapuio": 2539.1, + "Poço Fundo": 2414.9, + "Geraldton": 12960.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Feijó: (-8.17°, -70.35°)", + " Melipilla: (-33.69°, -71.22°)", + " São Miguel do Tapuio: (-5.50°, -41.32°)", + " Poço Fundo: (-21.78°, -45.97°)", + " Geraldton: (-28.78°, 114.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Geraldton: 12960.7 km from centroid", + " Feijó: 5264.5 km from centroid", + " Melipilla: 5007.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Geraldton", + "FINAL ANSWER: Geraldton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.86621, + "lon": 152.3479, + "name": "Bundaberg" + }, + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": -5.75611, + "lon": -78.44111, + "name": "Bagua Grande" + } + ], + "question": "Which location is the geographic outlier among: Bundaberg, Helensvale, Canning Vale, Mildura, Bagua Grande?", + "ground_truth": { + "answer": "Bagua Grande", + "outlier_distance_km": 16565.5, + "second_furthest_km": 5562.9, + "clarity_ratio": 2.98, + "median_distance_km": 5533.9, + "distances_to_centroid": { + "Bundaberg": 5533.9, + "Helensvale": 5562.9, + "Canning Vale": 2000.6, + "Mildura": 4443.5, + "Bagua Grande": 16565.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bundaberg: (-24.87°, 152.35°)", + " Helensvale: (-27.92°, 153.33°)", + " Canning Vale: (-32.06°, 115.92°)", + " Mildura: (-34.19°, 142.16°)", + " Bagua Grande: (-5.76°, -78.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bagua Grande: 16565.5 km from centroid", + " Helensvale: 5562.9 km from centroid", + " Bundaberg: 5533.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bagua Grande", + "FINAL ANSWER: Bagua Grande" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.16667, + "lon": -40.94278, + "name": "Carnaubal" + }, + { + "lat": -22.59139, + "lon": -46.52889, + "name": "Socorro" + }, + { + "lat": 9.25778, + "lon": -73.81228, + "name": "Chimichagua" + }, + { + "lat": -29.65056, + "lon": -50.78056, + "name": "Taquara" + }, + { + "lat": 61.21806, + "lon": -149.90028, + "name": "Anchorage" + } + ], + "question": "Which location is the geographic outlier among: Carnaubal, Socorro, Chimichagua, Taquara, Anchorage?", + "ground_truth": { + "answer": "Anchorage", + "outlier_distance_km": 9067.3, + "second_furthest_km": 4280.0, + "clarity_ratio": 2.12, + "median_distance_km": 3982.3, + "distances_to_centroid": { + "Carnaubal": 3579.8, + "Socorro": 3982.3, + "Chimichagua": 733.5, + "Taquara": 4280.0, + "Anchorage": 9067.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carnaubal: (-4.17°, -40.94°)", + " Socorro: (-22.59°, -46.53°)", + " Chimichagua: (9.26°, -73.81°)", + " Taquara: (-29.65°, -50.78°)", + " Anchorage: (61.22°, -149.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Anchorage: 9067.3 km from centroid", + " Taquara: 4280.0 km from centroid", + " Socorro: 3982.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Anchorage", + "FINAL ANSWER: Anchorage" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.39341, + "lon": -75.89232, + "name": "La Plata" + }, + { + "lat": -27.42039, + "lon": -59.03731, + "name": "Fontana" + }, + { + "lat": -18.91861, + "lon": -48.27722, + "name": "Uberlândia" + }, + { + "lat": -40.29313, + "lon": -73.08167, + "name": "La Unión" + }, + { + "lat": 29.39553, + "lon": 107.53939, + "name": "Baima" + } + ], + "question": "Which location is the geographic outlier among: La Plata, Fontana, Uberlândia, La Unión, Baima?", + "ground_truth": { + "answer": "Baima", + "outlier_distance_km": 15145.9, + "second_furthest_km": 5349.4, + "clarity_ratio": 2.83, + "median_distance_km": 5315.5, + "distances_to_centroid": { + "La Plata": 5315.5, + "Fontana": 3562.8, + "Uberlândia": 2175.6, + "La Unión": 5349.4, + "Baima": 15145.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Plata: (2.39°, -75.89°)", + " Fontana: (-27.42°, -59.04°)", + " Uberlândia: (-18.92°, -48.28°)", + " La Unión: (-40.29°, -73.08°)", + " Baima: (29.40°, 107.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baima: 15145.9 km from centroid", + " La Unión: 5349.4 km from centroid", + " La Plata: 5315.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Baima", + "FINAL ANSWER: Baima" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.50578, + "lon": 153.10236, + "name": "Carindale" + }, + { + "lat": -33.32711, + "lon": 115.64137, + "name": "Bunbury" + }, + { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + { + "lat": -27.66757, + "lon": 152.92488, + "name": "Springfield Lakes" + }, + { + "lat": 51.95453, + "lon": 8.6622, + "name": "Oerlinghausen" + } + ], + "question": "Which location is the geographic outlier among: Carindale, Bunbury, Camberwell, Springfield Lakes, Oerlinghausen?", + "ground_truth": { + "answer": "Oerlinghausen", + "outlier_distance_km": 12426.0, + "second_furthest_km": 4164.3, + "clarity_ratio": 2.98, + "median_distance_km": 4150.9, + "distances_to_centroid": { + "Carindale": 4164.3, + "Bunbury": 2052.3, + "Camberwell": 3898.3, + "Springfield Lakes": 4150.9, + "Oerlinghausen": 12426.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carindale: (-27.51°, 153.10°)", + " Bunbury: (-33.33°, 115.64°)", + " Camberwell: (-37.84°, 145.07°)", + " Springfield Lakes: (-27.67°, 152.92°)", + " Oerlinghausen: (51.95°, 8.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oerlinghausen: 12426.0 km from centroid", + " Carindale: 4164.3 km from centroid", + " Springfield Lakes: 4150.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oerlinghausen", + "FINAL ANSWER: Oerlinghausen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.7061, + "lon": 150.7094, + "name": "Cranebrook" + }, + { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + { + "lat": -33.9681, + "lon": 151.13564, + "name": "Kogarah" + }, + { + "lat": -32.73308, + "lon": 151.5574, + "name": "Maitland" + }, + { + "lat": 9.88333, + "lon": 36.61667, + "name": "Āyana" + } + ], + "question": "Which location is the geographic outlier among: Cranebrook, Sunbury, Kogarah, Maitland, Āyana?", + "ground_truth": { + "answer": "Āyana", + "outlier_distance_km": 10513.8, + "second_furthest_km": 2509.6, + "clarity_ratio": 4.19, + "median_distance_km": 2503.9, + "distances_to_centroid": { + "Cranebrook": 2458.3, + "Sunbury": 2138.7, + "Kogarah": 2503.9, + "Maitland": 2509.6, + "Āyana": 10513.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cranebrook: (-33.71°, 150.71°)", + " Sunbury: (-37.58°, 144.73°)", + " Kogarah: (-33.97°, 151.14°)", + " Maitland: (-32.73°, 151.56°)", + " Āyana: (9.88°, 36.62°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Āyana: 10513.8 km from centroid", + " Maitland: 2509.6 km from centroid", + " Kogarah: 2503.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Āyana", + "FINAL ANSWER: Āyana" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.56668, + "lon": 18.48335, + "name": "Atlantis" + }, + { + "lat": 6.54584, + "lon": -0.76264, + "name": "Nkawkaw" + }, + { + "lat": 10.3121, + "lon": 39.65888, + "name": "Mehal Mēda" + }, + { + "lat": -29.06415, + "lon": 30.59279, + "name": "Greytown" + }, + { + "lat": -37.88413, + "lon": 144.78367, + "name": "Altona Meadows" + } + ], + "question": "Which location is the geographic outlier among: Atlantis, Nkawkaw, Mehal Mēda, Greytown, Altona Meadows?", + "ground_truth": { + "answer": "Altona Meadows", + "outlier_distance_km": 9570.5, + "second_furthest_km": 5809.8, + "clarity_ratio": 1.65, + "median_distance_km": 3370.5, + "distances_to_centroid": { + "Atlantis": 3370.5, + "Nkawkaw": 5809.8, + "Mehal Mēda": 3101.2, + "Greytown": 2129.4, + "Altona Meadows": 9570.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Atlantis: (-33.57°, 18.48°)", + " Nkawkaw: (6.55°, -0.76°)", + " Mehal Mēda: (10.31°, 39.66°)", + " Greytown: (-29.06°, 30.59°)", + " Altona Meadows: (-37.88°, 144.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Altona Meadows: 9570.5 km from centroid", + " Nkawkaw: 5809.8 km from centroid", + " Atlantis: 3370.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Altona Meadows", + "FINAL ANSWER: Altona Meadows" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + { + "lat": -37.8676, + "lon": 144.98099, + "name": "Saint Kilda" + }, + { + "lat": -27.19354, + "lon": 153.02631, + "name": "Deception Bay" + }, + { + "lat": -37.81667, + "lon": 144.75, + "name": "Truganina" + }, + { + "lat": -2.00306, + "lon": -49.85444, + "name": "Oeiras do Pará" + } + ], + "question": "Which location is the geographic outlier among: Helensvale, Saint Kilda, Deception Bay, Truganina, Oeiras do Pará?", + "ground_truth": { + "answer": "Oeiras do Pará", + "outlier_distance_km": 16127.0, + "second_furthest_km": 4337.3, + "clarity_ratio": 3.72, + "median_distance_km": 4320.1, + "distances_to_centroid": { + "Helensvale": 4337.3, + "Saint Kilda": 3563.0, + "Deception Bay": 4320.1, + "Truganina": 3542.0, + "Oeiras do Pará": 16127.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Helensvale: (-27.92°, 153.33°)", + " Saint Kilda: (-37.87°, 144.98°)", + " Deception Bay: (-27.19°, 153.03°)", + " Truganina: (-37.82°, 144.75°)", + " Oeiras do Pará: (-2.00°, -49.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oeiras do Pará: 16127.0 km from centroid", + " Helensvale: 4337.3 km from centroid", + " Deception Bay: 4320.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oeiras do Pará", + "FINAL ANSWER: Oeiras do Pará" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.2376, + "lon": 30.78944, + "name": "Iţsā" + }, + { + "lat": 29.41345, + "lon": 30.86579, + "name": "Sinnūris" + }, + { + "lat": 8.83784, + "lon": 3.75628, + "name": "Igboho" + }, + { + "lat": 30.06667, + "lon": 31.3, + "name": "Madīnat an Naşr" + }, + { + "lat": 41.97263, + "lon": -71.32474, + "name": "North Attleborough Center" + } + ], + "question": "Which location is the geographic outlier among: Iţsā, Sinnūris, Igboho, Madīnat an Naşr, North Attleborough Center?", + "ground_truth": { + "answer": "North Attleborough Center", + "outlier_distance_km": 6908.5, + "second_furthest_km": 2556.3, + "clarity_ratio": 2.7, + "median_distance_km": 2516.7, + "distances_to_centroid": { + "Iţsā": 2510.3, + "Sinnūris": 2516.7, + "Igboho": 2124.8, + "Madīnat an Naşr": 2556.3, + "North Attleborough Center": 6908.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Iţsā: (29.24°, 30.79°)", + " Sinnūris: (29.41°, 30.87°)", + " Igboho: (8.84°, 3.76°)", + " Madīnat an Naşr: (30.07°, 31.30°)", + " North Attleborough Center: (41.97°, -71.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " North Attleborough Center: 6908.5 km from centroid", + " Madīnat an Naşr: 2556.3 km from centroid", + " Sinnūris: 2516.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: North Attleborough Center", + "FINAL ANSWER: North Attleborough Center" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.71657, + "lon": 137.93745, + "name": "Komagane" + }, + { + "lat": 10.97724, + "lon": 76.22541, + "name": "Perintalmanna" + }, + { + "lat": 19.55158, + "lon": 110.80279, + "name": "Wenchang" + }, + { + "lat": 14.6488, + "lon": 121.0509, + "name": "Quezon City" + }, + { + "lat": 40.19338, + "lon": -85.38636, + "name": "Muncie" + } + ], + "question": "Which location is the geographic outlier among: Komagane, Perintalmanna, Wenchang, Quezon City, Muncie?", + "ground_truth": { + "answer": "Muncie", + "outlier_distance_km": 12483.7, + "second_furthest_km": 6351.6, + "clarity_ratio": 1.97, + "median_distance_km": 5213.2, + "distances_to_centroid": { + "Komagane": 6351.6, + "Perintalmanna": 1534.7, + "Wenchang": 4011.8, + "Quezon City": 5213.2, + "Muncie": 12483.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Komagane: (35.72°, 137.94°)", + " Perintalmanna: (10.98°, 76.23°)", + " Wenchang: (19.55°, 110.80°)", + " Quezon City: (14.65°, 121.05°)", + " Muncie: (40.19°, -85.39°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Muncie: 12483.7 km from centroid", + " Komagane: 6351.6 km from centroid", + " Quezon City: 5213.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Muncie", + "FINAL ANSWER: Muncie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + { + "lat": -37.81667, + "lon": 145.23333, + "name": "Ringwood" + }, + { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": 36.81667, + "lon": 117.81667, + "name": "Zhoucun" + } + ], + "question": "Which location is the geographic outlier among: Melbourne City Centre, Ringwood, Bentleigh East, Saint Albans, Zhoucun?", + "ground_truth": { + "answer": "Zhoucun", + "outlier_distance_km": 7020.7, + "second_furthest_km": 1750.5, + "clarity_ratio": 4.01, + "median_distance_km": 1745.0, + "distances_to_centroid": { + "Melbourne City Centre": 1737.1, + "Ringwood": 1745.0, + "Bentleigh East": 1750.5, + "Saint Albans": 1723.8, + "Zhoucun": 7020.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Melbourne City Centre: (-37.82°, 144.97°)", + " Ringwood: (-37.82°, 145.23°)", + " Bentleigh East: (-37.92°, 145.05°)", + " Saint Albans: (-37.73°, 144.80°)", + " Zhoucun: (36.82°, 117.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhoucun: 7020.7 km from centroid", + " Bentleigh East: 1750.5 km from centroid", + " Ringwood: 1745.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhoucun", + "FINAL ANSWER: Zhoucun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.98333, + "lon": 37.85, + "name": "Hāgere Hiywet" + }, + { + "lat": 9.35, + "lon": 42.8, + "name": "Jijiga" + }, + { + "lat": -29.57366, + "lon": 31.11552, + "name": "Tongaat" + }, + { + "lat": 6.41667, + "lon": 38.31667, + "name": "Dīla" + }, + { + "lat": -10.40194, + "lon": -65.32667, + "name": "Nova Mamoré" + } + ], + "question": "Which location is the geographic outlier among: Hāgere Hiywet, Jijiga, Tongaat, Dīla, Nova Mamoré?", + "ground_truth": { + "answer": "Nova Mamoré", + "outlier_distance_km": 9102.6, + "second_furthest_km": 3306.7, + "clarity_ratio": 2.75, + "median_distance_km": 3178.5, + "distances_to_centroid": { + "Hāgere Hiywet": 2674.8, + "Jijiga": 3178.5, + "Tongaat": 3306.7, + "Dīla": 2594.9, + "Nova Mamoré": 9102.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hāgere Hiywet: (8.98°, 37.85°)", + " Jijiga: (9.35°, 42.80°)", + " Tongaat: (-29.57°, 31.12°)", + " Dīla: (6.42°, 38.32°)", + " Nova Mamoré: (-10.40°, -65.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nova Mamoré: 9102.6 km from centroid", + " Tongaat: 3306.7 km from centroid", + " Jijiga: 3178.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nova Mamoré", + "FINAL ANSWER: Nova Mamoré" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.47612, + "lon": 36.96144, + "name": "Kitengela" + }, + { + "lat": 3.93726, + "lon": 41.85688, + "name": "Mandera" + }, + { + "lat": 6.58412, + "lon": 3.98336, + "name": "Epe" + }, + { + "lat": -32.90769, + "lon": 27.50973, + "name": "Ndevana" + }, + { + "lat": 34.88333, + "lon": 136.58333, + "name": "Suzuka" + } + ], + "question": "Which location is the geographic outlier among: Kitengela, Mandera, Epe, Ndevana, Suzuka?", + "ground_truth": { + "answer": "Suzuka", + "outlier_distance_km": 9612.4, + "second_furthest_km": 5054.4, + "clarity_ratio": 1.9, + "median_distance_km": 4530.3, + "distances_to_centroid": { + "Kitengela": 1439.9, + "Mandera": 857.1, + "Epe": 5054.4, + "Ndevana": 4530.3, + "Suzuka": 9612.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kitengela: (-1.48°, 36.96°)", + " Mandera: (3.94°, 41.86°)", + " Epe: (6.58°, 3.98°)", + " Ndevana: (-32.91°, 27.51°)", + " Suzuka: (34.88°, 136.58°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Suzuka: 9612.4 km from centroid", + " Epe: 5054.4 km from centroid", + " Ndevana: 4530.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Suzuka", + "FINAL ANSWER: Suzuka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.50222, + "lon": -48.71139, + "name": "Macatuba" + }, + { + "lat": -33.44735, + "lon": -70.58279, + "name": "Ñuñoa" + }, + { + "lat": -2.03444, + "lon": -60.025, + "name": "Presidente Figueiredo" + }, + { + "lat": -30.08389, + "lon": -51.61611, + "name": "Eldorado do Sul" + }, + { + "lat": -6.39472, + "lon": 106.95917, + "name": "Cileungsir" + } + ], + "question": "Which location is the geographic outlier among: Macatuba, Ñuñoa, Presidente Figueiredo, Eldorado do Sul, Cileungsir?", + "ground_truth": { + "answer": "Cileungsir", + "outlier_distance_km": 14028.6, + "second_furthest_km": 4803.7, + "clarity_ratio": 2.92, + "median_distance_km": 4268.3, + "distances_to_centroid": { + "Macatuba": 2517.1, + "Ñuñoa": 4803.7, + "Presidente Figueiredo": 4268.3, + "Eldorado do Sul": 2975.4, + "Cileungsir": 14028.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Macatuba: (-22.50°, -48.71°)", + " Ñuñoa: (-33.45°, -70.58°)", + " Presidente Figueiredo: (-2.03°, -60.02°)", + " Eldorado do Sul: (-30.08°, -51.62°)", + " Cileungsir: (-6.39°, 106.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cileungsir: 14028.6 km from centroid", + " Ñuñoa: 4803.7 km from centroid", + " Presidente Figueiredo: 4268.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cileungsir", + "FINAL ANSWER: Cileungsir" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 58.36848, + "lon": 45.51622, + "name": "Shar’ya" + }, + { + "lat": 55.13061, + "lon": -1.59319, + "name": "Bedlington" + }, + { + "lat": 50.44767, + "lon": 23.41616, + "name": "Tomaszów Lubelski" + }, + { + "lat": 50.97281, + "lon": 18.21816, + "name": "Kluczbork" + }, + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + } + ], + "question": "Which location is the geographic outlier among: Shar’ya, Bedlington, Tomaszów Lubelski, Kluczbork, Newcastle?", + "ground_truth": { + "answer": "Newcastle", + "outlier_distance_km": 13267.1, + "second_furthest_km": 4221.5, + "clarity_ratio": 3.14, + "median_distance_km": 2826.4, + "distances_to_centroid": { + "Shar’ya": 2447.2, + "Bedlington": 4221.5, + "Tomaszów Lubelski": 2473.3, + "Kluczbork": 2826.4, + "Newcastle": 13267.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shar’ya: (58.37°, 45.52°)", + " Bedlington: (55.13°, -1.59°)", + " Tomaszów Lubelski: (50.45°, 23.42°)", + " Kluczbork: (50.97°, 18.22°)", + " Newcastle: (-32.93°, 151.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Newcastle: 13267.1 km from centroid", + " Bedlington: 4221.5 km from centroid", + " Kluczbork: 2826.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Newcastle", + "FINAL ANSWER: Newcastle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.93333, + "lon": 145.23333, + "name": "Rowville" + }, + { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + { + "lat": -39.09631, + "lon": -67.08374, + "name": "Villa Regina" + } + ], + "question": "Which location is the geographic outlier among: Rowville, Moonee Ponds, Blenheim, Wollongong city centre, Villa Regina?", + "ground_truth": { + "answer": "Villa Regina", + "outlier_distance_km": 11419.2, + "second_furthest_km": 5380.1, + "clarity_ratio": 2.12, + "median_distance_km": 3695.1, + "distances_to_centroid": { + "Rowville": 3102.6, + "Moonee Ponds": 3079.2, + "Blenheim": 5380.1, + "Wollongong city centre": 3695.1, + "Villa Regina": 11419.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rowville: (-37.93°, 145.23°)", + " Moonee Ponds: (-37.77°, 144.92°)", + " Blenheim: (-41.52°, 173.95°)", + " Wollongong city centre: (-34.43°, 150.89°)", + " Villa Regina: (-39.10°, -67.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Villa Regina: 11419.2 km from centroid", + " Blenheim: 5380.1 km from centroid", + " Wollongong city centre: 3695.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Villa Regina", + "FINAL ANSWER: Villa Regina" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.09417, + "lon": -42.83667, + "name": "Timon" + }, + { + "lat": -13.44083, + "lon": -49.14861, + "name": "Porangatu" + }, + { + "lat": -28.97111, + "lon": -51.06806, + "name": "São Marcos" + }, + { + "lat": -34.65142, + "lon": -58.64074, + "name": "Castelar" + }, + { + "lat": 42.86563, + "lon": -73.77095, + "name": "Clifton Park" + } + ], + "question": "Which location is the geographic outlier among: Timon, Porangatu, São Marcos, Castelar, Clifton Park?", + "ground_truth": { + "answer": "Clifton Park", + "outlier_distance_km": 5949.0, + "second_furthest_km": 3001.2, + "clarity_ratio": 1.98, + "median_distance_km": 2385.1, + "distances_to_centroid": { + "Timon": 1388.4, + "Porangatu": 898.3, + "São Marcos": 2385.1, + "Castelar": 3001.2, + "Clifton Park": 5949.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Timon: (-5.09°, -42.84°)", + " Porangatu: (-13.44°, -49.15°)", + " São Marcos: (-28.97°, -51.07°)", + " Castelar: (-34.65°, -58.64°)", + " Clifton Park: (42.87°, -73.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Clifton Park: 5949.0 km from centroid", + " Castelar: 3001.2 km from centroid", + " São Marcos: 2385.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Clifton Park", + "FINAL ANSWER: Clifton Park" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.71721, + "lon": -79.40604, + "name": "Lawrence Park South" + }, + { + "lat": 15.76889, + "lon": -96.135, + "name": "Crucecita" + }, + { + "lat": 40.00989, + "lon": -75.16387, + "name": "Nicetown-Tioga" + }, + { + "lat": 34.86414, + "lon": -118.16341, + "name": "Rosamond" + }, + { + "lat": -27.36541, + "lon": 29.88175, + "name": "Volksrust" + } + ], + "question": "Which location is the geographic outlier among: Lawrence Park South, Crucecita, Nicetown-Tioga, Rosamond, Volksrust?", + "ground_truth": { + "answer": "Volksrust", + "outlier_distance_km": 11803.7, + "second_furthest_km": 5104.2, + "clarity_ratio": 2.31, + "median_distance_km": 3046.9, + "distances_to_centroid": { + "Lawrence Park South": 2703.3, + "Crucecita": 3046.9, + "Nicetown-Tioga": 2183.9, + "Rosamond": 5104.2, + "Volksrust": 11803.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lawrence Park South: (43.72°, -79.41°)", + " Crucecita: (15.77°, -96.14°)", + " Nicetown-Tioga: (40.01°, -75.16°)", + " Rosamond: (34.86°, -118.16°)", + " Volksrust: (-27.37°, 29.88°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Volksrust: 11803.7 km from centroid", + " Rosamond: 5104.2 km from centroid", + " Crucecita: 3046.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Volksrust", + "FINAL ANSWER: Volksrust" + ] + }, + { + "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": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + { + "lat": 38.77144, + "lon": -90.37095, + "name": "Hazelwood" + } + ], + "question": "Which location is the geographic outlier among: Banora Point, Hobart, Ashburton, Auburn, Hazelwood?", + "ground_truth": { + "answer": "Hazelwood", + "outlier_distance_km": 17546.5, + "second_furthest_km": 6362.7, + "clarity_ratio": 2.76, + "median_distance_km": 4741.9, + "distances_to_centroid": { + "Banora Point": 4741.9, + "Hobart": 4405.7, + "Ashburton": 6362.7, + "Auburn": 4516.5, + "Hazelwood": 17546.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banora Point: (-28.21°, 153.54°)", + " Hobart: (-42.88°, 147.33°)", + " Ashburton: (-43.90°, 171.73°)", + " Auburn: (-33.85°, 151.03°)", + " Hazelwood: (38.77°, -90.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hazelwood: 17546.5 km from centroid", + " Ashburton: 6362.7 km from centroid", + " Banora Point: 4741.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hazelwood", + "FINAL ANSWER: Hazelwood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -8.45806, + "lon": -35.94472, + "name": "Agrestina" + }, + { + "lat": -5.1875, + "lon": -37.34417, + "name": "Mossoró" + }, + { + "lat": -18.57889, + "lon": -46.51806, + "name": "Patos de Minas" + }, + { + "lat": -12.13588, + "lon": -77.00742, + "name": "Santiago de Surco" + }, + { + "lat": 53.61122, + "lon": -0.96308, + "name": "Thorne" + } + ], + "question": "Which location is the geographic outlier among: Agrestina, Mossoró, Patos de Minas, Santiago de Surco, Thorne?", + "ground_truth": { + "answer": "Thorne", + "outlier_distance_km": 6749.1, + "second_furthest_km": 4419.1, + "clarity_ratio": 1.53, + "median_distance_km": 2395.9, + "distances_to_centroid": { + "Agrestina": 1214.1, + "Mossoró": 820.2, + "Patos de Minas": 2395.9, + "Santiago de Surco": 4419.1, + "Thorne": 6749.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Agrestina: (-8.46°, -35.94°)", + " Mossoró: (-5.19°, -37.34°)", + " Patos de Minas: (-18.58°, -46.52°)", + " Santiago de Surco: (-12.14°, -77.01°)", + " Thorne: (53.61°, -0.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Thorne: 6749.1 km from centroid", + " Santiago de Surco: 4419.1 km from centroid", + " Patos de Minas: 2395.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Thorne", + "FINAL ANSWER: Thorne" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + { + "lat": -41.13333, + "lon": 174.85, + "name": "Porirua" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + }, + { + "lat": 37.30216, + "lon": -120.48297, + "name": "Merced" + } + ], + "question": "Which location is the geographic outlier among: Shepparton, Porirua, Ashburton, Bundoora, Merced?", + "ground_truth": { + "answer": "Merced", + "outlier_distance_km": 15637.0, + "second_furthest_km": 6755.2, + "clarity_ratio": 2.31, + "median_distance_km": 6467.8, + "distances_to_centroid": { + "Shepparton": 4215.7, + "Porirua": 6755.2, + "Ashburton": 6467.8, + "Bundoora": 4204.7, + "Merced": 15637.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shepparton: (-36.38°, 145.40°)", + " Porirua: (-41.13°, 174.85°)", + " Ashburton: (-43.90°, 171.73°)", + " Bundoora: (-37.70°, 145.06°)", + " Merced: (37.30°, -120.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Merced: 15637.0 km from centroid", + " Porirua: 6755.2 km from centroid", + " Ashburton: 6467.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Merced", + "FINAL ANSWER: Merced" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 57.88227, + "lon": 54.71827, + "name": "Ochër" + }, + { + "lat": 43.32059, + "lon": 45.04903, + "name": "Sunzha" + }, + { + "lat": 47.73512, + "lon": -3.42952, + "name": "Ploemeur" + }, + { + "lat": 37.35813, + "lon": -6.03731, + "name": "San Juan de Aznalfarache" + }, + { + "lat": -9.58833, + "lon": -67.5325, + "name": "Porto Acre" + } + ], + "question": "Which location is the geographic outlier among: Ochër, Sunzha, Ploemeur, San Juan de Aznalfarache, Porto Acre?", + "ground_truth": { + "answer": "Porto Acre", + "outlier_distance_km": 9041.5, + "second_furthest_km": 4431.0, + "clarity_ratio": 2.04, + "median_distance_km": 3556.9, + "distances_to_centroid": { + "Ochër": 4431.0, + "Sunzha": 3556.9, + "Ploemeur": 1527.9, + "San Juan de Aznalfarache": 974.1, + "Porto Acre": 9041.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ochër: (57.88°, 54.72°)", + " Sunzha: (43.32°, 45.05°)", + " Ploemeur: (47.74°, -3.43°)", + " San Juan de Aznalfarache: (37.36°, -6.04°)", + " Porto Acre: (-9.59°, -67.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Porto Acre: 9041.5 km from centroid", + " Ochër: 4431.0 km from centroid", + " Sunzha: 3556.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Porto Acre", + "FINAL ANSWER: Porto Acre" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.52467, + "lon": -111.86382, + "name": "Draper" + }, + { + "lat": 42.04114, + "lon": -87.69006, + "name": "Evanston" + }, + { + "lat": 42.30008, + "lon": -83.01654, + "name": "Windsor" + }, + { + "lat": 42.88645, + "lon": -78.87837, + "name": "Buffalo" + }, + { + "lat": -24.00583, + "lon": -46.40278, + "name": "Praia Grande" + } + ], + "question": "Which location is the geographic outlier among: Draper, Evanston, Windsor, Buffalo, Praia Grande?", + "ground_truth": { + "answer": "Praia Grande", + "outlier_distance_km": 6969.2, + "second_furthest_km": 3044.8, + "clarity_ratio": 2.29, + "median_distance_km": 1590.4, + "distances_to_centroid": { + "Draper": 3044.8, + "Evanston": 1577.5, + "Windsor": 1512.4, + "Buffalo": 1590.4, + "Praia Grande": 6969.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Draper: (40.52°, -111.86°)", + " Evanston: (42.04°, -87.69°)", + " Windsor: (42.30°, -83.02°)", + " Buffalo: (42.89°, -78.88°)", + " Praia Grande: (-24.01°, -46.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Praia Grande: 6969.2 km from centroid", + " Draper: 3044.8 km from centroid", + " Buffalo: 1590.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Praia Grande", + "FINAL ANSWER: Praia Grande" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -13.18222, + "lon": -39.425, + "name": "Laje" + }, + { + "lat": -12.97563, + "lon": -38.49096, + "name": "Salvador" + }, + { + "lat": -5.26667, + "lon": -80.68333, + "name": "Catacaos" + }, + { + "lat": -25.44472, + "lon": -49.1925, + "name": "Pinhais" + }, + { + "lat": 12.15449, + "lon": 77.11051, + "name": "Kollegāl" + } + ], + "question": "Which location is the geographic outlier among: Laje, Salvador, Catacaos, Pinhais, Kollegāl?", + "ground_truth": { + "answer": "Kollegāl", + "outlier_distance_km": 11643.8, + "second_furthest_km": 6027.7, + "clarity_ratio": 1.93, + "median_distance_km": 3050.3, + "distances_to_centroid": { + "Laje": 1524.4, + "Salvador": 1420.9, + "Catacaos": 6027.7, + "Pinhais": 3050.3, + "Kollegāl": 11643.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Laje: (-13.18°, -39.42°)", + " Salvador: (-12.98°, -38.49°)", + " Catacaos: (-5.27°, -80.68°)", + " Pinhais: (-25.44°, -49.19°)", + " Kollegāl: (12.15°, 77.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kollegāl: 11643.8 km from centroid", + " Catacaos: 6027.7 km from centroid", + " Pinhais: 3050.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kollegāl", + "FINAL ANSWER: Kollegāl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + { + "lat": -38.03333, + "lon": 145.35, + "name": "Berwick" + }, + { + "lat": -36.90694, + "lon": 174.68704, + "name": "New Lynn" + }, + { + "lat": 34.07001, + "lon": 133.00023, + "name": "Imabari" + } + ], + "question": "Which location is the geographic outlier among: Glen Waverley, Logan City, Berwick, New Lynn, Imabari?", + "ground_truth": { + "answer": "Imabari", + "outlier_distance_km": 6419.9, + "second_furthest_km": 2926.5, + "clarity_ratio": 2.19, + "median_distance_km": 1921.8, + "distances_to_centroid": { + "Glen Waverley": 1909.7, + "Logan City": 763.7, + "Berwick": 1921.8, + "New Lynn": 2926.5, + "Imabari": 6419.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glen Waverley: (-37.88°, 145.16°)", + " Logan City: (-27.64°, 153.11°)", + " Berwick: (-38.03°, 145.35°)", + " New Lynn: (-36.91°, 174.69°)", + " Imabari: (34.07°, 133.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Imabari: 6419.9 km from centroid", + " New Lynn: 2926.5 km from centroid", + " Berwick: 1921.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Imabari", + "FINAL ANSWER: Imabari" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.83362, + "lon": 1.24759, + "name": "Limoges" + }, + { + "lat": 52.37193, + "lon": 9.97919, + "name": "Lehrte" + }, + { + "lat": 38.50754, + "lon": -0.23346, + "name": "Villajoyosa" + }, + { + "lat": 51.57515, + "lon": 0.18582, + "name": "Romford" + }, + { + "lat": 9.23478, + "lon": 40.75593, + "name": "Mī’ēso" + } + ], + "question": "Which location is the geographic outlier among: Limoges, Lehrte, Villajoyosa, Romford, Mī’ēso?", + "ground_truth": { + "answer": "Mī’ēso", + "outlier_distance_km": 4515.6, + "second_furthest_km": 1556.3, + "clarity_ratio": 2.9, + "median_distance_km": 1431.1, + "distances_to_centroid": { + "Limoges": 1025.2, + "Lehrte": 1431.1, + "Villajoyosa": 923.8, + "Romford": 1556.3, + "Mī’ēso": 4515.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Limoges: (45.83°, 1.25°)", + " Lehrte: (52.37°, 9.98°)", + " Villajoyosa: (38.51°, -0.23°)", + " Romford: (51.58°, 0.19°)", + " Mī’ēso: (9.23°, 40.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mī’ēso: 4515.6 km from centroid", + " Romford: 1556.3 km from centroid", + " Lehrte: 1431.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mī’ēso", + "FINAL ANSWER: Mī’ēso" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + { + "lat": -32.22099, + "lon": 116.009, + "name": "Byford" + }, + { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + { + "lat": -27.10876, + "lon": 152.94907, + "name": "Morayfield" + }, + { + "lat": 50.32797, + "lon": 7.22277, + "name": "Mayen" + } + ], + "question": "Which location is the geographic outlier among: Pakenham, Byford, Rochedale South, Morayfield, Mayen?", + "ground_truth": { + "answer": "Mayen", + "outlier_distance_km": 12533.9, + "second_furthest_km": 4177.6, + "clarity_ratio": 3.0, + "median_distance_km": 4150.0, + "distances_to_centroid": { + "Pakenham": 3946.6, + "Byford": 1925.2, + "Rochedale South": 4177.6, + "Morayfield": 4150.0, + "Mayen": 12533.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pakenham: (-38.07°, 145.47°)", + " Byford: (-32.22°, 116.01°)", + " Rochedale South: (-27.60°, 153.12°)", + " Morayfield: (-27.11°, 152.95°)", + " Mayen: (50.33°, 7.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mayen: 12533.9 km from centroid", + " Rochedale South: 4177.6 km from centroid", + " Morayfield: 4150.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mayen", + "FINAL ANSWER: Mayen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -11.66417, + "lon": -39.0075, + "name": "Serrinha" + }, + { + "lat": -23.21003, + "lon": -64.09965, + "name": "Embarcación" + }, + { + "lat": -21.52944, + "lon": -46.64389, + "name": "Caconde" + }, + { + "lat": -4.39143, + "lon": -59.58864, + "name": "Borba" + }, + { + "lat": 47.79292, + "lon": 1.06556, + "name": "Vendôme" + } + ], + "question": "Which location is the geographic outlier among: Serrinha, Embarcación, Caconde, Borba, Vendôme?", + "ground_truth": { + "answer": "Vendôme", + "outlier_distance_km": 6966.2, + "second_furthest_km": 3330.4, + "clarity_ratio": 2.09, + "median_distance_km": 2172.9, + "distances_to_centroid": { + "Serrinha": 1049.2, + "Embarcación": 3330.4, + "Caconde": 2172.9, + "Borba": 2000.3, + "Vendôme": 6966.