| [ |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -22.88583, |
| "lon": -48.445, |
| "name": "Botucatu" |
| }, |
| { |
| "lat": -18.16583, |
| "lon": -47.94639, |
| "name": "Catalão" |
| }, |
| { |
| "lat": -6.05675, |
| "lon": -77.16651, |
| "name": "Rioja" |
| }, |
| { |
| "lat": -31.36528, |
| "lon": -51.97833, |
| "name": "São Lourenço do Sul" |
| }, |
| { |
| "lat": 44.85469, |
| "lon": -93.47079, |
| "name": "Eden Prairie" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Botucatu, Catalão, Rioja, São Lourenço do Sul, Eden Prairie?", |
| "ground_truth": { |
| "answer": "Eden Prairie", |
| "outlier_distance_km": 6455.1, |
| "second_furthest_km": 3003.1, |
| "clarity_ratio": 2.15, |
| "median_distance_km": 2435.6, |
| "distances_to_centroid": { |
| "Botucatu": 2435.6, |
| "Catalão": 2137.8, |
| "Rioja": 1478.7, |
| "São Lourenço do Sul": 3003.1, |
| "Eden Prairie": 6455.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Botucatu: (-22.89°, -48.45°)", |
| " Catalão: (-18.17°, -47.95°)", |
| " Rioja: (-6.06°, -77.17°)", |
| " São Lourenço do Sul: (-31.37°, -51.98°)", |
| " Eden Prairie: (44.85°, -93.47°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Eden Prairie: 6455.1 km from centroid", |
| " São Lourenço do Sul: 3003.1 km from centroid", |
| " Botucatu: 2435.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Eden Prairie", |
| "FINAL ANSWER: Eden Prairie" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -2.27808, |
| "lon": 37.81867, |
| "name": "Makindu" |
| }, |
| { |
| "lat": -25.86522, |
| "lon": 25.64421, |
| "name": "Mafikeng" |
| }, |
| { |
| "lat": 12.6269, |
| "lon": 9.38807, |
| "name": "Gumel" |
| }, |
| { |
| "lat": 8.3, |
| "lon": 35.58333, |
| "name": "Metu" |
| }, |
| { |
| "lat": 52.2852, |
| "lon": -1.52, |
| "name": "Royal Leamington Spa" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Makindu, Mafikeng, Gumel, Metu, Royal Leamington Spa?", |
| "ground_truth": { |
| "answer": "Royal Leamington Spa", |
| "outlier_distance_km": 5239.3, |
| "second_furthest_km": 3905.7, |
| "clarity_ratio": 1.34, |
| "median_distance_km": 2212.3, |
| "distances_to_centroid": { |
| "Makindu": 2212.3, |
| "Mafikeng": 3905.7, |
| "Gumel": 1370.0, |
| "Metu": 1562.9, |
| "Royal Leamington Spa": 5239.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Makindu: (-2.28°, 37.82°)", |
| " Mafikeng: (-25.87°, 25.64°)", |
| " Gumel: (12.63°, 9.39°)", |
| " Metu: (8.30°, 35.58°)", |
| " Royal Leamington Spa: (52.29°, -1.52°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Royal Leamington Spa: 5239.3 km from centroid", |
| " Mafikeng: 3905.7 km from centroid", |
| " Makindu: 2212.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Royal Leamington Spa", |
| "FINAL ANSWER: Royal Leamington Spa" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 41.3799, |
| "lon": 2.18971, |
| "name": "la Barceloneta" |
| }, |
| { |
| "lat": 47.02413, |
| "lon": 4.83887, |
| "name": "Beaune" |
| }, |
| { |
| "lat": 41.11006, |
| "lon": 16.69086, |
| "name": "Bitonto" |
| }, |
| { |
| "lat": 45.46456, |
| "lon": 8.88453, |
| "name": "Magenta" |
| }, |
| { |
| "lat": 11.66667, |
| "lon": 38.8, |
| "name": "Filakit" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: la Barceloneta, Beaune, Bitonto, Magenta, Filakit?", |
| "ground_truth": { |
| "answer": "Filakit", |
| "outlier_distance_km": 3756.6, |
| "second_furthest_km": 1327.4, |
| "clarity_ratio": 2.83, |
| "median_distance_km": 1131.7, |
| "distances_to_centroid": { |
| "la Barceloneta": 1131.7, |
| "Beaune": 1327.4, |
| "Bitonto": 468.8, |
| "Magenta": 1009.8, |
| "Filakit": 3756.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " la Barceloneta: (41.38°, 2.19°)", |
| " Beaune: (47.02°, 4.84°)", |
| " Bitonto: (41.11°, 16.69°)", |
| " Magenta: (45.46°, 8.88°)", |
| " Filakit: (11.67°, 38.80°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Filakit: 3756.6 km from centroid", |
| " Beaune: 1327.4 km from centroid", |
| " la Barceloneta: 1131.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Filakit", |
| "FINAL ANSWER: Filakit" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 54.75472, |
| "lon": 61.32083, |
| "name": "Yemanzhelinsk" |
| }, |
| { |
| "lat": 52.01664, |
| "lon": 48.79895, |
| "name": "Pugachëv" |
| }, |
| { |
| "lat": 39.42814, |
| "lon": -0.41765, |
| "name": "Paiporta" |
| }, |
| { |
| "lat": 44.99242, |
| "lon": 10.74407, |
| "name": "Suzzara" |
| }, |
| { |
| "lat": -37.8318, |
| "lon": 140.77919, |
| "name": "Mount Gambier" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Yemanzhelinsk, Pugachëv, Paiporta, Suzzara, Mount Gambier?", |
| "ground_truth": { |
| "answer": "Mount Gambier", |
| "outlier_distance_km": 11918.7, |
| "second_furthest_km": 4822.6, |
| "clarity_ratio": 2.47, |
| "median_distance_km": 3924.3, |
| "distances_to_centroid": { |
| "Yemanzhelinsk": 2773.3, |
| "Pugachëv": 2390.1, |
| "Paiporta": 4822.6, |
| "Suzzara": 3924.3, |
| "Mount Gambier": 11918.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Yemanzhelinsk: (54.75°, 61.32°)", |
| " Pugachëv: (52.02°, 48.80°)", |
| " Paiporta: (39.43°, -0.42°)", |
| " Suzzara: (44.99°, 10.74°)", |
| " Mount Gambier: (-37.83°, 140.78°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Mount Gambier: 11918.7 km from centroid", |
| " Paiporta: 4822.6 km from centroid", |
| " Suzzara: 3924.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Mount Gambier", |
| "FINAL ANSWER: Mount Gambier" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 34.03528, |
| "lon": 117.57806, |
| "name": "Shuanggou" |
| }, |
| { |
| "lat": 37.92259, |
| "lon": 139.04125, |
| "name": "Niigata" |
| }, |
| { |
| "lat": 21.23742, |
| "lon": 76.22558, |
| "name": "Shāhpur" |
| }, |
| { |
| "lat": 28.9241, |
| "lon": 104.26154, |
| "name": "Juexi" |
| }, |
| { |
| "lat": 54.43109, |
| "lon": 18.46727, |
| "name": "Osowa" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Shuanggou, Niigata, Shāhpur, Juexi, Osowa?", |
| "ground_truth": { |
| "answer": "Osowa", |
| "outlier_distance_km": 5813.9, |
| "second_furthest_km": 4240.1, |
| "clarity_ratio": 1.37, |
| "median_distance_km": 2417.0, |
| "distances_to_centroid": { |
| "Shuanggou": 2417.0, |
| "Niigata": 4240.1, |
| "Shāhpur": 2133.5, |
| "Juexi": 1425.4, |
| "Osowa": 5813.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Shuanggou: (34.04°, 117.58°)", |
| " Niigata: (37.92°, 139.04°)", |
| " Shāhpur: (21.24°, 76.23°)", |
| " Juexi: (28.92°, 104.26°)", |
| " Osowa: (54.43°, 18.47°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Osowa: 5813.9 km from centroid", |
| " Niigata: 4240.1 km from centroid", |
| " Shuanggou: 2417.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Osowa", |
| "FINAL ANSWER: Osowa" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 34.14806, |
| "lon": -117.99895, |
| "name": "Monrovia" |
| }, |
| { |
| "lat": 41.90059, |
| "lon": -87.85673, |
| "name": "Melrose Park" |
| }, |
| { |
| "lat": 45.40008, |
| "lon": -74.03251, |
| "name": "Vaudreuil-Dorion" |
| }, |
| { |
| "lat": 48.23656, |
| "lon": -79.02311, |
| "name": "Rouyn-Noranda" |
| }, |
| { |
| "lat": -25.69776, |
| "lon": 31.564, |
| "name": "Driekoppies" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Monrovia, Melrose Park, Vaudreuil-Dorion, Rouyn-Noranda, Driekoppies?", |
| "ground_truth": { |
| "answer": "Driekoppies", |
| "outlier_distance_km": 11986.0, |
| "second_furthest_km": 4963.1, |
| "clarity_ratio": 2.42, |
| "median_distance_km": 2486.5, |
| "distances_to_centroid": { |
| "Monrovia": 4963.1, |
| "Melrose Park": 2486.5, |
| "Vaudreuil-Dorion": 1993.4, |
| "Rouyn-Noranda": 2453.8, |
| "Driekoppies": 11986.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Monrovia: (34.15°, -118.00°)", |
| " Melrose Park: (41.90°, -87.86°)", |
| " Vaudreuil-Dorion: (45.40°, -74.03°)", |
| " Rouyn-Noranda: (48.24°, -79.02°)", |
| " Driekoppies: (-25.70°, 31.56°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Driekoppies: 11986.0 km from centroid", |
| " Monrovia: 4963.1 km from centroid", |
| " Melrose Park: 2486.5 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Driekoppies", |
| "FINAL ANSWER: Driekoppies" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -20.03833, |
| "lon": -47.74694, |
| "name": "Igarapava" |
| }, |
| { |
| "lat": -18.41778, |
| "lon": -46.41806, |
| "name": "Presidente Olegário" |
| }, |
| { |
| "lat": -26.24333, |
| "lon": -48.63806, |
| "name": "São Francisco do Sul" |
| }, |
| { |
| "lat": 6.96321, |
| "lon": -75.41738, |
| "name": "Yarumal" |
| }, |
| { |
| "lat": 55.93924, |
| "lon": 92.37513, |
| "name": "Divnogorsk" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Igarapava, Presidente Olegário, São Francisco do Sul, Yarumal, Divnogorsk?", |
| "ground_truth": { |
| "answer": "Divnogorsk", |
| "outlier_distance_km": 11710.9, |
| "second_furthest_km": 5632.7, |
| "clarity_ratio": 2.08, |
| "median_distance_km": 3820.9, |
| "distances_to_centroid": { |
| "Igarapava": 3290.1, |
| "Presidente Olegário": 3068.5, |
| "São Francisco do Sul": 3820.9, |
| "Yarumal": 5632.7, |
| "Divnogorsk": 11710.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Igarapava: (-20.04°, -47.75°)", |
| " Presidente Olegário: (-18.42°, -46.42°)", |
| " São Francisco do Sul: (-26.24°, -48.64°)", |
| " Yarumal: (6.96°, -75.42°)", |
| " Divnogorsk: (55.94°, 92.38°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Divnogorsk: 11710.9 km from centroid", |
| " Yarumal: 5632.7 km from centroid", |
| " São Francisco do Sul: 3820.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Divnogorsk", |
| "FINAL ANSWER: Divnogorsk" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -29.12107, |
| "lon": 26.214, |
| "name": "Bloemfontein" |
| }, |
| { |
| "lat": -1.10148, |
| "lon": 37.0132, |
| "name": "Juja" |
| }, |
| { |
| "lat": 30.31263, |
| "lon": 32.30935, |
| "name": "Fāyīd" |
| }, |
| { |
| "lat": -0.42013, |
| "lon": 36.94759, |
| "name": "Nyeri" |
| }, |
| { |
| "lat": -33.92399, |
| "lon": 151.22749, |
| "name": "Kingsford" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Bloemfontein, Juja, Fāyīd, Nyeri, Kingsford?", |
| "ground_truth": { |
| "answer": "Kingsford", |
| "outlier_distance_km": 9993.9, |
| "second_furthest_km": 4885.1, |
| "clarity_ratio": 2.05, |
| "median_distance_km": 4044.5, |
| "distances_to_centroid": { |
| "Bloemfontein": 4044.5, |
| "Juja": 2279.0, |
| "Fāyīd": 4885.1, |
| "Nyeri": 2308.9, |
| "Kingsford": 9993.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Bloemfontein: (-29.12°, 26.21°)", |
| " Juja: (-1.10°, 37.01°)", |
| " Fāyīd: (30.31°, 32.31°)", |
| " Nyeri: (-0.42°, 36.95°)", |
| " Kingsford: (-33.92°, 151.23°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Kingsford: 9993.9 km from centroid", |
| " Fāyīd: 4885.1 km from centroid", |
| " Bloemfontein: 4044.5 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Kingsford", |
| "FINAL ANSWER: Kingsford" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -3.10222, |
| "lon": -67.93972, |
| "name": "Santo Antônio do Içá" |
| }, |
| { |
| "lat": -22.4625, |
| "lon": -42.65306, |
| "name": "Cachoeiras de Macacu" |
| }, |
| { |
| "lat": -7.86806, |
| "lon": -37.97472, |
| "name": "Flores" |
| }, |
| { |
| "lat": -6.4075, |
| "lon": -41.74556, |
| "name": "Valença do Piauí" |
| }, |
| { |
| "lat": 48.46686, |
| "lon": -81.33312, |
| "name": "Timmins" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Santo Antônio do Içá, Cachoeiras de Macacu, Flores, Valença do Piauí, Timmins?", |
| "ground_truth": { |
| "answer": "Timmins", |
| "outlier_distance_km": 5803.3, |
| "second_furthest_km": 2972.9, |
| "clarity_ratio": 1.95, |
| "median_distance_km": 2104.2, |
| "distances_to_centroid": { |
| "Santo Antônio do Içá": 1605.3, |
| "Cachoeiras de Macacu": 2972.9, |
| "Flores": 2104.2, |
| "Valença do Piauí": 1664.1, |
| "Timmins": 5803.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Santo Antônio do Içá: (-3.10°, -67.94°)", |
| " Cachoeiras de Macacu: (-22.46°, -42.65°)", |
| " Flores: (-7.87°, -37.97°)", |
| " Valença do Piauí: (-6.41°, -41.75°)", |
| " Timmins: (48.47°, -81.33°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Timmins: 5803.3 km from centroid", |
| " Cachoeiras de Macacu: 2972.9 km from centroid", |
| " Flores: 2104.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Timmins", |
| "FINAL ANSWER: Timmins" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -16.92366, |
| "lon": 145.76613, |
| "name": "Cairns" |
| }, |
| { |
| "lat": -37.75819, |
| "lon": 145.00583, |
| "name": "Thornbury" |
| }, |
| { |
| "lat": -38.68333, |
| "lon": 176.08333, |
| "name": "Taupo" |
| }, |
| { |
| "lat": -37.0646, |
| "lon": 174.94212, |
| "name": "Papakura" |
| }, |
| { |
| "lat": 10.78556, |
| "lon": -0.85139, |
| "name": "Bolgatanga" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Cairns, Thornbury, Taupo, Papakura, Bolgatanga?", |
| "ground_truth": { |
| "answer": "Bolgatanga", |
| "outlier_distance_km": 14444.3, |
| "second_furthest_km": 4776.1, |
| "clarity_ratio": 3.02, |
| "median_distance_km": 4660.2, |
| "distances_to_centroid": { |
| "Cairns": 1988.0, |
| "Thornbury": 2216.1, |
| "Taupo": 4776.1, |
| "Papakura": 4660.2, |
| "Bolgatanga": 14444.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Cairns: (-16.92°, 145.77°)", |
| " Thornbury: (-37.76°, 145.01°)", |
| " Taupo: (-38.68°, 176.08°)", |
| " Papakura: (-37.06°, 174.94°)", |
| " Bolgatanga: (10.79°, -0.85°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Bolgatanga: 14444.3 km from centroid", |
| " Taupo: 4776.1 km from centroid", |
| " Papakura: 4660.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Bolgatanga", |
| "FINAL ANSWER: Bolgatanga" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -27.28115, |
| "lon": 27.9709, |
| "name": "Heilbron" |
| }, |
| { |
| "lat": 4.93422, |
| "lon": -1.71454, |
| "name": "Sekondi" |
| }, |
| { |
| "lat": 14.16347, |
| "lon": 38.89924, |
| "name": "Adwa" |
| }, |
| { |
| "lat": -34.08401, |
| "lon": 18.82113, |
| "name": "Somerset West" |
| }, |
| { |
| "lat": -28.44917, |
| "lon": -52.2, |
| "name": "Marau" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Heilbron, Sekondi, Adwa, Somerset West, Marau?", |
| "ground_truth": { |
| "answer": "Marau", |
| "outlier_distance_km": 6211.7, |
| "second_furthest_km": 4768.0, |
| "clarity_ratio": 1.3, |
| "median_distance_km": 2673.8, |
| "distances_to_centroid": { |
| "Heilbron": 2673.8, |
| "Sekondi": 2300.5, |
| "Adwa": 4768.0, |
| "Somerset West": 2547.6, |
| "Marau": 6211.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Heilbron: (-27.28°, 27.97°)", |
| " Sekondi: (4.93°, -1.71°)", |
| " Adwa: (14.16°, 38.90°)", |
| " Somerset West: (-34.08°, 18.82°)", |
| " Marau: (-28.45°, -52.20°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Marau: 6211.7 km from centroid", |
| " Adwa: 4768.0 km from centroid", |
| " Heilbron: 2673.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Marau", |
| "FINAL ANSWER: Marau" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 51.45278, |
| "lon": -2.50833, |
| "name": "Kingswood" |
| }, |
| { |
| "lat": 43.72254, |
| "lon": 7.11183, |
| "name": "Vence" |
| }, |
| { |
| "lat": 55.1611, |
| "lon": 61.42877, |
| "name": "Chelyabinsk" |
| }, |
| { |
| "lat": 58.07756, |
| "lon": 60.7202, |
| "name": "Nizhnyaya Salda" |
| }, |
| { |
| "lat": -27.53221, |
| "lon": 153.22889, |
| "name": "Alexandra Hills" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Kingswood, Vence, Chelyabinsk, Nizhnyaya Salda, Alexandra Hills?", |
| "ground_truth": { |
| "answer": "Alexandra Hills", |
| "outlier_distance_km": 12374.1, |
| "second_furthest_km": 4845.6, |
| "clarity_ratio": 2.55, |
| "median_distance_km": 4188.3, |
| "distances_to_centroid": { |
| "Kingswood": 4845.6, |
| "Vence": 4188.3, |
| "Chelyabinsk": 2151.2, |
| "Nizhnyaya Salda": 2459.9, |
| "Alexandra Hills": 12374.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Kingswood: (51.45°, -2.51°)", |
| " Vence: (43.72°, 7.11°)", |
| " Chelyabinsk: (55.16°, 61.43°)", |
| " Nizhnyaya Salda: (58.08°, 60.72°)", |
| " Alexandra Hills: (-27.53°, 153.23°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Alexandra Hills: 12374.1 km from centroid", |
| " Kingswood: 4845.6 km from centroid", |
| " Vence: 4188.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Alexandra Hills", |
| "FINAL ANSWER: Alexandra Hills" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -34.40639, |
| "lon": -70.85834, |
| "name": "Rengo" |
| }, |
| { |
| "lat": -27.39184, |
| "lon": -55.92379, |
| "name": "Posadas" |
| }, |
| { |
| "lat": -9.93361, |
| "lon": -36.55417, |
| "name": "São Sebastião" |
| }, |
| { |
| "lat": 9.7174, |
| "lon": -75.12023, |
| "name": "El Carmen de Bolívar" |
| }, |
| { |
| "lat": 26.65817, |
| "lon": 31.67137, |
| "name": "Sāqultah" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Rengo, Posadas, São Sebastião, El Carmen de Bolívar, Sāqultah?", |
| "ground_truth": { |
| "answer": "Sāqultah", |
| "outlier_distance_km": 8700.9, |
| "second_furthest_km": 4285.4, |
| "clarity_ratio": 2.03, |
| "median_distance_km": 4179.7, |
| "distances_to_centroid": { |
| "Rengo": 4285.4, |
| "Posadas": 2732.3, |
| "São Sebastião": 616.6, |
| "El Carmen de Bolívar": 4179.7, |
| "Sāqultah": 8700.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Rengo: (-34.41°, -70.86°)", |
| " Posadas: (-27.39°, -55.92°)", |
