[ { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.35227, "lon": 18.64912, "name": "Gdańsk" }, { "lat": 54.5735, "lon": -5.88472, "name": "Castlereagh" }, { "lat": 55.39934, "lon": 37.80829, "name": "Vostryakovo" }, { "lat": 54.00734, "lon": 37.50647, "name": "Shchëkino" }, { "lat": 19.55939, "lon": -98.89884, "name": "Chiconcuac" } ], "question": "Which location is the geographic outlier among: Gdańsk, Castlereagh, Vostryakovo, Shchëkino, Chiconcuac?", "ground_truth": { "answer": "Chiconcuac", "outlier_distance_km": 8902.4, "second_furthest_km": 2855.9, "clarity_ratio": 3.12, "median_distance_km": 2837.9, "distances_to_centroid": { "Gdańsk": 1632.1, "Castlereagh": 819.8, "Vostryakovo": 2855.9, "Shchëkino": 2837.9, "Chiconcuac": 8902.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gdańsk: (54.35°, 18.65°)", " Castlereagh: (54.57°, -5.88°)", " Vostryakovo: (55.40°, 37.81°)", " Shchëkino: (54.01°, 37.51°)", " Chiconcuac: (19.56°, -98.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chiconcuac: 8902.4 km from centroid", " Vostryakovo: 2855.9 km from centroid", " Shchëkino: 2837.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chiconcuac", "FINAL ANSWER: Chiconcuac" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -24.1125, "lon": -49.33167, "name": "Itararé" }, { "lat": -14.2789, "lon": -38.99584, "name": "Itacaré" }, { "lat": -23.07444, "lon": -44.95972, "name": "Cunha" }, { "lat": -21.13556, "lon": -44.26167, "name": "São João del Rei" }, { "lat": 26.35937, "lon": 127.86735, "name": "Gushikawa" } ], "question": "Which location is the geographic outlier among: Itararé, Itacaré, Cunha, São João del Rei, Gushikawa?", "ground_truth": { "answer": "Gushikawa", "outlier_distance_km": 15293.1, "second_furthest_km": 4393.5, "clarity_ratio": 3.48, "median_distance_km": 3933.5, "distances_to_centroid": { "Itararé": 4393.5, "Itacaré": 3167.3, "Cunha": 3933.5, "São João del Rei": 3817.0, "Gushikawa": 15293.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itararé: (-24.11°, -49.33°)", " Itacaré: (-14.28°, -39.00°)", " Cunha: (-23.07°, -44.96°)", " São João del Rei: (-21.14°, -44.26°)", " Gushikawa: (26.36°, 127.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gushikawa: 15293.1 km from centroid", " Itararé: 4393.5 km from centroid", " Cunha: 3933.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gushikawa", "FINAL ANSWER: Gushikawa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.77976, "lon": -87.64588, "name": "Englewood" }, { "lat": 28.29306, "lon": -82.6901, "name": "Jasmine Estates" }, { "lat": 19.19354, "lon": -99.46585, "name": "Capulhuac de Mirafuentes" }, { "lat": 25.85704, "lon": -80.23699, "name": "West Little River" }, { "lat": -31.9652, "lon": 141.4512, "name": "Broken Hill" } ], "question": "Which location is the geographic outlier among: Englewood, Jasmine Estates, Capulhuac de Mirafuentes, West Little River, Broken Hill?", "ground_truth": { "answer": "Broken Hill", "outlier_distance_km": 18280.4, "second_furthest_km": 6089.1, "clarity_ratio": 3.0, "median_distance_km": 5176.5, "distances_to_centroid": { "Englewood": 5176.5, "Jasmine Estates": 4381.7, "Capulhuac de Mirafuentes": 6089.1, "West Little River": 4105.7, "Broken Hill": 18280.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Englewood: (41.78°, -87.65°)", " Jasmine Estates: (28.29°, -82.69°)", " Capulhuac de Mirafuentes: (19.19°, -99.47°)", " West Little River: (25.86°, -80.24°)", " Broken Hill: (-31.97°, 141.45°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Broken Hill: 18280.4 km from centroid", " Capulhuac de Mirafuentes: 6089.1 km from centroid", " Englewood: 5176.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Broken Hill", "FINAL ANSWER: Broken Hill" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.14711, "lon": 144.36069, "name": "Geelong" }, { "lat": -32.05799, "lon": 115.91814, "name": "Canning Vale" }, { "lat": -37.75, "lon": 144.96667, "name": "Coburg" }, { "lat": -41.28664, "lon": 174.77557, "name": "Wellington" }, { "lat": 48.87213, "lon": 9.27334, "name": "Remseck am Neckar" } ], "question": "Which location is the geographic outlier among: Geelong, Canning Vale, Coburg, Wellington, Remseck am Neckar?", "ground_truth": { "answer": "Remseck am Neckar", "outlier_distance_km": 13020.2, "second_furthest_km": 5813.9, "clarity_ratio": 2.24, "median_distance_km": 3269.2, "distances_to_centroid": { "Geelong": 3245.3, "Canning Vale": 1346.5, "Coburg": 3269.2, "Wellington": 5813.9, "Remseck am Neckar": 13020.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Geelong: (-38.15°, 144.36°)", " Canning Vale: (-32.06°, 115.92°)", " Coburg: (-37.75°, 144.97°)", " Wellington: (-41.29°, 174.78°)", " Remseck am Neckar: (48.87°, 9.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Remseck am Neckar: 13020.2 km from centroid", " Wellington: 5813.9 km from centroid", " Coburg: 3269.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Remseck am Neckar", "FINAL ANSWER: Remseck am Neckar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.48363, "lon": 7.03325, "name": "Owerri" }, { "lat": 7.23333, "lon": 37.88333, "name": "Duramē" }, { "lat": 0.49194, "lon": 35.74303, "name": "Kabarnet" }, { "lat": 13.15498, "lon": 10.63468, "name": "Kumagunnam" }, { "lat": -32.081, "lon": 116.0054, "name": "Gosnells" } ], "question": "Which location is the geographic outlier among: Owerri, Duramē, Kabarnet, Kumagunnam, Gosnells?", "ground_truth": { "answer": "Gosnells", "outlier_distance_km": 8487.5, "second_furthest_km": 3893.5, "clarity_ratio": 2.18, "median_distance_km": 3752.6, "distances_to_centroid": { "Owerri": 3893.5, "Duramē": 1012.4, "Kabarnet": 661.2, "Kumagunnam": 3752.6, "Gosnells": 8487.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Owerri: (5.48°, 7.03°)", " Duramē: (7.23°, 37.88°)", " Kabarnet: (0.49°, 35.74°)", " Kumagunnam: (13.15°, 10.63°)", " Gosnells: (-32.08°, 116.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gosnells: 8487.5 km from centroid", " Owerri: 3893.5 km from centroid", " Kumagunnam: 3752.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gosnells", "FINAL ANSWER: Gosnells" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.35578, "lon": -2.86572, "name": "Hunts Cross" }, { "lat": 51.88056, "lon": 45.00609, "name": "Atkarsk" }, { "lat": 55.59911, "lon": 37.35495, "name": "Moskovskiy" }, { "lat": 46.8458, "lon": -1.87942, "name": "Challans" }, { "lat": 40.98065, "lon": -73.68374, "name": "Rye" } ], "question": "Which location is the geographic outlier among: Hunts Cross, Atkarsk, Moskovskiy, Challans, Rye?", "ground_truth": { "answer": "Rye", "outlier_distance_km": 5656.8, "second_furthest_km": 3068.4, "clarity_ratio": 1.84, "median_distance_km": 2518.6, "distances_to_centroid": { "Hunts Cross": 475.4, "Atkarsk": 3068.4, "Moskovskiy": 2518.6, "Challans": 376.7, "Rye": 5656.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hunts Cross: (53.36°, -2.87°)", " Atkarsk: (51.88°, 45.01°)", " Moskovskiy: (55.60°, 37.35°)", " Challans: (46.85°, -1.88°)", " Rye: (40.98°, -73.68°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rye: 5656.8 km from centroid", " Atkarsk: 3068.4 km from centroid", " Moskovskiy: 2518.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rye", "FINAL ANSWER: Rye" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.61771, "lon": -58.60153, "name": "El Palomar" }, { "lat": -9.10528, "lon": -38.14917, "name": "Tacaratu" }, { "lat": -11.74611, "lon": -44.91, "name": "Riachão das Neves" }, { "lat": -15.73948, "lon": -47.85686, "name": "Lago Norte" }, { "lat": 30.18424, "lon": 106.3165, "name": "Qiantang" } ], "question": "Which location is the geographic outlier among: El Palomar, Tacaratu, Riachão das Neves, Lago Norte, Qiantang?", "ground_truth": { "answer": "Qiantang", "outlier_distance_km": 13620.5, "second_furthest_km": 5184.5, "clarity_ratio": 2.63, "median_distance_km": 3492.9, "distances_to_centroid": { "El Palomar": 5184.5, "Tacaratu": 2366.2, "Riachão das Neves": 3119.4, "Lago Norte": 3492.9, "Qiantang": 13620.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " El Palomar: (-34.62°, -58.60°)", " Tacaratu: (-9.11°, -38.15°)", " Riachão das Neves: (-11.75°, -44.91°)", " Lago Norte: (-15.74°, -47.86°)", " Qiantang: (30.18°, 106.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Qiantang: 13620.5 km from centroid", " El Palomar: 5184.5 km from centroid", " Lago Norte: 3492.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Qiantang", "FINAL ANSWER: Qiantang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.23848, "lon": 9.1018, "name": "Bad Rappenau" }, { "lat": 50.81667, "lon": 8.1, "name": "Wilnsdorf" }, { "lat": 56.15, "lon": 37.93333, "name": "Sofrino" }, { "lat": 47.77964, "lon": 10.61713, "name": "Marktoberdorf" }, { "lat": 5.96667, "lon": 41.03333, "name": "Ara Ali" } ], "question": "Which location is the geographic outlier among: Bad Rappenau, Wilnsdorf, Sofrino, Marktoberdorf, Ara Ali?", "ground_truth": { "answer": "Ara Ali", "outlier_distance_km": 4452.1, "second_furthest_km": 1973.4, "clarity_ratio": 2.26, "median_distance_km": 1409.0, "distances_to_centroid": { "Bad Rappenau": 1245.6, "Wilnsdorf": 1409.0, "Sofrino": 1973.4, "Marktoberdorf": 1061.6, "Ara Ali": 4452.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bad Rappenau: (49.24°, 9.10°)", " Wilnsdorf: (50.82°, 8.10°)", " Sofrino: (56.15°, 37.93°)", " Marktoberdorf: (47.78°, 10.62°)", " Ara Ali: (5.97°, 41.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ara Ali: 4452.1 km from centroid", " Sofrino: 1973.4 km from centroid", " Wilnsdorf: 1409.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ara Ali", "FINAL ANSWER: Ara Ali" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.88214, "lon": 144.98215, "name": "Elwood" }, { "lat": -38.16667, "lon": 145.16667, "name": "Langwarrin" }, { "lat": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" }, { "lat": -37.6, "lon": 145.15, "name": "Doreen" }, { "lat": 46.99651, "lon": -120.54785, "name": "Ellensburg" } ], "question": "Which location is the geographic outlier among: Elwood, Langwarrin, Bracken Ridge, Doreen, Ellensburg?", "ground_truth": { "answer": "Ellensburg", "outlier_distance_km": 15609.0, "second_furthest_km": 6104.2, "clarity_ratio": 2.56, "median_distance_km": 5404.2, "distances_to_centroid": { "Elwood": 5383.6, "Langwarrin": 5404.2, "Bracken Ridge": 6104.2, "Doreen": 5393.8, "Ellensburg": 15609.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Elwood: (-37.88°, 144.98°)", " Langwarrin: (-38.17°, 145.17°)", " Bracken Ridge: (-27.32°, 153.03°)", " Doreen: (-37.60°, 145.15°)", " Ellensburg: (47.00°, -120.55°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ellensburg: 15609.0 km from centroid", " Bracken Ridge: 6104.2 km from centroid", " Langwarrin: 5404.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ellensburg", "FINAL ANSWER: Ellensburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.16887, "lon": -4.15129, "name": "Loja" }, { "lat": 53.51619, "lon": -2.94117, "name": "Maghull" }, { "lat": 51.09162, "lon": 6.89217, "name": "Monheim am Rhein" }, { "lat": 39.4, "lon": -0.4, "name": "Catarroja" }, { "lat": -23.20083, "lon": -47.28694, "name": "Salto" } ], "question": "Which location is the geographic outlier among: Loja, Maghull, Monheim am Rhein, Catarroja, Salto?", "ground_truth": { "answer": "Salto", "outlier_distance_km": 7295.4, "second_furthest_km": 2554.1, "clarity_ratio": 2.86, "median_distance_km": 2494.8, "distances_to_centroid": { "Loja": 794.7, "Maghull": 2494.8, "Monheim am Rhein": 2554.1, "Catarroja": 1200.1, "Salto": 7295.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Loja: (37.17°, -4.15°)", " Maghull: (53.52°, -2.94°)", " Monheim am Rhein: (51.09°, 6.89°)", " Catarroja: (39.40°, -0.40°)", " Salto: (-23.20°, -47.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Salto: 7295.4 km from centroid", " Monheim am Rhein: 2554.1 km from centroid", " Maghull: 2494.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Salto", "FINAL ANSWER: Salto" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.38167, "lon": 3.32361, "name": "Soissons" }, { "lat": 51.56872, "lon": -0.07334, "name": "Stamford Hill" }, { "lat": 51.90006, "lon": -2.07972, "name": "Cheltenham" }, { "lat": 36.77629, "lon": -2.81456, "name": "El Ejido" }, { "lat": -27.19354, "lon": 153.02631, "name": "Deception Bay" } ], "question": "Which location is the geographic outlier among: Soissons, Stamford Hill, Cheltenham, El Ejido, Deception Bay?", "ground_truth": { "answer": "Deception Bay", "outlier_distance_km": 14526.8, "second_furthest_km": 3382.6, "clarity_ratio": 4.29, "median_distance_km": 3243.3, "distances_to_centroid": { "Soissons": 2914.3, "Stamford Hill": 3243.3, "Cheltenham": 3382.6, "El Ejido": 3049.5, "Deception Bay": 14526.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Soissons: (49.38°, 3.32°)", " Stamford Hill: (51.57°, -0.07°)", " Cheltenham: (51.90°, -2.08°)", " El Ejido: (36.78°, -2.81°)", " Deception Bay: (-27.19°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Deception Bay: 14526.8 km from centroid", " Cheltenham: 3382.6 km from centroid", " Stamford Hill: 3243.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Deception Bay", "FINAL ANSWER: Deception Bay" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -35.28346, "lon": 149.12807, "name": "Canberra" }, { "lat": -33.86785, "lon": 151.20732, "name": "Sydney" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -9.805, "lon": -37.68444, "name": "Poço Redondo" } ], "question": "Which location is the geographic outlier among: Canberra, Sydney, Cranbourne East, Epping, Poço Redondo?", "ground_truth": { "answer": "Poço Redondo", "outlier_distance_km": 14360.7, "second_furthest_km": 3801.8, "clarity_ratio": 3.78, "median_distance_km": 3598.4, "distances_to_centroid": { "Canberra": 3598.4, "Sydney": 3801.8, "Cranbourne East": 3256.9, "Epping": 3230.8, "Poço Redondo": 14360.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Canberra: (-35.28°, 149.13°)", " Sydney: (-33.87°, 151.21°)", " Cranbourne East: (-38.12°, 145.30°)", " Epping: (-37.65°, 145.03°)", " Poço Redondo: (-9.80°, -37.68°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Poço Redondo: 14360.7 km from centroid", " Sydney: 3801.8 km from centroid", " Canberra: 3598.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Poço Redondo", "FINAL ANSWER: Poço Redondo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.61019, "lon": 9.15301, "name": "Bovisio-Masciago" }, { "lat": 50.32738, "lon": 19.02901, "name": "Siemianowice Śląskie" }, { "lat": 51.22316, "lon": 1.4028, "name": "Deal" }, { "lat": 43.24622, "lon": 5.39788, "name": "Mazargues" }, { "lat": -25.61692, "lon": 27.99471, "name": "Ga-Rankuwa" } ], "question": "Which location is the geographic outlier among: Bovisio-Masciago, Siemianowice Śląskie, Deal, Mazargues, Ga-Rankuwa?", "ground_truth": { "answer": "Ga-Rankuwa", "outlier_distance_km": 6714.1, "second_furthest_km": 2225.2, "clarity_ratio": 3.02, "median_distance_km": 2002.1, "distances_to_centroid": { "Bovisio-Masciago": 1437.3, "Siemianowice Śląskie": 2002.1, "Deal": 2225.2, "Mazargues": 1304.7, "Ga-Rankuwa": 6714.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bovisio-Masciago: (45.61°, 9.15°)", " Siemianowice Śląskie: (50.33°, 19.03°)", " Deal: (51.22°, 1.40°)", " Mazargues: (43.25°, 5.40°)", " Ga-Rankuwa: (-25.62°, 27.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ga-Rankuwa: 6714.1 km from centroid", " Deal: 2225.2 km from centroid", " Siemianowice Śląskie: 2002.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ga-Rankuwa", "FINAL ANSWER: Ga-Rankuwa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.83634, "lon": 144.65952, "name": "Tarneit" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" }, { "lat": -37.80639, "lon": 145.03086, "name": "Kew" }, { "lat": -37.57742, "lon": 144.72607, "name": "Sunbury" }, { "lat": 56.99988, "lon": 40.97257, "name": "Ivanovo" } ], "question": "Which location is the geographic outlier among: Tarneit, Cheltenham, Kew, Sunbury, Ivanovo?", "ground_truth": { "answer": "Ivanovo", "outlier_distance_km": 11349.0, "second_furthest_km": 2940.1, "clarity_ratio": 3.86, "median_distance_km": 2927.2, "distances_to_centroid": { "Tarneit": 2904.6, "Cheltenham": 2940.1, "Kew": 2927.2, "Sunbury": 2890.2, "Ivanovo": 11349.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tarneit: (-37.84°, 144.66°)", " Cheltenham: (-37.97°, 145.05°)", " Kew: (-37.81°, 145.03°)", " Sunbury: (-37.58°, 144.73°)", " Ivanovo: (57.00°, 40.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ivanovo: 11349.0 km from centroid", " Cheltenham: 2940.1 km from centroid", " Kew: 2927.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ivanovo", "FINAL ANSWER: Ivanovo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 16.62473, "lon": -93.09894, "name": "Suchiapa" }, { "lat": 25.76343, "lon": -80.37311, "name": "Sweetwater" }, { "lat": 41.68338, "lon": -86.25001, "name": "South Bend" }, { "lat": 40.8601, "lon": -73.9093, "name": "University Heights" }, { "lat": 11.86064, "lon": 9.0027, "name": "Gaya" } ], "question": "Which location is the geographic outlier among: Suchiapa, Sweetwater, South Bend, University Heights, Gaya?", "ground_truth": { "answer": "Gaya", "outlier_distance_km": 7830.7, "second_furthest_km": 3130.6, "clarity_ratio": 2.5, "median_distance_km": 2508.2, "distances_to_centroid": { "Suchiapa": 3130.6, "Sweetwater": 1545.6, "South Bend": 2508.2, "University Heights": 1711.7, "Gaya": 7830.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Suchiapa: (16.62°, -93.10°)", " Sweetwater: (25.76°, -80.37°)", " South Bend: (41.68°, -86.25°)", " University Heights: (40.86°, -73.91°)", " Gaya: (11.86°, 9.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gaya: 7830.7 km from centroid", " Suchiapa: 3130.6 km from centroid", " South Bend: 2508.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gaya", "FINAL ANSWER: Gaya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.8303, "lon": -116.54529, "name": "Palm Springs" }, { "lat": 44.73191, "lon": -93.21772, "name": "Apple Valley" }, { "lat": 41.80065, "lon": -73.12122, "name": "Torrington" }, { "lat": 37.26804, "lon": -77.40726, "name": "Colonial Heights" }, { "lat": -24.715, "lon": -47.88111, "name": "Pariquera-Açu" } ], "question": "Which location is the geographic outlier among: Palm Springs, Apple Valley, Torrington, Colonial Heights, Pariquera-Açu?", "ground_truth": { "answer": "Pariquera-Açu", "outlier_distance_km": 6757.2, "second_furthest_km": 3432.7, "clarity_ratio": 1.97, "median_distance_km": 2267.8, "distances_to_centroid": { "Palm Springs": 3432.7, "Apple Valley": 2267.8, "Torrington": 1862.1, "Colonial Heights": 1252.9, "Pariquera-Açu": 6757.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Palm Springs: (33.83°, -116.55°)", " Apple Valley: (44.73°, -93.22°)", " Torrington: (41.80°, -73.12°)", " Colonial Heights: (37.27°, -77.41°)", " Pariquera-Açu: (-24.71°, -47.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pariquera-Açu: 6757.2 km from centroid", " Palm Springs: 3432.7 km from centroid", " Apple Valley: 2267.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pariquera-Açu", "FINAL ANSWER: Pariquera-Açu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.46005, "lon": -73.57058, "name": "Verdun" }, { "lat": 21.43434, "lon": -102.57427, "name": "Teocaltiche" }, { "lat": 42.97225, "lon": -85.95365, "name": "Allendale" }, { "lat": 32.46402, "lon": -86.4597, "name": "Prattville" }, { "lat": 27.49658, "lon": 77.46263, "name": "Govardhan" } ], "question": "Which location is the geographic outlier among: Verdun, Teocaltiche, Allendale, Prattville, Govardhan?", "ground_truth": { "answer": "Govardhan", "outlier_distance_km": 11494.5, "second_furthest_km": 4912.4, "clarity_ratio": 2.34, "median_distance_km": 2991.6, "distances_to_centroid": { "Verdun": 2082.0, "Teocaltiche": 4912.4, "Allendale": 2917.8, "Prattville": 2991.6, "Govardhan": 11494.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Verdun: (45.46°, -73.57°)", " Teocaltiche: (21.43°, -102.57°)", " Allendale: (42.97°, -85.95°)", " Prattville: (32.46°, -86.46°)", " Govardhan: (27.50°, 77.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Govardhan: 11494.5 km from centroid", " Teocaltiche: 4912.4 km from centroid", " Prattville: 2991.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Govardhan", "FINAL ANSWER: Govardhan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.92333, "lon": -40.88944, "name": "Ibiapina" }, { "lat": -29.44806, "lon": -51.80639, "name": "Teutônia" }, { "lat": -15.74937, "lon": -47.7686, "name": "Itapoã" }, { "lat": -18.59222, "lon": -48.705, "name": "Tupaciguara" }, { "lat": 12.96095, "lon": 80.24094, "name": "Perungudi" } ], "question": "Which location is the geographic outlier among: Ibiapina, Teutônia, Itapoã, Tupaciguara, Perungudi?", "ground_truth": { "answer": "Perungudi", "outlier_distance_km": 11564.6, "second_furthest_km": 3727.9, "clarity_ratio": 3.1, "median_distance_km": 3012.3, "distances_to_centroid": { "Ibiapina": 2245.2, "Teutônia": 3727.9, "Itapoã": 2859.1, "Tupaciguara": 3012.3, "Perungudi": 11564.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ibiapina: (-3.92°, -40.89°)", " Teutônia: (-29.45°, -51.81°)", " Itapoã: (-15.75°, -47.77°)", " Tupaciguara: (-18.59°, -48.70°)", " Perungudi: (12.96°, 80.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Perungudi: 11564.6 km from centroid", " Teutônia: 3727.9 km from centroid", " Tupaciguara: 3012.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Perungudi", "FINAL ANSWER: Perungudi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" }, { "lat": -36.84103, "lon": 174.65223, "name": "Te Atatu Peninsula" }, { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" }, { "lat": -33.7511, "lon": 151.28886, "name": "Dee Why" }, { "lat": 6.919, "lon": 37.529, "name": "Bale Hawassa" } ], "question": "Which location is the geographic outlier among: Ashburton, Te Atatu Peninsula, Palmerston, Dee Why, Bale Hawassa?", "ground_truth": { "answer": "Bale Hawassa", "outlier_distance_km": 10897.3, "second_furthest_km": 4181.6, "clarity_ratio": 2.61, "median_distance_km": 4128.1, "distances_to_centroid": { "Ashburton": 4128.1, "Te Atatu Peninsula": 4181.6, "Palmerston": 1303.4, "Dee Why": 2059.6, "Bale Hawassa": 10897.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ashburton: (-43.90°, 171.73°)", " Te Atatu Peninsula: (-36.84°, 174.65°)", " Palmerston: (-12.49°, 130.98°)", " Dee Why: (-33.75°, 151.29°)", " Bale Hawassa: (6.92°, 37.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bale Hawassa: 10897.3 km from centroid", " Te Atatu Peninsula: 4181.6 km from centroid", " Ashburton: 4128.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bale Hawassa", "FINAL ANSWER: Bale Hawassa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.46056, "lon": -40.21222, "name": "Santana do Acaraú" }, { "lat": -26.76389, "lon": -48.67167, "name": "Balneário Piçarras" }, { "lat": -21.26083, "lon": -50.64278, "name": "Guararapes" }, { "lat": -7.17846, "lon": -38.78003, "name": "Barro" }, { "lat": 40.80788, "lon": -73.94542, "name": "Harlem" } ], "question": "Which location is the geographic outlier among: Santana do Acaraú, Balneário Piçarras, Guararapes, Barro, Harlem?", "ground_truth": { "answer": "Harlem", "outlier_distance_km": 5481.9, "second_furthest_km": 2585.9, "clarity_ratio": 2.12, "median_distance_km": 1967.1, "distances_to_centroid": { "Santana do Acaraú": 1136.4, "Balneário Piçarras": 2585.9, "Guararapes": 1967.1, "Barro": 1352.6, "Harlem": 5481.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santana do Acaraú: (-3.46°, -40.21°)", " Balneário Piçarras: (-26.76°, -48.67°)", " Guararapes: (-21.26°, -50.64°)", " Barro: (-7.18°, -38.78°)", " Harlem: (40.81°, -73.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Harlem: 5481.9 km from centroid", " Balneário Piçarras: 2585.9 km from centroid", " Guararapes: 1967.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Harlem", "FINAL ANSWER: Harlem" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.6377, "lon": 102.79138, "name": "Nang Rong" }, { "lat": 10.38706, "lon": 107.23884, "name": "Xã Long Hải" }, { "lat": 3.31667, "lon": 101.46667, "name": "Batu Arang" }, { "lat": 22.21983, "lon": 72.06755, "name": "Barwala" }, { "lat": 28.81082, "lon": -81.87786, "name": "Leesburg" } ], "question": "Which location is the geographic outlier among: Nang Rong, Xã Long Hải, Batu Arang, Barwala, Leesburg?", "ground_truth": { "answer": "Leesburg", "outlier_distance_km": 13598.4, "second_furthest_km": 5105.3, "clarity_ratio": 2.66, "median_distance_km": 4708.5, "distances_to_centroid": { "Nang Rong": 4548.7, "Xã Long Hải": 5105.3, "Batu Arang": 4708.5, "Barwala": 1419.6, "Leesburg": 13598.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nang Rong: (14.64°, 102.79°)", " Xã Long Hải: (10.39°, 107.24°)", " Batu Arang: (3.32°, 101.47°)", " Barwala: (22.22°, 72.07°)", " Leesburg: (28.81°, -81.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Leesburg: 13598.4 km from centroid", " Xã Long Hải: 5105.3 km from centroid", " Batu Arang: 4708.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Leesburg", "FINAL ANSWER: Leesburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 47.58113, "lon": 41.0934, "name": "Konstantinovsk" }, { "lat": 48.45755, "lon": 11.13413, "name": "Aichach" }, { "lat": 45.49185, "lon": 9.29812, "name": "Segrate" }, { "lat": 53.25, "lon": -1.41667, "name": "Chesterfield" }, { "lat": -25.54073, "lon": 152.70493, "name": "Maryborough" } ], "question": "Which location is the geographic outlier among: Konstantinovsk, Aichach, Segrate, Chesterfield, Maryborough?", "ground_truth": { "answer": "Maryborough", "outlier_distance_km": 13330.1, "second_furthest_km": 4058.5, "clarity_ratio": 3.28, "median_distance_km": 3098.8, "distances_to_centroid": { "Konstantinovsk": 1532.0, "Aichach": 3059.9, "Segrate": 3098.8, "Chesterfield": 4058.5, "Maryborough": 13330.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Konstantinovsk: (47.58°, 41.09°)", " Aichach: (48.46°, 11.13°)", " Segrate: (45.49°, 9.30°)", " Chesterfield: (53.25°, -1.42°)", " Maryborough: (-25.54°, 152.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maryborough: 13330.1 km from centroid", " Chesterfield: 4058.5 km from centroid", " Segrate: 3098.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maryborough", "FINAL ANSWER: Maryborough" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.79538, "lon": -1.66134, "name": "Pudsey" }, { "lat": 52.17655, "lon": 4.50885, "name": "Merenwijk" }, { "lat": 48.93196, "lon": 9.2024, "name": "Freiberg am Neckar" }, { "lat": 45.61128, "lon": 8.84914, "name": "Busto Arsizio" }, { "lat": -33.73333, "lon": 150.93284, "name": "Glenwood" } ], "question": "Which location is the geographic outlier among: Pudsey, Merenwijk, Freiberg am Neckar, Busto Arsizio, Glenwood?", "ground_truth": { "answer": "Glenwood", "outlier_distance_km": 14235.8, "second_furthest_km": 3622.3, "clarity_ratio": 3.93, "median_distance_km": 3172.6, "distances_to_centroid": { "Pudsey": 3622.3, "Merenwijk": 3172.6, "Freiberg am Neckar": 2705.2, "Busto Arsizio": 2562.1, "Glenwood": 14235.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pudsey: (53.80°, -1.66°)", " Merenwijk: (52.18°, 4.51°)", " Freiberg am Neckar: (48.93°, 9.20°)", " Busto Arsizio: (45.61°, 8.85°)", " Glenwood: (-33.73°, 150.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glenwood: 14235.8 km from centroid", " Pudsey: 3622.3 km from centroid", " Merenwijk: 3172.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glenwood", "FINAL ANSWER: Glenwood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.90973, "lon": 64.4319, "name": "Kurtamysh" }, { "lat": 60.1444, "lon": 30.20165, "name": "Sertolovo" }, { "lat": 49.42275, "lon": 10.95766, "name": "Oberasbach" }, { "lat": 56.6977, "lon": 60.8369, "name": "Aramil" }, { "lat": -33.91972, "lon": 151.07592, "name": "Lakemba" } ], "question": "Which location is the geographic outlier among: Kurtamysh, Sertolovo, Oberasbach, Aramil, Lakemba?", "ground_truth": { "answer": "Lakemba", "outlier_distance_km": 12025.4, "second_furthest_km": 4349.1, "clarity_ratio": 2.77, "median_distance_km": 3440.5, "distances_to_centroid": { "Kurtamysh": 1942.6, "Sertolovo": 3440.5, "Oberasbach": 4349.1, "Aramil": 2149.2, "Lakemba": 12025.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kurtamysh: (54.91°, 64.43°)", " Sertolovo: (60.14°, 30.20°)", " Oberasbach: (49.42°, 10.96°)", " Aramil: (56.70°, 60.84°)", " Lakemba: (-33.92°, 151.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lakemba: 12025.4 km from centroid", " Oberasbach: 4349.1 km from centroid", " Sertolovo: 3440.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lakemba", "FINAL ANSWER: Lakemba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8, "lon": 144.96667, "name": "Carlton" }, { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" }, { "lat": -37.78821, "lon": 175.2902, "name": "Hamilton East" }, { "lat": -27.54333, "lon": 153.20287, "name": "Capalaba" }, { "lat": 16.57831, "lon": 100.30034, "name": "Bang Krathum" } ], "question": "Which location is the geographic outlier among: Carlton, Lower Hutt, Hamilton East, Capalaba, Bang Krathum?", "ground_truth": { "answer": "Bang Krathum", "outlier_distance_km": 7110.4, "second_furthest_km": 2897.2, "clarity_ratio": 2.45, "median_distance_km": 2761.2, "distances_to_centroid": { "Carlton": 1433.9, "Lower Hutt": 2897.2, "Hamilton East": 2761.2, "Capalaba": 409.7, "Bang Krathum": 7110.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Carlton: (-37.80°, 144.97°)", " Lower Hutt: (-41.22°, 174.92°)", " Hamilton East: (-37.79°, 175.29°)", " Capalaba: (-27.54°, 153.20°)", " Bang Krathum: (16.58°, 100.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bang Krathum: 7110.4 km from centroid", " Lower Hutt: 2897.2 km from centroid", " Hamilton East: 2761.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bang Krathum", "FINAL ANSWER: Bang Krathum" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 32.75684, "lon": 130.79043, "name": "Shimada" }, { "lat": 35.24762, "lon": 136.97229, "name": "Kasugai" }, { "lat": 10.96251, "lon": 78.11324, "name": "Senapparetti" }, { "lat": 22.74759, "lon": 86.22573, "name": "Sarjamda" }, { "lat": -38.65333, "lon": 178.00417, "name": "Gisborne" } ], "question": "Which location is the geographic outlier among: Shimada, Kasugai, Senapparetti, Sarjamda, Gisborne?", "ground_truth": { "answer": "Gisborne", "outlier_distance_km": 8133.3, "second_furthest_km": 4777.5, "clarity_ratio": 1.7, "median_distance_km": 3944.3, "distances_to_centroid": { "Shimada": 2411.2, "Kasugai": 2931.5, "Senapparetti": 4777.5, "Sarjamda": 3944.3, "Gisborne": 8133.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shimada: (32.76°, 130.79°)", " Kasugai: (35.25°, 136.97°)", " Senapparetti: (10.96°, 78.11°)", " Sarjamda: (22.75°, 86.23°)", " Gisborne: (-38.65°, 178.