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Serrinha: (-11.66°, -39.01°)", + " Embarcación: (-23.21°, -64.10°)", + " Caconde: (-21.53°, -46.64°)", + " Borba: (-4.39°, -59.59°)", + " Vendôme: (47.79°, 1.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Vendôme: 6966.2 km from centroid", + " Embarcación: 3330.4 km from centroid", + " Caconde: 2172.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Vendôme", + "FINAL ANSWER: Vendôme" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.07431, + "lon": 105.73974, + "name": "Bình Thủy" + }, + { + "lat": 8.28486, + "lon": 77.27551, + "name": "Kāttatturai" + }, + { + "lat": 20.66612, + "lon": 76.77386, + "name": "Bālāpur" + }, + { + "lat": 38.16143, + "lon": 106.58502, + "name": "Ningdong" + }, + { + "lat": -8.87556, + "lon": -36.36667, + "name": "São João" + } + ], + "question": "Which location is the geographic outlier among: Bình Thủy, Kāttatturai, Bālāpur, Ningdong, São João?", + "ground_truth": { + "answer": "São João", + "outlier_distance_km": 11565.3, + "second_furthest_km": 4829.5, + "clarity_ratio": 2.39, + "median_distance_km": 4338.0, + "distances_to_centroid": { + "Bình Thủy": 4338.0, + "Kāttatturai": 1367.7, + "Bālāpur": 1383.4, + "Ningdong": 4829.5, + "São João": 11565.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bình Thủy: (10.07°, 105.74°)", + " Kāttatturai: (8.28°, 77.28°)", + " Bālāpur: (20.67°, 76.77°)", + " Ningdong: (38.16°, 106.59°)", + " São João: (-8.88°, -36.37°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São João: 11565.3 km from centroid", + " Ningdong: 4829.5 km from centroid", + " Bình Thủy: 4338.0 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": -8.89778, + "lon": -35.14778, + "name": "São José da Coroa Grande" + }, + { + "lat": -26.02667, + "lon": -48.855, + "name": "Garuva" + }, + { + "lat": -6.64056, + "lon": -79.38917, + "name": "Chongoyape" + }, + { + "lat": -10.66722, + "lon": -39.49917, + "name": "Cansanção" + }, + { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + } + ], + "question": "Which location is the geographic outlier among: São José da Coroa Grande, Garuva, Chongoyape, Cansanção, Shepparton?", + "ground_truth": { + "answer": "Shepparton", + "outlier_distance_km": 13527.6, + "second_furthest_km": 7446.1, + "clarity_ratio": 1.82, + "median_distance_km": 3949.3, + "distances_to_centroid": { + "São José da Coroa Grande": 2737.0, + "Garuva": 3949.3, + "Chongoyape": 7446.1, + "Cansanção": 3114.8, + "Shepparton": 13527.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São José da Coroa Grande: (-8.90°, -35.15°)", + " Garuva: (-26.03°, -48.85°)", + " Chongoyape: (-6.64°, -79.39°)", + " Cansanção: (-10.67°, -39.50°)", + " Shepparton: (-36.38°, 145.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shepparton: 13527.6 km from centroid", + " Chongoyape: 7446.1 km from centroid", + " Garuva: 3949.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shepparton", + "FINAL ANSWER: Shepparton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.52314, + "lon": 151.31325, + "name": "Umina Beach" + }, + { + "lat": -37.75819, + "lon": 145.00583, + "name": "Thornbury" + }, + { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + { + "lat": -31.9652, + "lon": 141.4512, + "name": "Broken Hill" + }, + { + "lat": -1.06343, + "lon": 34.47313, + "name": "Migori" + } + ], + "question": "Which location is the geographic outlier among: Umina Beach, Thornbury, Elwood, Broken Hill, Migori?", + "ground_truth": { + "answer": "Migori", + "outlier_distance_km": 9850.7, + "second_furthest_km": 2707.5, + "clarity_ratio": 3.64, + "median_distance_km": 2255.4, + "distances_to_centroid": { + "Umina Beach": 2707.5, + "Thornbury": 2252.4, + "Elwood": 2255.4, + "Broken Hill": 1772.0, + "Migori": 9850.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Umina Beach: (-33.52°, 151.31°)", + " Thornbury: (-37.76°, 145.01°)", + " Elwood: (-37.88°, 144.98°)", + " Broken Hill: (-31.97°, 141.45°)", + " Migori: (-1.06°, 34.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Migori: 9850.7 km from centroid", + " Umina Beach: 2707.5 km from centroid", + " Elwood: 2255.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Migori", + "FINAL ANSWER: Migori" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.30556, + "lon": -49.05528, + "name": "Campina Grande do Sul" + }, + { + "lat": -0.71667, + "lon": -48.52333, + "name": "Soure" + }, + { + "lat": 4.53656, + "lon": -75.67263, + "name": "Armenia" + }, + { + "lat": -11.85889, + "lon": -40.4725, + "name": "Mundo Novo" + }, + { + "lat": 27.83598, + "lon": 74.31776, + "name": "Bīdāsar" + } + ], + "question": "Which location is the geographic outlier among: Campina Grande do Sul, Soure, Armenia, Mundo Novo, Bīdāsar?", + "ground_truth": { + "answer": "Bīdāsar", + "outlier_distance_km": 11263.1, + "second_furthest_km": 5346.3, + "clarity_ratio": 2.11, + "median_distance_km": 3521.7, + "distances_to_centroid": { + "Campina Grande do Sul": 3521.7, + "Soure": 2295.4, + "Armenia": 5346.3, + "Mundo Novo": 1833.0, + "Bīdāsar": 11263.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Campina Grande do Sul: (-25.31°, -49.06°)", + " Soure: (-0.72°, -48.52°)", + " Armenia: (4.54°, -75.67°)", + " Mundo Novo: (-11.86°, -40.47°)", + " Bīdāsar: (27.84°, 74.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bīdāsar: 11263.1 km from centroid", + " Armenia: 5346.3 km from centroid", + " Campina Grande do Sul: 3521.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bīdāsar", + "FINAL ANSWER: Bīdāsar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.48, + "lon": 102.41639, + "name": "Nianbo" + }, + { + "lat": 35.54651, + "lon": 139.51723, + "name": "Aobadai" + }, + { + "lat": 13.59072, + "lon": 100.10748, + "name": "Ban Phaeo" + }, + { + "lat": 15.44903, + "lon": 120.79627, + "name": "Zaragoza" + }, + { + "lat": 43.1875, + "lon": 44.90194, + "name": "Surkhakhi" + } + ], + "question": "Which location is the geographic outlier among: Nianbo, Aobadai, Ban Phaeo, Zaragoza, Surkhakhi?", + "ground_truth": { + "answer": "Surkhakhi", + "outlier_distance_km": 5231.7, + "second_furthest_km": 3626.3, + "clarity_ratio": 1.44, + "median_distance_km": 2473.5, + "distances_to_centroid": { + "Nianbo": 852.2, + "Aobadai": 3626.3, + "Ban Phaeo": 1703.3, + "Zaragoza": 2473.5, + "Surkhakhi": 5231.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nianbo: (36.48°, 102.42°)", + " Aobadai: (35.55°, 139.52°)", + " Ban Phaeo: (13.59°, 100.11°)", + " Zaragoza: (15.45°, 120.80°)", + " Surkhakhi: (43.19°, 44.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Surkhakhi: 5231.7 km from centroid", + " Aobadai: 3626.3 km from centroid", + " Zaragoza: 2473.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Surkhakhi", + "FINAL ANSWER: Surkhakhi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.26417, + "lon": -47.29917, + "name": "Itu" + }, + { + "lat": -23.56786, + "lon": -46.54599, + "name": "Vila Formosa" + }, + { + "lat": -22.89889, + "lon": -42.46985, + "name": "Saquarema" + }, + { + "lat": -27.27611, + "lon": -48.84944, + "name": "São João Batista" + }, + { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + } + ], + "question": "Which location is the geographic outlier among: Itu, Vila Formosa, Saquarema, São João Batista, Casula?", + "ground_truth": { + "answer": "Casula", + "outlier_distance_km": 12927.3, + "second_furthest_km": 4152.5, + "clarity_ratio": 3.11, + "median_distance_km": 4081.8, + "distances_to_centroid": { + "Itu": 4081.8, + "Vila Formosa": 3999.4, + "Saquarema": 3610.0, + "São João Batista": 4152.5, + "Casula": 12927.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Itu: (-23.26°, -47.30°)", + " Vila Formosa: (-23.57°, -46.55°)", + " Saquarema: (-22.90°, -42.47°)", + " São João Batista: (-27.28°, -48.85°)", + " Casula: (-33.95°, 150.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Casula: 12927.3 km from centroid", + " São João Batista: 4152.5 km from centroid", + " Itu: 4081.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Casula", + "FINAL ANSWER: Casula" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.01695, + "lon": -94.28161, + "name": "Blue Springs" + }, + { + "lat": 40.8501, + "lon": -73.93541, + "name": "Washington Heights" + }, + { + "lat": 19.54005, + "lon": -99.19538, + "name": "Tlalnepantla" + }, + { + "lat": 28.19013, + "lon": -105.47012, + "name": "Ciudad Delicias" + }, + { + "lat": 22.8774, + "lon": 88.75479, + "name": "Gobārdānga" + } + ], + "question": "Which location is the geographic outlier among: Blue Springs, Washington Heights, Tlalnepantla, Ciudad Delicias, Gobārdānga?", + "ground_truth": { + "answer": "Gobārdānga", + "outlier_distance_km": 13071.8, + "second_furthest_km": 4693.1, + "clarity_ratio": 2.79, + "median_distance_km": 4407.3, + "distances_to_centroid": { + "Blue Springs": 3543.1, + "Washington Heights": 1951.2, + "Tlalnepantla": 4407.3, + "Ciudad Delicias": 4693.1, + "Gobārdānga": 13071.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blue Springs: (39.02°, -94.28°)", + " Washington Heights: (40.85°, -73.94°)", + " Tlalnepantla: (19.54°, -99.20°)", + " Ciudad Delicias: (28.19°, -105.47°)", + " Gobārdānga: (22.88°, 88.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gobārdānga: 13071.8 km from centroid", + " Ciudad Delicias: 4693.1 km from centroid", + " Tlalnepantla: 4407.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gobārdānga", + "FINAL ANSWER: Gobārdānga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.4, + "lon": -0.4, + "name": "Catarroja" + }, + { + "lat": 40.36709, + "lon": -3.74608, + "name": "Buenavista" + }, + { + "lat": 49.13645, + "lon": 8.91229, + "name": "Eppingen" + }, + { + "lat": 52.25221, + "lon": 21.26902, + "name": "Sulejówek" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + } + ], + "question": "Which location is the geographic outlier among: Catarroja, Buenavista, Eppingen, Sulejówek, Wheelers Hill?", + "ground_truth": { + "answer": "Wheelers Hill", + "outlier_distance_km": 13657.0, + "second_furthest_km": 3683.1, + "clarity_ratio": 3.71, + "median_distance_km": 3383.9, + "distances_to_centroid": { + "Catarroja": 3383.9, + "Buenavista": 3683.1, + "Eppingen": 3132.3, + "Sulejówek": 2834.7, + "Wheelers Hill": 13657.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Catarroja: (39.40°, -0.40°)", + " Buenavista: (40.37°, -3.75°)", + " Eppingen: (49.14°, 8.91°)", + " Sulejówek: (52.25°, 21.27°)", + " Wheelers Hill: (-37.90°, 145.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wheelers Hill: 13657.0 km from centroid", + " Buenavista: 3683.1 km from centroid", + " Catarroja: 3383.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wheelers Hill", + "FINAL ANSWER: Wheelers Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.4668, + "lon": 8.99016, + "name": "Eberbach" + }, + { + "lat": 50.26526, + "lon": -5.05436, + "name": "Truro" + }, + { + "lat": 42.795, + "lon": -8.548, + "name": "Teo" + }, + { + "lat": 51.14648, + "lon": 0.87376, + "name": "Ashford" + }, + { + "lat": 50.03928, + "lon": -110.67661, + "name": "Medicine Hat" + } + ], + "question": "Which location is the geographic outlier among: Eberbach, Truro, Teo, Ashford, Medicine Hat?", + "ground_truth": { + "answer": "Medicine Hat", + "outlier_distance_km": 5967.2, + "second_furthest_km": 2304.3, + "clarity_ratio": 2.59, + "median_distance_km": 1713.1, + "distances_to_centroid": { + "Eberbach": 2304.3, + "Truro": 1295.3, + "Teo": 1290.6, + "Ashford": 1713.1, + "Medicine Hat": 5967.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Eberbach: (49.47°, 8.99°)", + " Truro: (50.27°, -5.05°)", + " Teo: (42.80°, -8.55°)", + " Ashford: (51.15°, 0.87°)", + " Medicine Hat: (50.04°, -110.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Medicine Hat: 5967.2 km from centroid", + " Eberbach: 2304.3 km from centroid", + " Ashford: 1713.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Medicine Hat", + "FINAL ANSWER: Medicine Hat" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": -40.63333, + "lon": 175.275, + "name": "Levin" + }, + { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + { + "lat": -38.65333, + "lon": 178.00417, + "name": "Gisborne" + }, + { + "lat": -25.668, + "lon": 28.73, + "name": "Ekangala" + } + ], + "question": "Which location is the geographic outlier among: Footscray, Levin, Blenheim, Gisborne, Ekangala?", + "ground_truth": { + "answer": "Ekangala", + "outlier_distance_km": 10032.1, + "second_furthest_km": 3308.5, + "clarity_ratio": 3.03, + "median_distance_km": 3052.7, + "distances_to_centroid": { + "Footscray": 431.0, + "Levin": 3052.7, + "Blenheim": 2938.0, + "Gisborne": 3308.5, + "Ekangala": 10032.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Footscray: (-37.80°, 144.90°)", + " Levin: (-40.63°, 175.28°)", + " Blenheim: (-41.52°, 173.95°)", + " Gisborne: (-38.65°, 178.00°)", + " Ekangala: (-25.67°, 28.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ekangala: 10032.1 km from centroid", + " Gisborne: 3308.5 km from centroid", + " Levin: 3052.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ekangala", + "FINAL ANSWER: Ekangala" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.814, + "lon": 144.96332, + "name": "Melbourne" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + { + "lat": -31.36528, + "lon": -51.97833, + "name": "São Lourenço do Sul" + } + ], + "question": "Which location is the geographic outlier among: Melbourne, Sunshine West, Rockhampton, Eight Mile Plains, São Lourenço do Sul?", + "ground_truth": { + "answer": "São Lourenço do Sul", + "outlier_distance_km": 12712.9, + "second_furthest_km": 4326.9, + "clarity_ratio": 2.94, + "median_distance_km": 4237.2, + "distances_to_centroid": { + "Melbourne": 3401.5, + "Sunshine West": 3388.5, + "Rockhampton": 4237.2, + "Eight Mile Plains": 4326.9, + "São Lourenço do Sul": 12712.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Melbourne: (-37.81°, 144.96°)", + " Sunshine West: (-37.79°, 144.82°)", + " Rockhampton: (-23.38°, 150.51°)", + " Eight Mile Plains: (-27.58°, 153.10°)", + " São Lourenço do Sul: (-31.37°, -51.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São Lourenço do Sul: 12712.9 km from centroid", + " Eight Mile Plains: 4326.9 km from centroid", + " Rockhampton: 4237.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São Lourenço do Sul", + "FINAL ANSWER: São Lourenço do Sul" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.75732, + "lon": -122.24401, + "name": "Kenmore" + }, + { + "lat": 40.59122, + "lon": -73.94458, + "name": "Sheepshead Bay" + }, + { + "lat": 49.28124, + "lon": -122.82457, + "name": "Port Moody" + }, + { + "lat": 26.18924, + "lon": -98.15529, + "name": "San Juan" + }, + { + "lat": -36.88041, + "lon": 174.79819, + "name": "Remuera" + } + ], + "question": "Which location is the geographic outlier among: Kenmore, Sheepshead Bay, Port Moody, San Juan, Remuera?", + "ground_truth": { + "answer": "Remuera", + "outlier_distance_km": 15742.9, + "second_furthest_km": 6789.3, + "clarity_ratio": 2.32, + "median_distance_km": 6765.8, + "distances_to_centroid": { + "Kenmore": 6765.8, + "Sheepshead Bay": 2897.9, + "Port Moody": 6789.3, + "San Juan": 4943.5, + "Remuera": 15742.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kenmore: (47.76°, -122.24°)", + " Sheepshead Bay: (40.59°, -73.94°)", + " Port Moody: (49.28°, -122.82°)", + " San Juan: (26.19°, -98.16°)", + " Remuera: (-36.88°, 174.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Remuera: 15742.9 km from centroid", + " Port Moody: 6789.3 km from centroid", + " Kenmore: 6765.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Remuera", + "FINAL ANSWER: Remuera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.88333, + "lon": 37.58333, + "name": "Altuf’yevskiy" + }, + { + "lat": 40.70211, + "lon": 14.48685, + "name": "Castellammare di Stabia" + }, + { + "lat": 59.83528, + "lon": 30.14667, + "name": "Sosnovaya Polyana" + }, + { + "lat": 45.4346, + "lon": 12.12942, + "name": "Mira Taglio" + }, + { + "lat": 29.38385, + "lon": -94.9027, + "name": "Texas City" + } + ], + "question": "Which location is the geographic outlier among: Altuf’yevskiy, Castellammare di Stabia, Sosnovaya Polyana, Mira Taglio, Texas City?", + "ground_truth": { + "answer": "Texas City", + "outlier_distance_km": 8039.0, + "second_furthest_km": 2800.5, + "clarity_ratio": 2.87, + "median_distance_km": 2488.7, + "distances_to_centroid": { + "Altuf’yevskiy": 2800.5, + "Castellammare di Stabia": 1326.7, + "Sosnovaya Polyana": 2488.7, + "Mira Taglio": 951.6, + "Texas City": 8039.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Altuf’yevskiy: (55.88°, 37.58°)", + " Castellammare di Stabia: (40.70°, 14.49°)", + " Sosnovaya Polyana: (59.84°, 30.15°)", + " Mira Taglio: (45.43°, 12.13°)", + " Texas City: (29.38°, -94.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Texas City: 8039.0 km from centroid", + " Altuf’yevskiy: 2800.5 km from centroid", + " Sosnovaya Polyana: 2488.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Texas City", + "FINAL ANSWER: Texas City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + { + "lat": -33.9681, + "lon": 151.13564, + "name": "Kogarah" + }, + { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + { + "lat": 43.60426, + "lon": 1.44367, + "name": "Toulouse" + } + ], + "question": "Which location is the geographic outlier among: Mackay, Highton, Kogarah, Mildura, Toulouse?", + "ground_truth": { + "answer": "Toulouse", + "outlier_distance_km": 13381.3, + "second_furthest_km": 3843.6, + "clarity_ratio": 3.48, + "median_distance_km": 3522.5, + "distances_to_centroid": { + "Mackay": 3344.8, + "Highton": 3522.5, + "Kogarah": 3843.6, + "Mildura": 3116.0, + "Toulouse": 13381.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mackay: (-21.15°, 149.17°)", + " Highton: (-38.17°, 144.31°)", + " Kogarah: (-33.97°, 151.14°)", + " Mildura: (-34.19°, 142.16°)", + " Toulouse: (43.60°, 1.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Toulouse: 13381.3 km from centroid", + " Kogarah: 3843.6 km from centroid", + " Highton: 3522.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Toulouse", + "FINAL ANSWER: Toulouse" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.78828, + "lon": 145.12373, + "name": "Doncaster" + }, + { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + { + "lat": -32.081, + "lon": 116.0054, + "name": "Gosnells" + }, + { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + { + "lat": 33.56394, + "lon": 114.04272, + "name": "Luohe" + } + ], + "question": "Which location is the geographic outlier among: Doncaster, Wyndham Vale, Gosnells, Carlton, Luohe?", + "ground_truth": { + "answer": "Luohe", + "outlier_distance_km": 6537.4, + "second_furthest_km": 2069.1, + "clarity_ratio": 3.16, + "median_distance_km": 2061.8, + "distances_to_centroid": { + "Doncaster": 2069.1, + "Wyndham Vale": 2051.9, + "Gosnells": 1987.4, + "Carlton": 2061.8, + "Luohe": 6537.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doncaster: (-37.79°, 145.12°)", + " Wyndham Vale: (-37.89°, 144.62°)", + " Gosnells: (-32.08°, 116.01°)", + " Carlton: (-37.80°, 144.97°)", + " Luohe: (33.56°, 114.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Luohe: 6537.4 km from centroid", + " Doncaster: 2069.1 km from centroid", + " Carlton: 2061.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Luohe", + "FINAL ANSWER: Luohe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 30.41552, + "lon": -107.91166, + "name": "Nuevo Casas Grandes" + }, + { + "lat": 33.03145, + "lon": -111.38734, + "name": "Florence" + }, + { + "lat": 25.66705, + "lon": -80.30811, + "name": "Pinecrest" + }, + { + "lat": 40.06928, + "lon": -75.16629, + "name": "West Oak Lane" + }, + { + "lat": 24.05979, + "lon": 77.40858, + "name": "Leteri" + } + ], + "question": "Which location is the geographic outlier among: Nuevo Casas Grandes, Florence, Pinecrest, West Oak Lane, Leteri?", + "ground_truth": { + "answer": "Leteri", + "outlier_distance_km": 12392.0, + "second_furthest_km": 4861.0, + "clarity_ratio": 2.55, + "median_distance_km": 4601.8, + "distances_to_centroid": { + "Nuevo Casas Grandes": 4601.8, + "Florence": 4861.0, + "Pinecrest": 2112.8, + "West Oak Lane": 1762.6, + "Leteri": 12392.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nuevo Casas Grandes: (30.42°, -107.91°)", + " Florence: (33.03°, -111.39°)", + " Pinecrest: (25.67°, -80.31°)", + " West Oak Lane: (40.07°, -75.17°)", + " Leteri: (24.06°, 77.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Leteri: 12392.0 km from centroid", + " Florence: 4861.0 km from centroid", + " Nuevo Casas Grandes: 4601.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Leteri", + "FINAL ANSWER: Leteri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.14501, + "lon": 114.56556, + "name": "Zhengding" + }, + { + "lat": 30.47798, + "lon": 77.12804, + "name": "Naraingarh" + }, + { + "lat": 24.28859, + "lon": 116.11768, + "name": "Meizhou" + }, + { + "lat": -6.9, + "lon": 109.08333, + "name": "Dukuhturi" + }, + { + "lat": -23.57595, + "lon": -46.46298, + "name": "Parque Do Carmo" + } + ], + "question": "Which location is the geographic outlier among: Zhengding, Naraingarh, Meizhou, Dukuhturi, Parque Do Carmo?", + "ground_truth": { + "answer": "Parque Do Carmo", + "outlier_distance_km": 13651.8, + "second_furthest_km": 4908.5, + "clarity_ratio": 2.78, + "median_distance_km": 4605.0, + "distances_to_centroid": { + "Zhengding": 4908.5, + "Naraingarh": 2024.8, + "Meizhou": 4605.0, + "Dukuhturi": 4428.0, + "Parque Do Carmo": 13651.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zhengding: (38.15°, 114.57°)", + " Naraingarh: (30.48°, 77.13°)", + " Meizhou: (24.29°, 116.12°)", + " Dukuhturi: (-6.90°, 109.08°)", + " Parque Do Carmo: (-23.58°, -46.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Parque Do Carmo: 13651.8 km from centroid", + " Zhengding: 4908.5 km from centroid", + " Meizhou: 4605.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Parque Do Carmo", + "FINAL ANSWER: Parque Do Carmo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.40583, + "lon": 109.60861, + "name": "Luorong" + }, + { + "lat": 29.61853, + "lon": 77.43908, + "name": "Jalālābad" + }, + { + "lat": 30.08274, + "lon": 106.32376, + "name": "Yunmen" + }, + { + "lat": 21.06532, + "lon": 105.74661, + "name": "Bắc Từ Liêm" + }, + { + "lat": -9.74056, + "lon": -36.50278, + "name": "Limoeiro de Anadia" + } + ], + "question": "Which location is the geographic outlier among: Luorong, Jalālābad, Yunmen, Bắc Từ Liêm, Limoeiro de Anadia?", + "ground_truth": { + "answer": "Limoeiro de Anadia", + "outlier_distance_km": 12346.6, + "second_furthest_km": 3864.2, + "clarity_ratio": 3.2, + "median_distance_km": 3613.4, + "distances_to_centroid": { + "Luorong": 3864.2, + "Jalālābad": 1272.2, + "Yunmen": 3613.4, + "Bắc Từ Liêm": 3470.7, + "Limoeiro de Anadia": 12346.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Luorong: (24.41°, 109.61°)", + " Jalālābad: (29.62°, 77.44°)", + " Yunmen: (30.08°, 106.32°)", + " Bắc Từ Liêm: (21.07°, 105.75°)", + " Limoeiro de Anadia: (-9.74°, -36.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Limoeiro de Anadia: 12346.6 km from centroid", + " Luorong: 3864.2 km from centroid", + " Yunmen: 3613.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Limoeiro de Anadia", + "FINAL ANSWER: Limoeiro de Anadia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.27784, + "lon": -123.12794, + "name": "Downtown" + }, + { + "lat": 43.71359, + "lon": -79.28138, + "name": "Clairlea-Birchmount" + }, + { + "lat": 29.16941, + "lon": -95.43188, + "name": "Angleton" + }, + { + "lat": 42.24087, + "lon": -83.26965, + "name": "Taylor" + }, + { + "lat": 30.04891, + "lon": 76.343, + "name": "Chīka" + } + ], + "question": "Which location is the geographic outlier among: Downtown, Clairlea-Birchmount, Angleton, Taylor, Chīka?", + "ground_truth": { + "answer": "Chīka", + "outlier_distance_km": 11165.4, + "second_furthest_km": 4951.8, + "clarity_ratio": 2.25, + "median_distance_km": 3332.9, + "distances_to_centroid": { + "Downtown": 4951.8, + "Clairlea-Birchmount": 1618.1, + "Angleton": 3332.9, + "Taylor": 1915.7, + "Chīka": 11165.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Downtown: (49.28°, -123.13°)", + " Clairlea-Birchmount: (43.71°, -79.28°)", + " Angleton: (29.17°, -95.43°)", + " Taylor: (42.24°, -83.27°)", + " Chīka: (30.05°, 76.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Chīka: 11165.4 km from centroid", + " Downtown: 4951.8 km from centroid", + " Angleton: 3332.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Chīka", + "FINAL ANSWER: Chīka" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -29.02889, + "lon": -51.18167, + "name": "Flores da Cunha" + }, + { + "lat": -34.43859, + "lon": -71.07751, + "name": "San Vicente de Tagua Tagua" + }, + { + "lat": -34.46971, + "lon": -58.52111, + "name": "San Isidro" + }, + { + "lat": -15.88378, + "lon": -48.01634, + "name": "Riacho Fundo" + }, + { + "lat": 24.86919, + "lon": 92.35543, + "name": "Karīmganj" + } + ], + "question": "Which location is the geographic outlier among: Flores da Cunha, San Vicente de Tagua Tagua, San Isidro, Riacho Fundo, Karīmganj?", + "ground_truth": { + "answer": "Karīmganj", + "outlier_distance_km": 13761.9, + "second_furthest_km": 4703.1, + "clarity_ratio": 2.93, + "median_distance_km": 3604.8, + "distances_to_centroid": { + "Flores da Cunha": 2731.8, + "San Vicente de Tagua Tagua": 4703.1, + "San Isidro": 3604.8, + "Riacho Fundo": 2215.1, + "Karīmganj": 13761.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Flores da Cunha: (-29.03°, -51.18°)", + " San Vicente de Tagua Tagua: (-34.44°, -71.08°)", + " San Isidro: (-34.47°, -58.52°)", + " Riacho Fundo: (-15.88°, -48.02°)", + " Karīmganj: (24.87°, 92.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Karīmganj: 13761.9 km from centroid", + " San Vicente de Tagua Tagua: 4703.1 km from centroid", + " San Isidro: 3604.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Karīmganj", + "FINAL ANSWER: Karīmganj" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 21.01951, + "lon": 105.93694, + "name": "Trâu Quỳ" + }, + { + "lat": 29.76416, + "lon": 107.67834, + "name": "Baoluan" + }, + { + "lat": 27.85161, + "lon": 75.27384, + "name": "Nawalgarh" + }, + { + "lat": 25.67467, + "lon": 94.11099, + "name": "Kohima" + }, + { + "lat": 40.94589, + "lon": -81.48317, + "name": "Green" + } + ], + "question": "Which location is the geographic outlier among: Trâu Quỳ, Baoluan, Nawalgarh, Kohima, Green?", + "ground_truth": { + "answer": "Green", + "outlier_distance_km": 11294.1, + "second_furthest_km": 4654.7, + "clarity_ratio": 2.43, + "median_distance_km": 4556.6, + "distances_to_centroid": { + "Trâu Quỳ": 4654.7, + "Baoluan": 4556.6, + "Nawalgarh": 1468.7, + "Kohima": 3348.4, + "Green": 11294.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Trâu Quỳ: (21.02°, 105.94°)", + " Baoluan: (29.76°, 107.68°)", + " Nawalgarh: (27.85°, 75.27°)", + " Kohima: (25.67°, 94.11°)", + " Green: (40.95°, -81.48°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Green: 11294.1 km from centroid", + " Trâu Quỳ: 4654.7 km from centroid", + " Baoluan: 4556.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Green", + "FINAL ANSWER: Green" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.31657, + "lon": 77.37079, + "name": "Kūmher" + }, + { + "lat": 23.26307, + "lon": 72.67386, + "name": "Pethāpur" + }, + { + "lat": 24.77888, + "lon": 82.096, + "name": "Hanumana" + }, + { + "lat": 12.30889, + "lon": 78.79137, + "name": "Chengam" + }, + { + "lat": 50.98464, + "lon": 23.1742, + "name": "Krasnystaw" + } + ], + "question": "Which location is the geographic outlier among: Kūmher, Pethāpur, Hanumana, Chengam, Krasnystaw?", + "ground_truth": { + "answer": "Krasnystaw", + "outlier_distance_km": 4460.6, + "second_furthest_km": 2119.1, + "clarity_ratio": 2.1, + "median_distance_km": 1557.1, + "distances_to_centroid": { + "Kūmher": 1041.0, + "Pethāpur": 769.1, + "Hanumana": 1557.1, + "Chengam": 2119.1, + "Krasnystaw": 4460.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kūmher: (27.32°, 77.37°)", + " Pethāpur: (23.26°, 72.67°)", + " Hanumana: (24.78°, 82.10°)", + " Chengam: (12.31°, 78.79°)", + " Krasnystaw: (50.98°, 23.17°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Krasnystaw: 4460.6 km from centroid", + " Chengam: 2119.1 km from centroid", + " Hanumana: 1557.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Krasnystaw", + "FINAL ANSWER: Krasnystaw" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.81667, + "lon": 40.51667, + "name": "Gelemso" + }, + { + "lat": 6.20228, + "lon": -1.66796, + "name": "Obuase" + }, + { + "lat": 29.30995, + "lon": 30.8418, + "name": "Al Fayyum" + }, + { + "lat": -25.44141, + "lon": 27.51114, + "name": "Hartbeestfontein-A" + }, + { + "lat": -37.9, + "lon": 145.18333, + "name": "Wheelers Hill" + } + ], + "question": "Which location is the geographic outlier among: Gelemso, Obuase, Al Fayyum, Hartbeestfontein-A, Wheelers Hill?", + "ground_truth": { + "answer": "Wheelers Hill", + "outlier_distance_km": 10333.9, + "second_furthest_km": 5677.4, + "clarity_ratio": 1.82, + "median_distance_km": 4134.5, + "distances_to_centroid": { + "Gelemso": 1657.6, + "Obuase": 5677.4, + "Al Fayyum": 4134.5, + "Hartbeestfontein-A": 3286.5, + "Wheelers Hill": 10333.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gelemso: (8.82°, 40.52°)", + " Obuase: (6.20°, -1.67°)", + " Al Fayyum: (29.31°, 30.84°)", + " Hartbeestfontein-A: (-25.44°, 27.51°)", + " Wheelers Hill: (-37.90°, 145.18°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wheelers Hill: 10333.9 km from centroid", + " Obuase: 5677.4 km from centroid", + " Al Fayyum: 4134.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wheelers Hill", + "FINAL ANSWER: Wheelers Hill" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.51121, + "lon": 44.59051, + "name": "Malgobek" + }, + { + "lat": 50.74162, + "lon": 8.20778, + "name": "Haiger" + }, + { + "lat": 50.80019, + "lon": 7.20769, + "name": "Siegburg" + }, + { + "lat": 50.2584, + "lon": 18.85632, + "name": "Ruda Śląska" + }, + { + "lat": 34.67147, + "lon": 116.49213, + "name": "Wanggou" + } + ], + "question": "Which location is the geographic outlier among: Malgobek, Haiger, Siegburg, Ruda Śląska, Wanggou?", + "ground_truth": { + "answer": "Wanggou", + "outlier_distance_km": 6421.5, + "second_furthest_km": 2392.3, + "clarity_ratio": 2.68, + "median_distance_km": 2321.9, + "distances_to_centroid": { + "Malgobek": 515.9, + "Haiger": 2321.9, + "Siegburg": 2392.3, + "Ruda Śląska": 1567.7, + "Wanggou": 6421.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Malgobek: (43.51°, 44.59°)", + " Haiger: (50.74°, 8.21°)", + " Siegburg: (50.80°, 7.21°)", + " Ruda Śląska: (50.26°, 18.86°)", + " Wanggou: (34.67°, 116.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wanggou: 6421.5 km from centroid", + " Siegburg: 2392.3 km from centroid", + " Haiger: 2321.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Wanggou", + "FINAL ANSWER: Wanggou" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -40.33494, + "lon": -72.95564, + "name": "Río Bueno" + }, + { + "lat": 5.42164, + "lon": -75.70318, + "name": "Riosucio" + }, + { + "lat": -14.40861, + "lon": -56.44611, + "name": "Diamantino" + }, + { + "lat": -26.42528, + "lon": -49.24306, + "name": "Corupá" + }, + { + "lat": 33.18333, + "lon": 129.9, + "name": "Arita" + } + ], + "question": "Which location is the geographic outlier among: Río Bueno, Riosucio, Diamantino, Corupá, Arita?", + "ground_truth": { + "answer": "Arita", + "outlier_distance_km": 16244.1, + "second_furthest_km": 5910.9, + "clarity_ratio": 2.75, + "median_distance_km": 5843.0, + "distances_to_centroid": { + "Río Bueno": 5910.9, + "Riosucio": 5843.0, + "Diamantino": 3497.5, + "Corupá": 3249.5, + "Arita": 16244.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Río Bueno: (-40.33°, -72.96°)", + " Riosucio: (5.42°, -75.70°)", + " Diamantino: (-14.41°, -56.45°)", + " Corupá: (-26.43°, -49.24°)", + " Arita: (33.18°, 129.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arita: 16244.1 km from centroid", + " Río Bueno: 5910.9 km from centroid", + " Riosucio: 5843.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arita", + "FINAL ANSWER: Arita" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.05305, + "lon": 13.79831, + "name": "Blasewitz" + }, + { + "lat": 55.66853, + "lon": 39.87488, + "name": "Roshal’" + }, + { + "lat": 52.18935, + "lon": -2.22001, + "name": "Worcester" + }, + { + "lat": 40.30571, + "lon": -3.73295, + "name": "Getafe" + }, + { + "lat": 30.15286, + "lon": 78.7771, + "name": "Pauri" + } + ], + "question": "Which location is the geographic outlier among: Blasewitz, Roshal’, Worcester, Getafe, Pauri?", + "ground_truth": { + "answer": "Pauri", + "outlier_distance_km": 4897.0, + "second_furthest_km": 2422.7, + "clarity_ratio": 2.02, + "median_distance_km": 2110.4, + "distances_to_centroid": { + "Blasewitz": 1023.3, + "Roshal’": 1489.7, + "Worcester": 2110.4, + "Getafe": 2422.7, + "Pauri": 4897.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Blasewitz: (51.05°, 13.80°)", + " Roshal’: (55.67°, 39.87°)", + " Worcester: (52.19°, -2.22°)", + " Getafe: (40.31°, -3.73°)", + " Pauri: (30.15°, 78.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pauri: 4897.0 km from centroid", + " Getafe: 2422.7 km from centroid", + " Worcester: 2110.