[ { "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": "Maracaçumé" }, { "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" ] } ]