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gisborne: 8133.3 km from centroid", " Senapparetti: 4777.5 km from centroid", " Sarjamda: 3944.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gisborne", "FINAL ANSWER: Gisborne" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.09917, "lon": -98.25417, "name": "Sanctorum" }, { "lat": 25.81201, "lon": -100.59874, "name": "García" }, { "lat": 41.36144, "lon": -81.81291, "name": "Middleburg Heights" }, { "lat": 17.4729, "lon": -91.4236, "name": "Tenosique" }, { "lat": 7.59054, "lon": -1.93947, "name": "Techiman" } ], "question": "Which location is the geographic outlier among: Sanctorum, García, Middleburg Heights, Tenosique, Techiman?", "ground_truth": { "answer": "Techiman", "outlier_distance_km": 7930.3, "second_furthest_km": 2644.4, "clarity_ratio": 3.0, "median_distance_km": 2462.0, "distances_to_centroid": { "Sanctorum": 2462.0, "García": 2644.4, "Middleburg Heights": 2222.0, "Tenosique": 1816.4, "Techiman": 7930.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sanctorum: (19.10°, -98.25°)", " García: (25.81°, -100.60°)", " Middleburg Heights: (41.36°, -81.81°)", " Tenosique: (17.47°, -91.42°)", " Techiman: (7.59°, -1.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Techiman: 7930.3 km from centroid", " García: 2644.4 km from centroid", " Sanctorum: 2462.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Techiman", "FINAL ANSWER: Techiman" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.88076, "lon": 27.39377, "name": "Qonce" }, { "lat": 7.81667, "lon": 4.91667, "name": "Oke Mesi" }, { "lat": 13.15611, "lon": 37.89806, "name": "Debark’" }, { "lat": -27.24179, "lon": 27.57422, "name": "Koppies" }, { "lat": 45.51564, "lon": -73.60865, "name": "Outremont" } ], "question": "Which location is the geographic outlier among: Qonce, Oke Mesi, Debark’, Koppies, Outremont?", "ground_truth": { "answer": "Outremont", "outlier_distance_km": 9008.3, "second_furthest_km": 4475.0, "clarity_ratio": 2.01, "median_distance_km": 3996.7, "distances_to_centroid": { "Qonce": 4475.0, "Oke Mesi": 727.7, "Debark’": 3872.0, "Koppies": 3996.7, "Outremont": 9008.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Qonce: (-32.88°, 27.39°)", " Oke Mesi: (7.82°, 4.92°)", " Debark’: (13.16°, 37.90°)", " Koppies: (-27.24°, 27.57°)", " Outremont: (45.52°, -73.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Outremont: 9008.3 km from centroid", " Qonce: 4475.0 km from centroid", " Koppies: 3996.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Outremont", "FINAL ANSWER: Outremont" ] }, { "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": -28.05, "lon": -56.03333, "name": "Gobernador Virasora" }, { "lat": -23.18639, "lon": -46.88417, "name": "Jundiaí" }, { "lat": -22.42861, "lon": -43.41861, "name": "Paty do Alferes" }, { "lat": -16.525, "lon": -50.37222, "name": "São Luís de Montes Belos" }, { "lat": 30.60427, "lon": 32.27225, "name": "Ismailia" } ], "question": "Which location is the geographic outlier among: Gobernador Virasora, Jundiaí, Paty do Alferes, São Luís de Montes Belos, Ismailia?", "ground_truth": { "answer": "Ismailia", "outlier_distance_km": 8406.6, "second_furthest_km": 3000.8, "clarity_ratio": 2.8, "median_distance_km": 1952.1, "distances_to_centroid": { "Gobernador Virasora": 3000.8, "Jundiaí": 1939.6, "Paty do Alferes": 1616.5, "São Luís de Montes Belos": 1952.1, "Ismailia": 8406.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gobernador Virasora: (-28.05°, -56.03°)", " Jundiaí: (-23.19°, -46.88°)", " Paty do Alferes: (-22.43°, -43.42°)", " São Luís de Montes Belos: (-16.52°, -50.37°)", " Ismailia: (30.60°, 32.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ismailia: 8406.6 km from centroid", " Gobernador Virasora: 3000.8 km from centroid", " São Luís de Montes Belos: 1952.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ismailia", "FINAL ANSWER: Ismailia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.03333, "lon": 145.3, "name": "Narre Warren" }, { "lat": -31.95224, "lon": 115.8614, "name": "Perth" }, { "lat": -25.54073, "lon": 152.70493, "name": "Maryborough" }, { "lat": -33.8, "lon": 151.18333, "name": "Chatswood" }, { "lat": -20.41667, "lon": -54.06667, "name": "Campo Verde" } ], "question": "Which location is the geographic outlier among: Narre Warren, Perth, Maryborough, Chatswood, Campo Verde?", "ground_truth": { "answer": "Campo Verde", "outlier_distance_km": 13865.4, "second_furthest_km": 4955.5, "clarity_ratio": 2.8, "median_distance_km": 4602.4, "distances_to_centroid": { "Narre Warren": 4037.0, "Perth": 1321.1, "Maryborough": 4955.5, "Chatswood": 4602.4, "Campo Verde": 13865.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Narre Warren: (-38.03°, 145.30°)", " Perth: (-31.95°, 115.86°)", " Maryborough: (-25.54°, 152.70°)", " Chatswood: (-33.80°, 151.18°)", " Campo Verde: (-20.42°, -54.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Campo Verde: 13865.4 km from centroid", " Maryborough: 4955.5 km from centroid", " Chatswood: 4602.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Campo Verde", "FINAL ANSWER: Campo Verde" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.71671, "lon": -52.50321, "name": "Vera Cruz" }, { "lat": -27.25806, "lon": -49.93389, "name": "Pouso Redondo" }, { "lat": 9.24194, "lon": -74.42667, "name": "Mompós" }, { "lat": -3.56222, "lon": -41.09222, "name": "Viçosa do Ceará" }, { "lat": 33.96173, "lon": -116.50353, "name": "Desert Hot Springs" } ], "question": "Which location is the geographic outlier among: Vera Cruz, Pouso Redondo, Mompós, Viçosa do Ceará, Desert Hot Springs?", "ground_truth": { "answer": "Desert Hot Springs", "outlier_distance_km": 6652.1, "second_furthest_km": 3289.0, "clarity_ratio": 2.02, "median_distance_km": 3200.7, "distances_to_centroid": { "Vera Cruz": 3289.0, "Pouso Redondo": 3200.7, "Mompós": 1641.4, "Viçosa do Ceará": 2863.3, "Desert Hot Springs": 6652.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vera Cruz: (-29.72°, -52.50°)", " Pouso Redondo: (-27.26°, -49.93°)", " Mompós: (9.24°, -74.43°)", " Viçosa do Ceará: (-3.56°, -41.09°)", " Desert Hot Springs: (33.96°, -116.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Desert Hot Springs: 6652.1 km from centroid", " Vera Cruz: 3289.0 km from centroid", " Pouso Redondo: 3200.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Desert Hot Springs", "FINAL ANSWER: Desert Hot Springs" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -6.8694, "lon": 109.1402, "name": "Tegal" }, { "lat": 34.33611, "lon": 117.56667, "name": "Tashan" }, { "lat": 6.11278, "lon": 125.17167, "name": "General Santos" }, { "lat": 20.33025, "lon": 110.16643, "name": "Xucheng" }, { "lat": 46.3168, "lon": -79.46633, "name": "North Bay" } ], "question": "Which location is the geographic outlier among: Tegal, Tashan, General Santos, Xucheng, North Bay?", "ground_truth": { "answer": "North Bay", "outlier_distance_km": 12250.1, "second_furthest_km": 5469.8, "clarity_ratio": 2.24, "median_distance_km": 4657.0, "distances_to_centroid": { "Tegal": 4657.0, "Tashan": 4324.6, "General Santos": 5469.8, "Xucheng": 3505.9, "North Bay": 12250.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tegal: (-6.87°, 109.14°)", " Tashan: (34.34°, 117.57°)", " General Santos: (6.11°, 125.17°)", " Xucheng: (20.33°, 110.17°)", " North Bay: (46.32°, -79.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Bay: 12250.1 km from centroid", " General Santos: 5469.8 km from centroid", " Tegal: 4657.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Bay", "FINAL ANSWER: North Bay" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.79798, "lon": 144.94512, "name": "North Melbourne" }, { "lat": -33.7511, "lon": 151.28886, "name": "Dee Why" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": -33.95222, "lon": 150.89949, "name": "Casula" }, { "lat": 40.9351, "lon": -74.01903, "name": "New Milford" } ], "question": "Which location is the geographic outlier among: North Melbourne, Dee Why, Taylors Lakes, Casula, New Milford?", "ground_truth": { "answer": "New Milford", "outlier_distance_km": 17726.3, "second_furthest_km": 4901.5, "clarity_ratio": 3.62, "median_distance_km": 4867.7, "distances_to_centroid": { "North Melbourne": 4410.3, "Dee Why": 4901.5, "Taylors Lakes": 4394.0, "Casula": 4867.7, "New Milford": 17726.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " North Melbourne: (-37.80°, 144.95°)", " Dee Why: (-33.75°, 151.29°)", " Taylors Lakes: (-37.70°, 144.79°)", " Casula: (-33.95°, 150.90°)", " New Milford: (40.94°, -74.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New Milford: 17726.3 km from centroid", " Dee Why: 4901.5 km from centroid", " Casula: 4867.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New Milford", "FINAL ANSWER: New Milford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.55808, "lon": 133.41796, "name": "Kannabechō-yahiro" }, { "lat": 39.74318, "lon": 98.51736, "name": "Jiuquan" }, { "lat": 11.28333, "lon": 106.13333, "name": "Phú Khương" }, { "lat": 26.64661, "lon": 77.61634, "name": "Bāri" }, { "lat": 41.71427, "lon": -72.65259, "name": "Wethersfield" } ], "question": "Which location is the geographic outlier among: Kannabechō-yahiro, Jiuquan, Phú Khương, Bāri, Wethersfield?", "ground_truth": { "answer": "Wethersfield", "outlier_distance_km": 11028.5, "second_furthest_km": 5975.5, "clarity_ratio": 1.85, "median_distance_km": 4425.6, "distances_to_centroid": { "Kannabechō-yahiro": 5975.5, "Jiuquan": 2876.0, "Phú Khương": 4425.6, "Bāri": 991.5, "Wethersfield": 11028.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kannabechō-yahiro: (34.56°, 133.42°)", " Jiuquan: (39.74°, 98.52°)", " Phú Khương: (11.28°, 106.13°)", " Bāri: (26.65°, 77.62°)", " Wethersfield: (41.71°, -72.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wethersfield: 11028.5 km from centroid", " Kannabechō-yahiro: 5975.5 km from centroid", " Phú Khương: 4425.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wethersfield", "FINAL ANSWER: Wethersfield" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.62907, "lon": -0.74934, "name": "High Wycombe" }, { "lat": 38.11631, "lon": -1.30043, "name": "Archena" }, { "lat": 58.28731, "lon": 59.74751, "name": "Kushva" }, { "lat": 40.73757, "lon": 13.86003, "name": "Forio" }, { "lat": 21.27307, "lon": 106.1946, "name": "Bắc Giang" } ], "question": "Which location is the geographic outlier among: High Wycombe, Archena, Kushva, Forio, Bắc Giang?", "ground_truth": { "answer": "Bắc Giang", "outlier_distance_km": 6873.7, "second_furthest_km": 3141.3, "clarity_ratio": 2.19, "median_distance_km": 2925.3, "distances_to_centroid": { "High Wycombe": 2925.3, "Archena": 3141.3, "Kushva": 2473.2, "Forio": 1810.6, "Bắc Giang": 6873.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " High Wycombe: (51.63°, -0.75°)", " Archena: (38.12°, -1.30°)", " Kushva: (58.29°, 59.75°)", " Forio: (40.74°, 13.86°)", " Bắc Giang: (21.27°, 106.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bắc Giang: 6873.7 km from centroid", " Archena: 3141.3 km from centroid", " High Wycombe: 2925.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bắc Giang", "FINAL ANSWER: Bắc Giang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -24.4875, "lon": -47.84361, "name": "Registro" }, { "lat": 6.96321, "lon": -75.41738, "name": "Yarumal" }, { "lat": -3.6, "lon": -39.43333, "name": "Turaru" }, { "lat": -21.99861, "lon": -49.45722, "name": "Pirajuí" }, { "lat": -7.72639, "lon": 109.00944, "name": "Cilacap" } ], "question": "Which location is the geographic outlier among: Registro, Yarumal, Turaru, Pirajuí, Cilacap?", "ground_truth": { "answer": "Cilacap", "outlier_distance_km": 14095.1, "second_furthest_km": 6358.6, "clarity_ratio": 2.22, "median_distance_km": 3340.5, "distances_to_centroid": { "Registro": 3287.8, "Yarumal": 6358.6, "Turaru": 2199.5, "Pirajuí": 3340.5, "Cilacap": 14095.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Registro: (-24.49°, -47.84°)", " Yarumal: (6.96°, -75.42°)", " Turaru: (-3.60°, -39.43°)", " Pirajuí: (-22.00°, -49.46°)", " Cilacap: (-7.73°, 109.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cilacap: 14095.1 km from centroid", " Yarumal: 6358.6 km from centroid", " Pirajuí: 3340.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cilacap", "FINAL ANSWER: Cilacap" ] }, { "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": -11.42047, "lon": -58.75488, "name": "Juína" }, { "lat": -7.87472, "lon": -35.45028, "name": "Limoeiro" }, { "lat": -25.73271, "lon": -59.10989, "name": "Pirané" }, { "lat": -16.06583, "lon": -47.97861, "name": "Valparaíso de Goiás" }, { "lat": 6.86472, "lon": 124.44167, "name": "Maganoy" } ], "question": "Which location is the geographic outlier among: Juína, Limoeiro, Pirané, Valparaíso de Goiás, Maganoy?", "ground_truth": { "answer": "Maganoy", "outlier_distance_km": 15580.7, "second_furthest_km": 4878.1, "clarity_ratio": 3.19, "median_distance_km": 4729.3, "distances_to_centroid": { "Juína": 4729.3, "Limoeiro": 2227.1, "Pirané": 4878.1, "Valparaíso de Goiás": 3569.7, "Maganoy": 15580.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Juína: (-11.42°, -58.75°)", " Limoeiro: (-7.87°, -35.45°)", " Pirané: (-25.73°, -59.11°)", " Valparaíso de Goiás: (-16.07°, -47.98°)", " Maganoy: (6.86°, 124.44°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maganoy: 15580.7 km from centroid", " Pirané: 4878.1 km from centroid", " Juína: 4729.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maganoy", "FINAL ANSWER: Maganoy" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": -33.73333, "lon": 150.88333, "name": "Quakers Hill" }, { "lat": -27.59521, "lon": 153.12332, "name": "Rochedale South" }, { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" }, { "lat": -23.54476, "lon": -46.64105, "name": "Republica" } ], "question": "Which location is the geographic outlier among: Taylors Lakes, Quakers Hill, Rochedale South, Dianella, Republica?", "ground_truth": { "answer": "Republica", "outlier_distance_km": 13181.9, "second_furthest_km": 4779.5, "clarity_ratio": 2.76, "median_distance_km": 4415.6, "distances_to_centroid": { "Taylors Lakes": 3826.5, "Quakers Hill": 4415.6, "Rochedale South": 4779.5, "Dianella": 1169.0, "Republica": 13181.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taylors Lakes: (-37.70°, 144.79°)", " Quakers Hill: (-33.73°, 150.88°)", " Rochedale South: (-27.60°, 153.12°)", " Dianella: (-31.89°, 115.87°)", " Republica: (-23.54°, -46.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Republica: 13181.9 km from centroid", " Rochedale South: 4779.5 km from centroid", " Quakers Hill: 4415.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Republica", "FINAL ANSWER: Republica" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.40477, "lon": -81.72291, "name": "Parma" }, { "lat": 41.52364, "lon": -90.57764, "name": "Davenport" }, { "lat": 44.46699, "lon": -73.17096, "name": "South Burlington" }, { "lat": 30.4013, "lon": -91.00094, "name": "Shenandoah" }, { "lat": 38.71528, "lon": 112.7575, "name": "Yuanping" } ], "question": "Which location is the geographic outlier among: Parma, Davenport, South Burlington, Shenandoah, Yuanping?", "ground_truth": { "answer": "Yuanping", "outlier_distance_km": 11042.0, "second_furthest_km": 4287.2, "clarity_ratio": 2.58, "median_distance_km": 3842.7, "distances_to_centroid": { "Parma": 3118.5, "Davenport": 3842.7, "South Burlington": 2409.2, "Shenandoah": 4287.2, "Yuanping": 11042.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parma: (41.40°, -81.72°)", " Davenport: (41.52°, -90.58°)", " South Burlington: (44.47°, -73.17°)", " Shenandoah: (30.40°, -91.00°)", " Yuanping: (38.72°, 112.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yuanping: 11042.0 km from centroid", " Shenandoah: 4287.2 km from centroid", " Davenport: 3842.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yuanping", "FINAL ANSWER: Yuanping" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.50321, "lon": 73.47242, "name": "Hālol" }, { "lat": 52.32148, "lon": 124.69761, "name": "Tahe" }, { "lat": 3.11898, "lon": 101.58656, "name": "Ara Damansara" }, { "lat": 1.45768, "lon": 103.64554, "name": "Horizon Hills" }, { "lat": -7.59111, "lon": -35.49139, "name": "São Vicente Férrer" } ], "question": "Which location is the geographic outlier among: Hālol, Tahe, Ara Damansara, Horizon Hills, São Vicente Férrer?", "ground_truth": { "answer": "São Vicente Férrer", "outlier_distance_km": 12262.3, "second_furthest_km": 6158.8, "clarity_ratio": 1.99, "median_distance_km": 3601.1, "distances_to_centroid": { "Hālol": 905.3, "Tahe": 6158.8, "Ara Damansara": 3316.4, "Horizon Hills": 3601.1, "São Vicente Férrer": 12262.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hālol: (22.50°, 73.47°)", " Tahe: (52.32°, 124.70°)", " Ara Damansara: (3.12°, 101.59°)", " Horizon Hills: (1.46°, 103.65°)", " São Vicente Férrer: (-7.59°, -35.49°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Vicente Férrer: 12262.3 km from centroid", " Tahe: 6158.8 km from centroid", " Horizon Hills: 3601.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Vicente Férrer", "FINAL ANSWER: São Vicente Férrer" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.83333, "lon": 145.05, "name": "Glenferrie" }, { "lat": -37.70462, "lon": 145.10302, "name": "Greensborough" }, { "lat": -39.93333, "lon": 175.05, "name": "Whanganui" }, { "lat": -33.92399, "lon": 151.22749, "name": "Kingsford" }, { "lat": -11.94194, "lon": -38.08444, "name": "Entre Rios" } ], "question": "Which location is the geographic outlier among: Glenferrie, Greensborough, Whanganui, Kingsford, Entre Rios?", "ground_truth": { "answer": "Entre Rios", "outlier_distance_km": 14362.1, "second_furthest_km": 5304.7, "clarity_ratio": 2.71, "median_distance_km": 3301.0, "distances_to_centroid": { "Glenferrie": 2733.1, "Greensborough": 2736.7, "Whanganui": 5304.7, "Kingsford": 3301.0, "Entre Rios": 14362.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Glenferrie: (-37.83°, 145.05°)", " Greensborough: (-37.70°, 145.10°)", " Whanganui: (-39.93°, 175.05°)", " Kingsford: (-33.92°, 151.23°)", " Entre Rios: (-11.94°, -38.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Entre Rios: 14362.1 km from centroid", " Whanganui: 5304.7 km from centroid", " Kingsford: 3301.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Entre Rios", "FINAL ANSWER: Entre Rios" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.95334, "lon": -77.36598, "name": "Pizarro" }, { "lat": -11.51917, "lon": -37.51167, "name": "Indiaroba" }, { "lat": -20.32972, "lon": -40.2925, "name": "Vila Velha" }, { "lat": -21.41222, "lon": -42.19667, "name": "Miracema" }, { "lat": 53.72947, "lon": -1.49697, "name": "Lofthouse" } ], "question": "Which location is the geographic outlier among: Pizarro, Indiaroba, Vila Velha, Miracema, Lofthouse?", "ground_truth": { "answer": "Lofthouse", "outlier_distance_km": 6820.8, "second_furthest_km": 4195.5, "clarity_ratio": 1.63, "median_distance_km": 2515.3, "distances_to_centroid": { "Pizarro": 4195.5, "Indiaroba": 1423.5, "Vila Velha": 2381.8, "Miracema": 2515.3, "Lofthouse": 6820.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pizarro: (4.95°, -77.37°)", " Indiaroba: (-11.52°, -37.51°)", " Vila Velha: (-20.33°, -40.29°)", " Miracema: (-21.41°, -42.20°)", " Lofthouse: (53.73°, -1.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lofthouse: 6820.8 km from centroid", " Pizarro: 4195.5 km from centroid", " Miracema: 2515.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lofthouse", "FINAL ANSWER: Lofthouse" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.36006, "lon": 72.93106, "name": "Vapi INA" }, { "lat": 10.78303, "lon": 76.33358, "name": "Vāniyamkulam" }, { "lat": 26.4835, "lon": 89.52286, "name": "Alīpur Duār" }, { "lat": 22.10833, "lon": 88.07889, "name": "Monoharpur" }, { "lat": 11.11128, "lon": 7.7227, "name": "Zaria" } ], "question": "Which location is the geographic outlier among: Vapi INA, Vāniyamkulam, Alīpur Duār, Monoharpur, Zaria?", "ground_truth": { "answer": "Zaria", "outlier_distance_km": 6391.8, "second_furthest_km": 2497.3, "clarity_ratio": 2.56, "median_distance_km": 2250.1, "distances_to_centroid": { "Vapi INA": 676.5, "Vāniyamkulam": 1304.0, "Alīpur Duār": 2497.3, "Monoharpur": 2250.1, "Zaria": 6391.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vapi INA: (20.36°, 72.93°)", " Vāniyamkulam: (10.78°, 76.33°)", " Alīpur Duār: (26.48°, 89.52°)", " Monoharpur: (22.11°, 88.08°)", " Zaria: (11.11°, 7.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zaria: 6391.8 km from centroid", " Alīpur Duār: 2497.3 km from centroid", " Monoharpur: 2250.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zaria", "FINAL ANSWER: Zaria" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.43278, "lon": 116.59111, "name": "Tangzhai" }, { "lat": -3.33984, "lon": 128.91975, "name": "Amahai" }, { "lat": 5.02298, "lon": 118.32897, "name": "Lahad Datu" }, { "lat": 26.38441, "lon": 73.54394, "name": "Pīpār" }, { "lat": 8.13373, "lon": 4.24014, "name": "Ogbomoso" } ], "question": "Which location is the geographic outlier among: Tangzhai, Amahai, Lahad Datu, Pīpār, Ogbomoso?", "ground_truth": { "answer": "Ogbomoso", "outlier_distance_km": 9154.7, "second_furthest_km": 4878.3, "clarity_ratio": 1.88, "median_distance_km": 3624.7, "distances_to_centroid": { "Tangzhai": 3624.7, "Amahai": 4878.3, "Lahad Datu": 3437.4, "Pīpār": 2054.5, "Ogbomoso": 9154.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tangzhai: (34.43°, 116.59°)", " Amahai: (-3.34°, 128.92°)", " Lahad Datu: (5.02°, 118.33°)", " Pīpār: (26.38°, 73.54°)", " Ogbomoso: (8.13°, 4.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ogbomoso: 9154.7 km from centroid", " Amahai: 4878.3 km from centroid", " Tangzhai: 3624.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ogbomoso", "FINAL ANSWER: Ogbomoso" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 8.4541, "lon": 39.21752, "name": "Wonji" }, { "lat": -33.57565, "lon": 22.44391, "name": "Dysselsdorp" }, { "lat": 10.52726, "lon": -0.36982, "name": "Nalerigu" }, { "lat": -30.69366, "lon": 26.71141, "name": "Aliwal North" }, { "lat": 34.02893, "lon": -84.19858, "name": "Johns Creek" } ], "question": "Which location is the geographic outlier among: Wonji, Dysselsdorp, Nalerigu, Aliwal North, Johns Creek?", "ground_truth": { "answer": "Johns Creek", "outlier_distance_km": 9683.9, "second_furthest_km": 4426.4, "clarity_ratio": 2.19, "median_distance_km": 4177.0, "distances_to_centroid": { "Wonji": 4426.4, "Dysselsdorp": 4149.0, "Nalerigu": 1426.5, "Aliwal North": 4177.0, "Johns Creek": 9683.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wonji: (8.45°, 39.22°)", " Dysselsdorp: (-33.58°, 22.44°)", " Nalerigu: (10.53°, -0.37°)", " Aliwal North: (-30.69°, 26.71°)", " Johns Creek: (34.03°, -84.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Johns Creek: 9683.9 km from centroid", " Wonji: 4426.4 km from centroid", " Aliwal North: 4177.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Johns Creek", "FINAL ANSWER: Johns Creek" ] }, { "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": 20.0409, "lon": 77.31501, "name": "Anshing" }, { "lat": 25.43745, "lon": 81.9055, "name": "Jhūsi" }, { "lat": 13.84725, "lon": 100.56373, "name": "Lat Yao" }, { "lat": 17.98372, "lon": 100.05217, "name": "Den Chai" }, { "lat": 5.55728, "lon": -0.1864, "name": "Osu" } ], "question": "Which location is the geographic outlier among: Anshing, Jhūsi, Lat Yao, Den Chai, Osu?", "ground_truth": { "answer": "Osu", "outlier_distance_km": 7928.5, "second_furthest_km": 3084.7, "clarity_ratio": 2.57, "median_distance_km": 2987.2, "distances_to_centroid": { "Anshing": 686.8, "Jhūsi": 1428.4, "Lat Yao": 3084.7, "Den Chai": 2987.2, "Osu": 7928.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Anshing: (20.04°, 77.32°)", " Jhūsi: (25.44°, 81.91°)", " Lat Yao: (13.85°, 100.56°)", " Den Chai: (17.98°, 100.05°)", " Osu: (5.56°, -0.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Osu: 7928.5 km from centroid", " Lat Yao: 3084.7 km from centroid", " Den Chai: 2987.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Osu", "FINAL ANSWER: Osu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.75083, "lon": -87.71453, "name": "Sheboygan" }, { "lat": 33.61309, "lon": -112.3246, "name": "El Mirage" }, { "lat": 40.75448, "lon": -86.35667, "name": "Logansport" }, { "lat": 49.81667, "lon": -119.48333, "name": "Okanagan Mission" }, { "lat": -30.74137, "lon": 30.45499, "name": "Port Shepstone" } ], "question": "Which location is the geographic outlier among: Sheboygan, El Mirage, Logansport, Okanagan Mission, Port Shepstone?", "ground_truth": { "answer": "Port Shepstone", "outlier_distance_km": 12909.5, "second_furthest_km": 4495.6, "clarity_ratio": 2.87, "median_distance_km": 3612.5, "distances_to_centroid": { "Sheboygan": 2137.7, "El Mirage": 3612.5, "Logansport": 1804.7, "Okanagan Mission": 4495.6, "Port Shepstone": 12909.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sheboygan: (43.75°, -87.71°)", " El Mirage: (33.61°, -112.32°)", " Logansport: (40.75°, -86.36°)", " Okanagan Mission: (49.82°, -119.48°)", " Port Shepstone: (-30.74°, 30.45°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Port Shepstone: 12909.5 km from centroid", " Okanagan Mission: 4495.6 km from centroid", " El Mirage: 3612.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Port Shepstone", "FINAL ANSWER: Port Shepstone" ] }, { "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": -38.14458, "lon": 145.12291, "name": "Frankston" }, { "lat": -38.15912, "lon": 145.93118, "name": "Warragul" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" }, { "lat": 40.5783, "lon": -4.00426, "name": "Galapagar" } ], "question": "Which location is the geographic outlier among: Frankston, Warragul, Melbourne City Centre, Bracken Ridge, Galapagar?", "ground_truth": { "answer": "Galapagar", "outlier_distance_km": 14041.0, "second_furthest_km": 3737.9, "clarity_ratio": 3.76, "median_distance_km": 3423.4, "distances_to_centroid": { "Frankston": 3360.2, "Warragul": 3423.4, "Melbourne City Centre": 3330.8, "Bracken Ridge": 3737.9, "Galapagar": 14041.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Frankston: (-38.14°, 145.12°)", " Warragul: (-38.16°, 145.93°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Bracken Ridge: (-27.32°, 153.03°)", " Galapagar: (40.58°, -4.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Galapagar: 14041.0 km from centroid", " Bracken Ridge: 3737.9 km from centroid", " Warragul: 3423.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Galapagar", "FINAL ANSWER: Galapagar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.03449, "lon": 16.98963, "name": "Noicattaro" }, { "lat": 44.77002, "lon": 39.87246, "name": "Belorechensk" }, { "lat": 52.225, "lon": 4.52222, "name": "Sassenheim" }, { "lat": 45.09228, "lon": 7.69399, "name": "Barriera di Milano" }, { "lat": -23.88782, "lon": 30.28708, "name": "Nkowakowa" } ], "question": "Which location is the geographic outlier among: Noicattaro, Belorechensk, Sassenheim, Barriera di Milano, Nkowakowa?", "ground_truth": { "answer": "Nkowakowa", "outlier_distance_km": 6295.5, "second_furthest_km": 2584.3, "clarity_ratio": 2.44, "median_distance_km": 2249.6, "distances_to_centroid": { "Noicattaro": 1053.5, "Belorechensk": 2249.6, "Sassenheim": 2584.3, "Barriera di Milano": 1810.3, "Nkowakowa": 6295.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Noicattaro: (41.03°, 16.99°)", " Belorechensk: (44.77°, 39.87°)", " Sassenheim: (52.23°, 4.52°)", " Barriera di Milano: (45.09°, 7.69°)", " Nkowakowa: (-23.89°, 30.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nkowakowa: 6295.5 km from centroid", " Sassenheim: 2584.3 km from centroid", " Belorechensk: 2249.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nkowakowa", "FINAL ANSWER: Nkowakowa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 17.73308, "lon": 83.31622, "name": "Rasapūdipalem" }, { "lat": 3.7755, "lon": 98.6832, "name": "Belawan" }, { "lat": 15.37794, "lon": 73.90352, "name": "Sancoale" }, { "lat": 21.11667, "lon": 105.86667, "name": "Cổ Lóa" }, { "lat": -33.91972, "lon": 151.07592, "name": "Lakemba" } ], "question": "Which location is the geographic outlier among: Rasapūdipalem, Belawan, Sancoale, Cổ Lóa, Lakemba?", "ground_truth": { "answer": "Lakemba", "outlier_distance_km": 6664.5, "second_furthest_km": 3345.1, "clarity_ratio": 1.99, "median_distance_km": 2539.3, "distances_to_centroid": { "Rasapūdipalem": 2539.3, "Belawan": 446.2, "Sancoale": 3345.1, "Cổ Lóa": 1847.1, "Lakemba": 6664.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rasapūdipalem: (17.73°, 83.32°)", " Belawan: (3.78°, 98.68°)", " Sancoale: (15.38°, 73.90°)", " Cổ Lóa: (21.12°, 105.87°)", " Lakemba: (-33.92°, 151.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lakemba: 6664.5 km from centroid", " Sancoale: 3345.1 km from centroid", " Rasapūdipalem: 2539.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lakemba", "FINAL ANSWER: Lakemba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.28333, "lon": -71.96667, "name": "Villanueva" }, { "lat": -21.67861, "lon": -49.7425, "name": "Lins" }, { "lat": -12.83333, "lon": -39.1, "name": "Sobradinho" }, { "lat": -20.02745, "lon": -40.74336, "name": "Santa Maria de Jetibá" }, { "lat": -33.88096, "lon": 151.07986, "name": "Strathfield" } ], "question": "Which location is the geographic outlier among: Villanueva, Lins, Sobradinho, Santa Maria de Jetibá, Strathfield?", "ground_truth": { "answer": "Strathfield", "outlier_distance_km": 14055.0, "second_furthest_km": 7221.8, "clarity_ratio": 1.95, "median_distance_km": 4191.2, "distances_to_centroid": { "Villanueva": 7221.8, "Lins": 4191.2, "Sobradinho": 3144.8, "Santa Maria de Jetibá": 3252.6, "Strathfield": 14055.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Villanueva: (5.28°, -71.97°)", " Lins: (-21.68°, -49.74°)", " Sobradinho: (-12.83°, -39.10°)", " Santa Maria de Jetibá: (-20.03°, -40.74°)", " Strathfield: (-33.88°, 151.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Strathfield: 14055.0 km from centroid", " Villanueva: 7221.8 km from centroid", " Lins: 4191.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Strathfield", "FINAL ANSWER: Strathfield" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 7.81667, "lon": 4.91667, "name": "Oke Mesi" }, { "lat": 30.06263, "lon": 31.24967, "name": "Cairo" }, { "lat": -26.37945, "lon": 28.92112, "name": "Lebohang" }, { "lat": 8.85299, "lon": 5.41641, "name": "Lafiagi" }, { "lat": -28.00029, "lon": 153.43088, "name": "Gold Coast" } ], "question": "Which location is the geographic outlier among: Oke Mesi, Cairo, Lebohang, Lafiagi, Gold Coast?", "ground_truth": { "answer": "Gold Coast", "outlier_distance_km": 11746.9, "second_furthest_km": 4541.9, "clarity_ratio": 2.59, "median_distance_km": 4512.6, "distances_to_centroid": { "Oke Mesi": 4541.9, "Cairo": 3795.1, "Lebohang": 3242.0, "Lafiagi": 4512.6, "Gold Coast": 11746.