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pauri", + "FINAL ANSWER: Pauri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.12242, + "lon": 32.46749, + "name": "Dishnā" + }, + { + "lat": -1.17641, + "lon": 36.7564, + "name": "Karuri" + }, + { + "lat": -33.57565, + "lon": 22.44391, + "name": "Dysselsdorp" + }, + { + "lat": 11.21566, + "lon": 38.36452, + "name": "Wegeda" + }, + { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + } + ], + "question": "Which location is the geographic outlier among: Dishnā, Karuri, Dysselsdorp, Wegeda, Cambridge?", + "ground_truth": { + "answer": "Cambridge", + "outlier_distance_km": 11600.8, + "second_furthest_km": 4944.1, + "clarity_ratio": 2.35, + "median_distance_km": 4812.4, + "distances_to_centroid": { + "Dishnā": 4812.4, + "Karuri": 2776.1, + "Dysselsdorp": 4944.1, + "Wegeda": 3233.3, + "Cambridge": 11600.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dishnā: (26.12°, 32.47°)", + " Karuri: (-1.18°, 36.76°)", + " Dysselsdorp: (-33.58°, 22.44°)", + " Wegeda: (11.22°, 38.36°)", + " Cambridge: (-37.88°, 175.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cambridge: 11600.8 km from centroid", + " Dysselsdorp: 4944.1 km from centroid", + " Dishnā: 4812.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cambridge", + "FINAL ANSWER: Cambridge" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.69863, + "lon": 144.78631, + "name": "Taylors Lakes" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": 7.11345, + "lon": 6.73866, + "name": "Idah" + } + ], + "question": "Which location is the geographic outlier among: Taylors Lakes, The Gap, Lidcombe, Wollongong, Idah?", + "ground_truth": { + "answer": "Idah", + "outlier_distance_km": 12808.2, + "second_furthest_km": 3155.4, + "clarity_ratio": 4.06, + "median_distance_km": 3020.4, + "distances_to_centroid": { + "Taylors Lakes": 2611.6, + "The Gap": 3155.4, + "Lidcombe": 3020.4, + "Wollongong": 3019.2, + "Idah": 12808.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taylors Lakes: (-37.70°, 144.79°)", + " The Gap: (-27.44°, 152.94°)", + " Lidcombe: (-33.86°, 151.04°)", + " Wollongong: (-34.42°, 150.89°)", + " Idah: (7.11°, 6.74°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Idah: 12808.2 km from centroid", + " The Gap: 3155.4 km from centroid", + " Lidcombe: 3020.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Idah", + "FINAL ANSWER: Idah" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.28908, + "lon": -4.01197, + "name": "Navalcarnero" + }, + { + "lat": 43.38285, + "lon": -3.22043, + "name": "Castro-Urdiales" + }, + { + "lat": 36.20983, + "lon": -5.38452, + "name": "San Roque" + }, + { + "lat": 51.12056, + "lon": 17.03761, + "name": "Rejon placu Świętego Macieja" + }, + { + "lat": 29.765, + "lon": 105.66645, + "name": "Zhong’ao" + } + ], + "question": "Which location is the geographic outlier among: Navalcarnero, Castro-Urdiales, San Roque, Rejon placu Świętego Macieja, Zhong’ao?", + "ground_truth": { + "answer": "Zhong’ao", + "outlier_distance_km": 7430.8, + "second_furthest_km": 2424.9, + "clarity_ratio": 3.06, + "median_distance_km": 2202.0, + "distances_to_centroid": { + "Navalcarnero": 2202.0, + "Castro-Urdiales": 2115.3, + "San Roque": 2424.9, + "Rejon placu Świętego Macieja": 1278.7, + "Zhong’ao": 7430.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Navalcarnero: (40.29°, -4.01°)", + " Castro-Urdiales: (43.38°, -3.22°)", + " San Roque: (36.21°, -5.38°)", + " Rejon placu Świętego Macieja: (51.12°, 17.04°)", + " Zhong’ao: (29.77°, 105.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Zhong’ao: 7430.8 km from centroid", + " San Roque: 2424.9 km from centroid", + " Navalcarnero: 2202.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Zhong’ao", + "FINAL ANSWER: Zhong’ao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 3.586, + "lon": 102.773, + "name": "Maran" + }, + { + "lat": 37.49583, + "lon": 121.25806, + "name": "Qingyang" + }, + { + "lat": 35.95694, + "lon": 139.38889, + "name": "Sakado" + }, + { + "lat": 8.97574, + "lon": 77.41923, + "name": "Sūrandai" + }, + { + "lat": -28.84556, + "lon": -51.89028, + "name": "Guaporé" + } + ], + "question": "Which location is the geographic outlier among: Maran, Qingyang, Sakado, Sūrandai, Guaporé?", + "ground_truth": { + "answer": "Guaporé", + "outlier_distance_km": 14463.9, + "second_furthest_km": 6717.4, + "clarity_ratio": 2.15, + "median_distance_km": 5199.5, + "distances_to_centroid": { + "Maran": 2886.6, + "Qingyang": 5199.5, + "Sakado": 6717.4, + "Sūrandai": 276.3, + "Guaporé": 14463.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Maran: (3.59°, 102.77°)", + " Qingyang: (37.50°, 121.26°)", + " Sakado: (35.96°, 139.39°)", + " Sūrandai: (8.98°, 77.42°)", + " Guaporé: (-28.85°, -51.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guaporé: 14463.9 km from centroid", + " Sakado: 6717.4 km from centroid", + " Qingyang: 5199.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guaporé", + "FINAL ANSWER: Guaporé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 47.81954, + "lon": -122.17624, + "name": "North Creek" + }, + { + "lat": 42.78702, + "lon": -73.97096, + "name": "Rotterdam" + }, + { + "lat": 40.45921, + "lon": -90.6718, + "name": "Macomb" + }, + { + "lat": 40.79895, + "lon": -81.37845, + "name": "Canton" + }, + { + "lat": 34.26411, + "lon": 117.36379, + "name": "Damiao" + } + ], + "question": "Which location is the geographic outlier among: North Creek, Rotterdam, Macomb, Canton, Damiao?", + "ground_truth": { + "answer": "Damiao", + "outlier_distance_km": 11524.7, + "second_furthest_km": 5546.8, + "clarity_ratio": 2.08, + "median_distance_km": 3377.1, + "distances_to_centroid": { + "North Creek": 5546.8, + "Rotterdam": 1967.9, + "Macomb": 3377.1, + "Canton": 2605.0, + "Damiao": 11524.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " North Creek: (47.82°, -122.18°)", + " Rotterdam: (42.79°, -73.97°)", + " Macomb: (40.46°, -90.67°)", + " Canton: (40.80°, -81.38°)", + " Damiao: (34.26°, 117.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Damiao: 11524.7 km from centroid", + " North Creek: 5546.8 km from centroid", + " Macomb: 3377.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Damiao", + "FINAL ANSWER: Damiao" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.47315, + "lon": 78.3031, + "name": "Jalesar" + }, + { + "lat": 23.01754, + "lon": 76.72208, + "name": "Ashta" + }, + { + "lat": 33.33205, + "lon": 106.15496, + "name": "Lüeyang Chengguanzhen" + }, + { + "lat": 13.68333, + "lon": 79.35, + "name": "Tirumala" + }, + { + "lat": 49.22219, + "lon": -123.00588, + "name": "Maywood" + } + ], + "question": "Which location is the geographic outlier among: Jalesar, Ashta, Lüeyang Chengguanzhen, Tirumala, Maywood?", + "ground_truth": { + "answer": "Maywood", + "outlier_distance_km": 11176.8, + "second_furthest_km": 5876.8, + "clarity_ratio": 1.9, + "median_distance_km": 4073.5, + "distances_to_centroid": { + "Jalesar": 3397.3, + "Ashta": 3376.5, + "Lüeyang Chengguanzhen": 5876.8, + "Tirumala": 4073.5, + "Maywood": 11176.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jalesar: (27.47°, 78.30°)", + " Ashta: (23.02°, 76.72°)", + " Lüeyang Chengguanzhen: (33.33°, 106.15°)", + " Tirumala: (13.68°, 79.35°)", + " Maywood: (49.22°, -123.01°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maywood: 11176.8 km from centroid", + " Lüeyang Chengguanzhen: 5876.8 km from centroid", + " Tirumala: 4073.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maywood", + "FINAL ANSWER: Maywood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.9464, + "lon": 113.35769, + "name": "Shiqiao" + }, + { + "lat": 13.7085, + "lon": 100.52619, + "name": "Sathon" + }, + { + "lat": 17.16116, + "lon": 104.14725, + "name": "Sakon Nakhon" + }, + { + "lat": 36.75541, + "lon": 81.60765, + "name": "Arix" + }, + { + "lat": 10.3121, + "lon": 39.65888, + "name": "Mehal Mēda" + } + ], + "question": "Which location is the geographic outlier among: Shiqiao, Sathon, Sakon Nakhon, Arix, Mehal Mēda?", + "ground_truth": { + "answer": "Mehal Mēda", + "outlier_distance_km": 5267.3, + "second_furthest_km": 2651.4, + "clarity_ratio": 1.99, + "median_distance_km": 1940.8, + "distances_to_centroid": { + "Shiqiao": 2651.4, + "Sathon": 1526.3, + "Sakon Nakhon": 1747.4, + "Arix": 1940.8, + "Mehal Mēda": 5267.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shiqiao: (22.95°, 113.36°)", + " Sathon: (13.71°, 100.53°)", + " Sakon Nakhon: (17.16°, 104.15°)", + " Arix: (36.76°, 81.61°)", + " Mehal Mēda: (10.31°, 39.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mehal Mēda: 5267.3 km from centroid", + " Shiqiao: 2651.4 km from centroid", + " Arix: 1940.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mehal Mēda", + "FINAL ANSWER: Mehal Mēda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.04325, + "lon": 99.08128, + "name": "Ban Tak" + }, + { + "lat": -8.1335, + "lon": 113.2248, + "name": "Lumajang" + }, + { + "lat": 36.41097, + "lon": 138.99621, + "name": "Kanekomachi" + }, + { + "lat": 28.73335, + "lon": 105.0683, + "name": "Jiang’an" + }, + { + "lat": 6.71897, + "lon": -1.61188, + "name": "New Tafo" + } + ], + "question": "Which location is the geographic outlier among: Ban Tak, Lumajang, Kanekomachi, Jiang’an, New Tafo?", + "ground_truth": { + "answer": "New Tafo", + "outlier_distance_km": 10072.0, + "second_furthest_km": 5226.6, + "clarity_ratio": 1.93, + "median_distance_km": 3647.5, + "distances_to_centroid": { + "Ban Tak": 871.8, + "Lumajang": 3647.5, + "Kanekomachi": 5226.6, + "Jiang’an": 2011.7, + "New Tafo": 10072.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ban Tak: (17.04°, 99.08°)", + " Lumajang: (-8.13°, 113.22°)", + " Kanekomachi: (36.41°, 139.00°)", + " Jiang’an: (28.73°, 105.07°)", + " New Tafo: (6.72°, -1.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " New Tafo: 10072.0 km from centroid", + " Kanekomachi: 5226.6 km from centroid", + " Lumajang: 3647.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: New Tafo", + "FINAL ANSWER: New Tafo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.34813, + "lon": 37.95063, + "name": "Damboya" + }, + { + "lat": 30.19327, + "lon": 31.13703, + "name": "Al Qanāţir al Khayrīyah" + }, + { + "lat": -26.06927, + "lon": 30.11489, + "name": "Carolina" + }, + { + "lat": 5.55602, + "lon": -0.1969, + "name": "Accra" + }, + { + "lat": 33.22375, + "lon": 132.56001, + "name": "Uwajima" + } + ], + "question": "Which location is the geographic outlier among: Damboya, Al Qanāţir al Khayrīyah, Carolina, Accra, Uwajima?", + "ground_truth": { + "answer": "Uwajima", + "outlier_distance_km": 9051.3, + "second_furthest_km": 5143.9, + "clarity_ratio": 1.76, + "median_distance_km": 4381.7, + "distances_to_centroid": { + "Damboya": 966.9, + "Al Qanāţir al Khayrīyah": 2736.6, + "Carolina": 4381.7, + "Accra": 5143.9, + "Uwajima": 9051.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Damboya: (7.35°, 37.95°)", + " Al Qanāţir al Khayrīyah: (30.19°, 31.14°)", + " Carolina: (-26.07°, 30.11°)", + " Accra: (5.56°, -0.20°)", + " Uwajima: (33.22°, 132.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uwajima: 9051.3 km from centroid", + " Accra: 5143.9 km from centroid", + " Carolina: 4381.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uwajima", + "FINAL ANSWER: Uwajima" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 52.59172, + "lon": 58.31132, + "name": "Baymak" + }, + { + "lat": 52.80521, + "lon": -2.11636, + "name": "Stafford" + }, + { + "lat": 40.43932, + "lon": -3.64928, + "name": "Concepción" + }, + { + "lat": 45.69651, + "lon": 9.1818, + "name": "Mariano Comense" + }, + { + "lat": -37.94853, + "lon": 145.15274, + "name": "Springvale" + } + ], + "question": "Which location is the geographic outlier among: Baymak, Stafford, Concepción, Mariano Comense, Springvale?", + "ground_truth": { + "answer": "Springvale", + "outlier_distance_km": 13165.0, + "second_furthest_km": 4267.5, + "clarity_ratio": 3.08, + "median_distance_km": 4165.3, + "distances_to_centroid": { + "Baymak": 2794.3, + "Stafford": 4267.5, + "Concepción": 4165.3, + "Mariano Comense": 3236.8, + "Springvale": 13165.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Baymak: (52.59°, 58.31°)", + " Stafford: (52.81°, -2.12°)", + " Concepción: (40.44°, -3.65°)", + " Mariano Comense: (45.70°, 9.18°)", + " Springvale: (-37.95°, 145.15°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Springvale: 13165.0 km from centroid", + " Stafford: 4267.5 km from centroid", + " Concepción: 4165.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Springvale", + "FINAL ANSWER: Springvale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 28.09193, + "lon": 30.75813, + "name": "Minya" + }, + { + "lat": -1.48256, + "lon": 40.03341, + "name": "Hola" + }, + { + "lat": 8.11667, + "lon": 38.36667, + "name": "Butajīra" + }, + { + "lat": 9.87342, + "lon": 7.95407, + "name": "Kachia" + }, + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + } + ], + "question": "Which location is the geographic outlier among: Minya, Hola, Butajīra, Kachia, Ballarat?", + "ground_truth": { + "answer": "Ballarat", + "outlier_distance_km": 10249.0, + "second_furthest_km": 4979.2, + "clarity_ratio": 2.06, + "median_distance_km": 3741.1, + "distances_to_centroid": { + "Minya": 3741.1, + "Hola": 1389.5, + "Butajīra": 1703.2, + "Kachia": 4979.2, + "Ballarat": 10249.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Minya: (28.09°, 30.76°)", + " Hola: (-1.48°, 40.03°)", + " Butajīra: (8.12°, 38.37°)", + " Kachia: (9.87°, 7.95°)", + " Ballarat: (-37.57°, 143.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ballarat: 10249.0 km from centroid", + " Kachia: 4979.2 km from centroid", + " Minya: 3741.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ballarat", + "FINAL ANSWER: Ballarat" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.91111, + "lon": -37.07167, + "name": "Aracaju" + }, + { + "lat": -8.00889, + "lon": -34.85528, + "name": "Olinda" + }, + { + "lat": -5.75611, + "lon": -78.44111, + "name": "Bagua Grande" + }, + { + "lat": 9.14334, + "lon": -74.22384, + "name": "Guamal" + }, + { + "lat": -37.88333, + "lon": 145.21667, + "name": "Wantirna South" + } + ], + "question": "Which location is the geographic outlier among: Aracaju, Olinda, Bagua Grande, Guamal, Wantirna South?", + "ground_truth": { + "answer": "Wantirna South", + "outlier_distance_km": 14267.3, + "second_furthest_km": 6897.1, + "clarity_ratio": 2.07, + "median_distance_km": 6820.5, + "distances_to_centroid": { + "Aracaju": 2314.9, + "Olinda": 2103.2, + "Bagua Grande": 6897.1, + "Guamal": 6820.5, + "Wantirna South": 14267.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aracaju: (-10.91°, -37.07°)", + " Olinda: (-8.01°, -34.86°)", + " Bagua Grande: (-5.76°, -78.44°)", + " Guamal: (9.14°, -74.22°)", + " Wantirna South: (-37.88°, 145.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Wantirna South: 14267.3 km from centroid", + " Bagua Grande: 6897.1 km from centroid", + " Guamal: 6820.5 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": 46.8458, + "lon": -1.87942, + "name": "Challans" + }, + { + "lat": 50.30582, + "lon": 18.9742, + "name": "Chorzów" + }, + { + "lat": 45.20978, + "lon": 5.77762, + "name": "Meylan" + }, + { + "lat": 41.41175, + "lon": 2.16784, + "name": "el Baix Guinardó" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + } + ], + "question": "Which location is the geographic outlier among: Challans, Chorzów, Meylan, el Baix Guinardó, Maroubra?", + "ground_truth": { + "answer": "Maroubra", + "outlier_distance_km": 14057.5, + "second_furthest_km": 3691.8, + "clarity_ratio": 3.81, + "median_distance_km": 3222.9, + "distances_to_centroid": { + "Challans": 3691.8, + "Chorzów": 2638.7, + "Meylan": 3074.5, + "el Baix Guinardó": 3222.9, + "Maroubra": 14057.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Challans: (46.85°, -1.88°)", + " Chorzów: (50.31°, 18.97°)", + " Meylan: (45.21°, 5.78°)", + " el Baix Guinardó: (41.41°, 2.17°)", + " Maroubra: (-33.95°, 151.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maroubra: 14057.5 km from centroid", + " Challans: 3691.8 km from centroid", + " el Baix Guinardó: 3222.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maroubra", + "FINAL ANSWER: Maroubra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.24038, + "lon": -76.83942, + "name": "Columbia" + }, + { + "lat": 33.86751, + "lon": -117.99812, + "name": "Buena Park" + }, + { + "lat": 39.21311, + "lon": -84.59939, + "name": "White Oak" + }, + { + "lat": 41.67705, + "lon": -71.26616, + "name": "Bristol" + }, + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + } + ], + "question": "Which location is the geographic outlier among: Columbia, Buena Park, White Oak, Bristol, Glen Waverley?", + "ground_truth": { + "answer": "Glen Waverley", + "outlier_distance_km": 18279.6, + "second_furthest_km": 7435.6, + "clarity_ratio": 2.46, + "median_distance_km": 4449.8, + "distances_to_centroid": { + "Columbia": 3801.5, + "Buena Park": 7435.6, + "White Oak": 4449.8, + "Bristol": 3465.5, + "Glen Waverley": 18279.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Columbia: (39.24°, -76.84°)", + " Buena Park: (33.87°, -118.00°)", + " White Oak: (39.21°, -84.60°)", + " Bristol: (41.68°, -71.27°)", + " Glen Waverley: (-37.88°, 145.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glen Waverley: 18279.6 km from centroid", + " Buena Park: 7435.6 km from centroid", + " White Oak: 4449.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glen Waverley", + "FINAL ANSWER: Glen Waverley" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 42.73698, + "lon": -84.48387, + "name": "East Lansing" + }, + { + "lat": 18.62936, + "lon": -95.51968, + "name": "Lerdo de Tejada" + }, + { + "lat": 36.98356, + "lon": -121.98052, + "name": "Live Oak" + }, + { + "lat": 61.32139, + "lon": -149.56778, + "name": "Eagle River" + }, + { + "lat": 45.43854, + "lon": 10.9938, + "name": "Verona" + } + ], + "question": "Which location is the geographic outlier among: East Lansing, Lerdo de Tejada, Live Oak, Eagle River, Verona?", + "ground_truth": { + "answer": "Verona", + "outlier_distance_km": 7497.5, + "second_furthest_km": 4615.7, + "clarity_ratio": 1.62, + "median_distance_km": 2942.1, + "distances_to_centroid": { + "East Lansing": 355.7, + "Lerdo de Tejada": 2587.9, + "Live Oak": 2942.1, + "Eagle River": 4615.7, + "Verona": 7497.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " East Lansing: (42.74°, -84.48°)", + " Lerdo de Tejada: (18.63°, -95.52°)", + " Live Oak: (36.98°, -121.98°)", + " Eagle River: (61.32°, -149.57°)", + " Verona: (45.44°, 10.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Verona: 7497.5 km from centroid", + " Eagle River: 4615.7 km from centroid", + " Live Oak: 2942.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Verona", + "FINAL ANSWER: Verona" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.01481, + "lon": 135.67755, + "name": "Arashiyama" + }, + { + "lat": 17.60184, + "lon": 80.70509, + "name": "Pāloncha" + }, + { + "lat": 26.92007, + "lon": 71.91631, + "name": "Pokaran" + }, + { + "lat": 29.9994, + "lon": 108.10913, + "name": "Nanbin" + }, + { + "lat": 42.85842, + "lon": -70.93005, + "name": "Amesbury" + } + ], + "question": "Which location is the geographic outlier among: Arashiyama, Pāloncha, Pokaran, Nanbin, Amesbury?", + "ground_truth": { + "answer": "Amesbury", + "outlier_distance_km": 10707.4, + "second_furthest_km": 6481.0, + "clarity_ratio": 1.65, + "median_distance_km": 4106.8, + "distances_to_centroid": { + "Arashiyama": 6481.0, + "Pāloncha": 2131.5, + "Pokaran": 773.8, + "Nanbin": 4106.8, + "Amesbury": 10707.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Arashiyama: (35.01°, 135.68°)", + " Pāloncha: (17.60°, 80.71°)", + " Pokaran: (26.92°, 71.92°)", + " Nanbin: (30.00°, 108.11°)", + " Amesbury: (42.86°, -70.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Amesbury: 10707.4 km from centroid", + " Arashiyama: 6481.0 km from centroid", + " Nanbin: 4106.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Amesbury", + "FINAL ANSWER: Amesbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.60861, + "lon": 14.98209, + "name": "Battipaglia" + }, + { + "lat": 53.39337, + "lon": -3.01479, + "name": "Birkenhead" + }, + { + "lat": 49.47593, + "lon": 10.98856, + "name": "Fürth" + }, + { + "lat": 40.389, + "lon": -3.70682, + "name": "Moscardó" + }, + { + "lat": -3.76585, + "lon": -49.67923, + "name": "Tucuruí" + } + ], + "question": "Which location is the geographic outlier among: Battipaglia, Birkenhead, Fürth, Moscardó, Tucuruí?", + "ground_truth": { + "answer": "Tucuruí", + "outlier_distance_km": 6328.6, + "second_furthest_km": 2035.7, + "clarity_ratio": 3.11, + "median_distance_km": 1946.5, + "distances_to_centroid": { + "Battipaglia": 1902.4, + "Birkenhead": 1946.5, + "Fürth": 2035.7, + "Moscardó": 528.3, + "Tucuruí": 6328.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Battipaglia: (40.61°, 14.98°)", + " Birkenhead: (53.39°, -3.01°)", + " Fürth: (49.48°, 10.99°)", + " Moscardó: (40.39°, -3.71°)", + " Tucuruí: (-3.77°, -49.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tucuruí: 6328.6 km from centroid", + " Fürth: 2035.7 km from centroid", + " Birkenhead: 1946.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tucuruí", + "FINAL ANSWER: Tucuruí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.25738, + "lon": 33.81291, + "name": "Hurghada" + }, + { + "lat": 8.49664, + "lon": 4.54214, + "name": "Ilorin" + }, + { + "lat": 5.35113, + "lon": -0.62313, + "name": "Winneba" + }, + { + "lat": 6.04024, + "lon": -0.80876, + "name": "Akwatia" + }, + { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + } + ], + "question": "Which location is the geographic outlier among: Hurghada, Ilorin, Winneba, Akwatia, Hoppers Crossing?", + "ground_truth": { + "answer": "Hoppers Crossing", + "outlier_distance_km": 11739.6, + "second_furthest_km": 4144.2, + "clarity_ratio": 2.83, + "median_distance_km": 4117.8, + "distances_to_centroid": { + "Hurghada": 2837.5, + "Ilorin": 3594.0, + "Winneba": 4117.8, + "Akwatia": 4144.2, + "Hoppers Crossing": 11739.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hurghada: (27.26°, 33.81°)", + " Ilorin: (8.50°, 4.54°)", + " Winneba: (5.35°, -0.62°)", + " Akwatia: (6.04°, -0.81°)", + " Hoppers Crossing: (-37.88°, 144.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hoppers Crossing: 11739.6 km from centroid", + " Akwatia: 4144.2 km from centroid", + " Winneba: 4117.8 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": 39.9036, + "lon": 8.59257, + "name": "Oristano" + }, + { + "lat": 48.63115, + "lon": 8.07607, + "name": "Achern" + }, + { + "lat": 43.94265, + "lon": 10.29754, + "name": "Camaiore" + }, + { + "lat": 55.01788, + "lon": -1.42559, + "name": "Tynemouth" + }, + { + "lat": 26.46146, + "lon": -80.07282, + "name": "Delray Beach" + } + ], + "question": "Which location is the geographic outlier among: Oristano, Achern, Camaiore, Tynemouth, Delray Beach?", + "ground_truth": { + "answer": "Delray Beach", + "outlier_distance_km": 6400.8, + "second_furthest_km": 1714.1, + "clarity_ratio": 3.73, + "median_distance_km": 1655.1, + "distances_to_centroid": { + "Oristano": 1655.1, + "Achern": 1605.0, + "Camaiore": 1714.1, + "Tynemouth": 1522.8, + "Delray Beach": 6400.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Oristano: (39.90°, 8.59°)", + " Achern: (48.63°, 8.08°)", + " Camaiore: (43.94°, 10.30°)", + " Tynemouth: (55.02°, -1.43°)", + " Delray Beach: (26.46°, -80.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Delray Beach: 6400.8 km from centroid", + " Camaiore: 1714.1 km from centroid", + " Oristano: 1655.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Delray Beach", + "FINAL ANSWER: Delray Beach" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.94639, + "lon": -44.91889, + "name": "Santo Antônio do Amparo" + }, + { + "lat": -13.26806, + "lon": -39.66278, + "name": "Ubaíra" + }, + { + "lat": -21.71417, + "lon": -52.42222, + "name": "Bataguassu" + }, + { + "lat": -3.89, + "lon": -38.45056, + "name": "Eusébio" + }, + { + "lat": 24.38251, + "lon": 80.78088, + "name": "Unchahra" + } + ], + "question": "Which location is the geographic outlier among: Santo Antônio do Amparo, Ubaíra, Bataguassu, Eusébio, Unchahra?", + "ground_truth": { + "answer": "Unchahra", + "outlier_distance_km": 11312.9, + "second_furthest_km": 3942.6, + "clarity_ratio": 2.87, + "median_distance_km": 3190.5, + "distances_to_centroid": { + "Santo Antônio do Amparo": 3190.5, + "Ubaíra": 2368.9, + "Bataguassu": 3942.6, + "Eusébio": 2188.8, + "Unchahra": 11312.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santo Antônio do Amparo: (-20.95°, -44.92°)", + " Ubaíra: (-13.27°, -39.66°)", + " Bataguassu: (-21.71°, -52.42°)", + " Eusébio: (-3.89°, -38.45°)", + " Unchahra: (24.38°, 80.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Unchahra: 11312.9 km from centroid", + " Bataguassu: 3942.6 km from centroid", + " Santo Antônio do Amparo: 3190.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Unchahra", + "FINAL ANSWER: Unchahra" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + { + "lat": -33.86482, + "lon": 151.20773, + "name": "Sydney Central Business District" + }, + { + "lat": 46.06787, + "lon": 11.12108, + "name": "Trento" + } + ], + "question": "Which location is the geographic outlier among: Ballarat, Glen Waverley, Landsdale, Sydney Central Business District, Trento?", + "ground_truth": { + "answer": "Trento", + "outlier_distance_km": 12453.4, + "second_furthest_km": 4077.2, + "clarity_ratio": 3.05, + "median_distance_km": 3714.8, + "distances_to_centroid": { + "Ballarat": 3595.6, + "Glen Waverley": 3714.8, + "Landsdale": 1443.6, + "Sydney Central Business District": 4077.2, + "Trento": 12453.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ballarat: (-37.57°, 143.85°)", + " Glen Waverley: (-37.88°, 145.16°)", + " Landsdale: (-31.81°, 115.87°)", + " Sydney Central Business District: (-33.86°, 151.21°)", + " Trento: (46.07°, 11.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Trento: 12453.4 km from centroid", + " Sydney Central Business District: 4077.2 km from centroid", + " Glen Waverley: 3714.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Trento", + "FINAL ANSWER: Trento" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.02167, + "lon": -46.635, + "name": "Augusto Corrêa" + }, + { + "lat": 9.73586, + "lon": -75.52626, + "name": "San Onofre" + }, + { + "lat": -24.1125, + "lon": -49.33167, + "name": "Itararé" + }, + { + "lat": -1.36556, + "lon": -48.37222, + "name": "Ananindeua" + }, + { + "lat": -34.75155, + "lon": 149.72086, + "name": "Goulburn" + } + ], + "question": "Which location is the geographic outlier among: Augusto Corrêa, San Onofre, Itararé, Ananindeua, Goulburn?", + "ground_truth": { + "answer": "Goulburn", + "outlier_distance_km": 14720.8, + "second_furthest_km": 7158.1, + "clarity_ratio": 2.06, + "median_distance_km": 4036.1, + "distances_to_centroid": { + "Augusto Corrêa": 3748.2, + "San Onofre": 7158.1, + "Itararé": 4036.1, + "Ananindeua": 3922.4, + "Goulburn": 14720.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Augusto Corrêa: (-1.02°, -46.63°)", + " San Onofre: (9.74°, -75.53°)", + " Itararé: (-24.11°, -49.33°)", + " Ananindeua: (-1.37°, -48.37°)", + " Goulburn: (-34.75°, 149.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Goulburn: 14720.8 km from centroid", + " San Onofre: 7158.1 km from centroid", + " Itararé: 4036.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Goulburn", + "FINAL ANSWER: Goulburn" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.91989, + "lon": -110.89888, + "name": "Heroica Guaymas" + }, + { + "lat": 39.84031, + "lon": -88.9548, + "name": "Decatur" + }, + { + "lat": 31.85425, + "lon": -110.9937, + "name": "Green Valley" + }, + { + "lat": 40.72593, + "lon": -73.51429, + "name": "Levittown" + }, + { + "lat": 39.50263, + "lon": -0.44079, + "name": "Paterna" + } + ], + "question": "Which location is the geographic outlier among: Heroica Guaymas, Decatur, Green Valley, Levittown, Paterna?", + "ground_truth": { + "answer": "Paterna", + "outlier_distance_km": 6529.6, + "second_furthest_km": 3306.5, + "clarity_ratio": 1.97, + "median_distance_km": 3157.6, + "distances_to_centroid": { + "Heroica Guaymas": 3306.5, + "Decatur": 1135.8, + "Green Valley": 3157.6, + "Levittown": 608.3, + "Paterna": 6529.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Heroica Guaymas: (27.92°, -110.90°)", + " Decatur: (39.84°, -88.95°)", + " Green Valley: (31.85°, -110.99°)", + " Levittown: (40.73°, -73.51°)", + " Paterna: (39.50°, -0.44°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Paterna: 6529.6 km from centroid", + " Heroica Guaymas: 3306.5 km from centroid", + " Green Valley: 3157.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Paterna", + "FINAL ANSWER: Paterna" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 55.70196, + "lon": 37.81178, + "name": "Vykhino-Zhulebino" + }, + { + "lat": 50.63945, + "lon": 20.30454, + "name": "Jędrzejów" + }, + { + "lat": 51.22172, + "lon": 6.77616, + "name": "Düsseldorf" + }, + { + "lat": 57.00816, + "lon": 61.46344, + "name": "Asbest" + }, + { + "lat": 33.53865, + "lon": -112.18599, + "name": "Glendale" + } + ], + "question": "Which location is the geographic outlier among: Vykhino-Zhulebino, Jędrzejów, Düsseldorf, Asbest, Glendale?", + "ground_truth": { + "answer": "Glendale", + "outlier_distance_km": 8773.3, + "second_furthest_km": 3853.6, + "clarity_ratio": 2.28, + "median_distance_km": 2424.9, + "distances_to_centroid": { + "Vykhino-Zhulebino": 2424.9, + "Jędrzejów": 1247.5, + "Düsseldorf": 331.1, + "Asbest": 3853.6, + "Glendale": 8773.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vykhino-Zhulebino: (55.70°, 37.81°)", + " Jędrzejów: (50.64°, 20.30°)", + " Düsseldorf: (51.22°, 6.78°)", + " Asbest: (57.01°, 61.46°)", + " Glendale: (33.54°, -112.19°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glendale: 8773.3 km from centroid", + " Asbest: 3853.6 km from centroid", + " Vykhino-Zhulebino: 2424.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glendale", + "FINAL ANSWER: Glendale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + { + "lat": -41.31667, + "lon": 173.23333, + "name": "Stoke" + }, + { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + { + "lat": -37.69863, + "lon": 144.78631, + "name": "Taylors Lakes" + }, + { + "lat": 35.72528, + "lon": 139.21778, + "name": "Itsukaichi" + } + ], + "question": "Which location is the geographic outlier among: Rockhampton, Stoke, Maroubra, Taylors Lakes, Itsukaichi?", + "ground_truth": { + "answer": "Itsukaichi", + "outlier_distance_km": 6350.0, + "second_furthest_km": 3104.9, + "clarity_ratio": 2.05, + "median_distance_km": 2068.1, + "distances_to_centroid": { + "Rockhampton": 385.8, + "Stoke": 3104.9, + "Maroubra": 1538.4, + "Taylors Lakes": 2068.1, + "Itsukaichi": 6350.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rockhampton: (-23.38°, 150.51°)", + " Stoke: (-41.32°, 173.23°)", + " Maroubra: (-33.95°, 151.23°)", + " Taylors Lakes: (-37.70°, 144.79°)", + " Itsukaichi: (35.73°, 139.22°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itsukaichi: 6350.0 km from centroid", + " Stoke: 3104.9 km from centroid", + " Taylors Lakes: 2068.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itsukaichi", + "FINAL ANSWER: Itsukaichi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.7133, + "lon": -93.42273, + "name": "Prior Lake" + }, + { + "lat": 18.0883, + "lon": -96.12535, + "name": "Tuxtepec" + }, + { + "lat": 38.43283, + "lon": -90.37762, + "name": "Arnold" + }, + { + "lat": 39.9356, + "lon": -91.40987, + "name": "Quincy" + }, + { + "lat": 31.44268, + "lon": 75.49847, + "name": "Kartārpur" + } + ], + "question": "Which location is the geographic outlier among: Prior Lake, Tuxtepec, Arnold, Quincy, Kartārpur?", + "ground_truth": { + "answer": "Kartārpur", + "outlier_distance_km": 11280.7, + "second_furthest_km": 4080.8, + "clarity_ratio": 2.76, + "median_distance_km": 3117.3, + "distances_to_centroid": { + "Prior Lake": 3117.3, + "Tuxtepec": 4080.8, + "Arnold": 2810.5, + "Quincy": 2900.8, + "Kartārpur": 11280.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Prior Lake: (44.71°, -93.42°)", + " Tuxtepec: (18.09°, -96.13°)", + " Arnold: (38.43°, -90.38°)", + " Quincy: (39.94°, -91.41°)", + " Kartārpur: (31.44°, 75.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kartārpur: 11280.7 km from centroid", + " Tuxtepec: 4080.8 km from centroid", + " Prior Lake: 3117.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kartārpur", + "FINAL ANSWER: Kartārpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.24762, + "lon": 11.09111, + "name": "Roth" + }, + { + "lat": 51.55657, + "lon": 7.31155, + "name": "Castrop-Rauxel" + }, + { + "lat": 48.80867, + "lon": 9.15719, + "name": "Stuttgart Feuerbach" + }, + { + "lat": 50.82928, + "lon": 6.90499, + "name": "Brühl" + }, + { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + } + ], + "question": "Which location is the geographic outlier among: Roth, Castrop-Rauxel, Stuttgart Feuerbach, Brühl, Mooroolbark?", + "ground_truth": { + "answer": "Mooroolbark", + "outlier_distance_km": 13720.6, + "second_furthest_km": 3136.8, + "clarity_ratio": 4.37, + "median_distance_km": 3120.3, + "distances_to_centroid": { + "Roth": 2773.6, + "Castrop-Rauxel": 3136.8, + "Stuttgart Feuerbach": 2869.4, + "Brühl": 3120.3, + "Mooroolbark": 13720.