| " São Sebastião: (-9.93°, -36.55°)", |
| " El Carmen de Bolívar: (9.72°, -75.12°)", |
| " Sāqultah: (26.66°, 31.67°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Sāqultah: 8700.9 km from centroid", |
| " Rengo: 4285.4 km from centroid", |
| " El Carmen de Bolívar: 4179.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Sāqultah", |
| "FINAL ANSWER: Sāqultah" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 40.12617, |
| "lon": -82.92907, |
| "name": "Westerville" |
| }, |
| { |
| "lat": 49.28333, |
| "lon": -123.03333, |
| "name": "Hastings-Sunrise" |
| }, |
| { |
| "lat": 25.87972, |
| "lon": -97.50417, |
| "name": "Heroica Matamoros" |
| }, |
| { |
| "lat": 41.13998, |
| "lon": -104.82025, |
| "name": "Cheyenne" |
| }, |
| { |
| "lat": -27.45556, |
| "lon": -53.93194, |
| "name": "Três Passos" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Westerville, Hastings-Sunrise, Heroica Matamoros, Cheyenne, Três Passos?", |
| "ground_truth": { |
| "answer": "Três Passos", |
| "outlier_distance_km": 7214.2, |
| "second_furthest_km": 3707.5, |
| "clarity_ratio": 1.95, |
| "median_distance_km": 2051.7, |
| "distances_to_centroid": { |
| "Westerville": 1821.4, |
| "Hastings-Sunrise": 3707.5, |
| "Heroica Matamoros": 506.5, |
| "Cheyenne": 2051.7, |
| "Três Passos": 7214.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Westerville: (40.13°, -82.93°)", |
| " Hastings-Sunrise: (49.28°, -123.03°)", |
| " Heroica Matamoros: (25.88°, -97.50°)", |
| " Cheyenne: (41.14°, -104.82°)", |
| " Três Passos: (-27.46°, -53.93°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Três Passos: 7214.2 km from centroid", |
| " Hastings-Sunrise: 3707.5 km from centroid", |
| " Cheyenne: 2051.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Três Passos", |
| "FINAL ANSWER: Três Passos" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -23.62028, |
| "lon": -45.41306, |
| "name": "Caraguatatuba" |
| }, |
| { |
| "lat": -16.70806, |
| "lon": -49.09306, |
| "name": "Senador Canedo" |
| }, |
| { |
| "lat": -25.11364, |
| "lon": -64.12628, |
| "name": "Joaquín V. González" |
| }, |
| { |
| "lat": -3.63333, |
| "lon": -44.37667, |
| "name": "Cantanhede" |
| }, |
| { |
| "lat": 14.05603, |
| "lon": 101.37218, |
| "name": "Thambon Na Mueang" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Caraguatatuba, Senador Canedo, Joaquín V. González, Cantanhede, Thambon Na Mueang?", |
| "ground_truth": { |
| "answer": "Thambon Na Mueang", |
| "outlier_distance_km": 13692.8, |
| "second_furthest_km": 4863.2, |
| "clarity_ratio": 2.82, |
| "median_distance_km": 3166.3, |
| "distances_to_centroid": { |
| "Caraguatatuba": 3002.1, |
| "Senador Canedo": 3166.3, |
| "Joaquín V. González": 4863.2, |
| "Cantanhede": 2774.0, |
| "Thambon Na Mueang": 13692.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Caraguatatuba: (-23.62°, -45.41°)", |
| " Senador Canedo: (-16.71°, -49.09°)", |
| " Joaquín V. González: (-25.11°, -64.13°)", |
| " Cantanhede: (-3.63°, -44.38°)", |
| " Thambon Na Mueang: (14.06°, 101.37°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Thambon Na Mueang: 13692.8 km from centroid", |
| " Joaquín V. González: 4863.2 km from centroid", |
| " Senador Canedo: 3166.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Thambon Na Mueang", |
| "FINAL ANSWER: Thambon Na Mueang" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 43.21667, |
| "lon": -2.73333, |
| "name": "Amorebieta" |
| }, |
| { |
| "lat": 40.49367, |
| "lon": -3.6359, |
| "name": "Valdefuentes" |
| }, |
| { |
| "lat": 59.15838, |
| "lon": 57.5705, |
| "name": "Aleksandrovsk" |
| }, |
| { |
| "lat": 56.33169, |
| "lon": 36.7292, |
| "name": "Klin" |
| }, |
| { |
| "lat": 31.30862, |
| "lon": -110.94217, |
| "name": "Nogales" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Amorebieta, Valdefuentes, Aleksandrovsk, Klin, Nogales?", |
| "ground_truth": { |
| "answer": "Nogales", |
| "outlier_distance_km": 8674.1, |
| "second_furthest_km": 4260.5, |
| "clarity_ratio": 2.04, |
| "median_distance_km": 3039.3, |
| "distances_to_centroid": { |
| "Amorebieta": 353.2, |
| "Valdefuentes": 628.5, |
| "Aleksandrovsk": 4260.5, |
| "Klin": 3039.3, |
| "Nogales": 8674.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Amorebieta: (43.22°, -2.73°)", |
| " Valdefuentes: (40.49°, -3.64°)", |
| " Aleksandrovsk: (59.16°, 57.57°)", |
| " Klin: (56.33°, 36.73°)", |
| " Nogales: (31.31°, -110.94°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Nogales: 8674.1 km from centroid", |
| " Aleksandrovsk: 4260.5 km from centroid", |
| " Klin: 3039.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Nogales", |
| "FINAL ANSWER: Nogales" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 36.32745, |
| "lon": -119.64568, |
| "name": "Hanford" |
| }, |
| { |
| "lat": 16.09007, |
| "lon": -93.7546, |
| "name": "Tonalá" |
| }, |
| { |
| "lat": 40.84829, |
| "lon": -74.58148, |
| "name": "Randolph" |
| }, |
| { |
| "lat": 40.68677, |
| "lon": -73.37345, |
| "name": "Lindenhurst" |
| }, |
| { |
| "lat": 2.80922, |
| "lon": 40.92885, |
| "name": "El Wak" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Hanford, Tonalá, Randolph, Lindenhurst, El Wak?", |
| "ground_truth": { |
| "answer": "El Wak", |
| "outlier_distance_km": 11337.9, |
| "second_furthest_km": 5270.7, |
| "clarity_ratio": 2.15, |
| "median_distance_km": 3299.6, |
| "distances_to_centroid": { |
| "Hanford": 5270.7, |
| "Tonalá": 3299.6, |
| "Randolph": 1781.8, |
| "Lindenhurst": 1709.6, |
| "El Wak": 11337.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Hanford: (36.33°, -119.65°)", |
| " Tonalá: (16.09°, -93.75°)", |
| " Randolph: (40.85°, -74.58°)", |
| " Lindenhurst: (40.69°, -73.37°)", |
| " El Wak: (2.81°, 40.93°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " El Wak: 11337.9 km from centroid", |
| " Hanford: 5270.7 km from centroid", |
| " Tonalá: 3299.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: El Wak", |
| "FINAL ANSWER: El Wak" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -8.11278, |
| "lon": -35.01472, |
| "name": "Jaboatão dos Guararapes" |
| }, |
| { |
| "lat": -28.4602, |
| "lon": -62.83354, |
| "name": "Añatuya" |
| }, |
| { |
| "lat": -1.15194, |
| "lon": -48.12944, |
| "name": "Santo Antônio do Tauá" |
| }, |
| { |
| "lat": -22.72306, |
| "lon": -44.13556, |
| "name": "Rio Claro" |
| }, |
| { |
| "lat": -33.83333, |
| "lon": 150.98333, |
| "name": "Merrylands" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Jaboatão dos Guararapes, Añatuya, Santo Antônio do Tauá, Rio Claro, Merrylands?", |
| "ground_truth": { |
| "answer": "Merrylands", |
| "outlier_distance_km": 13740.5, |
| "second_furthest_km": 5656.1, |
| "clarity_ratio": 2.43, |
| "median_distance_km": 4812.1, |
| "distances_to_centroid": { |
| "Jaboatão dos Guararapes": 3167.2, |
| "Añatuya": 5656.1, |
| "Santo Antônio do Tauá": 4812.1, |
| "Rio Claro": 3789.8, |
| "Merrylands": 13740.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Jaboatão dos Guararapes: (-8.11°, -35.01°)", |
| " Añatuya: (-28.46°, -62.83°)", |
| " Santo Antônio do Tauá: (-1.15°, -48.13°)", |
| " Rio Claro: (-22.72°, -44.14°)", |
| " Merrylands: (-33.83°, 150.98°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Merrylands: 13740.5 km from centroid", |
| " Añatuya: 5656.1 km from centroid", |
| " Santo Antônio do Tauá: 4812.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Merrylands", |
| "FINAL ANSWER: Merrylands" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 50.93182, |
| "lon": 6.99469, |
| "name": "Humboldtkolonie" |
| }, |
| { |
| "lat": 54.11896, |
| "lon": 37.54459, |
| "name": "Kosaya Gora" |
| }, |
| { |
| "lat": 52.74328, |
| "lon": 23.58122, |
| "name": "Hajnówka" |
| }, |
| { |
| "lat": 51.57558, |
| "lon": 8.10619, |
| "name": "Soest" |
| }, |
| { |
| "lat": 8.33069, |
| "lon": 77.26732, |
| "name": "Tiruvattār" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Humboldtkolonie, Kosaya Gora, Hajnówka, Soest, Tiruvattār?", |
| "ground_truth": { |
| "answer": "Tiruvattār", |
| "outlier_distance_km": 5964.1, |
| "second_furthest_km": 1958.0, |
| "clarity_ratio": 3.05, |
| "median_distance_km": 1905.4, |
| "distances_to_centroid": { |
| "Humboldtkolonie": 1958.0, |
| "Kosaya Gora": 1277.2, |
| "Hajnówka": 1150.3, |
| "Soest": 1905.4, |
| "Tiruvattār": 5964.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Humboldtkolonie: (50.93°, 6.99°)", |
| " Kosaya Gora: (54.12°, 37.54°)", |
| " Hajnówka: (52.74°, 23.58°)", |
| " Soest: (51.58°, 8.11°)", |
| " Tiruvattār: (8.33°, 77.27°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Tiruvattār: 5964.1 km from centroid", |
| " Humboldtkolonie: 1958.0 km from centroid", |
| " Soest: 1905.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Tiruvattār", |
| "FINAL ANSWER: Tiruvattār" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 50.22683, |
| "lon": 8.61816, |
| "name": "Bad Homburg vor der Höhe" |
| }, |
| { |
| "lat": 36.73028, |
| "lon": 14.84672, |
| "name": "Pozzallo" |
| }, |
| { |
| "lat": 51.845, |
| "lon": 4.32917, |
| "name": "Spijkenisse" |
| }, |
| { |
| "lat": 43.48451, |
| "lon": -8.23293, |
| "name": "Ferrol" |
| }, |
| { |
| "lat": 4.81367, |
| "lon": -74.35453, |
| "name": "Facatativá" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Bad Homburg vor der Höhe, Pozzallo, Spijkenisse, Ferrol, Facatativá?", |
| "ground_truth": { |
| "answer": "Facatativá", |
| "outlier_distance_km": 7348.2, |
| "second_furthest_km": 2283.5, |
| "clarity_ratio": 3.22, |
| "median_distance_km": 2108.1, |
| "distances_to_centroid": { |
| "Bad Homburg vor der Höhe": 2108.1, |
| "Pozzallo": 2283.5, |
| "Spijkenisse": 2000.4, |
| "Ferrol": 712.6, |
| "Facatativá": 7348.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Bad Homburg vor der Höhe: (50.23°, 8.62°)", |
| " Pozzallo: (36.73°, 14.85°)", |
| " Spijkenisse: (51.84°, 4.33°)", |
| " Ferrol: (43.48°, -8.23°)", |
| " Facatativá: (4.81°, -74.35°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Facatativá: 7348.2 km from centroid", |
| " Pozzallo: 2283.5 km from centroid", |
| " Bad Homburg vor der Höhe: 2108.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Facatativá", |
| "FINAL ANSWER: Facatativá" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 6.25, |
| "lon": 37.56667, |
| "name": "Ch’ench’a" |
| }, |
| { |
| "lat": 31.0475, |
| "lon": 30.85487, |
| "name": "Qillīn" |
| }, |
| { |
| "lat": 7.83879, |
| "lon": 4.48672, |
| "name": "Ilobu" |
| }, |
| { |
| "lat": 25.75089, |
| "lon": 32.6776, |
| "name": "Az Zaynīyah Qiblī" |
| }, |
| { |
| "lat": 31.05601, |
| "lon": -97.46445, |
| "name": "Belton" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Ch’ench’a, Qillīn, Ilobu, Az Zaynīyah Qiblī, Belton?", |
| "ground_truth": { |
| "answer": "Belton", |
| "outlier_distance_km": 9670.5, |
| "second_furthest_km": 4180.8, |
| "clarity_ratio": 2.31, |
| "median_distance_km": 3224.5, |
| "distances_to_centroid": { |
| "Ch’ench’a": 4180.8, |
| "Qillīn": 3146.7, |
| "Ilobu": 1429.1, |
| "Az Zaynīyah Qiblī": 3224.5, |
| "Belton": 9670.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Ch’ench’a: (6.25°, 37.57°)", |
| " Qillīn: (31.05°, 30.85°)", |
| " Ilobu: (7.84°, 4.49°)", |
| " Az Zaynīyah Qiblī: (25.75°, 32.68°)", |
| " Belton: (31.06°, -97.46°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Belton: 9670.5 km from centroid", |
| " Ch’ench’a: 4180.8 km from centroid", |
| " Az Zaynīyah Qiblī: 3224.5 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Belton", |
| "FINAL ANSWER: Belton" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 37.92595, |
| "lon": 115.21907, |
| "name": "Xinji" |
| }, |
| { |
| "lat": 30.84134, |
| "lon": 75.98547, |
| "name": "Sānehwāl" |
| }, |
| { |
| "lat": 36.85, |
| "lon": 138.36667, |
| "name": "Iiyama" |
| }, |
| { |
| "lat": 17.28937, |
| "lon": 74.18183, |
| "name": "Karād" |
| }, |
| { |
| "lat": -41.13827, |
| "lon": 175.0502, |
| "name": "Upper Hutt" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Xinji, Sānehwāl, Iiyama, Karād, Upper Hutt?", |
| "ground_truth": { |
| "answer": "Upper Hutt", |
| "outlier_distance_km": 8829.7, |
| "second_furthest_km": 4418.1, |
| "clarity_ratio": 2.0, |
| "median_distance_km": 4332.7, |
| "distances_to_centroid": { |
| "Xinji": 2399.3, |
| "Sānehwāl": 4332.7, |
| "Iiyama": 3183.9, |
| "Karād": 4418.1, |
| "Upper Hutt": 8829.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Xinji: (37.93°, 115.22°)", |
| " Sānehwāl: (30.84°, 75.99°)", |
| " Iiyama: (36.85°, 138.37°)", |
| " Karād: (17.29°, 74.18°)", |
| " Upper Hutt: (-41.14°, 175.05°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Upper Hutt: 8829.7 km from centroid", |
| " Karād: 4418.1 km from centroid", |
| " Sānehwāl: 4332.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Upper Hutt", |
| "FINAL ANSWER: Upper Hutt" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 48.5498, |
| "lon": 8.72366, |
| "name": "Nagold" |
| }, |
| { |
| "lat": 48.13743, |
| "lon": 11.57549, |
| "name": "Munich" |
| }, |
| { |
| "lat": 54.60343, |
| "lon": 86.27577, |
| "name": "Polysayevo" |
| }, |
| { |
| "lat": 50.58286, |
| "lon": 22.05334, |
| "name": "Stalowa Wola" |
| }, |
| { |
| "lat": -33.72197, |
| "lon": 151.04607, |
| "name": "Cherrybrook" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Nagold, Munich, Polysayevo, Stalowa Wola, Cherrybrook?", |
| "ground_truth": { |
| "answer": "Cherrybrook", |
| "outlier_distance_km": 12416.5, |
| "second_furthest_km": 4209.7, |
| "clarity_ratio": 2.95, |
| "median_distance_km": 3995.2, |
| "distances_to_centroid": { |
| "Nagold": 4209.7, |
| "Munich": 3995.2, |
| "Polysayevo": 3314.5, |
| "Stalowa Wola": 3326.3, |
| "Cherrybrook": 12416.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Nagold: (48.55°, 8.72°)", |
| " Munich: (48.14°, 11.58°)", |
| " Polysayevo: (54.60°, 86.28°)", |
| " Stalowa Wola: (50.58°, 22.05°)", |
| " Cherrybrook: (-33.72°, 151.05°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Cherrybrook: 12416.5 km from centroid", |
| " Nagold: 4209.7 km from centroid", |
| " Munich: 3995.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Cherrybrook", |
| "FINAL ANSWER: Cherrybrook" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 7.40353, |
| "lon": -2.46635, |
| "name": "Nsoatre" |
| }, |
| { |
| "lat": 7.68287, |
| "lon": 4.81769, |
| "name": "Ijebu-Jesa" |
| }, |
| { |
| "lat": 6.63105, |
| "lon": 8.05814, |
| "name": "Effium" |
| }, |
| { |
| "lat": -26.39015, |
| "lon": 30.78742, |
| "name": "Fernie" |
| }, |
| { |
| "lat": 28.71974, |
| "lon": 77.26781, |
| "name": "Mustafābād" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Nsoatre, Ijebu-Jesa, Effium, Fernie, Mustafābād?", |
| "ground_truth": { |
| "answer": "Mustafābād", |
| "outlier_distance_km": 6227.0, |
| "second_furthest_km": 3552.4, |
| "clarity_ratio": 1.75, |
| "median_distance_km": 2906.1, |
| "distances_to_centroid": { |
| "Nsoatre": 2906.1, |
| "Ijebu-Jesa": 2110.4, |
| "Effium": 1741.5, |
| "Fernie": 3552.4, |
| "Mustafābād": 6227.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Nsoatre: (7.40°, -2.47°)", |
| " Ijebu-Jesa: (7.68°, 4.82°)", |
| " Effium: (6.63°, 8.06°)", |
| " Fernie: (-26.39°, 30.79°)", |
| " Mustafābād: (28.72°, 77.27°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Mustafābād: 6227.0 km from centroid", |
| " Fernie: 3552.4 km from centroid", |
| " Nsoatre: 2906.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Mustafābād", |
| "FINAL ANSWER: Mustafābād" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 9.16095, |
| "lon": -75.04811, |
| "name": "Galeras" |
| }, |
| { |
| "lat": 5.25397, |
| "lon": -75.15403, |
| "name": "Manzanares" |
| }, |
| { |
| "lat": -22.85222, |
| "lon": -43.77528, |
| "name": "Itaguaí" |
| }, |
| { |
| "lat": -27.50766, |
| "lon": -58.55625, |
| "name": "San Luis del Palmar" |
| }, |
| { |
| "lat": 52.4581, |
| "lon": 13.28702, |
| "name": "Dahlem" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Galeras, Manzanares, Itaguaí, San Luis del Palmar, Dahlem?", |
| "ground_truth": { |
| "answer": "Dahlem", |
| "outlier_distance_km": 7801.8, |
| "second_furthest_km": 3613.1, |
| "clarity_ratio": 2.16, |
| "median_distance_km": 3074.6, |
| "distances_to_centroid": { |
| "Galeras": 3074.6, |
| "Manzanares": 3035.1, |
| "Itaguaí": 2941.7, |
| "San Luis del Palmar": 3613.1, |
| "Dahlem": 7801.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Galeras: (9.16°, -75.05°)", |
| " Manzanares: (5.25°, -75.15°)", |
| " Itaguaí: (-22.85°, -43.78°)", |
| " San Luis del Palmar: (-27.51°, -58.56°)", |
| " Dahlem: (52.46°, 13.29°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Dahlem: 7801.8 km from centroid", |
| " San Luis del Palmar: 3613.1 km from centroid", |
| " Galeras: 3074.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Dahlem", |
| "FINAL ANSWER: Dahlem" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 41.00176, |
| "lon": -73.66568, |
| "name": "Port Chester" |
| }, |
| { |
| "lat": 18.9378, |
| "lon": -103.96417, |
| "name": "Ciudad de Armería" |
| }, |
| { |
| "lat": 36.58597, |
| "lon": -79.39502, |
| "name": "Danville" |
| }, |
| { |
| "lat": 43.6135, |
| "lon": -116.20345, |
| "name": "Boise" |
| }, |
| { |
| "lat": -2.00082, |
| "lon": -54.08102, |
| "name": "Monte Alegre" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Port Chester, Ciudad de Armería, Danville, Boise, Monte Alegre?", |