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Oke Mesi: (7.82°, 4.92°)", " Cairo: (30.06°, 31.25°)", " Lebohang: (-26.38°, 28.92°)", " Lafiagi: (8.85°, 5.42°)", " Gold Coast: (-28.00°, 153.43°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gold Coast: 11746.9 km from centroid", " Oke Mesi: 4541.9 km from centroid", " Lafiagi: 4512.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gold Coast", "FINAL ANSWER: Gold Coast" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.84048, "lon": 10.95198, "name": "Arnstadt" }, { "lat": 51.06098, "lon": 0.16342, "name": "Crowborough" }, { "lat": 55.92721, "lon": 39.46072, "name": "Petushki" }, { "lat": 44.05, "lon": 43.05036, "name": "Pyatigorsk" }, { "lat": -8.35778, "lon": -36.69639, "name": "Pesqueira" } ], "question": "Which location is the geographic outlier among: Arnstadt, Crowborough, Petushki, Pyatigorsk, Pesqueira?", "ground_truth": { "answer": "Pesqueira", "outlier_distance_km": 7211.5, "second_furthest_km": 2818.7, "clarity_ratio": 2.56, "median_distance_km": 2690.4, "distances_to_centroid": { "Arnstadt": 1349.9, "Crowborough": 1629.8, "Petushki": 2818.7, "Pyatigorsk": 2690.4, "Pesqueira": 7211.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Arnstadt: (50.84°, 10.95°)", " Crowborough: (51.06°, 0.16°)", " Petushki: (55.93°, 39.46°)", " Pyatigorsk: (44.05°, 43.05°)", " Pesqueira: (-8.36°, -36.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pesqueira: 7211.5 km from centroid", " Petushki: 2818.7 km from centroid", " Pyatigorsk: 2690.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pesqueira", "FINAL ANSWER: Pesqueira" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.16297, "lon": 132.22, "name": "Iwakuni" }, { "lat": 25.1543, "lon": 73.08157, "name": "Sumerpur" }, { "lat": 23.54109, "lon": 74.4425, "name": "Bānswāra" }, { "lat": 26.61667, "lon": 101.27154, "name": "Zhongxin" }, { "lat": -43.58333, "lon": 172.38333, "name": "Rolleston" } ], "question": "Which location is the geographic outlier among: Iwakuni, Sumerpur, Bānswāra, Zhongxin, Rolleston?", "ground_truth": { "answer": "Rolleston", "outlier_distance_km": 8872.9, "second_furthest_km": 4150.5, "clarity_ratio": 2.14, "median_distance_km": 3981.1, "distances_to_centroid": { "Iwakuni": 3187.8, "Sumerpur": 4150.5, "Bānswāra": 3981.1, "Zhongxin": 1787.2, "Rolleston": 8872.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Iwakuni: (34.16°, 132.22°)", " Sumerpur: (25.15°, 73.08°)", " Bānswāra: (23.54°, 74.44°)", " Zhongxin: (26.62°, 101.27°)", " Rolleston: (-43.58°, 172.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rolleston: 8872.9 km from centroid", " Sumerpur: 4150.5 km from centroid", " Bānswāra: 3981.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rolleston", "FINAL ANSWER: Rolleston" ] }, { "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": -27.61025, "lon": 153.05388, "name": "Sunnybank Hills" }, { "lat": -33.75881, "lon": 150.99292, "name": "Baulkham Hills" }, { "lat": -33.83902, "lon": 151.23956, "name": "Mosman" }, { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" }, { "lat": 5.01789, "lon": -72.74675, "name": "Tauramena" } ], "question": "Which location is the geographic outlier among: Sunnybank Hills, Baulkham Hills, Mosman, Saint Albans, Tauramena?", "ground_truth": { "answer": "Tauramena", "outlier_distance_km": 17720.3, "second_furthest_km": 4707.5, "clarity_ratio": 3.76, "median_distance_km": 4477.6, "distances_to_centroid": { "Sunnybank Hills": 4707.5, "Baulkham Hills": 4454.9, "Mosman": 4477.6, "Saint Albans": 3926.4, "Tauramena": 17720.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunnybank Hills: (-27.61°, 153.05°)", " Baulkham Hills: (-33.76°, 150.99°)", " Mosman: (-33.84°, 151.24°)", " Saint Albans: (-37.73°, 144.80°)", " Tauramena: (5.02°, -72.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tauramena: 17720.3 km from centroid", " Sunnybank Hills: 4707.5 km from centroid", " Mosman: 4477.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tauramena", "FINAL ANSWER: Tauramena" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 21.01667, "lon": 107.3, "name": "Cẩm Phả Mines" }, { "lat": 31.68137, "lon": 75.63549, "name": "Urmar" }, { "lat": 26.43903, "lon": 99.44061, "name": "Jinding" }, { "lat": 4.4683, "lon": 97.9683, "name": "Langsa" }, { "lat": -23.56439, "lon": -46.61695, "name": "Cambuci" } ], "question": "Which location is the geographic outlier among: Cẩm Phả Mines, Urmar, Jinding, Langsa, Cambuci?", "ground_truth": { "answer": "Cambuci", "outlier_distance_km": 12900.9, "second_furthest_km": 4425.0, "clarity_ratio": 2.92, "median_distance_km": 3773.3, "distances_to_centroid": { "Cẩm Phả Mines": 4425.0, "Urmar": 2369.5, "Jinding": 3773.3, "Langsa": 3533.3, "Cambuci": 12900.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cẩm Phả Mines: (21.02°, 107.30°)", " Urmar: (31.68°, 75.64°)", " Jinding: (26.44°, 99.44°)", " Langsa: (4.47°, 97.97°)", " Cambuci: (-23.56°, -46.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cambuci: 12900.9 km from centroid", " Cẩm Phả Mines: 4425.0 km from centroid", " Jinding: 3773.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cambuci", "FINAL ANSWER: Cambuci" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.25, "lon": -123.06667, "name": "Kensington-Cedar Cottage" }, { "lat": 26.19063, "lon": -97.6961, "name": "Harlingen" }, { "lat": 40.48643, "lon": -86.1336, "name": "Kokomo" }, { "lat": 41.05899, "lon": -74.02181, "name": "Pearl River" }, { "lat": 52.11457, "lon": 8.67343, "name": "Herford" } ], "question": "Which location is the geographic outlier among: Kensington-Cedar Cottage, Harlingen, Kokomo, Pearl River, Herford?", "ground_truth": { "answer": "Herford", "outlier_distance_km": 6057.3, "second_furthest_km": 3806.8, "clarity_ratio": 1.59, "median_distance_km": 2743.1, "distances_to_centroid": { "Kensington-Cedar Cottage": 3806.8, "Harlingen": 2743.1, "Kokomo": 988.7, "Pearl River": 91.8, "Herford": 6057.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kensington-Cedar Cottage: (49.25°, -123.07°)", " Harlingen: (26.19°, -97.70°)", " Kokomo: (40.49°, -86.13°)", " Pearl River: (41.06°, -74.02°)", " Herford: (52.11°, 8.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Herford: 6057.3 km from centroid", " Kensington-Cedar Cottage: 3806.8 km from centroid", " Harlingen: 2743.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Herford", "FINAL ANSWER: Herford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.58333, "lon": 3.0, "name": "Noyon" }, { "lat": 49.38167, "lon": 3.32361, "name": "Soissons" }, { "lat": 53.35, "lon": -1.55, "name": "Fulwood" }, { "lat": 53.63738, "lon": 9.91973, "name": "Schnelsen" }, { "lat": 31.02795, "lon": 30.71493, "name": "Shubrākhīt" } ], "question": "Which location is the geographic outlier among: Noyon, Soissons, Fulwood, Schnelsen, Shubrākhīt?", "ground_truth": { "answer": "Shubrākhīt", "outlier_distance_km": 2588.2, "second_furthest_km": 1001.5, "clarity_ratio": 2.58, "median_distance_km": 696.5, "distances_to_centroid": { "Noyon": 509.7, "Soissons": 478.9, "Fulwood": 1001.5, "Schnelsen": 696.5, "Shubrākhīt": 2588.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Noyon: (49.58°, 3.00°)", " Soissons: (49.38°, 3.32°)", " Fulwood: (53.35°, -1.55°)", " Schnelsen: (53.64°, 9.92°)", " Shubrākhīt: (31.03°, 30.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shubrākhīt: 2588.2 km from centroid", " Fulwood: 1001.5 km from centroid", " Schnelsen: 696.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shubrākhīt", "FINAL ANSWER: Shubrākhīt" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.86667, "lon": 145.28333, "name": "Boronia" }, { "lat": -37.81667, "lon": 144.75, "name": "Truganina" }, { "lat": -33.92019, "lon": 151.22241, "name": "Kensington" }, { "lat": -33.77271, "lon": 151.08184, "name": "Epping" }, { "lat": -11.95972, "lon": -40.16806, "name": "Baixa Grande" } ], "question": "Which location is the geographic outlier among: Boronia, Truganina, Kensington, Epping, Baixa Grande?", "ground_truth": { "answer": "Baixa Grande", "outlier_distance_km": 14293.5, "second_furthest_km": 3813.6, "clarity_ratio": 3.75, "median_distance_km": 3802.7, "distances_to_centroid": { "Boronia": 3262.9, "Truganina": 3215.8, "Kensington": 3813.6, "Epping": 3802.7, "Baixa Grande": 14293.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Boronia: (-37.87°, 145.28°)", " Truganina: (-37.82°, 144.75°)", " Kensington: (-33.92°, 151.22°)", " Epping: (-33.77°, 151.08°)", " Baixa Grande: (-11.96°, -40.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Baixa Grande: 14293.5 km from centroid", " Kensington: 3813.6 km from centroid", " Epping: 3802.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Baixa Grande", "FINAL ANSWER: Baixa Grande" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.65333, "lon": 178.00417, "name": "Gisborne" }, { "lat": -37.87709, "lon": 145.12939, "name": "Mount Waverley" }, { "lat": -33.95, "lon": 151.11667, "name": "Bexley" }, { "lat": -32.06003, "lon": 115.955, "name": "Thornlie" }, { "lat": 4.88333, "lon": 38.08333, "name": "Yabēlo" } ], "question": "Which location is the geographic outlier among: Gisborne, Mount Waverley, Bexley, Thornlie, Yabēlo?", "ground_truth": { "answer": "Yabēlo", "outlier_distance_km": 10020.0, "second_furthest_km": 4961.7, "clarity_ratio": 2.02, "median_distance_km": 2528.0, "distances_to_centroid": { "Gisborne": 4961.7, "Mount Waverley": 2147.8, "Bexley": 2528.0, "Thornlie": 1062.4, "Yabēlo": 10020.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gisborne: (-38.65°, 178.00°)", " Mount Waverley: (-37.88°, 145.13°)", " Bexley: (-33.95°, 151.12°)", " Thornlie: (-32.06°, 115.95°)", " Yabēlo: (4.88°, 38.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yabēlo: 10020.0 km from centroid", " Gisborne: 4961.7 km from centroid", " Bexley: 2528.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yabēlo", "FINAL ANSWER: Yabēlo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.42158, "lon": 14.28217, "name": "Francavilla al Mare" }, { "lat": 43.71795, "lon": 10.94758, "name": "Empoli" }, { "lat": 50.58008, "lon": 16.50164, "name": "Nowa Ruda" }, { "lat": 53.84587, "lon": -0.42332, "name": "Beverley" }, { "lat": -32.45242, "lon": -71.23106, "name": "La Ligua" } ], "question": "Which location is the geographic outlier among: Francavilla al Mare, Empoli, Nowa Ruda, Beverley, La Ligua?", "ground_truth": { "answer": "La Ligua", "outlier_distance_km": 9883.2, "second_furthest_km": 2804.8, "clarity_ratio": 3.52, "median_distance_km": 2510.6, "distances_to_centroid": { "Francavilla al Mare": 2154.3, "Empoli": 2000.2, "Nowa Ruda": 2804.8, "Beverley": 2510.6, "La Ligua": 9883.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Francavilla al Mare: (42.42°, 14.28°)", " Empoli: (43.72°, 10.95°)", " Nowa Ruda: (50.58°, 16.50°)", " Beverley: (53.85°, -0.42°)", " La Ligua: (-32.45°, -71.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " La Ligua: 9883.2 km from centroid", " Nowa Ruda: 2804.8 km from centroid", " Beverley: 2510.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: La Ligua", "FINAL ANSWER: La Ligua" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.27519, "lon": -89.78117, "name": "Slidell" }, { "lat": 41.86614, "lon": -88.10701, "name": "Wheaton" }, { "lat": 19.95232, "lon": -102.30781, "name": "Jacona de Plancarte" }, { "lat": 40.71649, "lon": -73.88125, "name": "Middle Village" }, { "lat": 19.90873, "lon": 109.68717, "name": "Lingao" } ], "question": "Which location is the geographic outlier among: Slidell, Wheaton, Jacona de Plancarte, Middle Village, Lingao?", "ground_truth": { "answer": "Lingao", "outlier_distance_km": 13955.0, "second_furthest_km": 5451.2, "clarity_ratio": 2.56, "median_distance_km": 3900.5, "distances_to_centroid": { "Slidell": 3900.5, "Wheaton": 3700.7, "Jacona de Plancarte": 5451.2, "Middle Village": 2514.8, "Lingao": 13955.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Slidell: (30.28°, -89.78°)", " Wheaton: (41.87°, -88.11°)", " Jacona de Plancarte: (19.95°, -102.31°)", " Middle Village: (40.72°, -73.88°)", " Lingao: (19.91°, 109.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lingao: 13955.0 km from centroid", " Jacona de Plancarte: 5451.2 km from centroid", " Slidell: 3900.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lingao", "FINAL ANSWER: Lingao" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.61372, "lon": -0.1269, "name": "la Nucia" }, { "lat": 53.85342, "lon": 46.3513, "name": "Inza" }, { "lat": 54.1522, "lon": 19.40884, "name": "Elbląg" }, { "lat": 49.40076, "lon": 1.04582, "name": "Le Grand-Quevilly" }, { "lat": 34.20011, "lon": -90.57093, "name": "Clarksdale" } ], "question": "Which location is the geographic outlier among: la Nucia, Inza, Elbląg, Le Grand-Quevilly, Clarksdale?", "ground_truth": { "answer": "Clarksdale", "outlier_distance_km": 7057.0, "second_furthest_km": 3674.5, "clarity_ratio": 1.92, "median_distance_km": 1933.1, "distances_to_centroid": { "la Nucia": 910.0, "Inza": 3674.5, "Elbląg": 1933.1, "Le Grand-Quevilly": 573.4, "Clarksdale": 7057.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " la Nucia: (38.61°, -0.13°)", " Inza: (53.85°, 46.35°)", " Elbląg: (54.15°, 19.41°)", " Le Grand-Quevilly: (49.40°, 1.05°)", " Clarksdale: (34.20°, -90.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Clarksdale: 7057.0 km from centroid", " Inza: 3674.5 km from centroid", " Elbląg: 1933.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Clarksdale", "FINAL ANSWER: Clarksdale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -9.22139, "lon": -37.74861, "name": "Inhapi" }, { "lat": -29.08056, "lon": -53.83583, "name": "Tupanciretã" }, { "lat": -33.03016, "lon": -60.64045, "name": "Gobernador Gálvez" }, { "lat": 3.68549, "lon": -76.31372, "name": "El Cerrito" }, { "lat": 37.59493, "lon": -120.95771, "name": "Ceres" } ], "question": "Which location is the geographic outlier among: Inhapi, Tupanciretã, Gobernador Gálvez, El Cerrito, Ceres?", "ground_truth": { "answer": "Ceres", "outlier_distance_km": 7165.9, "second_furthest_km": 3560.1, "clarity_ratio": 2.01, "median_distance_km": 3153.4, "distances_to_centroid": { "Inhapi": 3560.1, "Tupanciretã": 3070.5, "Gobernador Gálvez": 3153.4, "El Cerrito": 1292.2, "Ceres": 7165.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Inhapi: (-9.22°, -37.75°)", " Tupanciretã: (-29.08°, -53.84°)", " Gobernador Gálvez: (-33.03°, -60.64°)", " El Cerrito: (3.69°, -76.31°)", " Ceres: (37.59°, -120.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ceres: 7165.9 km from centroid", " Inhapi: 3560.1 km from centroid", " Gobernador Gálvez: 3153.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ceres", "FINAL ANSWER: Ceres" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.8178, "lon": 151.00348, "name": "Parramatta" }, { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" }, { "lat": -31.9652, "lon": 141.4512, "name": "Broken Hill" }, { "lat": -35.28346, "lon": 149.12807, "name": "Canberra" }, { "lat": -26.04027, "lon": 30.79268, "name": "Nhlazatje" } ], "question": "Which location is the geographic outlier among: Parramatta, Dianella, Broken Hill, Canberra, Nhlazatje?", "ground_truth": { "answer": "Nhlazatje", "outlier_distance_km": 8244.6, "second_furthest_km": 3111.7, "clarity_ratio": 2.65, "median_distance_km": 2930.7, "distances_to_centroid": { "Parramatta": 3111.7, "Dianella": 168.2, "Broken Hill": 2242.9, "Canberra": 2930.7, "Nhlazatje": 8244.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parramatta: (-33.82°, 151.00°)", " Dianella: (-31.89°, 115.87°)", " Broken Hill: (-31.97°, 141.45°)", " Canberra: (-35.28°, 149.13°)", " Nhlazatje: (-26.04°, 30.79°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nhlazatje: 8244.6 km from centroid", " Parramatta: 3111.7 km from centroid", " Canberra: 2930.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nhlazatje", "FINAL ANSWER: Nhlazatje" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.74194, "lon": -47.49472, "name": "Ulianópolis" }, { "lat": -22.98444, "lon": -43.22315, "name": "Leblon" }, { "lat": -22.41139, "lon": -47.56139, "name": "Rio Claro" }, { "lat": -2.24444, "lon": -49.49583, "name": "Cametá" }, { "lat": 30.4428, "lon": 30.96975, "name": "Sirs al Layyānah" } ], "question": "Which location is the geographic outlier among: Ulianópolis, Leblon, Rio Claro, Cametá, Sirs al Layyānah?", "ground_truth": { "answer": "Sirs al Layyānah", "outlier_distance_km": 7645.8, "second_furthest_km": 2673.6, "clarity_ratio": 2.86, "median_distance_km": 2448.4, "distances_to_centroid": { "Ulianópolis": 1790.3, "Leblon": 2448.4, "Rio Claro": 2673.6, "Cametá": 2024.8, "Sirs al Layyānah": 7645.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ulianópolis: (-3.74°, -47.49°)", " Leblon: (-22.98°, -43.22°)", " Rio Claro: (-22.41°, -47.56°)", " Cametá: (-2.24°, -49.50°)", " Sirs al Layyānah: (30.44°, 30.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sirs al Layyānah: 7645.8 km from centroid", " Rio Claro: 2673.6 km from centroid", " Leblon: 2448.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sirs al Layyānah", "FINAL ANSWER: Sirs al Layyānah" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.67552, "lon": 8.46934, "name": "Acqui Terme" }, { "lat": 54.19609, "lon": 37.61822, "name": "Tula" }, { "lat": 41.00997, "lon": 17.00558, "name": "Rutigliano" }, { "lat": 50.55162, "lon": 9.67518, "name": "Fulda" }, { "lat": -26.68443, "lon": 153.05705, "name": "Buderim" } ], "question": "Which location is the geographic outlier among: Acqui Terme, Tula, Rutigliano, Fulda, Buderim?", "ground_truth": { "answer": "Buderim", "outlier_distance_km": 13152.3, "second_furthest_km": 3500.2, "clarity_ratio": 3.76, "median_distance_km": 3413.2, "distances_to_centroid": { "Acqui Terme": 3413.2, "Tula": 2457.9, "Rutigliano": 2653.6, "Fulda": 3500.2, "Buderim": 13152.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Acqui Terme: (44.68°, 8.47°)", " Tula: (54.20°, 37.62°)", " Rutigliano: (41.01°, 17.01°)", " Fulda: (50.55°, 9.68°)", " Buderim: (-26.68°, 153.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Buderim: 13152.3 km from centroid", " Fulda: 3500.2 km from centroid", " Acqui Terme: 3413.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Buderim", "FINAL ANSWER: Buderim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.91176, "lon": -80.20033, "name": "Golden Glades" }, { "lat": 19.26755, "lon": -99.61925, "name": "San Francisco Cuaxusco" }, { "lat": 42.8078, "lon": -87.92425, "name": "Caledonia" }, { "lat": 41.72059, "lon": -87.70172, "name": "Evergreen Park" }, { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" } ], "question": "Which location is the geographic outlier among: Golden Glades, San Francisco Cuaxusco, Caledonia, Evergreen Park, Palmerston?", "ground_truth": { "answer": "Palmerston", "outlier_distance_km": 18721.1, "second_furthest_km": 5653.8, "clarity_ratio": 3.31, "median_distance_km": 4484.2, "distances_to_centroid": { "Golden Glades": 3567.4, "San Francisco Cuaxusco": 5653.8, "Caledonia": 4484.2, "Evergreen Park": 4436.9, "Palmerston": 18721.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Golden Glades: (25.91°, -80.20°)", " San Francisco Cuaxusco: (19.27°, -99.62°)", " Caledonia: (42.81°, -87.92°)", " Evergreen Park: (41.72°, -87.70°)", " Palmerston: (-12.49°, 130.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palmerston: 18721.1 km from centroid", " San Francisco Cuaxusco: 5653.8 km from centroid", " Caledonia: 4484.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palmerston", "FINAL ANSWER: Palmerston" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.56849, "lon": -54.7579, "name": "Montecarlo" }, { "lat": -34.16327, "lon": -58.95919, "name": "Campana" }, { "lat": -20.28389, "lon": -50.24639, "name": "Fernandópolis" }, { "lat": -19.70027, "lon": -43.9602, "name": "São José da Lapa" }, { "lat": 38.58055, "lon": -0.10321, "name": "l'Alfàs del Pi" } ], "question": "Which location is the geographic outlier among: Montecarlo, Campana, Fernandópolis, São José da Lapa, l'Alfàs del Pi?", "ground_truth": { "answer": "l'Alfàs del Pi", "outlier_distance_km": 7122.3, "second_furthest_km": 2986.6, "clarity_ratio": 2.38, "median_distance_km": 2087.8, "distances_to_centroid": { "Montecarlo": 2087.8, "Campana": 2986.6, "Fernandópolis": 1269.4, "São José da Lapa": 846.9, "l'Alfàs del Pi": 7122.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Montecarlo: (-26.57°, -54.76°)", " Campana: (-34.16°, -58.96°)", " Fernandópolis: (-20.28°, -50.25°)", " São José da Lapa: (-19.70°, -43.96°)", " l'Alfàs del Pi: (38.58°, -0.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " l'Alfàs del Pi: 7122.3 km from centroid", " Campana: 2986.6 km from centroid", " Montecarlo: 2087.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: l'Alfàs del Pi", "FINAL ANSWER: l'Alfàs del Pi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.10107, "lon": -122.65883, "name": "Langley" }, { "lat": 29.95465, "lon": -90.07507, "name": "New Orleans" }, { "lat": 40.94038, "lon": -74.13181, "name": "Fair Lawn" }, { "lat": 33.64113, "lon": -117.91867, "name": "Costa Mesa" }, { "lat": -34.4187, "lon": 19.23446, "name": "Hermanus" } ], "question": "Which location is the geographic outlier among: Langley, New Orleans, Fair Lawn, Costa Mesa, Hermanus?", "ground_truth": { "answer": "Hermanus", "outlier_distance_km": 12028.2, "second_furthest_km": 4841.1, "clarity_ratio": 2.48, "median_distance_km": 4096.6, "distances_to_centroid": { "Langley": 4841.1, "New Orleans": 1452.7, "Fair Lawn": 1921.2, "Costa Mesa": 4096.6, "Hermanus": 12028.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Langley: (49.10°, -122.66°)", " New Orleans: (29.95°, -90.08°)", " Fair Lawn: (40.94°, -74.13°)", " Costa Mesa: (33.64°, -117.92°)", " Hermanus: (-34.42°, 19.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hermanus: 12028.2 km from centroid", " Langley: 4841.1 km from centroid", " Costa Mesa: 4096.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hermanus", "FINAL ANSWER: Hermanus" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.15388, "lon": 18.66031, "name": "Moorreesburg" }, { "lat": 6.55504, "lon": 3.34363, "name": "Oshodi" }, { "lat": 7.43636, "lon": 5.45925, "name": "Emure-Ekiti" }, { "lat": -29.32816, "lon": 31.28954, "name": "KwaDukuza" }, { "lat": 33.86585, "lon": -118.08312, "name": "Artesia" } ], "question": "Which location is the geographic outlier among: Moorreesburg, Oshodi, Emure-Ekiti, KwaDukuza, Artesia?", "ground_truth": { "answer": "Artesia", "outlier_distance_km": 11683.5, "second_furthest_km": 5413.8, "clarity_ratio": 2.16, "median_distance_km": 4622.5, "distances_to_centroid": { "Moorreesburg": 4622.5, "Oshodi": 1990.5, "Emure-Ekiti": 2241.2, "KwaDukuza": 5413.8, "Artesia": 11683.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Moorreesburg: (-33.15°, 18.66°)", " Oshodi: (6.56°, 3.34°)", " Emure-Ekiti: (7.44°, 5.46°)", " KwaDukuza: (-29.33°, 31.29°)", " Artesia: (33.87°, -118.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Artesia: 11683.5 km from centroid", " KwaDukuza: 5413.8 km from centroid", " Moorreesburg: 4622.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Artesia", "FINAL ANSWER: Artesia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.85, "lon": 136.45, "name": "Kameyama" }, { "lat": 32.30173, "lon": 130.50376, "name": "Sashiki" }, { "lat": 23.66278, "lon": 87.69695, "name": "Bolpur" }, { "lat": 29.82587, "lon": 107.06019, "name": "Fengcheng" }, { "lat": 50.87197, "lon": 9.70891, "name": "Bad Hersfeld" } ], "question": "Which location is the geographic outlier among: Kameyama, Sashiki, Bolpur, Fengcheng, Bad Hersfeld?", "ground_truth": { "answer": "Bad Hersfeld", "outlier_distance_km": 6770.9, "second_furthest_km": 3831.9, "clarity_ratio": 1.77, "median_distance_km": 3355.7, "distances_to_centroid": { "Kameyama": 3831.9, "Sashiki": 3355.7, "Bolpur": 1344.6, "Fengcheng": 1301.5, "Bad Hersfeld": 6770.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kameyama: (34.85°, 136.45°)", " Sashiki: (32.30°, 130.50°)", " Bolpur: (23.66°, 87.70°)", " Fengcheng: (29.83°, 107.06°)", " Bad Hersfeld: (50.87°, 9.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bad Hersfeld: 6770.9 km from centroid", " Kameyama: 3831.9 km from centroid", " Sashiki: 3355.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bad Hersfeld", "FINAL ANSWER: Bad Hersfeld" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.06069, "lon": -2.50192, "name": "Wa" }, { "lat": -26.49155, "lon": 29.22878, "name": "Trichardt" }, { "lat": 7.06205, "lon": 38.47635, "name": "Awasa" }, { "lat": 12.76889, "lon": 37.62389, "name": "Amba Giorgis" }, { "lat": 37.55855, "lon": -122.27108, "name": "Foster City" } ], "question": "Which location is the geographic outlier among: Wa, Trichardt, Awasa, Amba Giorgis, Foster City?", "ground_truth": { "answer": "Foster City", "outlier_distance_km": 11856.3, "second_furthest_km": 5257.4, "clarity_ratio": 2.26, "median_distance_km": 4668.7, "distances_to_centroid": { "Wa": 257.6, "Trichardt": 5257.4, "Awasa": 4668.7, "Amba Giorgis": 4562.7, "Foster City": 11856.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wa: (10.06°, -2.50°)", " Trichardt: (-26.49°, 29.23°)", " Awasa: (7.06°, 38.48°)", " Amba Giorgis: (12.77°, 37.62°)", " Foster City: (37.56°, -122.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Foster City: 11856.3 km from centroid", " Trichardt: 5257.4 km from centroid", " Awasa: 4668.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Foster City", "FINAL ANSWER: Foster City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.4693, "lon": -72.94237, "name": "Puerto Montt" }, { "lat": -27.49362, "lon": -64.85972, "name": "Termas de Río Hondo" }, { "lat": -25.5302, "lon": -49.20836, "name": "São José dos Pinhais" }, { "lat": -12.74083, "lon": -38.62083, "name": "Madre de Deus" }, { "lat": 2.11667, "lon": 111.51667, "name": "Sarikei" } ], "question": "Which location is the geographic outlier among: Puerto Montt, Termas de Río Hondo, São José dos Pinhais, Madre de Deus, Sarikei?", "ground_truth": { "answer": "Sarikei", "outlier_distance_km": 14644.0, "second_furthest_km": 5190.9, "clarity_ratio": 2.82, "median_distance_km": 4301.6, "distances_to_centroid": { "Puerto Montt": 5190.9, "Termas de Río Hondo": 4301.6, "São José dos Pinhais": 2736.5, "Madre de Deus": 1914.7, "Sarikei": 14644.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Puerto Montt: (-41.47°, -72.94°)", " Termas de Río Hondo: (-27.49°, -64.86°)", " São José dos Pinhais: (-25.53°, -49.21°)", " Madre de Deus: (-12.74°, -38.62°)", " Sarikei: (2.12°, 111.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sarikei: 14644.0 km from centroid", " Puerto Montt: 5190.9 km from centroid", " Termas de Río Hondo: 4301.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sarikei", "FINAL ANSWER: Sarikei" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -15.8091, "lon": -48.13096, "name": "Ceilândia" }, { "lat": -23.31861, "lon": -46.58667, "name": "Mairiporã" }, { "lat": -0.15491, "lon": -50.0615, "name": "Tucumã" }, { "lat": -11.81361, "lon": -37.61056, "name": "Conde" }, { "lat": -37.76667, "lon": 144.91667, "name": "Moonee Ponds" } ], "question": "Which location is the geographic outlier among: Ceilândia, Mairiporã, Tucumã, Conde, Moonee Ponds?", "ground_truth": { "answer": "Moonee Ponds", "outlier_distance_km": 13199.0, "second_furthest_km": 5048.2, "clarity_ratio": 2.61, "median_distance_km": 4323.2, "distances_to_centroid": { "Ceilândia": 4323.2, "Mairiporã": 4104.5, "Tucumã": 5048.2, "Conde": 3300.7, "Moonee Ponds": 13199.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ceilândia: (-15.81°, -48.13°)", " Mairiporã: (-23.32°, -46.59°)", " Tucumã: (-0.15°, -50.06°)", " Conde: (-11.81°, -37.61°)", " Moonee Ponds: (-37.77°, 144.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Moonee Ponds: 13199.0 km from centroid", " Tucumã: 5048.2 km from centroid", " Ceilândia: 4323.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Moonee Ponds", "FINAL ANSWER: Moonee Ponds" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.99167, "lon": 71.46793, "name": "Dhrāngadhra" }, { "lat": 22.53589, "lon": 114.0771, "name": "Shenzhen City Centre" }, { "lat": 29.81527, "lon": 106.42906, "name": "Longfeng" }, { "lat": 1.16667, "lon": 108.96667, "name": "Pemangkat" }, { "lat": -36.8, "lon": 174.75, "name": "North Shore" } ], "question": "Which location is the geographic outlier among: Dhrāngadhra, Shenzhen City Centre, Longfeng, Pemangkat, North Shore?", "ground_truth": { "answer": "North Shore", "outlier_distance_km": 7943.1, "second_furthest_km": 4946.4, "clarity_ratio": 1.61, "median_distance_km": 2596.4, "distances_to_centroid": { "Dhrāngadhra": 4946.4, "Shenzhen City Centre": 1626.7, "Longfeng": 2596.4, "Pemangkat": 1017.3, "North Shore": 7943.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dhrāngadhra: (22.99°, 71.47°)", " Shenzhen City Centre: (22.54°, 114.08°)", " Longfeng: (29.82°, 106.43°)", " Pemangkat: (1.17°, 108.97°)", " North Shore: (-36.80°, 174.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Shore: 7943.1 km from centroid", " Dhrāngadhra: 4946.4 km from centroid", " Longfeng: 2596.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Shore", "FINAL ANSWER: North Shore" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -15.63361, "lon": -47.83478, "name": "Sobradinho II" }, { "lat": -26.34067, "lon": -60.43207, "name": "Tres Isletas" }, { "lat": -9.39861, "lon": -40.50083, "name": "Petrolina" }, { "lat": -23.61277, "lon": -46.42667, "name": "Iguatemi" }, { "lat": -36.75818, "lon": 144.28024, "name": "Bendigo" } ], "question": "Which location is the geographic outlier among: Sobradinho II, Tres Isletas, Petrolina, Iguatemi, Bendigo?", "ground_truth": { "answer": "Bendigo", "outlier_distance_km": 12917.6, "second_furthest_km": 5078.8, "clarity_ratio": 2.54, "median_distance_km": 4017.9, "distances_to_centroid": { "Sobradinho II": 4017.9, "Tres Isletas": 5078.8, "Petrolina": 3537.4, "Iguatemi": 3703.1, "Bendigo": 12917.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sobradinho II: (-15.63°, -47.83°)", " Tres Isletas: (-26.34°, -60.43°)", " Petrolina: (-9.40°, -40.50°)", " Iguatemi: (-23.61°, -46.43°)", " Bendigo: (-36.76°, 144.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bendigo: 12917.6 km from centroid", " Tres Isletas: 5078.8 km from centroid", " Sobradinho II: 4017.