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Roth: (49.25°, 11.09°)", + " Castrop-Rauxel: (51.56°, 7.31°)", + " Stuttgart Feuerbach: (48.81°, 9.16°)", + " Brühl: (50.83°, 6.90°)", + " Mooroolbark: (-37.78°, 145.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mooroolbark: 13720.6 km from centroid", + " Castrop-Rauxel: 3136.8 km from centroid", + " Brühl: 3120.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mooroolbark", + "FINAL ANSWER: Mooroolbark" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.74761, + "lon": -116.97307, + "name": "Hemet" + }, + { + "lat": 40.79871, + "lon": -74.23904, + "name": "West Orange" + }, + { + "lat": 17.54528, + "lon": -98.57599, + "name": "Tlapa de Comonfort" + }, + { + "lat": 32.52321, + "lon": -92.63793, + "name": "Ruston" + }, + { + "lat": 29.97371, + "lon": 32.52627, + "name": "Suez" + } + ], + "question": "Which location is the geographic outlier among: Hemet, West Orange, Tlapa de Comonfort, Ruston, Suez?", + "ground_truth": { + "answer": "Suez", + "outlier_distance_km": 9396.5, + "second_furthest_km": 4388.4, + "clarity_ratio": 2.14, + "median_distance_km": 3244.5, + "distances_to_centroid": { + "Hemet": 4388.4, + "West Orange": 1163.4, + "Tlapa de Comonfort": 3244.5, + "Ruston": 2146.5, + "Suez": 9396.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hemet: (33.75°, -116.97°)", + " West Orange: (40.80°, -74.24°)", + " Tlapa de Comonfort: (17.55°, -98.58°)", + " Ruston: (32.52°, -92.64°)", + " Suez: (29.97°, 32.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Suez: 9396.5 km from centroid", + " Hemet: 4388.4 km from centroid", + " Tlapa de Comonfort: 3244.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Suez", + "FINAL ANSWER: Suez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 38.84028, + "lon": -97.61142, + "name": "Salina" + }, + { + "lat": 42.10704, + "lon": -72.62037, + "name": "West Springfield" + }, + { + "lat": 41.82649, + "lon": -72.73009, + "name": "Bloomfield" + }, + { + "lat": 19.8173, + "lon": -97.35992, + "name": "Teziutlan" + }, + { + "lat": 49.83383, + "lon": 19.9383, + "name": "Myślenice" + } + ], + "question": "Which location is the geographic outlier among: Salina, West Springfield, Bloomfield, Teziutlan, Myślenice?", + "ground_truth": { + "answer": "Myślenice", + "outlier_distance_km": 6462.2, + "second_furthest_km": 3808.4, + "clarity_ratio": 1.7, + "median_distance_km": 2895.4, + "distances_to_centroid": { + "Salina": 2895.4, + "West Springfield": 828.4, + "Bloomfield": 823.4, + "Teziutlan": 3808.4, + "Myślenice": 6462.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Salina: (38.84°, -97.61°)", + " West Springfield: (42.11°, -72.62°)", + " Bloomfield: (41.83°, -72.73°)", + " Teziutlan: (19.82°, -97.36°)", + " Myślenice: (49.83°, 19.94°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Myślenice: 6462.2 km from centroid", + " Teziutlan: 3808.4 km from centroid", + " Salina: 2895.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Myślenice", + "FINAL ANSWER: Myślenice" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + }, + { + "lat": -35.02692, + "lon": 117.88369, + "name": "Albany" + }, + { + "lat": -37.78821, + "lon": 175.2902, + "name": "Hamilton East" + }, + { + "lat": -40.91667, + "lon": 175.01667, + "name": "Paraparaumu" + }, + { + "lat": 51.61634, + "lon": 7.52872, + "name": "Lünen" + } + ], + "question": "Which location is the geographic outlier among: Adelaide, Albany, Hamilton East, Paraparaumu, Lünen?", + "ground_truth": { + "answer": "Lünen", + "outlier_distance_km": 13425.2, + "second_furthest_km": 5458.0, + "clarity_ratio": 2.46, + "median_distance_km": 5431.1, + "distances_to_centroid": { + "Adelaide": 2317.6, + "Albany": 1804.4, + "Hamilton East": 5431.1, + "Paraparaumu": 5458.0, + "Lünen": 13425.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adelaide: (-34.93°, 138.60°)", + " Albany: (-35.03°, 117.88°)", + " Hamilton East: (-37.79°, 175.29°)", + " Paraparaumu: (-40.92°, 175.02°)", + " Lünen: (51.62°, 7.53°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lünen: 13425.2 km from centroid", + " Paraparaumu: 5458.0 km from centroid", + " Hamilton East: 5431.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lünen", + "FINAL ANSWER: Lünen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.50316, + "lon": -58.70596, + "name": "Los Polvorines" + }, + { + "lat": -9.40472, + "lon": -35.50722, + "name": "Barra de Santo Antônio" + }, + { + "lat": -15.675, + "lon": -38.94722, + "name": "Canavieiras" + }, + { + "lat": -29.62056, + "lon": -54.17889, + "name": "São Pedro do Sul" + }, + { + "lat": 8.0618, + "lon": 123.7477, + "name": "Tangub" + } + ], + "question": "Which location is the geographic outlier among: Los Polvorines, Barra de Santo Antônio, Canavieiras, São Pedro do Sul, Tangub?", + "ground_truth": { + "answer": "Tangub", + "outlier_distance_km": 15206.1, + "second_furthest_km": 4995.0, + "clarity_ratio": 3.04, + "median_distance_km": 4471.5, + "distances_to_centroid": { + "Los Polvorines": 4995.0, + "Barra de Santo Antônio": 2582.4, + "Canavieiras": 2803.0, + "São Pedro do Sul": 4471.5, + "Tangub": 15206.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Los Polvorines: (-34.50°, -58.71°)", + " Barra de Santo Antônio: (-9.40°, -35.51°)", + " Canavieiras: (-15.68°, -38.95°)", + " São Pedro do Sul: (-29.62°, -54.18°)", + " Tangub: (8.06°, 123.75°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tangub: 15206.1 km from centroid", + " Los Polvorines: 4995.0 km from centroid", + " São Pedro do Sul: 4471.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tangub", + "FINAL ANSWER: Tangub" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.77808, + "lon": -6.3515, + "name": "Sanlúcar de Barrameda" + }, + { + "lat": 51.21977, + "lon": 7.6273, + "name": "Lüdenscheid" + }, + { + "lat": 48.84868, + "lon": 2.62435, + "name": "Noisiel" + }, + { + "lat": 51.59054, + "lon": -0.14212, + "name": "Muswell Hill" + }, + { + "lat": 29.33609, + "lon": 78.22608, + "name": "Jhālu" + } + ], + "question": "Which location is the geographic outlier among: Sanlúcar de Barrameda, Lüdenscheid, Noisiel, Muswell Hill, Jhālu?", + "ground_truth": { + "answer": "Jhālu", + "outlier_distance_km": 5617.2, + "second_furthest_km": 2066.4, + "clarity_ratio": 2.72, + "median_distance_km": 1523.3, + "distances_to_centroid": { + "Sanlúcar de Barrameda": 2066.4, + "Lüdenscheid": 1076.5, + "Noisiel": 1209.9, + "Muswell Hill": 1523.3, + "Jhālu": 5617.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sanlúcar de Barrameda: (36.78°, -6.35°)", + " Lüdenscheid: (51.22°, 7.63°)", + " Noisiel: (48.85°, 2.62°)", + " Muswell Hill: (51.59°, -0.14°)", + " Jhālu: (29.34°, 78.23°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jhālu: 5617.2 km from centroid", + " Sanlúcar de Barrameda: 2066.4 km from centroid", + " Muswell Hill: 1523.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jhālu", + "FINAL ANSWER: Jhālu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.88835, + "lon": -118.30896, + "name": "Gardena" + }, + { + "lat": 39.97776, + "lon": -105.13193, + "name": "Louisville" + }, + { + "lat": 40.73121, + "lon": -74.27348, + "name": "Maplewood" + }, + { + "lat": 20.08355, + "lon": -98.36288, + "name": "Tulancingo" + }, + { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + } + ], + "question": "Which location is the geographic outlier among: Gardena, Louisville, Maplewood, Tulancingo, Greensborough?", + "ground_truth": { + "answer": "Greensborough", + "outlier_distance_km": 17497.5, + "second_furthest_km": 6839.4, + "clarity_ratio": 2.56, + "median_distance_km": 5676.9, + "distances_to_centroid": { + "Gardena": 6839.4, + "Louisville": 5676.9, + "Maplewood": 3294.3, + "Tulancingo": 5023.8, + "Greensborough": 17497.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Gardena: (33.89°, -118.31°)", + " Louisville: (39.98°, -105.13°)", + " Maplewood: (40.73°, -74.27°)", + " Tulancingo: (20.08°, -98.36°)", + " Greensborough: (-37.70°, 145.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greensborough: 17497.5 km from centroid", + " Gardena: 6839.4 km from centroid", + " Louisville: 5676.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greensborough", + "FINAL ANSWER: Greensborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.99975, + "lon": -87.69284, + "name": "West Ridge" + }, + { + "lat": 33.98668, + "lon": -118.18535, + "name": "Maywood" + }, + { + "lat": 42.3876, + "lon": -71.0995, + "name": "Somerville" + }, + { + "lat": 45.5152, + "lon": -73.46818, + "name": "Longueuil" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + } + ], + "question": "Which location is the geographic outlier among: West Ridge, Maywood, Somerville, Longueuil, Lidcombe?", + "ground_truth": { + "answer": "Lidcombe", + "outlier_distance_km": 18648.7, + "second_furthest_km": 7412.4, + "clarity_ratio": 2.52, + "median_distance_km": 4681.8, + "distances_to_centroid": { + "West Ridge": 4681.8, + "Maywood": 7412.4, + "Somerville": 3370.7, + "Longueuil": 3683.8, + "Lidcombe": 18648.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " West Ridge: (42.00°, -87.69°)", + " Maywood: (33.99°, -118.19°)", + " Somerville: (42.39°, -71.10°)", + " Longueuil: (45.52°, -73.47°)", + " Lidcombe: (-33.86°, 151.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lidcombe: 18648.7 km from centroid", + " Maywood: 7412.4 km from centroid", + " West Ridge: 4681.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lidcombe", + "FINAL ANSWER: Lidcombe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 35.91014, + "lon": -79.07529, + "name": "Carrboro" + }, + { + "lat": 32.74255, + "lon": -117.03142, + "name": "Lemon Grove" + }, + { + "lat": 20.38897, + "lon": -99.99637, + "name": "San Juan del Río" + }, + { + "lat": 40.89288, + "lon": -73.97264, + "name": "Englewood" + }, + { + "lat": 23.19602, + "lon": 71.79171, + "name": "Patdi" + } + ], + "question": "Which location is the geographic outlier among: Carrboro, Lemon Grove, San Juan del Río, Englewood, Patdi?", + "ground_truth": { + "answer": "Patdi", + "outlier_distance_km": 12102.4, + "second_furthest_km": 5366.2, + "clarity_ratio": 2.26, + "median_distance_km": 4180.9, + "distances_to_centroid": { + "Carrboro": 1894.7, + "Lemon Grove": 5366.2, + "San Juan del Río": 4180.9, + "Englewood": 1719.7, + "Patdi": 12102.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Carrboro: (35.91°, -79.08°)", + " Lemon Grove: (32.74°, -117.03°)", + " San Juan del Río: (20.39°, -100.00°)", + " Englewood: (40.89°, -73.97°)", + " Patdi: (23.20°, 71.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Patdi: 12102.4 km from centroid", + " Lemon Grove: 5366.2 km from centroid", + " San Juan del Río: 4180.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Patdi", + "FINAL ANSWER: Patdi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.75752, + "lon": 87.13599, + "name": "Novokuznetsk" + }, + { + "lat": 50.4133, + "lon": 9.00638, + "name": "Nidda" + }, + { + "lat": 50.90395, + "lon": -1.40428, + "name": "Southampton" + }, + { + "lat": 50.5442, + "lon": 9.71792, + "name": "Künzell" + }, + { + "lat": -25.78842, + "lon": 31.05319, + "name": "Barberton" + } + ], + "question": "Which location is the geographic outlier among: Novokuznetsk, Nidda, Southampton, Künzell, Barberton?", + "ground_truth": { + "answer": "Barberton", + "outlier_distance_km": 6879.3, + "second_furthest_km": 4953.4, + "clarity_ratio": 1.39, + "median_distance_km": 2809.6, + "distances_to_centroid": { + "Novokuznetsk": 4953.4, + "Nidda": 2164.0, + "Southampton": 2809.6, + "Künzell": 2136.2, + "Barberton": 6879.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Novokuznetsk: (53.76°, 87.14°)", + " Nidda: (50.41°, 9.01°)", + " Southampton: (50.90°, -1.40°)", + " Künzell: (50.54°, 9.72°)", + " Barberton: (-25.79°, 31.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barberton: 6879.3 km from centroid", + " Novokuznetsk: 4953.4 km from centroid", + " Southampton: 2809.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barberton", + "FINAL ANSWER: Barberton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -18.91806, + "lon": -54.84417, + "name": "Rio Verde de Mato Grosso" + }, + { + "lat": -21.12, + "lon": -42.94278, + "name": "Ubá" + }, + { + "lat": -2.99, + "lon": -65.10833, + "name": "Uarini" + }, + { + "lat": -30.3875, + "lon": -56.45139, + "name": "Quaraí" + }, + { + "lat": 5.53711, + "lon": -0.69984, + "name": "Swedru" + } + ], + "question": "Which location is the geographic outlier among: Rio Verde de Mato Grosso, Ubá, Uarini, Quaraí, Swedru?", + "ground_truth": { + "answer": "Swedru", + "outlier_distance_km": 5231.6, + "second_furthest_km": 2599.6, + "clarity_ratio": 2.01, + "median_distance_km": 2263.2, + "distances_to_centroid": { + "Rio Verde de Mato Grosso": 1299.7, + "Ubá": 846.5, + "Uarini": 2599.6, + "Quaraí": 2263.2, + "Swedru": 5231.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Rio Verde de Mato Grosso: (-18.92°, -54.84°)", + " Ubá: (-21.12°, -42.94°)", + " Uarini: (-2.99°, -65.11°)", + " Quaraí: (-30.39°, -56.45°)", + " Swedru: (5.54°, -0.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Swedru: 5231.6 km from centroid", + " Uarini: 2599.6 km from centroid", + " Quaraí: 2263.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Swedru", + "FINAL ANSWER: Swedru" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.45197, + "lon": 3.33115, + "name": "Ajegunle" + }, + { + "lat": 6.01962, + "lon": 6.91729, + "name": "Nnewi" + }, + { + "lat": 8.939, + "lon": 4.78227, + "name": "Bode Saadu" + }, + { + "lat": 30.78847, + "lon": 31.00192, + "name": "Tanta" + }, + { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + } + ], + "question": "Which location is the geographic outlier among: Ajegunle, Nnewi, Bode Saadu, Tanta, Maroochydore?", + "ground_truth": { + "answer": "Maroochydore", + "outlier_distance_km": 12571.4, + "second_furthest_km": 4039.4, + "clarity_ratio": 3.11, + "median_distance_km": 3889.2, + "distances_to_centroid": { + "Ajegunle": 4039.4, + "Nnewi": 3643.0, + "Bode Saadu": 3889.2, + "Tanta": 3001.0, + "Maroochydore": 12571.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ajegunle: (6.45°, 3.33°)", + " Nnewi: (6.02°, 6.92°)", + " Bode Saadu: (8.94°, 4.78°)", + " Tanta: (30.79°, 31.00°)", + " Maroochydore: (-26.66°, 153.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maroochydore: 12571.4 km from centroid", + " Ajegunle: 4039.4 km from centroid", + " Bode Saadu: 3889.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maroochydore", + "FINAL ANSWER: Maroochydore" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.7426, + "lon": -2.997, + "name": "Lytham St Annes" + }, + { + "lat": 56.10921, + "lon": 94.58698, + "name": "Zelenogorsk" + }, + { + "lat": 59.76831, + "lon": 60.0062, + "name": "Karpinsk" + }, + { + "lat": 53.32641, + "lon": 9.86812, + "name": "Buchholz in der Nordheide" + }, + { + "lat": 39.61721, + "lon": -104.95081, + "name": "Greenwood Village" + } + ], + "question": "Which location is the geographic outlier among: Lytham St Annes, Zelenogorsk, Karpinsk, Buchholz in der Nordheide, Greenwood Village?", + "ground_truth": { + "answer": "Greenwood Village", + "outlier_distance_km": 8075.7, + "second_furthest_km": 5082.1, + "clarity_ratio": 1.59, + "median_distance_km": 3047.0, + "distances_to_centroid": { + "Lytham St Annes": 962.2, + "Zelenogorsk": 5082.1, + "Karpinsk": 3047.0, + "Buchholz in der Nordheide": 132.0, + "Greenwood Village": 8075.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lytham St Annes: (53.74°, -3.00°)", + " Zelenogorsk: (56.11°, 94.59°)", + " Karpinsk: (59.77°, 60.01°)", + " Buchholz in der Nordheide: (53.33°, 9.87°)", + " Greenwood Village: (39.62°, -104.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Greenwood Village: 8075.7 km from centroid", + " Zelenogorsk: 5082.1 km from centroid", + " Karpinsk: 3047.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Greenwood Village", + "FINAL ANSWER: Greenwood Village" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.42477, + "lon": -71.958, + "name": "San Carlos" + }, + { + "lat": -29.15, + "lon": -59.65, + "name": "Reconquista" + }, + { + "lat": -6.72917, + "lon": -38.44889, + "name": "São João do Rio do Peixe" + }, + { + "lat": 6.96321, + "lon": -75.41738, + "name": "Yarumal" + }, + { + "lat": -34.04526, + "lon": 24.92146, + "name": "Jeffreys Bay" + } + ], + "question": "Which location is the geographic outlier among: San Carlos, Reconquista, São João do Rio do Peixe, Yarumal, Jeffreys Bay?", + "ground_truth": { + "answer": "Jeffreys Bay", + "outlier_distance_km": 6896.1, + "second_furthest_km": 4543.0, + "clarity_ratio": 1.52, + "median_distance_km": 3272.5, + "distances_to_centroid": { + "San Carlos": 3272.5, + "Reconquista": 1877.1, + "São João do Rio do Peixe": 1584.6, + "Yarumal": 4543.0, + "Jeffreys Bay": 6896.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Carlos: (-36.42°, -71.96°)", + " Reconquista: (-29.15°, -59.65°)", + " São João do Rio do Peixe: (-6.73°, -38.45°)", + " Yarumal: (6.96°, -75.42°)", + " Jeffreys Bay: (-34.05°, 24.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Jeffreys Bay: 6896.1 km from centroid", + " Yarumal: 4543.0 km from centroid", + " San Carlos: 3272.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Jeffreys Bay", + "FINAL ANSWER: Jeffreys Bay" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.43084, + "lon": 152.90894, + "name": "Port Macquarie" + }, + { + "lat": -32.32889, + "lon": 115.83047, + "name": "Baldivis" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": -36.9382, + "lon": 174.84019, + "name": "Otahuhu" + }, + { + "lat": -14.79083, + "lon": -71.40986, + "name": "Yauri" + } + ], + "question": "Which location is the geographic outlier among: Port Macquarie, Baldivis, Chatswood, Otahuhu, Yauri?", + "ground_truth": { + "answer": "Yauri", + "outlier_distance_km": 15032.6, + "second_furthest_km": 6416.0, + "clarity_ratio": 2.34, + "median_distance_km": 4580.6, + "distances_to_centroid": { + "Port Macquarie": 4580.6, + "Baldivis": 1097.0, + "Chatswood": 4379.2, + "Otahuhu": 6416.0, + "Yauri": 15032.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Port Macquarie: (-31.43°, 152.91°)", + " Baldivis: (-32.33°, 115.83°)", + " Chatswood: (-33.80°, 151.18°)", + " Otahuhu: (-36.94°, 174.84°)", + " Yauri: (-14.79°, -71.41°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yauri: 15032.6 km from centroid", + " Otahuhu: 6416.0 km from centroid", + " Port Macquarie: 4580.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yauri", + "FINAL ANSWER: Yauri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.08401, + "lon": 18.82113, + "name": "Somerset West" + }, + { + "lat": 7.93333, + "lon": 38.71667, + "name": "Ziway" + }, + { + "lat": -34.58301, + "lon": 19.35048, + "name": "Gansbaai" + }, + { + "lat": -27.28115, + "lon": 27.9709, + "name": "Heilbron" + }, + { + "lat": 19.41116, + "lon": -102.05644, + "name": "Uruapan" + } + ], + "question": "Which location is the geographic outlier among: Somerset West, Ziway, Gansbaai, Heilbron, Uruapan?", + "ground_truth": { + "answer": "Uruapan", + "outlier_distance_km": 11808.7, + "second_furthest_km": 4851.1, + "clarity_ratio": 2.43, + "median_distance_km": 3217.1, + "distances_to_centroid": { + "Somerset West": 2917.2, + "Ziway": 4851.1, + "Gansbaai": 2990.9, + "Heilbron": 3217.1, + "Uruapan": 11808.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Somerset West: (-34.08°, 18.82°)", + " Ziway: (7.93°, 38.72°)", + " Gansbaai: (-34.58°, 19.35°)", + " Heilbron: (-27.28°, 27.97°)", + " Uruapan: (19.41°, -102.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Uruapan: 11808.7 km from centroid", + " Ziway: 4851.1 km from centroid", + " Heilbron: 3217.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Uruapan", + "FINAL ANSWER: Uruapan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.13873, + "lon": -45.11881, + "name": "Olho d’Água das Cunhãs" + }, + { + "lat": -12.5125, + "lon": -38.49528, + "name": "São Sebastião do Passé" + }, + { + "lat": -4.22583, + "lon": -38.73056, + "name": "Redenção" + }, + { + "lat": -31.43722, + "lon": -68.52556, + "name": "Albardón" + }, + { + "lat": -33.75881, + "lon": 150.99292, + "name": "Baulkham Hills" + } + ], + "question": "Which location is the geographic outlier among: Olho d’Água das Cunhãs, São Sebastião do Passé, Redenção, Albardón, Baulkham Hills?", + "ground_truth": { + "answer": "Baulkham Hills", + "outlier_distance_km": 13924.3, + "second_furthest_km": 6258.6, + "clarity_ratio": 2.22, + "median_distance_km": 4299.6, + "distances_to_centroid": { + "Olho d’Água das Cunhãs": 4299.6, + "São Sebastião do Passé": 3317.8, + "Redenção": 3648.7, + "Albardón": 6258.6, + "Baulkham Hills": 13924.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Olho d’Água das Cunhãs: (-4.14°, -45.12°)", + " São Sebastião do Passé: (-12.51°, -38.50°)", + " Redenção: (-4.23°, -38.73°)", + " Albardón: (-31.44°, -68.53°)", + " Baulkham Hills: (-33.76°, 150.99°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baulkham Hills: 13924.3 km from centroid", + " Albardón: 6258.6 km from centroid", + " Olho d’Água das Cunhãs: 4299.6 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": 19.09917, + "lon": -98.25417, + "name": "Sanctorum" + }, + { + "lat": 39.61366, + "lon": -86.10665, + "name": "Greenwood" + }, + { + "lat": 38.84622, + "lon": -77.30637, + "name": "Fairfax" + }, + { + "lat": 41.68199, + "lon": -85.97667, + "name": "Elkhart" + }, + { + "lat": -26.1844, + "lon": 27.70203, + "name": "Randfontein" + } + ], + "question": "Which location is the geographic outlier among: Sanctorum, Greenwood, Fairfax, Elkhart, Randfontein?", + "ground_truth": { + "answer": "Randfontein", + "outlier_distance_km": 11252.0, + "second_furthest_km": 3574.2, + "clarity_ratio": 3.15, + "median_distance_km": 2946.2, + "distances_to_centroid": { + "Sanctorum": 3574.2, + "Greenwood": 2815.1, + "Fairfax": 2203.4, + "Elkhart": 2946.2, + "Randfontein": 11252.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sanctorum: (19.10°, -98.25°)", + " Greenwood: (39.61°, -86.11°)", + " Fairfax: (38.85°, -77.31°)", + " Elkhart: (41.68°, -85.98°)", + " Randfontein: (-26.18°, 27.70°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Randfontein: 11252.0 km from centroid", + " Sanctorum: 3574.2 km from centroid", + " Elkhart: 2946.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Randfontein", + "FINAL ANSWER: Randfontein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8, + "lon": 145.28333, + "name": "Croydon" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -27.35364, + "lon": 152.96848, + "name": "Albany Creek" + }, + { + "lat": -26.53333, + "lon": 29.06667, + "name": "eMbalenhle" + } + ], + "question": "Which location is the geographic outlier among: Croydon, Chatswood, Mandurah, Albany Creek, eMbalenhle?", + "ground_truth": { + "answer": "eMbalenhle", + "outlier_distance_km": 8482.8, + "second_furthest_km": 3323.3, + "clarity_ratio": 2.55, + "median_distance_km": 3023.4, + "distances_to_centroid": { + "Croydon": 2503.7, + "Chatswood": 3023.4, + "Mandurah": 311.7, + "Albany Creek": 3323.3, + "eMbalenhle": 8482.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Croydon: (-37.80°, 145.28°)", + " Chatswood: (-33.80°, 151.18°)", + " Mandurah: (-32.53°, 115.72°)", + " Albany Creek: (-27.35°, 152.97°)", + " eMbalenhle: (-26.53°, 29.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " eMbalenhle: 8482.8 km from centroid", + " Albany Creek: 3323.3 km from centroid", + " Chatswood: 3023.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: eMbalenhle", + "FINAL ANSWER: eMbalenhle" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.21398, + "lon": -83.29489, + "name": "Morristown" + }, + { + "lat": 38.96955, + "lon": -77.3861, + "name": "Herndon" + }, + { + "lat": 42.58759, + "lon": -72.59953, + "name": "Greenfield" + }, + { + "lat": 40.68038, + "lon": -73.45512, + "name": "Massapequa Park" + }, + { + "lat": 31.24193, + "lon": 30.94504, + "name": "Ar Riyāḑ" + } + ], + "question": "Which location is the geographic outlier among: Morristown, Herndon, Greenfield, Massapequa Park, Ar Riyāḑ?", + "ground_truth": { + "answer": "Ar Riyāḑ", + "outlier_distance_km": 7629.2, + "second_furthest_km": 2494.0, + "clarity_ratio": 3.06, + "median_distance_km": 1934.1, + "distances_to_centroid": { + "Morristown": 2494.0, + "Herndon": 1934.1, + "Greenfield": 1564.1, + "Massapequa Park": 1600.3, + "Ar Riyāḑ": 7629.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morristown: (36.21°, -83.29°)", + " Herndon: (38.97°, -77.39°)", + " Greenfield: (42.59°, -72.60°)", + " Massapequa Park: (40.68°, -73.46°)", + " Ar Riyāḑ: (31.24°, 30.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ar Riyāḑ: 7629.2 km from centroid", + " Morristown: 2494.0 km from centroid", + " Herndon: 1934.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ar Riyāḑ", + "FINAL ANSWER: Ar Riyāḑ" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.45195, + "lon": -1.57866, + "name": "Bekwai" + }, + { + "lat": 8.1, + "lon": 36.95, + "name": "Suntu" + }, + { + "lat": -1.17139, + "lon": 36.83556, + "name": "Kiambu" + }, + { + "lat": -26.05501, + "lon": 30.82292, + "name": "Lukwatini" + }, + { + "lat": -21.09, + "lon": -45.56583, + "name": "Boa Esperança" + } + ], + "question": "Which location is the geographic outlier among: Bekwai, Suntu, Kiambu, Lukwatini, Boa Esperança?", + "ground_truth": { + "answer": "Boa Esperança", + "outlier_distance_km": 6326.6, + "second_furthest_km": 3270.2, + "clarity_ratio": 1.93, + "median_distance_km": 2967.1, + "distances_to_centroid": { + "Bekwai": 2063.8, + "Suntu": 3270.2, + "Kiambu": 2877.7, + "Lukwatini": 2967.1, + "Boa Esperança": 6326.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bekwai: (6.45°, -1.58°)", + " Suntu: (8.10°, 36.95°)", + " Kiambu: (-1.17°, 36.84°)", + " Lukwatini: (-26.06°, 30.82°)", + " Boa Esperança: (-21.09°, -45.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Boa Esperança: 6326.6 km from centroid", + " Suntu: 3270.2 km from centroid", + " Lukwatini: 2967.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Boa Esperança", + "FINAL ANSWER: Boa Esperança" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + }, + { + "lat": -13.48694, + "lon": -39.04389, + "name": "Cairu" + } + ], + "question": "Which location is the geographic outlier among: Newcastle, Epping, Glen Waverley, Warwick, Cairu?", + "ground_truth": { + "answer": "Cairu", + "outlier_distance_km": 14208.4, + "second_furthest_km": 3970.3, + "clarity_ratio": 3.58, + "median_distance_km": 3857.2, + "distances_to_centroid": { + "Newcastle": 3857.2, + "Epping": 3236.4, + "Glen Waverley": 3250.2, + "Warwick": 3970.3, + "Cairu": 14208.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newcastle: (-32.93°, 151.78°)", + " Epping: (-37.65°, 145.03°)", + " Glen Waverley: (-37.88°, 145.16°)", + " Warwick: (-28.22°, 152.03°)", + " Cairu: (-13.49°, -39.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cairu: 14208.4 km from centroid", + " Warwick: 3970.3 km from centroid", + " Newcastle: 3857.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cairu", + "FINAL ANSWER: Cairu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -38.11342, + "lon": 145.28326, + "name": "Cranbourne" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + }, + { + "lat": -37.8, + "lon": 144.9, + "name": "Footscray" + }, + { + "lat": -27.87683, + "lon": 153.28572, + "name": "Upper Coomera" + }, + { + "lat": -29.58667, + "lon": -51.37556, + "name": "São Sebastião do Caí" + } + ], + "question": "Which location is the geographic outlier among: Cranbourne, Liverpool, Footscray, Upper Coomera, São Sebastião do Caí?", + "ground_truth": { + "answer": "São Sebastião do Caí", + "outlier_distance_km": 12695.0, + "second_furthest_km": 4285.7, + "clarity_ratio": 2.96, + "median_distance_km": 3887.6, + "distances_to_centroid": { + "Cranbourne": 3326.9, + "Liverpool": 3887.6, + "Footscray": 3294.9, + "Upper Coomera": 4285.7, + "São Sebastião do Caí": 12695.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cranbourne: (-38.11°, 145.28°)", + " Liverpool: (-33.92°, 150.93°)", + " Footscray: (-37.80°, 144.90°)", + " Upper Coomera: (-27.88°, 153.29°)", + " 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: 12695.0 km from centroid", + " Upper Coomera: 4285.7 km from centroid", + " Liverpool: 3887.6 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": -16.06583, + "lon": -47.97861, + "name": "Valparaíso de Goiás" + }, + { + "lat": -9.47833, + "lon": -35.85333, + "name": "Rio Largo" + }, + { + "lat": -5.73333, + "lon": -44.15833, + "name": "Fortuna" + }, + { + "lat": -2.76194, + "lon": -42.27444, + "name": "Tutóia" + }, + { + "lat": 30.7263, + "lon": 107.65726, + "name": "Mingda" + } + ], + "question": "Which location is the geographic outlier among: Valparaíso de Goiás, Rio Largo, Fortuna, Tutóia, Mingda?", + "ground_truth": { + "answer": "Mingda", + "outlier_distance_km": 12896.0, + "second_furthest_km": 4247.4, + "clarity_ratio": 3.04, + "median_distance_km": 3556.1, + "distances_to_centroid": { + "Valparaíso de Goiás": 4247.4, + "Rio Largo": 2761.3, + "Fortuna": 3556.1, + "Tutóia": 3314.9, + "Mingda": 12896.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Valparaíso de Goiás: (-16.07°, -47.98°)", + " Rio Largo: (-9.48°, -35.85°)", + " Fortuna: (-5.73°, -44.16°)", + " Tutóia: (-2.76°, -42.27°)", + " Mingda: (30.73°, 107.66°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mingda: 12896.0 km from centroid", + " Valparaíso de Goiás: 4247.4 km from centroid", + " Fortuna: 3556.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mingda", + "FINAL ANSWER: Mingda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.35869, + "lon": -80.0831, + "name": "Boca Raton" + }, + { + "lat": 38.64255, + "lon": -90.32373, + "name": "Clayton" + }, + { + "lat": 40.84288, + "lon": -73.29289, + "name": "Commack" + }, + { + "lat": 40.56233, + "lon": -74.13986, + "name": "Staten Island" + }, + { + "lat": -36.96587, + "lon": 174.82389, + "name": "Mangere East" + } + ], + "question": "Which location is the geographic outlier among: Boca Raton, Clayton, Commack, Staten Island, Mangere East?", + "ground_truth": { + "answer": "Mangere East", + "outlier_distance_km": 17207.5, + "second_furthest_km": 6095.6, + "clarity_ratio": 2.82, + "median_distance_km": 5214.6, + "distances_to_centroid": { + "Boca Raton": 5214.6, + "Clayton": 6095.6, + "Commack": 4673.0, + "Staten Island": 4736.0, + "Mangere East": 17207.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Boca Raton: (26.36°, -80.08°)", + " Clayton: (38.64°, -90.32°)", + " Commack: (40.84°, -73.29°)", + " Staten Island: (40.56°, -74.14°)", + " Mangere East: (-36.97°, 174.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mangere East: 17207.5 km from centroid", + " Clayton: 6095.6 km from centroid", + " Boca Raton: 5214.6 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": -26.71667, + "lon": 27.1, + "name": "Potchefstroom" + }, + { + "lat": -23.30246, + "lon": 30.71868, + "name": "Giyani" + }, + { + "lat": 7.13333, + "lon": 37.95, + "name": "Shonē" + }, + { + "lat": -1.24627, + "lon": 36.66291, + "name": "Kikuyu" + }, + { + "lat": 50.0888, + "lon": 9.06455, + "name": "Alzenau in Unterfranken" + } + ], + "question": "Which location is the geographic outlier among: Potchefstroom, Giyani, Shonē, Kikuyu, Alzenau in Unterfranken?", + "ground_truth": { + "answer": "Alzenau in Unterfranken", + "outlier_distance_km": 5734.0, + "second_furthest_km": 3105.9, + "clarity_ratio": 1.85, + "median_distance_km": 2736.1, + "distances_to_centroid": { + "Potchefstroom": 3105.9, + "Giyani": 2736.1, + "Shonē": 1257.4, + "Kikuyu": 968.6, + "Alzenau in Unterfranken": 5734.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Potchefstroom: (-26.72°, 27.10°)", + " Giyani: (-23.30°, 30.72°)", + " Shonē: (7.13°, 37.95°)", + " Kikuyu: (-1.25°, 36.66°)", + " Alzenau in Unterfranken: (50.09°, 9.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Alzenau in Unterfranken: 5734.0 km from centroid", + " Potchefstroom: 3105.9 km from centroid", + " Giyani: 2736.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Alzenau in Unterfranken", + "FINAL ANSWER: Alzenau in Unterfranken" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 43.64791, + "lon": -79.40849, + "name": "Trinity-Bellwoods" + }, + { + "lat": 41.76371, + "lon": -72.68509, + "name": "Hartford" + }, + { + "lat": 19.71306, + "lon": -98.96833, + "name": "Tecámac de Felipe Villanueva" + }, + { + "lat": 19.02492, + "lon": -102.09318, + "name": "Nueva Italia de Ruiz" + }, + { + "lat": 7.28889, + "lon": 36.24167, + "name": "Bonga" + } + ], + "question": "Which location is the geographic outlier among: Trinity-Bellwoods, Hartford, Tecámac de Felipe Villanueva, Nueva Italia de Ruiz, Bonga?", + "ground_truth": { + "answer": "Bonga", + "outlier_distance_km": 10597.7, + "second_furthest_km": 4038.1, + "clarity_ratio": 2.62, + "median_distance_km": 3702.9, + "distances_to_centroid": { + "Trinity-Bellwoods": 2411.2, + "Hartford": 1919.7, + "Tecámac de Felipe Villanueva": 3702.9, + "Nueva Italia de Ruiz": 4038.1, + "Bonga": 10597.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Trinity-Bellwoods: (43.65°, -79.41°)", + " Hartford: (41.76°, -72.69°)", + " Tecámac de Felipe Villanueva: (19.71°, -98.97°)", + " Nueva Italia de Ruiz: (19.02°, -102.09°)", + " Bonga: (7.29°, 36.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bonga: 10597.7 km from centroid", + " Nueva Italia de Ruiz: 4038.1 km from centroid", + " Tecámac de Felipe Villanueva: 3702.