| "ground_truth": { |
| "answer": "Monte Alegre", |
| "outlier_distance_km": 4702.6, |
| "second_furthest_km": 3269.4, |
| "clarity_ratio": 1.44, |
| "median_distance_km": 2118.9, |
| "distances_to_centroid": { |
| "Port Chester": 1836.1, |
| "Ciudad de Armería": 2118.9, |
| "Danville": 1147.7, |
| "Boise": 3269.4, |
| "Monte Alegre": 4702.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Port Chester: (41.00°, -73.67°)", |
| " Ciudad de Armería: (18.94°, -103.96°)", |
| " Danville: (36.59°, -79.40°)", |
| " Boise: (43.61°, -116.20°)", |
| " Monte Alegre: (-2.00°, -54.08°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Monte Alegre: 4702.6 km from centroid", |
| " Boise: 3269.4 km from centroid", |
| " Ciudad de Armería: 2118.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Monte Alegre", |
| "FINAL ANSWER: Monte Alegre" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -27.56056, |
| "lon": 151.95386, |
| "name": "Toowoomba" |
| }, |
| { |
| "lat": -33.78333, |
| "lon": 150.93333, |
| "name": "Seven Hills" |
| }, |
| { |
| "lat": -35.73167, |
| "lon": 174.32391, |
| "name": "Whangarei" |
| }, |
| { |
| "lat": -33.9049, |
| "lon": 151.01996, |
| "name": "Yagoona" |
| }, |
| { |
| "lat": 44.54804, |
| "lon": 129.62594, |
| "name": "Mudanjiang" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Toowoomba, Seven Hills, Whangarei, Yagoona, Mudanjiang?", |
| "ground_truth": { |
| "answer": "Mudanjiang", |
| "outlier_distance_km": 7227.0, |
| "second_furthest_km": 3039.9, |
| "clarity_ratio": 2.38, |
| "median_distance_km": 1848.7, |
| "distances_to_centroid": { |
| "Toowoomba": 1143.1, |
| "Seven Hills": 1835.5, |
| "Whangarei": 3039.9, |
| "Yagoona": 1848.7, |
| "Mudanjiang": 7227.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Toowoomba: (-27.56°, 151.95°)", |
| " Seven Hills: (-33.78°, 150.93°)", |
| " Whangarei: (-35.73°, 174.32°)", |
| " Yagoona: (-33.90°, 151.02°)", |
| " Mudanjiang: (44.55°, 129.63°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Mudanjiang: 7227.0 km from centroid", |
| " Whangarei: 3039.9 km from centroid", |
| " Yagoona: 1848.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Mudanjiang", |
| "FINAL ANSWER: Mudanjiang" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 46.84158, |
| "lon": -0.49042, |
| "name": "Bressuire" |
| }, |
| { |
| "lat": 40.43355, |
| "lon": -3.68429, |
| "name": "Castellana" |
| }, |
| { |
| "lat": 50.93333, |
| "lon": 9.21667, |
| "name": "Schwalmstadt" |
| }, |
| { |
| "lat": 38.99915, |
| "lon": -3.36991, |
| "name": "Manzanares" |
| }, |
| { |
| "lat": 8.55142, |
| "lon": 76.96079, |
| "name": "Kudappanakkunnu" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Bressuire, Castellana, Schwalmstadt, Manzanares, Kudappanakkunnu?", |
| "ground_truth": { |
| "answer": "Kudappanakkunnu", |
| "outlier_distance_km": 6896.8, |
| "second_furthest_km": 1717.6, |
| "clarity_ratio": 4.02, |
| "median_distance_km": 1713.7, |
| "distances_to_centroid": { |
| "Bressuire": 1713.7, |
| "Castellana": 1717.6, |
| "Schwalmstadt": 1616.8, |
| "Manzanares": 1681.0, |
| "Kudappanakkunnu": 6896.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Bressuire: (46.84°, -0.49°)", |
| " Castellana: (40.43°, -3.68°)", |
| " Schwalmstadt: (50.93°, 9.22°)", |
| " Manzanares: (39.00°, -3.37°)", |
| " Kudappanakkunnu: (8.55°, 76.96°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Kudappanakkunnu: 6896.8 km from centroid", |
| " Castellana: 1717.6 km from centroid", |
| " Bressuire: 1713.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Kudappanakkunnu", |
| "FINAL ANSWER: Kudappanakkunnu" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -32.06003, |
| "lon": 115.955, |
| "name": "Thornlie" |
| }, |
| { |
| "lat": -33.76667, |
| "lon": 150.81667, |
| "name": "Mount Druitt" |
| }, |
| { |
| "lat": -41.13827, |
| "lon": 175.0502, |
| "name": "Upper Hutt" |
| }, |
| { |
| "lat": -27.56056, |
| "lon": 151.95386, |
| "name": "Toowoomba" |
| }, |
| { |
| "lat": 31.55371, |
| "lon": 25.15793, |
| "name": "As Sallūm" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Thornlie, Mount Druitt, Upper Hutt, Toowoomba, As Sallūm?", |
| "ground_truth": { |
| "answer": "As Sallūm", |
| "outlier_distance_km": 11973.8, |
| "second_furthest_km": 5308.0, |
| "clarity_ratio": 2.26, |
| "median_distance_km": 3034.6, |
| "distances_to_centroid": { |
| "Thornlie": 1493.6, |
| "Mount Druitt": 3034.6, |
| "Upper Hutt": 5308.0, |
| "Toowoomba": 2955.1, |
| "As Sallūm": 11973.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Thornlie: (-32.06°, 115.95°)", |
| " Mount Druitt: (-33.77°, 150.82°)", |
| " Upper Hutt: (-41.14°, 175.05°)", |
| " Toowoomba: (-27.56°, 151.95°)", |
| " As Sallūm: (31.55°, 25.16°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " As Sallūm: 11973.8 km from centroid", |
| " Upper Hutt: 5308.0 km from centroid", |
| " Mount Druitt: 3034.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: As Sallūm", |
| "FINAL ANSWER: As Sallūm" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -4.03972, |
| "lon": -38.63722, |
| "name": "Guaiúba" |
| }, |
| { |
| "lat": -7.14, |
| "lon": -35.08639, |
| "name": "Cruz do Espírito Santo" |
| }, |
| { |
| "lat": -26.56472, |
| "lon": -52.32833, |
| "name": "Abelardo Luz" |
| }, |
| { |
| "lat": -17.345, |
| "lon": -44.94194, |
| "name": "Pirapora" |
| }, |
| { |
| "lat": 60.91, |
| "lon": 34.16188, |
| "name": "Podporozh’ye" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Guaiúba, Cruz do Espírito Santo, Abelardo Luz, Pirapora, Podporozh’ye?", |
| "ground_truth": { |
| "answer": "Podporozh’ye", |
| "outlier_distance_km": 8401.1, |
| "second_furthest_km": 4082.4, |
| "clarity_ratio": 2.06, |
| "median_distance_km": 2818.6, |
| "distances_to_centroid": { |
| "Guaiúba": 1379.6, |
| "Cruz do Espírito Santo": 1259.4, |
| "Abelardo Luz": 4082.4, |
| "Pirapora": 2818.6, |
| "Podporozh’ye": 8401.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Guaiúba: (-4.04°, -38.64°)", |
| " Cruz do Espírito Santo: (-7.14°, -35.09°)", |
| " Abelardo Luz: (-26.56°, -52.33°)", |
| " Pirapora: (-17.34°, -44.94°)", |
| " Podporozh’ye: (60.91°, 34.16°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Podporozh’ye: 8401.1 km from centroid", |
| " Abelardo Luz: 4082.4 km from centroid", |
| " Pirapora: 2818.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Podporozh’ye", |
| "FINAL ANSWER: Podporozh’ye" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 42.3242, |
| "lon": -83.40021, |
| "name": "Westland" |
| }, |
| { |
| "lat": 38.81084, |
| "lon": -94.92719, |
| "name": "Gardner" |
| }, |
| { |
| "lat": 32.54044, |
| "lon": -82.90375, |
| "name": "Dublin" |
| }, |
| { |
| "lat": 42.7262, |
| "lon": -71.19089, |
| "name": "Methuen" |
| }, |
| { |
| "lat": 5.65396, |
| "lon": 0.0264, |
| "name": "Tema New Town" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Westland, Gardner, Dublin, Methuen, Tema New Town?", |
| "ground_truth": { |
| "answer": "Tema New Town", |
| "outlier_distance_km": 7470.8, |
| "second_furthest_km": 2656.3, |
| "clarity_ratio": 2.81, |
| "median_distance_km": 1852.0, |
| "distances_to_centroid": { |
| "Westland": 1852.0, |
| "Gardner": 2656.3, |
| "Dublin": 1539.3, |
| "Methuen": 1219.3, |
| "Tema New Town": 7470.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Westland: (42.32°, -83.40°)", |
| " Gardner: (38.81°, -94.93°)", |
| " Dublin: (32.54°, -82.90°)", |
| " Methuen: (42.73°, -71.19°)", |
| " Tema New Town: (5.65°, 0.03°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Tema New Town: 7470.8 km from centroid", |
| " Gardner: 2656.3 km from centroid", |
| " Westland: 1852.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Tema New Town", |
| "FINAL ANSWER: Tema New Town" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -32.83211, |
| "lon": 151.35623, |
| "name": "Cessnock" |
| }, |
| { |
| "lat": -37.74981, |
| "lon": 144.9109, |
| "name": "Essendon" |
| }, |
| { |
| "lat": -37.8, |
| "lon": 144.9, |
| "name": "Footscray" |
| }, |
| { |
| "lat": -33.91439, |
| "lon": 151.24895, |
| "name": "Randwick" |
| }, |
| { |
| "lat": 7.85868, |
| "lon": 10.97187, |
| "name": "Beli" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Cessnock, Essendon, Footscray, Randwick, Beli?", |
| "ground_truth": { |
| "answer": "Beli", |
| "outlier_distance_km": 12352.1, |
| "second_furthest_km": 3021.9, |
| "clarity_ratio": 4.09, |
| "median_distance_km": 3020.1, |
| "distances_to_centroid": { |
| "Cessnock": 3020.1, |
| "Essendon": 2566.7, |
| "Footscray": 2567.8, |
| "Randwick": 3021.9, |
| "Beli": 12352.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Cessnock: (-32.83°, 151.36°)", |
| " Essendon: (-37.75°, 144.91°)", |
| " Footscray: (-37.80°, 144.90°)", |
| " Randwick: (-33.91°, 151.25°)", |
| " Beli: (7.86°, 10.97°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Beli: 12352.1 km from centroid", |
| " Randwick: 3021.9 km from centroid", |
| " Cessnock: 3020.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Beli", |
| "FINAL ANSWER: Beli" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -33.92893, |
| "lon": 151.05111, |
| "name": "Punchbowl" |
| }, |
| { |
| "lat": -27.96724, |
| "lon": 153.39796, |
| "name": "Southport" |
| }, |
| { |
| "lat": -33.9681, |
| "lon": 151.13564, |
| "name": "Kogarah" |
| }, |
| { |
| "lat": -12.46113, |
| "lon": 130.84185, |
| "name": "Darwin" |
| }, |
| { |
| "lat": -6.10167, |
| "lon": -49.59806, |
| "name": "Curionópolis" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Punchbowl, Southport, Kogarah, Darwin, Curionópolis?", |
| "ground_truth": { |
| "answer": "Curionópolis", |
| "outlier_distance_km": 15933.2, |
| "second_furthest_km": 4630.6, |
| "clarity_ratio": 3.44, |
| "median_distance_km": 4418.1, |
| "distances_to_centroid": { |
| "Punchbowl": 4410.0, |
| "Southport": 4630.6, |
| "Kogarah": 4418.1, |
| "Darwin": 2738.5, |
| "Curionópolis": 15933.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Punchbowl: (-33.93°, 151.05°)", |
| " Southport: (-27.97°, 153.40°)", |
| " Kogarah: (-33.97°, 151.14°)", |
| " Darwin: (-12.46°, 130.84°)", |
| " Curionópolis: (-6.10°, -49.60°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Curionópolis: 15933.2 km from centroid", |
| " Southport: 4630.6 km from centroid", |
| " Kogarah: 4418.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Curionópolis", |
| "FINAL ANSWER: Curionópolis" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 46.23958, |
| "lon": -119.10057, |
| "name": "Pasco" |
| }, |
| { |
| "lat": 40.59344, |
| "lon": -74.1632, |
| "name": "New Springville" |
| }, |
| { |
| "lat": 33.63967, |
| "lon": -117.84164, |
| "name": "UC Irvine" |
| }, |
| { |
| "lat": 42.27756, |
| "lon": -83.74088, |
| "name": "Ann Arbor" |
| }, |
| { |
| "lat": -25.76972, |
| "lon": -49.71583, |
| "name": "Lapa" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Pasco, New Springville, UC Irvine, Ann Arbor, Lapa?", |
| "ground_truth": { |
| "answer": "Lapa", |
| "outlier_distance_km": 7249.0, |
| "second_furthest_km": 3372.6, |
| "clarity_ratio": 2.15, |
| "median_distance_km": 2846.6, |
| "distances_to_centroid": { |
| "Pasco": 3372.6, |
| "New Springville": 1994.9, |
| "UC Irvine": 2846.6, |
| "Ann Arbor": 1719.8, |
| "Lapa": 7249.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Pasco: (46.24°, -119.10°)", |
| " New Springville: (40.59°, -74.16°)", |
| " UC Irvine: (33.64°, -117.84°)", |
| " Ann Arbor: (42.28°, -83.74°)", |
| " Lapa: (-25.77°, -49.72°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Lapa: 7249.0 km from centroid", |
| " Pasco: 3372.6 km from centroid", |
| " UC Irvine: 2846.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Lapa", |
| "FINAL ANSWER: Lapa" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -31.84062, |
| "lon": 115.89549, |
| "name": "Ballajura" |
| }, |
| { |
| "lat": -37.91928, |
| "lon": 145.05301, |
| "name": "Bentleigh East" |
| }, |
| { |
| "lat": -38.26667, |
| "lon": 145.01667, |
| "name": "Mount Martha" |
| }, |
| { |
| "lat": -37.73333, |
| "lon": 144.8, |
| "name": "Saint Albans" |
| }, |
| { |
| "lat": 9.25778, |
| "lon": -73.81228, |
| "name": "Chimichagua" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Ballajura, Bentleigh East, Mount Martha, Saint Albans, Chimichagua?", |
| "ground_truth": { |
| "answer": "Chimichagua", |
| "outlier_distance_km": 17710.8, |
| "second_furthest_km": 4741.4, |
| "clarity_ratio": 3.74, |
| "median_distance_km": 4737.9, |
| "distances_to_centroid": { |
| "Ballajura": 2042.8, |
| "Bentleigh East": 4741.4, |
| "Mount Martha": 4737.9, |
| "Saint Albans": 4719.4, |
| "Chimichagua": 17710.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Ballajura: (-31.84°, 115.90°)", |
| " Bentleigh East: (-37.92°, 145.05°)", |
| " Mount Martha: (-38.27°, 145.02°)", |
| " Saint Albans: (-37.73°, 144.80°)", |
| " Chimichagua: (9.26°, -73.81°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Chimichagua: 17710.8 km from centroid", |
| " Bentleigh East: 4741.4 km from centroid", |
| " Mount Martha: 4737.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Chimichagua", |
| "FINAL ANSWER: Chimichagua" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -37.0646, |
| "lon": 174.94212, |
| "name": "Papakura" |
| }, |
| { |
| "lat": -33.85, |
| "lon": 151.03333, |
| "name": "Auburn" |
| }, |
| { |
| "lat": -36.75818, |
| "lon": 144.28024, |
| "name": "Bendigo" |
| }, |
| { |
| "lat": -20.72523, |
| "lon": 139.49727, |
| "name": "Mount Isa" |
| }, |
| { |
| "lat": 6.7, |
| "lon": 6.33333, |
| "name": "Uromi" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Papakura, Auburn, Bendigo, Mount Isa, Uromi?", |
| "ground_truth": { |
| "answer": "Uromi", |
| "outlier_distance_km": 13033.2, |
| "second_furthest_km": 5078.6, |
| "clarity_ratio": 2.57, |
| "median_distance_km": 2890.7, |
| "distances_to_centroid": { |
| "Papakura": 5078.6, |
| "Auburn": 2890.7, |
| "Bendigo": 2435.3, |
| "Mount Isa": 1718.5, |
| "Uromi": 13033.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Papakura: (-37.06°, 174.94°)", |
| " Auburn: (-33.85°, 151.03°)", |
| " Bendigo: (-36.76°, 144.28°)", |
| " Mount Isa: (-20.73°, 139.50°)", |
| " Uromi: (6.70°, 6.33°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Uromi: 13033.2 km from centroid", |
| " Papakura: 5078.6 km from centroid", |
| " Auburn: 2890.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Uromi", |
| "FINAL ANSWER: Uromi" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 44.05755, |
| "lon": 12.56528, |
| "name": "Rimini" |
| }, |
| { |
| "lat": 45.78693, |
| "lon": 4.9251, |
| "name": "Vaulx-en-Velin" |
| }, |
| { |
| "lat": 36.9838, |
| "lon": -5.93933, |
| "name": "Las Cabezas de San Juan" |
| }, |
| { |
| "lat": 60.01667, |
| "lon": 30.35, |
| "name": "Sosnovka" |
| }, |
| { |
| "lat": -37.87822, |
| "lon": 175.4402, |
| "name": "Cambridge" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Rimini, Vaulx-en-Velin, Las Cabezas de San Juan, Sosnovka, Cambridge?", |
| "ground_truth": { |
| "answer": "Cambridge", |
| "outlier_distance_km": 15538.9, |
| "second_furthest_km": 4604.8, |
| "clarity_ratio": 3.37, |
| "median_distance_km": 3775.9, |
| "distances_to_centroid": { |
| "Rimini": 3144.7, |
| "Vaulx-en-Velin": 3775.9, |
| "Las Cabezas de San Juan": 4604.8, |
| "Sosnovka": 3501.3, |
| "Cambridge": 15538.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Rimini: (44.06°, 12.57°)", |
| " Vaulx-en-Velin: (45.79°, 4.93°)", |
| " Las Cabezas de San Juan: (36.98°, -5.94°)", |
| " Sosnovka: (60.02°, 30.35°)", |
| " Cambridge: (-37.88°, 175.44°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Cambridge: 15538.9 km from centroid", |
| " Las Cabezas de San Juan: 4604.8 km from centroid", |
| " Vaulx-en-Velin: 3775.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Cambridge", |
| "FINAL ANSWER: Cambridge" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 15.87944, |
| "lon": 108.335, |
| "name": "Hoi An" |
| }, |
| { |
| "lat": 30.421, |
| "lon": 112.8919, |
| "name": "Qianjiang" |
| }, |
| { |
| "lat": 26.31688, |
| "lon": 89.66549, |
| "name": "Tufānganj" |
| }, |
| { |
| "lat": 29.05028, |
| "lon": 106.73639, |
| "name": "Sanjiao" |
| }, |
| { |
| "lat": 31.70932, |
| "lon": -98.99116, |
| "name": "Brownwood" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Hoi An, Qianjiang, Tufānganj, Sanjiao, Brownwood?", |
| "ground_truth": { |
| "answer": "Brownwood", |
| "outlier_distance_km": 13269.3, |
| "second_furthest_km": 4783.1, |
| "clarity_ratio": 2.77, |
| "median_distance_km": 4749.9, |
| "distances_to_centroid": { |
| "Hoi An": 4749.9, |
| "Qianjiang": 4783.1, |
| "Tufānganj": 2577.1, |
| "Sanjiao": 4213.0, |
| "Brownwood": 13269.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Hoi An: (15.88°, 108.33°)", |
| " Qianjiang: (30.42°, 112.89°)", |
| " Tufānganj: (26.32°, 89.67°)", |
| " Sanjiao: (29.05°, 106.74°)", |
| " Brownwood: (31.71°, -98.99°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Brownwood: 13269.3 km from centroid", |
| " Qianjiang: 4783.1 km from centroid", |
| " Hoi An: 4749.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Brownwood", |
| "FINAL ANSWER: Brownwood" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -33.77271, |
| "lon": 151.08184, |
| "name": "Epping" |
| }, |
| { |
| "lat": -41.51603, |
| "lon": 173.9528, |
| "name": "Blenheim" |
| }, |