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bendigo", "FINAL ANSWER: Bendigo" ] }, { "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": 53.27875, "lon": -2.90134, "name": "Ellesmere Port Town" }, { "lat": 49.01068, "lon": 2.04028, "name": "Jouy-le-Moutier" }, { "lat": 59.84389, "lon": 30.45111, "name": "Obukhovo" }, { "lat": 47.21997, "lon": 39.70769, "name": "Rostov-na-Donu" }, { "lat": -29.81782, "lon": -51.14551, "name": "Sapucaia do Sul" } ], "question": "Which location is the geographic outlier among: Ellesmere Port Town, Jouy-le-Moutier, Obukhovo, Rostov-na-Donu, Sapucaia do Sul?", "ground_truth": { "answer": "Sapucaia do Sul", "outlier_distance_km": 9281.6, "second_furthest_km": 3282.0, "clarity_ratio": 2.83, "median_distance_km": 3218.7, "distances_to_centroid": { "Ellesmere Port Town": 1997.6, "Jouy-le-Moutier": 1462.8, "Obukhovo": 3282.0, "Rostov-na-Donu": 3218.7, "Sapucaia do Sul": 9281.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ellesmere Port Town: (53.28°, -2.90°)", " Jouy-le-Moutier: (49.01°, 2.04°)", " Obukhovo: (59.84°, 30.45°)", " Rostov-na-Donu: (47.22°, 39.71°)", " Sapucaia do Sul: (-29.82°, -51.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sapucaia do Sul: 9281.6 km from centroid", " Obukhovo: 3282.0 km from centroid", " Rostov-na-Donu: 3218.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sapucaia do Sul", "FINAL ANSWER: Sapucaia do Sul" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 47.41052, "lon": -122.17369, "name": "East Hill-Meridian" }, { "lat": 49.26028, "lon": -122.83815, "name": "Central Coquitlam" }, { "lat": 38.99817, "lon": -77.28832, "name": "Great Falls" }, { "lat": 37.52966, "lon": -122.04024, "name": "Newark" }, { "lat": -12.15833, "lon": -39.73722, "name": "Ipirá" } ], "question": "Which location is the geographic outlier among: East Hill-Meridian, Central Coquitlam, Great Falls, Newark, Ipirá?", "ground_truth": { "answer": "Ipirá", "outlier_distance_km": 7815.7, "second_furthest_km": 2872.7, "clarity_ratio": 2.72, "median_distance_km": 2726.2, "distances_to_centroid": { "East Hill-Meridian": 2726.2, "Central Coquitlam": 2872.7, "Great Falls": 1915.0, "Newark": 2368.2, "Ipirá": 7815.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " East Hill-Meridian: (47.41°, -122.17°)", " Central Coquitlam: (49.26°, -122.84°)", " Great Falls: (39.00°, -77.29°)", " Newark: (37.53°, -122.04°)", " Ipirá: (-12.16°, -39.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ipirá: 7815.7 km from centroid", " Central Coquitlam: 2872.7 km from centroid", " East Hill-Meridian: 2726.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ipirá", "FINAL ANSWER: Ipirá" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.1709, "lon": 115.4077, "name": "Tanjung" }, { "lat": 28.67957, "lon": 77.06799, "name": "Nāngloi Jāt" }, { "lat": 42.11667, "lon": 118.78333, "name": "Mujiayingzi" }, { "lat": 18.191, "lon": 79.943, "name": "Mulugu" }, { "lat": 30.67436, "lon": -96.36996, "name": "Bryan" } ], "question": "Which location is the geographic outlier among: Tanjung, Nāngloi Jāt, Mujiayingzi, Mulugu, Bryan?", "ground_truth": { "answer": "Bryan", "outlier_distance_km": 13442.4, "second_furthest_km": 6734.2, "clarity_ratio": 2.0, "median_distance_km": 5832.5, "distances_to_centroid": { "Tanjung": 6734.2, "Nāngloi Jāt": 1894.9, "Mujiayingzi": 5832.5, "Mulugu": 2255.7, "Bryan": 13442.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tanjung: (-2.17°, 115.41°)", " Nāngloi Jāt: (28.68°, 77.07°)", " Mujiayingzi: (42.12°, 118.78°)", " Mulugu: (18.19°, 79.94°)", " Bryan: (30.67°, -96.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bryan: 13442.4 km from centroid", " Tanjung: 6734.2 km from centroid", " Mujiayingzi: 5832.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bryan", "FINAL ANSWER: Bryan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.15534, "lon": 12.75638, "name": "Damboa" }, { "lat": 31.35573, "lon": 31.68484, "name": "Kafr Sa‘d" }, { "lat": -26.96501, "lon": 30.43571, "name": "Driefontein" }, { "lat": -25.63473, "lon": 27.78022, "name": "Brits" }, { "lat": -33.82346, "lon": 150.94607, "name": "Greystanes" } ], "question": "Which location is the geographic outlier among: Damboa, Kafr Sa‘d, Driefontein, Brits, Greystanes?", "ground_truth": { "answer": "Greystanes", "outlier_distance_km": 10394.9, "second_furthest_km": 4901.7, "clarity_ratio": 2.12, "median_distance_km": 4748.3, "distances_to_centroid": { "Damboa": 4748.3, "Kafr Sa‘d": 4901.7, "Driefontein": 2939.5, "Brits": 3063.7, "Greystanes": 10394.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Damboa: (11.16°, 12.76°)", " Kafr Sa‘d: (31.36°, 31.68°)", " Driefontein: (-26.97°, 30.44°)", " Brits: (-25.63°, 27.78°)", " Greystanes: (-33.82°, 150.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Greystanes: 10394.9 km from centroid", " Kafr Sa‘d: 4901.7 km from centroid", " Damboa: 4748.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Greystanes", "FINAL ANSWER: Greystanes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.97889, "lon": -49.87056, "name": "Ourinhos" }, { "lat": -23.83222, "lon": -46.81139, "name": "Embu-Guaçu" }, { "lat": -3.54281, "lon": -45.60852, "name": "Bom Jardim" }, { "lat": -8.60111, "lon": -38.56861, "name": "Floresta" }, { "lat": 7.87377, "lon": 5.07691, "name": "Ipoti" } ], "question": "Which location is the geographic outlier among: Ourinhos, Embu-Guaçu, Bom Jardim, Floresta, Ipoti?", "ground_truth": { "answer": "Ipoti", "outlier_distance_km": 4887.1, "second_furthest_km": 2111.5, "clarity_ratio": 2.31, "median_distance_km": 1954.0, "distances_to_centroid": { "Ourinhos": 2111.5, "Embu-Guaçu": 1954.0, "Bom Jardim": 1371.3, "Floresta": 415.2, "Ipoti": 4887.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ourinhos: (-22.98°, -49.87°)", " Embu-Guaçu: (-23.83°, -46.81°)", " Bom Jardim: (-3.54°, -45.61°)", " Floresta: (-8.60°, -38.57°)", " Ipoti: (7.87°, 5.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ipoti: 4887.1 km from centroid", " Ourinhos: 2111.5 km from centroid", " Embu-Guaçu: 1954.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ipoti", "FINAL ANSWER: Ipoti" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.40477, "lon": -81.72291, "name": "Parma" }, { "lat": 29.94296, "lon": -89.96537, "name": "Chalmette" }, { "lat": 39.38984, "lon": -74.52404, "name": "Pleasantville" }, { "lat": 39.4667, "lon": -87.41391, "name": "Terre Haute" }, { "lat": 30.72508, "lon": 31.67148, "name": "Abū Kabīr" } ], "question": "Which location is the geographic outlier among: Parma, Chalmette, Pleasantville, Terre Haute, Abū Kabīr?", "ground_truth": { "answer": "Abū Kabīr", "outlier_distance_km": 8221.5, "second_furthest_km": 2830.0, "clarity_ratio": 2.91, "median_distance_km": 2392.1, "distances_to_centroid": { "Parma": 1931.8, "Chalmette": 2830.0, "Pleasantville": 1290.5, "Terre Haute": 2392.1, "Abū Kabīr": 8221.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parma: (41.40°, -81.72°)", " Chalmette: (29.94°, -89.97°)", " Pleasantville: (39.39°, -74.52°)", " Terre Haute: (39.47°, -87.41°)", " Abū Kabīr: (30.73°, 31.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Abū Kabīr: 8221.5 km from centroid", " Chalmette: 2830.0 km from centroid", " Terre Haute: 2392.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Abū Kabīr", "FINAL ANSWER: Abū Kabīr" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -16.92366, "lon": 145.76613, "name": "Cairns" }, { "lat": -38.21792, "lon": 145.03876, "name": "Mornington" }, { "lat": -33.88834, "lon": 151.12274, "name": "Ashfield" }, { "lat": -33.41665, "lon": 149.5806, "name": "Bathurst" }, { "lat": 49.68866, "lon": 21.77058, "name": "Krosno" } ], "question": "Which location is the geographic outlier among: Cairns, Mornington, Ashfield, Bathurst, Krosno?", "ground_truth": { "answer": "Krosno", "outlier_distance_km": 12014.6, "second_furthest_km": 3577.5, "clarity_ratio": 3.36, "median_distance_km": 3429.2, "distances_to_centroid": { "Cairns": 2486.0, "Mornington": 3429.2, "Ashfield": 3577.5, "Bathurst": 3428.0, "Krosno": 12014.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cairns: (-16.92°, 145.77°)", " Mornington: (-38.22°, 145.04°)", " Ashfield: (-33.89°, 151.12°)", " Bathurst: (-33.42°, 149.58°)", " Krosno: (49.69°, 21.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Krosno: 12014.6 km from centroid", " Ashfield: 3577.5 km from centroid", " Mornington: 3429.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Krosno", "FINAL ANSWER: Krosno" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.65682, "lon": 153.07955, "name": "Sunshine Coast" }, { "lat": -37.90561, "lon": 145.00279, "name": "Brighton" }, { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" }, { "lat": -38.03333, "lon": 145.3, "name": "Narre Warren" }, { "lat": 35.89685, "lon": 140.66666, "name": "Kamisu" } ], "question": "Which location is the geographic outlier among: Sunshine Coast, Brighton, Carnegie, Narre Warren, Kamisu?", "ground_truth": { "answer": "Kamisu", "outlier_distance_km": 6340.8, "second_furthest_km": 1903.7, "clarity_ratio": 3.33, "median_distance_km": 1890.5, "distances_to_centroid": { "Sunshine Coast": 975.6, "Brighton": 1890.5, "Carnegie": 1889.0, "Narre Warren": 1903.7, "Kamisu": 6340.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunshine Coast: (-26.66°, 153.08°)", " Brighton: (-37.91°, 145.00°)", " Carnegie: (-37.89°, 145.06°)", " Narre Warren: (-38.03°, 145.30°)", " Kamisu: (35.90°, 140.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kamisu: 6340.8 km from centroid", " Narre Warren: 1903.7 km from centroid", " Brighton: 1890.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kamisu", "FINAL ANSWER: Kamisu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.66333, "lon": -45.37167, "name": "Turiaçu" }, { "lat": -10.73333, "lon": -37.49333, "name": "Campo do Brito" }, { "lat": -11.31667, "lon": -38.23333, "name": "Itapicuru" }, { "lat": -1.96083, "lon": -48.19667, "name": "Acará" }, { "lat": 12.73647, "lon": 77.83264, "name": "Hosūr" } ], "question": "Which location is the geographic outlier among: Turiaçu, Campo do Brito, Itapicuru, Acará, Hosūr?", "ground_truth": { "answer": "Hosūr", "outlier_distance_km": 10734.9, "second_furthest_km": 3323.2, "clarity_ratio": 3.23, "median_distance_km": 3010.7, "distances_to_centroid": { "Turiaçu": 3010.7, "Campo do Brito": 2304.1, "Itapicuru": 2403.3, "Acará": 3323.2, "Hosūr": 10734.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Turiaçu: (-1.66°, -45.37°)", " Campo do Brito: (-10.73°, -37.49°)", " Itapicuru: (-11.32°, -38.23°)", " Acará: (-1.96°, -48.20°)", " Hosūr: (12.74°, 77.83°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hosūr: 10734.9 km from centroid", " Acará: 3323.2 km from centroid", " Turiaçu: 3010.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hosūr", "FINAL ANSWER: Hosūr" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 31.63622, "lon": -106.29054, "name": "Socorro Mission Number 1 Colonia" }, { "lat": 38.1302, "lon": -121.27245, "name": "Lodi" }, { "lat": 32.4425, "lon": -117.03417, "name": "Pórticos de San Antonio" }, { "lat": 39.7661, "lon": -105.07721, "name": "Wheat Ridge" }, { "lat": -31.84062, "lon": 115.89549, "name": "Ballajura" } ], "question": "Which location is the geographic outlier among: Socorro Mission Number 1 Colonia, Lodi, Pórticos de San Antonio, Wheat Ridge, Ballajura?", "ground_truth": { "answer": "Ballajura", "outlier_distance_km": 18892.8, "second_furthest_km": 5458.8, "clarity_ratio": 3.46, "median_distance_km": 5057.3, "distances_to_centroid": { "Socorro Mission Number 1 Colonia": 4041.9, "Lodi": 5458.8, "Pórticos de San Antonio": 5057.3, "Wheat Ridge": 4111.1, "Ballajura": 18892.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Socorro Mission Number 1 Colonia: (31.64°, -106.29°)", " Lodi: (38.13°, -121.27°)", " Pórticos de San Antonio: (32.44°, -117.03°)", " Wheat Ridge: (39.77°, -105.08°)", " Ballajura: (-31.84°, 115.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ballajura: 18892.8 km from centroid", " Lodi: 5458.8 km from centroid", " Pórticos de San Antonio: 5057.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ballajura", "FINAL ANSWER: Ballajura" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.69639, "lon": -44.82722, "name": "Oliveira" }, { "lat": -21.53194, "lon": -42.64306, "name": "Leopoldina" }, { "lat": -7.77833, "lon": -39.94111, "name": "Bodocó" }, { "lat": -16.76769, "lon": -47.6153, "name": "Cristalina" }, { "lat": 5.8231, "lon": 116.0466, "name": "Kinarut" } ], "question": "Which location is the geographic outlier among: Oliveira, Leopoldina, Bodocó, Cristalina, Kinarut?", "ground_truth": { "answer": "Kinarut", "outlier_distance_km": 14251.8, "second_furthest_km": 3884.6, "clarity_ratio": 3.67, "median_distance_km": 3639.6, "distances_to_centroid": { "Oliveira": 3639.6, "Leopoldina": 3435.3, "Bodocó": 3119.2, "Cristalina": 3884.6, "Kinarut": 14251.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Oliveira: (-20.70°, -44.83°)", " Leopoldina: (-21.53°, -42.64°)", " Bodocó: (-7.78°, -39.94°)", " Cristalina: (-16.77°, -47.62°)", " Kinarut: (5.82°, 116.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kinarut: 14251.8 km from centroid", " Cristalina: 3884.6 km from centroid", " Oliveira: 3639.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kinarut", "FINAL ANSWER: Kinarut" ] }, { "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": -37.62581, "lon": 144.92555, "name": "Roxburgh Park" }, { "lat": -38.38176, "lon": 142.48799, "name": "Warrnambool" }, { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" }, { "lat": -33.80383, "lon": 150.98768, "name": "Westmead" }, { "lat": 31.60351, "lon": -94.65549, "name": "Nacogdoches" } ], "question": "Which location is the geographic outlier among: Roxburgh Park, Warrnambool, Hoppers Crossing, Westmead, Nacogdoches?", "ground_truth": { "answer": "Nacogdoches", "outlier_distance_km": 18482.7, "second_furthest_km": 5280.6, "clarity_ratio": 3.5, "median_distance_km": 4748.3, "distances_to_centroid": { "Roxburgh Park": 4748.3, "Warrnambool": 4546.8, "Hoppers Crossing": 4731.6, "Westmead": 5280.6, "Nacogdoches": 18482.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Roxburgh Park: (-37.63°, 144.93°)", " Warrnambool: (-38.38°, 142.49°)", " Hoppers Crossing: (-37.88°, 144.70°)", " Westmead: (-33.80°, 150.99°)", " Nacogdoches: (31.60°, -94.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nacogdoches: 18482.7 km from centroid", " Westmead: 5280.6 km from centroid", " Roxburgh Park: 4748.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nacogdoches", "FINAL ANSWER: Nacogdoches" ] }, { "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": 10.7719, "lon": 122.9817, "name": "Binonga" }, { "lat": 24.1483, "lon": 115.72272, "name": "Xingning" }, { "lat": 20.3306, "lon": 74.24467, "name": "Chāndor" }, { "lat": 36.41667, "lon": 118.5, "name": "Yeyuan" }, { "lat": 12.6, "lon": 37.46667, "name": "Gonder" } ], "question": "Which location is the geographic outlier among: Binonga, Xingning, Chāndor, Yeyuan, Gonder?", "ground_truth": { "answer": "Gonder", "outlier_distance_km": 6038.6, "second_furthest_km": 3311.8, "clarity_ratio": 1.82, "median_distance_km": 2953.7, "distances_to_centroid": { "Binonga": 3311.8, "Xingning": 2281.0, "Chāndor": 2033.4, "Yeyuan": 2953.7, "Gonder": 6038.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Binonga: (10.77°, 122.98°)", " Xingning: (24.15°, 115.72°)", " Chāndor: (20.33°, 74.24°)", " Yeyuan: (36.42°, 118.50°)", " Gonder: (12.60°, 37.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gonder: 6038.6 km from centroid", " Binonga: 3311.8 km from centroid", " Yeyuan: 2953.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gonder", "FINAL ANSWER: Gonder" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.64881, "lon": -60.70868, "name": "Santa Fe" }, { "lat": -33.13044, "lon": -64.35272, "name": "Río Cuarto" }, { "lat": -23.16056, "lon": -49.96944, "name": "Jacarezinho" }, { "lat": -24.20833, "lon": -50.94944, "name": "Ortigueira" }, { "lat": 48.93196, "lon": 9.2024, "name": "Freiberg am Neckar" } ], "question": "Which location is the geographic outlier among: Santa Fe, Río Cuarto, Jacarezinho, Ortigueira, Freiberg am Neckar?", "ground_truth": { "answer": "Freiberg am Neckar", "outlier_distance_km": 8563.7, "second_furthest_km": 3119.6, "clarity_ratio": 2.75, "median_distance_km": 2759.1, "distances_to_centroid": { "Santa Fe": 2759.1, "Río Cuarto": 3119.6, "Jacarezinho": 1362.2, "Ortigueira": 1514.1, "Freiberg am Neckar": 8563.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Fe: (-31.65°, -60.71°)", " Río Cuarto: (-33.13°, -64.35°)", " Jacarezinho: (-23.16°, -49.97°)", " Ortigueira: (-24.21°, -50.95°)", " Freiberg am Neckar: (48.93°, 9.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Freiberg am Neckar: 8563.7 km from centroid", " Río Cuarto: 3119.6 km from centroid", " Santa Fe: 2759.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Freiberg am Neckar", "FINAL ANSWER: Freiberg am Neckar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.92806, "lon": -41.70917, "name": "Piracuruca" }, { "lat": -34.63333, "lon": -58.41667, "name": "Boedo" }, { "lat": -10.91111, "lon": -37.07167, "name": "Aracaju" }, { "lat": -3.86778, "lon": -54.22, "name": "Placas" }, { "lat": 35.77432, "lon": 139.81654, "name": "Aoi" } ], "question": "Which location is the geographic outlier among: Piracuruca, Boedo, Aracaju, Placas, Aoi?", "ground_truth": { "answer": "Aoi", "outlier_distance_km": 15297.0, "second_furthest_km": 6039.6, "clarity_ratio": 2.53, "median_distance_km": 4870.9, "distances_to_centroid": { "Piracuruca": 3483.0, "Boedo": 6039.6, "Aracaju": 3061.1, "Placas": 4870.9, "Aoi": 15297.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Piracuruca: (-3.93°, -41.71°)", " Boedo: (-34.63°, -58.42°)", " Aracaju: (-10.91°, -37.07°)", " Placas: (-3.87°, -54.22°)", " Aoi: (35.77°, 139.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Aoi: 15297.0 km from centroid", " Boedo: 6039.6 km from centroid", " Placas: 4870.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Aoi", "FINAL ANSWER: Aoi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 13.66314, "lon": 100.38781, "name": "Ban Khlong Bang Phran" }, { "lat": 29.10023, "lon": 106.39536, "name": "Xihu" }, { "lat": 34.74807, "lon": 134.91284, "name": "Inami" }, { "lat": 11.10944, "lon": 125.01556, "name": "Tanauan" }, { "lat": -22.88416, "lon": 30.49358, "name": "Tshitereke" } ], "question": "Which location is the geographic outlier among: Ban Khlong Bang Phran, Xihu, Inami, Tanauan, Tshitereke?", "ground_truth": { "answer": "Tshitereke", "outlier_distance_km": 8503.9, "second_furthest_km": 4294.7, "clarity_ratio": 1.98, "median_distance_km": 2788.3, "distances_to_centroid": { "Ban Khlong Bang Phran": 117.4, "Xihu": 1913.6, "Inami": 4294.7, "Tanauan": 2788.3, "Tshitereke": 8503.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ban Khlong Bang Phran: (13.66°, 100.39°)", " Xihu: (29.10°, 106.40°)", " Inami: (34.75°, 134.91°)", " Tanauan: (11.11°, 125.02°)", " Tshitereke: (-22.88°, 30.49°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tshitereke: 8503.9 km from centroid", " Inami: 4294.7 km from centroid", " Tanauan: 2788.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tshitereke", "FINAL ANSWER: Tshitereke" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.96083, "lon": -46.33361, "name": "Santos" }, { "lat": -21.35944, "lon": -48.06556, "name": "Pradópolis" }, { "lat": -9.70926, "lon": -36.44785, "name": "Cajueiro" }, { "lat": -30.95619, "lon": -58.7797, "name": "Federal" }, { "lat": 42.89175, "lon": -71.31201, "name": "Derry Village" } ], "question": "Which location is the geographic outlier among: Santos, Pradópolis, Cajueiro, Federal, Derry Village?", "ground_truth": { "answer": "Derry Village", "outlier_distance_km": 6046.9, "second_furthest_km": 2576.1, "clarity_ratio": 2.35, "median_distance_km": 1816.0, "distances_to_centroid": { "Santos": 1816.0, "Pradópolis": 1483.9, "Cajueiro": 1731.9, "Federal": 2576.1, "Derry Village": 6046.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santos: (-23.96°, -46.33°)", " Pradópolis: (-21.36°, -48.07°)", " Cajueiro: (-9.71°, -36.45°)", " Federal: (-30.96°, -58.78°)", " Derry Village: (42.89°, -71.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Derry Village: 6046.9 km from centroid", " Federal: 2576.1 km from centroid", " Santos: 1816.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Derry Village", "FINAL ANSWER: Derry Village" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.96587, "lon": 174.82389, "name": "Mangere East" }, { "lat": -37.78828, "lon": 145.12373, "name": "Doncaster" }, { "lat": -41.27078, "lon": 173.28404, "name": "Nelson" }, { "lat": -33.90741, "lon": 151.15546, "name": "Marrickville" }, { "lat": 27.89232, "lon": -101.42319, "name": "Palau" } ], "question": "Which location is the geographic outlier among: Mangere East, Doncaster, Nelson, Marrickville, Palau?", "ground_truth": { "answer": "Palau", "outlier_distance_km": 17001.7, "second_furthest_km": 6360.1, "clarity_ratio": 2.67, "median_distance_km": 6180.9, "distances_to_centroid": { "Mangere East": 6360.1, "Doncaster": 3752.8, "Nelson": 6180.9, "Marrickville": 4234.1, "Palau": 17001.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mangere East: (-36.97°, 174.82°)", " Doncaster: (-37.79°, 145.12°)", " Nelson: (-41.27°, 173.28°)", " Marrickville: (-33.91°, 151.16°)", " Palau: (27.89°, -101.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palau: 17001.7 km from centroid", " Mangere East: 6360.1 km from centroid", " Nelson: 6180.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palau", "FINAL ANSWER: Palau" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.22099, "lon": 116.009, "name": "Byford" }, { "lat": -37.88461, "lon": 145.29539, "name": "Ferntree Gully" }, { "lat": -33.72976, "lon": 151.15977, "name": "Saint Ives" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": -20.75389, "lon": -42.88194, "name": "Viçosa" } ], "question": "Which location is the geographic outlier among: Byford, Ferntree Gully, Saint Ives, Melbourne City Centre, Viçosa?", "ground_truth": { "answer": "Viçosa", "outlier_distance_km": 13067.7, "second_furthest_km": 4454.6, "clarity_ratio": 2.93, "median_distance_km": 3865.3, "distances_to_centroid": { "Byford": 1230.1, "Ferntree Gully": 3865.3, "Saint Ives": 4454.6, "Melbourne City Centre": 3837.0, "Viçosa": 13067.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Byford: (-32.22°, 116.01°)", " Ferntree Gully: (-37.88°, 145.30°)", " Saint Ives: (-33.73°, 151.16°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Viçosa: (-20.75°, -42.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Viçosa: 13067.7 km from centroid", " Saint Ives: 4454.6 km from centroid", " Ferntree Gully: 3865.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Viçosa", "FINAL ANSWER: Viçosa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 21.45713, "lon": 110.76591, "name": "Wuchuan" }, { "lat": 11.58528, "lon": 122.75111, "name": "Roxas City" }, { "lat": 35.0292, "lon": 126.7175, "name": "Naju" }, { "lat": 34.98333, "lon": 133.46667, "name": "Niimi" }, { "lat": 40.66312, "lon": -73.76221, "name": "Springfield Gardens" } ], "question": "Which location is the geographic outlier among: Wuchuan, Roxas City, Naju, Niimi, Springfield Gardens?", "ground_truth": { "answer": "Springfield Gardens", "outlier_distance_km": 11963.5, "second_furthest_km": 4676.8, "clarity_ratio": 2.56, "median_distance_km": 4445.2, "distances_to_centroid": { "Wuchuan": 2808.3, "Roxas City": 4445.2, "Naju": 4063.3, "Niimi": 4676.8, "Springfield Gardens": 11963.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wuchuan: (21.46°, 110.77°)", " Roxas City: (11.59°, 122.75°)", " Naju: (35.03°, 126.72°)", " Niimi: (34.98°, 133.47°)", " Springfield Gardens: (40.66°, -73.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Springfield Gardens: 11963.5 km from centroid", " Niimi: 4676.8 km from centroid", " Roxas City: 4445.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Springfield Gardens", "FINAL ANSWER: Springfield Gardens" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.90012, "lon": -79.13289, "name": "Pickering" }, { "lat": 38.70824, "lon": -121.32995, "name": "Antelope" }, { "lat": 43.66962, "lon": -79.37525, "name": "North St.James Town" }, { "lat": 32.31232, "lon": -106.77834, "name": "Las Cruces" }, { "lat": 30.31679, "lon": 74.91254, "name": "Goniāna Mandi" } ], "question": "Which location is the geographic outlier among: Pickering, Antelope, North St.James Town, Las Cruces, Goniāna Mandi?", "ground_truth": { "answer": "Goniāna Mandi", "outlier_distance_km": 11237.0, "second_furthest_km": 5059.7, "clarity_ratio": 2.22, "median_distance_km": 4052.6, "distances_to_centroid": { "Pickering": 1564.0, "Antelope": 5059.7, "North St.James Town": 1573.8, "Las Cruces": 4052.6, "Goniāna Mandi": 11237.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pickering: (43.90°, -79.13°)", " Antelope: (38.71°, -121.33°)", " North St.James Town: (43.67°, -79.38°)", " Las Cruces: (32.31°, -106.78°)", " Goniāna Mandi: (30.32°, 74.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Goniāna Mandi: 11237.0 km from centroid", " Antelope: 5059.7 km from centroid", " Las Cruces: 4052.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Goniāna Mandi", "FINAL ANSWER: Goniāna Mandi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.78761, "lon": 145.14888, "name": "Doncaster East" }, { "lat": -36.88041, "lon": 174.79819, "name": "Remuera" }, { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" }, { "lat": -37.8, "lon": 144.96667, "name": "Carlton" }, { "lat": 45.75, "lon": 126.65, "name": "Harbin" } ], "question": "Which location is the geographic outlier among: Doncaster East, Remuera, Mackay, Carlton, Harbin?", "ground_truth": { "answer": "Harbin", "outlier_distance_km": 7367.2, "second_furthest_km": 3377.5, "clarity_ratio": 2.18, "median_distance_km": 2270.3, "distances_to_centroid": { "Doncaster East": 2266.5, "Remuera": 3377.5, "Mackay": 412.1, "Carlton": 2270.3, "Harbin": 7367.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Doncaster East: (-37.79°, 145.15°)", " Remuera: (-36.88°, 174.80°)", " Mackay: (-21.15°, 149.17°)", " Carlton: (-37.80°, 144.97°)", " Harbin: (45.75°, 126.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Harbin: 7367.2 km from centroid", " Remuera: 3377.5 km from centroid", " Carlton: 2270.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Harbin", "FINAL ANSWER: Harbin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.41012, "lon": 5.30838, "name": "Les Pennes-Mirabeau" }, { "lat": 45.07073, "lon": 7.51465, "name": "Rivoli" }, { "lat": 49.20724, "lon": 2.58661, "name": "Senlis" }, { "lat": 51.65468, "lon": -0.27762, "name": "Borehamwood" }, { "lat": 6.64738, "lon": -75.46031, "name": "Santa Rosa de Osos" } ], "question": "Which location is the geographic outlier among: Les Pennes-Mirabeau, Rivoli, Senlis, Borehamwood, Santa Rosa de Osos?", "ground_truth": { "answer": "Santa Rosa de Osos", "outlier_distance_km": 7260.9, "second_furthest_km": 1736.1, "clarity_ratio": 4.18, "median_distance_km": 1658.2, "distances_to_centroid": { "Les Pennes-Mirabeau": 1521.6, "Rivoli": 1736.1, "Senlis": 1608.1, "Borehamwood": 1658.2, "Santa Rosa de Osos": 7260.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Les Pennes-Mirabeau: (43.41°, 5.31°)", " Rivoli: (45.07°, 7.51°)", " Senlis: (49.21°, 2.59°)", " Borehamwood: (51.65°, -0.28°)", " Santa Rosa de Osos: (6.65°, -75.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santa Rosa de Osos: 7260.9 km from centroid", " Rivoli: 1736.1 km from centroid", " Borehamwood: 1658.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santa Rosa de Osos", "FINAL ANSWER: Santa Rosa de Osos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.66331, "lon": 28.59016, "name": "Balfour" }, { "lat": 0.2332, "lon": 37.94086, "name": "Maua" }, { "lat": 9.88333, "lon": 38.26667, "name": "Dayē" }, { "lat": -33.01167, "lon": 17.9442, "name": "Saldanha" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" } ], "question": "Which location is the geographic outlier among: Balfour, Maua, Dayē, Saldanha, Cheltenham?", "ground_truth": { "answer": "Cheltenham", "outlier_distance_km": 8948.2, "second_furthest_km": 3948.4, "clarity_ratio": 2.27, "median_distance_km": 3478.1, "distances_to_centroid": { "Balfour": 2760.3, "Maua": 2610.1, "Dayē": 3478.1, "Saldanha": 3948.4, "Cheltenham": 8948.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Balfour: (-26.66°, 28.59°)", " Maua: (0.23°, 37.94°)", " Dayē: (9.88°, 38.27°)", " Saldanha: (-33.01°, 17.94°)", " Cheltenham: (-37.97°, 145.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cheltenham: 8948.2 km from centroid", " Saldanha: 3948.4 km from centroid", " Dayē: 3478.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cheltenham", "FINAL ANSWER: Cheltenham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.57957, "lon": 36.70392, "name": "Kubinka" }, { "lat": 41.47063, "lon": 2.08611, "name": "Sant Cugat del Vallès" }, { "lat": 51.35806, "lon": 9.47974, "name": "Vellmar" }, { "lat": 42.795, "lon": -8.548, "name": "Teo" }, { "lat": 4.39928, "lon": 113.99163, "name": "Miri" } ], "question": "Which location is the geographic outlier among: Kubinka, Sant Cugat del Vallès, Vellmar, Teo, Miri?", "ground_truth": { "answer": "Miri", "outlier_distance_km": 9117.0, "second_furthest_km": 3294.5, "clarity_ratio": 2.77, "median_distance_km": 2433.2, "distances_to_centroid": { "Kubinka": 1882.8, "Sant Cugat del Vallès": 2433.2, "Vellmar": 2136.5, "Teo": 3294.5, "Miri": 9117.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kubinka: (55.58°, 36.70°)", " Sant Cugat del Vallès: (41.47°, 2.09°)", " Vellmar: (51.36°, 9.48°)", " Teo: (42.80°, -8.55°)", " Miri: (4.40°, 113.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Miri: 9117.0 km from centroid", " Teo: 3294.5 km from centroid", " Sant Cugat del Vallès: 2433.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Miri", "FINAL ANSWER: Miri" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.16917, "lon": 71.66671, "name": "Botad" }, { "lat": 24.77985, "lon": 102.57548, "name": "Haikou" }, { "lat": 11.27271, "lon": 76.22571, "name": "Nilambūr" }, { "lat": 14.1463, "lon": 121.4729, "name": "Majayjay" }, { "lat": 53.30182, "lon": -1.12404, "name": "Worksop" } ], "question": "Which location is the geographic outlier among: Botad, Haikou, Nilambūr, Majayjay, Worksop?", "ground_truth": { "answer": "Worksop", "outlier_distance_km": 6832.7, "second_furthest_km": 5076.1, "clarity_ratio": 1.35, "median_distance_km": 2859.2, "distances_to_centroid": { "Botad": 416.3, "Haikou": 2859.2, "Nilambūr": 1556.5, "Majayjay": 5076.1, "Worksop": 6832.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Botad: (22.17°, 71.67°)", " Haikou: (24.78°, 102.58°)", " Nilambūr: (11.27°, 76.23°)", " Majayjay: (14.15°, 121.47°)", " Worksop: (53.30°, -1.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Worksop: 6832.7 km from centroid", " Majayjay: 5076.1 km from centroid", " Haikou: 2859.