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bonga", + "FINAL ANSWER: Bonga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -0.49887, + "lon": 37.28031, + "name": "Kerugoya" + }, + { + "lat": 14.07294, + "lon": 36.56828, + "name": "May Cadera" + }, + { + "lat": 5.78917, + "lon": 7.83829, + "name": "Amaigbo" + }, + { + "lat": 7.94783, + "lon": 4.78836, + "name": "Otan Ayegbaju" + }, + { + "lat": -16.39899, + "lon": -71.53747, + "name": "Arequipa" + } + ], + "question": "Which location is the geographic outlier among: Kerugoya, May Cadera, Amaigbo, Otan Ayegbaju, Arequipa?", + "ground_truth": { + "answer": "Arequipa", + "outlier_distance_km": 8430.4, + "second_furthest_km": 3918.1, + "clarity_ratio": 2.15, + "median_distance_km": 3824.0, + "distances_to_centroid": { + "Kerugoya": 3824.0, + "May Cadera": 3918.1, + "Amaigbo": 671.0, + "Otan Ayegbaju": 671.4, + "Arequipa": 8430.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kerugoya: (-0.50°, 37.28°)", + " May Cadera: (14.07°, 36.57°)", + " Amaigbo: (5.79°, 7.84°)", + " Otan Ayegbaju: (7.95°, 4.79°)", + " Arequipa: (-16.40°, -71.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Arequipa: 8430.4 km from centroid", + " May Cadera: 3918.1 km from centroid", + " Kerugoya: 3824.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Arequipa", + "FINAL ANSWER: Arequipa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.71056, + "lon": -46.41333, + "name": "Ribeirão Pires" + }, + { + "lat": 6.28535, + "lon": -75.33385, + "name": "San Vicente" + }, + { + "lat": -12.78691, + "lon": -74.97298, + "name": "Huancavelica" + }, + { + "lat": -7.74778, + "lon": -34.82556, + "name": "Ilha de Itamaracá" + }, + { + "lat": 28.35831, + "lon": 33.07829, + "name": "Ras Gharib" + } + ], + "question": "Which location is the geographic outlier among: Ribeirão Pires, San Vicente, Huancavelica, Ilha de Itamaracá, Ras Gharib?", + "ground_truth": { + "answer": "Ras Gharib", + "outlier_distance_km": 8433.4, + "second_furthest_km": 4067.1, + "clarity_ratio": 2.07, + "median_distance_km": 4060.5, + "distances_to_centroid": { + "Ribeirão Pires": 2528.7, + "San Vicente": 4060.5, + "Huancavelica": 4067.1, + "Ilha de Itamaracá": 842.9, + "Ras Gharib": 8433.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ribeirão Pires: (-23.71°, -46.41°)", + " San Vicente: (6.29°, -75.33°)", + " Huancavelica: (-12.79°, -74.97°)", + " Ilha de Itamaracá: (-7.75°, -34.83°)", + " Ras Gharib: (28.36°, 33.08°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ras Gharib: 8433.4 km from centroid", + " Huancavelica: 4067.1 km from centroid", + " San Vicente: 4060.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ras Gharib", + "FINAL ANSWER: Ras Gharib" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 29.56884, + "lon": -97.96473, + "name": "Seguin" + }, + { + "lat": 39.84395, + "lon": -84.12466, + "name": "Huber Heights" + }, + { + "lat": 35.28275, + "lon": -120.65962, + "name": "San Luis Obispo" + }, + { + "lat": 38.61095, + "lon": -77.33971, + "name": "Montclair" + }, + { + "lat": -37.75, + "lon": 145.01667, + "name": "Preston" + } + ], + "question": "Which location is the geographic outlier among: Seguin, Huber Heights, San Luis Obispo, Montclair, Preston?", + "ground_truth": { + "answer": "Preston", + "outlier_distance_km": 17833.2, + "second_furthest_km": 7228.7, + "clarity_ratio": 2.47, + "median_distance_km": 5165.7, + "distances_to_centroid": { + "Seguin": 5165.7, + "Huber Heights": 4078.8, + "San Luis Obispo": 7228.7, + "Montclair": 3486.3, + "Preston": 17833.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Seguin: (29.57°, -97.96°)", + " Huber Heights: (39.84°, -84.12°)", + " San Luis Obispo: (35.28°, -120.66°)", + " Montclair: (38.61°, -77.34°)", + " Preston: (-37.75°, 145.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Preston: 17833.2 km from centroid", + " San Luis Obispo: 7228.7 km from centroid", + " Seguin: 5165.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Preston", + "FINAL ANSWER: Preston" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.6021, + "lon": -3.34211, + "name": "Pontypridd" + }, + { + "lat": 53.7446, + "lon": -0.33525, + "name": "Kingston upon Hull" + }, + { + "lat": 48.8898, + "lon": 2.15863, + "name": "Chatou" + }, + { + "lat": 45.11326, + "lon": 41.0365, + "name": "Novokubansk" + }, + { + "lat": -33.91667, + "lon": 151.03333, + "name": "Bankstown" + } + ], + "question": "Which location is the geographic outlier among: Pontypridd, Kingston upon Hull, Chatou, Novokubansk, Bankstown?", + "ground_truth": { + "answer": "Bankstown", + "outlier_distance_km": 13913.7, + "second_furthest_km": 3905.9, + "clarity_ratio": 3.56, + "median_distance_km": 3789.2, + "distances_to_centroid": { + "Pontypridd": 3905.9, + "Kingston upon Hull": 3789.2, + "Chatou": 3445.8, + "Novokubansk": 1360.7, + "Bankstown": 13913.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pontypridd: (51.60°, -3.34°)", + " Kingston upon Hull: (53.74°, -0.34°)", + " Chatou: (48.89°, 2.16°)", + " Novokubansk: (45.11°, 41.04°)", + " Bankstown: (-33.92°, 151.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bankstown: 13913.7 km from centroid", + " Pontypridd: 3905.9 km from centroid", + " Kingston upon Hull: 3789.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bankstown", + "FINAL ANSWER: Bankstown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.72677, + "lon": -73.6343, + "name": "Garden City" + }, + { + "lat": 38.20091, + "lon": -84.87328, + "name": "Frankfort" + }, + { + "lat": 33.41477, + "lon": -111.90931, + "name": "Tempe" + }, + { + "lat": 18.42131, + "lon": -95.11398, + "name": "Catemaco" + }, + { + "lat": 9.63497, + "lon": 106.49237, + "name": "Duyên Hải" + } + ], + "question": "Which location is the geographic outlier among: Garden City, Frankfort, Tempe, Catemaco, Duyên Hải?", + "ground_truth": { + "answer": "Duyên Hải", + "outlier_distance_km": 15215.7, + "second_furthest_km": 5695.6, + "clarity_ratio": 2.67, + "median_distance_km": 4528.1, + "distances_to_centroid": { + "Garden City": 2435.7, + "Frankfort": 3257.0, + "Tempe": 5695.6, + "Catemaco": 4528.1, + "Duyên Hải": 15215.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Garden City: (40.73°, -73.63°)", + " Frankfort: (38.20°, -84.87°)", + " Tempe: (33.41°, -111.91°)", + " Catemaco: (18.42°, -95.11°)", + " Duyên Hải: (9.63°, 106.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Duyên Hải: 15215.7 km from centroid", + " Tempe: 5695.6 km from centroid", + " Catemaco: 4528.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Duyên Hải", + "FINAL ANSWER: Duyên Hải" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.05584, + "lon": 145.90375, + "name": "Burnie" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": -36.12179, + "lon": 146.88809, + "name": "Wodonga" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + }, + { + "lat": 54.06398, + "lon": 54.93378, + "name": "Rayevskiy" + } + ], + "question": "Which location is the geographic outlier among: Burnie, The Gap, Wodonga, Glenferrie, Rayevskiy?", + "ground_truth": { + "answer": "Rayevskiy", + "outlier_distance_km": 10605.4, + "second_furthest_km": 3052.7, + "clarity_ratio": 3.47, + "median_distance_km": 2724.5, + "distances_to_centroid": { + "Burnie": 3052.7, + "The Gap": 2667.3, + "Wodonga": 2692.5, + "Glenferrie": 2724.5, + "Rayevskiy": 10605.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Burnie: (-41.06°, 145.90°)", + " The Gap: (-27.44°, 152.94°)", + " Wodonga: (-36.12°, 146.89°)", + " Glenferrie: (-37.83°, 145.05°)", + " Rayevskiy: (54.06°, 54.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rayevskiy: 10605.4 km from centroid", + " Burnie: 3052.7 km from centroid", + " Glenferrie: 2724.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rayevskiy", + "FINAL ANSWER: Rayevskiy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -25.88278, + "lon": -48.57472, + "name": "Guaratuba" + }, + { + "lat": -18.44833, + "lon": -50.45167, + "name": "Quirinópolis" + }, + { + "lat": -13.44083, + "lon": -49.14861, + "name": "Porangatu" + }, + { + "lat": -27.34361, + "lon": -51.61194, + "name": "Capinzal" + }, + { + "lat": 40.04622, + "lon": -75.35991, + "name": "Radnor" + } + ], + "question": "Which location is the geographic outlier among: Guaratuba, Quirinópolis, Porangatu, Capinzal, Radnor?", + "ground_truth": { + "answer": "Radnor", + "outlier_distance_km": 5842.5, + "second_furthest_km": 2069.5, + "clarity_ratio": 2.82, + "median_distance_km": 1995.7, + "distances_to_centroid": { + "Guaratuba": 1995.7, + "Quirinópolis": 1159.5, + "Porangatu": 808.4, + "Capinzal": 2069.5, + "Radnor": 5842.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Guaratuba: (-25.88°, -48.57°)", + " Quirinópolis: (-18.45°, -50.45°)", + " Porangatu: (-13.44°, -49.15°)", + " Capinzal: (-27.34°, -51.61°)", + " Radnor: (40.05°, -75.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Radnor: 5842.5 km from centroid", + " Capinzal: 2069.5 km from centroid", + " Guaratuba: 1995.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Radnor", + "FINAL ANSWER: Radnor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 12.51921, + "lon": 78.21382, + "name": "Krishnagiri" + }, + { + "lat": 13.921, + "lon": 122.1002, + "name": "Gumaca" + }, + { + "lat": 41.71972, + "lon": 125.92639, + "name": "Tonghua" + }, + { + "lat": 35.43333, + "lon": 126.7, + "name": "Koch'ang" + }, + { + "lat": -28.21344, + "lon": -49.16383, + "name": "São José" + } + ], + "question": "Which location is the geographic outlier among: Krishnagiri, Gumaca, Tonghua, Koch'ang, São José?", + "ground_truth": { + "answer": "São José", + "outlier_distance_km": 14676.3, + "second_furthest_km": 5233.2, + "clarity_ratio": 2.8, + "median_distance_km": 5086.5, + "distances_to_centroid": { + "Krishnagiri": 395.1, + "Gumaca": 4446.3, + "Tonghua": 5233.2, + "Koch'ang": 5086.5, + "São José": 14676.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Krishnagiri: (12.52°, 78.21°)", + " Gumaca: (13.92°, 122.10°)", + " Tonghua: (41.72°, 125.93°)", + " Koch'ang: (35.43°, 126.70°)", + " São José: (-28.21°, -49.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " São José: 14676.3 km from centroid", + " Tonghua: 5233.2 km from centroid", + " Koch'ang: 5086.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: São José", + "FINAL ANSWER: São José" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 7.68287, + "lon": 4.81769, + "name": "Ijebu-Jesa" + }, + { + "lat": 6.71897, + "lon": -1.61188, + "name": "New Tafo" + }, + { + "lat": 5.61455, + "lon": 7.81191, + "name": "Ohafia-Ifigh" + }, + { + "lat": 7.11345, + "lon": 6.73866, + "name": "Idah" + }, + { + "lat": -7.99194, + "lon": -38.29833, + "name": "Serra Talhada" + } + ], + "question": "Which location is the geographic outlier among: Ijebu-Jesa, New Tafo, Ohafia-Ifigh, Idah, Serra Talhada?", + "ground_truth": { + "answer": "Serra Talhada", + "outlier_distance_km": 4013.6, + "second_furthest_km": 1335.8, + "clarity_ratio": 3.0, + "median_distance_km": 1254.8, + "distances_to_centroid": { + "Ijebu-Jesa": 1076.4, + "New Tafo": 424.0, + "Ohafia-Ifigh": 1335.8, + "Idah": 1254.8, + "Serra Talhada": 4013.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ijebu-Jesa: (7.68°, 4.82°)", + " New Tafo: (6.72°, -1.61°)", + " Ohafia-Ifigh: (5.61°, 7.81°)", + " Idah: (7.11°, 6.74°)", + " Serra Talhada: (-7.99°, -38.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Serra Talhada: 4013.6 km from centroid", + " Ohafia-Ifigh: 1335.8 km from centroid", + " Idah: 1254.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Serra Talhada", + "FINAL ANSWER: Serra Talhada" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.9992, + "lon": 10.41062, + "name": "Darazo" + }, + { + "lat": 8.58679, + "lon": 39.12111, + "name": "Mojo" + }, + { + "lat": 7.15109, + "lon": 35.81703, + "name": "Wacha" + }, + { + "lat": 9.87342, + "lon": 7.95407, + "name": "Kachia" + }, + { + "lat": 10.32361, + "lon": 123.92222, + "name": "Mandaue City" + } + ], + "question": "Which location is the geographic outlier among: Darazo, Mojo, Wacha, Kachia, Mandaue City?", + "ground_truth": { + "answer": "Mandaue City", + "outlier_distance_km": 8790.9, + "second_furthest_km": 3889.4, + "clarity_ratio": 2.26, + "median_distance_km": 3618.0, + "distances_to_centroid": { + "Darazo": 3618.0, + "Mojo": 483.1, + "Wacha": 875.3, + "Kachia": 3889.4, + "Mandaue City": 8790.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Darazo: (11.00°, 10.41°)", + " Mojo: (8.59°, 39.12°)", + " Wacha: (7.15°, 35.82°)", + " Kachia: (9.87°, 7.95°)", + " Mandaue City: (10.32°, 123.92°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mandaue City: 8790.9 km from centroid", + " Kachia: 3889.4 km from centroid", + " Darazo: 3618.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mandaue City", + "FINAL ANSWER: Mandaue City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.68149, + "lon": -73.39984, + "name": "Copiague" + }, + { + "lat": 24.55524, + "lon": -81.78163, + "name": "Key West" + }, + { + "lat": 25.94065, + "lon": -80.2456, + "name": "Carol City" + }, + { + "lat": 40.88939, + "lon": -111.88077, + "name": "Bountiful" + }, + { + "lat": -13.62611, + "lon": -41.32694, + "name": "Barra da Estiva" + } + ], + "question": "Which location is the geographic outlier among: Copiague, Key West, Carol City, Bountiful, Barra da Estiva?", + "ground_truth": { + "answer": "Barra da Estiva", + "outlier_distance_km": 5733.3, + "second_furthest_km": 3702.0, + "clarity_ratio": 1.55, + "median_distance_km": 1932.3, + "distances_to_centroid": { + "Copiague": 1932.3, + "Key West": 422.6, + "Carol City": 356.8, + "Bountiful": 3702.0, + "Barra da Estiva": 5733.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Copiague: (40.68°, -73.40°)", + " Key West: (24.56°, -81.78°)", + " Carol City: (25.94°, -80.25°)", + " Bountiful: (40.89°, -111.88°)", + " Barra da Estiva: (-13.63°, -41.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Barra da Estiva: 5733.3 km from centroid", + " Bountiful: 3702.0 km from centroid", + " Copiague: 1932.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Barra da Estiva", + "FINAL ANSWER: Barra da Estiva" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -5.10667, + "lon": -38.3725, + "name": "Morada Nova" + }, + { + "lat": -19.27444, + "lon": -44.40417, + "name": "Paraopeba" + }, + { + "lat": -8.09056, + "lon": -39.57833, + "name": "Parnamirim" + }, + { + "lat": -22.95972, + "lon": -44.04056, + "name": "Mangaratiba" + }, + { + "lat": 55.66951, + "lon": 86.27485, + "name": "Berëzovskiy" + } + ], + "question": "Which location is the geographic outlier among: Morada Nova, Paraopeba, Parnamirim, Mangaratiba, Berëzovskiy?", + "ground_truth": { + "answer": "Berëzovskiy", + "outlier_distance_km": 10770.4, + "second_furthest_km": 3964.5, + "clarity_ratio": 2.72, + "median_distance_km": 3767.1, + "distances_to_centroid": { + "Morada Nova": 2547.0, + "Paraopeba": 3767.1, + "Parnamirim": 2762.7, + "Mangaratiba": 3964.5, + "Berëzovskiy": 10770.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morada Nova: (-5.11°, -38.37°)", + " Paraopeba: (-19.27°, -44.40°)", + " Parnamirim: (-8.09°, -39.58°)", + " Mangaratiba: (-22.96°, -44.04°)", + " Berëzovskiy: (55.67°, 86.27°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Berëzovskiy: 10770.4 km from centroid", + " Mangaratiba: 3964.5 km from centroid", + " Paraopeba: 3767.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Berëzovskiy", + "FINAL ANSWER: Berëzovskiy" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -24.15667, + "lon": -54.09694, + "name": "Terra Roxa" + }, + { + "lat": -31.64881, + "lon": -60.70868, + "name": "Santa Fe" + }, + { + "lat": -12.67, + "lon": -39.10194, + "name": "Cruz das Almas" + }, + { + "lat": -26.48417, + "lon": -51.99056, + "name": "Palmas" + }, + { + "lat": 11.73333, + "lon": 38.46667, + "name": "Nefas Mewch’a" + } + ], + "question": "Which location is the geographic outlier among: Terra Roxa, Santa Fe, Cruz das Almas, Palmas, Nefas Mewch’a?", + "ground_truth": { + "answer": "Nefas Mewch’a", + "outlier_distance_km": 8513.5, + "second_furthest_km": 3212.1, + "clarity_ratio": 2.65, + "median_distance_km": 2301.4, + "distances_to_centroid": { + "Terra Roxa": 2301.4, + "Santa Fe": 3212.1, + "Cruz das Almas": 748.4, + "Palmas": 2200.2, + "Nefas Mewch’a": 8513.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Terra Roxa: (-24.16°, -54.10°)", + " Santa Fe: (-31.65°, -60.71°)", + " Cruz das Almas: (-12.67°, -39.10°)", + " Palmas: (-26.48°, -51.99°)", + " Nefas Mewch’a: (11.73°, 38.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nefas Mewch’a: 8513.5 km from centroid", + " Santa Fe: 3212.1 km from centroid", + " Terra Roxa: 2301.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nefas Mewch’a", + "FINAL ANSWER: Nefas Mewch’a" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.18924, + "lon": -98.15529, + "name": "San Juan" + }, + { + "lat": 32.93457, + "lon": -97.25168, + "name": "Keller" + }, + { + "lat": 46.04178, + "lon": -73.11358, + "name": "Sorel-Tracy" + }, + { + "lat": 40.8501, + "lon": -73.93541, + "name": "Washington Heights" + }, + { + "lat": -33.91075, + "lon": 19.1198, + "name": "Franschhoek" + } + ], + "question": "Which location is the geographic outlier among: San Juan, Keller, Sorel-Tracy, Washington Heights, Franschhoek?", + "ground_truth": { + "answer": "Franschhoek", + "outlier_distance_km": 10836.6, + "second_furthest_km": 3410.1, + "clarity_ratio": 3.18, + "median_distance_km": 3398.2, + "distances_to_centroid": { + "San Juan": 3410.1, + "Keller": 3398.2, + "Sorel-Tracy": 2735.1, + "Washington Heights": 2225.9, + "Franschhoek": 10836.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Juan: (26.19°, -98.16°)", + " Keller: (32.93°, -97.25°)", + " Sorel-Tracy: (46.04°, -73.11°)", + " Washington Heights: (40.85°, -73.94°)", + " Franschhoek: (-33.91°, 19.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Franschhoek: 10836.6 km from centroid", + " San Juan: 3410.1 km from centroid", + " Keller: 3398.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Franschhoek", + "FINAL ANSWER: Franschhoek" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.75379, + "lon": -2.35863, + "name": "Accrington" + }, + { + "lat": 55.71667, + "lon": 37.41667, + "name": "Bol’shaya Setun’" + }, + { + "lat": 59.8393, + "lon": 30.49873, + "name": "Rybatskoye" + }, + { + "lat": 51.50417, + "lon": 3.88889, + "name": "Goes" + }, + { + "lat": 4.08466, + "lon": -76.19536, + "name": "Tuluá" + } + ], + "question": "Which location is the geographic outlier among: Accrington, Bol’shaya Setun’, Rybatskoye, Goes, Tuluá?", + "ground_truth": { + "answer": "Tuluá", + "outlier_distance_km": 8497.5, + "second_furthest_km": 2949.8, + "clarity_ratio": 2.88, + "median_distance_km": 2676.4, + "distances_to_centroid": { + "Accrington": 978.3, + "Bol’shaya Setun’": 2949.8, + "Rybatskoye": 2676.4, + "Goes": 822.2, + "Tuluá": 8497.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Accrington: (53.75°, -2.36°)", + " Bol’shaya Setun’: (55.72°, 37.42°)", + " Rybatskoye: (59.84°, 30.50°)", + " Goes: (51.50°, 3.89°)", + " Tuluá: (4.08°, -76.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tuluá: 8497.5 km from centroid", + " Bol’shaya Setun’: 2949.8 km from centroid", + " Rybatskoye: 2676.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tuluá", + "FINAL ANSWER: Tuluá" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.92866, + "lon": 138.59863, + "name": "Adelaide" + }, + { + "lat": -33.7061, + "lon": 150.7094, + "name": "Cranebrook" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": -32.05799, + "lon": 115.91814, + "name": "Canning Vale" + }, + { + "lat": 44.95302, + "lon": -92.99522, + "name": "Maplewood" + } + ], + "question": "Which location is the geographic outlier among: Adelaide, Cranebrook, Wollongong, Canning Vale, Maplewood?", + "ground_truth": { + "answer": "Maplewood", + "outlier_distance_km": 16976.5, + "second_furthest_km": 6006.6, + "clarity_ratio": 2.83, + "median_distance_km": 5987.2, + "distances_to_centroid": { + "Adelaide": 4895.2, + "Cranebrook": 5987.2, + "Wollongong": 6006.6, + "Canning Vale": 2806.9, + "Maplewood": 16976.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Adelaide: (-34.93°, 138.60°)", + " Cranebrook: (-33.71°, 150.71°)", + " Wollongong: (-34.42°, 150.89°)", + " Canning Vale: (-32.06°, 115.92°)", + " Maplewood: (44.95°, -93.00°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Maplewood: 16976.5 km from centroid", + " Wollongong: 6006.6 km from centroid", + " Cranebrook: 5987.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Maplewood", + "FINAL ANSWER: Maplewood" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.62839, + "lon": -84.15938, + "name": "Centerville" + }, + { + "lat": 41.60003, + "lon": -87.93811, + "name": "Homer Glen" + }, + { + "lat": 40.0645, + "lon": -75.1875, + "name": "East Mount Airy" + }, + { + "lat": 40.92501, + "lon": -98.34201, + "name": "Grand Island" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + } + ], + "question": "Which location is the geographic outlier among: Centerville, Homer Glen, East Mount Airy, Grand Island, Dunedin?", + "ground_truth": { + "answer": "Dunedin", + "outlier_distance_km": 16612.4, + "second_furthest_km": 6139.8, + "clarity_ratio": 2.71, + "median_distance_km": 5273.5, + "distances_to_centroid": { + "Centerville": 4933.2, + "Homer Glen": 5273.5, + "East Mount Airy": 4188.5, + "Grand Island": 6139.8, + "Dunedin": 16612.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Centerville: (39.63°, -84.16°)", + " Homer Glen: (41.60°, -87.94°)", + " East Mount Airy: (40.06°, -75.19°)", + " Grand Island: (40.93°, -98.34°)", + " Dunedin: (-45.87°, 170.50°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Dunedin: 16612.4 km from centroid", + " Grand Island: 6139.8 km from centroid", + " Homer Glen: 5273.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Dunedin", + "FINAL ANSWER: Dunedin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 54.65983, + "lon": -5.90858, + "name": "Newtownabbey" + }, + { + "lat": 48.65698, + "lon": 9.22049, + "name": "Filderstadt" + }, + { + "lat": 54.58048, + "lon": 16.86194, + "name": "Ustka" + }, + { + "lat": 50.74114, + "lon": 8.28699, + "name": "Dillenburg" + }, + { + "lat": 5.25198, + "lon": 100.49046, + "name": "Val Dor" + } + ], + "question": "Which location is the geographic outlier among: Newtownabbey, Filderstadt, Ustka, Dillenburg, Val Dor?", + "ground_truth": { + "answer": "Val Dor", + "outlier_distance_km": 8364.6, + "second_furthest_km": 2642.0, + "clarity_ratio": 3.17, + "median_distance_km": 1594.3, + "distances_to_centroid": { + "Newtownabbey": 2642.0, + "Filderstadt": 1438.8, + "Ustka": 1464.3, + "Dillenburg": 1594.3, + "Val Dor": 8364.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Newtownabbey: (54.66°, -5.91°)", + " Filderstadt: (48.66°, 9.22°)", + " Ustka: (54.58°, 16.86°)", + " Dillenburg: (50.74°, 8.29°)", + " Val Dor: (5.25°, 100.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Val Dor: 8364.6 km from centroid", + " Newtownabbey: 2642.0 km from centroid", + " Dillenburg: 1594.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Val Dor", + "FINAL ANSWER: Val Dor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.65002, + "lon": -98.65628, + "name": "Zacualtipán" + }, + { + "lat": 40.23126, + "lon": -74.67223, + "name": "Mercerville-Hamilton Square" + }, + { + "lat": 40.42118, + "lon": -79.7881, + "name": "Monroeville" + }, + { + "lat": 34.26945, + "lon": -118.78148, + "name": "Simi Valley" + }, + { + "lat": 12.30696, + "lon": 78.07022, + "name": "Pālakkodu" + } + ], + "question": "Which location is the geographic outlier among: Zacualtipán, Mercerville-Hamilton Square, Monroeville, Simi Valley, Pālakkodu?", + "ground_truth": { + "answer": "Pālakkodu", + "outlier_distance_km": 13451.2, + "second_furthest_km": 5606.8, + "clarity_ratio": 2.4, + "median_distance_km": 4115.8, + "distances_to_centroid": { + "Zacualtipán": 4115.8, + "Mercerville-Hamilton Square": 1867.8, + "Monroeville": 2254.0, + "Simi Valley": 5606.8, + "Pālakkodu": 13451.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zacualtipán: (20.65°, -98.66°)", + " Mercerville-Hamilton Square: (40.23°, -74.67°)", + " Monroeville: (40.42°, -79.79°)", + " Simi Valley: (34.27°, -118.78°)", + " Pālakkodu: (12.31°, 78.07°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pālakkodu: 13451.2 km from centroid", + " Simi Valley: 5606.8 km from centroid", + " Zacualtipán: 4115.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pālakkodu", + "FINAL ANSWER: Pālakkodu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.1839, + "lon": 88.27171, + "name": "Murshidābād" + }, + { + "lat": -6.17694, + "lon": 106.94667, + "name": "Utan" + }, + { + "lat": 27.36173, + "lon": 93.03991, + "name": "Seppa" + }, + { + "lat": 24.513, + "lon": 75.7469, + "name": "Bhānpura" + }, + { + "lat": -33.91938, + "lon": 150.92588, + "name": "Liverpool" + } + ], + "question": "Which location is the geographic outlier among: Murshidābād, Utan, Seppa, Bhānpura, Liverpool?", + "ground_truth": { + "answer": "Liverpool", + "outlier_distance_km": 6805.7, + "second_furthest_km": 3479.3, + "clarity_ratio": 1.96, + "median_distance_km": 2475.9, + "distances_to_centroid": { + "Murshidābād": 2455.1, + "Utan": 1550.2, + "Seppa": 2475.9, + "Bhānpura": 3479.3, + "Liverpool": 6805.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Murshidābād: (24.18°, 88.27°)", + " Utan: (-6.18°, 106.95°)", + " Seppa: (27.36°, 93.04°)", + " Bhānpura: (24.51°, 75.75°)", + " Liverpool: (-33.92°, 150.93°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Liverpool: 6805.7 km from centroid", + " Bhānpura: 3479.3 km from centroid", + " Seppa: 2475.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Liverpool", + "FINAL ANSWER: Liverpool" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + { + "lat": -34.06564, + "lon": 151.01266, + "name": "Engadine" + }, + { + "lat": -37.62581, + "lon": 144.92555, + "name": "Roxburgh Park" + }, + { + "lat": -37.75, + "lon": 145.35, + "name": "Lilydale" + }, + { + "lat": -22.97111, + "lon": 30.67361, + "name": "Malamulele" + } + ], + "question": "Which location is the geographic outlier among: Forest Lake, Engadine, Roxburgh Park, Lilydale, Malamulele?", + "ground_truth": { + "answer": "Malamulele", + "outlier_distance_km": 9060.2, + "second_furthest_km": 2735.3, + "clarity_ratio": 3.31, + "median_distance_km": 2430.3, + "distances_to_centroid": { + "Forest Lake": 2735.3, + "Engadine": 2430.3, + "Roxburgh Park": 1919.9, + "Lilydale": 1959.4, + "Malamulele": 9060.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Forest Lake: (-27.63°, 152.97°)", + " Engadine: (-34.07°, 151.01°)", + " Roxburgh Park: (-37.63°, 144.93°)", + " Lilydale: (-37.75°, 145.35°)", + " Malamulele: (-22.97°, 30.67°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Malamulele: 9060.2 km from centroid", + " Forest Lake: 2735.3 km from centroid", + " Engadine: 2430.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Malamulele", + "FINAL ANSWER: Malamulele" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.68435, + "lon": -100.31721, + "name": "Monterrey" + }, + { + "lat": 16.79944, + "lon": -93.27219, + "name": "Berriozábal" + }, + { + "lat": 25.77427, + "lon": -80.19366, + "name": "Miami" + }, + { + "lat": 21.24893, + "lon": -102.33036, + "name": "San Juan de los Lagos" + }, + { + "lat": 51.23367, + "lon": 12.71959, + "name": "Grimma" + } + ], + "question": "Which location is the geographic outlier among: Monterrey, Berriozábal, Miami, San Juan de los Lagos, Grimma?", + "ground_truth": { + "answer": "Grimma", + "outlier_distance_km": 7301.3, + "second_furthest_km": 3083.5, + "clarity_ratio": 2.37, + "median_distance_km": 2748.1, + "distances_to_centroid": { + "Monterrey": 2748.1, + "Berriozábal": 2457.7, + "Miami": 790.0, + "San Juan de los Lagos": 3083.5, + "Grimma": 7301.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Monterrey: (25.68°, -100.32°)", + " Berriozábal: (16.80°, -93.27°)", + " Miami: (25.77°, -80.19°)", + " San Juan de los Lagos: (21.25°, -102.33°)", + " Grimma: (51.23°, 12.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Grimma: 7301.3 km from centroid", + " San Juan de los Lagos: 3083.5 km from centroid", + " Monterrey: 2748.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Grimma", + "FINAL ANSWER: Grimma" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.79065, + "lon": -80.13005, + "name": "Miami Beach" + }, + { + "lat": 40.79677, + "lon": -74.48154, + "name": "Morristown" + }, + { + "lat": 43.64455, + "lon": -79.40712, + "name": "Niagara" + }, + { + "lat": 31.13489, + "lon": -97.77561, + "name": "Fort Cavazos" + }, + { + "lat": 36.4, + "lon": 139.33333, + "name": "Kiryū" + } + ], + "question": "Which location is the geographic outlier among: Miami Beach, Morristown, Niagara, Fort Cavazos, Kiryū?", + "ground_truth": { + "answer": "Kiryū", + "outlier_distance_km": 12011.1, + "second_furthest_km": 5446.1, + "clarity_ratio": 2.21, + "median_distance_km": 4095.0, + "distances_to_centroid": { + "Miami Beach": 4095.0, + "Morristown": 3176.5, + "Niagara": 3580.3, + "Fort Cavazos": 5446.1, + "Kiryū": 12011.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Miami Beach: (25.79°, -80.13°)", + " Morristown: (40.80°, -74.48°)", + " Niagara: (43.64°, -79.41°)", + " Fort Cavazos: (31.13°, -97.78°)", + " Kiryū: (36.40°, 139.33°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kiryū: 12011.1 km from centroid", + " Fort Cavazos: 5446.1 km from centroid", + " Miami Beach: 4095.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kiryū", + "FINAL ANSWER: Kiryū" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -34.05515, + "lon": 18.47617, + "name": "Retreat" + }, + { + "lat": 30.97478, + "lon": 31.87231, + "name": "Şān al Ḩajar al Qiblīyah" + }, + { + "lat": 6.55459, + "lon": 45.38992, + "name": "Neefkuceliye" + }, + { + "lat": 31.35573, + "lon": 31.68484, + "name": "Kafr Sa‘d" + }, + { + "lat": -37.83333, + "lon": 145.05, + "name": "Glenferrie" + } + ], + "question": "Which location is the geographic outlier among: Retreat, Şān al Ḩajar al Qiblīyah, Neefkuceliye, Kafr Sa‘d, Glenferrie?", + "ground_truth": { + "answer": "Glenferrie", + "outlier_distance_km": 10015.3, + "second_furthest_km": 5278.7, + "clarity_ratio": 1.9, + "median_distance_km": 4290.6, + "distances_to_centroid": { + "Retreat": 5278.7, + "Şān al Ḩajar al Qiblīyah": 4246.3, + "Neefkuceliye": 1286.0, + "Kafr Sa‘d": 4290.6, + "Glenferrie": 10015.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Retreat: (-34.06°, 18.48°)", + " Şān al Ḩajar al Qiblīyah: (30.97°, 31.87°)", + " Neefkuceliye: (6.55°, 45.39°)", + " Kafr Sa‘d: (31.36°, 31.68°)", + " Glenferrie: (-37.83°, 145.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Glenferrie: 10015.3 km from centroid", + " Retreat: 5278.7 km from centroid", + " Kafr Sa‘d: 4290.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Glenferrie", + "FINAL ANSWER: Glenferrie" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + }, + { + "lat": -27.44187, + "lon": 152.93861, + "name": "The Gap" + }, + { + "lat": -37.81667, + "lon": 145.2, + "name": "Mitcham" + }, + { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + { + "lat": 31.16757, + "lon": 31.80125, + "name": "Mīt Salsīl" + } + ], + "question": "Which location is the geographic outlier among: Doncaster East, The Gap, Mitcham, Kellyville, Mīt Salsīl?", + "ground_truth": { + "answer": "Mīt Salsīl", + "outlier_distance_km": 11511.6, + "second_furthest_km": 2890.6, + "clarity_ratio": 3.98, + "median_distance_km": 2889.1, + "distances_to_centroid": { + "Doncaster East": 2665.1, + "The Gap": 2890.6, + "Mitcham": 2670.6, + "Kellyville": 2889.1, + "Mīt Salsīl": 11511.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Doncaster East: (-37.79°, 145.15°)", + " The Gap: (-27.44°, 152.94°)", + " Mitcham: (-37.82°, 145.20°)", + " Kellyville: (-33.71°, 150.95°)", + " Mīt Salsīl: (31.17°, 31.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mīt Salsīl: 11511.6 km from centroid", + " The Gap: 2890.6 km from centroid", + " Kellyville: 2889.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mīt Salsīl", + "FINAL ANSWER: Mīt Salsīl" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.46013, + "lon": -46.5749, + "name": "Jaçanã" + }, + { + "lat": -20.18417, + "lon": -44.77111, + "name": "Carmo do Cajuru" + }, + { + "lat": -1.515, + "lon": -48.04472, + "name": "Bujaru" + }, + { + "lat": -31.76997, + "lon": -52.34101, + "name": "Pelotas" + }, + { + "lat": -30.29626, + "lon": 153.11351, + "name": "Coffs Harbour" + } + ], + "question": "Which location is the geographic outlier among: Jaçanã, Carmo do Cajuru, Bujaru, Pelotas, Coffs Harbour?", + "ground_truth": { + "answer": "Coffs Harbour", + "outlier_distance_km": 13908.0, + "second_furthest_km": 4895.1, + "clarity_ratio": 2.84, + "median_distance_km": 4548.8, + "distances_to_centroid": { + "Jaçanã": 3987.0, + "Carmo do Cajuru": 3844.3, + "Bujaru": 4895.1, + "Pelotas": 4548.8, + "Coffs Harbour": 13908.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Jaçanã: (-23.46°, -46.57°)", + " Carmo do Cajuru: (-20.18°, -44.77°)", + " Bujaru: (-1.51°, -48.04°)", + " Pelotas: (-31.77°, -52.34°)", + " Coffs Harbour: (-30.30°, 153.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Coffs Harbour: 13908.0 km from centroid", + " Bujaru: 4895.1 km from centroid", + " Pelotas: 4548.