| { |
| "lat": -32.05251, |
| "lon": 115.88782, |
| "name": "Willetton" |
| }, |
| { |
| "lat": -33.8178, |
| "lon": 151.00348, |
| "name": "Parramatta" |
| }, |
| { |
| "lat": 49.68369, |
| "lon": 8.61839, |
| "name": "Bensheim" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Epping, Blenheim, Willetton, Parramatta, Bensheim?", |
| "ground_truth": { |
| "answer": "Bensheim", |
| "outlier_distance_km": 13084.5, |
| "second_furthest_km": 5685.8, |
| "clarity_ratio": 2.3, |
| "median_distance_km": 3520.2, |
| "distances_to_centroid": { |
| "Epping": 3520.2, |
| "Blenheim": 5685.8, |
| "Willetton": 1587.2, |
| "Parramatta": 3515.3, |
| "Bensheim": 13084.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Epping: (-33.77°, 151.08°)", |
| " Blenheim: (-41.52°, 173.95°)", |
| " Willetton: (-32.05°, 115.89°)", |
| " Parramatta: (-33.82°, 151.00°)", |
| " Bensheim: (49.68°, 8.62°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Bensheim: 13084.5 km from centroid", |
| " Blenheim: 5685.8 km from centroid", |
| " Epping: 3520.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Bensheim", |
| "FINAL ANSWER: Bensheim" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 33.09179, |
| "lon": -97.04668, |
| "name": "Highland Village" |
| }, |
| { |
| "lat": 37.87715, |
| "lon": -122.17969, |
| "name": "Orinda" |
| }, |
| { |
| "lat": 22.36094, |
| "lon": -97.89997, |
| "name": "Miramar" |
| }, |
| { |
| "lat": 40.80899, |
| "lon": -73.92291, |
| "name": "Mott Haven" |
| }, |
| { |
| "lat": 51.16158, |
| "lon": 13.4737, |
| "name": "Meissen" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Highland Village, Orinda, Miramar, Mott Haven, Meissen?", |
| "ground_truth": { |
| "answer": "Meissen", |
| "outlier_distance_km": 6830.6, |
| "second_furthest_km": 4075.4, |
| "clarity_ratio": 1.68, |
| "median_distance_km": 2698.0, |
| "distances_to_centroid": { |
| "Highland Village": 2003.8, |
| "Orinda": 4075.4, |
| "Miramar": 2698.0, |
| "Mott Haven": 439.0, |
| "Meissen": 6830.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Highland Village: (33.09°, -97.05°)", |
| " Orinda: (37.88°, -122.18°)", |
| " Miramar: (22.36°, -97.90°)", |
| " Mott Haven: (40.81°, -73.92°)", |
| " Meissen: (51.16°, 13.47°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Meissen: 6830.6 km from centroid", |
| " Orinda: 4075.4 km from centroid", |
| " Miramar: 2698.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Meissen", |
| "FINAL ANSWER: Meissen" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -38.11342, |
| "lon": 145.28326, |
| "name": "Cranbourne" |
| }, |
| { |
| "lat": -38.03333, |
| "lon": 145.35, |
| "name": "Berwick" |
| }, |
| { |
| "lat": -27.49325, |
| "lon": 153.05826, |
| "name": "Coorparoo" |
| }, |
| { |
| "lat": -31.76737, |
| "lon": 115.96936, |
| "name": "Ellenbrook" |
| }, |
| { |
| "lat": 6.04024, |
| "lon": -0.80876, |
| "name": "Akwatia" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Cranbourne, Berwick, Coorparoo, Ellenbrook, Akwatia?", |
| "ground_truth": { |
| "answer": "Akwatia", |
| "outlier_distance_km": 12556.3, |
| "second_furthest_km": 4087.1, |
| "clarity_ratio": 3.07, |
| "median_distance_km": 3420.6, |
| "distances_to_centroid": { |
| "Cranbourne": 3417.0, |
| "Berwick": 3420.6, |
| "Coorparoo": 4087.1, |
| "Ellenbrook": 772.4, |
| "Akwatia": 12556.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Cranbourne: (-38.11°, 145.28°)", |
| " Berwick: (-38.03°, 145.35°)", |
| " Coorparoo: (-27.49°, 153.06°)", |
| " Ellenbrook: (-31.77°, 115.97°)", |
| " Akwatia: (6.04°, -0.81°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Akwatia: 12556.3 km from centroid", |
| " Coorparoo: 4087.1 km from centroid", |
| " Berwick: 3420.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Akwatia", |
| "FINAL ANSWER: Akwatia" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 45.40008, |
| "lon": -74.13256, |
| "name": "Saint-Lazare" |
| }, |
| { |
| "lat": 25.62177, |
| "lon": -80.32477, |
| "name": "Palmetto Bay" |
| }, |
| { |
| "lat": 20.05161, |
| "lon": -99.34397, |
| "name": "Tula de Allende" |
| }, |
| { |
| "lat": 41.1145, |
| "lon": -83.17797, |
| "name": "Tiffin" |
| }, |
| { |
| "lat": -26.65682, |
| "lon": 153.07955, |
| "name": "Sunshine Coast" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Saint-Lazare, Palmetto Bay, Tula de Allende, Tiffin, Sunshine Coast?", |
| "ground_truth": { |
| "answer": "Sunshine Coast", |
| "outlier_distance_km": 18838.6, |
| "second_furthest_km": 6469.3, |
| "clarity_ratio": 2.91, |
| "median_distance_km": 4872.7, |
| "distances_to_centroid": { |
| "Saint-Lazare": 4337.0, |
| "Palmetto Bay": 4453.8, |
| "Tula de Allende": 6469.3, |
| "Tiffin": 4872.7, |
| "Sunshine Coast": 18838.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Saint-Lazare: (45.40°, -74.13°)", |
| " Palmetto Bay: (25.62°, -80.32°)", |
| " Tula de Allende: (20.05°, -99.34°)", |
| " Tiffin: (41.11°, -83.18°)", |
| " Sunshine Coast: (-26.66°, 153.08°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Sunshine Coast: 18838.6 km from centroid", |
| " Tula de Allende: 6469.3 km from centroid", |
| " Tiffin: 4872.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Sunshine Coast", |
| "FINAL ANSWER: Sunshine Coast" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 30.91204, |
| "lon": 75.85379, |
| "name": "Ludhiana" |
| }, |
| { |
| "lat": 19.92672, |
| "lon": 74.7275, |
| "name": "Vaijāpur" |
| }, |
| { |
| "lat": 25.46335, |
| "lon": 99.52826, |
| "name": "Bonan" |
| }, |
| { |
| "lat": 31.35333, |
| "lon": 106.06309, |
| "name": "Nanlong" |
| }, |
| { |
| "lat": 51.18035, |
| "lon": 14.43494, |
| "name": "Bautzen" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Ludhiana, Vaijāpur, Bonan, Nanlong, Bautzen?", |
| "ground_truth": { |
| "answer": "Bautzen", |
| "outlier_distance_km": 5250.6, |
| "second_furthest_km": 3015.8, |
| "clarity_ratio": 1.74, |
| "median_distance_km": 2570.3, |
| "distances_to_centroid": { |
| "Ludhiana": 190.0, |
| "Vaijāpur": 1318.0, |
| "Bonan": 2570.3, |
| "Nanlong": 3015.8, |
| "Bautzen": 5250.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Ludhiana: (30.91°, 75.85°)", |
| " Vaijāpur: (19.93°, 74.73°)", |
| " Bonan: (25.46°, 99.53°)", |
| " Nanlong: (31.35°, 106.06°)", |
| " Bautzen: (51.18°, 14.43°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Bautzen: 5250.6 km from centroid", |
| " Nanlong: 3015.8 km from centroid", |
| " Bonan: 2570.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Bautzen", |
| "FINAL ANSWER: Bautzen" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -27.58333, |
| "lon": 153.1, |
| "name": "Eight Mile Plains" |
| }, |
| { |
| "lat": -37.78333, |
| "lon": 175.28333, |
| "name": "Hamilton" |
| }, |
| { |
| "lat": -33.8188, |
| "lon": 151.1062, |
| "name": "Ryde" |
| }, |
| { |
| "lat": -37.9, |
| "lon": 145.18333, |
| "name": "Wheelers Hill" |
| }, |
| { |
| "lat": 43.70313, |
| "lon": 7.26608, |
| "name": "Nice" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Eight Mile Plains, Hamilton, Ryde, Wheelers Hill, Nice?", |
| "ground_truth": { |
| "answer": "Nice", |
| "outlier_distance_km": 13752.5, |
| "second_furthest_km": 5169.9, |
| "clarity_ratio": 2.66, |
| "median_distance_km": 2971.8, |
| "distances_to_centroid": { |
| "Eight Mile Plains": 2897.8, |
| "Hamilton": 5169.9, |
| "Ryde": 2971.8, |
| "Wheelers Hill": 2808.8, |
| "Nice": 13752.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Eight Mile Plains: (-27.58°, 153.10°)", |
| " Hamilton: (-37.78°, 175.28°)", |
| " Ryde: (-33.82°, 151.11°)", |
| " Wheelers Hill: (-37.90°, 145.18°)", |
| " Nice: (43.70°, 7.27°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Nice: 13752.5 km from centroid", |
| " Hamilton: 5169.9 km from centroid", |
| " Ryde: 2971.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Nice", |
| "FINAL ANSWER: Nice" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 47.56013, |
| "lon": 7.78715, |
| "name": "Rheinfelden" |
| }, |
| { |
| "lat": 50.10068, |
| "lon": 11.45032, |
| "name": "Kulmbach" |
| }, |
| { |
| "lat": 51.15914, |
| "lon": 11.11524, |
| "name": "Sömmerda" |
| }, |
| { |
| "lat": 50.9466, |
| "lon": 17.2926, |
| "name": "Oława" |
| }, |
| { |
| "lat": 42.1103, |
| "lon": -88.03424, |
| "name": "Palatine" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Rheinfelden, Kulmbach, Sömmerda, Oława, Palatine?", |
| "ground_truth": { |
| "answer": "Palatine", |
| "outlier_distance_km": 6009.2, |
| "second_furthest_km": 1838.9, |
| "clarity_ratio": 3.27, |
| "median_distance_km": 1426.5, |
| "distances_to_centroid": { |
| "Rheinfelden": 1182.5, |
| "Kulmbach": 1426.5, |
| "Sömmerda": 1408.4, |
| "Oława": 1838.9, |
| "Palatine": 6009.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Rheinfelden: (47.56°, 7.79°)", |
| " Kulmbach: (50.10°, 11.45°)", |
| " Sömmerda: (51.16°, 11.12°)", |
| " Oława: (50.95°, 17.29°)", |
| " Palatine: (42.11°, -88.03°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Palatine: 6009.2 km from centroid", |
| " Oława: 1838.9 km from centroid", |
| " Kulmbach: 1426.5 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Palatine", |
| "FINAL ANSWER: Palatine" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 51.58294, |
| "lon": 21.54779, |
| "name": "Kozienice" |
| }, |
| { |
| "lat": 49.24762, |
| "lon": 11.09111, |
| "name": "Roth" |
| }, |
| { |
| "lat": 48.10881, |
| "lon": 11.72653, |
| "name": "Haar" |
| }, |
| { |
| "lat": 39.50263, |
| "lon": -0.44079, |
| "name": "Paterna" |
| }, |
| { |
| "lat": 27.73976, |
| "lon": 75.78652, |
| "name": "Neem ka Thana" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Kozienice, Roth, Haar, Paterna, Neem ka Thana?", |
| "ground_truth": { |
| "answer": "Neem ka Thana", |
| "outlier_distance_km": 4912.1, |
| "second_furthest_km": 2068.8, |
| "clarity_ratio": 2.37, |
| "median_distance_km": 1190.6, |
| "distances_to_centroid": { |
| "Kozienice": 945.3, |
| "Roth": 1190.6, |
| "Haar": 1091.1, |
| "Paterna": 2068.8, |
| "Neem ka Thana": 4912.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Kozienice: (51.58°, 21.55°)", |
| " Roth: (49.25°, 11.09°)", |
| " Haar: (48.11°, 11.73°)", |
| " Paterna: (39.50°, -0.44°)", |
| " Neem ka Thana: (27.74°, 75.79°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Neem ka Thana: 4912.1 km from centroid", |
| " Paterna: 2068.8 km from centroid", |
| " Roth: 1190.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Neem ka Thana", |
| "FINAL ANSWER: Neem ka Thana" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -33.85, |
| "lon": 151.03333, |
| "name": "Auburn" |
| }, |
| { |
| "lat": -33.95, |
| "lon": 151.13333, |
| "name": "Rockdale" |
| }, |
| { |
| "lat": -32.5269, |
| "lon": 115.7217, |
| "name": "Mandurah" |
| }, |
| { |
| "lat": -38.65333, |
| "lon": 178.00417, |
| "name": "Gisborne" |
| }, |
| { |
| "lat": 20.9, |
| "lon": 105.58333, |
| "name": "Xuân Mai" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Auburn, Rockdale, Mandurah, Gisborne, Xuân Mai?", |
| "ground_truth": { |
| "answer": "Xuân Mai", |
| "outlier_distance_km": 6215.2, |
| "second_furthest_km": 3923.4, |
| "clarity_ratio": 1.58, |
| "median_distance_km": 2598.6, |
| "distances_to_centroid": { |
| "Auburn": 1544.3, |
| "Rockdale": 1558.7, |
| "Mandurah": 2598.6, |
| "Gisborne": 3923.4, |
| "Xuân Mai": 6215.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Auburn: (-33.85°, 151.03°)", |
| " Rockdale: (-33.95°, 151.13°)", |
| " Mandurah: (-32.53°, 115.72°)", |
| " Gisborne: (-38.65°, 178.00°)", |
| " Xuân Mai: (20.90°, 105.58°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Xuân Mai: 6215.2 km from centroid", |
| " Gisborne: 3923.4 km from centroid", |
| " Mandurah: 2598.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Xuân Mai", |
| "FINAL ANSWER: Xuân Mai" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 50.9236, |
| "lon": 22.22706, |
| "name": "Kraśnik" |
| }, |
| { |
| "lat": 51.28333, |
| "lon": -0.83333, |
| "name": "Fleet" |
| }, |
| { |
| "lat": 53.59782, |
| "lon": 34.33825, |
| "name": "Dyat’kovo" |
| }, |
| { |
| "lat": 41.68921, |
| "lon": 2.48965, |
| "name": "Sant Celoni" |
| }, |
| { |
| "lat": 34.69804, |
| "lon": -118.13674, |
| "name": "Lancaster" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Kraśnik, Fleet, Dyat’kovo, Sant Celoni, Lancaster?", |
| "ground_truth": { |
| "answer": "Lancaster", |
| "outlier_distance_km": 8365.7, |
| "second_furthest_km": 3340.3, |
| "clarity_ratio": 2.5, |
| "median_distance_km": 2536.6, |
| "distances_to_centroid": { |
| "Kraśnik": 2536.6, |
| "Fleet": 975.9, |
| "Dyat’kovo": 3340.3, |
| "Sant Celoni": 1268.7, |
| "Lancaster": 8365.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Kraśnik: (50.92°, 22.23°)", |
| " Fleet: (51.28°, -0.83°)", |
| " Dyat’kovo: (53.60°, 34.34°)", |
| " Sant Celoni: (41.69°, 2.49°)", |
| " Lancaster: (34.70°, -118.14°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Lancaster: 8365.7 km from centroid", |
| " Dyat’kovo: 3340.3 km from centroid", |
| " Kraśnik: 2536.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Lancaster", |
| "FINAL ANSWER: Lancaster" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -16.17028, |
| "lon": -42.29028, |
| "name": "Salinas" |
| }, |
| { |
| "lat": -28.64397, |
| "lon": -53.60633, |
| "name": "Cruz Alta" |
| }, |
| { |
| "lat": -32.94682, |
| "lon": -60.63932, |
| "name": "Rosario" |
| }, |
| { |
| "lat": -33.98219, |
| "lon": -70.7104, |
| "name": "San Francisco de Mostazal" |
| }, |
| { |
| "lat": 41.41885, |
| "lon": 2.17364, |
| "name": "el Guinardó" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Salinas, Cruz Alta, Rosario, San Francisco de Mostazal, el Guinardó?", |
| "ground_truth": { |
| "answer": "el Guinardó", |
| "outlier_distance_km": 7840.8, |
| "second_furthest_km": 3403.8, |
| "clarity_ratio": 2.3, |
| "median_distance_km": 2628.3, |
| "distances_to_centroid": { |
| "Salinas": 374.6, |
| "Cruz Alta": 1847.5, |
| "Rosario": 2628.3, |
| "San Francisco de Mostazal": 3403.8, |
| "el Guinardó": 7840.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Salinas: (-16.17°, -42.29°)", |
| " Cruz Alta: (-28.64°, -53.61°)", |
| " Rosario: (-32.95°, -60.64°)", |
| " San Francisco de Mostazal: (-33.98°, -70.71°)", |
| " el Guinardó: (41.42°, 2.17°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " el Guinardó: 7840.8 km from centroid", |
| " San Francisco de Mostazal: 3403.8 km from centroid", |
| " Rosario: 2628.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: el Guinardó", |
| "FINAL ANSWER: el Guinardó" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 53.62744, |
| "lon": 21.81253, |
| "name": "Pisz" |
| }, |
| { |
| "lat": 50.9856, |
| "lon": 7.13298, |
| "name": "Bergisch Gladbach" |
| }, |
| { |
| "lat": 50.7282, |
| "lon": 16.65141, |
| "name": "Dzierżoniów" |
| }, |
| { |
| "lat": 52.44859, |
| "lon": -2.04938, |
| "name": "Halesowen" |
| }, |
| { |
| "lat": 29.36857, |
| "lon": -94.97131, |
| "name": "La Marque" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Pisz, Bergisch Gladbach, Dzierżoniów, Halesowen, La Marque?", |
| "ground_truth": { |
| "answer": "La Marque", |
| "outlier_distance_km": 7275.7, |
| "second_furthest_km": 2348.2, |
| "clarity_ratio": 3.1, |
| "median_distance_km": 1984.2, |
| "distances_to_centroid": { |
| "Pisz": 2348.2, |
| "Bergisch Gladbach": 1321.9, |
| "Dzierżoniów": 1984.2, |
| "Halesowen": 810.6, |
| "La Marque": 7275.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Pisz: (53.63°, 21.81°)", |
| " Bergisch Gladbach: (50.99°, 7.13°)", |
| " Dzierżoniów: (50.73°, 16.65°)", |
| " Halesowen: (52.45°, -2.05°)", |
| " La Marque: (29.37°, -94.97°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " La Marque: 7275.7 km from centroid", |
| " Pisz: 2348.2 km from centroid", |
| " Dzierżoniów: 1984.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: La Marque", |
| "FINAL ANSWER: La Marque" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -34.75155, |
| "lon": 149.72086, |
| "name": "Goulburn" |
| }, |
| { |
| "lat": -37.83961, |
| "lon": 144.94228, |
| "name": "Port Melbourne" |
| }, |
| { |
| "lat": -27.61025, |
| "lon": 153.05388, |
| "name": "Sunnybank Hills" |
| }, |
| { |
| "lat": -34.91119, |
| "lon": 138.70735, |
| "name": "Adelaide Hills" |
| }, |
| { |
| "lat": 11.12018, |
| "lon": 76.11996, |
| "name": "Manjeri" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Goulburn, Port Melbourne, Sunnybank Hills, Adelaide Hills, Manjeri?", |
| "ground_truth": { |
| "answer": "Manjeri", |
| "outlier_distance_km": 7300.9, |
| "second_furthest_km": 2070.9, |
| "clarity_ratio": 3.53, |
| "median_distance_km": 1991.4, |
| "distances_to_centroid": { |
| "Goulburn": 1991.4, |
| "Port Melbourne": 1866.4, |
| "Sunnybank Hills": 2070.9, |
| "Adelaide Hills": 1272.7, |
| "Manjeri": 7300.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Goulburn: (-34.75°, 149.72°)", |
| " Port Melbourne: (-37.84°, 144.94°)", |
| " Sunnybank Hills: (-27.61°, 153.05°)", |
| " Adelaide Hills: (-34.91°, 138.71°)", |
| " Manjeri: (11.12°, 76.12°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Manjeri: 7300.9 km from centroid", |
| " Sunnybank Hills: 2070.9 km from centroid", |
| " Goulburn: 1991.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Manjeri", |
| "FINAL ANSWER: Manjeri" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 5.01806, |
| "lon": -1.66437, |