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Worksop", "FINAL ANSWER: Worksop" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 23.25999, "lon": 76.14567, "name": "Maksi" }, { "lat": 15.87944, "lon": 108.335, "name": "Hoi An" }, { "lat": 15.76983, "lon": 76.75581, "name": "Sindhnūr" }, { "lat": 28.99242, "lon": 116.66754, "name": "Poyang" }, { "lat": -20.97194, "lon": -46.11889, "name": "Carmo do Rio Claro" } ], "question": "Which location is the geographic outlier among: Maksi, Hoi An, Sindhnūr, Poyang, Carmo do Rio Claro?", "ground_truth": { "answer": "Carmo do Rio Claro", "outlier_distance_km": 12813.9, "second_furthest_km": 5492.9, "clarity_ratio": 2.33, "median_distance_km": 4532.1, "distances_to_centroid": { "Maksi": 1573.8, "Hoi An": 4532.1, "Sindhnūr": 1175.4, "Poyang": 5492.9, "Carmo do Rio Claro": 12813.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maksi: (23.26°, 76.15°)", " Hoi An: (15.88°, 108.33°)", " Sindhnūr: (15.77°, 76.76°)", " Poyang: (28.99°, 116.67°)", " Carmo do Rio Claro: (-20.97°, -46.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carmo do Rio Claro: 12813.9 km from centroid", " Poyang: 5492.9 km from centroid", " Hoi An: 4532.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carmo do Rio Claro", "FINAL ANSWER: Carmo do Rio Claro" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.36568, "lon": -122.61231, "name": "West Linn" }, { "lat": 42.4801, "lon": -71.0995, "name": "Stoneham" }, { "lat": 44.56247, "lon": -92.5338, "name": "Red Wing" }, { "lat": 29.58497, "lon": -81.20784, "name": "Palm Coast" }, { "lat": 38.58203, "lon": 77.47622, "name": "Alamaiti" } ], "question": "Which location is the geographic outlier among: West Linn, Stoneham, Red Wing, Palm Coast, Alamaiti?", "ground_truth": { "answer": "Alamaiti", "outlier_distance_km": 10162.8, "second_furthest_km": 5166.4, "clarity_ratio": 1.97, "median_distance_km": 2859.5, "distances_to_centroid": { "West Linn": 5166.4, "Stoneham": 1124.6, "Red Wing": 2859.5, "Palm Coast": 2409.6, "Alamaiti": 10162.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " West Linn: (45.37°, -122.61°)", " Stoneham: (42.48°, -71.10°)", " Red Wing: (44.56°, -92.53°)", " Palm Coast: (29.58°, -81.21°)", " Alamaiti: (38.58°, 77.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alamaiti: 10162.8 km from centroid", " West Linn: 5166.4 km from centroid", " Red Wing: 2859.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alamaiti", "FINAL ANSWER: Alamaiti" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.74778, "lon": -34.82556, "name": "Ilha de Itamaracá" }, { "lat": -3.45778, "lon": -42.37028, "name": "Luzilândia" }, { "lat": 3.00945, "lon": -76.48494, "name": "Santander de Quilichao" }, { "lat": -22.06806, "lon": -46.56917, "name": "Andradas" }, { "lat": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" } ], "question": "Which location is the geographic outlier among: Ilha de Itamaracá, Luzilândia, Santander de Quilichao, Andradas, Bracken Ridge?", "ground_truth": { "answer": "Bracken Ridge", "outlier_distance_km": 15301.4, "second_furthest_km": 7584.6, "clarity_ratio": 2.02, "median_distance_km": 4110.0, "distances_to_centroid": { "Ilha de Itamaracá": 2812.7, "Luzilândia": 3735.1, "Santander de Quilichao": 7584.6, "Andradas": 4110.0, "Bracken Ridge": 15301.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ilha de Itamaracá: (-7.75°, -34.83°)", " Luzilândia: (-3.46°, -42.37°)", " Santander de Quilichao: (3.01°, -76.48°)", " Andradas: (-22.07°, -46.57°)", " Bracken Ridge: (-27.32°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bracken Ridge: 15301.4 km from centroid", " Santander de Quilichao: 7584.6 km from centroid", " Andradas: 4110.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bracken Ridge", "FINAL ANSWER: Bracken Ridge" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -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": 42.26121, "lon": -71.4634, "name": "Ashland" }, { "lat": 36.85245, "lon": -121.4016, "name": "Hollister" }, { "lat": 40.82593, "lon": -74.20903, "name": "Montclair" }, { "lat": 39.83776, "lon": -105.00137, "name": "Sherrelwood" }, { "lat": 11.10389, "lon": 5.25556, "name": "Rijau" } ], "question": "Which location is the geographic outlier among: Ashland, Hollister, Montclair, Sherrelwood, Rijau?", "ground_truth": { "answer": "Rijau", "outlier_distance_km": 8276.5, "second_furthest_km": 4312.2, "clarity_ratio": 1.92, "median_distance_km": 2863.1, "distances_to_centroid": { "Ashland": 914.1, "Hollister": 4312.2, "Montclair": 743.1, "Sherrelwood": 2863.1, "Rijau": 8276.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ashland: (42.26°, -71.46°)", " Hollister: (36.85°, -121.40°)", " Montclair: (40.83°, -74.21°)", " Sherrelwood: (39.84°, -105.00°)", " Rijau: (11.10°, 5.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rijau: 8276.5 km from centroid", " Hollister: 4312.2 km from centroid", " Sherrelwood: 2863.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rijau", "FINAL ANSWER: Rijau" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 1.53741, "lon": 103.65779, "name": "Skudai" }, { "lat": 34.35833, "lon": 117.05278, "name": "Liuji" }, { "lat": 13.5848, "lon": 124.2374, "name": "Virac" }, { "lat": 28.83379, "lon": 106.75535, "name": "Fuhuan" }, { "lat": 52.7025, "lon": 21.08276, "name": "Pułtusk" } ], "question": "Which location is the geographic outlier among: Skudai, Liuji, Virac, Fuhuan, Pułtusk?", "ground_truth": { "answer": "Pułtusk", "outlier_distance_km": 6628.2, "second_furthest_km": 3394.0, "clarity_ratio": 1.95, "median_distance_km": 2910.3, "distances_to_centroid": { "Skudai": 2910.3, "Liuji": 2336.0, "Virac": 3394.0, "Fuhuan": 1237.3, "Pułtusk": 6628.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Skudai: (1.54°, 103.66°)", " Liuji: (34.36°, 117.05°)", " Virac: (13.58°, 124.24°)", " Fuhuan: (28.83°, 106.76°)", " Pułtusk: (52.70°, 21.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pułtusk: 6628.2 km from centroid", " Virac: 3394.0 km from centroid", " Skudai: 2910.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pułtusk", "FINAL ANSWER: Pułtusk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -13.18222, "lon": -39.425, "name": "Laje" }, { "lat": -19.73639, "lon": -45.25222, "name": "Bom Despacho" }, { "lat": -29.44806, "lon": -51.80639, "name": "Teutônia" }, { "lat": -34.65072, "lon": -59.43143, "name": "Mercedes" }, { "lat": 52.9771, "lon": 49.7086, "name": "Chapayevsk" } ], "question": "Which location is the geographic outlier among: Laje, Bom Despacho, Teutônia, Mercedes, Chapayevsk?", "ground_truth": { "answer": "Chapayevsk", "outlier_distance_km": 10059.8, "second_furthest_km": 4207.6, "clarity_ratio": 2.39, "median_distance_km": 3285.7, "distances_to_centroid": { "Laje": 1213.0, "Bom Despacho": 2107.5, "Teutônia": 3285.7, "Mercedes": 4207.6, "Chapayevsk": 10059.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Laje: (-13.18°, -39.42°)", " Bom Despacho: (-19.74°, -45.25°)", " Teutônia: (-29.45°, -51.81°)", " Mercedes: (-34.65°, -59.43°)", " Chapayevsk: (52.98°, 49.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chapayevsk: 10059.8 km from centroid", " Mercedes: 4207.6 km from centroid", " Teutônia: 3285.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chapayevsk", "FINAL ANSWER: Chapayevsk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.46171, "lon": 8.84949, "name": "Marsberg" }, { "lat": 52.41074, "lon": -1.81952, "name": "Shirley" }, { "lat": 53.11724, "lon": -2.17584, "name": "Biddulph" }, { "lat": 52.15045, "lon": 7.33664, "name": "Steinfurt" }, { "lat": -22.84333, "lon": -47.60611, "name": "Rio das Pedras" } ], "question": "Which location is the geographic outlier among: Marsberg, Shirley, Biddulph, Steinfurt, Rio das Pedras?", "ground_truth": { "answer": "Rio das Pedras", "outlier_distance_km": 7915.4, "second_furthest_km": 2015.3, "clarity_ratio": 3.93, "median_distance_km": 2002.0, "distances_to_centroid": { "Marsberg": 2015.3, "Shirley": 1734.0, "Biddulph": 1803.7, "Steinfurt": 2002.0, "Rio das Pedras": 7915.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Marsberg: (51.46°, 8.85°)", " Shirley: (52.41°, -1.82°)", " Biddulph: (53.12°, -2.18°)", " Steinfurt: (52.15°, 7.34°)", " Rio das Pedras: (-22.84°, -47.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rio das Pedras: 7915.4 km from centroid", " Marsberg: 2015.3 km from centroid", " Steinfurt: 2002.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rio das Pedras", "FINAL ANSWER: Rio das Pedras" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.99994, "lon": 14.99389, "name": "Termoli" }, { "lat": 48.82538, "lon": 2.47458, "name": "Joinville-le-Pont" }, { "lat": 59.2239, "lon": 39.88398, "name": "Vologda" }, { "lat": 55.90288, "lon": -3.52261, "name": "Livingston" }, { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" } ], "question": "Which location is the geographic outlier among: Termoli, Joinville-le-Pont, Vologda, Livingston, Ashburton?", "ground_truth": { "answer": "Ashburton", "outlier_distance_km": 15263.1, "second_furthest_km": 4540.5, "clarity_ratio": 3.36, "median_distance_km": 3967.1, "distances_to_centroid": { "Termoli": 2854.0, "Joinville-le-Pont": 3967.1, "Vologda": 3006.8, "Livingston": 4540.5, "Ashburton": 15263.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Termoli: (42.00°, 14.99°)", " Joinville-le-Pont: (48.83°, 2.47°)", " Vologda: (59.22°, 39.88°)", " Livingston: (55.90°, -3.52°)", " Ashburton: (-43.90°, 171.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ashburton: 15263.1 km from centroid", " Livingston: 4540.5 km from centroid", " Joinville-le-Pont: 3967.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ashburton", "FINAL ANSWER: Ashburton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.32861, "lon": -35.3325, "name": "Itabaiana" }, { "lat": -9.39861, "lon": -40.50083, "name": "Petrolina" }, { "lat": -19.67722, "lon": -51.19083, "name": "Paranaíba" }, { "lat": -38.82225, "lon": -68.06293, "name": "Cinco Saltos" }, { "lat": 55.14941, "lon": 124.73676, "name": "Tynda" } ], "question": "Which location is the geographic outlier among: Itabaiana, Petrolina, Paranaíba, Cinco Saltos, Tynda?", "ground_truth": { "answer": "Tynda", "outlier_distance_km": 13243.9, "second_furthest_km": 6665.9, "clarity_ratio": 1.99, "median_distance_km": 4383.0, "distances_to_centroid": { "Itabaiana": 2380.9, "Petrolina": 2978.1, "Paranaíba": 4383.0, "Cinco Saltos": 6665.9, "Tynda": 13243.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itabaiana: (-7.33°, -35.33°)", " Petrolina: (-9.40°, -40.50°)", " Paranaíba: (-19.68°, -51.19°)", " Cinco Saltos: (-38.82°, -68.06°)", " Tynda: (55.15°, 124.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tynda: 13243.9 km from centroid", " Cinco Saltos: 6665.9 km from centroid", " Paranaíba: 4383.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tynda", "FINAL ANSWER: Tynda" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.6558, "lon": 37.37454, "name": "Kinoi" }, { "lat": 5.61411, "lon": -1.5502, "name": "Twifu Praso" }, { "lat": -1.4563, "lon": 36.97826, "name": "Athi River" }, { "lat": -29.57366, "lon": 31.11552, "name": "Tongaat" }, { "lat": 41.11121, "lon": -74.06848, "name": "Monsey" } ], "question": "Which location is the geographic outlier among: Kinoi, Twifu Praso, Athi River, Tongaat, Monsey?", "ground_truth": { "answer": "Monsey", "outlier_distance_km": 8968.4, "second_furthest_km": 4486.0, "clarity_ratio": 2.0, "median_distance_km": 3526.1, "distances_to_centroid": { "Kinoi": 3526.1, "Twifu Praso": 890.3, "Athi River": 3479.4, "Tongaat": 4486.0, "Monsey": 8968.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kinoi: (-1.66°, 37.37°)", " Twifu Praso: (5.61°, -1.55°)", " Athi River: (-1.46°, 36.98°)", " Tongaat: (-29.57°, 31.12°)", " Monsey: (41.11°, -74.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Monsey: 8968.4 km from centroid", " Tongaat: 4486.0 km from centroid", " Kinoi: 3526.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Monsey", "FINAL ANSWER: Monsey" ] }, { "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": -17.03139, "lon": -48.29583, "name": "Orizona" }, { "lat": -13.37028, "lon": -39.07306, "name": "Valença" }, { "lat": -5.56667, "lon": -46.74222, "name": "Amarante do Maranhão" }, { "lat": -1.29389, "lon": -47.92639, "name": "Castanhal" }, { "lat": 9.1756, "lon": 76.47129, "name": "Kandalloor" } ], "question": "Which location is the geographic outlier among: Orizona, Valença, Amarante do Maranhão, Castanhal, Kandalloor?", "ground_truth": { "answer": "Kandalloor", "outlier_distance_km": 10936.4, "second_furthest_km": 3218.0, "clarity_ratio": 3.4, "median_distance_km": 3013.8, "distances_to_centroid": { "Orizona": 3218.0, "Valença": 2148.4, "Amarante do Maranhão": 2836.0, "Castanhal": 3013.8, "Kandalloor": 10936.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Orizona: (-17.03°, -48.30°)", " Valença: (-13.37°, -39.07°)", " Amarante do Maranhão: (-5.57°, -46.74°)", " Castanhal: (-1.29°, -47.93°)", " Kandalloor: (9.18°, 76.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kandalloor: 10936.4 km from centroid", " Orizona: 3218.0 km from centroid", " Castanhal: 3013.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kandalloor", "FINAL ANSWER: Kandalloor" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.42903, "lon": 50.80598, "name": "Nurlat" }, { "lat": 52.26059, "lon": 21.16355, "name": "Rembertów" }, { "lat": 55.92721, "lon": 39.46072, "name": "Petushki" }, { "lat": 51.60799, "lon": -3.10081, "name": "Risca" }, { "lat": 19.15892, "lon": -98.40824, "name": "Huejotzingo" } ], "question": "Which location is the geographic outlier among: Nurlat, Rembertów, Petushki, Risca, Huejotzingo?", "ground_truth": { "answer": "Huejotzingo", "outlier_distance_km": 9229.3, "second_furthest_km": 3479.6, "clarity_ratio": 2.65, "median_distance_km": 2759.5, "distances_to_centroid": { "Nurlat": 3479.6, "Rembertów": 1512.7, "Petushki": 2759.5, "Risca": 661.1, "Huejotzingo": 9229.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nurlat: (54.43°, 50.81°)", " Rembertów: (52.26°, 21.16°)", " Petushki: (55.93°, 39.46°)", " Risca: (51.61°, -3.10°)", " Huejotzingo: (19.16°, -98.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Huejotzingo: 9229.3 km from centroid", " Nurlat: 3479.6 km from centroid", " Petushki: 2759.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Huejotzingo", "FINAL ANSWER: Huejotzingo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.96724, "lon": 153.39796, "name": "Southport" }, { "lat": -38.03333, "lon": 145.35, "name": "Berwick" }, { "lat": -37.6, "lon": 145.15, "name": "Doreen" }, { "lat": -37.91482, "lon": 144.75088, "name": "Point Cook" }, { "lat": 45.47154, "lon": 9.18763, "name": "Brera" } ], "question": "Which location is the geographic outlier among: Southport, Berwick, Doreen, Point Cook, Brera?", "ground_truth": { "answer": "Brera", "outlier_distance_km": 13090.0, "second_furthest_km": 3569.3, "clarity_ratio": 3.67, "median_distance_km": 3252.8, "distances_to_centroid": { "Southport": 3569.3, "Berwick": 3252.8, "Doreen": 3212.1, "Point Cook": 3201.7, "Brera": 13090.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Southport: (-27.97°, 153.40°)", " Berwick: (-38.03°, 145.35°)", " Doreen: (-37.60°, 145.15°)", " Point Cook: (-37.91°, 144.75°)", " Brera: (45.47°, 9.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brera: 13090.0 km from centroid", " Southport: 3569.3 km from centroid", " Berwick: 3252.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brera", "FINAL ANSWER: Brera" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.80938, "lon": -79.22344, "name": "Malvern" }, { "lat": 34.75405, "lon": -77.43024, "name": "Jacksonville" }, { "lat": 35.23338, "lon": -106.66447, "name": "Rio Rancho" }, { "lat": 45.36678, "lon": -73.56588, "name": "Saint-Constant" }, { "lat": 54.36677, "lon": 77.3068, "name": "Kupino" } ], "question": "Which location is the geographic outlier among: Malvern, Jacksonville, Rio Rancho, Saint-Constant, Kupino?", "ground_truth": { "answer": "Kupino", "outlier_distance_km": 8195.9, "second_furthest_km": 4721.7, "clarity_ratio": 1.74, "median_distance_km": 2371.8, "distances_to_centroid": { "Malvern": 2204.8, "Jacksonville": 2371.8, "Rio Rancho": 4721.7, "Saint-Constant": 1750.3, "Kupino": 8195.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Malvern: (43.81°, -79.22°)", " Jacksonville: (34.75°, -77.43°)", " Rio Rancho: (35.23°, -106.66°)", " Saint-Constant: (45.37°, -73.57°)", " Kupino: (54.37°, 77.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kupino: 8195.9 km from centroid", " Rio Rancho: 4721.7 km from centroid", " Jacksonville: 2371.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kupino", "FINAL ANSWER: Kupino" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.78088, "lon": -90.42179, "name": "Farmington" }, { "lat": 17.59917, "lon": -99.17389, "name": "Chilapa de Álvarez" }, { "lat": 19.87444, "lon": -98.93472, "name": "Don Antonio" }, { "lat": 22.36094, "lon": -97.89997, "name": "Miramar" }, { "lat": 10.3766, "lon": 123.9573, "name": "Consolacion" } ], "question": "Which location is the geographic outlier among: Farmington, Chilapa de Álvarez, Don Antonio, Miramar, Consolacion?", "ground_truth": { "answer": "Consolacion", "outlier_distance_km": 16438.6, "second_furthest_km": 4892.5, "clarity_ratio": 3.36, "median_distance_km": 4815.4, "distances_to_centroid": { "Farmington": 4044.5, "Chilapa de Álvarez": 4892.5, "Don Antonio": 4815.4, "Miramar": 4664.5, "Consolacion": 16438.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Farmington: (37.78°, -90.42°)", " Chilapa de Álvarez: (17.60°, -99.17°)", " Don Antonio: (19.87°, -98.93°)", " Miramar: (22.36°, -97.90°)", " Consolacion: (10.38°, 123.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Consolacion: 16438.6 km from centroid", " Chilapa de Álvarez: 4892.5 km from centroid", " Don Antonio: 4815.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Consolacion", "FINAL ANSWER: Consolacion" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 13.49923, "lon": 39.63723, "name": "Dolo" }, { "lat": -26.55, "lon": 29.16667, "name": "Secunda" }, { "lat": 7.43636, "lon": 5.45925, "name": "Emure-Ekiti" }, { "lat": 12.00012, "lon": 8.51672, "name": "Kano" }, { "lat": 37.48522, "lon": -122.23635, "name": "Redwood City" } ], "question": "Which location is the geographic outlier among: Dolo, Secunda, Emure-Ekiti, Kano, Redwood City?", "ground_truth": { "answer": "Redwood City", "outlier_distance_km": 11489.1, "second_furthest_km": 5605.0, "clarity_ratio": 2.05, "median_distance_km": 5204.4, "distances_to_centroid": { "Dolo": 5204.4, "Secunda": 5605.0, "Emure-Ekiti": 1477.1, "Kano": 1829.6, "Redwood City": 11489.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dolo: (13.50°, 39.64°)", " Secunda: (-26.55°, 29.17°)", " Emure-Ekiti: (7.44°, 5.46°)", " Kano: (12.00°, 8.52°)", " Redwood City: (37.49°, -122.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Redwood City: 11489.1 km from centroid", " Secunda: 5605.0 km from centroid", " Dolo: 5204.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Redwood City", "FINAL ANSWER: Redwood City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.83136, "lon": 20.05595, "name": "Ashton" }, { "lat": 5.80865, "lon": 8.08098, "name": "Ugep" }, { "lat": -33.963, "lon": 22.46173, "name": "George" }, { "lat": -28.33523, "lon": 31.41617, "name": "Ulundi" }, { "lat": 51.39822, "lon": -0.19837, "name": "Morden" } ], "question": "Which location is the geographic outlier among: Ashton, Ugep, George, Ulundi, Morden?", "ground_truth": { "answer": "Morden", "outlier_distance_km": 6769.4, "second_furthest_km": 2977.4, "clarity_ratio": 2.27, "median_distance_km": 2921.0, "distances_to_centroid": { "Ashton": 2921.0, "Ugep": 1768.8, "George": 2977.4, "Ulundi": 2777.9, "Morden": 6769.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ashton: (-33.83°, 20.06°)", " Ugep: (5.81°, 8.08°)", " George: (-33.96°, 22.46°)", " Ulundi: (-28.34°, 31.42°)", " Morden: (51.40°, -0.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Morden: 6769.4 km from centroid", " George: 2977.4 km from centroid", " Ashton: 2921.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Morden", "FINAL ANSWER: Morden" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.24206, "lon": 46.00013, "name": "Tsotsin-Yurt" }, { "lat": 45.35405, "lon": 10.84462, "name": "Villafranca di Verona" }, { "lat": 52.34198, "lon": 35.35917, "name": "Zheleznogorsk" }, { "lat": 36.16809, "lon": -5.34777, "name": "La Línea de la Concepción" }, { "lat": 33.23333, "lon": 130.3, "name": "Saga" } ], "question": "Which location is the geographic outlier among: Tsotsin-Yurt, Villafranca di Verona, Zheleznogorsk, La Línea de la Concepción, Saga?", "ground_truth": { "answer": "Saga", "outlier_distance_km": 7378.0, "second_furthest_km": 4201.4, "clarity_ratio": 1.76, "median_distance_km": 2626.3, "distances_to_centroid": { "Tsotsin-Yurt": 247.3, "Villafranca di Verona": 2626.3, "Zheleznogorsk": 1293.1, "La Línea de la Concepción": 4201.4, "Saga": 7378.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tsotsin-Yurt: (43.24°, 46.00°)", " Villafranca di Verona: (45.35°, 10.84°)", " Zheleznogorsk: (52.34°, 35.36°)", " La Línea de la Concepción: (36.17°, -5.35°)", " Saga: (33.23°, 130.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saga: 7378.0 km from centroid", " La Línea de la Concepción: 4201.4 km from centroid", " Villafranca di Verona: 2626.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saga", "FINAL ANSWER: Saga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.06611, "lon": -50.14722, "name": "Buritama" }, { "lat": -22.02861, "lon": -42.36083, "name": "Cordeiro" }, { "lat": -19.67722, "lon": -51.19083, "name": "Paranaíba" }, { "lat": -9.66583, "lon": -35.73528, "name": "Maceió" }, { "lat": 38.70882, "lon": 141.15578, "name": "Tome" } ], "question": "Which location is the geographic outlier among: Buritama, Cordeiro, Paranaíba, Maceió, Tome?", "ground_truth": { "answer": "Tome", "outlier_distance_km": 15280.9, "second_furthest_km": 4909.9, "clarity_ratio": 3.11, "median_distance_km": 4835.3, "distances_to_centroid": { "Buritama": 4835.3, "Cordeiro": 4090.6, "Paranaíba": 4909.9, "Maceió": 3106.4, "Tome": 15280.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Buritama: (-21.07°, -50.15°)", " Cordeiro: (-22.03°, -42.36°)", " Paranaíba: (-19.68°, -51.19°)", " Maceió: (-9.67°, -35.74°)", " Tome: (38.71°, 141.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tome: 15280.9 km from centroid", " Paranaíba: 4909.9 km from centroid", " Buritama: 4835.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tome", "FINAL ANSWER: Tome" ] }, { "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": 34.87905, "lon": -76.90133, "name": "Havelock" }, { "lat": 43.87111, "lon": -79.43725, "name": "Richmond Hill" }, { "lat": 47.44843, "lon": -122.15734, "name": "Fairwood" }, { "lat": 64.83778, "lon": -147.71639, "name": "Fairbanks" }, { "lat": 51.7, "lon": -0.6, "name": "Chesham" } ], "question": "Which location is the geographic outlier among: Havelock, Richmond Hill, Fairwood, Fairbanks, Chesham?", "ground_truth": { "answer": "Chesham", "outlier_distance_km": 5701.0, "second_furthest_km": 4003.4, "clarity_ratio": 1.42, "median_distance_km": 2714.0, "distances_to_centroid": { "Havelock": 1671.8, "Richmond Hill": 691.1, "Fairwood": 2714.0, "Fairbanks": 4003.4, "Chesham": 5701.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Havelock: (34.88°, -76.90°)", " Richmond Hill: (43.87°, -79.44°)", " Fairwood: (47.45°, -122.16°)", " Fairbanks: (64.84°, -147.72°)", " Chesham: (51.70°, -0.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chesham: 5701.0 km from centroid", " Fairbanks: 4003.4 km from centroid", " Fairwood: 2714.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chesham", "FINAL ANSWER: Chesham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.81358, "lon": 27.81695, "name": "Sasolburg" }, { "lat": 13.95, "lon": 40.66667, "name": "Arerti" }, { "lat": 7.06667, "lon": 37.7, "name": "Āreka" }, { "lat": 7.12294, "lon": 40.00412, "name": "Bale Robe" }, { "lat": -23.41944, "lon": -51.42444, "name": "Arapongas" } ], "question": "Which location is the geographic outlier among: Sasolburg, Arerti, Āreka, Bale Robe, Arapongas?", "ground_truth": { "answer": "Arapongas", "outlier_distance_km": 7811.8, "second_furthest_km": 3148.0, "clarity_ratio": 2.48, "median_distance_km": 2665.5, "distances_to_centroid": { "Sasolburg": 2662.3, "Arerti": 3148.0, "Āreka": 2441.2, "Bale Robe": 2665.5, "Arapongas": 7811.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sasolburg: (-26.81°, 27.82°)", " Arerti: (13.95°, 40.67°)", " Āreka: (7.07°, 37.70°)", " Bale Robe: (7.12°, 40.00°)", " Arapongas: (-23.42°, -51.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arapongas: 7811.8 km from centroid", " Arerti: 3148.0 km from centroid", " Bale Robe: 2665.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arapongas", "FINAL ANSWER: Arapongas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -16.92366, "lon": 145.76613, "name": "Cairns" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" }, { "lat": -36.90694, "lon": 174.68704, "name": "New Lynn" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": 23.89921, "lon": 79.19393, "name": "Patharia" } ], "question": "Which location is the geographic outlier among: Cairns, Launceston, New Lynn, Taylors Lakes, Patharia?", "ground_truth": { "answer": "Patharia", "outlier_distance_km": 8165.6, "second_furthest_km": 3872.7, "clarity_ratio": 2.11, "median_distance_km": 2333.3, "distances_to_centroid": { "Cairns": 952.0, "Launceston": 2333.3, "New Lynn": 3872.7, "Taylors Lakes": 1872.2, "Patharia": 8165.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cairns: (-16.92°, 145.77°)", " Launceston: (-41.44°, 147.13°)", " New Lynn: (-36.91°, 174.69°)", " Taylors Lakes: (-37.70°, 144.79°)", " Patharia: (23.90°, 79.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Patharia: 8165.6 km from centroid", " New Lynn: 3872.7 km from centroid", " Launceston: 2333.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Patharia", "FINAL ANSWER: Patharia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.53611, "lon": -117.29116, "name": "Victorville" }, { "lat": 31.15013, "lon": -81.49147, "name": "Brunswick" }, { "lat": 40.50035, "lon": -79.74949, "name": "Plum" }, { "lat": 41.58227, "lon": -85.83444, "name": "Goshen" }, { "lat": -28.21344, "lon": -49.16383, "name": "São José" } ], "question": "Which location is the geographic outlier among: Victorville, Brunswick, Plum, Goshen, São José?", "ground_truth": { "answer": "São José", "outlier_distance_km": 6819.3, "second_furthest_km": 3537.4, "clarity_ratio": 1.93, "median_distance_km": 1986.2, "distances_to_centroid": { "Victorville": 3537.4, "Brunswick": 813.8, "Plum": 1865.2, "Goshen": 1986.2, "São José": 6819.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Victorville: (34.54°, -117.29°)", " Brunswick: (31.15°, -81.49°)", " Plum: (40.50°, -79.75°)", " Goshen: (41.58°, -85.83°)", " São José: (-28.21°, -49.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São José: 6819.3 km from centroid", " Victorville: 3537.4 km from centroid", " Goshen: 1986.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São José", "FINAL ANSWER: São José" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.4165, "lon": 0.42709, "name": "Benicarló" }, { "lat": 50.89772, "lon": 14.80764, "name": "Zittau" }, { "lat": 52.41289, "lon": 17.08503, "name": "Swarzędz" }, { "lat": 59.859, "lon": 30.388, "name": "Kupchino" }, { "lat": 38.67852, "lon": -121.7733, "name": "Woodland" } ], "question": "Which location is the geographic outlier among: Benicarló, Zittau, Swarzędz, Kupchino, Woodland?", "ground_truth": { "answer": "Woodland", "outlier_distance_km": 8126.6, "second_furthest_km": 2961.0, "clarity_ratio": 2.74, "median_distance_km": 2078.8, "distances_to_centroid": { "Benicarló": 1317.3, "Zittau": 1924.0, "Swarzędz": 2078.8, "Kupchino": 2961.0, "Woodland": 8126.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Benicarló: (40.42°, 0.43°)", " Zittau: (50.90°, 14.81°)", " Swarzędz: (52.41°, 17.09°)", " Kupchino: (59.86°, 30.39°)", " Woodland: (38.68°, -121.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Woodland: 8126.6 km from centroid", " Kupchino: 2961.0 km from centroid", " Swarzędz: 2078.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Woodland", "FINAL ANSWER: Woodland" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.59521, "lon": 153.12332, "name": "Rochedale South" }, { "lat": -34.06564, "lon": 151.01266, "name": "Engadine" }, { "lat": -31.9652, "lon": 141.4512, "name": "Broken Hill" }, { "lat": -37.88333, "lon": 145.21667, "name": "Wantirna South" }, { "lat": 12.17024, "lon": 6.66412, "name": "Gusau" } ], "question": "Which location is the geographic outlier among: Rochedale South, Engadine, Broken Hill, Wantirna South, Gusau?", "ground_truth": { "answer": "Gusau", "outlier_distance_km": 12854.5, "second_furthest_km": 3383.7, "clarity_ratio": 3.8, "median_distance_km": 3253.2, "distances_to_centroid": { "Rochedale South": 3383.7, "Engadine": 3253.2, "Broken Hill": 2332.0, "Wantirna South": 2892.4, "Gusau": 12854.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rochedale South: (-27.60°, 153.12°)", " Engadine: (-34.07°, 151.01°)", " Broken Hill: (-31.97°, 141.45°)", " Wantirna South: (-37.88°, 145.22°)", " Gusau: (12.17°, 6.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gusau: 12854.5 km from centroid", " Rochedale South: 3383.7 km from centroid", " Engadine: 3253.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gusau", "FINAL ANSWER: Gusau" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.63838, "lon": 11.18419, "name": "San Giovanni in Persiceto" }, { "lat": 40.37846, "lon": -3.6739, "name": "Entrevías" }, { "lat": 50.94823, "lon": 10.70193, "name": "Gotha" }, { "lat": 40.79968, "lon": 16.92298, "name": "Gioia del Colle" }, { "lat": 21.33555, "lon": -158.0582, "name": "Kapolei" } ], "question": "Which location is the geographic outlier among: San Giovanni in Persiceto, Entrevías, Gotha, Gioia del Colle, Kapolei?", "ground_truth": { "answer": "Kapolei", "outlier_distance_km": 11694.1, "second_furthest_km": 3494.0, "clarity_ratio": 3.35, "median_distance_km": 2997.4, "distances_to_centroid": { "San Giovanni in Persiceto": 2977.2, "Entrevías": 1779.0, "Gotha": 2997.4, "Gioia del Colle": 3494.0, "Kapolei": 11694.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Giovanni in Persiceto: (44.64°, 11.18°)", " Entrevías: (40.38°, -3.67°)", " Gotha: (50.95°, 10.70°)", " Gioia del Colle: (40.80°, 16.92°)", " Kapolei: (21.34°, -158.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kapolei: 11694.1 km from centroid", " Gioia del Colle: 3494.0 km from centroid", " Gotha: 2997.