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Coffs Harbour", + "FINAL ANSWER: Coffs Harbour" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.22235, + "lon": 6.90831, + "name": "Erkrath" + }, + { + "lat": 51.68033, + "lon": 7.82089, + "name": "Hamm" + }, + { + "lat": 51.17423, + "lon": -0.15919, + "name": "Horley" + }, + { + "lat": 50.81854, + "lon": 6.27184, + "name": "Eschweiler" + }, + { + "lat": 6.18461, + "lon": -75.59913, + "name": "Itagüí" + } + ], + "question": "Which location is the geographic outlier among: Erkrath, Hamm, Horley, Eschweiler, Itagüí?", + "ground_truth": { + "answer": "Itagüí", + "outlier_distance_km": 7471.3, + "second_furthest_km": 1762.9, + "clarity_ratio": 4.24, + "median_distance_km": 1682.8, + "distances_to_centroid": { + "Erkrath": 1682.8, + "Hamm": 1762.9, + "Horley": 1289.4, + "Eschweiler": 1622.0, + "Itagüí": 7471.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Erkrath: (51.22°, 6.91°)", + " Hamm: (51.68°, 7.82°)", + " Horley: (51.17°, -0.16°)", + " Eschweiler: (50.82°, 6.27°)", + " Itagüí: (6.18°, -75.60°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Itagüí: 7471.3 km from centroid", + " Hamm: 1762.9 km from centroid", + " Erkrath: 1682.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Itagüí", + "FINAL ANSWER: Itagüí" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -3.98417, + "lon": -38.62028, + "name": "Pacatuba" + }, + { + "lat": -1.975, + "lon": -48.95972, + "name": "Igarapé Miri" + }, + { + "lat": -2.76194, + "lon": -42.27444, + "name": "Tutóia" + }, + { + "lat": -21.205, + "lon": -41.88778, + "name": "Itaperuna" + }, + { + "lat": -22.88416, + "lon": 30.49358, + "name": "Tshitereke" + } + ], + "question": "Which location is the geographic outlier among: Pacatuba, Igarapé Miri, Tutóia, Itaperuna, Tshitereke?", + "ground_truth": { + "answer": "Tshitereke", + "outlier_distance_km": 6364.1, + "second_furthest_km": 2478.0, + "clarity_ratio": 2.57, + "median_distance_km": 1876.1, + "distances_to_centroid": { + "Pacatuba": 1357.2, + "Igarapé Miri": 2478.0, + "Tutóia": 1774.1, + "Itaperuna": 1876.1, + "Tshitereke": 6364.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pacatuba: (-3.98°, -38.62°)", + " Igarapé Miri: (-1.98°, -48.96°)", + " Tutóia: (-2.76°, -42.27°)", + " Itaperuna: (-21.20°, -41.89°)", + " Tshitereke: (-22.88°, 30.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tshitereke: 6364.1 km from centroid", + " Igarapé Miri: 2478.0 km from centroid", + " Itaperuna: 1876.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tshitereke", + "FINAL ANSWER: Tshitereke" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.97453, + "lon": -92.01653, + "name": "Cabot" + }, + { + "lat": 16.32463, + "lon": -95.24104, + "name": "Santo Domingo Tehuantepec" + }, + { + "lat": 18.15056, + "lon": -94.5525, + "name": "Fraccionamiento Ciudad Olmeca" + }, + { + "lat": 40.84829, + "lon": -74.58148, + "name": "Randolph" + }, + { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + } + ], + "question": "Which location is the geographic outlier among: Cabot, Santo Domingo Tehuantepec, Fraccionamiento Ciudad Olmeca, Randolph, Cessnock?", + "ground_truth": { + "answer": "Cessnock", + "outlier_distance_km": 17719.4, + "second_furthest_km": 5782.5, + "clarity_ratio": 3.06, + "median_distance_km": 5687.4, + "distances_to_centroid": { + "Cabot": 5500.0, + "Santo Domingo Tehuantepec": 5782.5, + "Fraccionamiento Ciudad Olmeca": 5687.4, + "Randolph": 4286.6, + "Cessnock": 17719.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cabot: (34.97°, -92.02°)", + " Santo Domingo Tehuantepec: (16.32°, -95.24°)", + " Fraccionamiento Ciudad Olmeca: (18.15°, -94.55°)", + " Randolph: (40.85°, -74.58°)", + " Cessnock: (-32.83°, 151.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cessnock: 17719.4 km from centroid", + " Santo Domingo Tehuantepec: 5782.5 km from centroid", + " Fraccionamiento Ciudad Olmeca: 5687.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cessnock", + "FINAL ANSWER: Cessnock" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -4.02694, + "lon": -38.305, + "name": "Pindoretama" + }, + { + "lat": -3.32083, + "lon": -45.01083, + "name": "Cajari" + }, + { + "lat": -39.80867, + "lon": -73.21821, + "name": "Las Animas" + }, + { + "lat": -21.92194, + "lon": -50.73389, + "name": "Bastos" + }, + { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + } + ], + "question": "Which location is the geographic outlier among: Pindoretama, Cajari, Las Animas, Bastos, Corio?", + "ground_truth": { + "answer": "Corio", + "outlier_distance_km": 12973.2, + "second_furthest_km": 6030.2, + "clarity_ratio": 2.15, + "median_distance_km": 4041.0, + "distances_to_centroid": { + "Pindoretama": 3384.8, + "Cajari": 4041.0, + "Las Animas": 6030.2, + "Bastos": 3932.8, + "Corio": 12973.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pindoretama: (-4.03°, -38.30°)", + " Cajari: (-3.32°, -45.01°)", + " Las Animas: (-39.81°, -73.22°)", + " Bastos: (-21.92°, -50.73°)", + " Corio: (-38.08°, 144.38°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Corio: 12973.2 km from centroid", + " Las Animas: 6030.2 km from centroid", + " Cajari: 4041.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Corio", + "FINAL ANSWER: Corio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -42.87936, + "lon": 147.32941, + "name": "Hobart" + }, + { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + { + "lat": 9.00114, + "lon": -73.97581, + "name": "El Banco" + } + ], + "question": "Which location is the geographic outlier among: Hobart, Ashburton, Campsie, Earlwood, El Banco?", + "ground_truth": { + "answer": "El Banco", + "outlier_distance_km": 17749.2, + "second_furthest_km": 5662.3, + "clarity_ratio": 3.13, + "median_distance_km": 3958.1, + "distances_to_centroid": { + "Hobart": 3694.5, + "Ashburton": 5662.3, + "Campsie": 3956.1, + "Earlwood": 3958.1, + "El Banco": 17749.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hobart: (-42.88°, 147.33°)", + " Ashburton: (-43.90°, 171.73°)", + " Campsie: (-33.91°, 151.10°)", + " Earlwood: (-33.92°, 151.13°)", + " El Banco: (9.00°, -73.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " El Banco: 17749.2 km from centroid", + " Ashburton: 5662.3 km from centroid", + " Earlwood: 3958.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: El Banco", + "FINAL ANSWER: El Banco" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.35, + "lon": 123.55, + "name": "San Jose" + }, + { + "lat": -1.1767, + "lon": 136.082, + "name": "Biak" + }, + { + "lat": 29.94167, + "lon": 108.08442, + "name": "Xialu" + }, + { + "lat": 16.99154, + "lon": 73.31022, + "name": "Ratnagiri" + }, + { + "lat": -33.4608, + "lon": 18.72714, + "name": "Malmesbury" + } + ], + "question": "Which location is the geographic outlier among: San Jose, Biak, Xialu, Ratnagiri, Malmesbury?", + "ground_truth": { + "answer": "Malmesbury", + "outlier_distance_km": 8786.1, + "second_furthest_km": 4951.5, + "clarity_ratio": 1.77, + "median_distance_km": 3582.3, + "distances_to_centroid": { + "San Jose": 3582.3, + "Biak": 4951.5, + "Xialu": 3236.8, + "Ratnagiri": 2420.8, + "Malmesbury": 8786.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Jose: (13.35°, 123.55°)", + " Biak: (-1.18°, 136.08°)", + " Xialu: (29.94°, 108.08°)", + " Ratnagiri: (16.99°, 73.31°)", + " Malmesbury: (-33.46°, 18.73°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Malmesbury: 8786.1 km from centroid", + " Biak: 4951.5 km from centroid", + " San Jose: 3582.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Malmesbury", + "FINAL ANSWER: Malmesbury" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.85783, + "lon": 7.39577, + "name": "Nsukka" + }, + { + "lat": -26.30176, + "lon": 29.98696, + "name": "Breyten" + }, + { + "lat": 8.05627, + "lon": -1.73058, + "name": "Kintampo" + }, + { + "lat": 6.50153, + "lon": 3.35808, + "name": "Surulere" + }, + { + "lat": 19.64186, + "lon": 109.3545, + "name": "Guangcun" + } + ], + "question": "Which location is the geographic outlier among: Nsukka, Breyten, Kintampo, Surulere, Guangcun?", + "ground_truth": { + "answer": "Guangcun", + "outlier_distance_km": 8817.0, + "second_furthest_km": 3520.3, + "clarity_ratio": 2.5, + "median_distance_km": 3253.0, + "distances_to_centroid": { + "Nsukka": 2505.4, + "Breyten": 3253.0, + "Kintampo": 3520.3, + "Surulere": 2942.1, + "Guangcun": 8817.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nsukka: (6.86°, 7.40°)", + " Breyten: (-26.30°, 29.99°)", + " Kintampo: (8.06°, -1.73°)", + " Surulere: (6.50°, 3.36°)", + " Guangcun: (19.64°, 109.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Guangcun: 8817.0 km from centroid", + " Kintampo: 3520.3 km from centroid", + " Breyten: 3253.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Guangcun", + "FINAL ANSWER: Guangcun" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -10.83444, + "lon": -38.53583, + "name": "Ribeira do Pombal" + }, + { + "lat": -22.50972, + "lon": -47.77806, + "name": "Charqueada" + }, + { + "lat": -5.40232, + "lon": -80.74224, + "name": "La Unión" + }, + { + "lat": -29.66917, + "lon": -52.78889, + "name": "Candelária" + }, + { + "lat": 16.99154, + "lon": 73.31022, + "name": "Ratnagiri" + } + ], + "question": "Which location is the geographic outlier among: Ribeira do Pombal, Charqueada, La Unión, Candelária, Ratnagiri?", + "ground_truth": { + "answer": "Ratnagiri", + "outlier_distance_km": 11668.2, + "second_furthest_km": 5686.1, + "clarity_ratio": 2.05, + "median_distance_km": 3252.2, + "distances_to_centroid": { + "Ribeira do Pombal": 1010.6, + "Charqueada": 2389.3, + "La Unión": 5686.1, + "Candelária": 3252.2, + "Ratnagiri": 11668.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ribeira do Pombal: (-10.83°, -38.54°)", + " Charqueada: (-22.51°, -47.78°)", + " La Unión: (-5.40°, -80.74°)", + " Candelária: (-29.67°, -52.79°)", + " Ratnagiri: (16.99°, 73.31°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ratnagiri: 11668.2 km from centroid", + " La Unión: 5686.1 km from centroid", + " Candelária: 3252.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ratnagiri", + "FINAL ANSWER: Ratnagiri" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.33863, + "lon": -80.1869, + "name": "Sandalfoot Cove" + }, + { + "lat": 43.15357, + "lon": -93.20104, + "name": "Mason City" + }, + { + "lat": 28.33584, + "lon": -81.35313, + "name": "Buenaventura Lakes" + }, + { + "lat": 45.63922, + "lon": -73.82757, + "name": "Sainte-Thérèse" + }, + { + "lat": 43.8245, + "lon": 11.13027, + "name": "Campi Bisenzio" + } + ], + "question": "Which location is the geographic outlier among: Sandalfoot Cove, Mason City, Buenaventura Lakes, Sainte-Thérèse, Campi Bisenzio?", + "ground_truth": { + "answer": "Campi Bisenzio", + "outlier_distance_km": 6119.8, + "second_furthest_km": 2583.2, + "clarity_ratio": 2.37, + "median_distance_km": 1998.0, + "distances_to_centroid": { + "Sandalfoot Cove": 1998.0, + "Mason City": 2583.2, + "Buenaventura Lakes": 1947.1, + "Sainte-Thérèse": 1250.1, + "Campi Bisenzio": 6119.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Sandalfoot Cove: (26.34°, -80.19°)", + " Mason City: (43.15°, -93.20°)", + " Buenaventura Lakes: (28.34°, -81.35°)", + " Sainte-Thérèse: (45.64°, -73.83°)", + " Campi Bisenzio: (43.82°, 11.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Campi Bisenzio: 6119.8 km from centroid", + " Mason City: 2583.2 km from centroid", + " Sandalfoot Cove: 1998.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Campi Bisenzio", + "FINAL ANSWER: Campi Bisenzio" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -14.86611, + "lon": -40.83944, + "name": "Vitória da Conquista" + }, + { + "lat": 6.11284, + "lon": -75.98378, + "name": "Betulia" + }, + { + "lat": -28.02333, + "lon": -48.61333, + "name": "Garopaba" + }, + { + "lat": -33.15365, + "lon": -60.51168, + "name": "Arroyo Seco" + }, + { + "lat": 11.99564, + "lon": 75.28717, + "name": "Cherukunnu" + } + ], + "question": "Which location is the geographic outlier among: Vitória da Conquista, Betulia, Garopaba, Arroyo Seco, Cherukunnu?", + "ground_truth": { + "answer": "Cherukunnu", + "outlier_distance_km": 11925.5, + "second_furthest_km": 5440.1, + "clarity_ratio": 2.19, + "median_distance_km": 3911.5, + "distances_to_centroid": { + "Vitória da Conquista": 1214.8, + "Betulia": 5440.1, + "Garopaba": 2653.1, + "Arroyo Seco": 3911.5, + "Cherukunnu": 11925.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vitória da Conquista: (-14.87°, -40.84°)", + " Betulia: (6.11°, -75.98°)", + " Garopaba: (-28.02°, -48.61°)", + " Arroyo Seco: (-33.15°, -60.51°)", + " Cherukunnu: (12.00°, 75.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cherukunnu: 11925.5 km from centroid", + " Betulia: 5440.1 km from centroid", + " Arroyo Seco: 3911.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cherukunnu", + "FINAL ANSWER: Cherukunnu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 39.04167, + "lon": -94.72024, + "name": "Shawnee" + }, + { + "lat": 31.85425, + "lon": -110.9937, + "name": "Green Valley" + }, + { + "lat": 35.139, + "lon": -79.00603, + "name": "Fort Bragg" + }, + { + "lat": 44.9279, + "lon": -122.98371, + "name": "Four Corners" + }, + { + "lat": 26.42237, + "lon": 90.98004, + "name": "Howli" + } + ], + "question": "Which location is the geographic outlier among: Shawnee, Green Valley, Fort Bragg, Four Corners, Howli?", + "ground_truth": { + "answer": "Howli", + "outlier_distance_km": 12622.5, + "second_furthest_km": 5056.0, + "clarity_ratio": 2.5, + "median_distance_km": 4385.6, + "distances_to_centroid": { + "Shawnee": 2790.9, + "Green Valley": 4385.6, + "Fort Bragg": 1420.1, + "Four Corners": 5056.0, + "Howli": 12622.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Shawnee: (39.04°, -94.72°)", + " Green Valley: (31.85°, -110.99°)", + " Fort Bragg: (35.14°, -79.01°)", + " Four Corners: (44.93°, -122.98°)", + " Howli: (26.42°, 90.98°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Howli: 12622.5 km from centroid", + " Four Corners: 5056.0 km from centroid", + " Green Valley: 4385.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Howli", + "FINAL ANSWER: Howli" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 26.04949, + "lon": 32.24142, + "name": "Nag Hammâdi" + }, + { + "lat": 7.38299, + "lon": 4.26031, + "name": "Modakeke" + }, + { + "lat": 8.3, + "lon": 38.95, + "name": "‘Alem T’ēna" + }, + { + "lat": 31.19688, + "lon": 31.5243, + "name": "Shirbīn" + }, + { + "lat": 34.01949, + "lon": -118.49138, + "name": "Santa Monica" + } + ], + "question": "Which location is the geographic outlier among: Nag Hammâdi, Modakeke, ‘Alem T’ēna, Shirbīn, Santa Monica?", + "ground_truth": { + "answer": "Santa Monica", + "outlier_distance_km": 10880.2, + "second_furthest_km": 4649.3, + "clarity_ratio": 2.34, + "median_distance_km": 3544.3, + "distances_to_centroid": { + "Nag Hammâdi": 3544.3, + "Modakeke": 1709.5, + "‘Alem T’ēna": 4649.3, + "Shirbīn": 3527.9, + "Santa Monica": 10880.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Nag Hammâdi: (26.05°, 32.24°)", + " Modakeke: (7.38°, 4.26°)", + " ‘Alem T’ēna: (8.30°, 38.95°)", + " Shirbīn: (31.20°, 31.52°)", + " Santa Monica: (34.02°, -118.49°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santa Monica: 10880.2 km from centroid", + " ‘Alem T’ēna: 4649.3 km from centroid", + " Nag Hammâdi: 3544.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santa Monica", + "FINAL ANSWER: Santa Monica" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + }, + { + "lat": -41.27078, + "lon": 173.28404, + "name": "Nelson" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -37.75, + "lon": 145.01667, + "name": "Preston" + }, + { + "lat": 44.35258, + "lon": 2.57338, + "name": "Rodez" + } + ], + "question": "Which location is the geographic outlier among: Banora Point, Nelson, Ellenbrook, Preston, Rodez?", + "ground_truth": { + "answer": "Rodez", + "outlier_distance_km": 13476.6, + "second_furthest_km": 5749.8, + "clarity_ratio": 2.34, + "median_distance_km": 3743.3, + "distances_to_centroid": { + "Banora Point": 3743.3, + "Nelson": 5749.8, + "Ellenbrook": 1443.0, + "Preston": 3344.2, + "Rodez": 13476.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Banora Point: (-28.21°, 153.54°)", + " Nelson: (-41.27°, 173.28°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Preston: (-37.75°, 145.02°)", + " Rodez: (44.35°, 2.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rodez: 13476.6 km from centroid", + " Nelson: 5749.8 km from centroid", + " Banora Point: 3743.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rodez", + "FINAL ANSWER: Rodez" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.21641, + "lon": 83.0358, + "name": "Renukūt" + }, + { + "lat": 17.17859, + "lon": 77.28998, + "name": "Sedam" + }, + { + "lat": 17.90802, + "lon": 77.51524, + "name": "Bidar" + }, + { + "lat": 29.02841, + "lon": 79.05654, + "name": "Suār" + }, + { + "lat": 51.3025, + "lon": 37.84613, + "name": "Staryy Oskol" + } + ], + "question": "Which location is the geographic outlier among: Renukūt, Sedam, Bidar, Suār, Staryy Oskol?", + "ground_truth": { + "answer": "Staryy Oskol", + "outlier_distance_km": 3789.4, + "second_furthest_km": 1360.3, + "clarity_ratio": 2.79, + "median_distance_km": 1300.6, + "distances_to_centroid": { + "Renukūt": 1275.1, + "Sedam": 1360.3, + "Bidar": 1300.6, + "Suār": 801.7, + "Staryy Oskol": 3789.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Renukūt: (24.22°, 83.04°)", + " Sedam: (17.18°, 77.29°)", + " Bidar: (17.91°, 77.52°)", + " Suār: (29.03°, 79.06°)", + " Staryy Oskol: (51.30°, 37.85°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Staryy Oskol: 3789.4 km from centroid", + " Sedam: 1360.3 km from centroid", + " Bidar: 1300.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Staryy Oskol", + "FINAL ANSWER: Staryy Oskol" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.79962, + "lon": 38.9967, + "name": "Bryukhovetskaya" + }, + { + "lat": 40.46206, + "lon": -3.6766, + "name": "Chamartín" + }, + { + "lat": 51.57835, + "lon": -0.33208, + "name": "Harrow" + }, + { + "lat": 48.84226, + "lon": 2.18232, + "name": "Garches" + }, + { + "lat": -26.84493, + "lon": 26.76829, + "name": "Stilfontein" + } + ], + "question": "Which location is the geographic outlier among: Bryukhovetskaya, Chamartín, Harrow, Garches, Stilfontein?", + "ground_truth": { + "answer": "Stilfontein", + "outlier_distance_km": 6705.3, + "second_furthest_km": 2720.7, + "clarity_ratio": 2.46, + "median_distance_km": 2428.4, + "distances_to_centroid": { + "Bryukhovetskaya": 2720.7, + "Chamartín": 1748.8, + "Harrow": 2428.4, + "Garches": 2075.5, + "Stilfontein": 6705.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bryukhovetskaya: (45.80°, 39.00°)", + " Chamartín: (40.46°, -3.68°)", + " Harrow: (51.58°, -0.33°)", + " Garches: (48.84°, 2.18°)", + " Stilfontein: (-26.84°, 26.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Stilfontein: 6705.3 km from centroid", + " Bryukhovetskaya: 2720.7 km from centroid", + " Harrow: 2428.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Stilfontein", + "FINAL ANSWER: Stilfontein" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 2.5703, + "lon": 101.833, + "name": "Lukut" + }, + { + "lat": 32.31625, + "lon": 75.60741, + "name": "Sujānpur" + }, + { + "lat": 10.02674, + "lon": 76.22229, + "name": "Elamkunnapuzha" + }, + { + "lat": 8.30972, + "lon": 125.00194, + "name": "Impasugong" + }, + { + "lat": 8.43497, + "lon": 12.05107, + "name": "Ganye" + } + ], + "question": "Which location is the geographic outlier among: Lukut, Sujānpur, Elamkunnapuzha, Impasugong, Ganye?", + "ground_truth": { + "answer": "Ganye", + "outlier_distance_km": 7225.2, + "second_furthest_km": 5139.6, + "clarity_ratio": 1.41, + "median_distance_km": 2825.1, + "distances_to_centroid": { + "Lukut": 2825.1, + "Sujānpur": 2237.2, + "Elamkunnapuzha": 331.0, + "Impasugong": 5139.6, + "Ganye": 7225.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lukut: (2.57°, 101.83°)", + " Sujānpur: (32.32°, 75.61°)", + " Elamkunnapuzha: (10.03°, 76.22°)", + " Impasugong: (8.31°, 125.00°)", + " Ganye: (8.43°, 12.05°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ganye: 7225.2 km from centroid", + " Impasugong: 5139.6 km from centroid", + " Lukut: 2825.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ganye", + "FINAL ANSWER: Ganye" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -20.61444, + "lon": -42.14861, + "name": "Divino" + }, + { + "lat": -26.24333, + "lon": -48.63806, + "name": "São Francisco do Sul" + }, + { + "lat": -1.89969, + "lon": -50.20821, + "name": "Bagre" + }, + { + "lat": -10.21167, + "lon": -63.82861, + "name": "Buritis" + }, + { + "lat": 38.45396, + "lon": 77.24918, + "name": "Mixia" + } + ], + "question": "Which location is the geographic outlier among: Divino, São Francisco do Sul, Bagre, Buritis, Mixia?", + "ground_truth": { + "answer": "Mixia", + "outlier_distance_km": 11401.6, + "second_furthest_km": 4278.0, + "clarity_ratio": 2.67, + "median_distance_km": 3481.2, + "distances_to_centroid": { + "Divino": 2570.6, + "São Francisco do Sul": 3481.2, + "Bagre": 2752.7, + "Buritis": 4278.0, + "Mixia": 11401.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Divino: (-20.61°, -42.15°)", + " São Francisco do Sul: (-26.24°, -48.64°)", + " Bagre: (-1.90°, -50.21°)", + " Buritis: (-10.21°, -63.83°)", + " Mixia: (38.45°, 77.25°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mixia: 11401.6 km from centroid", + " Buritis: 4278.0 km from centroid", + " São Francisco do Sul: 3481.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mixia", + "FINAL ANSWER: Mixia" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.84853, + "lon": 174.76349, + "name": "Auckland" + }, + { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + { + "lat": -32.5269, + "lon": 115.7217, + "name": "Mandurah" + }, + { + "lat": -41.33333, + "lon": 173.18333, + "name": "Richmond" + }, + { + "lat": 37.18856, + "lon": -3.71887, + "name": "Santafé" + } + ], + "question": "Which location is the geographic outlier among: Auckland, Cranbourne West, Mandurah, Richmond, Santafé?", + "ground_truth": { + "answer": "Santafé", + "outlier_distance_km": 14513.7, + "second_furthest_km": 5365.7, + "clarity_ratio": 2.7, + "median_distance_km": 5268.2, + "distances_to_centroid": { + "Auckland": 5365.7, + "Cranbourne West": 2899.0, + "Mandurah": 1249.7, + "Richmond": 5268.2, + "Santafé": 14513.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Auckland: (-36.85°, 174.76°)", + " Cranbourne West: (-38.10°, 145.27°)", + " Mandurah: (-32.53°, 115.72°)", + " Richmond: (-41.33°, 173.18°)", + " Santafé: (37.19°, -3.72°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Santafé: 14513.7 km from centroid", + " Auckland: 5365.7 km from centroid", + " Richmond: 5268.2 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Santafé", + "FINAL ANSWER: Santafé" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 44.0038, + "lon": 10.10674, + "name": "Marina di Massa" + }, + { + "lat": 50.74699, + "lon": 6.49069, + "name": "Kreuzau" + }, + { + "lat": 51.26011, + "lon": 7.76608, + "name": "Werdohl" + }, + { + "lat": 53.1235, + "lon": 18.00762, + "name": "Bydgoszcz" + }, + { + "lat": -37.69825, + "lon": 145.05967, + "name": "Bundoora" + } + ], + "question": "Which location is the geographic outlier among: Marina di Massa, Kreuzau, Werdohl, Bydgoszcz, Bundoora?", + "ground_truth": { + "answer": "Bundoora", + "outlier_distance_km": 13555.9, + "second_furthest_km": 3256.8, + "clarity_ratio": 4.16, + "median_distance_km": 3205.4, + "distances_to_centroid": { + "Marina di Massa": 2707.5, + "Kreuzau": 3256.8, + "Werdohl": 3205.4, + "Bydgoszcz": 2791.0, + "Bundoora": 13555.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Marina di Massa: (44.00°, 10.11°)", + " Kreuzau: (50.75°, 6.49°)", + " Werdohl: (51.26°, 7.77°)", + " Bydgoszcz: (53.12°, 18.01°)", + " Bundoora: (-37.70°, 145.06°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bundoora: 13555.9 km from centroid", + " Kreuzau: 3256.8 km from centroid", + " Werdohl: 3205.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Bundoora", + "FINAL ANSWER: Bundoora" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -41.31667, + "lon": 173.23333, + "name": "Stoke" + }, + { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + { + "lat": -39.4926, + "lon": 176.91233, + "name": "Napier" + }, + { + "lat": 29.77851, + "lon": 106.28512, + "name": "Qitang" + } + ], + "question": "Which location is the geographic outlier among: Stoke, Newcastle, Bentleigh East, Napier, Qitang?", + "ground_truth": { + "answer": "Qitang", + "outlier_distance_km": 7660.1, + "second_furthest_km": 2976.2, + "clarity_ratio": 2.57, + "median_distance_km": 2812.0, + "distances_to_centroid": { + "Stoke": 2812.0, + "Newcastle": 957.4, + "Bentleigh East": 1596.6, + "Napier": 2976.2, + "Qitang": 7660.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Stoke: (-41.32°, 173.23°)", + " Newcastle: (-32.93°, 151.78°)", + " Bentleigh East: (-37.92°, 145.05°)", + " Napier: (-39.49°, 176.91°)", + " Qitang: (29.78°, 106.29°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Qitang: 7660.1 km from centroid", + " Napier: 2976.2 km from centroid", + " Stoke: 2812.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Qitang", + "FINAL ANSWER: Qitang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 50.28337, + "lon": -107.80135, + "name": "Swift Current" + }, + { + "lat": 42.86663, + "lon": -106.31308, + "name": "Casper" + }, + { + "lat": 36.52977, + "lon": -87.35945, + "name": "Clarksville" + }, + { + "lat": 44.52358, + "lon": -89.57456, + "name": "Stevens Point" + }, + { + "lat": -23.83222, + "lon": -46.81139, + "name": "Embu-Guaçu" + } + ], + "question": "Which location is the geographic outlier among: Swift Current, Casper, Clarksville, Stevens Point, Embu-Guaçu?", + "ground_truth": { + "answer": "Embu-Guaçu", + "outlier_distance_km": 7405.9, + "second_furthest_km": 2809.6, + "clarity_ratio": 2.64, + "median_distance_km": 2189.0, + "distances_to_centroid": { + "Swift Current": 2809.6, + "Casper": 2189.0, + "Clarksville": 718.1, + "Stevens Point": 1616.3, + "Embu-Guaçu": 7405.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Swift Current: (50.28°, -107.80°)", + " Casper: (42.87°, -106.31°)", + " Clarksville: (36.53°, -87.36°)", + " Stevens Point: (44.52°, -89.57°)", + " Embu-Guaçu: (-23.83°, -46.81°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Embu-Guaçu: 7405.9 km from centroid", + " Swift Current: 2809.6 km from centroid", + " Casper: 2189.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Embu-Guaçu", + "FINAL ANSWER: Embu-Guaçu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.77483, + "lon": -84.29631, + "name": "Decatur" + }, + { + "lat": 39.95622, + "lon": -75.05795, + "name": "Pennsauken" + }, + { + "lat": 44.7133, + "lon": -93.42273, + "name": "Prior Lake" + }, + { + "lat": 37.98869, + "lon": -84.47772, + "name": "Lexington" + }, + { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + } + ], + "question": "Which location is the geographic outlier among: Decatur, Pennsauken, Prior Lake, Lexington, Bracken Ridge?", + "ground_truth": { + "answer": "Bracken Ridge", + "outlier_distance_km": 19019.3, + "second_furthest_km": 5425.4, + "clarity_ratio": 3.51, + "median_distance_km": 4641.2, + "distances_to_centroid": { + "Decatur": 4622.6, + "Pennsauken": 3861.5, + "Prior Lake": 5425.4, + "Lexington": 4641.2, + "Bracken Ridge": 19019.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Decatur: (33.77°, -84.30°)", + " Pennsauken: (39.96°, -75.06°)", + " Prior Lake: (44.71°, -93.42°)", + " Lexington: (37.99°, -84.48°)", + " Bracken Ridge: (-27.32°, 153.03°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Bracken Ridge: 19019.3 km from centroid", + " Prior Lake: 5425.4 km from centroid", + " Lexington: 4641.2 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": -38.14711, + "lon": 144.36069, + "name": "Geelong" + }, + { + "lat": -25.54073, + "lon": 152.70493, + "name": "Maryborough" + }, + { + "lat": -32.22099, + "lon": 116.009, + "name": "Byford" + }, + { + "lat": -33.8188, + "lon": 151.1062, + "name": "Ryde" + }, + { + "lat": 50.91234, + "lon": -1.30076, + "name": "Hedge End" + } + ], + "question": "Which location is the geographic outlier among: Geelong, Maryborough, Byford, Ryde, Hedge End?", + "ground_truth": { + "answer": "Hedge End", + "outlier_distance_km": 13027.6, + "second_furthest_km": 4341.4, + "clarity_ratio": 3.0, + "median_distance_km": 4296.8, + "distances_to_centroid": { + "Geelong": 3979.8, + "Maryborough": 4296.8, + "Byford": 1862.6, + "Ryde": 4341.4, + "Hedge End": 13027.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Geelong: (-38.15°, 144.36°)", + " Maryborough: (-25.54°, 152.70°)", + " Byford: (-32.22°, 116.01°)", + " Ryde: (-33.82°, 151.11°)", + " Hedge End: (50.91°, -1.30°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Hedge End: 13027.6 km from centroid", + " Ryde: 4341.4 km from centroid", + " Maryborough: 4296.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Hedge End", + "FINAL ANSWER: Hedge End" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 8.9, + "lon": 39.91667, + "name": "Metahāra" + }, + { + "lat": 10.71668, + "lon": 39.86997, + "name": "Kemisē" + }, + { + "lat": -28.31971, + "lon": 27.62082, + "name": "Senekal" + }, + { + "lat": -27.64685, + "lon": 25.60697, + "name": "Bloemhof" + }, + { + "lat": -23.52098, + "lon": -51.68179, + "name": "Mandaguari" + } + ], + "question": "Which location is the geographic outlier among: Metahāra, Kemisē, Senekal, Bloemhof, Mandaguari?", + "ground_truth": { + "answer": "Mandaguari", + "outlier_distance_km": 7249.2, + "second_furthest_km": 3628.1, + "clarity_ratio": 2.0, + "median_distance_km": 3495.9, + "distances_to_centroid": { + "Metahāra": 3495.9, + "Kemisē": 3628.1, + "Senekal": 2166.7, + "Bloemhof": 1995.8, + "Mandaguari": 7249.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Metahāra: (8.90°, 39.92°)", + " Kemisē: (10.72°, 39.87°)", + " Senekal: (-28.32°, 27.62°)", + " Bloemhof: (-27.65°, 25.61°)", + " Mandaguari: (-23.52°, -51.68°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mandaguari: 7249.2 km from centroid", + " Kemisē: 3628.1 km from centroid", + " Metahāra: 3495.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mandaguari", + "FINAL ANSWER: Mandaguari" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.63884, + "lon": -59.77938, + "name": "Saladillo" + }, + { + "lat": -23.56729, + "lon": -46.69232, + "name": "Pinheiros" + }, + { + "lat": -22.72528, + "lon": -47.64917, + "name": "Piracicaba" + }, + { + "lat": -29.7175, + "lon": -52.42583, + "name": "Santa Cruz do Sul" + }, + { + "lat": 37.12084, + "lon": -5.45403, + "name": "Morón de la Frontera" + } + ], + "question": "Which location is the geographic outlier among: Saladillo, Pinheiros, Piracicaba, Santa Cruz do Sul, Morón de la Frontera?", + "ground_truth": { + "answer": "Morón de la Frontera", + "outlier_distance_km": 6958.1, + "second_furthest_km": 2882.5, + "clarity_ratio": 2.41, + "median_distance_km": 1940.9, + "distances_to_centroid": { + "Saladillo": 2882.5, + "Pinheiros": 1063.1, + "Piracicaba": 1029.9, + "Santa Cruz do Sul": 1940.9, + "Morón de la Frontera": 6958.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Saladillo: (-35.64°, -59.78°)", + " Pinheiros: (-23.57°, -46.69°)", + " Piracicaba: (-22.73°, -47.65°)", + " Santa Cruz do Sul: (-29.72°, -52.43°)", + " Morón de la Frontera: (37.12°, -5.45°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morón de la Frontera: 6958.1 km from centroid", + " Saladillo: 2882.5 km from centroid", + " Santa Cruz do Sul: 1940.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morón de la Frontera", + "FINAL ANSWER: Morón de la Frontera" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.23958, + "lon": 20.17004, + "name": "Działdowo" + }, + { + "lat": 53.65, + "lon": -2.61667, + "name": "Chorley" + }, + { + "lat": 50.81795, + "lon": -0.37538, + "name": "Worthing" + }, + { + "lat": 48.66181, + "lon": 2.35338, + "name": "Morsang-sur-Orge" + }, + { + "lat": 9.56561, + "lon": 36.63569, + "name": "Gutin" + } + ], + "question": "Which location is the geographic outlier among: Działdowo, Chorley, Worthing, Morsang-sur-Orge, Gutin?", + "ground_truth": { + "answer": "Gutin", + "outlier_distance_km": 4475.9, + "second_furthest_km": 1543.2, + "clarity_ratio": 2.9, + "median_distance_km": 1297.0, + "distances_to_centroid": { + "Działdowo": 1297.0, + "Chorley": 1543.2, + "Worthing": 1220.0, + "Morsang-sur-Orge": 916.7, + "Gutin": 4475.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Działdowo: (53.24°, 20.17°)", + " Chorley: (53.65°, -2.62°)", + " Worthing: (50.82°, -0.38°)", + " Morsang-sur-Orge: (48.66°, 2.35°)", + " Gutin: (9.57°, 36.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gutin: 4475.9 km from centroid", + " Chorley: 1543.2 km from centroid", + " Działdowo: 1297.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gutin", + "FINAL ANSWER: Gutin" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.4557, + "lon": 100.6288, + "name": "Pantai Remis" + }, + { + "lat": 28.45208, + "lon": 104.34491, + "name": "Shuanglong" + }, + { + "lat": 6.184, + "lon": 100.37752, + "name": "Anak Bukit" + }, + { + "lat": 34.57444, + "lon": 117.09528, + "name": "Wuduan" + }, + { + "lat": -29.08056, + "lon": -53.83583, + "name": "Tupanciretã" + } + ], + "question": "Which location is the geographic outlier among: Pantai Remis, Shuanglong, Anak Bukit, Wuduan, Tupanciretã?", + "ground_truth": { + "answer": "Tupanciretã", + "outlier_distance_km": 14120.2, + "second_furthest_km": 5250.1, + "clarity_ratio": 2.69, + "median_distance_km": 3867.9, + "distances_to_centroid": { + "Pantai Remis": 3011.5, + "Shuanglong": 3867.9, + "Anak Bukit": 2953.2, + "Wuduan": 5250.1, + "Tupanciretã": 14120.