| "name": "Shama Junction" |
| }, |
| { |
| "lat": 9.87342, |
| "lon": 7.95407, |
| "name": "Kachia" |
| }, |
| { |
| "lat": -30.69366, |
| "lon": 26.71141, |
| "name": "Aliwal North" |
| }, |
| { |
| "lat": 5.2717, |
| "lon": -1.0152, |
| "name": "Mankesim" |
| }, |
| { |
| "lat": -37.8, |
| "lon": 144.96667, |
| "name": "Carlton" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Shama Junction, Kachia, Aliwal North, Mankesim, Carlton?", |
| "ground_truth": { |
| "answer": "Carlton", |
| "outlier_distance_km": 11018.9, |
| "second_furthest_km": 4418.2, |
| "clarity_ratio": 2.49, |
| "median_distance_km": 4362.1, |
| "distances_to_centroid": { |
| "Shama Junction": 4418.2, |
| "Kachia": 3733.3, |
| "Aliwal North": 2504.9, |
| "Mankesim": 4362.1, |
| "Carlton": 11018.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Shama Junction: (5.02°, -1.66°)", |
| " Kachia: (9.87°, 7.95°)", |
| " Aliwal North: (-30.69°, 26.71°)", |
| " Mankesim: (5.27°, -1.02°)", |
| " Carlton: (-37.80°, 144.97°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Carlton: 11018.9 km from centroid", |
| " Shama Junction: 4418.2 km from centroid", |
| " Mankesim: 4362.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Carlton", |
| "FINAL ANSWER: Carlton" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 39.42814, |
| "lon": -0.41765, |
| "name": "Paiporta" |
| }, |
| { |
| "lat": 45.70843, |
| "lon": 8.90763, |
| "name": "Tradate" |
| }, |
| { |
| "lat": 49.74657, |
| "lon": 8.11513, |
| "name": "Alzey" |
| }, |
| { |
| "lat": 55.88431, |
| "lon": 38.7864, |
| "name": "Elektrogorsk" |
| }, |
| { |
| "lat": -33.9049, |
| "lon": 151.01996, |
| "name": "Yagoona" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Paiporta, Tradate, Alzey, Elektrogorsk, Yagoona?", |
| "ground_truth": { |
| "answer": "Yagoona", |
| "outlier_distance_km": 13564.2, |
| "second_furthest_km": 3848.4, |
| "clarity_ratio": 3.52, |
| "median_distance_km": 3422.6, |
| "distances_to_centroid": { |
| "Paiporta": 3848.4, |
| "Tradate": 3204.0, |
| "Alzey": 3422.6, |
| "Elektrogorsk": 2732.6, |
| "Yagoona": 13564.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Paiporta: (39.43°, -0.42°)", |
| " Tradate: (45.71°, 8.91°)", |
| " Alzey: (49.75°, 8.12°)", |
| " Elektrogorsk: (55.88°, 38.79°)", |
| " Yagoona: (-33.90°, 151.02°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Yagoona: 13564.2 km from centroid", |
| " Paiporta: 3848.4 km from centroid", |
| " Alzey: 3422.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Yagoona", |
| "FINAL ANSWER: Yagoona" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -38.03333, |
| "lon": 145.35, |
| "name": "Berwick" |
| }, |
| { |
| "lat": -28.00274, |
| "lon": 153.42999, |
| "name": "Surfers Paradise" |
| }, |
| { |
| "lat": -33.79728, |
| "lon": 150.7847, |
| "name": "St Clair" |
| }, |
| { |
| "lat": -37.78333, |
| "lon": 175.28333, |
| "name": "Hamilton" |
| }, |
| { |
| "lat": -22.22917, |
| "lon": -50.89306, |
| "name": "Rancharia" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Berwick, Surfers Paradise, St Clair, Hamilton, Rancharia?", |
| "ground_truth": { |
| "answer": "Rancharia", |
| "outlier_distance_km": 13799.0, |
| "second_furthest_km": 5460.7, |
| "clarity_ratio": 2.53, |
| "median_distance_km": 3727.8, |
| "distances_to_centroid": { |
| "Berwick": 2850.1, |
| "Surfers Paradise": 3727.8, |
| "St Clair": 3350.2, |
| "Hamilton": 5460.7, |
| "Rancharia": 13799.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Berwick: (-38.03°, 145.35°)", |
| " Surfers Paradise: (-28.00°, 153.43°)", |
| " St Clair: (-33.80°, 150.78°)", |
| " Hamilton: (-37.78°, 175.28°)", |
| " Rancharia: (-22.23°, -50.89°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Rancharia: 13799.0 km from centroid", |
| " Hamilton: 5460.7 km from centroid", |
| " Surfers Paradise: 3727.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Rancharia", |
| "FINAL ANSWER: Rancharia" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 35.75647, |
| "lon": -83.97046, |
| "name": "Maryville" |
| }, |
| { |
| "lat": 20.37237, |
| "lon": -101.06249, |
| "name": "Jaral del Progreso" |
| }, |
| { |
| "lat": 40.86867, |
| "lon": -82.31822, |
| "name": "Ashland" |
| }, |
| { |
| "lat": 42.49276, |
| "lon": -92.34296, |
| "name": "Waterloo" |
| }, |
| { |
| "lat": 40.38897, |
| "lon": -3.74569, |
| "name": "Latina" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Maryville, Jaral del Progreso, Ashland, Waterloo, Latina?", |
| "ground_truth": { |
| "answer": "Latina", |
| "outlier_distance_km": 5890.9, |
| "second_furthest_km": 3258.9, |
| "clarity_ratio": 1.81, |
| "median_distance_km": 1835.8, |
| "distances_to_centroid": { |
| "Maryville": 1016.4, |
| "Jaral del Progreso": 3258.9, |
| "Ashland": 999.0, |
| "Waterloo": 1835.8, |
| "Latina": 5890.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Maryville: (35.76°, -83.97°)", |
| " Jaral del Progreso: (20.37°, -101.06°)", |
| " Ashland: (40.87°, -82.32°)", |
| " Waterloo: (42.49°, -92.34°)", |
| " Latina: (40.39°, -3.75°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Latina: 5890.9 km from centroid", |
| " Jaral del Progreso: 3258.9 km from centroid", |
| " Waterloo: 1835.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Latina", |
| "FINAL ANSWER: Latina" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 31.09311, |
| "lon": 30.31418, |
| "name": "Abū Ḩummuş" |
| }, |
| { |
| "lat": 30.90711, |
| "lon": 32.02341, |
| "name": "Munsha‘at Abū ‘Umar" |
| }, |
| { |
| "lat": 6.45197, |
| "lon": 3.33115, |
| "name": "Ajegunle" |
| }, |
| { |
| "lat": -0.15816, |
| "lon": 35.19645, |
| "name": "Muhoroni" |
| }, |
| { |
| "lat": -36.88158, |
| "lon": 174.76204, |
| "name": "Mount Eden" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Abū Ḩummuş, Munsha‘at Abū ‘Umar, Ajegunle, Muhoroni, Mount Eden?", |
| "ground_truth": { |
| "answer": "Mount Eden", |
| "outlier_distance_km": 13044.5, |
| "second_furthest_km": 5721.2, |
| "clarity_ratio": 2.28, |
| "median_distance_km": 3779.6, |
| "distances_to_centroid": { |
| "Abū Ḩummuş": 3779.6, |
| "Munsha‘at Abū ‘Umar": 3646.0, |
| "Ajegunle": 5721.2, |
| "Muhoroni": 2324.7, |
| "Mount Eden": 13044.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Abū Ḩummuş: (31.09°, 30.31°)", |
| " Munsha‘at Abū ‘Umar: (30.91°, 32.02°)", |
| " Ajegunle: (6.45°, 3.33°)", |
| " Muhoroni: (-0.16°, 35.20°)", |
| " Mount Eden: (-36.88°, 174.76°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Mount Eden: 13044.5 km from centroid", |
| " Ajegunle: 5721.2 km from centroid", |
| " Abū Ḩummuş: 3779.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Mount Eden", |
| "FINAL ANSWER: Mount Eden" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -19.96778, |
| "lon": -44.19833, |
| "name": "Betim" |
| }, |
| { |
| "lat": -19.55778, |
| "lon": -44.08139, |
| "name": "Matozinhos" |
| }, |
| { |
| "lat": -8.76194, |
| "lon": -63.90389, |
| "name": "Porto Velho" |
| }, |
| { |
| "lat": -36.74553, |
| "lon": -72.47481, |
| "name": "Quillón" |
| }, |
| { |
| "lat": -33.88834, |
| "lon": 151.12274, |
| "name": "Ashfield" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Betim, Matozinhos, Porto Velho, Quillón, Ashfield?", |
| "ground_truth": { |
| "answer": "Ashfield", |
| "outlier_distance_km": 13429.4, |
| "second_furthest_km": 5646.0, |
| "clarity_ratio": 2.38, |
| "median_distance_km": 5479.2, |
| "distances_to_centroid": { |
| "Betim": 3067.0, |
| "Matozinhos": 3066.0, |
| "Porto Velho": 5479.2, |
| "Quillón": 5646.0, |
| "Ashfield": 13429.4 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Betim: (-19.97°, -44.20°)", |
| " Matozinhos: (-19.56°, -44.08°)", |
| " Porto Velho: (-8.76°, -63.90°)", |
| " Quillón: (-36.75°, -72.47°)", |
| " Ashfield: (-33.89°, 151.12°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Ashfield: 13429.4 km from centroid", |
| " Quillón: 5646.0 km from centroid", |
| " Porto Velho: 5479.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Ashfield", |
| "FINAL ANSWER: Ashfield" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -26.84806, |
| "lon": -52.99194, |
| "name": "Pinhalzinho" |
| }, |
| { |
| "lat": -11.25583, |
| "lon": -39.37472, |
| "name": "Santaluz" |
| }, |
| { |
| "lat": -12.53028, |
| "lon": -38.29917, |
| "name": "Mata de São João" |
| }, |
| { |
| "lat": -24.28139, |
| "lon": -47.45972, |
| "name": "Miracatu" |
| }, |
| { |
| "lat": 58.36848, |
| "lon": 45.51622, |
| "name": "Shar’ya" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Pinhalzinho, Santaluz, Mata de São João, Miracatu, Shar’ya?", |
| "ground_truth": { |
| "answer": "Shar’ya", |
| "outlier_distance_km": 9290.5, |
| "second_furthest_km": 3844.2, |
| "clarity_ratio": 2.42, |
| "median_distance_km": 3237.2, |
| "distances_to_centroid": { |
| "Pinhalzinho": 3844.2, |
| "Santaluz": 1669.4, |
| "Mata de São João": 1652.2, |
| "Miracatu": 3237.2, |
| "Shar’ya": 9290.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Pinhalzinho: (-26.85°, -52.99°)", |
| " Santaluz: (-11.26°, -39.37°)", |
| " Mata de São João: (-12.53°, -38.30°)", |
| " Miracatu: (-24.28°, -47.46°)", |
| " Shar’ya: (58.37°, 45.52°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Shar’ya: 9290.5 km from centroid", |
| " Pinhalzinho: 3844.2 km from centroid", |
| " Miracatu: 3237.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Shar’ya", |
| "FINAL ANSWER: Shar’ya" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -21.41972, |
| "lon": -50.0775, |
| "name": "Penápolis" |
| }, |
| { |
| "lat": -29.71671, |
| "lon": -52.50321, |
| "name": "Vera Cruz" |
| }, |
| { |
| "lat": -14.89528, |
| "lon": -41.96861, |
| "name": "Condeúba" |
| }, |
| { |
| "lat": -7.19111, |
| "lon": -48.20722, |
| "name": "Araguaína" |
| }, |
| { |
| "lat": 29.69224, |
| "lon": 75.23608, |
| "name": "Sardulgarh" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Penápolis, Vera Cruz, Condeúba, Araguaína, Sardulgarh?", |
| "ground_truth": { |
| "answer": "Sardulgarh", |
| "outlier_distance_km": 11325.9, |
| "second_furthest_km": 3816.4, |
| "clarity_ratio": 2.97, |
| "median_distance_km": 3176.3, |
| "distances_to_centroid": { |
| "Penápolis": 3176.3, |
| "Vera Cruz": 3816.4, |
| "Condeúba": 2122.9, |
| "Araguaína": 2725.2, |
| "Sardulgarh": 11325.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Penápolis: (-21.42°, -50.08°)", |
| " Vera Cruz: (-29.72°, -52.50°)", |
| " Condeúba: (-14.90°, -41.97°)", |
| " Araguaína: (-7.19°, -48.21°)", |
| " Sardulgarh: (29.69°, 75.24°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Sardulgarh: 11325.9 km from centroid", |
| " Vera Cruz: 3816.4 km from centroid", |
| " Penápolis: 3176.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Sardulgarh", |
| "FINAL ANSWER: Sardulgarh" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -44.39672, |
| "lon": 171.25364, |
| "name": "Timaru" |
| }, |
| { |
| "lat": -33.7457, |
| "lon": 151.04764, |
| "name": "West Pennant Hills" |
| }, |
| { |
| "lat": -27.91828, |
| "lon": 153.33275, |
| "name": "Helensvale" |
| }, |
| { |
| "lat": -33.77271, |
| "lon": 151.08184, |
| "name": "Epping" |
| }, |
| { |
| "lat": 45.54672, |
| "lon": 11.5475, |
| "name": "Vicenza" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Timaru, West Pennant Hills, Helensvale, Epping, Vicenza?", |
| "ground_truth": { |
| "answer": "Vicenza", |
| "outlier_distance_km": 13509.0, |
| "second_furthest_km": 4925.2, |
| "clarity_ratio": 2.74, |
| "median_distance_km": 2852.2, |
| "distances_to_centroid": { |
| "Timaru": 4925.2, |
| "West Pennant Hills": 2848.0, |
| "Helensvale": 2800.6, |
| "Epping": 2852.2, |
| "Vicenza": 13509.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Timaru: (-44.40°, 171.25°)", |
| " West Pennant Hills: (-33.75°, 151.05°)", |
| " Helensvale: (-27.92°, 153.33°)", |
| " Epping: (-33.77°, 151.08°)", |
| " Vicenza: (45.55°, 11.55°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Vicenza: 13509.0 km from centroid", |
| " Timaru: 4925.2 km from centroid", |
| " Epping: 2852.2 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Vicenza", |
| "FINAL ANSWER: Vicenza" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 39.01817, |
| "lon": -77.20859, |
| "name": "Potomac" |
| }, |
| { |
| "lat": 45.08608, |
| "lon": -93.26328, |
| "name": "Fridley" |
| }, |
| { |
| "lat": 44.25011, |
| "lon": -79.46632, |
| "name": "Keswick" |
| }, |
| { |
| "lat": 38.889, |
| "lon": -77.00025, |
| "name": "Capitol Hill" |
| }, |
| { |
| "lat": 51.1209, |
| "lon": 38.5116, |
| "name": "Rossosh’" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Potomac, Fridley, Keswick, Capitol Hill, Rossosh’?", |
| "ground_truth": { |
| "answer": "Rossosh’", |
| "outlier_distance_km": 6755.5, |
| "second_furthest_km": 2809.0, |
| "clarity_ratio": 2.4, |
| "median_distance_km": 1739.4, |
| "distances_to_centroid": { |
| "Potomac": 1705.3, |
| "Fridley": 2809.0, |
| "Keswick": 1739.4, |
| "Capitol Hill": 1694.7, |
| "Rossosh’": 6755.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Potomac: (39.02°, -77.21°)", |
| " Fridley: (45.09°, -93.26°)", |
| " Keswick: (44.25°, -79.47°)", |
| " Capitol Hill: (38.89°, -77.00°)", |
| " Rossosh’: (51.12°, 38.51°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Rossosh’: 6755.5 km from centroid", |
| " Fridley: 2809.0 km from centroid", |
| " Keswick: 1739.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Rossosh’", |
| "FINAL ANSWER: Rossosh’" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 48.89281, |
| "lon": 2.13308, |
| "name": "Le Vésinet" |
| }, |
| { |
| "lat": 37.97872, |
| "lon": -0.68222, |
| "name": "Torrevieja" |
| }, |
| { |
| "lat": 59.57639, |
| "lon": 30.12833, |
| "name": "Gatchina" |
| }, |
| { |
| "lat": 44.93553, |
| "lon": 10.51898, |
| "name": "Viadana" |
| }, |
| { |
| "lat": 7.20417, |
| "lon": 124.43972, |
| "name": "Budta" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Le Vésinet, Torrevieja, Gatchina, Viadana, Budta?", |
| "ground_truth": { |
| "answer": "Budta", |
| "outlier_distance_km": 9592.8, |
| "second_furthest_km": 2932.2, |
| "clarity_ratio": 3.27, |
| "median_distance_km": 2658.8, |
| "distances_to_centroid": { |
| "Le Vésinet": 2658.8, |
| "Torrevieja": 2932.2, |
| "Gatchina": 2219.4, |
| "Viadana": 1953.7, |
| "Budta": 9592.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Le Vésinet: (48.89°, 2.13°)", |
| " Torrevieja: (37.98°, -0.68°)", |
| " Gatchina: (59.58°, 30.13°)", |
| " Viadana: (44.94°, 10.52°)", |
| " Budta: (7.20°, 124.44°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Budta: 9592.8 km from centroid", |
| " Torrevieja: 2932.2 km from centroid", |
| " Le Vésinet: 2658.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Budta", |
| "FINAL ANSWER: Budta" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -22.23333, |
| "lon": -53.34306, |
| "name": "Nova Andradina" |
| }, |
| { |
| "lat": -19.88639, |
| "lon": -43.80667, |
| "name": "Sabará" |
| }, |
| { |
| "lat": -35.5952, |
| "lon": -71.72924, |
| "name": "San Javier" |
| }, |
| { |
| "lat": -19.63006, |
| "lon": -43.9009, |
| "name": "Lagoa Santa" |
| }, |
| { |
| "lat": -27.94402, |
| "lon": 153.39815, |
| "name": "Labrador" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Nova Andradina, Sabará, San Javier, Lagoa Santa, Labrador?", |
| "ground_truth": { |
| "answer": "Labrador", |
| "outlier_distance_km": 13914.4, |
| "second_furthest_km": 5775.6, |
| "clarity_ratio": 2.41, |
| "median_distance_km": 4219.3, |
| "distances_to_centroid": { |
| "Nova Andradina": 4219.3, |
| "Sabará": 3323.0, |
| "San Javier": 5775.6, |
| "Lagoa Santa": 3340.3, |
| "Labrador": 13914.4 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Nova Andradina: (-22.23°, -53.34°)", |
| " Sabará: (-19.89°, -43.81°)", |
| " San Javier: (-35.60°, -71.73°)", |
| " Lagoa Santa: (-19.63°, -43.90°)", |
| " Labrador: (-27.94°, 153.40°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Labrador: 13914.4 km from centroid", |
| " San Javier: 5775.6 km from centroid", |
| " Nova Andradina: 4219.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Labrador", |
| "FINAL ANSWER: Labrador" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 36.02153, |
| "lon": -80.382, |
| "name": "Clemmons" |
| }, |
| { |
| "lat": 39.53316, |
| "lon": -76.33746, |
| "name": "South Bel Air" |
| }, |
| { |
| "lat": 37.77817, |
| "lon": -81.18816, |
| "name": "Beckley" |
| }, |
| { |
| "lat": 25.67066, |
| "lon": -80.40117, |
| "name": "The Crossings" |
| }, |
| { |
| "lat": 14.71694, |
| "lon": 120.95806, |
| "name": "Malanday" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Clemmons, South Bel Air, Beckley, The Crossings, Malanday?", |
| "ground_truth": { |
| "answer": "Malanday", |
| "outlier_distance_km": 14543.8, |
| "second_furthest_km": 4028.2, |
| "clarity_ratio": 3.61, |
| "median_distance_km": 3879.9, |
| "distances_to_centroid": { |
| "Clemmons": 3815.6, |
| "South Bel Air": 3465.1, |
| "Beckley": 3879.9, |
| "The Crossings": 4028.2, |
| "Malanday": 14543.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Clemmons: (36.02°, -80.38°)", |
| " South Bel Air: (39.53°, -76.34°)", |
| " Beckley: (37.78°, -81.19°)", |
| " The Crossings: (25.67°, -80.40°)", |
| " Malanday: (14.72°, 120.96°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Malanday: 14543.8 km from centroid", |
| " The Crossings: 4028.2 km from centroid", |