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kapolei", "FINAL ANSWER: Kapolei" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.14665, "lon": 36.96087, "name": "Ruiru" }, { "lat": 31.07287, "lon": 31.49503, "name": "Maḩallat Damanah" }, { "lat": -1.03326, "lon": 37.06933, "name": "Thika" }, { "lat": -24.72459, "lon": 31.19939, "name": "Thulamahashi" }, { "lat": 26.26265, "lon": 127.76147, "name": "Ginowan" } ], "question": "Which location is the geographic outlier among: Ruiru, Maḩallat Damanah, Thika, Thulamahashi, Ginowan?", "ground_truth": { "answer": "Ginowan", "outlier_distance_km": 8201.2, "second_furthest_km": 4153.9, "clarity_ratio": 1.97, "median_distance_km": 3562.7, "distances_to_centroid": { "Ruiru": 1943.4, "Maḩallat Damanah": 3562.7, "Thika": 1927.2, "Thulamahashi": 4153.9, "Ginowan": 8201.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ruiru: (-1.15°, 36.96°)", " Maḩallat Damanah: (31.07°, 31.50°)", " Thika: (-1.03°, 37.07°)", " Thulamahashi: (-24.72°, 31.20°)", " Ginowan: (26.26°, 127.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ginowan: 8201.2 km from centroid", " Thulamahashi: 4153.9 km from centroid", " Maḩallat Damanah: 3562.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ginowan", "FINAL ANSWER: Ginowan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.865, "lon": -39.5875, "name": "Ibicaraí" }, { "lat": -3.89, "lon": -38.45056, "name": "Eusébio" }, { "lat": -22.88583, "lon": -48.445, "name": "Botucatu" }, { "lat": -23.87833, "lon": -47.99722, "name": "São Miguel Arcanjo" }, { "lat": 18.15056, "lon": -94.5525, "name": "Fraccionamiento Ciudad Olmeca" } ], "question": "Which location is the geographic outlier among: Ibicaraí, Eusébio, Botucatu, São Miguel Arcanjo, Fraccionamiento Ciudad Olmeca?", "ground_truth": { "answer": "Fraccionamiento Ciudad Olmeca", "outlier_distance_km": 5425.2, "second_furthest_km": 1805.3, "clarity_ratio": 3.01, "median_distance_km": 1716.3, "distances_to_centroid": { "Ibicaraí": 1657.0, "Eusébio": 1805.3, "Botucatu": 1596.9, "São Miguel Arcanjo": 1716.3, "Fraccionamiento Ciudad Olmeca": 5425.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ibicaraí: (-14.87°, -39.59°)", " Eusébio: (-3.89°, -38.45°)", " Botucatu: (-22.89°, -48.45°)", " São Miguel Arcanjo: (-23.88°, -48.00°)", " Fraccionamiento Ciudad Olmeca: (18.15°, -94.55°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fraccionamiento Ciudad Olmeca: 5425.2 km from centroid", " Eusébio: 1805.3 km from centroid", " São Miguel Arcanjo: 1716.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fraccionamiento Ciudad Olmeca", "FINAL ANSWER: Fraccionamiento Ciudad Olmeca" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.45389, "lon": 4.1975, "name": "Birnin Kebbi" }, { "lat": 6.73156, "lon": -1.6137, "name": "Tafo" }, { "lat": 30.71524, "lon": 31.2592, "name": "Mīt Ghamr" }, { "lat": 6.81944, "lon": 3.91731, "name": "Ijebu Ode" }, { "lat": -38.15912, "lon": 145.93118, "name": "Warragul" } ], "question": "Which location is the geographic outlier among: Birnin Kebbi, Tafo, Mīt Ghamr, Ijebu Ode, Warragul?", "ground_truth": { "answer": "Warragul", "outlier_distance_km": 11935.1, "second_furthest_km": 4258.9, "clarity_ratio": 2.8, "median_distance_km": 3707.4, "distances_to_centroid": { "Birnin Kebbi": 3707.4, "Tafo": 4258.9, "Mīt Ghamr": 3057.1, "Ijebu Ode": 3649.6, "Warragul": 11935.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Birnin Kebbi: (12.45°, 4.20°)", " Tafo: (6.73°, -1.61°)", " Mīt Ghamr: (30.72°, 31.26°)", " Ijebu Ode: (6.82°, 3.92°)", " Warragul: (-38.16°, 145.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Warragul: 11935.1 km from centroid", " Tafo: 4258.9 km from centroid", " Birnin Kebbi: 3707.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Warragul", "FINAL ANSWER: Warragul" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.0646, "lon": 174.94212, "name": "Papakura" }, { "lat": -37.87811, "lon": 145.16476, "name": "Glen Waverley" }, { "lat": -32.92953, "lon": 151.7801, "name": "Newcastle" }, { "lat": -37.63333, "lon": 144.86667, "name": "Greenvale" }, { "lat": 42.3751, "lon": -70.98283, "name": "Winthrop" } ], "question": "Which location is the geographic outlier among: Papakura, Glen Waverley, Newcastle, Greenvale, Winthrop?", "ground_truth": { "answer": "Winthrop", "outlier_distance_km": 17596.7, "second_furthest_km": 6534.0, "clarity_ratio": 2.69, "median_distance_km": 4413.6, "distances_to_centroid": { "Papakura": 6534.0, "Glen Waverley": 3950.4, "Newcastle": 4413.6, "Greenvale": 3916.8, "Winthrop": 17596.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Papakura: (-37.06°, 174.94°)", " Glen Waverley: (-37.88°, 145.16°)", " Newcastle: (-32.93°, 151.78°)", " Greenvale: (-37.63°, 144.87°)", " Winthrop: (42.38°, -70.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Winthrop: 17596.7 km from centroid", " Papakura: 6534.0 km from centroid", " Newcastle: 4413.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Winthrop", "FINAL ANSWER: Winthrop" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.16667, "lon": 145.16667, "name": "Langwarrin" }, { "lat": -31.84062, "lon": 115.89549, "name": "Ballajura" }, { "lat": -27.35364, "lon": 152.96848, "name": "Albany Creek" }, { "lat": -36.8282, "lon": 174.62019, "name": "Massey East" }, { "lat": -18.75639, "lon": -44.43083, "name": "Curvelo" } ], "question": "Which location is the geographic outlier among: Langwarrin, Ballajura, Albany Creek, Massey East, Curvelo?", "ground_truth": { "answer": "Curvelo", "outlier_distance_km": 13828.4, "second_furthest_km": 6004.8, "clarity_ratio": 2.3, "median_distance_km": 4280.5, "distances_to_centroid": { "Langwarrin": 3414.8, "Ballajura": 684.7, "Albany Creek": 4280.5, "Massey East": 6004.8, "Curvelo": 13828.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Langwarrin: (-38.17°, 145.17°)", " Ballajura: (-31.84°, 115.90°)", " Albany Creek: (-27.35°, 152.97°)", " Massey East: (-36.83°, 174.62°)", " Curvelo: (-18.76°, -44.43°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Curvelo: 13828.4 km from centroid", " Massey East: 6004.8 km from centroid", " Albany Creek: 4280.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Curvelo", "FINAL ANSWER: Curvelo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.32674, "lon": -78.92197, "name": "Johnstown" }, { "lat": 38.25424, "lon": -85.75941, "name": "Louisville" }, { "lat": 34.81521, "lon": -102.39932, "name": "Hereford" }, { "lat": 43.81205, "lon": -79.33082, "name": "Steeles" }, { "lat": 31.00205, "lon": 31.62626, "name": "Aş Şalāḩāt" } ], "question": "Which location is the geographic outlier among: Johnstown, Louisville, Hereford, Steeles, Aş Şalāḩāt?", "ground_truth": { "answer": "Aş Şalāḩāt", "outlier_distance_km": 8329.7, "second_furthest_km": 3525.8, "clarity_ratio": 2.36, "median_distance_km": 1995.5, "distances_to_centroid": { "Johnstown": 1409.7, "Louisville": 1995.5, "Hereford": 3525.8, "Steeles": 1537.2, "Aş Şalāḩāt": 8329.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Johnstown: (40.33°, -78.92°)", " Louisville: (38.25°, -85.76°)", " Hereford: (34.82°, -102.40°)", " Steeles: (43.81°, -79.33°)", " Aş Şalāḩāt: (31.00°, 31.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Aş Şalāḩāt: 8329.7 km from centroid", " Hereford: 3525.8 km from centroid", " Louisville: 1995.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Aş Şalāḩāt", "FINAL ANSWER: Aş Şalāḩāt" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": -27.49325, "lon": 153.05826, "name": "Coorparoo" }, { "lat": -36.99282, "lon": 174.87986, "name": "Manukau City" }, { "lat": -42.87936, "lon": 147.32941, "name": "Hobart" }, { "lat": 2.7717, "lon": -77.66536, "name": "Timbiquí" } ], "question": "Which location is the geographic outlier among: Cranbourne East, Coorparoo, Manukau City, Hobart, Timbiquí?", "ground_truth": { "answer": "Timbiquí", "outlier_distance_km": 17074.2, "second_furthest_km": 6147.2, "clarity_ratio": 2.78, "median_distance_km": 4342.2, "distances_to_centroid": { "Cranbourne East": 3547.5, "Coorparoo": 4342.2, "Manukau City": 6147.2, "Hobart": 3801.9, "Timbiquí": 17074.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cranbourne East: (-38.12°, 145.30°)", " Coorparoo: (-27.49°, 153.06°)", " Manukau City: (-36.99°, 174.88°)", " Hobart: (-42.88°, 147.33°)", " Timbiquí: (2.77°, -77.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Timbiquí: 17074.2 km from centroid", " Manukau City: 6147.2 km from centroid", " Coorparoo: 4342.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Timbiquí", "FINAL ANSWER: Timbiquí" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.33316, "lon": 37.64587, "name": "Chuka" }, { "lat": -28.52423, "lon": 28.81582, "name": "Phuthaditjhaba" }, { "lat": -28.78301, "lon": 32.03768, "name": "Richards Bay" }, { "lat": 6.66819, "lon": 9.16453, "name": "Obudu" }, { "lat": -9.33806, "lon": -38.25472, "name": "Glória" } ], "question": "Which location is the geographic outlier among: Chuka, Phuthaditjhaba, Richards Bay, Obudu, Glória?", "ground_truth": { "answer": "Glória", "outlier_distance_km": 5696.6, "second_furthest_km": 2928.4, "clarity_ratio": 1.95, "median_distance_km": 2645.1, "distances_to_centroid": { "Chuka": 2928.4, "Phuthaditjhaba": 2398.2, "Richards Bay": 2645.1, "Obudu": 2147.0, "Glória": 5696.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chuka: (-0.33°, 37.65°)", " Phuthaditjhaba: (-28.52°, 28.82°)", " Richards Bay: (-28.78°, 32.04°)", " Obudu: (6.67°, 9.16°)", " Glória: (-9.34°, -38.25°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glória: 5696.6 km from centroid", " Chuka: 2928.4 km from centroid", " Richards Bay: 2645.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glória", "FINAL ANSWER: Glória" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.56839, "lon": -73.20568, "name": "Beloeil" }, { "lat": 17.98625, "lon": -92.93928, "name": "Villahermosa" }, { "lat": 37.90631, "lon": -122.06496, "name": "Walnut Creek" }, { "lat": 44.82774, "lon": -92.94382, "name": "Cottage Grove" }, { "lat": 48.85029, "lon": 2.14523, "name": "La Celle-Saint-Cloud" } ], "question": "Which location is the geographic outlier among: Beloeil, Villahermosa, Walnut Creek, Cottage Grove, La Celle-Saint-Cloud?", "ground_truth": { "answer": "La Celle-Saint-Cloud", "outlier_distance_km": 6058.6, "second_furthest_km": 3985.6, "clarity_ratio": 1.52, "median_distance_km": 2866.0, "distances_to_centroid": { "Beloeil": 757.9, "Villahermosa": 2866.0, "Walnut Creek": 3985.6, "Cottage Grove": 1553.8, "La Celle-Saint-Cloud": 6058.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Beloeil: (45.57°, -73.21°)", " Villahermosa: (17.99°, -92.94°)", " Walnut Creek: (37.91°, -122.06°)", " Cottage Grove: (44.83°, -92.94°)", " La Celle-Saint-Cloud: (48.85°, 2.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " La Celle-Saint-Cloud: 6058.6 km from centroid", " Walnut Creek: 3985.6 km from centroid", " Villahermosa: 2866.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: La Celle-Saint-Cloud", "FINAL ANSWER: La Celle-Saint-Cloud" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.52806, "lon": 37.59917, "name": "Drozhzhino" }, { "lat": 50.14264, "lon": 19.13149, "name": "Lędziny" }, { "lat": 51.3025, "lon": 37.84613, "name": "Staryy Oskol" }, { "lat": 46.37049, "lon": 6.47985, "name": "Thonon-les-Bains" }, { "lat": 7.43636, "lon": 5.45925, "name": "Emure-Ekiti" } ], "question": "Which location is the geographic outlier among: Drozhzhino, Lędziny, Staryy Oskol, Thonon-les-Bains, Emure-Ekiti?", "ground_truth": { "answer": "Emure-Ekiti", "outlier_distance_km": 4162.8, "second_furthest_km": 1896.3, "clarity_ratio": 2.2, "median_distance_km": 1613.5, "distances_to_centroid": { "Drozhzhino": 1896.3, "Lędziny": 903.6, "Staryy Oskol": 1613.5, "Thonon-les-Bains": 1267.6, "Emure-Ekiti": 4162.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Drozhzhino: (55.53°, 37.60°)", " Lędziny: (50.14°, 19.13°)", " Staryy Oskol: (51.30°, 37.85°)", " Thonon-les-Bains: (46.37°, 6.48°)", " Emure-Ekiti: (7.44°, 5.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Emure-Ekiti: 4162.8 km from centroid", " Drozhzhino: 1896.3 km from centroid", " Staryy Oskol: 1613.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Emure-Ekiti", "FINAL ANSWER: Emure-Ekiti" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.11342, "lon": 145.28326, "name": "Cranbourne" }, { "lat": -39.93333, "lon": 175.05, "name": "Whanganui" }, { "lat": -37.71667, "lon": 145.0, "name": "Reservoir" }, { "lat": -34.75155, "lon": 149.72086, "name": "Goulburn" }, { "lat": -34.64203, "lon": -60.47124, "name": "Chacabuco" } ], "question": "Which location is the geographic outlier among: Cranbourne, Whanganui, Reservoir, Goulburn, Chacabuco?", "ground_truth": { "answer": "Chacabuco", "outlier_distance_km": 11995.7, "second_furthest_km": 5468.9, "clarity_ratio": 2.19, "median_distance_km": 3480.6, "distances_to_centroid": { "Cranbourne": 3013.8, "Whanganui": 5468.9, "Reservoir": 2996.0, "Goulburn": 3480.6, "Chacabuco": 11995.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cranbourne: (-38.11°, 145.28°)", " Whanganui: (-39.93°, 175.05°)", " Reservoir: (-37.72°, 145.00°)", " Goulburn: (-34.75°, 149.72°)", " Chacabuco: (-34.64°, -60.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chacabuco: 11995.7 km from centroid", " Whanganui: 5468.9 km from centroid", " Goulburn: 3480.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chacabuco", "FINAL ANSWER: Chacabuco" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.63806, "lon": -51.00694, "name": "Sapiranga" }, { "lat": -5.61278, "lon": -38.76694, "name": "Jaguaretama" }, { "lat": -35.6593, "lon": -63.75787, "name": "General Pico" }, { "lat": -25.51626, "lon": -48.52537, "name": "Paranaguá" }, { "lat": 46.23958, "lon": -119.10057, "name": "Pasco" } ], "question": "Which location is the geographic outlier among: Sapiranga, Jaguaretama, General Pico, Paranaguá, Pasco?", "ground_truth": { "answer": "Pasco", "outlier_distance_km": 8292.0, "second_furthest_km": 2849.4, "clarity_ratio": 2.91, "median_distance_km": 2846.8, "distances_to_centroid": { "Sapiranga": 2576.1, "Jaguaretama": 2846.8, "General Pico": 2849.4, "Paranaguá": 2388.4, "Pasco": 8292.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sapiranga: (-29.64°, -51.01°)", " Jaguaretama: (-5.61°, -38.77°)", " General Pico: (-35.66°, -63.76°)", " Paranaguá: (-25.52°, -48.53°)", " Pasco: (46.24°, -119.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pasco: 8292.0 km from centroid", " General Pico: 2849.4 km from centroid", " Jaguaretama: 2846.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pasco", "FINAL ANSWER: Pasco" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.785, "lon": -53.07333, "name": "Cruzeiro do Oeste" }, { "lat": -19.76694, "lon": -44.08667, "name": "Ribeirão das Neves" }, { "lat": -35.63884, "lon": -59.77938, "name": "Saladillo" }, { "lat": -33.59473, "lon": -71.60746, "name": "San Antonio" }, { "lat": 54.46405, "lon": 17.02872, "name": "Słupsk" } ], "question": "Which location is the geographic outlier among: Cruzeiro do Oeste, Ribeirão das Neves, Saladillo, San Antonio, Słupsk?", "ground_truth": { "answer": "Słupsk", "outlier_distance_km": 9203.9, "second_furthest_km": 3846.1, "clarity_ratio": 2.39, "median_distance_km": 3193.4, "distances_to_centroid": { "Cruzeiro do Oeste": 1763.8, "Ribeirão das Neves": 920.9, "Saladillo": 3193.4, "San Antonio": 3846.1, "Słupsk": 9203.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cruzeiro do Oeste: (-23.79°, -53.07°)", " Ribeirão das Neves: (-19.77°, -44.09°)", " Saladillo: (-35.64°, -59.78°)", " San Antonio: (-33.59°, -71.61°)", " Słupsk: (54.46°, 17.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Słupsk: 9203.9 km from centroid", " San Antonio: 3846.1 km from centroid", " Saladillo: 3193.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Słupsk", "FINAL ANSWER: Słupsk" ] }, { "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": -15.79444, "lon": -48.77583, "name": "Cocalzinho de Goiás" }, { "lat": -21.51472, "lon": -51.43361, "name": "Junqueirópolis" }, { "lat": -34.47513, "lon": -58.75367, "name": "Tortuguitas" }, { "lat": -3.12873, "lon": -58.15501, "name": "Urucurituba" }, { "lat": 52.40881, "lon": 7.97288, "name": "Bramsche" } ], "question": "Which location is the geographic outlier among: Cocalzinho de Goiás, Junqueirópolis, Tortuguitas, Urucurituba, Bramsche?", "ground_truth": { "answer": "Bramsche", "outlier_distance_km": 7862.7, "second_furthest_km": 3762.2, "clarity_ratio": 2.09, "median_distance_km": 2157.0, "distances_to_centroid": { "Cocalzinho de Goiás": 1467.3, "Junqueirópolis": 2157.0, "Tortuguitas": 3762.2, "Urucurituba": 1817.7, "Bramsche": 7862.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cocalzinho de Goiás: (-15.79°, -48.78°)", " Junqueirópolis: (-21.51°, -51.43°)", " Tortuguitas: (-34.48°, -58.75°)", " Urucurituba: (-3.13°, -58.16°)", " Bramsche: (52.41°, 7.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bramsche: 7862.7 km from centroid", " Tortuguitas: 3762.2 km from centroid", " Junqueirópolis: 2157.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bramsche", "FINAL ANSWER: Bramsche" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.80413, "lon": -93.16689, "name": "Eagan" }, { "lat": 20.73072, "lon": -105.28257, "name": "Mezcales" }, { "lat": 34.01949, "lon": -118.49138, "name": "Santa Monica" }, { "lat": 37.5841, "lon": -122.36608, "name": "Burlingame" }, { "lat": 24.8, "lon": 113.58333, "name": "Shaoguan" } ], "question": "Which location is the geographic outlier among: Eagan, Mezcales, Santa Monica, Burlingame, Shaoguan?", "ground_truth": { "answer": "Shaoguan", "outlier_distance_km": 13654.7, "second_furthest_km": 5164.9, "clarity_ratio": 2.64, "median_distance_km": 4909.3, "distances_to_centroid": { "Eagan": 2778.9, "Mezcales": 4169.5, "Santa Monica": 4909.3, "Burlingame": 5164.9, "Shaoguan": 13654.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Eagan: (44.80°, -93.17°)", " Mezcales: (20.73°, -105.28°)", " Santa Monica: (34.02°, -118.49°)", " Burlingame: (37.58°, -122.37°)", " Shaoguan: (24.80°, 113.58°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shaoguan: 13654.7 km from centroid", " Burlingame: 5164.9 km from centroid", " Santa Monica: 4909.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shaoguan", "FINAL ANSWER: Shaoguan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.8327, "lon": 5.7934, "name": "Lindenholt" }, { "lat": 39.85316, "lon": 3.12138, "name": "Alcúdia" }, { "lat": 42.69764, "lon": 2.89541, "name": "Perpignan" }, { "lat": 40.45178, "lon": -3.58667, "name": "Alameda de Osuna" }, { "lat": 39.7, "lon": 141.15, "name": "Morioka" } ], "question": "Which location is the geographic outlier among: Lindenholt, Alcúdia, Perpignan, Alameda de Osuna, Morioka?", "ground_truth": { "answer": "Morioka", "outlier_distance_km": 8526.4, "second_furthest_km": 2773.9, "clarity_ratio": 3.07, "median_distance_km": 2248.1, "distances_to_centroid": { "Lindenholt": 2053.6, "Alcúdia": 2248.1, "Perpignan": 2191.7, "Alameda de Osuna": 2773.9, "Morioka": 8526.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lindenholt: (51.83°, 5.79°)", " Alcúdia: (39.85°, 3.12°)", " Perpignan: (42.70°, 2.90°)", " Alameda de Osuna: (40.45°, -3.59°)", " Morioka: (39.70°, 141.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Morioka: 8526.4 km from centroid", " Alameda de Osuna: 2773.9 km from centroid", " Alcúdia: 2248.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Morioka", "FINAL ANSWER: Morioka" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.96014, "lon": 2.87885, "name": "Meaux" }, { "lat": 43.64561, "lon": 0.58856, "name": "Auch" }, { "lat": 51.33705, "lon": -0.74261, "name": "Camberley" }, { "lat": 50.68135, "lon": 8.30369, "name": "Herborn" }, { "lat": -37.75819, "lon": 145.00583, "name": "Thornbury" } ], "question": "Which location is the geographic outlier among: Meaux, Auch, Camberley, Herborn, Thornbury?", "ground_truth": { "answer": "Thornbury", "outlier_distance_km": 14037.3, "second_furthest_km": 3423.0, "clarity_ratio": 4.1, "median_distance_km": 3070.0, "distances_to_centroid": { "Meaux": 3070.0, "Auch": 3002.2, "Camberley": 3423.0, "Herborn": 2857.3, "Thornbury": 14037.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Meaux: (48.96°, 2.88°)", " Auch: (43.65°, 0.59°)", " Camberley: (51.34°, -0.74°)", " Herborn: (50.68°, 8.30°)", " Thornbury: (-37.76°, 145.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Thornbury: 14037.3 km from centroid", " Camberley: 3423.0 km from centroid", " Meaux: 3070.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Thornbury", "FINAL ANSWER: Thornbury" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.15667, "lon": -50.38667, "name": "Afuá" }, { "lat": -28.93575, "lon": -49.49538, "name": "Araranguá" }, { "lat": -39.64355, "lon": -72.33269, "name": "Panguipulli" }, { "lat": -34.46971, "lon": -58.52111, "name": "San Isidro" }, { "lat": 47.80527, "lon": -122.24064, "name": "Bothell West" } ], "question": "Which location is the geographic outlier among: Afuá, Araranguá, Panguipulli, San Isidro, Bothell West?", "ground_truth": { "answer": "Bothell West", "outlier_distance_km": 8288.0, "second_furthest_km": 3180.7, "clarity_ratio": 2.61, "median_distance_km": 2956.4, "distances_to_centroid": { "Afuá": 2541.7, "Araranguá": 2956.4, "Panguipulli": 3180.7, "San Isidro": 2874.5, "Bothell West": 8288.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Afuá: (-0.16°, -50.39°)", " Araranguá: (-28.94°, -49.50°)", " Panguipulli: (-39.64°, -72.33°)", " San Isidro: (-34.47°, -58.52°)", " Bothell West: (47.81°, -122.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bothell West: 8288.0 km from centroid", " Panguipulli: 3180.7 km from centroid", " Araranguá: 2956.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bothell West", "FINAL ANSWER: Bothell West" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 60.15328, "lon": 59.95205, "name": "Severoural’sk" }, { "lat": 42.66123, "lon": 13.69901, "name": "Teramo" }, { "lat": 37.65896, "lon": -5.52751, "name": "Lora del Río" }, { "lat": 49.11624, "lon": -1.09031, "name": "Saint-Lô" }, { "lat": 36.16667, "lon": 139.53333, "name": "Hanyū" } ], "question": "Which location is the geographic outlier among: Severoural’sk, Teramo, Lora del Río, Saint-Lô, Hanyū?", "ground_truth": { "answer": "Hanyū", "outlier_distance_km": 7817.7, "second_furthest_km": 3937.1, "clarity_ratio": 1.99, "median_distance_km": 3195.1, "distances_to_centroid": { "Severoural’sk": 2073.4, "Teramo": 2218.5, "Lora del Río": 3937.1, "Saint-Lô": 3195.1, "Hanyū": 7817.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Severoural’sk: (60.15°, 59.95°)", " Teramo: (42.66°, 13.70°)", " Lora del Río: (37.66°, -5.53°)", " Saint-Lô: (49.12°, -1.09°)", " Hanyū: (36.17°, 139.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hanyū: 7817.7 km from centroid", " Lora del Río: 3937.1 km from centroid", " Saint-Lô: 3195.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hanyū", "FINAL ANSWER: Hanyū" ] }, { "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": -38.07758, "lon": 145.29871, "name": "Cranbourne North" }, { "lat": -34.91119, "lon": 138.70735, "name": "Adelaide Hills" }, { "lat": -33.73333, "lon": 150.88333, "name": "Quakers Hill" }, { "lat": -37.74981, "lon": 144.9109, "name": "Essendon" }, { "lat": 47.51659, "lon": -52.78135, "name": "Mount Pearl" } ], "question": "Which location is the geographic outlier among: Cranbourne North, Adelaide Hills, Quakers Hill, Essendon, Mount Pearl?", "ground_truth": { "answer": "Mount Pearl", "outlier_distance_km": 16318.0, "second_furthest_km": 4752.8, "clarity_ratio": 3.43, "median_distance_km": 4363.9, "distances_to_centroid": { "Cranbourne North": 4363.9, "Adelaide Hills": 3694.7, "Quakers Hill": 4752.8, "Essendon": 4320.7, "Mount Pearl": 16318.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cranbourne North: (-38.08°, 145.30°)", " Adelaide Hills: (-34.91°, 138.71°)", " Quakers Hill: (-33.73°, 150.88°)", " Essendon: (-37.75°, 144.91°)", " Mount Pearl: (47.52°, -52.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mount Pearl: 16318.0 km from centroid", " Quakers Hill: 4752.8 km from centroid", " Cranbourne North: 4363.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mount Pearl", "FINAL ANSWER: Mount Pearl" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.75675, "lon": 34.59833, "name": "Rongo" }, { "lat": -30.64966, "lon": 24.0123, "name": "De Aar" }, { "lat": -33.83136, "lon": 20.05595, "name": "Ashton" }, { "lat": 10.48536, "lon": 5.14501, "name": "Ibeto" }, { "lat": -33.73333, "lon": 150.93284, "name": "Glenwood" } ], "question": "Which location is the geographic outlier among: Rongo, De Aar, Ashton, Ibeto, Glenwood?", "ground_truth": { "answer": "Glenwood", "outlier_distance_km": 10151.8, "second_furthest_km": 5558.2, "clarity_ratio": 1.83, "median_distance_km": 3219.3, "distances_to_centroid": { "Rongo": 2317.6, "De Aar": 2727.4, "Ashton": 3219.3, "Ibeto": 5558.2, "Glenwood": 10151.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rongo: (-0.76°, 34.60°)", " De Aar: (-30.65°, 24.01°)", " Ashton: (-33.83°, 20.06°)", " Ibeto: (10.49°, 5.15°)", " Glenwood: (-33.73°, 150.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glenwood: 10151.8 km from centroid", " Ibeto: 5558.2 km from centroid", " Ashton: 3219.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glenwood", "FINAL ANSWER: Glenwood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 31.64637, "lon": 130.99068, "name": "Soo" }, { "lat": 10.455, "lon": 124.0106, "name": "Compostela" }, { "lat": 36.36417, "lon": 119.07694, "name": "Linghe" }, { "lat": 5.48333, "lon": 100.38333, "name": "Kampung Teluk Air Tawar" }, { "lat": -3.8325, "lon": -45.1525, "name": "Pio XII" } ], "question": "Which location is the geographic outlier among: Soo, Compostela, Linghe, Kampung Teluk Air Tawar, Pio XII?", "ground_truth": { "answer": "Pio XII", "outlier_distance_km": 14497.1, "second_furthest_km": 4867.2, "clarity_ratio": 2.98, "median_distance_km": 4169.4, "distances_to_centroid": { "Soo": 4867.2, "Compostela": 4169.4, "Linghe": 3979.4, "Kampung Teluk Air Tawar": 1970.2, "Pio XII": 14497.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Soo: (31.65°, 130.99°)", " Compostela: (10.46°, 124.01°)", " Linghe: (36.36°, 119.08°)", " Kampung Teluk Air Tawar: (5.48°, 100.38°)", " Pio XII: (-3.83°, -45.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pio XII: 14497.1 km from centroid", " Soo: 4867.2 km from centroid", " Compostela: 4169.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pio XII", "FINAL ANSWER: Pio XII" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.40304, "lon": 134.77118, "name": "Yabu" }, { "lat": -7.61278, "lon": 110.78389, "name": "Baki" }, { "lat": 21.65921, "lon": 109.20011, "name": "Hepu" }, { "lat": 34.20442, "lon": 117.28386, "name": "Xuzhou" }, { "lat": -13.03667, "lon": -46.77167, "name": "Campos Belos" } ], "question": "Which location is the geographic outlier among: Yabu, Baki, Hepu, Xuzhou, Campos Belos?", "ground_truth": { "answer": "Campos Belos", "outlier_distance_km": 14815.8, "second_furthest_km": 5479.1, "clarity_ratio": 2.7, "median_distance_km": 3930.9, "distances_to_centroid": { "Yabu": 5479.1, "Baki": 3728.4, "Hepu": 2685.0, "Xuzhou": 3930.9, "Campos Belos": 14815.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yabu: (35.40°, 134.77°)", " Baki: (-7.61°, 110.78°)", " Hepu: (21.66°, 109.20°)", " Xuzhou: (34.20°, 117.28°)", " Campos Belos: (-13.04°, -46.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Campos Belos: 14815.8 km from centroid", " Yabu: 5479.1 km from centroid", " Xuzhou: 3930.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Campos Belos", "FINAL ANSWER: Campos Belos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.68866, "lon": 21.77058, "name": "Krosno" }, { "lat": 53.16495, "lon": -1.19384, "name": "Mansfield Woodhouse" }, { "lat": 52.96572, "lon": 10.56111, "name": "Uelzen" }, { "lat": 41.19997, "lon": 1.5683, "name": "Calafell" }, { "lat": 41.1476, "lon": -73.98931, "name": "New City" } ], "question": "Which location is the geographic outlier among: Krosno, Mansfield Woodhouse, Uelzen, Calafell, New City?", "ground_truth": { "answer": "New City", "outlier_distance_km": 5114.5, "second_furthest_km": 2202.3, "clarity_ratio": 2.32, "median_distance_km": 1456.6, "distances_to_centroid": { "Krosno": 2202.3, "Mansfield Woodhouse": 792.3, "Uelzen": 1456.6, "Calafell": 1057.1, "New City": 5114.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Krosno: (49.69°, 21.77°)", " Mansfield Woodhouse: (53.16°, -1.19°)", " Uelzen: (52.97°, 10.56°)", " Calafell: (41.20°, 1.57°)", " New City: (41.15°, -73.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New City: 5114.5 km from centroid", " Krosno: 2202.3 km from centroid", " Uelzen: 1456.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New City", "FINAL ANSWER: New City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.66819, "lon": 9.16453, "name": "Obudu" }, { "lat": -28.78301, "lon": 32.03768, "name": "Richards Bay" }, { "lat": 27.25738, "lon": 33.81291, "name": "Hurghada" }, { "lat": -1.08083, "lon": 35.87111, "name": "Narok" }, { "lat": 34.97528, "lon": 127.58917, "name": "Kwangyang" } ], "question": "Which location is the geographic outlier among: Obudu, Richards Bay, Hurghada, Narok, Kwangyang?", "ground_truth": { "answer": "Kwangyang", "outlier_distance_km": 8592.3, "second_furthest_km": 4401.5, "clarity_ratio": 1.95, "median_distance_km": 4250.7, "distances_to_centroid": { "Obudu": 4250.7, "Richards Bay": 4401.5, "Hurghada": 2610.7, "Narok": 1641.9, "Kwangyang": 8592.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Obudu: (6.67°, 9.16°)", " Richards Bay: (-28.78°, 32.04°)", " Hurghada: (27.26°, 33.81°)", " Narok: (-1.08°, 35.87°)", " Kwangyang: (34.98°, 127.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kwangyang: 8592.3 km from centroid", " Richards Bay: 4401.5 km from centroid", " Obudu: 4250.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kwangyang", "FINAL ANSWER: Kwangyang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.70773, "lon": 6.43402, "name": "Kwale" }, { "lat": 30.03103, "lon": 31.11109, "name": "Kirdāsah" }, { "lat": 7.50251, "lon": 5.06258, "name": "Igbara-Odo" }, { "lat": 4.92675, "lon": 6.26764, "name": "Yenagoa" }, { "lat": 41.51198, "lon": -87.96561, "name": "New Lenox" } ], "question": "Which location is the geographic outlier among: Kwale, Kirdāsah, Igbara-Odo, Yenagoa, New Lenox?", "ground_truth": { "answer": "New Lenox", "outlier_distance_km": 7891.9, "second_furthest_km": 4153.8, "clarity_ratio": 1.9, "median_distance_km": 2106.5, "distances_to_centroid": { "Kwale": 2060.1, "Kirdāsah": 4153.8, "Igbara-Odo": 1814.2, "Yenagoa": 2106.5, "New Lenox": 7891.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kwale: (5.71°, 6.43°)", " Kirdāsah: (30.03°, 31.11°)", " Igbara-Odo: (7.50°, 5.06°)", " Yenagoa: (4.93°, 6.27°)", " New Lenox: (41.51°, -87.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New Lenox: 7891.9 km from centroid", " Kirdāsah: 4153.8 km from centroid", " Yenagoa: 2106.