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Pantai Remis: (4.46°, 100.63°)", + " Shuanglong: (28.45°, 104.34°)", + " Anak Bukit: (6.18°, 100.38°)", + " Wuduan: (34.57°, 117.10°)", + " Tupanciretã: (-29.08°, -53.84°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tupanciretã: 14120.2 km from centroid", + " Wuduan: 5250.1 km from centroid", + " Shuanglong: 3867.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tupanciretã", + "FINAL ANSWER: Tupanciretã" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 10.3242, + "lon": -74.96017, + "name": "Santa Lucía" + }, + { + "lat": -32.035, + "lon": -52.09861, + "name": "Rio Grande" + }, + { + "lat": -11.80694, + "lon": -39.38556, + "name": "Riachão do Jacuípe" + }, + { + "lat": -20.97194, + "lon": -46.11889, + "name": "Carmo do Rio Claro" + }, + { + "lat": 13.9411, + "lon": 121.1631, + "name": "Lipa City" + } + ], + "question": "Which location is the geographic outlier among: Santa Lucía, Rio Grande, Riachão do Jacuípe, Carmo do Rio Claro, Lipa City?", + "ground_truth": { + "answer": "Lipa City", + "outlier_distance_km": 15547.0, + "second_furthest_km": 6599.9, + "clarity_ratio": 2.36, + "median_distance_km": 4387.7, + "distances_to_centroid": { + "Santa Lucía": 6599.9, + "Rio Grande": 4387.7, + "Riachão do Jacuípe": 2346.9, + "Carmo do Rio Claro": 3311.6, + "Lipa City": 15547.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santa Lucía: (10.32°, -74.96°)", + " Rio Grande: (-32.03°, -52.10°)", + " Riachão do Jacuípe: (-11.81°, -39.39°)", + " Carmo do Rio Claro: (-20.97°, -46.12°)", + " Lipa City: (13.94°, 121.16°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lipa City: 15547.0 km from centroid", + " Santa Lucía: 6599.9 km from centroid", + " Rio Grande: 4387.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lipa City", + "FINAL ANSWER: Lipa City" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.73333, + "lon": 150.93284, + "name": "Glenwood" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": -38.16604, + "lon": 145.13643, + "name": "Frankston South" + }, + { + "lat": -37.65, + "lon": 145.1, + "name": "South Morang" + }, + { + "lat": 40.85593, + "lon": -73.20067, + "name": "Smithtown" + } + ], + "question": "Which location is the geographic outlier among: Glenwood, Ellenbrook, Frankston South, South Morang, Smithtown?", + "ground_truth": { + "answer": "Smithtown", + "outlier_distance_km": 17519.1, + "second_furthest_km": 5514.3, + "clarity_ratio": 3.18, + "median_distance_km": 5040.7, + "distances_to_centroid": { + "Glenwood": 5514.3, + "Ellenbrook": 2310.1, + "Frankston South": 5040.7, + "South Morang": 5028.4, + "Smithtown": 17519.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Glenwood: (-33.73°, 150.93°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Frankston South: (-38.17°, 145.14°)", + " South Morang: (-37.65°, 145.10°)", + " Smithtown: (40.86°, -73.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Smithtown: 17519.1 km from centroid", + " Glenwood: 5514.3 km from centroid", + " Frankston South: 5040.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Smithtown", + "FINAL ANSWER: Smithtown" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.57788, + "lon": -73.99403, + "name": "Coney Island" + }, + { + "lat": 31.02526, + "lon": -114.84173, + "name": "San Felipe" + }, + { + "lat": 49.27738, + "lon": -123.07079, + "name": "Grandview-Woodlands" + }, + { + "lat": 49.16638, + "lon": -121.95257, + "name": "Chilliwack" + }, + { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + } + ], + "question": "Which location is the geographic outlier among: Coney Island, San Felipe, Grandview-Woodlands, Chilliwack, Willetton?", + "ground_truth": { + "answer": "Willetton", + "outlier_distance_km": 19517.4, + "second_furthest_km": 5543.4, + "clarity_ratio": 3.52, + "median_distance_km": 5461.6, + "distances_to_centroid": { + "Coney Island": 1729.1, + "San Felipe": 4940.0, + "Grandview-Woodlands": 5543.4, + "Chilliwack": 5461.6, + "Willetton": 19517.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Coney Island: (40.58°, -73.99°)", + " San Felipe: (31.03°, -114.84°)", + " Grandview-Woodlands: (49.28°, -123.07°)", + " Chilliwack: (49.17°, -121.95°)", + " Willetton: (-32.05°, 115.89°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Willetton: 19517.4 km from centroid", + " Grandview-Woodlands: 5543.4 km from centroid", + " Chilliwack: 5461.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Willetton", + "FINAL ANSWER: Willetton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.43404, + "lon": -3.70379, + "name": "Chamberí" + }, + { + "lat": 51.4386, + "lon": -3.17342, + "name": "Penarth" + }, + { + "lat": 51.99223, + "lon": 8.79301, + "name": "Lage" + }, + { + "lat": 50.98854, + "lon": 7.41391, + "name": "Engelskirchen" + }, + { + "lat": -5.1875, + "lon": -37.34417, + "name": "Mossoró" + } + ], + "question": "Which location is the geographic outlier among: Chamberí, Penarth, Lage, Engelskirchen, Mossoró?", + "ground_truth": { + "answer": "Mossoró", + "outlier_distance_km": 5808.2, + "second_furthest_km": 1922.9, + "clarity_ratio": 3.02, + "median_distance_km": 1776.0, + "distances_to_centroid": { + "Chamberí": 322.7, + "Penarth": 1513.7, + "Lage": 1922.9, + "Engelskirchen": 1776.0, + "Mossoró": 5808.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Chamberí: (40.43°, -3.70°)", + " Penarth: (51.44°, -3.17°)", + " Lage: (51.99°, 8.79°)", + " Engelskirchen: (50.99°, 7.41°)", + " Mossoró: (-5.19°, -37.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mossoró: 5808.2 km from centroid", + " Lage: 1922.9 km from centroid", + " Engelskirchen: 1776.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mossoró", + "FINAL ANSWER: Mossoró" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 40.09923, + "lon": -83.11408, + "name": "Dublin" + }, + { + "lat": 41.31256, + "lon": -81.44011, + "name": "Twinsburg" + }, + { + "lat": 34.18667, + "lon": -118.44897, + "name": "Van Nuys" + }, + { + "lat": 37.30588, + "lon": -89.51815, + "name": "Cape Girardeau" + }, + { + "lat": 20.19966, + "lon": 83.90938, + "name": "Baliguda" + } + ], + "question": "Which location is the geographic outlier among: Dublin, Twinsburg, Van Nuys, Cape Girardeau, Baliguda?", + "ground_truth": { + "answer": "Baliguda", + "outlier_distance_km": 12694.5, + "second_furthest_km": 5481.9, + "clarity_ratio": 2.32, + "median_distance_km": 2863.7, + "distances_to_centroid": { + "Dublin": 2316.5, + "Twinsburg": 2199.8, + "Van Nuys": 5481.9, + "Cape Girardeau": 2863.7, + "Baliguda": 12694.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Dublin: (40.10°, -83.11°)", + " Twinsburg: (41.31°, -81.44°)", + " Van Nuys: (34.19°, -118.45°)", + " Cape Girardeau: (37.31°, -89.52°)", + " Baliguda: (20.20°, 83.91°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Baliguda: 12694.5 km from centroid", + " Van Nuys: 5481.9 km from centroid", + " Cape Girardeau: 2863.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Baliguda", + "FINAL ANSWER: Baliguda" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 14.52541, + "lon": 102.24591, + "name": "Khon Buri" + }, + { + "lat": 34.00964, + "lon": 131.86637, + "name": "Kudamatsu" + }, + { + "lat": 37.97451, + "lon": 140.77202, + "name": "Kakuda" + }, + { + "lat": 36.2378, + "lon": 139.19023, + "name": "Honjō" + }, + { + "lat": 6.55504, + "lon": 3.34363, + "name": "Oshodi" + } + ], + "question": "Which location is the geographic outlier among: Khon Buri, Kudamatsu, Kakuda, Honjō, Oshodi?", + "ground_truth": { + "answer": "Oshodi", + "outlier_distance_km": 10694.4, + "second_furthest_km": 3738.2, + "clarity_ratio": 2.86, + "median_distance_km": 3568.4, + "distances_to_centroid": { + "Khon Buri": 1267.0, + "Kudamatsu": 2870.1, + "Kakuda": 3738.2, + "Honjō": 3568.4, + "Oshodi": 10694.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Khon Buri: (14.53°, 102.25°)", + " Kudamatsu: (34.01°, 131.87°)", + " Kakuda: (37.97°, 140.77°)", + " Honjō: (36.24°, 139.19°)", + " Oshodi: (6.56°, 3.34°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Oshodi: 10694.4 km from centroid", + " Kakuda: 3738.2 km from centroid", + " Honjō: 3568.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Oshodi", + "FINAL ANSWER: Oshodi" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.80128, + "lon": -73.39616, + "name": "Cañete" + }, + { + "lat": -10.33528, + "lon": -67.18556, + "name": "Plácido de Castro" + }, + { + "lat": -33.73257, + "lon": -70.74281, + "name": "Buin" + }, + { + "lat": -11.04404, + "lon": -41.97102, + "name": "Jussara" + }, + { + "lat": 7.06273, + "lon": -1.4001, + "name": "Mampong" + } + ], + "question": "Which location is the geographic outlier among: Cañete, Plácido de Castro, Buin, Jussara, Mampong?", + "ground_truth": { + "answer": "Mampong", + "outlier_distance_km": 6073.4, + "second_furthest_km": 3171.7, + "clarity_ratio": 1.91, + "median_distance_km": 2700.3, + "distances_to_centroid": { + "Cañete": 3171.7, + "Plácido de Castro": 1910.8, + "Buin": 2700.3, + "Jussara": 1182.5, + "Mampong": 6073.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cañete: (-37.80°, -73.40°)", + " Plácido de Castro: (-10.34°, -67.19°)", + " Buin: (-33.73°, -70.74°)", + " Jussara: (-11.04°, -41.97°)", + " Mampong: (7.06°, -1.40°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Mampong: 6073.4 km from centroid", + " Cañete: 3171.7 km from centroid", + " Buin: 2700.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Mampong", + "FINAL ANSWER: Mampong" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 24.97916, + "lon": 32.87722, + "name": "Edfu" + }, + { + "lat": 31.19688, + "lon": 31.5243, + "name": "Shirbīn" + }, + { + "lat": 27.3126, + "lon": 30.96987, + "name": "Manfalūţ" + }, + { + "lat": 11.66667, + "lon": 38.8, + "name": "Filakit" + }, + { + "lat": -5.90181, + "lon": -76.12234, + "name": "Yurimaguas" + } + ], + "question": "Which location is the geographic outlier among: Edfu, Shirbīn, Manfalūţ, Filakit, Yurimaguas?", + "ground_truth": { + "answer": "Yurimaguas", + "outlier_distance_km": 9969.7, + "second_furthest_km": 3000.0, + "clarity_ratio": 3.32, + "median_distance_km": 2494.8, + "distances_to_centroid": { + "Edfu": 2336.3, + "Shirbīn": 2494.8, + "Manfalūţ": 2244.7, + "Filakit": 3000.0, + "Yurimaguas": 9969.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Edfu: (24.98°, 32.88°)", + " Shirbīn: (31.20°, 31.52°)", + " Manfalūţ: (27.31°, 30.97°)", + " Filakit: (11.67°, 38.80°)", + " Yurimaguas: (-5.90°, -76.12°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Yurimaguas: 9969.7 km from centroid", + " Filakit: 3000.0 km from centroid", + " Shirbīn: 2494.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Yurimaguas", + "FINAL ANSWER: Yurimaguas" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.97704, + "lon": 9.15214, + "name": "Aschaffenburg" + }, + { + "lat": 53.59266, + "lon": 9.87697, + "name": "Lurup" + }, + { + "lat": 47.05893, + "lon": -0.87974, + "name": "Cholet" + }, + { + "lat": 41.9908, + "lon": 12.09082, + "name": "Cerveteri" + }, + { + "lat": -33.2914, + "lon": -66.32467, + "name": "San Luis" + } + ], + "question": "Which location is the geographic outlier among: Aschaffenburg, Lurup, Cholet, Cerveteri, San Luis?", + "ground_truth": { + "answer": "San Luis", + "outlier_distance_km": 9531.1, + "second_furthest_km": 2774.1, + "clarity_ratio": 3.44, + "median_distance_km": 2427.0, + "distances_to_centroid": { + "Aschaffenburg": 2427.0, + "Lurup": 2774.1, + "Cholet": 1773.3, + "Cerveteri": 2045.0, + "San Luis": 9531.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Aschaffenburg: (49.98°, 9.15°)", + " Lurup: (53.59°, 9.88°)", + " Cholet: (47.06°, -0.88°)", + " Cerveteri: (41.99°, 12.09°)", + " San Luis: (-33.29°, -66.32°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " San Luis: 9531.1 km from centroid", + " Lurup: 2774.1 km from centroid", + " Aschaffenburg: 2427.0 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": 51.49007, + "lon": 40.42236, + "name": "Anna" + }, + { + "lat": 56.44222, + "lon": 60.18778, + "name": "Polevskoy" + }, + { + "lat": 40.47353, + "lon": -3.87182, + "name": "Majadahonda" + }, + { + "lat": 44.74471, + "lon": -0.68194, + "name": "Cestas" + }, + { + "lat": 41.76955, + "lon": -71.12866, + "name": "Somerset" + } + ], + "question": "Which location is the geographic outlier among: Anna, Polevskoy, Majadahonda, Cestas, Somerset?", + "ground_truth": { + "answer": "Somerset", + "outlier_distance_km": 5834.5, + "second_furthest_km": 3831.9, + "clarity_ratio": 1.52, + "median_distance_km": 2594.5, + "distances_to_centroid": { + "Anna": 2594.5, + "Polevskoy": 3831.9, + "Majadahonda": 1013.9, + "Cestas": 504.4, + "Somerset": 5834.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Anna: (51.49°, 40.42°)", + " Polevskoy: (56.44°, 60.19°)", + " Majadahonda: (40.47°, -3.87°)", + " Cestas: (44.74°, -0.68°)", + " Somerset: (41.77°, -71.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Somerset: 5834.5 km from centroid", + " Polevskoy: 3831.9 km from centroid", + " Anna: 2594.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Somerset", + "FINAL ANSWER: Somerset" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 51.7604, + "lon": -0.56528, + "name": "Berkhamsted" + }, + { + "lat": 52.19551, + "lon": 9.46421, + "name": "Bad Münder am Deister" + }, + { + "lat": 55.50194, + "lon": 36.02722, + "name": "Mozhaysk" + }, + { + "lat": 54.08905, + "lon": 13.40244, + "name": "Universitäts- und Hansestadt Greifswald" + }, + { + "lat": 14.16347, + "lon": 38.89924, + "name": "Adwa" + } + ], + "question": "Which location is the geographic outlier among: Berkhamsted, Bad Münder am Deister, Mozhaysk, Universitäts- und Hansestadt Greifswald, Adwa?", + "ground_truth": { + "answer": "Adwa", + "outlier_distance_km": 3938.0, + "second_furthest_km": 1617.5, + "clarity_ratio": 2.43, + "median_distance_km": 1605.1, + "distances_to_centroid": { + "Berkhamsted": 1617.5, + "Bad Münder am Deister": 1037.6, + "Mozhaysk": 1605.1, + "Universitäts- und Hansestadt Greifswald": 1043.7, + "Adwa": 3938.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Berkhamsted: (51.76°, -0.57°)", + " Bad Münder am Deister: (52.20°, 9.46°)", + " Mozhaysk: (55.50°, 36.03°)", + " Universitäts- und Hansestadt Greifswald: (54.09°, 13.40°)", + " Adwa: (14.16°, 38.90°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Adwa: 3938.0 km from centroid", + " Berkhamsted: 1617.5 km from centroid", + " Mozhaysk: 1605.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Adwa", + "FINAL ANSWER: Adwa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -1.78079, + "lon": 37.62882, + "name": "Wote" + }, + { + "lat": 25.69893, + "lon": 32.6421, + "name": "Luxor" + }, + { + "lat": 12.40592, + "lon": 4.64605, + "name": "Tambuwal" + }, + { + "lat": 7.62329, + "lon": 5.22087, + "name": "Ado-Ekiti" + }, + { + "lat": 28.07807, + "lon": -82.76371, + "name": "Palm Harbor" + } + ], + "question": "Which location is the geographic outlier among: Wote, Luxor, Tambuwal, Ado-Ekiti, Palm Harbor?", + "ground_truth": { + "answer": "Palm Harbor", + "outlier_distance_km": 8512.6, + "second_furthest_km": 4570.4, + "clarity_ratio": 1.86, + "median_distance_km": 3672.1, + "distances_to_centroid": { + "Wote": 4570.4, + "Luxor": 3672.1, + "Tambuwal": 601.9, + "Ado-Ekiti": 980.5, + "Palm Harbor": 8512.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Wote: (-1.78°, 37.63°)", + " Luxor: (25.70°, 32.64°)", + " Tambuwal: (12.41°, 4.65°)", + " Ado-Ekiti: (7.62°, 5.22°)", + " Palm Harbor: (28.08°, -82.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Palm Harbor: 8512.6 km from centroid", + " Wote: 4570.4 km from centroid", + " Luxor: 3672.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Palm Harbor", + "FINAL ANSWER: Palm Harbor" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 6.25532, + "lon": 45.3853, + "name": "Lasoano" + }, + { + "lat": 10.71668, + "lon": 39.86997, + "name": "Kemisē" + }, + { + "lat": 31.10483, + "lon": 30.64135, + "name": "Ar Raḩmānīyah" + }, + { + "lat": 7.10168, + "lon": 7.65945, + "name": "Otukpa" + }, + { + "lat": 25.91176, + "lon": -80.20033, + "name": "Golden Glades" + } + ], + "question": "Which location is the geographic outlier among: Lasoano, Kemisē, Ar Raḩmānīyah, Otukpa, Golden Glades?", + "ground_truth": { + "answer": "Golden Glades", + "outlier_distance_km": 9118.7, + "second_furthest_km": 4146.5, + "clarity_ratio": 2.2, + "median_distance_km": 3425.0, + "distances_to_centroid": { + "Lasoano": 4146.5, + "Kemisē": 3425.0, + "Ar Raḩmānīyah": 2773.5, + "Otukpa": 1019.6, + "Golden Glades": 9118.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lasoano: (6.26°, 45.39°)", + " Kemisē: (10.72°, 39.87°)", + " Ar Raḩmānīyah: (31.10°, 30.64°)", + " Otukpa: (7.10°, 7.66°)", + " Golden Glades: (25.91°, -80.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Golden Glades: 9118.7 km from centroid", + " Lasoano: 4146.5 km from centroid", + " Kemisē: 3425.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Golden Glades", + "FINAL ANSWER: Golden Glades" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.83543, + "lon": -76.29827, + "name": "Portsmouth" + }, + { + "lat": 40.77205, + "lon": -73.93014, + "name": "Astoria" + }, + { + "lat": 40.04622, + "lon": -75.35991, + "name": "Radnor" + }, + { + "lat": 18.15056, + "lon": -94.5525, + "name": "Fraccionamiento Ciudad Olmeca" + }, + { + "lat": -23.81305, + "lon": -64.79353, + "name": "Libertador General San Martín" + } + ], + "question": "Which location is the geographic outlier among: Portsmouth, Astoria, Radnor, Fraccionamiento Ciudad Olmeca, Libertador General San Martín?", + "ground_truth": { + "answer": "Libertador General San Martín", + "outlier_distance_km": 5304.8, + "second_furthest_km": 2063.1, + "clarity_ratio": 2.57, + "median_distance_km": 1968.4, + "distances_to_centroid": { + "Portsmouth": 1606.7, + "Astoria": 2063.1, + "Radnor": 1968.4, + "Fraccionamiento Ciudad Olmeca": 1890.7, + "Libertador General San Martín": 5304.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Portsmouth: (36.84°, -76.30°)", + " Astoria: (40.77°, -73.93°)", + " Radnor: (40.05°, -75.36°)", + " Fraccionamiento Ciudad Olmeca: (18.15°, -94.55°)", + " Libertador General San Martín: (-23.81°, -64.79°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Libertador General San Martín: 5304.8 km from centroid", + " Astoria: 2063.1 km from centroid", + " Radnor: 1968.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Libertador General San Martín", + "FINAL ANSWER: Libertador General San Martín" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + { + "lat": -33.8, + "lon": 151.18333, + "name": "Chatswood" + }, + { + "lat": 12.9534, + "lon": 79.13373, + "name": "Kalinjur" + } + ], + "question": "Which location is the geographic outlier among: Tauranga, Campsie, Dunedin, Chatswood, Kalinjur?", + "ground_truth": { + "answer": "Kalinjur", + "outlier_distance_km": 8461.3, + "second_furthest_km": 3051.8, + "clarity_ratio": 2.77, + "median_distance_km": 2979.0, + "distances_to_centroid": { + "Tauranga": 3051.8, + "Campsie": 869.9, + "Dunedin": 2979.0, + "Chatswood": 864.8, + "Kalinjur": 8461.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tauranga: (-37.69°, 176.17°)", + " Campsie: (-33.91°, 151.10°)", + " Dunedin: (-45.87°, 170.50°)", + " Chatswood: (-33.80°, 151.18°)", + " Kalinjur: (12.95°, 79.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kalinjur: 8461.3 km from centroid", + " Tauranga: 3051.8 km from centroid", + " Dunedin: 2979.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kalinjur", + "FINAL ANSWER: Kalinjur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.1625, + "lon": 6.37639, + "name": "Leek" + }, + { + "lat": 51.5144, + "lon": -0.13535, + "name": "Soho" + }, + { + "lat": 41.36718, + "lon": 2.0574, + "name": "Sant Joan Despí" + }, + { + "lat": 45.67206, + "lon": 8.82691, + "name": "Cassano Magnago" + }, + { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + } + ], + "question": "Which location is the geographic outlier among: Leek, Soho, Sant Joan Despí, Cassano Magnago, Traralgon?", + "ground_truth": { + "answer": "Traralgon", + "outlier_distance_km": 14016.2, + "second_furthest_km": 3545.5, + "clarity_ratio": 3.95, + "median_distance_km": 3277.5, + "distances_to_centroid": { + "Leek": 3277.5, + "Soho": 3545.5, + "Sant Joan Despí": 2982.1, + "Cassano Magnago": 2653.3, + "Traralgon": 14016.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Leek: (53.16°, 6.38°)", + " Soho: (51.51°, -0.14°)", + " Sant Joan Despí: (41.37°, 2.06°)", + " Cassano Magnago: (45.67°, 8.83°)", + " Traralgon: (-38.20°, 146.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Traralgon: 14016.2 km from centroid", + " Soho: 3545.5 km from centroid", + " Leek: 3277.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Traralgon", + "FINAL ANSWER: Traralgon" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 5.70773, + "lon": 6.43402, + "name": "Kwale" + }, + { + "lat": 6.6, + "lon": 38.41667, + "name": "Wendo" + }, + { + "lat": 27.18096, + "lon": 31.18368, + "name": "Assiut" + }, + { + "lat": 25.25, + "lon": 30.55, + "name": "Al-Khārijah" + }, + { + "lat": 40.62205, + "lon": -74.24459, + "name": "Linden" + } + ], + "question": "Which location is the geographic outlier among: Kwale, Wendo, Assiut, Al-Khārijah, Linden?", + "ground_truth": { + "answer": "Linden", + "outlier_distance_km": 7740.4, + "second_furthest_km": 3794.0, + "clarity_ratio": 2.04, + "median_distance_km": 2593.5, + "distances_to_centroid": { + "Kwale": 1708.4, + "Wendo": 3794.0, + "Assiut": 2593.5, + "Al-Khārijah": 2501.8, + "Linden": 7740.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Kwale: (5.71°, 6.43°)", + " Wendo: (6.60°, 38.42°)", + " Assiut: (27.18°, 31.18°)", + " Al-Khārijah: (25.25°, 30.55°)", + " Linden: (40.62°, -74.24°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Linden: 7740.4 km from centroid", + " Wendo: 3794.0 km from centroid", + " Assiut: 2593.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Linden", + "FINAL ANSWER: Linden" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + { + "lat": -34.78254, + "lon": 138.61077, + "name": "Parafield Gardens" + }, + { + "lat": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -34.28853, + "lon": 146.05093, + "name": "Griffith" + }, + { + "lat": 20.57806, + "lon": 86.56063, + "name": "Patāmundai" + } + ], + "question": "Which location is the geographic outlier among: Alexandra Hills, Parafield Gardens, Bexley, Griffith, Patāmundai?", + "ground_truth": { + "answer": "Patāmundai", + "outlier_distance_km": 7084.0, + "second_furthest_km": 2053.5, + "clarity_ratio": 3.45, + "median_distance_km": 1927.6, + "distances_to_centroid": { + "Alexandra Hills": 1927.6, + "Parafield Gardens": 1462.2, + "Bexley": 2053.5, + "Griffith": 1734.8, + "Patāmundai": 7084.0 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Alexandra Hills: (-27.53°, 153.23°)", + " Parafield Gardens: (-34.78°, 138.61°)", + " Bexley: (-33.95°, 151.12°)", + " Griffith: (-34.29°, 146.05°)", + " Patāmundai: (20.58°, 86.56°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Patāmundai: 7084.0 km from centroid", + " Bexley: 2053.5 km from centroid", + " Alexandra Hills: 1927.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Patāmundai", + "FINAL ANSWER: Patāmundai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -28.00274, + "lon": 153.42999, + "name": "Surfers Paradise" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -37.65, + "lon": 145.03333, + "name": "Epping" + }, + { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + { + "lat": 19.8173, + "lon": -97.35992, + "name": "Teziutlan" + } + ], + "question": "Which location is the geographic outlier among: Surfers Paradise, Glenroy, Epping, Wollongong, Teziutlan?", + "ground_truth": { + "answer": "Teziutlan", + "outlier_distance_km": 18236.1, + "second_furthest_km": 5389.7, + "clarity_ratio": 3.38, + "median_distance_km": 5096.4, + "distances_to_centroid": { + "Surfers Paradise": 5389.7, + "Glenroy": 4580.0, + "Epping": 4588.1, + "Wollongong": 5096.4, + "Teziutlan": 18236.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Surfers Paradise: (-28.00°, 153.43°)", + " Glenroy: (-37.70°, 144.93°)", + " Epping: (-37.65°, 145.03°)", + " Wollongong: (-34.42°, 150.89°)", + " Teziutlan: (19.82°, -97.36°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Teziutlan: 18236.1 km from centroid", + " Surfers Paradise: 5389.7 km from centroid", + " Wollongong: 5096.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Teziutlan", + "FINAL ANSWER: Teziutlan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 45.58058, + "lon": 39.65741, + "name": "Vyselki" + }, + { + "lat": 45.06982, + "lon": 11.79022, + "name": "Rovigo" + }, + { + "lat": 48.53053, + "lon": 11.505, + "name": "Pfaffenhofen an der Ilm" + }, + { + "lat": 52.25116, + "lon": 10.81683, + "name": "Königslutter am Elm" + }, + { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + } + ], + "question": "Which location is the geographic outlier among: Vyselki, Rovigo, Pfaffenhofen an der Ilm, Königslutter am Elm, Sunshine West?", + "ground_truth": { + "answer": "Sunshine West", + "outlier_distance_km": 12937.7, + "second_furthest_km": 3584.4, + "clarity_ratio": 3.61, + "median_distance_km": 3355.3, + "distances_to_centroid": { + "Vyselki": 1688.6, + "Rovigo": 3193.3, + "Pfaffenhofen an der Ilm": 3355.3, + "Königslutter am Elm": 3584.4, + "Sunshine West": 12937.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vyselki: (45.58°, 39.66°)", + " Rovigo: (45.07°, 11.79°)", + " Pfaffenhofen an der Ilm: (48.53°, 11.51°)", + " Königslutter am Elm: (52.25°, 10.82°)", + " Sunshine West: (-37.79°, 144.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sunshine West: 12937.7 km from centroid", + " Königslutter am Elm: 3584.4 km from centroid", + " Pfaffenhofen an der Ilm: 3355.3 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": -33.95, + "lon": 151.11667, + "name": "Bexley" + }, + { + "lat": -37.7, + "lon": 144.93333, + "name": "Glenroy" + }, + { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + { + "lat": 39.52079, + "lon": 116.71471, + "name": "Langfang" + } + ], + "question": "Which location is the geographic outlier among: Bexley, Glenroy, Ashfield, Ellenbrook, Langfang?", + "ground_truth": { + "answer": "Langfang", + "outlier_distance_km": 6867.1, + "second_furthest_km": 2414.3, + "clarity_ratio": 2.84, + "median_distance_km": 2196.0, + "distances_to_centroid": { + "Bexley": 2190.7, + "Glenroy": 2196.0, + "Ashfield": 2186.4, + "Ellenbrook": 2414.3, + "Langfang": 6867.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Bexley: (-33.95°, 151.12°)", + " Glenroy: (-37.70°, 144.93°)", + " Ashfield: (-33.89°, 151.12°)", + " Ellenbrook: (-31.77°, 115.97°)", + " Langfang: (39.52°, 116.71°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Langfang: 6867.1 km from centroid", + " Ellenbrook: 2414.3 km from centroid", + " Glenroy: 2196.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Langfang", + "FINAL ANSWER: Langfang" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.12084, + "lon": -5.45403, + "name": "Morón de la Frontera" + }, + { + "lat": 46.8458, + "lon": -1.87942, + "name": "Challans" + }, + { + "lat": 56.22761, + "lon": 32.77474, + "name": "Nelidovo" + }, + { + "lat": 51.28333, + "lon": -0.83333, + "name": "Fleet" + }, + { + "lat": 7.43636, + "lon": 5.45925, + "name": "Emure-Ekiti" + } + ], + "question": "Which location is the geographic outlier among: Morón de la Frontera, Challans, Nelidovo, Fleet, Emure-Ekiti?", + "ground_truth": { + "answer": "Emure-Ekiti", + "outlier_distance_km": 3597.2, + "second_furthest_km": 2672.0, + "clarity_ratio": 1.35, + "median_distance_km": 1384.1, + "distances_to_centroid": { + "Morón de la Frontera": 1040.7, + "Challans": 1011.1, + "Nelidovo": 2672.0, + "Fleet": 1384.1, + "Emure-Ekiti": 3597.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Morón de la Frontera: (37.12°, -5.45°)", + " Challans: (46.85°, -1.88°)", + " Nelidovo: (56.23°, 32.77°)", + " Fleet: (51.28°, -0.83°)", + " Emure-Ekiti: (7.44°, 5.46°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Emure-Ekiti: 3597.2 km from centroid", + " Nelidovo: 2672.0 km from centroid", + " Fleet: 1384.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Emure-Ekiti", + "FINAL ANSWER: Emure-Ekiti" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.72111, + "lon": -103.38742, + "name": "Zapopan" + }, + { + "lat": 37.72493, + "lon": -122.15608, + "name": "San Leandro" + }, + { + "lat": 43.21555, + "lon": -88.03001, + "name": "Mequon" + }, + { + "lat": 50.03928, + "lon": -110.67661, + "name": "Medicine Hat" + }, + { + "lat": 4.02219, + "lon": 101.02083, + "name": "Teluk Intan" + } + ], + "question": "Which location is the geographic outlier among: Zapopan, San Leandro, Mequon, Medicine Hat, Teluk Intan?", + "ground_truth": { + "answer": "Teluk Intan", + "outlier_distance_km": 15819.7, + "second_furthest_km": 5242.8, + "clarity_ratio": 3.02, + "median_distance_km": 4327.3, + "distances_to_centroid": { + "Zapopan": 4020.9, + "San Leandro": 5242.8, + "Mequon": 2455.2, + "Medicine Hat": 4327.3, + "Teluk Intan": 15819.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Zapopan: (20.72°, -103.39°)", + " San Leandro: (37.72°, -122.16°)", + " Mequon: (43.22°, -88.03°)", + " Medicine Hat: (50.04°, -110.68°)", + " Teluk Intan: (4.02°, 101.02°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Teluk Intan: 15819.7 km from centroid", + " San Leandro: 5242.8 km from centroid", + " Medicine Hat: 4327.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Teluk Intan", + "FINAL ANSWER: Teluk Intan" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 20.23031, + "lon": -99.21396, + "name": "Mixquiahuala de Juarez" + }, + { + "lat": 41.80503, + "lon": -87.86923, + "name": "La Grange" + }, + { + "lat": 15.13924, + "lon": -92.4634, + "name": "Huixtla" + }, + { + "lat": 43.6135, + "lon": -116.20345, + "name": "Boise" + }, + { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + } + ], + "question": "Which location is the geographic outlier among: Mixquiahuala de Juarez, La Grange, Huixtla, Boise, Scarborough?", + "ground_truth": { + "answer": "Scarborough", + "outlier_distance_km": 18240.4, + "second_furthest_km": 6273.0, + "clarity_ratio": 2.91, + "median_distance_km": 4539.3, + "distances_to_centroid": { + "Mixquiahuala de Juarez": 4539.3, + "La Grange": 4032.0, + "Huixtla": 3893.9, + "Boise": 6273.0, + "Scarborough": 18240.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mixquiahuala de Juarez: (20.23°, -99.21°)", + " La Grange: (41.81°, -87.87°)", + " Huixtla: (15.14°, -92.46°)", + " Boise: (43.61°, -116.20°)", + " Scarborough: (-31.90°, 115.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Scarborough: 18240.4 km from centroid", + " Boise: 6273.0 km from centroid", + " Mixquiahuala de Juarez: 4539.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Scarborough", + "FINAL ANSWER: Scarborough" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -33.58331, + "lon": -70.63419, + "name": "La Pintana" + }, + { + "lat": -40.81519, + "lon": -63.0004, + "name": "Viedma" + }, + { + "lat": -21.97556, + "lon": -45.35028, + "name": "Lambari" + }, + { + "lat": -25.51626, + "lon": -48.52537, + "name": "Paranaguá" + }, + { + "lat": 17.5921, + "lon": 74.19966, + "name": "Rahimatpur" + } + ], + "question": "Which location is the geographic outlier among: La Pintana, Viedma, Lambari, Paranaguá, Rahimatpur?", + "ground_truth": { + "answer": "Rahimatpur", + "outlier_distance_km": 12191.3, + "second_furthest_km": 4167.7, + "clarity_ratio": 2.93, + "median_distance_km": 3766.5, + "distances_to_centroid": { + "La Pintana": 4167.7, + "Viedma": 3766.5, + "Lambari": 1524.9, + "Paranaguá": 1896.0, + "Rahimatpur": 12191.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " La Pintana: (-33.58°, -70.63°)", + " Viedma: (-40.82°, -63.00°)", + " Lambari: (-21.98°, -45.35°)", + " Paranaguá: (-25.52°, -48.53°)", + " Rahimatpur: (17.59°, 74.20°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rahimatpur: 12191.3 km from centroid", + " La Pintana: 4167.7 km from centroid", + " Viedma: 3766.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rahimatpur", + "FINAL ANSWER: Rahimatpur" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.4717, + "lon": -46.57923, + "name": "Vila Galvão" + }, + { + "lat": 6.15153, + "lon": -75.61657, + "name": "Sabaneta" + }, + { + "lat": -5.32222, + "lon": -41.5525, + "name": "Castelo do Piauí" + }, + { + "lat": -11.42047, + "lon": -58.75488, + "name": "Juína" + }, + { + "lat": 7.13333, + "lon": 37.95, + "name": "Shonē" + } + ], + "question": "Which location is the geographic outlier among: Vila Galvão, Sabaneta, Castelo do Piauí, Juína, Shonē?", + "ground_truth": { + "answer": "Shonē", + "outlier_distance_km": 8421.7, + "second_furthest_km": 4483.9, + "clarity_ratio": 1.88, + "median_distance_km": 2493.4, + "distances_to_centroid": { + "Vila Galvão": 2262.2, + "Sabaneta": 4483.9, + "Castelo do Piauí": 513.9, + "Juína": 2493.4, + "Shonē": 8421.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Vila Galvão: (-23.47°, -46.58°)", + " Sabaneta: (6.15°, -75.62°)", + " Castelo do Piauí: (-5.32°, -41.55°)", + " Juína: (-11.42°, -58.75°)", + " Shonē: (7.13°, 37.