| [ |
| { |
| "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" |
| ] |
| } |
| ] |
|
|