| " Beckley: 3879.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Malanday", |
| "FINAL ANSWER: Malanday" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -21.78778, |
| "lon": -46.56139, |
| "name": "Poços de Caldas" |
| }, |
| { |
| "lat": -17.51944, |
| "lon": -39.19556, |
| "name": "Alcobaça" |
| }, |
| { |
| "lat": -1.89528, |
| "lon": -49.38056, |
| "name": "Limoeiro do Ajuru" |
| }, |
| { |
| "lat": -9.38861, |
| "lon": -37.99917, |
| "name": "Delmiro Gouveia" |
| }, |
| { |
| "lat": -34.06564, |
| "lon": 151.01266, |
| "name": "Engadine" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Poços de Caldas, Alcobaça, Limoeiro do Ajuru, Delmiro Gouveia, Engadine?", |
| "ground_truth": { |
| "answer": "Engadine", |
| "outlier_distance_km": 13776.3, |
| "second_furthest_km": 5189.1, |
| "clarity_ratio": 2.65, |
| "median_distance_km": 4440.1, |
| "distances_to_centroid": { |
| "Poços de Caldas": 4440.1, |
| "Alcobaça": 3688.3, |
| "Limoeiro do Ajuru": 5189.1, |
| "Delmiro Gouveia": 3725.0, |
| "Engadine": 13776.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Poços de Caldas: (-21.79°, -46.56°)", |
| " Alcobaça: (-17.52°, -39.20°)", |
| " Limoeiro do Ajuru: (-1.90°, -49.38°)", |
| " Delmiro Gouveia: (-9.39°, -38.00°)", |
| " Engadine: (-34.07°, 151.01°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Engadine: 13776.3 km from centroid", |
| " Limoeiro do Ajuru: 5189.1 km from centroid", |
| " Poços de Caldas: 4440.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Engadine", |
| "FINAL ANSWER: Engadine" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -32.05799, |
| "lon": 115.91814, |
| "name": "Canning Vale" |
| }, |
| { |
| "lat": -12.46113, |
| "lon": 130.84185, |
| "name": "Darwin" |
| }, |
| { |
| "lat": -33.95, |
| "lon": 151.23333, |
| "name": "Maroubra" |
| }, |
| { |
| "lat": -40.35636, |
| "lon": 175.61113, |
| "name": "Palmerston North" |
| }, |
| { |
| "lat": 47.87663, |
| "lon": 11.70181, |
| "name": "Holzkirchen" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Canning Vale, Darwin, Maroubra, Palmerston North, Holzkirchen?", |
| "ground_truth": { |
| "answer": "Holzkirchen", |
| "outlier_distance_km": 12313.2, |
| "second_furthest_km": 6341.5, |
| "clarity_ratio": 1.94, |
| "median_distance_km": 4075.6, |
| "distances_to_centroid": { |
| "Canning Vale": 1990.2, |
| "Darwin": 1503.2, |
| "Maroubra": 4075.6, |
| "Palmerston North": 6341.5, |
| "Holzkirchen": 12313.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Canning Vale: (-32.06°, 115.92°)", |
| " Darwin: (-12.46°, 130.84°)", |
| " Maroubra: (-33.95°, 151.23°)", |
| " Palmerston North: (-40.36°, 175.61°)", |
| " Holzkirchen: (47.88°, 11.70°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Holzkirchen: 12313.2 km from centroid", |
| " Palmerston North: 6341.5 km from centroid", |
| " Maroubra: 4075.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Holzkirchen", |
| "FINAL ANSWER: Holzkirchen" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -30.50123, |
| "lon": 151.66553, |
| "name": "Armidale" |
| }, |
| { |
| "lat": -37.87397, |
| "lon": 145.04253, |
| "name": "Malvern East" |
| }, |
| { |
| "lat": -38.16604, |
| "lon": 145.13643, |
| "name": "Frankston South" |
| }, |
| { |
| "lat": -34.03857, |
| "lon": 151.10005, |
| "name": "Miranda" |
| }, |
| { |
| "lat": -2.08033, |
| "lon": 37.47202, |
| "name": "Emali" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Armidale, Malvern East, Frankston South, Miranda, Emali?", |
| "ground_truth": { |
| "answer": "Emali", |
| "outlier_distance_km": 9761.5, |
| "second_furthest_km": 2479.8, |
| "clarity_ratio": 3.94, |
| "median_distance_km": 2448.0, |
| "distances_to_centroid": { |
| "Armidale": 2479.8, |
| "Malvern East": 2041.2, |
| "Frankston South": 2062.5, |
| "Miranda": 2448.0, |
| "Emali": 9761.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Armidale: (-30.50°, 151.67°)", |
| " Malvern East: (-37.87°, 145.04°)", |
| " Frankston South: (-38.17°, 145.14°)", |
| " Miranda: (-34.04°, 151.10°)", |
| " Emali: (-2.08°, 37.47°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Emali: 9761.5 km from centroid", |
| " Armidale: 2479.8 km from centroid", |
| " Miranda: 2448.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Emali", |
| "FINAL ANSWER: Emali" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 47.1069, |
| "lon": 39.41486, |
| "name": "Azov" |
| }, |
| { |
| "lat": 48.99712, |
| "lon": 2.28249, |
| "name": "Eaubonne" |
| }, |
| { |
| "lat": 50.80019, |
| "lon": 7.20769, |
| "name": "Siegburg" |
| }, |
| { |
| "lat": 53.67661, |
| "lon": 10.23705, |
| "name": "Ahrensburg" |
| }, |
| { |
| "lat": 5.13428, |
| "lon": 100.49549, |
| "name": "Bandar Baharu" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Azov, Eaubonne, Siegburg, Ahrensburg, Bandar Baharu?", |
| "ground_truth": { |
| "answer": "Bandar Baharu", |
| "outlier_distance_km": 7845.1, |
| "second_furthest_km": 2467.2, |
| "clarity_ratio": 3.18, |
| "median_distance_km": 2176.4, |
| "distances_to_centroid": { |
| "Azov": 891.9, |
| "Eaubonne": 2467.2, |
| "Siegburg": 2176.4, |
| "Ahrensburg": 2130.9, |
| "Bandar Baharu": 7845.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Azov: (47.11°, 39.41°)", |
| " Eaubonne: (49.00°, 2.28°)", |
| " Siegburg: (50.80°, 7.21°)", |
| " Ahrensburg: (53.68°, 10.24°)", |
| " Bandar Baharu: (5.13°, 100.50°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Bandar Baharu: 7845.1 km from centroid", |
| " Eaubonne: 2467.2 km from centroid", |
| " Siegburg: 2176.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Bandar Baharu", |
| "FINAL ANSWER: Bandar Baharu" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 7.56229, |
| "lon": 6.65497, |
| "name": "Ajaokuta" |
| }, |
| { |
| "lat": 30.03103, |
| "lon": 31.11109, |
| "name": "Kirdāsah" |
| }, |
| { |
| "lat": 9.08044, |
| "lon": 6.0099, |
| "name": "Bida" |
| }, |
| { |
| "lat": -29.06415, |
| "lon": 30.59279, |
| "name": "Greytown" |
| }, |
| { |
| "lat": 32.51917, |
| "lon": 108.53232, |
| "name": "Ziyang Chengguanzhen" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Ajaokuta, Kirdāsah, Bida, Greytown, Ziyang Chengguanzhen?", |
| "ground_truth": { |
| "answer": "Ziyang Chengguanzhen", |
| "outlier_distance_km": 7723.8, |
| "second_furthest_km": 4393.8, |
| "clarity_ratio": 1.76, |
| "median_distance_km": 3352.6, |
| "distances_to_centroid": { |
| "Ajaokuta": 3298.6, |
| "Kirdāsah": 2295.7, |
| "Bida": 3352.6, |
| "Greytown": 4393.8, |
| "Ziyang Chengguanzhen": 7723.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Ajaokuta: (7.56°, 6.65°)", |
| " Kirdāsah: (30.03°, 31.11°)", |
| " Bida: (9.08°, 6.01°)", |
| " Greytown: (-29.06°, 30.59°)", |
| " Ziyang Chengguanzhen: (32.52°, 108.53°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Ziyang Chengguanzhen: 7723.8 km from centroid", |
| " Greytown: 4393.8 km from centroid", |
| " Bida: 3352.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Ziyang Chengguanzhen", |
| "FINAL ANSWER: Ziyang Chengguanzhen" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 7.85257, |
| "lon": 38.18529, |
| "name": "Worabe" |
| }, |
| { |
| "lat": 5.79473, |
| "lon": 0.89728, |
| "name": "Anloga" |
| }, |
| { |
| "lat": -30.28666, |
| "lon": 30.75316, |
| "name": "Scottburgh" |
| }, |
| { |
| "lat": 31.2163, |
| "lon": 34.11074, |
| "name": "Ash Shaykh Zuwayd" |
| }, |
| { |
| "lat": -3.77611, |
| "lon": -73.28139, |
| "name": "San Juan" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Worabe, Anloga, Scottburgh, Ash Shaykh Zuwayd, San Juan?", |
| "ground_truth": { |
| "answer": "San Juan", |
| "outlier_distance_km": 8850.0, |
| "second_furthest_km": 4453.8, |
| "clarity_ratio": 1.99, |
| "median_distance_km": 4365.7, |
| "distances_to_centroid": { |
| "Worabe": 3604.6, |
| "Anloga": 707.5, |
| "Scottburgh": 4453.8, |
| "Ash Shaykh Zuwayd": 4365.7, |
| "San Juan": 8850.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Worabe: (7.85°, 38.19°)", |
| " Anloga: (5.79°, 0.90°)", |
| " Scottburgh: (-30.29°, 30.75°)", |
| " Ash Shaykh Zuwayd: (31.22°, 34.11°)", |
| " San Juan: (-3.78°, -73.28°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " San Juan: 8850.0 km from centroid", |
| " Scottburgh: 4453.8 km from centroid", |
| " Ash Shaykh Zuwayd: 4365.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: San Juan", |
| "FINAL ANSWER: San Juan" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -33.75881, |
| "lon": 150.99292, |
| "name": "Baulkham Hills" |
| }, |
| { |
| "lat": -33.95, |
| "lon": 151.11667, |
| "name": "Bexley" |
| }, |
| { |
| "lat": -33.52314, |
| "lon": 151.31325, |
| "name": "Umina Beach" |
| }, |
| { |
| "lat": -31.88775, |
| "lon": 115.9099, |
| "name": "Morley" |
| }, |
| { |
| "lat": 10.65, |
| "lon": 36.21667, |
| "name": "Dibate" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Baulkham Hills, Bexley, Umina Beach, Morley, Dibate?", |
| "ground_truth": { |
| "answer": "Dibate", |
| "outlier_distance_km": 9988.5, |
| "second_furthest_km": 3090.7, |
| "clarity_ratio": 3.23, |
| "median_distance_km": 3082.3, |
| "distances_to_centroid": { |
| "Baulkham Hills": 3066.8, |
| "Bexley": 3082.3, |
| "Umina Beach": 3090.7, |
| "Morley": 966.9, |
| "Dibate": 9988.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Baulkham Hills: (-33.76°, 150.99°)", |
| " Bexley: (-33.95°, 151.12°)", |
| " Umina Beach: (-33.52°, 151.31°)", |
| " Morley: (-31.89°, 115.91°)", |
| " Dibate: (10.65°, 36.22°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Dibate: 9988.5 km from centroid", |
| " Umina Beach: 3090.7 km from centroid", |
| " Bexley: 3082.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Dibate", |
| "FINAL ANSWER: Dibate" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 2.06895, |
| "lon": -77.05273, |
| "name": "Patía" |
| }, |
| { |
| "lat": -23.60583, |
| "lon": -46.47889, |
| "name": "São Mateus" |
| }, |
| { |
| "lat": -28.275, |
| "lon": -49.16556, |
| "name": "Braço do Norte" |
| }, |
| { |
| "lat": -15.30833, |
| "lon": -49.59833, |
| "name": "Ceres" |
| }, |
| { |
| "lat": 54.13579, |
| "lon": -1.52826, |
| "name": "Ripon" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Patía, São Mateus, Braço do Norte, Ceres, Ripon?", |
| "ground_truth": { |
| "answer": "Ripon", |
| "outlier_distance_km": 7417.4, |
| "second_furthest_km": 3620.6, |
| "clarity_ratio": 2.05, |
| "median_distance_km": 2937.1, |
| "distances_to_centroid": { |
| "Patía": 3620.6, |
| "São Mateus": 2387.7, |
| "Braço do Norte": 2937.1, |
| "Ceres": 1551.3, |
| "Ripon": 7417.4 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Patía: (2.07°, -77.05°)", |
| " São Mateus: (-23.61°, -46.48°)", |
| " Braço do Norte: (-28.27°, -49.17°)", |
| " Ceres: (-15.31°, -49.60°)", |
| " Ripon: (54.14°, -1.53°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Ripon: 7417.4 km from centroid", |
| " Patía: 3620.6 km from centroid", |
| " Braço do Norte: 2937.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Ripon", |
| "FINAL ANSWER: Ripon" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 21.0315, |
| "lon": -101.87833, |
| "name": "Purísima de Bustos" |
| }, |
| { |
| "lat": 42.10482, |
| "lon": -70.94532, |
| "name": "Abington" |
| }, |
| { |
| "lat": 32.566, |
| "lon": -116.63187, |
| "name": "Tecate" |
| }, |
| { |
| "lat": 42.15843, |
| "lon": -72.32869, |
| "name": "Palmer" |
| }, |
| { |
| "lat": 14.47995, |
| "lon": 78.82346, |
| "name": "Kadapa" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Purísima de Bustos, Abington, Tecate, Palmer, Kadapa?", |
| "ground_truth": { |
| "answer": "Kadapa", |
| "outlier_distance_km": 13107.4, |
| "second_furthest_km": 5618.5, |
| "clarity_ratio": 2.33, |
| "median_distance_km": 4623.9, |
| "distances_to_centroid": { |
| "Purísima de Bustos": 4623.9, |
| "Abington": 1819.7, |
| "Tecate": 5618.5, |
| "Palmer": 1911.9, |
| "Kadapa": 13107.4 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Purísima de Bustos: (21.03°, -101.88°)", |
| " Abington: (42.10°, -70.95°)", |
| " Tecate: (32.57°, -116.63°)", |
| " Palmer: (42.16°, -72.33°)", |
| " Kadapa: (14.48°, 78.82°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Kadapa: 13107.4 km from centroid", |
| " Tecate: 5618.5 km from centroid", |
| " Purísima de Bustos: 4623.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Kadapa", |
| "FINAL ANSWER: Kadapa" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 30.12511, |
| "lon": 31.25053, |
| "name": "Shubrā al Khaymah" |
| }, |
| { |
| "lat": -29.12107, |
| "lon": 26.214, |
| "name": "Bloemfontein" |
| }, |
| { |
| "lat": -26.31401, |
| "lon": 26.82223, |
| "name": "Ventersdorp" |
| }, |
| { |
| "lat": 31.19688, |
| "lon": 31.5243, |
| "name": "Shirbīn" |
| }, |
| { |
| "lat": 6.46065, |
| "lon": -71.73618, |
| "name": "Tame" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Shubrā al Khaymah, Bloemfontein, Ventersdorp, Shirbīn, Tame?", |
| "ground_truth": { |
| "answer": "Tame", |
| "outlier_distance_km": 8933.3, |
| "second_furthest_km": 3985.1, |
| "clarity_ratio": 2.24, |
| "median_distance_km": 3971.9, |
| "distances_to_centroid": { |
| "Shubrā al Khaymah": 3878.5, |
| "Bloemfontein": 3971.9, |
| "Ventersdorp": 3740.1, |
| "Shirbīn": 3985.1, |
| "Tame": 8933.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Shubrā al Khaymah: (30.13°, 31.25°)", |
| " Bloemfontein: (-29.12°, 26.21°)", |
| " Ventersdorp: (-26.31°, 26.82°)", |
| " Shirbīn: (31.20°, 31.52°)", |
| " Tame: (6.46°, -71.74°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Tame: 8933.3 km from centroid", |
| " Shirbīn: 3985.1 km from centroid", |
| " Bloemfontein: 3971.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Tame", |
| "FINAL ANSWER: Tame" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -26.08111, |
| "lon": -53.055, |
| "name": "Francisco Beltrão" |
| }, |
| { |
| "lat": -20.05639, |
| "lon": -44.18833, |
| "name": "Mário Campos" |
| }, |
| { |
| "lat": -5.37139, |
| "lon": -45.63639, |
| "name": "Jenipapo dos Vieiras" |
| }, |
| { |
| "lat": -20.84889, |
| "lon": -41.11278, |
| "name": "Cachoeiro de Itapemirim" |
| }, |
| { |
| "lat": 36.62364, |
| "lon": -6.35997, |
| "name": "Rota" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Francisco Beltrão, Mário Campos, Jenipapo dos Vieiras, Cachoeiro de Itapemirim, Rota?", |
| "ground_truth": { |
| "answer": "Rota", |
| "outlier_distance_km": 5882.0, |
| "second_furthest_km": 2636.5, |
| "clarity_ratio": 2.23, |
| "median_distance_km": 1579.7, |
| "distances_to_centroid": { |
| "Francisco Beltrão": 2636.5, |
| "Mário Campos": 1579.7, |
| "Jenipapo dos Vieiras": 859.2, |
| "Cachoeiro de Itapemirim": 1558.4, |
| "Rota": 5882.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Francisco Beltrão: (-26.08°, -53.05°)", |
| " Mário Campos: (-20.06°, -44.19°)", |
| " Jenipapo dos Vieiras: (-5.37°, -45.64°)", |
| " Cachoeiro de Itapemirim: (-20.85°, -41.11°)", |
| " Rota: (36.62°, -6.36°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Rota: 5882.0 km from centroid", |
| " Francisco Beltrão: 2636.5 km from centroid", |
| " Mário Campos: 1579.7 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Rota", |
| "FINAL ANSWER: Rota" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 37.04248, |
| "lon": 119.47654, |
| "name": "Xiaying" |
| }, |
| { |
| "lat": 26.38371, |
| "lon": 79.94926, |
| "name": "Akbarpur" |
| }, |
| { |
| "lat": 19.85723, |
| "lon": 109.26271, |
| "name": "Eman" |
| }, |
| { |
| "lat": 30.9525, |
| "lon": 118.75528, |
| "name": "Xuancheng" |
| }, |
| { |
| "lat": 8.53895, |
| "lon": 7.70821, |
| "name": "Nasarawa" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Xiaying, Akbarpur, Eman, Xuancheng, Nasarawa?", |
| "ground_truth": { |
| "answer": "Nasarawa", |
| "outlier_distance_km": 8539.7, |
| "second_furthest_km": 3374.1, |
| "clarity_ratio": 2.53, |
| "median_distance_km": 3190.3, |
| "distances_to_centroid": { |
| "Xiaying": 3374.1, |
| "Akbarpur": 739.2, |
| "Eman": 2344.7, |
| "Xuancheng": 3190.3, |
| "Nasarawa": 8539.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Xiaying: (37.04°, 119.48°)", |
| " Akbarpur: (26.38°, 79.95°)", |
| " Eman: (19.86°, 109.26°)", |
| " Xuancheng: (30.95°, 118.76°)", |
| " Nasarawa: (8.54°, 7.71°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Nasarawa: 8539.7 km from centroid", |
| " Xiaying: 3374.1 km from centroid", |
| " Xuancheng: 3190.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Nasarawa", |
| "FINAL ANSWER: Nasarawa" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -36.9382, |
| "lon": 174.84019, |
| "name": "Otahuhu" |
| }, |
| { |
| "lat": -36.99282, |
| "lon": 174.87986, |
| "name": "Manukau City" |
| }, |
| { |
| "lat": -36.8582, |
| "lon": 174.62019, |
| "name": "Lincoln" |
| }, |
| { |
| "lat": -41.21667, |
| "lon": 174.91667, |
| "name": "Lower Hutt" |
| }, |
| { |
| "lat": -22.74389, |
| "lon": -43.7075, |
| "name": "Seropédica" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Otahuhu, Manukau City, Lincoln, Lower Hutt, Seropédica?", |
| "ground_truth": { |
| "answer": "Seropédica", |
| "outlier_distance_km": 13576.6, |
| "second_furthest_km": 3910.7, |
| "clarity_ratio": 3.47, |
| "median_distance_km": 3908.3, |
| "distances_to_centroid": { |
| "Otahuhu": 3908.3, |
| "Manukau City": 3910.7, |
| "Lincoln": 3890.6, |
| "Lower Hutt": 3855.4, |
| "Seropédica": 13576.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Otahuhu: (-36.94°, 174.84°)", |