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Shonē: 8421.7 km from centroid", + " Sabaneta: 4483.9 km from centroid", + " Juína: 2493.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Shonē", + "FINAL ANSWER: Shonē" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.8525, + "lon": -46.9425, + "name": "São Lourenço da Serra" + }, + { + "lat": 4.96531, + "lon": -73.91301, + "name": "Tocancipá" + }, + { + "lat": -28.40833, + "lon": -54.96083, + "name": "São Luiz Gonzaga" + }, + { + "lat": -15.64667, + "lon": -56.1325, + "name": "Várzea Grande" + }, + { + "lat": 35.42291, + "lon": 136.76039, + "name": "Gifu" + } + ], + "question": "Which location is the geographic outlier among: São Lourenço da Serra, Tocancipá, São Luiz Gonzaga, Várzea Grande, Gifu?", + "ground_truth": { + "answer": "Gifu", + "outlier_distance_km": 15867.1, + "second_furthest_km": 6203.4, + "clarity_ratio": 2.56, + "median_distance_km": 4559.7, + "distances_to_centroid": { + "São Lourenço da Serra": 3614.8, + "Tocancipá": 6203.4, + "São Luiz Gonzaga": 4559.7, + "Várzea Grande": 4200.5, + "Gifu": 15867.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " São Lourenço da Serra: (-23.85°, -46.94°)", + " Tocancipá: (4.97°, -73.91°)", + " São Luiz Gonzaga: (-28.41°, -54.96°)", + " Várzea Grande: (-15.65°, -56.13°)", + " Gifu: (35.42°, 136.76°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gifu: 15867.1 km from centroid", + " Tocancipá: 6203.4 km from centroid", + " São Luiz Gonzaga: 4559.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gifu", + "FINAL ANSWER: Gifu" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 33.20566, + "lon": 130.37527, + "name": "Ōkawa" + }, + { + "lat": 31.17664, + "lon": 108.13155, + "name": "Zhonghe" + }, + { + "lat": 11.57506, + "lon": 77.59043, + "name": "Anthiyur" + }, + { + "lat": 25.66742, + "lon": 116.75429, + "name": "Wenheng" + }, + { + "lat": 53.58453, + "lon": 9.76594, + "name": "Rissen" + } + ], + "question": "Which location is the geographic outlier among: Ōkawa, Zhonghe, Anthiyur, Wenheng, Rissen?", + "ground_truth": { + "answer": "Rissen", + "outlier_distance_km": 6567.2, + "second_furthest_km": 3922.4, + "clarity_ratio": 1.67, + "median_distance_km": 2818.3, + "distances_to_centroid": { + "Ōkawa": 3922.4, + "Zhonghe": 1864.4, + "Anthiyur": 2439.2, + "Wenheng": 2818.3, + "Rissen": 6567.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ōkawa: (33.21°, 130.38°)", + " Zhonghe: (31.18°, 108.13°)", + " Anthiyur: (11.58°, 77.59°)", + " Wenheng: (25.67°, 116.75°)", + " Rissen: (53.58°, 9.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Rissen: 6567.2 km from centroid", + " Ōkawa: 3922.4 km from centroid", + " Wenheng: 2818.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Rissen", + "FINAL ANSWER: Rissen" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + { + "lat": -27.20338, + "lon": 152.95923, + "name": "Narangba" + }, + { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + { + "lat": 30.81609, + "lon": 108.26216, + "name": "Lihe" + } + ], + "question": "Which location is the geographic outlier among: Epsom, Papatoetoe, Narangba, Cranbourne East, Lihe?", + "ground_truth": { + "answer": "Lihe", + "outlier_distance_km": 7421.4, + "second_furthest_km": 2838.2, + "clarity_ratio": 2.61, + "median_distance_km": 2828.3, + "distances_to_centroid": { + "Epsom": 2828.3, + "Papatoetoe": 2838.2, + "Narangba": 639.6, + "Cranbourne East": 1914.5, + "Lihe": 7421.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Epsom: (-36.89°, 174.77°)", + " Papatoetoe: (-36.97°, 174.84°)", + " Narangba: (-27.20°, 152.96°)", + " Cranbourne East: (-38.12°, 145.30°)", + " Lihe: (30.82°, 108.26°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lihe: 7421.4 km from centroid", + " Papatoetoe: 2838.2 km from centroid", + " Epsom: 2828.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lihe", + "FINAL ANSWER: Lihe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 19.20959, + "lon": -98.75636, + "name": "San Rafael" + }, + { + "lat": 43.25655, + "lon": -79.08527, + "name": "Niagara-on-the-Lake" + }, + { + "lat": 34.07751, + "lon": -117.68978, + "name": "Montclair" + }, + { + "lat": 41.05899, + "lon": -74.02181, + "name": "Pearl River" + }, + { + "lat": -7.59083, + "lon": -37.53944, + "name": "Tabira" + } + ], + "question": "Which location is the geographic outlier among: San Rafael, Niagara-on-the-Lake, Montclair, Pearl River, Tabira?", + "ground_truth": { + "answer": "Tabira", + "outlier_distance_km": 6032.3, + "second_furthest_km": 3584.8, + "clarity_ratio": 1.68, + "median_distance_km": 1931.0, + "distances_to_centroid": { + "San Rafael": 1931.0, + "Niagara-on-the-Lake": 1930.2, + "Montclair": 3584.8, + "Pearl River": 1807.4, + "Tabira": 6032.3 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " San Rafael: (19.21°, -98.76°)", + " Niagara-on-the-Lake: (43.26°, -79.09°)", + " Montclair: (34.08°, -117.69°)", + " Pearl River: (41.06°, -74.02°)", + " Tabira: (-7.59°, -37.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tabira: 6032.3 km from centroid", + " Montclair: 3584.8 km from centroid", + " San Rafael: 1931.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tabira", + "FINAL ANSWER: Tabira" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 27.72297, + "lon": 75.47178, + "name": "Udaipur" + }, + { + "lat": 10.87995, + "lon": 76.002, + "name": "Naduvattam" + }, + { + "lat": 26.17668, + "lon": 90.62634, + "name": "Goālpāra" + }, + { + "lat": 2.01667, + "lon": 111.91667, + "name": "Julau" + }, + { + "lat": -26.93139, + "lon": -48.95889, + "name": "Gaspar" + } + ], + "question": "Which location is the geographic outlier among: Udaipur, Naduvattam, Goālpāra, Julau, Gaspar?", + "ground_truth": { + "answer": "Gaspar", + "outlier_distance_km": 12383.7, + "second_furthest_km": 5673.5, + "clarity_ratio": 2.18, + "median_distance_km": 3725.4, + "distances_to_centroid": { + "Udaipur": 2670.9, + "Naduvattam": 1675.5, + "Goālpāra": 3725.4, + "Julau": 5673.5, + "Gaspar": 12383.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Udaipur: (27.72°, 75.47°)", + " Naduvattam: (10.88°, 76.00°)", + " Goālpāra: (26.18°, 90.63°)", + " Julau: (2.02°, 111.92°)", + " Gaspar: (-26.93°, -48.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Gaspar: 12383.7 km from centroid", + " Julau: 5673.5 km from centroid", + " Goālpāra: 3725.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Gaspar", + "FINAL ANSWER: Gaspar" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 36.92077, + "lon": -6.07529, + "name": "Lebrija" + }, + { + "lat": 51.41655, + "lon": 21.96939, + "name": "Puławy" + }, + { + "lat": 38.42539, + "lon": -6.41734, + "name": "Zafra" + }, + { + "lat": 39.2989, + "lon": 16.25307, + "name": "Cosenza" + }, + { + "lat": 20.62354, + "lon": 79.96454, + "name": "Desāīganj" + } + ], + "question": "Which location is the geographic outlier among: Lebrija, Puławy, Zafra, Cosenza, Desāīganj?", + "ground_truth": { + "answer": "Desāīganj", + "outlier_distance_km": 5917.2, + "second_furthest_km": 2412.5, + "clarity_ratio": 2.45, + "median_distance_km": 2404.7, + "distances_to_centroid": { + "Lebrija": 2404.7, + "Puławy": 1566.9, + "Zafra": 2412.5, + "Cosenza": 478.7, + "Desāīganj": 5917.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Lebrija: (36.92°, -6.08°)", + " Puławy: (51.42°, 21.97°)", + " Zafra: (38.43°, -6.42°)", + " Cosenza: (39.30°, 16.25°)", + " Desāīganj: (20.62°, 79.96°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Desāīganj: 5917.2 km from centroid", + " Zafra: 2412.5 km from centroid", + " Lebrija: 2404.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Desāīganj", + "FINAL ANSWER: Desāīganj" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -23.44417, + "lon": -46.91778, + "name": "Santana de Parnaíba" + }, + { + "lat": -22.98436, + "lon": -43.20285, + "name": "Ipanema" + }, + { + "lat": -6.72917, + "lon": -38.44889, + "name": "São João do Rio do Peixe" + }, + { + "lat": -32.85704, + "lon": -61.15114, + "name": "Carcarañá" + }, + { + "lat": 40.6462, + "lon": 17.51661, + "name": "Ceglie Messapica" + } + ], + "question": "Which location is the geographic outlier among: Santana de Parnaíba, Ipanema, São João do Rio do Peixe, Carcarañá, Ceglie Messapica?", + "ground_truth": { + "answer": "Ceglie Messapica", + "outlier_distance_km": 7668.2, + "second_furthest_km": 3808.8, + "clarity_ratio": 2.01, + "median_distance_km": 2077.3, + "distances_to_centroid": { + "Santana de Parnaíba": 2077.3, + "Ipanema": 1806.6, + "São João do Rio do Peixe": 512.6, + "Carcarañá": 3808.8, + "Ceglie Messapica": 7668.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Santana de Parnaíba: (-23.44°, -46.92°)", + " Ipanema: (-22.98°, -43.20°)", + " São João do Rio do Peixe: (-6.73°, -38.45°)", + " Carcarañá: (-32.86°, -61.15°)", + " Ceglie Messapica: (40.65°, 17.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Ceglie Messapica: 7668.2 km from centroid", + " Carcarañá: 3808.8 km from centroid", + " Santana de Parnaíba: 2077.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Ceglie Messapica", + "FINAL ANSWER: Ceglie Messapica" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 37.69465, + "lon": -122.11385, + "name": "Ashland" + }, + { + "lat": 34.44361, + "lon": -118.60953, + "name": "Valencia" + }, + { + "lat": 40.9805, + "lon": -111.88744, + "name": "Farmington" + }, + { + "lat": 47.67399, + "lon": -122.12151, + "name": "Redmond" + }, + { + "lat": 58.59382, + "lon": 35.80244, + "name": "Pestovo" + } + ], + "question": "Which location is the geographic outlier among: Ashland, Valencia, Farmington, Redmond, Pestovo?", + "ground_truth": { + "answer": "Pestovo", + "outlier_distance_km": 7498.2, + "second_furthest_km": 2948.0, + "clarity_ratio": 2.54, + "median_distance_km": 2836.6, + "distances_to_centroid": { + "Ashland": 2948.0, + "Valencia": 2836.6, + "Farmington": 1996.8, + "Redmond": 2673.6, + "Pestovo": 7498.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ashland: (37.69°, -122.11°)", + " Valencia: (34.44°, -118.61°)", + " Farmington: (40.98°, -111.89°)", + " Redmond: (47.67°, -122.12°)", + " Pestovo: (58.59°, 35.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Pestovo: 7498.2 km from centroid", + " Ashland: 2948.0 km from centroid", + " Valencia: 2836.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Pestovo", + "FINAL ANSWER: Pestovo" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + { + "lat": -27.98941, + "lon": 153.33633, + "name": "Nerang" + }, + { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + { + "lat": 22.19994, + "lon": 84.86176, + "name": "Raurkela Industrial Township" + } + ], + "question": "Which location is the geographic outlier among: Hawthorn South, Nerang, Saint Albans, Tuggeranong Administrative District, Raurkela Industrial Township?", + "ground_truth": { + "answer": "Raurkela Industrial Township", + "outlier_distance_km": 7453.6, + "second_furthest_km": 1879.6, + "clarity_ratio": 3.97, + "median_distance_km": 1865.8, + "distances_to_centroid": { + "Hawthorn South": 1851.8, + "Nerang": 1865.8, + "Saint Albans": 1831.4, + "Tuggeranong Administrative District": 1879.6, + "Raurkela Industrial Township": 7453.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Hawthorn South: (-37.83°, 145.04°)", + " Nerang: (-27.99°, 153.34°)", + " Saint Albans: (-37.73°, 144.80°)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + " Raurkela Industrial Township: (22.20°, 84.86°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Raurkela Industrial Township: 7453.6 km from centroid", + " Tuggeranong Administrative District: 1879.6 km from centroid", + " Nerang: 1865.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Raurkela Industrial Township", + "FINAL ANSWER: Raurkela Industrial Township" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 13.77698, + "lon": 100.4567, + "name": "Taling Chan" + }, + { + "lat": 21.26644, + "lon": 79.11559, + "name": "Chicholi" + }, + { + "lat": 30.41908, + "lon": 107.53848, + "name": "Zhoujia" + }, + { + "lat": 21.33726, + "lon": 71.3035, + "name": "Savarkundla" + }, + { + "lat": 5.58365, + "lon": -0.10722, + "name": "Teshi Old Town" + } + ], + "question": "Which location is the geographic outlier among: Taling Chan, Chicholi, Zhoujia, Savarkundla, Teshi Old Town?", + "ground_truth": { + "answer": "Teshi Old Town", + "outlier_distance_km": 7890.9, + "second_furthest_km": 3846.8, + "clarity_ratio": 2.05, + "median_distance_km": 3116.4, + "distances_to_centroid": { + "Taling Chan": 3116.4, + "Chicholi": 838.8, + "Zhoujia": 3846.8, + "Savarkundla": 320.3, + "Teshi Old Town": 7890.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Taling Chan: (13.78°, 100.46°)", + " Chicholi: (21.27°, 79.12°)", + " Zhoujia: (30.42°, 107.54°)", + " Savarkundla: (21.34°, 71.30°)", + " Teshi Old Town: (5.58°, -0.11°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Teshi Old Town: 7890.9 km from centroid", + " Zhoujia: 3846.8 km from centroid", + " Taling Chan: 3116.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Teshi Old Town", + "FINAL ANSWER: Teshi Old Town" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 25.5022, + "lon": 86.46708, + "name": "Khagaria" + }, + { + "lat": 13.01927, + "lon": 76.12434, + "name": "Satyāmangala" + }, + { + "lat": 26.11667, + "lon": 79.73333, + "name": "Kālpi" + }, + { + "lat": 29.28917, + "lon": 121.42472, + "name": "Ninghai" + }, + { + "lat": -33.65249, + "lon": 115.3455, + "name": "Busselton" + } + ], + "question": "Which location is the geographic outlier among: Khagaria, Satyāmangala, Kālpi, Ninghai, Busselton?", + "ground_truth": { + "answer": "Busselton", + "outlier_distance_km": 5486.9, + "second_furthest_km": 3267.6, + "clarity_ratio": 1.68, + "median_distance_km": 2297.9, + "distances_to_centroid": { + "Khagaria": 1788.5, + "Satyāmangala": 2139.9, + "Kālpi": 2297.9, + "Ninghai": 3267.6, + "Busselton": 5486.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Khagaria: (25.50°, 86.47°)", + " Satyāmangala: (13.02°, 76.12°)", + " Kālpi: (26.12°, 79.73°)", + " Ninghai: (29.29°, 121.42°)", + " Busselton: (-33.65°, 115.35°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Busselton: 5486.9 km from centroid", + " Ninghai: 3267.6 km from centroid", + " Kālpi: 2297.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Busselton", + "FINAL ANSWER: Busselton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.36, + "lon": 2.13986, + "name": "la Marina de Port" + }, + { + "lat": 54.12226, + "lon": 17.98119, + "name": "Kościerzyna" + }, + { + "lat": 52.60831, + "lon": 1.73052, + "name": "Great Yarmouth" + }, + { + "lat": 52.30273, + "lon": -0.69446, + "name": "Wellingborough" + }, + { + "lat": -33.79728, + "lon": 150.7847, + "name": "St Clair" + } + ], + "question": "Which location is the geographic outlier among: la Marina de Port, Kościerzyna, Great Yarmouth, Wellingborough, St Clair?", + "ground_truth": { + "answer": "St Clair", + "outlier_distance_km": 14221.7, + "second_furthest_km": 3500.9, + "clarity_ratio": 4.06, + "median_distance_km": 3366.1, + "distances_to_centroid": { + "la Marina de Port": 2968.2, + "Kościerzyna": 2647.9, + "Great Yarmouth": 3366.1, + "Wellingborough": 3500.9, + "St Clair": 14221.7 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " la Marina de Port: (41.36°, 2.14°)", + " Kościerzyna: (54.12°, 17.98°)", + " Great Yarmouth: (52.61°, 1.73°)", + " Wellingborough: (52.30°, -0.69°)", + " St Clair: (-33.80°, 150.78°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " St Clair: 14221.7 km from centroid", + " Wellingborough: 3500.9 km from centroid", + " Great Yarmouth: 3366.1 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": -27.75431, + "lon": 26.64382, + "name": "Allanridge" + }, + { + "lat": 26.04949, + "lon": 32.24142, + "name": "Nag Hammâdi" + }, + { + "lat": 9.15203, + "lon": 39.02335, + "name": "Sendafa" + }, + { + "lat": 12.03219, + "lon": 39.04756, + "name": "Lalibela" + }, + { + "lat": 36.1, + "lon": 139.8, + "name": "Sakai" + } + ], + "question": "Which location is the geographic outlier among: Allanridge, Nag Hammâdi, Sendafa, Lalibela, Sakai?", + "ground_truth": { + "answer": "Sakai", + "outlier_distance_km": 8787.8, + "second_furthest_km": 5314.1, + "clarity_ratio": 1.65, + "median_distance_km": 2938.8, + "distances_to_centroid": { + "Allanridge": 5314.1, + "Nag Hammâdi": 2938.8, + "Sendafa": 1800.3, + "Lalibela": 1778.7, + "Sakai": 8787.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Allanridge: (-27.75°, 26.64°)", + " Nag Hammâdi: (26.05°, 32.24°)", + " Sendafa: (9.15°, 39.02°)", + " Lalibela: (12.03°, 39.05°)", + " Sakai: (36.10°, 139.80°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Sakai: 8787.8 km from centroid", + " Allanridge: 5314.1 km from centroid", + " Nag Hammâdi: 2938.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Sakai", + "FINAL ANSWER: Sakai" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 41.66199, + "lon": -86.15862, + "name": "Mishawaka" + }, + { + "lat": 31.80877, + "lon": -85.96995, + "name": "Troy" + }, + { + "lat": 40.0645, + "lon": -75.1875, + "name": "East Mount Airy" + }, + { + "lat": 40.88232, + "lon": -74.0832, + "name": "Lodi" + }, + { + "lat": 52.52323, + "lon": -1.46523, + "name": "Nuneaton" + } + ], + "question": "Which location is the geographic outlier among: Mishawaka, Troy, East Mount Airy, Lodi, Nuneaton?", + "ground_truth": { + "answer": "Nuneaton", + "outlier_distance_km": 4783.1, + "second_furthest_km": 2178.4, + "clarity_ratio": 2.2, + "median_distance_km": 1792.5, + "distances_to_centroid": { + "Mishawaka": 1792.5, + "Troy": 2178.4, + "East Mount Airy": 905.9, + "Lodi": 798.0, + "Nuneaton": 4783.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Mishawaka: (41.66°, -86.16°)", + " Troy: (31.81°, -85.97°)", + " East Mount Airy: (40.06°, -75.19°)", + " Lodi: (40.88°, -74.08°)", + " Nuneaton: (52.52°, -1.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nuneaton: 4783.1 km from centroid", + " Troy: 2178.4 km from centroid", + " Mishawaka: 1792.5 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nuneaton", + "FINAL ANSWER: Nuneaton" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 4.74215, + "lon": 7.08368, + "name": "Okrika" + }, + { + "lat": -27.342, + "lon": 31.58, + "name": "Ncotshane" + }, + { + "lat": -26.33172, + "lon": 26.32065, + "name": "Coligny" + }, + { + "lat": -3.93938, + "lon": 39.74877, + "name": "Mtwapa" + }, + { + "lat": -33.86436, + "lon": 151.0397, + "name": "Lidcombe" + } + ], + "question": "Which location is the geographic outlier among: Okrika, Ncotshane, Coligny, Mtwapa, Lidcombe?", + "ground_truth": { + "answer": "Lidcombe", + "outlier_distance_km": 9815.9, + "second_furthest_km": 5425.3, + "clarity_ratio": 1.81, + "median_distance_km": 2744.8, + "distances_to_centroid": { + "Okrika": 5425.3, + "Ncotshane": 2294.9, + "Coligny": 2744.8, + "Mtwapa": 1941.2, + "Lidcombe": 9815.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Okrika: (4.74°, 7.08°)", + " Ncotshane: (-27.34°, 31.58°)", + " Coligny: (-26.33°, 26.32°)", + " Mtwapa: (-3.94°, 39.75°)", + " Lidcombe: (-33.86°, 151.04°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Lidcombe: 9815.9 km from centroid", + " Okrika: 5425.3 km from centroid", + " Coligny: 2744.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Lidcombe", + "FINAL ANSWER: Lidcombe" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 34.17482, + "lon": -86.84361, + "name": "Cullman" + }, + { + "lat": 30.29469, + "lon": -81.39314, + "name": "Jacksonville Beach" + }, + { + "lat": 34.18084, + "lon": -118.30897, + "name": "Burbank" + }, + { + "lat": 40.82232, + "lon": -74.15987, + "name": "Nutley" + }, + { + "lat": -27.56056, + "lon": 151.95386, + "name": "Toowoomba" + } + ], + "question": "Which location is the geographic outlier among: Cullman, Jacksonville Beach, Burbank, Nutley, Toowoomba?", + "ground_truth": { + "answer": "Toowoomba", + "outlier_distance_km": 18519.8, + "second_furthest_km": 7443.1, + "clarity_ratio": 2.49, + "median_distance_km": 4566.4, + "distances_to_centroid": { + "Cullman": 4566.4, + "Jacksonville Beach": 4026.1, + "Burbank": 7443.1, + "Nutley": 3657.8, + "Toowoomba": 18519.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Cullman: (34.17°, -86.84°)", + " Jacksonville Beach: (30.29°, -81.39°)", + " Burbank: (34.18°, -118.31°)", + " Nutley: (40.82°, -74.16°)", + " Toowoomba: (-27.56°, 151.95°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Toowoomba: 18519.8 km from centroid", + " Burbank: 7443.1 km from centroid", + " Cullman: 4566.4 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Toowoomba", + "FINAL ANSWER: Toowoomba" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 9.8, + "lon": 38.73333, + "name": "Fichē" + }, + { + "lat": -24.95911, + "lon": 31.17025, + "name": "Hlanganani" + }, + { + "lat": 29.03556, + "lon": 31.11792, + "name": "New Bani Sewif City" + }, + { + "lat": 7.15109, + "lon": 35.81703, + "name": "Wacha" + }, + { + "lat": 37.83493, + "lon": -122.12969, + "name": "Moraga" + } + ], + "question": "Which location is the geographic outlier among: Fichē, Hlanganani, New Bani Sewif City, Wacha, Moraga?", + "ground_truth": { + "answer": "Moraga", + "outlier_distance_km": 12076.8, + "second_furthest_km": 5104.1, + "clarity_ratio": 2.37, + "median_distance_km": 3913.1, + "distances_to_centroid": { + "Fichē": 3913.1, + "Hlanganani": 5104.1, + "New Bani Sewif City": 3491.8, + "Wacha": 3639.8, + "Moraga": 12076.8 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Fichē: (9.80°, 38.73°)", + " Hlanganani: (-24.96°, 31.17°)", + " New Bani Sewif City: (29.04°, 31.12°)", + " Wacha: (7.15°, 35.82°)", + " Moraga: (37.83°, -122.13°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Moraga: 12076.8 km from centroid", + " Hlanganani: 5104.1 km from centroid", + " Fichē: 3913.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Moraga", + "FINAL ANSWER: Moraga" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -31.43722, + "lon": -68.52556, + "name": "Albardón" + }, + { + "lat": -2.99, + "lon": -65.10833, + "name": "Uarini" + }, + { + "lat": -3.63333, + "lon": -44.37667, + "name": "Cantanhede" + }, + { + "lat": -15.86527, + "lon": -47.81477, + "name": "Jardim Botânico" + }, + { + "lat": 1.25881, + "lon": 35.09569, + "name": "Makutano" + } + ], + "question": "Which location is the geographic outlier among: Albardón, Uarini, Cantanhede, Jardim Botânico, Makutano?", + "ground_truth": { + "answer": "Makutano", + "outlier_distance_km": 8203.5, + "second_furthest_km": 3893.5, + "clarity_ratio": 2.11, + "median_distance_km": 3090.6, + "distances_to_centroid": { + "Albardón": 3893.5, + "Uarini": 3090.6, + "Cantanhede": 1029.9, + "Jardim Botânico": 1202.5, + "Makutano": 8203.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Albardón: (-31.44°, -68.53°)", + " Uarini: (-2.99°, -65.11°)", + " Cantanhede: (-3.63°, -44.38°)", + " Jardim Botânico: (-15.87°, -47.81°)", + " Makutano: (1.26°, 35.10°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Makutano: 8203.5 km from centroid", + " Albardón: 3893.5 km from centroid", + " Uarini: 3090.6 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Makutano", + "FINAL ANSWER: Makutano" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 22.39309, + "lon": -97.93857, + "name": "Altamira" + }, + { + "lat": 39.934, + "lon": -74.74849, + "name": "Vincentown" + }, + { + "lat": 44.00012, + "lon": -77.24946, + "name": "Prince Edward" + }, + { + "lat": 50.01634, + "lon": -125.24459, + "name": "Campbell River" + }, + { + "lat": 34.05, + "lon": 131.81667, + "name": "Tokuyama" + } + ], + "question": "Which location is the geographic outlier among: Altamira, Vincentown, Prince Edward, Campbell River, Tokuyama?", + "ground_truth": { + "answer": "Tokuyama", + "outlier_distance_km": 11994.6, + "second_furthest_km": 5986.8, + "clarity_ratio": 2.0, + "median_distance_km": 4978.7, + "distances_to_centroid": { + "Altamira": 4978.7, + "Vincentown": 2254.5, + "Prince Edward": 2471.7, + "Campbell River": 5986.8, + "Tokuyama": 11994.6 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Altamira: (22.39°, -97.94°)", + " Vincentown: (39.93°, -74.75°)", + " Prince Edward: (44.00°, -77.25°)", + " Campbell River: (50.02°, -125.24°)", + " Tokuyama: (34.05°, 131.82°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Tokuyama: 11994.6 km from centroid", + " Campbell River: 5986.8 km from centroid", + " Altamira: 4978.7 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Tokuyama", + "FINAL ANSWER: Tokuyama" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 49.34449, + "lon": 7.18045, + "name": "Neunkirchen" + }, + { + "lat": 37.97872, + "lon": -0.68222, + "name": "Torrevieja" + }, + { + "lat": 50.73583, + "lon": -1.78129, + "name": "Christchurch" + }, + { + "lat": 53.46057, + "lon": 9.98388, + "name": "Harburg" + }, + { + "lat": 12.92475, + "lon": 13.56617, + "name": "Kukawa" + } + ], + "question": "Which location is the geographic outlier among: Neunkirchen, Torrevieja, Christchurch, Harburg, Kukawa?", + "ground_truth": { + "answer": "Kukawa", + "outlier_distance_km": 3203.5, + "second_furthest_km": 1435.0, + "clarity_ratio": 2.23, + "median_distance_km": 1235.8, + "distances_to_centroid": { + "Neunkirchen": 947.8, + "Torrevieja": 632.8, + "Christchurch": 1235.8, + "Harburg": 1435.0, + "Kukawa": 3203.5 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Neunkirchen: (49.34°, 7.18°)", + " Torrevieja: (37.98°, -0.68°)", + " Christchurch: (50.74°, -1.78°)", + " Harburg: (53.46°, 9.98°)", + " Kukawa: (12.92°, 13.57°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kukawa: 3203.5 km from centroid", + " Harburg: 1435.0 km from centroid", + " Christchurch: 1235.8 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kukawa", + "FINAL ANSWER: Kukawa" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + { + "lat": -33.76667, + "lon": 150.91667, + "name": "Blacktown" + }, + { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + }, + { + "lat": 59.37627, + "lon": 28.61409, + "name": "Kingisepp" + } + ], + "question": "Which location is the geographic outlier among: Tuggeranong Administrative District, Bentleigh East, Blacktown, Greensborough, Kingisepp?", + "ground_truth": { + "answer": "Kingisepp", + "outlier_distance_km": 11924.9, + "second_furthest_km": 3281.4, + "clarity_ratio": 3.63, + "median_distance_km": 3227.1, + "distances_to_centroid": { + "Tuggeranong Administrative District": 3227.1, + "Bentleigh East": 3111.3, + "Blacktown": 3281.4, + "Greensborough": 3098.6, + "Kingisepp": 11924.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Tuggeranong Administrative District: (-35.42°, 149.07°)", + " Bentleigh East: (-37.92°, 145.05°)", + " Blacktown: (-33.77°, 150.92°)", + " Greensborough: (-37.70°, 145.10°)", + " Kingisepp: (59.38°, 28.61°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Kingisepp: 11924.9 km from centroid", + " Blacktown: 3281.4 km from centroid", + " Tuggeranong Administrative District: 3227.1 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Kingisepp", + "FINAL ANSWER: Kingisepp" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 53.33333, + "lon": 8.48333, + "name": "Brake (Unterweser)" + }, + { + "lat": 53.1235, + "lon": 18.00762, + "name": "Bydgoszcz" + }, + { + "lat": 48.86625, + "lon": 2.37142, + "name": "Folie Méricourt" + }, + { + "lat": 55.82299, + "lon": 37.81306, + "name": "Gol’yanovo" + }, + { + "lat": -28.21298, + "lon": 153.53634, + "name": "Banora Point" + } + ], + "question": "Which location is the geographic outlier among: Brake (Unterweser), Bydgoszcz, Folie Méricourt, Gol’yanovo, Banora Point?", + "ground_truth": { + "answer": "Banora Point", + "outlier_distance_km": 13475.9, + "second_furthest_km": 3612.9, + "clarity_ratio": 3.73, + "median_distance_km": 3308.4, + "distances_to_centroid": { + "Brake (Unterweser)": 3308.4, + "Bydgoszcz": 2727.6, + "Folie Méricourt": 3612.9, + "Gol’yanovo": 2189.9, + "Banora Point": 13475.9 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Brake (Unterweser): (53.33°, 8.48°)", + " Bydgoszcz: (53.12°, 18.01°)", + " Folie Méricourt: (48.87°, 2.37°)", + " Gol’yanovo: (55.82°, 37.81°)", + " Banora Point: (-28.21°, 153.54°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Banora Point: 13475.9 km from centroid", + " Folie Méricourt: 3612.9 km from centroid", + " Brake (Unterweser): 3308.4 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": -33.73378, + "lon": 18.97523, + "name": "Paarl" + }, + { + "lat": 7.23333, + "lon": 37.88333, + "name": "Duramē" + }, + { + "lat": 7.06667, + "lon": 37.7, + "name": "Āreka" + }, + { + "lat": 11.8277, + "lon": 39.59164, + "name": "Weldiya" + }, + { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + } + ], + "question": "Which location is the geographic outlier among: Paarl, Duramē, Āreka, Weldiya, Morphett Vale?", + "ground_truth": { + "answer": "Morphett Vale", + "outlier_distance_km": 8917.2, + "second_furthest_km": 4589.3, + "clarity_ratio": 1.94, + "median_distance_km": 2803.9, + "distances_to_centroid": { + "Paarl": 4589.3, + "Duramē": 2546.5, + "Āreka": 2548.7, + "Weldiya": 2803.9, + "Morphett Vale": 8917.2 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Paarl: (-33.73°, 18.98°)", + " Duramē: (7.23°, 37.88°)", + " Āreka: (7.07°, 37.70°)", + " Weldiya: (11.83°, 39.59°)", + " Morphett Vale: (-35.13°, 138.52°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Morphett Vale: 8917.2 km from centroid", + " Paarl: 4589.3 km from centroid", + " Weldiya: 2803.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Morphett Vale", + "FINAL ANSWER: Morphett Vale" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -22.87278, + "lon": -42.34306, + "name": "Araruama" + }, + { + "lat": -10.21111, + "lon": -36.84028, + "name": "Propriá" + }, + { + "lat": -22.73083, + "lon": -45.12472, + "name": "Lorena" + }, + { + "lat": 9.10569, + "lon": -75.39812, + "name": "Chinú" + }, + { + "lat": 27.56155, + "lon": 73.47141, + "name": "Nokha" + } + ], + "question": "Which location is the geographic outlier among: Araruama, Propriá, Lorena, Chinú, Nokha?", + "ground_truth": { + "answer": "Nokha", + "outlier_distance_km": 11063.4, + "second_furthest_km": 5741.2, + "clarity_ratio": 1.93, + "median_distance_km": 2998.9, + "distances_to_centroid": { + "Araruama": 2804.8, + "Propriá": 1462.4, + "Lorena": 2998.9, + "Chinú": 5741.2, + "Nokha": 11063.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Araruama: (-22.87°, -42.34°)", + " Propriá: (-10.21°, -36.84°)", + " Lorena: (-22.73°, -45.12°)", + " Chinú: (9.11°, -75.40°)", + " Nokha: (27.56°, 73.47°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Nokha: 11063.4 km from centroid", + " Chinú: 5741.2 km from centroid", + " Lorena: 2998.9 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Nokha", + "FINAL ANSWER: Nokha" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + { + "lat": -25.28762, + "lon": 152.76936, + "name": "Hervey Bay" + }, + { + "lat": -36.90694, + "lon": 174.68704, + "name": "New Lynn" + }, + { + "lat": -38.21792, + "lon": 145.03876, + "name": "Mornington" + }, + { + "lat": 11.75617, + "lon": 79.76693, + "name": "Cuddalore" + } + ], + "question": "Which location is the geographic outlier among: Avondale, Hervey Bay, New Lynn, Mornington, Cuddalore?", + "ground_truth": { + "answer": "Cuddalore", + "outlier_distance_km": 8203.4, + "second_furthest_km": 3068.3, + "clarity_ratio": 2.67, + "median_distance_km": 3068.0, + "distances_to_centroid": { + "Avondale": 3068.3, + "Hervey Bay": 742.4, + "New Lynn": 3068.0, + "Mornington": 1458.1, + "Cuddalore": 8203.4 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Avondale: (-36.88°, 174.70°)", + " Hervey Bay: (-25.29°, 152.77°)", + " New Lynn: (-36.91°, 174.69°)", + " Mornington: (-38.22°, 145.04°)", + " Cuddalore: (11.76°, 79.77°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Cuddalore: 8203.4 km from centroid", + " Avondale: 3068.3 km from centroid", + " New Lynn: 3068.0 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Cuddalore", + "FINAL ANSWER: Cuddalore" + ] + }, + { + "task": "spatial_patterns", + "subtask": "outlier_detection", + "points": [ + { + "lat": 17.2675, + "lon": 103.22472, + "name": "Ban Nong Wua So" + }, + { + "lat": 13.53671, + "lon": 99.81712, + "name": "Ratchaburi" + }, + { + "lat": 35.00268, + "lon": 134.35896, + "name": "Sayō" + }, + { + "lat": 35.99472, + "lon": 119.3975, + "name": "Zhucheng" + }, + { + "lat": 25.66477, + "lon": 32.63539, + "name": "Al Bayāḑīyah" + } + ], + "question": "Which location is the geographic outlier among: Ban Nong Wua So, Ratchaburi, Sayō, Zhucheng, Al Bayāḑīyah?", + "ground_truth": { + "answer": "Al Bayāḑīyah", + "outlier_distance_km": 6471.1, + "second_furthest_km": 3636.8, + "clarity_ratio": 1.78, + "median_distance_km": 2356.3, + "distances_to_centroid": { + "Ban Nong Wua So": 1068.3, + "Ratchaburi": 1344.7, + "Sayō": 3636.8, + "Zhucheng": 2356.3, + "Al Bayāḑīyah": 6471.1 + } + }, + "reasoning_steps": [ + "Step 1: Identify all points (5 locations)", + " Ban Nong Wua So: (17.27°, 103.22°)", + " Ratchaburi: (13.54°, 99.82°)", + " Sayō: (35.00°, 134.36°)", + " Zhucheng: (35.99°, 119.40°)", + " Al Bayāḑīyah: (25.66°, 32.64°)", + "Step 2: Calculate centroid of all points", + "Step 3: Calculate distance from each point to centroid", + " Al Bayāḑīyah: 6471.1 km from centroid", + " Sayō: 3636.8 km from centroid", + " Zhucheng: 2356.3 km from centroid", + "Step 4: Identify geographic outlier (furthest from centroid)", + " Outlier: Al Bayāḑīyah", + "FINAL ANSWER: Al Bayāḑīyah" + ] + } +] \ No newline at end of file