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New Lenox", "FINAL ANSWER: New Lenox" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.88165, "lon": 47.63919, "name": "Kaspiysk" }, { "lat": 41.3845, "lon": 2.18152, "name": "Sant Pere, Santa Caterina i La Ribera" }, { "lat": 43.30047, "lon": 5.40563, "name": "La Blancarde" }, { "lat": 53.50291, "lon": -1.3458, "name": "Wath upon Dearne" }, { "lat": 26.8589, "lon": 100.914, "name": "Zhanhe" } ], "question": "Which location is the geographic outlier among: Kaspiysk, Sant Pere, Santa Caterina i La Ribera, La Blancarde, Wath upon Dearne, Zhanhe?", "ground_truth": { "answer": "Zhanhe", "outlier_distance_km": 6459.3, "second_furthest_km": 2730.0, "clarity_ratio": 2.37, "median_distance_km": 2386.0, "distances_to_centroid": { "Kaspiysk": 1378.5, "Sant Pere, Santa Caterina i La Ribera": 2386.0, "La Blancarde": 2097.2, "Wath upon Dearne": 2730.0, "Zhanhe": 6459.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kaspiysk: (42.88°, 47.64°)", " Sant Pere, Santa Caterina i La Ribera: (41.38°, 2.18°)", " La Blancarde: (43.30°, 5.41°)", " Wath upon Dearne: (53.50°, -1.35°)", " Zhanhe: (26.86°, 100.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zhanhe: 6459.3 km from centroid", " Wath upon Dearne: 2730.0 km from centroid", " Sant Pere, Santa Caterina i La Ribera: 2386.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zhanhe", "FINAL ANSWER: Zhanhe" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.81843, "lon": -73.14372, "name": "West Torrington" }, { "lat": 19.27127, "lon": -99.45787, "name": "Ocoyoacac" }, { "lat": 19.32932, "lon": -98.1664, "name": "Contla" }, { "lat": 27.50641, "lon": -99.50754, "name": "Laredo" }, { "lat": 4.75477, "lon": 115.01011, "name": "Limbang" } ], "question": "Which location is the geographic outlier among: West Torrington, Ocoyoacac, Contla, Laredo, Limbang?", "ground_truth": { "answer": "Limbang", "outlier_distance_km": 16623.2, "second_furthest_km": 5020.0, "clarity_ratio": 3.31, "median_distance_km": 4886.4, "distances_to_centroid": { "West Torrington": 2968.9, "Ocoyoacac": 5020.0, "Contla": 4886.4, "Laredo": 4883.4, "Limbang": 16623.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " West Torrington: (41.82°, -73.14°)", " Ocoyoacac: (19.27°, -99.46°)", " Contla: (19.33°, -98.17°)", " Laredo: (27.51°, -99.51°)", " Limbang: (4.75°, 115.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Limbang: 16623.2 km from centroid", " Ocoyoacac: 5020.0 km from centroid", " Contla: 4886.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Limbang", "FINAL ANSWER: Limbang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.88076, "lon": 27.39377, "name": "Qonce" }, { "lat": 9.61524, "lon": 6.54776, "name": "Minna" }, { "lat": 31.01887, "lon": 33.0098, "name": "Bi’r al ‘Abd" }, { "lat": 26.33721, "lon": 31.89295, "name": "Girga" }, { "lat": -38.07758, "lon": 145.29871, "name": "Cranbourne North" } ], "question": "Which location is the geographic outlier among: Qonce, Minna, Bi’r al ‘Abd, Girga, Cranbourne North?", "ground_truth": { "answer": "Cranbourne North", "outlier_distance_km": 10518.5, "second_furthest_km": 4821.3, "clarity_ratio": 2.18, "median_distance_km": 4213.1, "distances_to_centroid": { "Qonce": 4213.1, "Minna": 4821.3, "Bi’r al ‘Abd": 3912.5, "Girga": 3521.7, "Cranbourne North": 10518.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Qonce: (-32.88°, 27.39°)", " Minna: (9.62°, 6.55°)", " Bi’r al ‘Abd: (31.02°, 33.01°)", " Girga: (26.34°, 31.89°)", " Cranbourne North: (-38.08°, 145.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cranbourne North: 10518.5 km from centroid", " Minna: 4821.3 km from centroid", " Qonce: 4213.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cranbourne North", "FINAL ANSWER: Cranbourne North" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 13.7068, "lon": 123.2087, "name": "Calabanga" }, { "lat": 35.405, "lon": 116.58139, "name": "Jining" }, { "lat": 34.36861, "lon": 117.115, "name": "Liuxin" }, { "lat": 29.15196, "lon": 108.74289, "name": "Apengjiang" }, { "lat": -23.83322, "lon": 30.16351, "name": "Tzaneen" } ], "question": "Which location is the geographic outlier among: Calabanga, Jining, Liuxin, Apengjiang, Tzaneen?", "ground_truth": { "answer": "Tzaneen", "outlier_distance_km": 8796.5, "second_furthest_km": 2610.8, "clarity_ratio": 3.37, "median_distance_km": 2608.4, "distances_to_centroid": { "Calabanga": 2610.8, "Jining": 2608.4, "Liuxin": 2565.6, "Apengjiang": 1598.3, "Tzaneen": 8796.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Calabanga: (13.71°, 123.21°)", " Jining: (35.41°, 116.58°)", " Liuxin: (34.37°, 117.11°)", " Apengjiang: (29.15°, 108.74°)", " Tzaneen: (-23.83°, 30.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tzaneen: 8796.5 km from centroid", " Calabanga: 2610.8 km from centroid", " Jining: 2608.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tzaneen", "FINAL ANSWER: Tzaneen" ] }, { "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": -8.52278, "lon": -36.44444, "name": "São Bento do Una" }, { "lat": -18.03111, "lon": -41.685, "name": "Itambacuri" }, { "lat": -29.71671, "lon": -52.50321, "name": "Vera Cruz" }, { "lat": -29.44806, "lon": -50.58361, "name": "São Francisco de Paula" }, { "lat": 29.21081, "lon": -81.02283, "name": "Daytona Beach" } ], "question": "Which location is the geographic outlier among: São Bento do Una, Itambacuri, Vera Cruz, São Francisco de Paula, Daytona Beach?", "ground_truth": { "answer": "Daytona Beach", "outlier_distance_km": 5449.0, "second_furthest_km": 2047.7, "clarity_ratio": 2.66, "median_distance_km": 2027.0, "distances_to_centroid": { "São Bento do Una": 1779.6, "Itambacuri": 1377.8, "Vera Cruz": 2047.7, "São Francisco de Paula": 2027.0, "Daytona Beach": 5449.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Bento do Una: (-8.52°, -36.44°)", " Itambacuri: (-18.03°, -41.69°)", " Vera Cruz: (-29.72°, -52.50°)", " São Francisco de Paula: (-29.45°, -50.58°)", " Daytona Beach: (29.21°, -81.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Daytona Beach: 5449.0 km from centroid", " Vera Cruz: 2047.7 km from centroid", " São Francisco de Paula: 2027.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Daytona Beach", "FINAL ANSWER: Daytona Beach" ] }, { "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": -37.86667, "lon": 145.06667, "name": "Glen Iris" }, { "lat": -34.91119, "lon": 138.70735, "name": "Adelaide Hills" }, { "lat": -33.83902, "lon": 151.23956, "name": "Mosman" }, { "lat": -37.66667, "lon": 145.06667, "name": "Mill Park" }, { "lat": 8.71742, "lon": 76.72582, "name": "Vettūr" } ], "question": "Which location is the geographic outlier among: Glen Iris, Adelaide Hills, Mosman, Mill Park, Vettūr?", "ground_truth": { "answer": "Vettūr", "outlier_distance_km": 7103.9, "second_furthest_km": 2042.1, "clarity_ratio": 3.48, "median_distance_km": 1751.9, "distances_to_centroid": { "Glen Iris": 1751.9, "Adelaide Hills": 1113.7, "Mosman": 2042.1, "Mill Park": 1738.0, "Vettūr": 7103.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Glen Iris: (-37.87°, 145.07°)", " Adelaide Hills: (-34.91°, 138.71°)", " Mosman: (-33.84°, 151.24°)", " Mill Park: (-37.67°, 145.07°)", " Vettūr: (8.72°, 76.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vettūr: 7103.9 km from centroid", " Mosman: 2042.1 km from centroid", " Glen Iris: 1751.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vettūr", "FINAL ANSWER: Vettūr" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.5391, "lon": 121.0726, "name": "Pateros" }, { "lat": 30.65723, "lon": 109.44599, "name": "Xinglong" }, { "lat": 38.55258, "lon": 106.34805, "name": "Xigang" }, { "lat": 10.81942, "lon": 76.0064, "name": "Kāladi" }, { "lat": 38.44047, "lon": -122.71443, "name": "Santa Rosa" } ], "question": "Which location is the geographic outlier among: Pateros, Xinglong, Xigang, Kāladi, Santa Rosa?", "ground_truth": { "answer": "Santa Rosa", "outlier_distance_km": 12782.3, "second_furthest_km": 6636.4, "clarity_ratio": 1.93, "median_distance_km": 4995.3, "distances_to_centroid": { "Pateros": 6636.4, "Xinglong": 4995.3, "Xigang": 4661.2, "Kāladi": 2574.8, "Santa Rosa": 12782.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pateros: (14.54°, 121.07°)", " Xinglong: (30.66°, 109.45°)", " Xigang: (38.55°, 106.35°)", " Kāladi: (10.82°, 76.01°)", " Santa Rosa: (38.44°, -122.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santa Rosa: 12782.3 km from centroid", " Pateros: 6636.4 km from centroid", " Xinglong: 4995.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santa Rosa", "FINAL ANSWER: Santa Rosa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.93245, "lon": -95.38021, "name": "Aldine" }, { "lat": 40.82927, "lon": -73.90653, "name": "Morrisania" }, { "lat": 46.34515, "lon": -72.5477, "name": "Trois-Rivières" }, { "lat": 46.09454, "lon": -64.7965, "name": "Moncton" }, { "lat": 24.63881, "lon": 93.99639, "name": "Thoubāl" } ], "question": "Which location is the geographic outlier among: Aldine, Morrisania, Trois-Rivières, Moncton, Thoubāl?", "ground_truth": { "answer": "Thoubāl", "outlier_distance_km": 11740.2, "second_furthest_km": 4895.5, "clarity_ratio": 2.4, "median_distance_km": 2713.5, "distances_to_centroid": { "Aldine": 4895.5, "Morrisania": 2713.5, "Trois-Rivières": 2647.6, "Moncton": 2064.6, "Thoubāl": 11740.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Aldine: (29.93°, -95.38°)", " Morrisania: (40.83°, -73.91°)", " Trois-Rivières: (46.35°, -72.55°)", " Moncton: (46.09°, -64.80°)", " Thoubāl: (24.64°, 94.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Thoubāl: 11740.2 km from centroid", " Aldine: 4895.5 km from centroid", " Morrisania: 2713.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Thoubāl", "FINAL ANSWER: Thoubāl" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 2.43986, "lon": -60.91146, "name": "Mucajaí" }, { "lat": -29.33528, "lon": -49.72694, "name": "Torres" }, { "lat": -11.04404, "lon": -41.97102, "name": "Jussara" }, { "lat": -34.5664, "lon": -59.11478, "name": "Luján" }, { "lat": -37.83961, "lon": 144.94228, "name": "Port Melbourne" } ], "question": "Which location is the geographic outlier among: Mucajaí, Torres, Jussara, Luján, Port Melbourne?", "ground_truth": { "answer": "Port Melbourne", "outlier_distance_km": 12977.8, "second_furthest_km": 5836.8, "clarity_ratio": 2.22, "median_distance_km": 4646.8, "distances_to_centroid": { "Mucajaí": 5836.8, "Torres": 3716.9, "Jussara": 3279.0, "Luján": 4646.8, "Port Melbourne": 12977.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mucajaí: (2.44°, -60.91°)", " Torres: (-29.34°, -49.73°)", " Jussara: (-11.04°, -41.97°)", " Luján: (-34.57°, -59.11°)", " Port Melbourne: (-37.84°, 144.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Port Melbourne: 12977.8 km from centroid", " Mucajaí: 5836.8 km from centroid", " Luján: 4646.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Port Melbourne", "FINAL ANSWER: Port Melbourne" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.61366, "lon": -86.10665, "name": "Greenwood" }, { "lat": 40.40816, "lon": -74.35432, "name": "South Old Bridge" }, { "lat": 19.20959, "lon": -98.75636, "name": "San Rafael" }, { "lat": 33.976, "lon": -118.06909, "name": "West Whittier-Los Nietos" }, { "lat": 27.25738, "lon": 33.81291, "name": "Hurghada" } ], "question": "Which location is the geographic outlier among: Greenwood, South Old Bridge, San Rafael, West Whittier-Los Nietos, Hurghada?", "ground_truth": { "answer": "Hurghada", "outlier_distance_km": 9495.9, "second_furthest_km": 4562.5, "clarity_ratio": 2.08, "median_distance_km": 3320.7, "distances_to_centroid": { "Greenwood": 1773.8, "South Old Bridge": 1054.1, "San Rafael": 3320.7, "West Whittier-Los Nietos": 4562.5, "Hurghada": 9495.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Greenwood: (39.61°, -86.11°)", " South Old Bridge: (40.41°, -74.35°)", " San Rafael: (19.21°, -98.76°)", " West Whittier-Los Nietos: (33.98°, -118.07°)", " Hurghada: (27.26°, 33.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hurghada: 9495.9 km from centroid", " West Whittier-Los Nietos: 4562.5 km from centroid", " San Rafael: 3320.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hurghada", "FINAL ANSWER: Hurghada" ] }, { "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": 51.52392, "lon": 6.9285, "name": "Bottrop" }, { "lat": 40.85907, "lon": 14.17314, "name": "Pianura" }, { "lat": 49.50126, "lon": 11.74598, "name": "Sulzbach-Rosenberg" }, { "lat": 51.46, "lon": -2.12472, "name": "Chippenham" }, { "lat": -23.15306, "lon": -47.05778, "name": "Itupeva" } ], "question": "Which location is the geographic outlier among: Bottrop, Pianura, Sulzbach-Rosenberg, Chippenham, Itupeva?", "ground_truth": { "answer": "Itupeva", "outlier_distance_km": 7865.5, "second_furthest_km": 2114.4, "clarity_ratio": 3.72, "median_distance_km": 2110.1, "distances_to_centroid": { "Bottrop": 2110.1, "Pianura": 1712.0, "Sulzbach-Rosenberg": 2114.4, "Chippenham": 1939.4, "Itupeva": 7865.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bottrop: (51.52°, 6.93°)", " Pianura: (40.86°, 14.17°)", " Sulzbach-Rosenberg: (49.50°, 11.75°)", " Chippenham: (51.46°, -2.12°)", " Itupeva: (-23.15°, -47.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Itupeva: 7865.5 km from centroid", " Sulzbach-Rosenberg: 2114.4 km from centroid", " Bottrop: 2110.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Itupeva", "FINAL ANSWER: Itupeva" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.25318, "lon": 108.65785, "name": "Shangchong" }, { "lat": 25.36379, "lon": 82.18655, "name": "Handiā" }, { "lat": 14.67611, "lon": 120.53611, "name": "Balanga" }, { "lat": 34.71667, "lon": 116.76667, "name": "Lulou" }, { "lat": 51.76263, "lon": 6.39778, "name": "Rees" } ], "question": "Which location is the geographic outlier among: Shangchong, Handiā, Balanga, Lulou, Rees?", "ground_truth": { "answer": "Rees", "outlier_distance_km": 6765.8, "second_furthest_km": 3855.1, "clarity_ratio": 1.76, "median_distance_km": 2823.3, "distances_to_centroid": { "Shangchong": 2176.6, "Handiā": 740.2, "Balanga": 3855.1, "Lulou": 2823.3, "Rees": 6765.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shangchong: (26.25°, 108.66°)", " Handiā: (25.36°, 82.19°)", " Balanga: (14.68°, 120.54°)", " Lulou: (34.72°, 116.77°)", " Rees: (51.76°, 6.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rees: 6765.8 km from centroid", " Balanga: 3855.1 km from centroid", " Lulou: 2823.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rees", "FINAL ANSWER: Rees" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 8.3, "lon": 38.95, "name": "‘Alem T’ēna" }, { "lat": 8.4939, "lon": 8.51532, "name": "Lafia" }, { "lat": 30.71524, "lon": 31.2592, "name": "Mīt Ghamr" }, { "lat": 11.71391, "lon": 11.08108, "name": "Potiskum" }, { "lat": 34.93873, "lon": -82.22706, "name": "Greer" } ], "question": "Which location is the geographic outlier among: ‘Alem T’ēna, Lafia, Mīt Ghamr, Potiskum, Greer?", "ground_truth": { "answer": "Greer", "outlier_distance_km": 8269.5, "second_furthest_km": 4202.0, "clarity_ratio": 1.97, "median_distance_km": 3267.1, "distances_to_centroid": { "‘Alem T’ēna": 4202.0, "Lafia": 1375.4, "Mīt Ghamr": 3267.1, "Potiskum": 1295.2, "Greer": 8269.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " ‘Alem T’ēna: (8.30°, 38.95°)", " Lafia: (8.49°, 8.52°)", " Mīt Ghamr: (30.72°, 31.26°)", " Potiskum: (11.71°, 11.08°)", " Greer: (34.94°, -82.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Greer: 8269.5 km from centroid", " ‘Alem T’ēna: 4202.0 km from centroid", " Mīt Ghamr: 3267.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Greer", "FINAL ANSWER: Greer" ] }, { "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": 40.4165, "lon": -3.70256, "name": "Madrid" }, { "lat": 51.69868, "lon": 17.43738, "name": "Krotoszyn" }, { "lat": 56.63877, "lon": 47.89078, "name": "Yoshkar-Ola" }, { "lat": 48.84258, "lon": 2.40014, "name": "Picpus" }, { "lat": 0.00624, "lon": 37.07398, "name": "Nanyuki" } ], "question": "Which location is the geographic outlier among: Madrid, Krotoszyn, Yoshkar-Ola, Picpus, Nanyuki?", "ground_truth": { "answer": "Nanyuki", "outlier_distance_km": 4715.8, "second_furthest_km": 2766.6, "clarity_ratio": 1.7, "median_distance_km": 2034.9, "distances_to_centroid": { "Madrid": 2034.9, "Krotoszyn": 1371.1, "Yoshkar-Ola": 2766.6, "Picpus": 1751.7, "Nanyuki": 4715.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Madrid: (40.42°, -3.70°)", " Krotoszyn: (51.70°, 17.44°)", " Yoshkar-Ola: (56.64°, 47.89°)", " Picpus: (48.84°, 2.40°)", " Nanyuki: (0.01°, 37.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nanyuki: 4715.8 km from centroid", " Yoshkar-Ola: 2766.6 km from centroid", " Madrid: 2034.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nanyuki", "FINAL ANSWER: Nanyuki" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.6103, "lon": -114.59635, "name": "Blythe" }, { "lat": 29.56523, "lon": -98.3364, "name": "Live Oak" }, { "lat": 29.95465, "lon": -90.07507, "name": "New Orleans" }, { "lat": 44.08054, "lon": -103.23101, "name": "Rapid City" }, { "lat": 3.7899, "lon": 101.857, "name": "Raub" } ], "question": "Which location is the geographic outlier among: Blythe, Live Oak, New Orleans, Rapid City, Raub?", "ground_truth": { "answer": "Raub", "outlier_distance_km": 16006.6, "second_furthest_km": 5104.1, "clarity_ratio": 3.14, "median_distance_km": 4135.8, "distances_to_centroid": { "Blythe": 5104.1, "Live Oak": 3634.6, "New Orleans": 2836.6, "Rapid City": 4135.8, "Raub": 16006.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Blythe: (33.61°, -114.60°)", " Live Oak: (29.57°, -98.34°)", " New Orleans: (29.95°, -90.08°)", " Rapid City: (44.08°, -103.23°)", " Raub: (3.79°, 101.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Raub: 16006.6 km from centroid", " Blythe: 5104.1 km from centroid", " Rapid City: 4135.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Raub", "FINAL ANSWER: Raub" ] }, { "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": -38.13874, "lon": 176.24516, "name": "Rotorua" }, { "lat": -37.81667, "lon": 144.75, "name": "Truganina" }, { "lat": -37.80639, "lon": 145.03086, "name": "Kew" }, { "lat": -28.21298, "lon": 153.53634, "name": "Banora Point" }, { "lat": 27.93789, "lon": -82.23644, "name": "Valrico" } ], "question": "Which location is the geographic outlier among: Rotorua, Truganina, Kew, Banora Point, Valrico?", "ground_truth": { "answer": "Valrico", "outlier_distance_km": 18886.4, "second_furthest_km": 6658.4, "clarity_ratio": 2.84, "median_distance_km": 4635.3, "distances_to_centroid": { "Rotorua": 6658.4, "Truganina": 3915.0, "Kew": 3938.6, "Banora Point": 4635.3, "Valrico": 18886.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rotorua: (-38.14°, 176.25°)", " Truganina: (-37.82°, 144.75°)", " Kew: (-37.81°, 145.03°)", " Banora Point: (-28.21°, 153.54°)", " Valrico: (27.94°, -82.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Valrico: 18886.4 km from centroid", " Rotorua: 6658.4 km from centroid", " Banora Point: 4635.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Valrico", "FINAL ANSWER: Valrico" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, { "lat": -27.10876, "lon": 152.94907, "name": "Morayfield" }, { "lat": -38.14458, "lon": 145.12291, "name": "Frankston" }, { "lat": -26.65682, "lon": 153.07955, "name": "Sunshine Coast" }, { "lat": 5.53711, "lon": -0.69984, "name": "Swedru" } ], "question": "Which location is the geographic outlier among: Kallangur, Morayfield, Frankston, Sunshine Coast, Swedru?", "ground_truth": { "answer": "Swedru", "outlier_distance_km": 13457.6, "second_furthest_km": 3292.7, "clarity_ratio": 4.09, "median_distance_km": 3285.2, "distances_to_centroid": { "Kallangur": 3285.2, "Morayfield": 3280.6, "Frankston": 2887.6, "Sunshine Coast": 3292.7, "Swedru": 13457.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kallangur: (-27.25°, 152.99°)", " Morayfield: (-27.11°, 152.95°)", " Frankston: (-38.14°, 145.12°)", " Sunshine Coast: (-26.66°, 153.08°)", " Swedru: (5.54°, -0.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Swedru: 13457.6 km from centroid", " Sunshine Coast: 3292.7 km from centroid", " Kallangur: 3285.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Swedru", "FINAL ANSWER: Swedru" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.0888, "lon": 9.06455, "name": "Alzenau in Unterfranken" }, { "lat": 50.91485, "lon": 6.8118, "name": "Frechen" }, { "lat": 41.32784, "lon": 2.09472, "name": "El Prat de Llobregat" }, { "lat": 55.67344, "lon": 84.39463, "name": "Bolotnoye" }, { "lat": -33.73333, "lon": 150.93284, "name": "Glenwood" } ], "question": "Which location is the geographic outlier among: Alzenau in Unterfranken, Frechen, El Prat de Llobregat, Bolotnoye, Glenwood?", "ground_truth": { "answer": "Glenwood", "outlier_distance_km": 12810.2, "second_furthest_km": 4351.0, "clarity_ratio": 2.94, "median_distance_km": 4067.2, "distances_to_centroid": { "Alzenau in Unterfranken": 3891.3, "Frechen": 4067.2, "El Prat de Llobregat": 4351.0, "Bolotnoye": 3630.7, "Glenwood": 12810.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Alzenau in Unterfranken: (50.09°, 9.06°)", " Frechen: (50.91°, 6.81°)", " El Prat de Llobregat: (41.33°, 2.09°)", " Bolotnoye: (55.67°, 84.39°)", " Glenwood: (-33.73°, 150.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glenwood: 12810.2 km from centroid", " El Prat de Llobregat: 4351.0 km from centroid", " Frechen: 4067.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glenwood", "FINAL ANSWER: Glenwood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.11342, "lon": 145.28326, "name": "Cranbourne" }, { "lat": -38.14458, "lon": 145.12291, "name": "Frankston" }, { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, { "lat": -37.9, "lon": 144.66667, "name": "Werribee" }, { "lat": 14.71694, "lon": 120.95806, "name": "Malanday" } ], "question": "Which location is the geographic outlier among: Cranbourne, Frankston, Kallangur, Werribee, Malanday?", "ground_truth": { "answer": "Malanday", "outlier_distance_km": 4993.9, "second_furthest_km": 1457.8, "clarity_ratio": 3.43, "median_distance_km": 1457.8, "distances_to_centroid": { "Cranbourne": 1457.8, "Frankston": 1457.8, "Kallangur": 1135.0, "Werribee": 1422.6, "Malanday": 4993.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cranbourne: (-38.11°, 145.28°)", " Frankston: (-38.14°, 145.12°)", " Kallangur: (-27.25°, 152.99°)", " Werribee: (-37.90°, 144.67°)", " Malanday: (14.72°, 120.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Malanday: 4993.9 km from centroid", " Cranbourne: 1457.8 km from centroid", " Frankston: 1457.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Malanday", "FINAL ANSWER: Malanday" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.40793, "lon": 108.21732, "name": "Xituo" }, { "lat": 24.00826, "lon": 76.7325, "name": "Rājgarh" }, { "lat": 26.44212, "lon": 92.03047, "name": "Mangaldai" }, { "lat": 22.42347, "lon": 71.19641, "name": "Chotila" }, { "lat": 31.5084, "lon": 31.84106, "name": "‘Izbat al Burj" } ], "question": "Which location is the geographic outlier among: Xituo, Rājgarh, Mangaldai, Chotila, ‘Izbat al Burj?", "ground_truth": { "answer": "‘Izbat al Burj", "outlier_distance_km": 4286.5, "second_furthest_km": 3155.2, "clarity_ratio": 1.36, "median_distance_km": 1592.1, "distances_to_centroid": { "Xituo": 3155.2, "Rājgarh": 336.1, "Mangaldai": 1592.1, "Chotila": 699.9, "‘Izbat al Burj": 4286.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Xituo: (30.41°, 108.22°)", " Rājgarh: (24.01°, 76.73°)", " Mangaldai: (26.44°, 92.03°)", " Chotila: (22.42°, 71.20°)", " ‘Izbat al Burj: (31.51°, 31.84°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " ‘Izbat al Burj: 4286.5 km from centroid", " Xituo: 3155.2 km from centroid", " Mangaldai: 1592.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: ‘Izbat al Burj", "FINAL ANSWER: ‘Izbat al Burj" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.93422, "lon": -80.09421, "name": "Jupiter" }, { "lat": 36.50921, "lon": -86.885, "name": "Springfield" }, { "lat": 38.52005, "lon": -89.98399, "name": "Belleville" }, { "lat": 41.47892, "lon": -87.45476, "name": "Schererville" }, { "lat": -4.05466, "lon": 39.66359, "name": "Mombasa" } ], "question": "Which location is the geographic outlier among: Jupiter, Springfield, Belleville, Schererville, Mombasa?", "ground_truth": { "answer": "Mombasa", "outlier_distance_km": 11261.0, "second_furthest_km": 2933.0, "clarity_ratio": 3.84, "median_distance_km": 2838.9, "distances_to_centroid": { "Jupiter": 1890.7, "Springfield": 2612.0, "Belleville": 2933.0, "Schererville": 2838.9, "Mombasa": 11261.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jupiter: (26.93°, -80.09°)", " Springfield: (36.51°, -86.89°)", " Belleville: (38.52°, -89.98°)", " Schererville: (41.48°, -87.45°)", " Mombasa: (-4.05°, 39.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mombasa: 11261.0 km from centroid", " Belleville: 2933.0 km from centroid", " Schererville: 2838.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mombasa", "FINAL ANSWER: Mombasa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 3.0693, "lon": 101.6074, "name": "Bandar Sunway" }, { "lat": 33.66972, "lon": 118.18889, "name": "Guiren" }, { "lat": 19.33159, "lon": 79.46605, "name": "Kagaznāgār" }, { "lat": 2.3125, "lon": 102.2805, "name": "Durian Tunggal" }, { "lat": 40.93064, "lon": -73.10179, "name": "Setauket-East Setauket" } ], "question": "Which location is the geographic outlier among: Bandar Sunway, Guiren, Kagaznāgār, Durian Tunggal, Setauket-East Setauket?", "ground_truth": { "answer": "Setauket-East Setauket", "outlier_distance_km": 12028.7, "second_furthest_km": 5373.9, "clarity_ratio": 2.24, "median_distance_km": 4426.1, "distances_to_centroid": { "Bandar Sunway": 4320.2, "Guiren": 5373.9, "Kagaznāgār": 1444.1, "Durian Tunggal": 4426.1, "Setauket-East Setauket": 12028.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bandar Sunway: (3.07°, 101.61°)", " Guiren: (33.67°, 118.19°)", " Kagaznāgār: (19.33°, 79.47°)", " Durian Tunggal: (2.31°, 102.28°)", " Setauket-East Setauket: (40.93°, -73.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Setauket-East Setauket: 12028.7 km from centroid", " Guiren: 5373.9 km from centroid", " Durian Tunggal: 4426.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Setauket-East Setauket", "FINAL ANSWER: Setauket-East Setauket" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.18461, "lon": -75.59913, "name": "Itagüí" }, { "lat": -4.02694, "lon": -38.305, "name": "Pindoretama" }, { "lat": -9.72283, "lon": -63.31022, "name": "Alto Paraíso" }, { "lat": -11.61667, "lon": -38.8, "name": "Biritinga" }, { "lat": 31.13159, "lon": 33.79844, "name": "Arīsh" } ], "question": "Which location is the geographic outlier among: Itagüí, Pindoretama, Alto Paraíso, Biritinga, Arīsh?", "ground_truth": { "answer": "Arīsh", "outlier_distance_km": 7994.9, "second_furthest_km": 4360.9, "clarity_ratio": 1.83, "median_distance_km": 3266.2, "distances_to_centroid": { "Itagüí": 4360.9, "Pindoretama": 742.9, "Alto Paraíso": 3266.2, "Biritinga": 1579.1, "Arīsh": 7994.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itagüí: (6.18°, -75.60°)", " Pindoretama: (-4.03°, -38.30°)", " Alto Paraíso: (-9.72°, -63.31°)", " Biritinga: (-11.62°, -38.80°)", " Arīsh: (31.13°, 33.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arīsh: 7994.9 km from centroid", " Itagüí: 4360.9 km from centroid", " Alto Paraíso: 3266.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arīsh", "FINAL ANSWER: Arīsh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.33732, "lon": -75.55795, "name": "Bello" }, { "lat": -23.87833, "lon": -47.99722, "name": "São Miguel Arcanjo" }, { "lat": -21.77389, "lon": -47.08639, "name": "Casa Branca" }, { "lat": -34.45867, "lon": -58.91398, "name": "Pilar" }, { "lat": -27.56056, "lon": 151.95386, "name": "Toowoomba" } ], "question": "Which location is the geographic outlier among: Bello, São Miguel Arcanjo, Casa Branca, Pilar, Toowoomba?", "ground_truth": { "answer": "Toowoomba", "outlier_distance_km": 14528.8, "second_furthest_km": 7193.9, "clarity_ratio": 2.02, "median_distance_km": 4526.5, "distances_to_centroid": { "Bello": 7193.9, "São Miguel Arcanjo": 3363.3, "Casa Branca": 3275.1, "Pilar": 4526.5, "Toowoomba": 14528.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bello: (6.34°, -75.56°)", " São Miguel Arcanjo: (-23.88°, -48.00°)", " Casa Branca: (-21.77°, -47.09°)", " Pilar: (-34.46°, -58.91°)", " Toowoomba: (-27.56°, 151.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Toowoomba: 14528.8 km from centroid", " Bello: 7193.9 km from centroid", " Pilar: 4526.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Toowoomba", "FINAL ANSWER: Toowoomba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.59368, "lon": 10.01123, "name": "Winterhude" }, { "lat": 52.43367, "lon": 8.61263, "name": "Rahden" }, { "lat": 41.62965, "lon": -0.93873, "name": "Montecanal" }, { "lat": 49.2144, "lon": 8.36687, "name": "Germersheim" }, { "lat": 6.41667, "lon": 39.85, "name": "Mena" } ], "question": "Which location is the geographic outlier among: Winterhude, Rahden, Montecanal, Germersheim, Mena?", "ground_truth": { "answer": "Mena", "outlier_distance_km": 4638.4, "second_furthest_km": 1457.9, "clarity_ratio": 3.18, "median_distance_km": 1354.5, "distances_to_centroid": { "Winterhude": 1457.9, "Rahden": 1354.5, "Montecanal": 1185.9, "Germersheim": 1023.6, "Mena": 4638.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Winterhude: (53.59°, 10.01°)", " Rahden: (52.43°, 8.61°)", " Montecanal: (41.63°, -0.94°)", " Germersheim: (49.21°, 8.37°)", " Mena: (6.42°, 39.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mena: 4638.4 km from centroid", " Winterhude: 1457.9 km from centroid", " Rahden: 1354.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mena", "FINAL ANSWER: Mena" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.99694, "lon": -40.27194, "name": "Lagoa Grande" }, { "lat": -3.14306, "lon": -58.44417, "name": "Itacoatiara" }, { "lat": -5.895, "lon": -35.76278, "name": "São Paulo do Potengi" }, { "lat": -21.01778, "lon": -47.76389, "name": "Jardinópolis" }, { "lat": 11.21836, "lon": 75.83248, "name": "Olavanna" } ], "question": "Which location is the geographic outlier among: Lagoa Grande, Itacoatiara, São Paulo do Potengi, Jardinópolis, Olavanna?", "ground_truth": { "answer": "Olavanna", "outlier_distance_km": 10901.0, "second_furthest_km": 4128.4, "clarity_ratio": 2.64, "median_distance_km": 3331.4, "distances_to_centroid": { "Lagoa Grande": 2128.5, "Itacoatiara": 4128.4, "São Paulo do Potengi": 1602.5, "Jardinópolis": 3331.4, "Olavanna": 10901.