| " Manukau City: (-36.99°, 174.88°)", |
| " Lincoln: (-36.86°, 174.62°)", |
| " Lower Hutt: (-41.22°, 174.92°)", |
| " Seropédica: (-22.74°, -43.71°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Seropédica: 13576.6 km from centroid", |
| " Manukau City: 3910.7 km from centroid", |
| " Otahuhu: 3908.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Seropédica", |
| "FINAL ANSWER: Seropédica" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -37.96667, |
| "lon": 145.16667, |
| "name": "Noble Park" |
| }, |
| { |
| "lat": -26.65682, |
| "lon": 153.07955, |
| "name": "Sunshine Coast" |
| }, |
| { |
| "lat": -33.86482, |
| "lon": 151.20773, |
| "name": "Sydney Central Business District" |
| }, |
| { |
| "lat": -37.90561, |
| "lon": 145.00279, |
| "name": "Brighton" |
| }, |
| { |
| "lat": 7.06667, |
| "lon": 37.7, |
| "name": "Āreka" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Noble Park, Sunshine Coast, Sydney Central Business District, Brighton, Āreka?", |
| "ground_truth": { |
| "answer": "Āreka", |
| "outlier_distance_km": 10223.6, |
| "second_furthest_km": 2654.0, |
| "clarity_ratio": 3.85, |
| "median_distance_km": 2541.3, |
| "distances_to_centroid": { |
| "Noble Park": 2214.6, |
| "Sunshine Coast": 2654.0, |
| "Sydney Central Business District": 2541.3, |
| "Brighton": 2198.8, |
| "Āreka": 10223.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Noble Park: (-37.97°, 145.17°)", |
| " Sunshine Coast: (-26.66°, 153.08°)", |
| " Sydney Central Business District: (-33.86°, 151.21°)", |
| " Brighton: (-37.91°, 145.00°)", |
| " Āreka: (7.07°, 37.70°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Āreka: 10223.6 km from centroid", |
| " Sunshine Coast: 2654.0 km from centroid", |
| " Sydney Central Business District: 2541.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Āreka", |
| "FINAL ANSWER: Āreka" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -27.89944, |
| "lon": -53.31361, |
| "name": "Palmeira das Missões" |
| }, |
| { |
| "lat": -7.85583, |
| "lon": -35.58833, |
| "name": "João Alfredo" |
| }, |
| { |
| "lat": -8.88202, |
| "lon": -36.50216, |
| "name": "Garanhuns" |
| }, |
| { |
| "lat": -22.92389, |
| "lon": -45.46167, |
| "name": "Pindamonhangaba" |
| }, |
| { |
| "lat": -27.61025, |
| "lon": 153.05388, |
| "name": "Sunnybank Hills" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Palmeira das Missões, João Alfredo, Garanhuns, Pindamonhangaba, Sunnybank Hills?", |
| "ground_truth": { |
| "answer": "Sunnybank Hills", |
| "outlier_distance_km": 14249.6, |
| "second_furthest_km": 5135.0, |
| "clarity_ratio": 2.78, |
| "median_distance_km": 4357.4, |
| "distances_to_centroid": { |
| "Palmeira das Missões": 5135.0, |
| "João Alfredo": 3671.3, |
| "Garanhuns": 3721.4, |
| "Pindamonhangaba": 4357.4, |
| "Sunnybank Hills": 14249.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Palmeira das Missões: (-27.90°, -53.31°)", |
| " João Alfredo: (-7.86°, -35.59°)", |
| " Garanhuns: (-8.88°, -36.50°)", |
| " Pindamonhangaba: (-22.92°, -45.46°)", |
| " Sunnybank Hills: (-27.61°, 153.05°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Sunnybank Hills: 14249.6 km from centroid", |
| " Palmeira das Missões: 5135.0 km from centroid", |
| " Pindamonhangaba: 4357.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Sunnybank Hills", |
| "FINAL ANSWER: Sunnybank Hills" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 2.64644, |
| "lon": -75.97269, |
| "name": "Belalcázar" |
| }, |
| { |
| "lat": -15.61532, |
| "lon": -43.59187, |
| "name": "Barreiro do Jaíba" |
| }, |
| { |
| "lat": -22.8375, |
| "lon": -51.97306, |
| "name": "Colorado" |
| }, |
| { |
| "lat": 3.69637, |
| "lon": -73.69957, |
| "name": "San Martín" |
| }, |
| { |
| "lat": -33.94185, |
| "lon": 150.8717, |
| "name": "Prestons" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Belalcázar, Barreiro do Jaíba, Colorado, San Martín, Prestons?", |
| "ground_truth": { |
| "answer": "Prestons", |
| "outlier_distance_km": 14660.8, |
| "second_furthest_km": 6540.8, |
| "clarity_ratio": 2.24, |
| "median_distance_km": 6336.0, |
| "distances_to_centroid": { |
| "Belalcázar": 6540.8, |
| "Barreiro do Jaíba": 2674.0, |
| "Colorado": 3650.2, |
| "San Martín": 6336.0, |
| "Prestons": 14660.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Belalcázar: (2.65°, -75.97°)", |
| " Barreiro do Jaíba: (-15.62°, -43.59°)", |
| " Colorado: (-22.84°, -51.97°)", |
| " San Martín: (3.70°, -73.70°)", |
| " Prestons: (-33.94°, 150.87°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Prestons: 14660.8 km from centroid", |
| " Belalcázar: 6540.8 km from centroid", |
| " San Martín: 6336.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Prestons", |
| "FINAL ANSWER: Prestons" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 48.65412, |
| "lon": 2.39343, |
| "name": "Grigny" |
| }, |
| { |
| "lat": 47.75935, |
| "lon": 8.8403, |
| "name": "Singen" |
| }, |
| { |
| "lat": 49.8414, |
| "lon": 7.86713, |
| "name": "Bad Kreuznach" |
| }, |
| { |
| "lat": 51.47924, |
| "lon": 11.91605, |
| "name": "Halle-Neustadt" |
| }, |
| { |
| "lat": -6.78889, |
| "lon": -39.29583, |
| "name": "Várzea Alegre" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Grigny, Singen, Bad Kreuznach, Halle-Neustadt, Várzea Alegre?", |
| "ground_truth": { |
| "answer": "Várzea Alegre", |
| "outlier_distance_km": 6335.9, |
| "second_furthest_km": 1818.3, |
| "clarity_ratio": 3.48, |
| "median_distance_km": 1500.1, |
| "distances_to_centroid": { |
| "Grigny": 1208.3, |
| "Singen": 1361.8, |
| "Bad Kreuznach": 1500.1, |
| "Halle-Neustadt": 1818.3, |
| "Várzea Alegre": 6335.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Grigny: (48.65°, 2.39°)", |
| " Singen: (47.76°, 8.84°)", |
| " Bad Kreuznach: (49.84°, 7.87°)", |
| " Halle-Neustadt: (51.48°, 11.92°)", |
| " Várzea Alegre: (-6.79°, -39.30°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Várzea Alegre: 6335.9 km from centroid", |
| " Halle-Neustadt: 1818.3 km from centroid", |
| " Bad Kreuznach: 1500.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Várzea Alegre", |
| "FINAL ANSWER: Várzea Alegre" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -22.995, |
| "lon": -47.50778, |
| "name": "Capivari" |
| }, |
| { |
| "lat": -23.54583, |
| "lon": -47.18333, |
| "name": "Mairinque" |
| }, |
| { |
| "lat": -6.66028, |
| "lon": -69.87361, |
| "name": "Eirunepé" |
| }, |
| { |
| "lat": 4.45265, |
| "lon": -75.78746, |
| "name": "La Tebaida" |
| }, |
| { |
| "lat": 53.11254, |
| "lon": 6.0989, |
| "name": "Drachten" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Capivari, Mairinque, Eirunepé, La Tebaida, Drachten?", |
| "ground_truth": { |
| "answer": "Drachten", |
| "outlier_distance_km": 7566.8, |
| "second_furthest_km": 3238.1, |
| "clarity_ratio": 2.34, |
| "median_distance_km": 2715.5, |
| "distances_to_centroid": { |
| "Capivari": 2654.9, |
| "Mairinque": 2715.5, |
| "Eirunepé": 2688.7, |
| "La Tebaida": 3238.1, |
| "Drachten": 7566.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Capivari: (-23.00°, -47.51°)", |
| " Mairinque: (-23.55°, -47.18°)", |
| " Eirunepé: (-6.66°, -69.87°)", |
| " La Tebaida: (4.45°, -75.79°)", |
| " Drachten: (53.11°, 6.10°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Drachten: 7566.8 km from centroid", |
| " La Tebaida: 3238.1 km from centroid", |
| " Mairinque: 2715.5 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Drachten", |
| "FINAL ANSWER: Drachten" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 31.10442, |
| "lon": 77.16662, |
| "name": "Shimla" |
| }, |
| { |
| "lat": 21.16516, |
| "lon": 77.3091, |
| "name": "Anjangaon" |
| }, |
| { |
| "lat": 29.80147, |
| "lon": 76.92825, |
| "name": "Tirāwari" |
| }, |
| { |
| "lat": 10.80603, |
| "lon": 78.75031, |
| "name": "Ellakkudi" |
| }, |
| { |
| "lat": 31.18287, |
| "lon": 32.03108, |
| "name": "Al Maţarīyah" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Shimla, Anjangaon, Tirāwari, Ellakkudi, Al Maţarīyah?", |
| "ground_truth": { |
| "answer": "Al Maţarīyah", |
| "outlier_distance_km": 3627.1, |
| "second_furthest_km": 1899.9, |
| "clarity_ratio": 1.91, |
| "median_distance_km": 1105.9, |
| "distances_to_centroid": { |
| "Shimla": 1105.9, |
| "Anjangaon": 994.3, |
| "Tirāwari": 1005.3, |
| "Ellakkudi": 1899.9, |
| "Al Maţarīyah": 3627.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Shimla: (31.10°, 77.17°)", |
| " Anjangaon: (21.17°, 77.31°)", |
| " Tirāwari: (29.80°, 76.93°)", |
| " Ellakkudi: (10.81°, 78.75°)", |
| " Al Maţarīyah: (31.18°, 32.03°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Al Maţarīyah: 3627.1 km from centroid", |
| " Ellakkudi: 1899.9 km from centroid", |
| " Shimla: 1105.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Al Maţarīyah", |
| "FINAL ANSWER: Al Maţarīyah" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 42.73253, |
| "lon": -84.55553, |
| "name": "Lansing" |
| }, |
| { |
| "lat": 39.14539, |
| "lon": -77.14415, |
| "name": "Redland" |
| }, |
| { |
| "lat": 49.10797, |
| "lon": -122.7276, |
| "name": "Cloverdale" |
| }, |
| { |
| "lat": 34.15917, |
| "lon": -118.50119, |
| "name": "Encino" |
| }, |
| { |
| "lat": 0.20387, |
| "lon": 35.105, |
| "name": "Kapsabet" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Lansing, Redland, Cloverdale, Encino, Kapsabet?", |
| "ground_truth": { |
| "answer": "Kapsabet", |
| "outlier_distance_km": 11724.9, |
| "second_furthest_km": 4396.3, |
| "clarity_ratio": 2.67, |
| "median_distance_km": 4128.8, |
| "distances_to_centroid": { |
| "Lansing": 1441.2, |
| "Redland": 748.0, |
| "Cloverdale": 4396.3, |
| "Encino": 4128.8, |
| "Kapsabet": 11724.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Lansing: (42.73°, -84.56°)", |
| " Redland: (39.15°, -77.14°)", |
| " Cloverdale: (49.11°, -122.73°)", |
| " Encino: (34.16°, -118.50°)", |
| " Kapsabet: (0.20°, 35.10°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Kapsabet: 11724.9 km from centroid", |
| " Cloverdale: 4396.3 km from centroid", |
| " Encino: 4128.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Kapsabet", |
| "FINAL ANSWER: Kapsabet" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 12.66644, |
| "lon": 100.90073, |
| "name": "Sattahip" |
| }, |
| { |
| "lat": 37.40458, |
| "lon": 136.89912, |
| "name": "Wajima" |
| }, |
| { |
| "lat": 37.14828, |
| "lon": 138.23642, |
| "name": "Jōetsu" |
| }, |
| { |
| "lat": 13.21055, |
| "lon": 79.0956, |
| "name": "Chittoor" |
| }, |
| { |
| "lat": 8.66762, |
| "lon": 3.39393, |
| "name": "Saki" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Sattahip, Wajima, Jōetsu, Chittoor, Saki?", |
| "ground_truth": { |
| "answer": "Saki", |
| "outlier_distance_km": 9477.8, |
| "second_furthest_km": 4761.1, |
| "clarity_ratio": 1.99, |
| "median_distance_km": 4648.0, |
| "distances_to_centroid": { |
| "Sattahip": 1409.5, |
| "Wajima": 4648.0, |
| "Jōetsu": 4761.1, |
| "Chittoor": 1642.9, |
| "Saki": 9477.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Sattahip: (12.67°, 100.90°)", |
| " Wajima: (37.40°, 136.90°)", |
| " Jōetsu: (37.15°, 138.24°)", |
| " Chittoor: (13.21°, 79.10°)", |
| " Saki: (8.67°, 3.39°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Saki: 9477.8 km from centroid", |
| " Jōetsu: 4761.1 km from centroid", |
| " Wajima: 4648.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Saki", |
| "FINAL ANSWER: Saki" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -27.3171, |
| "lon": 153.03097, |
| "name": "Bracken Ridge" |
| }, |
| { |
| "lat": -41.51603, |
| "lon": 173.9528, |
| "name": "Blenheim" |
| }, |
| { |
| "lat": -33.80383, |
| "lon": 150.98768, |
| "name": "Westmead" |
| }, |
| { |
| "lat": -36.8582, |
| "lon": 174.62019, |
| "name": "Lincoln" |
| }, |
| { |
| "lat": 29.62173, |
| "lon": 105.69265, |
| "name": "Baoxing" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Bracken Ridge, Blenheim, Westmead, Lincoln, Baoxing?", |
| "ground_truth": { |
| "answer": "Baoxing", |
| "outlier_distance_km": 7555.8, |
| "second_furthest_km": 3009.5, |
| "clarity_ratio": 2.51, |
| "median_distance_km": 2759.6, |
| "distances_to_centroid": { |
| "Bracken Ridge": 610.0, |
| "Blenheim": 3009.5, |
| "Westmead": 1317.0, |
| "Lincoln": 2759.6, |
| "Baoxing": 7555.8 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Bracken Ridge: (-27.32°, 153.03°)", |
| " Blenheim: (-41.52°, 173.95°)", |
| " Westmead: (-33.80°, 150.99°)", |
| " Lincoln: (-36.86°, 174.62°)", |
| " Baoxing: (29.62°, 105.69°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Baoxing: 7555.8 km from centroid", |
| " Blenheim: 3009.5 km from centroid", |
| " Lincoln: 2759.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Baoxing", |
| "FINAL ANSWER: Baoxing" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 38.17492, |
| "lon": -122.2608, |
| "name": "American Canyon" |
| }, |
| { |
| "lat": 39.91789, |
| "lon": -75.22796, |
| "name": "Elmwood" |
| }, |
| { |
| "lat": 41.9659, |
| "lon": -87.65262, |
| "name": "Uptown" |
| }, |
| { |
| "lat": 42.12922, |
| "lon": -80.08506, |
| "name": "Erie" |
| }, |
| { |
| "lat": 13.83224, |
| "lon": 120.63219, |
| "name": "Calatagan" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: American Canyon, Elmwood, Uptown, Erie, Calatagan?", |
| "ground_truth": { |
| "answer": "Calatagan", |
| "outlier_distance_km": 14452.3, |
| "second_furthest_km": 6369.9, |
| "clarity_ratio": 2.27, |
| "median_distance_km": 3419.1, |
| "distances_to_centroid": { |
| "American Canyon": 6369.9, |
| "Elmwood": 2368.3, |
| "Uptown": 3419.1, |
| "Erie": 2795.9, |
| "Calatagan": 14452.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " American Canyon: (38.17°, -122.26°)", |
| " Elmwood: (39.92°, -75.23°)", |
| " Uptown: (41.97°, -87.65°)", |
| " Erie: (42.13°, -80.09°)", |
| " Calatagan: (13.83°, 120.63°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Calatagan: 14452.3 km from centroid", |
| " American Canyon: 6369.9 km from centroid", |
| " Uptown: 3419.1 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Calatagan", |
| "FINAL ANSWER: Calatagan" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -34.60306, |
| "lon": -58.54074, |
| "name": "Santos Lugares" |
| }, |
| { |
| "lat": -34.65118, |
| "lon": -58.62205, |
| "name": "Morón" |
| }, |
| { |
| "lat": -28.55104, |
| "lon": -56.04125, |
| "name": "Santo Tomé" |
| }, |
| { |
| "lat": -12.76556, |
| "lon": -39.42833, |
| "name": "Castro Alves" |
| }, |
| { |
| "lat": 66.53373, |
| "lon": 66.60955, |
| "name": "Salekhard" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Santos Lugares, Morón, Santo Tomé, Castro Alves, Salekhard?", |
| "ground_truth": { |
| "answer": "Salekhard", |
| "outlier_distance_km": 11162.6, |
| "second_furthest_km": 4150.8, |
| "clarity_ratio": 2.69, |
| "median_distance_km": 4141.6, |
| "distances_to_centroid": { |
| "Santos Lugares": 4141.6, |
| "Morón": 4150.8, |
| "Santo Tomé": 3562.1, |
| "Castro Alves": 1200.1, |
| "Salekhard": 11162.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Santos Lugares: (-34.60°, -58.54°)", |
| " Morón: (-34.65°, -58.62°)", |
| " Santo Tomé: (-28.55°, -56.04°)", |
| " Castro Alves: (-12.77°, -39.43°)", |
| " Salekhard: (66.53°, 66.61°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Salekhard: 11162.6 km from centroid", |
| " Morón: 4150.8 km from centroid", |
| " Santos Lugares: 4141.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Salekhard", |
| "FINAL ANSWER: Salekhard" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -0.5, |
| "lon": 34.4, |
| "name": "Awendo" |
| }, |
| { |
| "lat": 10.95627, |
| "lon": 36.50456, |
| "name": "Chagni" |
| }, |
| { |
| "lat": -26.25, |
| "lon": 29.26, |
| "name": "Kriel" |
| }, |
| { |
| "lat": 12.76889, |
| "lon": 37.62389, |
| "name": "Amba Giorgis" |
| }, |
| { |
| "lat": 41.77809, |
| "lon": -87.66672, |
| "name": "West Englewood" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Awendo, Chagni, Kriel, Amba Giorgis, West Englewood?", |
| "ground_truth": { |
| "answer": "West Englewood", |
| "outlier_distance_km": 10065.1, |
| "second_furthest_km": 4313.6, |
| "clarity_ratio": 2.33, |
| "median_distance_km": 3069.0, |
| "distances_to_centroid": { |
| "Awendo": 2854.0, |
| "Chagni": 2926.0, |
| "Kriel": 4313.6, |
| "Amba Giorgis": 3069.0, |
| "West Englewood": 10065.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Awendo: (-0.50°, 34.40°)", |
| " Chagni: (10.96°, 36.50°)", |
| " Kriel: (-26.25°, 29.26°)", |
| " Amba Giorgis: (12.77°, 37.62°)", |
| " West Englewood: (41.78°, -87.67°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " West Englewood: 10065.1 km from centroid", |
| " Kriel: 4313.6 km from centroid", |
| " Amba Giorgis: 3069.0 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: West Englewood", |
| "FINAL ANSWER: West Englewood" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -32.24295, |
| "lon": 148.60484, |
| "name": "Dubbo" |
| }, |
| { |
| "lat": -38.14458, |
| "lon": 145.12291, |
| "name": "Frankston" |
| }, |
| { |
| "lat": -31.76737, |
| "lon": 115.96936, |
| "name": "Ellenbrook" |
| }, |
| { |
| "lat": -33.79728, |
| "lon": 150.7847, |
| "name": "St Clair" |
| }, |
| { |
| "lat": -0.52731, |
| "lon": 34.45714, |
| "name": "Homa Bay" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Dubbo, Frankston, Ellenbrook, St Clair, Homa Bay?", |
| "ground_truth": { |
