[ { "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": 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": 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": -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": 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": 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": 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": -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": 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": 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": -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": 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": 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": 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": 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": 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": 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": -34.05515, "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": 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": -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": 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": 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": -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": -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": 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": 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": 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": 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": 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": 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" ] } ]