| "answer": "Homa Bay", |
| "outlier_distance_km": 9440.3, |
| "second_furthest_km": 3116.3, |
| "clarity_ratio": 3.03, |
| "median_distance_km": 2901.5, |
| "distances_to_centroid": { |
| "Dubbo": 2901.5, |
| "Frankston": 2713.3, |
| "Ellenbrook": 576.5, |
| "St Clair": 3116.3, |
| "Homa Bay": 9440.3 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Dubbo: (-32.24°, 148.60°)", |
| " Frankston: (-38.14°, 145.12°)", |
| " Ellenbrook: (-31.77°, 115.97°)", |
| " St Clair: (-33.80°, 150.78°)", |
| " Homa Bay: (-0.53°, 34.46°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Homa Bay: 9440.3 km from centroid", |
| " St Clair: 3116.3 km from centroid", |
| " Dubbo: 2901.5 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Homa Bay", |
| "FINAL ANSWER: Homa Bay" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -28.11694, |
| "lon": 153.46584, |
| "name": "Palm Beach" |
| }, |
| { |
| "lat": -37.88214, |
| "lon": 144.98215, |
| "name": "Elwood" |
| }, |
| { |
| "lat": -27.66757, |
| "lon": 152.92488, |
| "name": "Springfield Lakes" |
| }, |
| { |
| "lat": -35.13333, |
| "lon": 138.51667, |
| "name": "Morphett Vale" |
| }, |
| { |
| "lat": 40.04559, |
| "lon": -86.0086, |
| "name": "Noblesville" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Palm Beach, Elwood, Springfield Lakes, Morphett Vale, Noblesville?", |
| "ground_truth": { |
| "answer": "Noblesville", |
| "outlier_distance_km": 17451.6, |
| "second_furthest_km": 5475.8, |
| "clarity_ratio": 3.19, |
| "median_distance_km": 5422.4, |
| "distances_to_centroid": { |
| "Palm Beach": 5475.8, |
| "Elwood": 4830.7, |
| "Springfield Lakes": 5422.4, |
| "Morphett Vale": 4190.4, |
| "Noblesville": 17451.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Palm Beach: (-28.12°, 153.47°)", |
| " Elwood: (-37.88°, 144.98°)", |
| " Springfield Lakes: (-27.67°, 152.92°)", |
| " Morphett Vale: (-35.13°, 138.52°)", |
| " Noblesville: (40.05°, -86.01°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Noblesville: 17451.6 km from centroid", |
| " Palm Beach: 5475.8 km from centroid", |
| " Springfield Lakes: 5422.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Noblesville", |
| "FINAL ANSWER: Noblesville" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 10.60857, |
| "lon": 106.67135, |
| "name": "Cần Giuộc" |
| }, |
| { |
| "lat": 28.6, |
| "lon": 77.13333, |
| "name": "Delhi Cantonment" |
| }, |
| { |
| "lat": 29.53284, |
| "lon": 108.77478, |
| "name": "Qianjiang" |
| }, |
| { |
| "lat": 17.1307, |
| "lon": 76.94361, |
| "name": "Shāhābād" |
| }, |
| { |
| "lat": 5.35113, |
| "lon": -0.62313, |
| "name": "Winneba" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Cần Giuộc, Delhi Cantonment, Qianjiang, Shāhābād, Winneba?", |
| "ground_truth": { |
| "answer": "Winneba", |
| "outlier_distance_km": 8176.7, |
| "second_furthest_km": 3755.3, |
| "clarity_ratio": 2.18, |
| "median_distance_km": 3636.3, |
| "distances_to_centroid": { |
| "Cần Giuộc": 3636.3, |
| "Delhi Cantonment": 1201.0, |
| "Qianjiang": 3755.3, |
| "Shāhābād": 357.3, |
| "Winneba": 8176.7 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Cần Giuộc: (10.61°, 106.67°)", |
| " Delhi Cantonment: (28.60°, 77.13°)", |
| " Qianjiang: (29.53°, 108.77°)", |
| " Shāhābād: (17.13°, 76.94°)", |
| " Winneba: (5.35°, -0.62°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Winneba: 8176.7 km from centroid", |
| " Qianjiang: 3755.3 km from centroid", |
| " Cần Giuộc: 3636.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Winneba", |
| "FINAL ANSWER: Winneba" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 54.64261, |
| "lon": 83.30353, |
| "name": "Iskitim" |
| }, |
| { |
| "lat": 52.39836, |
| "lon": -0.72571, |
| "name": "Kettering" |
| }, |
| { |
| "lat": 49.92139, |
| "lon": 8.48255, |
| "name": "Groß-Gerau" |
| }, |
| { |
| "lat": 38.22008, |
| "lon": 15.24023, |
| "name": "Milazzo" |
| }, |
| { |
| "lat": -38.26667, |
| "lon": 145.01667, |
| "name": "Mount Martha" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Iskitim, Kettering, Groß-Gerau, Milazzo, Mount Martha?", |
| "ground_truth": { |
| "answer": "Mount Martha", |
| "outlier_distance_km": 12477.6, |
| "second_furthest_km": 4695.6, |
| "clarity_ratio": 2.66, |
| "median_distance_km": 4010.4, |
| "distances_to_centroid": { |
| "Iskitim": 3667.5, |
| "Kettering": 4695.6, |
| "Groß-Gerau": 4010.4, |
| "Milazzo": 3266.2, |
| "Mount Martha": 12477.6 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Iskitim: (54.64°, 83.30°)", |
| " Kettering: (52.40°, -0.73°)", |
| " Groß-Gerau: (49.92°, 8.48°)", |
| " Milazzo: (38.22°, 15.24°)", |
| " Mount Martha: (-38.27°, 145.02°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Mount Martha: 12477.6 km from centroid", |
| " Kettering: 4695.6 km from centroid", |
| " Groß-Gerau: 4010.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Mount Martha", |
| "FINAL ANSWER: Mount Martha" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -17.89194, |
| "lon": -39.37194, |
| "name": "Nova Viçosa" |
| }, |
| { |
| "lat": -22.52694, |
| "lon": -41.945, |
| "name": "Rio das Ostras" |
| }, |
| { |
| "lat": -28.84556, |
| "lon": -51.89028, |
| "name": "Guaporé" |
| }, |
| { |
| "lat": -30.60106, |
| "lon": -71.19901, |
| "name": "Ovalle" |
| }, |
| { |
| "lat": 10.96209, |
| "lon": 79.39124, |
| "name": "Kumbakonam" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Nova Viçosa, Rio das Ostras, Guaporé, Ovalle, Kumbakonam?", |
| "ground_truth": { |
| "answer": "Kumbakonam", |
| "outlier_distance_km": 11885.2, |
| "second_furthest_km": 4860.9, |
| "clarity_ratio": 2.45, |
| "median_distance_km": 2998.9, |
| "distances_to_centroid": { |
| "Nova Viçosa": 1520.6, |
| "Rio das Ostras": 1844.2, |
| "Guaporé": 2998.9, |
| "Ovalle": 4860.9, |
| "Kumbakonam": 11885.2 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Nova Viçosa: (-17.89°, -39.37°)", |
| " Rio das Ostras: (-22.53°, -41.95°)", |
| " Guaporé: (-28.85°, -51.89°)", |
| " Ovalle: (-30.60°, -71.20°)", |
| " Kumbakonam: (10.96°, 79.39°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Kumbakonam: 11885.2 km from centroid", |
| " Ovalle: 4860.9 km from centroid", |
| " Guaporé: 2998.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Kumbakonam", |
| "FINAL ANSWER: Kumbakonam" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 13.56083, |
| "lon": 38.97389, |
| "name": "Ābīy Ādī" |
| }, |
| { |
| "lat": -28.27276, |
| "lon": 29.12946, |
| "name": "Harrismith" |
| }, |
| { |
| "lat": 7.36983, |
| "lon": 4.1863, |
| "name": "Ikire" |
| }, |
| { |
| "lat": 25.61988, |
| "lon": 32.54305, |
| "name": "Armant" |
| }, |
| { |
| "lat": 38.00492, |
| "lon": -121.80579, |
| "name": "Antioch" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Ābīy Ādī, Harrismith, Ikire, Armant, Antioch?", |
| "ground_truth": { |
| "answer": "Antioch", |
| "outlier_distance_km": 11600.9, |
| "second_furthest_km": 5617.4, |
| "clarity_ratio": 2.07, |
| "median_distance_km": 4602.8, |
| "distances_to_centroid": { |
| "Ābīy Ādī": 4602.8, |
| "Harrismith": 5617.4, |
| "Ikire": 937.3, |
| "Armant": 4095.3, |
| "Antioch": 11600.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Ābīy Ādī: (13.56°, 38.97°)", |
| " Harrismith: (-28.27°, 29.13°)", |
| " Ikire: (7.37°, 4.19°)", |
| " Armant: (25.62°, 32.54°)", |
| " Antioch: (38.00°, -121.81°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Antioch: 11600.9 km from centroid", |
| " Harrismith: 5617.4 km from centroid", |
| " Ābīy Ādī: 4602.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Antioch", |
| "FINAL ANSWER: Antioch" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -33.08338, |
| "lon": -68.47312, |
| "name": "San Martín" |
| }, |
| { |
| "lat": -23.18111, |
| "lon": -46.395, |
| "name": "Nazaré Paulista" |
| }, |
| { |
| "lat": -6.25444, |
| "lon": -39.20194, |
| "name": "Quixelô" |
| }, |
| { |
| "lat": -19.53791, |
| "lon": -49.48813, |
| "name": "Campina Verde" |
| }, |
| { |
| "lat": 12.54654, |
| "lon": 77.42005, |
| "name": "Kanakapura" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: San Martín, Nazaré Paulista, Quixelô, Campina Verde, Kanakapura?", |
| "ground_truth": { |
| "answer": "Kanakapura", |
| "outlier_distance_km": 11681.0, |
| "second_furthest_km": 4853.4, |
| "clarity_ratio": 2.41, |
| "median_distance_km": 2655.6, |
| "distances_to_centroid": { |
| "San Martín": 4853.4, |
| "Nazaré Paulista": 2454.4, |
| "Quixelô": 1749.2, |
| "Campina Verde": 2655.6, |
| "Kanakapura": 11681.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " San Martín: (-33.08°, -68.47°)", |
| " Nazaré Paulista: (-23.18°, -46.40°)", |
| " Quixelô: (-6.25°, -39.20°)", |
| " Campina Verde: (-19.54°, -49.49°)", |
| " Kanakapura: (12.55°, 77.42°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Kanakapura: 11681.0 km from centroid", |
| " San Martín: 4853.4 km from centroid", |
| " Campina Verde: 2655.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Kanakapura", |
| "FINAL ANSWER: Kanakapura" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 8.98333, |
| "lon": 37.85, |
| "name": "Hāgere Hiywet" |
| }, |
| { |
| "lat": -25.70866, |
| "lon": 31.51025, |
| "name": "Schoemansdal" |
| }, |
| { |
| "lat": 30.37746, |
| "lon": 30.35032, |
| "name": "Madīnat Wādī an Naţrūn" |
| }, |
| { |
| "lat": 6.58222, |
| "lon": 46.43333, |
| "name": "Qorof" |
| }, |
| { |
| "lat": -38.0965, |
| "lon": 145.26707, |
| "name": "Cranbourne West" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Hāgere Hiywet, Schoemansdal, Madīnat Wādī an Naţrūn, Qorof, Cranbourne West?", |
| "ground_truth": { |
| "answer": "Cranbourne West", |
| "outlier_distance_km": 9498.9, |
| "second_furthest_km": 4801.3, |
| "clarity_ratio": 1.98, |
| "median_distance_km": 3770.8, |
| "distances_to_centroid": { |
| "Hāgere Hiywet": 2660.6, |
| "Schoemansdal": 3770.8, |
| "Madīnat Wādī an Naţrūn": 4801.3, |
| "Qorof": 1733.5, |
| "Cranbourne West": 9498.9 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Hāgere Hiywet: (8.98°, 37.85°)", |
| " Schoemansdal: (-25.71°, 31.51°)", |
| " Madīnat Wādī an Naţrūn: (30.38°, 30.35°)", |
| " Qorof: (6.58°, 46.43°)", |
| " Cranbourne West: (-38.10°, 145.27°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Cranbourne West: 9498.9 km from centroid", |
| " Madīnat Wādī an Naţrūn: 4801.3 km from centroid", |
| " Schoemansdal: 3770.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Cranbourne West", |
| "FINAL ANSWER: Cranbourne West" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 43.2397, |
| "lon": -2.8858, |
| "name": "Basauri" |
| }, |
| { |
| "lat": 47.57143, |
| "lon": 10.70171, |
| "name": "Füssen" |
| }, |
| { |
| "lat": 45.76124, |
| "lon": 4.85184, |
| "name": "Lyon 03" |
| }, |
| { |
| "lat": 47.73512, |
| "lon": -3.42952, |
| "name": "Ploemeur" |
| }, |
| { |
| "lat": 35.65127, |
| "lon": -78.83362, |
| "name": "Holly Springs" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Basauri, Füssen, Lyon 03, Ploemeur, Holly Springs?", |
| "ground_truth": { |
| "answer": "Holly Springs", |
| "outlier_distance_km": 5477.1, |
| "second_furthest_km": 1941.6, |
| "clarity_ratio": 2.82, |
| "median_distance_km": 1488.6, |
| "distances_to_centroid": { |
| "Basauri": 891.5, |
| "Füssen": 1941.6, |
| "Lyon 03": 1488.6, |
| "Ploemeur": 911.6, |
| "Holly Springs": 5477.1 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Basauri: (43.24°, -2.89°)", |
| " Füssen: (47.57°, 10.70°)", |
| " Lyon 03: (45.76°, 4.85°)", |
| " Ploemeur: (47.74°, -3.43°)", |
| " Holly Springs: (35.65°, -78.83°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Holly Springs: 5477.1 km from centroid", |
| " Füssen: 1941.6 km from centroid", |
| " Lyon 03: 1488.6 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Holly Springs", |
| "FINAL ANSWER: Holly Springs" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 10.87995, |
| "lon": 76.002, |
| "name": "Naduvattam" |
| }, |
| { |
| "lat": 50.78333, |
| "lon": 121.51667, |
| "name": "Genhe" |
| }, |
| { |
| "lat": 35.87291, |
| "lon": 137.97503, |
| "name": "Minamiminowa" |
| }, |
| { |
| "lat": 39.74326, |
| "lon": 118.45099, |
| "name": "Tangjiazhuang" |
| }, |
| { |
| "lat": -28.56003, |
| "lon": -66.80737, |
| "name": "Aimogasta" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Naduvattam, Genhe, Minamiminowa, Tangjiazhuang, Aimogasta?", |
| "ground_truth": { |
| "answer": "Aimogasta", |
| "outlier_distance_km": 16350.5, |
| "second_furthest_km": 6009.4, |
| "clarity_ratio": 2.72, |
| "median_distance_km": 4988.3, |
| "distances_to_centroid": { |
| "Naduvattam": 1217.5, |
| "Genhe": 4988.3, |
| "Minamiminowa": 6009.4, |
| "Tangjiazhuang": 4351.4, |
| "Aimogasta": 16350.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Naduvattam: (10.88°, 76.00°)", |
| " Genhe: (50.78°, 121.52°)", |
| " Minamiminowa: (35.87°, 137.98°)", |
| " Tangjiazhuang: (39.74°, 118.45°)", |
| " Aimogasta: (-28.56°, -66.81°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Aimogasta: 16350.5 km from centroid", |
| " Minamiminowa: 6009.4 km from centroid", |
| " Genhe: 4988.3 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Aimogasta", |
| "FINAL ANSWER: Aimogasta" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 11.80937, |
| "lon": 8.84422, |
| "name": "Wudil" |
| }, |
| { |
| "lat": 6.3, |
| "lon": 36.88333, |
| "name": "Felege Neway" |
| }, |
| { |
| "lat": -1.03326, |
| "lon": 37.06933, |
| "name": "Thika" |
| }, |
| { |
| "lat": -28.23078, |
| "lon": 28.30707, |
| "name": "Bethlehem" |
| }, |
| { |
| "lat": -5.25806, |
| "lon": -44.64889, |
| "name": "Tuntum" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Wudil, Felege Neway, Thika, Bethlehem, Tuntum?", |
| "ground_truth": { |
| "answer": "Tuntum", |
| "outlier_distance_km": 6426.5, |
| "second_furthest_km": 3197.8, |
| "clarity_ratio": 2.01, |
| "median_distance_km": 2827.8, |
| "distances_to_centroid": { |
| "Wudil": 1748.7, |
| "Felege Neway": 2827.8, |
| "Thika": 2653.8, |
| "Bethlehem": 3197.8, |
| "Tuntum": 6426.5 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Wudil: (11.81°, 8.84°)", |
| " Felege Neway: (6.30°, 36.88°)", |
| " Thika: (-1.03°, 37.07°)", |
| " Bethlehem: (-28.23°, 28.31°)", |
| " Tuntum: (-5.26°, -44.65°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Tuntum: 6426.5 km from centroid", |
| " Bethlehem: 3197.8 km from centroid", |
| " Felege Neway: 2827.8 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Tuntum", |
| "FINAL ANSWER: Tuntum" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": -0.21209, |
| "lon": 36.27248, |
| "name": "Upper Gilgil" |
| }, |
| { |
| "lat": 27.55642, |
| "lon": 30.81057, |
| "name": "Dayrūţ" |
| }, |
| { |
| "lat": -27.36541, |
| "lon": 29.88175, |
| "name": "Volksrust" |
| }, |
| { |
| "lat": 5.91793, |
| "lon": 0.98789, |
| "name": "Keta" |
| }, |
| { |
| "lat": -41.43876, |
| "lon": 147.13467, |
| "name": "Launceston" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Upper Gilgil, Dayrūţ, Volksrust, Keta, Launceston?", |
| "ground_truth": { |
| "answer": "Launceston", |
| "outlier_distance_km": 10155.0, |
| "second_furthest_km": 5522.0, |
| "clarity_ratio": 1.84, |
| "median_distance_km": 4323.4, |
| "distances_to_centroid": { |
| "Upper Gilgil": 1608.0, |
| "Dayrūţ": 4323.4, |
| "Volksrust": 3024.0, |
| "Keta": 5522.0, |
| "Launceston": 10155.0 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Upper Gilgil: (-0.21°, 36.27°)", |
| " Dayrūţ: (27.56°, 30.81°)", |
| " Volksrust: (-27.37°, 29.88°)", |
| " Keta: (5.92°, 0.99°)", |
| " Launceston: (-41.44°, 147.13°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Launceston: 10155.0 km from centroid", |
| " Keta: 5522.0 km from centroid", |
| " Dayrūţ: 4323.4 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Launceston", |
| "FINAL ANSWER: Launceston" |
| ] |
| }, |
| { |
| "task": "spatial_patterns", |
| "subtask": "outlier_detection", |
| "points": [ |
| { |
| "lat": 13.73028, |
| "lon": 100.65138, |
| "name": "Suan Luang" |
| }, |
| { |
| "lat": 20.79393, |
| "lon": 70.70216, |
| "name": "Kodīnar" |
| }, |
| { |
| "lat": 30.39733, |
| "lon": 107.46953, |
| "name": "Caohui" |
| }, |
| { |
| "lat": 4.48178, |
| "lon": 118.61119, |
| "name": "Semporna" |
| }, |
| { |
| "lat": 42.97839, |
| "lon": -78.79976, |
| "name": "Amherst" |
| } |
| ], |
| "question": "Which location is the geographic outlier among: Suan Luang, Kodīnar, Caohui, Semporna, Amherst?", |
| "ground_truth": { |
| "answer": "Amherst", |
| "outlier_distance_km": 11788.4, |
| "second_furthest_km": 6222.4, |
| "clarity_ratio": 1.89, |
| "median_distance_km": 4415.9, |
| "distances_to_centroid": { |
| "Suan Luang": 4010.4, |
| "Kodīnar": 744.8, |
| "Caohui": 4415.9, |
| "Semporna": 6222.4, |
| "Amherst": 11788.4 |
| } |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify all points (5 locations)", |
| " Suan Luang: (13.73°, 100.65°)", |
| " Kodīnar: (20.79°, 70.70°)", |
| " Caohui: (30.40°, 107.47°)", |
| " Semporna: (4.48°, 118.61°)", |
| " Amherst: (42.98°, -78.80°)", |
| "Step 2: Calculate centroid of all points", |
| "Step 3: Calculate distance from each point to centroid", |
| " Amherst: 11788.4 km from centroid", |
| " Semporna: 6222.4 km from centroid", |
| " Caohui: 4415.9 km from centroid", |
| "Step 4: Identify geographic outlier (furthest from centroid)", |
| " Outlier: Amherst", |
| "FINAL ANSWER: Amherst" |
| ] |
| } |
| ] |
|
|