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lagoa Grande: (-9.00°, -40.27°)", " Itacoatiara: (-3.14°, -58.44°)", " São Paulo do Potengi: (-5.89°, -35.76°)", " Jardinópolis: (-21.02°, -47.76°)", " Olavanna: (11.22°, 75.83°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Olavanna: 10901.0 km from centroid", " Itacoatiara: 4128.4 km from centroid", " Jardinópolis: 3331.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Olavanna", "FINAL ANSWER: Olavanna" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.62099, "lon": -47.35422, "name": "Salinópolis" }, { "lat": -6.40111, "lon": -38.86222, "name": "Icó" }, { "lat": -23.49032, "lon": -46.6387, "name": "Santana" }, { "lat": -20.43278, "lon": -51.3425, "name": "Ilha Solteira" }, { "lat": 34.26695, "lon": -118.3023, "name": "Sunland" } ], "question": "Which location is the geographic outlier among: Salinópolis, Icó, Santana, Ilha Solteira, Sunland?", "ground_truth": { "answer": "Sunland", "outlier_distance_km": 7338.1, "second_furthest_km": 2691.2, "clarity_ratio": 2.73, "median_distance_km": 2421.0, "distances_to_centroid": { "Salinópolis": 1491.6, "Icó": 2421.0, "Santana": 2691.2, "Ilha Solteira": 2144.5, "Sunland": 7338.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Salinópolis: (-0.62°, -47.35°)", " Icó: (-6.40°, -38.86°)", " Santana: (-23.49°, -46.64°)", " Ilha Solteira: (-20.43°, -51.34°)", " Sunland: (34.27°, -118.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sunland: 7338.1 km from centroid", " Santana: 2691.2 km from centroid", " Icó: 2421.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sunland", "FINAL ANSWER: Sunland" ] }, { "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": -6.25444, "lon": -39.20194, "name": "Quixelô" }, { "lat": -41.31946, "lon": -72.98538, "name": "Puerto Varas" }, { "lat": -15.73948, "lon": -47.85686, "name": "Lago Norte" }, { "lat": -8.37915, "lon": -74.55387, "name": "Pucallpa" }, { "lat": -38.07758, "lon": 145.29871, "name": "Cranbourne North" } ], "question": "Which location is the geographic outlier among: Quixelô, Puerto Varas, Lago Norte, Pucallpa, Cranbourne North?", "ground_truth": { "answer": "Cranbourne North", "outlier_distance_km": 13111.9, "second_furthest_km": 6233.5, "clarity_ratio": 2.1, "median_distance_km": 5540.2, "distances_to_centroid": { "Quixelô": 2881.2, "Puerto Varas": 5540.2, "Lago Norte": 3225.6, "Pucallpa": 6233.5, "Cranbourne North": 13111.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Quixelô: (-6.25°, -39.20°)", " Puerto Varas: (-41.32°, -72.99°)", " Lago Norte: (-15.74°, -47.86°)", " Pucallpa: (-8.38°, -74.55°)", " Cranbourne North: (-38.08°, 145.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cranbourne North: 13111.9 km from centroid", " Pucallpa: 6233.5 km from centroid", " Puerto Varas: 5540.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cranbourne North", "FINAL ANSWER: Cranbourne North" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.96519, "lon": 8.95129, "name": "Babenhausen" }, { "lat": 51.43218, "lon": 6.87967, "name": "Mülheim" }, { "lat": 49.43333, "lon": 6.85, "name": "Schmelz" }, { "lat": 50.79899, "lon": -1.09125, "name": "Portsmouth" }, { "lat": -36.8582, "lon": 174.62019, "name": "Lincoln" } ], "question": "Which location is the geographic outlier among: Babenhausen, Mülheim, Schmelz, Portsmouth, Lincoln?", "ground_truth": { "answer": "Lincoln", "outlier_distance_km": 15959.7, "second_furthest_km": 3817.1, "clarity_ratio": 4.18, "median_distance_km": 3320.9, "distances_to_centroid": { "Babenhausen": 3118.7, "Mülheim": 3320.9, "Schmelz": 3232.6, "Portsmouth": 3817.1, "Lincoln": 15959.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Babenhausen: (49.97°, 8.95°)", " Mülheim: (51.43°, 6.88°)", " Schmelz: (49.43°, 6.85°)", " Portsmouth: (50.80°, -1.09°)", " Lincoln: (-36.86°, 174.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lincoln: 15959.7 km from centroid", " Portsmouth: 3817.1 km from centroid", " Mülheim: 3320.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lincoln", "FINAL ANSWER: Lincoln" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.63371, "lon": -74.40737, "name": "Plainfield" }, { "lat": 34.50083, "lon": -117.18588, "name": "Apple Valley" }, { "lat": 45.63076, "lon": -72.95699, "name": "Saint-Hyacinthe" }, { "lat": 51.03341, "lon": -113.81867, "name": "Chestermere" }, { "lat": 26.37345, "lon": 84.33489, "name": "Mirganj" } ], "question": "Which location is the geographic outlier among: Plainfield, Apple Valley, Saint-Hyacinthe, Chestermere, Mirganj?", "ground_truth": { "answer": "Mirganj", "outlier_distance_km": 11740.7, "second_furthest_km": 5120.2, "clarity_ratio": 2.29, "median_distance_km": 4371.7, "distances_to_centroid": { "Plainfield": 1329.1, "Apple Valley": 5120.2, "Saint-Hyacinthe": 1333.1, "Chestermere": 4371.7, "Mirganj": 11740.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Plainfield: (40.63°, -74.41°)", " Apple Valley: (34.50°, -117.19°)", " Saint-Hyacinthe: (45.63°, -72.96°)", " Chestermere: (51.03°, -113.82°)", " Mirganj: (26.37°, 84.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mirganj: 11740.7 km from centroid", " Apple Valley: 5120.2 km from centroid", " Chestermere: 4371.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mirganj", "FINAL ANSWER: Mirganj" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.83861, "lon": -44.80833, "name": "Cruzília" }, { "lat": -14.97583, "lon": -41.41083, "name": "Tremedal" }, { "lat": -18.16583, "lon": -47.94639, "name": "Catalão" }, { "lat": -23.785, "lon": -53.07333, "name": "Cruzeiro do Oeste" }, { "lat": 57.5888, "lon": 34.56854, "name": "Vyshniy Volochëk" } ], "question": "Which location is the geographic outlier among: Cruzília, Tremedal, Catalão, Cruzeiro do Oeste, Vyshniy Volochëk?", "ground_truth": { "answer": "Vyshniy Volochëk", "outlier_distance_km": 8966.4, "second_furthest_km": 3250.5, "clarity_ratio": 2.76, "median_distance_km": 2490.0, "distances_to_centroid": { "Cruzília": 2490.0, "Tremedal": 1686.3, "Catalão": 2446.6, "Cruzeiro do Oeste": 3250.5, "Vyshniy Volochëk": 8966.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cruzília: (-21.84°, -44.81°)", " Tremedal: (-14.98°, -41.41°)", " Catalão: (-18.17°, -47.95°)", " Cruzeiro do Oeste: (-23.79°, -53.07°)", " Vyshniy Volochëk: (57.59°, 34.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vyshniy Volochëk: 8966.4 km from centroid", " Cruzeiro do Oeste: 3250.5 km from centroid", " Cruzília: 2490.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vyshniy Volochëk", "FINAL ANSWER: Vyshniy Volochëk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.5, "lon": 35.5, "name": "Nejo" }, { "lat": -33.96333, "lon": 18.47639, "name": "Rondebosch" }, { "lat": 12.92475, "lon": 13.56617, "name": "Kukawa" }, { "lat": 29.60018, "lon": 32.31671, "name": "Ain Sukhna" }, { "lat": 3.38333, "lon": 101.41667, "name": "Batang Berjuntai" } ], "question": "Which location is the geographic outlier among: Nejo, Rondebosch, Kukawa, Ain Sukhna, Batang Berjuntai?", "ground_truth": { "answer": "Batang Berjuntai", "outlier_distance_km": 6784.7, "second_furthest_km": 4828.8, "clarity_ratio": 1.41, "median_distance_km": 3084.0, "distances_to_centroid": { "Nejo": 781.7, "Rondebosch": 4828.8, "Kukawa": 3084.0, "Ain Sukhna": 2935.9, "Batang Berjuntai": 6784.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nejo: (9.50°, 35.50°)", " Rondebosch: (-33.96°, 18.48°)", " Kukawa: (12.92°, 13.57°)", " Ain Sukhna: (29.60°, 32.32°)", " Batang Berjuntai: (3.38°, 101.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Batang Berjuntai: 6784.7 km from centroid", " Rondebosch: 4828.8 km from centroid", " Kukawa: 3084.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Batang Berjuntai", "FINAL ANSWER: Batang Berjuntai" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.71667, "lon": 116.4, "name": "Tambunan" }, { "lat": 10.07431, "lon": 105.73974, "name": "Bình Thủy" }, { "lat": 16.58534, "lon": 79.32046, "name": "Vijayapuri North" }, { "lat": 9.53539, "lon": 76.32205, "name": "Pathirappally" }, { "lat": 39.02861, "lon": -96.8314, "name": "Junction City" } ], "question": "Which location is the geographic outlier among: Tambunan, Bình Thủy, Vijayapuri North, Pathirappally, Junction City?", "ground_truth": { "answer": "Junction City", "outlier_distance_km": 13264.9, "second_furthest_km": 6653.1, "clarity_ratio": 1.99, "median_distance_km": 5396.3, "distances_to_centroid": { "Tambunan": 6653.1, "Bình Thủy": 5396.3, "Vijayapuri North": 2466.5, "Pathirappally": 2302.5, "Junction City": 13264.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tambunan: (5.72°, 116.40°)", " Bình Thủy: (10.07°, 105.74°)", " Vijayapuri North: (16.59°, 79.32°)", " Pathirappally: (9.54°, 76.32°)", " Junction City: (39.03°, -96.83°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Junction City: 13264.9 km from centroid", " Tambunan: 6653.1 km from centroid", " Bình Thủy: 5396.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Junction City", "FINAL ANSWER: Junction City" ] }, { "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": -38.14711, "lon": 144.36069, "name": "Geelong" }, { "lat": -33.9049, "lon": 151.01996, "name": "Yagoona" }, { "lat": -31.95224, "lon": 115.8614, "name": "Perth" }, { "lat": -41.33333, "lon": 173.18333, "name": "Richmond" }, { "lat": 50.91667, "lon": 8.1, "name": "Netphen" } ], "question": "Which location is the geographic outlier among: Geelong, Yagoona, Perth, Richmond, Netphen?", "ground_truth": { "answer": "Netphen", "outlier_distance_km": 13047.2, "second_furthest_km": 5710.2, "clarity_ratio": 2.28, "median_distance_km": 3621.6, "distances_to_centroid": { "Geelong": 3291.0, "Yagoona": 3621.6, "Perth": 1477.0, "Richmond": 5710.2, "Netphen": 13047.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Geelong: (-38.15°, 144.36°)", " Yagoona: (-33.90°, 151.02°)", " Perth: (-31.95°, 115.86°)", " Richmond: (-41.33°, 173.18°)", " Netphen: (50.92°, 8.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Netphen: 13047.2 km from centroid", " Richmond: 5710.2 km from centroid", " Yagoona: 3621.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Netphen", "FINAL ANSWER: Netphen" ] }, { "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": 45.35753, "lon": 11.78725, "name": "Abano Terme" }, { "lat": 43.64229, "lon": 5.09478, "name": "Salon-de-Provence" }, { "lat": 52.0, "lon": 8.4, "name": "Steinhagen" }, { "lat": 45.44694, "lon": 8.62118, "name": "Novara" }, { "lat": 28.68012, "lon": 77.02975, "name": "Mūndka" } ], "question": "Which location is the geographic outlier among: Abano Terme, Salon-de-Provence, Steinhagen, Novara, Mūndka?", "ground_truth": { "answer": "Mūndka", "outlier_distance_km": 5096.3, "second_furthest_km": 1433.6, "clarity_ratio": 3.55, "median_distance_km": 1381.6, "distances_to_centroid": { "Abano Terme": 868.0, "Salon-de-Provence": 1381.6, "Steinhagen": 1433.6, "Novara": 1112.3, "Mūndka": 5096.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Abano Terme: (45.36°, 11.79°)", " Salon-de-Provence: (43.64°, 5.09°)", " Steinhagen: (52.00°, 8.40°)", " Novara: (45.45°, 8.62°)", " Mūndka: (28.68°, 77.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mūndka: 5096.3 km from centroid", " Steinhagen: 1433.6 km from centroid", " Salon-de-Provence: 1381.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mūndka", "FINAL ANSWER: Mūndka" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81667, "lon": 144.75, "name": "Truganina" }, { "lat": -36.93754, "lon": 174.65584, "name": "Titirangi" }, { "lat": -33.95222, "lon": 150.89949, "name": "Casula" }, { "lat": -40.35636, "lon": 175.61113, "name": "Palmerston North" }, { "lat": 24.98773, "lon": 118.3858, "name": "Ximeicun" } ], "question": "Which location is the geographic outlier among: Truganina, Titirangi, Casula, Palmerston North, Ximeicun?", "ground_truth": { "answer": "Ximeicun", "outlier_distance_km": 6664.8, "second_furthest_km": 2729.5, "clarity_ratio": 2.44, "median_distance_km": 2469.1, "distances_to_centroid": { "Truganina": 1636.5, "Titirangi": 2469.1, "Casula": 1033.6, "Palmerston North": 2729.5, "Ximeicun": 6664.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Truganina: (-37.82°, 144.75°)", " Titirangi: (-36.94°, 174.66°)", " Casula: (-33.95°, 150.90°)", " Palmerston North: (-40.36°, 175.61°)", " Ximeicun: (24.99°, 118.39°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ximeicun: 6664.8 km from centroid", " Palmerston North: 2729.5 km from centroid", " Titirangi: 2469.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ximeicun", "FINAL ANSWER: Ximeicun" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.22661, "lon": -121.97468, "name": "Los Gatos" }, { "lat": 34.28195, "lon": -118.43897, "name": "San Fernando" }, { "lat": 45.53338, "lon": -73.28246, "name": "Saint-Basile-le-Grand" }, { "lat": 32.22174, "lon": -110.92648, "name": "Tucson" }, { "lat": -37.6, "lon": 145.15, "name": "Doreen" } ], "question": "Which location is the geographic outlier among: Los Gatos, San Fernando, Saint-Basile-le-Grand, Tucson, Doreen?", "ground_truth": { "answer": "Doreen", "outlier_distance_km": 17382.4, "second_furthest_km": 6459.9, "clarity_ratio": 2.69, "median_distance_km": 6171.2, "distances_to_centroid": { "Los Gatos": 6459.9, "San Fernando": 6171.2, "Saint-Basile-le-Grand": 3023.0, "Tucson": 5490.4, "Doreen": 17382.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Los Gatos: (37.23°, -121.97°)", " San Fernando: (34.28°, -118.44°)", " Saint-Basile-le-Grand: (45.53°, -73.28°)", " Tucson: (32.22°, -110.93°)", " Doreen: (-37.60°, 145.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Doreen: 17382.4 km from centroid", " Los Gatos: 6459.9 km from centroid", " San Fernando: 6171.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Doreen", "FINAL ANSWER: Doreen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.50597, "lon": 133.50391, "name": "Kasaoka" }, { "lat": 36.08333, "lon": 140.11667, "name": "Tsukuba" }, { "lat": 37.75266, "lon": 128.87239, "name": "Gangneung" }, { "lat": 25.59474, "lon": 79.5666, "name": "Rāth" }, { "lat": 42.6987, "lon": -71.13506, "name": "North Andover" } ], "question": "Which location is the geographic outlier among: Kasaoka, Tsukuba, Gangneung, Rāth, North Andover?", "ground_truth": { "answer": "North Andover", "outlier_distance_km": 10925.8, "second_furthest_km": 5150.5, "clarity_ratio": 2.12, "median_distance_km": 4626.0, "distances_to_centroid": { "Kasaoka": 4626.0, "Tsukuba": 5150.5, "Gangneung": 4136.4, "Rāth": 1110.8, "North Andover": 10925.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kasaoka: (34.51°, 133.50°)", " Tsukuba: (36.08°, 140.12°)", " Gangneung: (37.75°, 128.87°)", " Rāth: (25.59°, 79.57°)", " North Andover: (42.70°, -71.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Andover: 10925.8 km from centroid", " Tsukuba: 5150.5 km from centroid", " Kasaoka: 4626.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Andover", "FINAL ANSWER: North Andover" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -5.14556, "lon": -38.09806, "name": "Limoeiro do Norte" }, { "lat": -10.16931, "lon": -54.93439, "name": "Matupá" }, { "lat": -8.09056, "lon": -39.57833, "name": "Parnamirim" }, { "lat": -23.66778, "lon": -46.46139, "name": "Mauá" }, { "lat": -37.84205, "lon": 145.0694, "name": "Camberwell" } ], "question": "Which location is the geographic outlier among: Limoeiro do Norte, Matupá, Parnamirim, Mauá, Camberwell?", "ground_truth": { "answer": "Camberwell", "outlier_distance_km": 13247.2, "second_furthest_km": 5245.0, "clarity_ratio": 2.53, "median_distance_km": 4188.2, "distances_to_centroid": { "Limoeiro do Norte": 3652.4, "Matupá": 5245.0, "Parnamirim": 3686.4, "Mauá": 4188.2, "Camberwell": 13247.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Limoeiro do Norte: (-5.15°, -38.10°)", " Matupá: (-10.17°, -54.93°)", " Parnamirim: (-8.09°, -39.58°)", " Mauá: (-23.67°, -46.46°)", " Camberwell: (-37.84°, 145.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Camberwell: 13247.2 km from centroid", " Matupá: 5245.0 km from centroid", " Mauá: 4188.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Camberwell", "FINAL ANSWER: Camberwell" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.95, "lon": 151.23333, "name": "Maroubra" }, { "lat": -31.8075, "lon": 115.86599, "name": "Landsdale" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": -26.66008, "lon": 153.09953, "name": "Maroochydore" }, { "lat": 28.6678, "lon": 77.02011, "name": "Bakarwāla" } ], "question": "Which location is the geographic outlier among: Maroubra, Landsdale, Cranbourne East, Maroochydore, Bakarwāla?", "ground_truth": { "answer": "Bakarwāla", "outlier_distance_km": 7762.0, "second_furthest_km": 2698.0, "clarity_ratio": 2.88, "median_distance_km": 2598.5, "distances_to_centroid": { "Maroubra": 2698.0, "Landsdale": 1788.6, "Cranbourne East": 2549.8, "Maroochydore": 2598.5, "Bakarwāla": 7762.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maroubra: (-33.95°, 151.23°)", " Landsdale: (-31.81°, 115.87°)", " Cranbourne East: (-38.12°, 145.30°)", " Maroochydore: (-26.66°, 153.10°)", " Bakarwāla: (28.67°, 77.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bakarwāla: 7762.0 km from centroid", " Maroubra: 2698.0 km from centroid", " Maroochydore: 2598.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bakarwāla", "FINAL ANSWER: Bakarwāla" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.002, "lon": 29.034, "name": "Phola" }, { "lat": -32.72173, "lon": 25.58804, "name": "Somerset East" }, { "lat": 6.17811, "lon": 6.52461, "name": "Ogwashi-Uku" }, { "lat": 25.29336, "lon": 32.55402, "name": "Esna" }, { "lat": -9.95051, "lon": -54.90822, "name": "Guarantã do Norte" } ], "question": "Which location is the geographic outlier among: Phola, Somerset East, Ogwashi-Uku, Esna, Guarantã do Norte?", "ground_truth": { "answer": "Guarantã do Norte", "outlier_distance_km": 6884.3, "second_furthest_km": 4521.7, "clarity_ratio": 1.52, "median_distance_km": 3359.6, "distances_to_centroid": { "Phola": 3054.6, "Somerset East": 3359.6, "Ogwashi-Uku": 1520.5, "Esna": 4521.7, "Guarantã do Norte": 6884.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Phola: (-26.00°, 29.03°)", " Somerset East: (-32.72°, 25.59°)", " Ogwashi-Uku: (6.18°, 6.52°)", " Esna: (25.29°, 32.55°)", " Guarantã do Norte: (-9.95°, -54.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Guarantã do Norte: 6884.3 km from centroid", " Esna: 4521.7 km from centroid", " Somerset East: 3359.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Guarantã do Norte", "FINAL ANSWER: Guarantã do Norte" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.2973, "lon": 121.4598, "name": "Lumbang" }, { "lat": 38.10472, "lon": 140.85944, "name": "Iwanuma" }, { "lat": 33.45737, "lon": 132.4328, "name": "Yawatahama" }, { "lat": 14.42922, "lon": 120.87989, "name": "Noveleta" }, { "lat": 40.00112, "lon": 3.84144, "name": "Ciutadella" } ], "question": "Which location is the geographic outlier among: Lumbang, Iwanuma, Yawatahama, Noveleta, Ciutadella?", "ground_truth": { "answer": "Ciutadella", "outlier_distance_km": 8826.3, "second_furthest_km": 3593.6, "clarity_ratio": 2.46, "median_distance_km": 2782.9, "distances_to_centroid": { "Lumbang": 2373.1, "Iwanuma": 3593.6, "Yawatahama": 2782.9, "Noveleta": 2317.5, "Ciutadella": 8826.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lumbang: (14.30°, 121.46°)", " Iwanuma: (38.10°, 140.86°)", " Yawatahama: (33.46°, 132.43°)", " Noveleta: (14.43°, 120.88°)", " Ciutadella: (40.00°, 3.84°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ciutadella: 8826.3 km from centroid", " Iwanuma: 3593.6 km from centroid", " Yawatahama: 2782.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ciutadella", "FINAL ANSWER: Ciutadella" ] }, { "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": 41.1176, "lon": -73.4079, "name": "Norwalk" }, { "lat": 40.84235, "lon": -124.06367, "name": "Bayside" }, { "lat": 20.99165, "lon": -101.28434, "name": "Marfil" }, { "lat": 26.2173, "lon": -80.22588, "name": "North Lauderdale" }, { "lat": -21.09083, "lon": -45.09139, "name": "Perdões" } ], "question": "Which location is the geographic outlier among: Norwalk, Bayside, Marfil, North Lauderdale, Perdões?", "ground_truth": { "answer": "Perdões", "outlier_distance_km": 6414.1, "second_furthest_km": 4250.7, "clarity_ratio": 1.51, "median_distance_km": 2418.7, "distances_to_centroid": { "Norwalk": 2418.7, "Bayside": 4250.7, "Marfil": 1706.8, "North Lauderdale": 692.2, "Perdões": 6414.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Norwalk: (41.12°, -73.41°)", " Bayside: (40.84°, -124.06°)", " Marfil: (20.99°, -101.28°)", " North Lauderdale: (26.22°, -80.23°)", " Perdões: (-21.09°, -45.09°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Perdões: 6414.1 km from centroid", " Bayside: 4250.7 km from centroid", " Norwalk: 2418.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Perdões", "FINAL ANSWER: Perdões" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.32059, "lon": 45.04903, "name": "Sunzha" }, { "lat": 55.75, "lon": 37.56667, "name": "Dorogomilovo" }, { "lat": 51.21338, "lon": 17.38986, "name": "Oleśnica" }, { "lat": 48.64244, "lon": 12.49283, "name": "Dingolfing" }, { "lat": 5.28515, "lon": -2.76658, "name": "Elubo" } ], "question": "Which location is the geographic outlier among: Sunzha, Dorogomilovo, Oleśnica, Dingolfing, Elubo?", "ground_truth": { "answer": "Elubo", "outlier_distance_km": 4656.8, "second_furthest_km": 2010.6, "clarity_ratio": 2.32, "median_distance_km": 1920.1, "distances_to_centroid": { "Sunzha": 1920.1, "Dorogomilovo": 2010.6, "Oleśnica": 1205.1, "Dingolfing": 1142.7, "Elubo": 4656.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunzha: (43.32°, 45.05°)", " Dorogomilovo: (55.75°, 37.57°)", " Oleśnica: (51.21°, 17.39°)", " Dingolfing: (48.64°, 12.49°)", " Elubo: (5.29°, -2.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Elubo: 4656.8 km from centroid", " Dorogomilovo: 2010.6 km from centroid", " Sunzha: 1920.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Elubo", "FINAL ANSWER: Elubo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 46.73239, "lon": -117.00017, "name": "Moscow" }, { "lat": 34.23087, "lon": -111.32514, "name": "Payson" }, { "lat": 44.76306, "lon": -85.62063, "name": "Traverse City" }, { "lat": 24.80209, "lon": -107.39421, "name": "Culiacán" }, { "lat": -11.61667, "lon": -38.8, "name": "Biritinga" } ], "question": "Which location is the geographic outlier among: Moscow, Payson, Traverse City, Culiacán, Biritinga?", "ground_truth": { "answer": "Biritinga", "outlier_distance_km": 7211.5, "second_furthest_km": 3028.7, "clarity_ratio": 2.38, "median_distance_km": 1972.0, "distances_to_centroid": { "Moscow": 3028.7, "Payson": 1969.9, "Traverse City": 1972.0, "Culiacán": 1566.1, "Biritinga": 7211.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Moscow: (46.73°, -117.00°)", " Payson: (34.23°, -111.33°)", " Traverse City: (44.76°, -85.62°)", " Culiacán: (24.80°, -107.39°)", " Biritinga: (-11.62°, -38.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Biritinga: 7211.5 km from centroid", " Moscow: 3028.7 km from centroid", " Traverse City: 1972.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Biritinga", "FINAL ANSWER: Biritinga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.76667, "lon": 150.81667, "name": "Mount Druitt" }, { "lat": -42.87936, "lon": 147.32941, "name": "Hobart" }, { "lat": -38.14458, "lon": 145.12291, "name": "Frankston" }, { "lat": -38.07758, "lon": 145.29871, "name": "Cranbourne North" }, { "lat": 29.891, "lon": 107.21971, "name": "Linfeng" } ], "question": "Which location is the geographic outlier among: Mount Druitt, Hobart, Frankston, Cranbourne North, Linfeng?", "ground_truth": { "answer": "Linfeng", "outlier_distance_km": 6951.0, "second_furthest_km": 2166.3, "clarity_ratio": 3.21, "median_distance_km": 1608.5, "distances_to_centroid": { "Mount Druitt": 1521.5, "Hobart": 2166.3, "Frankston": 1608.5, "Cranbourne North": 1607.6, "Linfeng": 6951.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mount Druitt: (-33.77°, 150.82°)", " Hobart: (-42.88°, 147.33°)", " Frankston: (-38.14°, 145.12°)", " Cranbourne North: (-38.08°, 145.30°)", " Linfeng: (29.89°, 107.22°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Linfeng: 6951.0 km from centroid", " Hobart: 2166.3 km from centroid", " Frankston: 1608.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Linfeng", "FINAL ANSWER: Linfeng" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.93333, "lon": 145.23333, "name": "Rowville" }, { "lat": -37.75819, "lon": 145.00583, "name": "Thornbury" }, { "lat": -37.91928, "lon": 145.05301, "name": "Bentleigh East" }, { "lat": -33.95, "lon": 151.13333, "name": "Rockdale" }, { "lat": 42.41843, "lon": -71.10616, "name": "Medford" } ], "question": "Which location is the geographic outlier among: Rowville, Thornbury, Bentleigh East, Rockdale, Medford?", "ground_truth": { "answer": "Medford", "outlier_distance_km": 17575.1, "second_furthest_km": 4906.7, "clarity_ratio": 3.58, "median_distance_km": 4445.9, "distances_to_centroid": { "Rowville": 4445.9, "Thornbury": 4422.1, "Bentleigh East": 4430.2, "Rockdale": 4906.7, "Medford": 17575.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rowville: (-37.93°, 145.23°)", " Thornbury: (-37.76°, 145.01°)", " Bentleigh East: (-37.92°, 145.05°)", " Rockdale: (-33.95°, 151.13°)", " Medford: (42.42°, -71.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Medford: 17575.1 km from centroid", " Rockdale: 4906.7 km from centroid", " Rowville: 4445.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Medford", "FINAL ANSWER: Medford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.26237, "lon": -62.71128, "name": "Rufino" }, { "lat": -25.43998, "lon": -54.40161, "name": "Santa Terezinha de Itaipu" }, { "lat": -17.69139, "lon": -42.51583, "name": "Capelinha" }, { "lat": -8.48639, "lon": -36.23306, "name": "Cachoeirinha" }, { "lat": 40.90751, "lon": 14.293, "name": "Casoria" } ], "question": "Which location is the geographic outlier among: Rufino, Santa Terezinha de Itaipu, Capelinha, Cachoeirinha, Casoria?", "ground_truth": { "answer": "Casoria", "outlier_distance_km": 7583.5, "second_furthest_km": 3891.2, "clarity_ratio": 1.95, "median_distance_km": 2645.6, "distances_to_centroid": { "Rufino": 3891.2, "Santa Terezinha de Itaipu": 2645.6, "Capelinha": 1176.6, "Cachoeirinha": 57.2, "Casoria": 7583.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rufino: (-34.26°, -62.71°)", " Santa Terezinha de Itaipu: (-25.44°, -54.40°)", " Capelinha: (-17.69°, -42.52°)", " Cachoeirinha: (-8.49°, -36.23°)", " Casoria: (40.91°, 14.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Casoria: 7583.5 km from centroid", " Rufino: 3891.2 km from centroid", " Santa Terezinha de Itaipu: 2645.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Casoria", "FINAL ANSWER: Casoria" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.14816, "lon": 31.12733, "name": "Būsh" }, { "lat": 5.88333, "lon": 38.98333, "name": "Kibre Mengist" }, { "lat": 11.60462, "lon": 40.01662, "name": "Sifra" }, { "lat": -1.69405, "lon": 40.17015, "name": "Masalani" }, { "lat": 35.85, "lon": 117.7, "name": "Dongdu" } ], "question": "Which location is the geographic outlier among: Būsh, Kibre Mengist, Sifra, Masalani, Dongdu?", "ground_truth": { "answer": "Dongdu", "outlier_distance_km": 6649.3, "second_furthest_km": 2712.7, "clarity_ratio": 2.45, "median_distance_km": 2473.1, "distances_to_centroid": { "Būsh": 2712.7, "Kibre Mengist": 1960.1, "Sifra": 1550.6, "Masalani": 2473.1, "Dongdu": 6649.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Būsh: (29.15°, 31.13°)", " Kibre Mengist: (5.88°, 38.98°)", " Sifra: (11.60°, 40.02°)", " Masalani: (-1.69°, 40.17°)", " Dongdu: (35.85°, 117.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dongdu: 6649.3 km from centroid", " Būsh: 2712.7 km from centroid", " Masalani: 2473.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dongdu", "FINAL ANSWER: Dongdu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.44722, "lon": -40.77111, "name": "Dormentes" }, { "lat": -29.22694, "lon": -53.68167, "name": "Júlio de Castilhos" }, { "lat": -16.805, "lon": -49.92583, "name": "Palmeiras de Goiás" }, { "lat": -20.15139, "lon": -41.62278, "name": "Lajinha" }, { "lat": 7.75537, "lon": -0.98085, "name": "Atebubu" } ], "question": "Which location is the geographic outlier among: Dormentes, Júlio de Castilhos, Palmeiras de Goiás, Lajinha, Atebubu?", "ground_truth": { "answer": "Atebubu", "outlier_distance_km": 4657.0, "second_furthest_km": 2434.0, "clarity_ratio": 1.91, "median_distance_km": 1397.8, "distances_to_centroid": { "Dormentes": 660.2, "Júlio de Castilhos": 2434.0, "Palmeiras de Goiás": 1397.8, "Lajinha": 877.5, "Atebubu": 4657.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dormentes: (-8.45°, -40.77°)", " Júlio de Castilhos: (-29.23°, -53.68°)", " Palmeiras de Goiás: (-16.80°, -49.93°)", " Lajinha: (-20.15°, -41.62°)", " Atebubu: (7.76°, -0.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Atebubu: 4657.0 km from centroid", " Júlio de Castilhos: 2434.0 km from centroid", " Palmeiras de Goiás: 1397.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Atebubu", "FINAL ANSWER: Atebubu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.96944, "lon": 117.88056, "name": "Qing’an" }, { "lat": 33.7722, "lon": 120.26176, "name": "Hede" }, { "lat": 16.28053, "lon": 101.95422, "name": "Kaset Sombun" }, { "lat": 34.20488, "lon": 105.33651, "name": "Changdao" }, { "lat": -33.98219, "lon": -70.7104, "name": "San Francisco de Mostazal" } ], "question": "Which location is the geographic outlier among: Qing’an, Hede, Kaset Sombun, Changdao, San Francisco de Mostazal?", "ground_truth": { "answer": "San Francisco de Mostazal", "outlier_distance_km": 16102.3, "second_furthest_km": 4881.4, "clarity_ratio": 3.3, "median_distance_km": 4671.0, "distances_to_centroid": { "Qing’an": 4671.0, "Hede": 4881.4, "Kaset Sombun": 2877.2, "Changdao": 3586.3, "San Francisco de Mostazal": 16102.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Qing’an: (33.97°, 117.88°)", " Hede: (33.77°, 120.26°)", " Kaset Sombun: (16.28°, 101.95°)", " Changdao: (34.20°, 105.34°)", " San Francisco de Mostazal: (-33.98°, -70.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Francisco de Mostazal: 16102.3 km from centroid", " Hede: 4881.4 km from centroid", " Qing’an: 4671.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Francisco de Mostazal", "FINAL ANSWER: San Francisco de Mostazal" ] }, { "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": -39.4926, "lon": 176.91233, "name": "Napier" }, { "lat": -33.79176, "lon": 151.08057, "name": "Eastwood" }, { "lat": -27.62329, "lon": 153.04785, "name": "Calamvale" }, { "lat": -27.08465, "lon": 152.9511, "name": "Caboolture" }, { "lat": 38.06084, "lon": -97.92977, "name": "Hutchinson" } ], "question": "Which location is the geographic outlier among: Napier, Eastwood, Calamvale, Caboolture, Hutchinson?", "ground_truth": { "answer": "Hutchinson", "outlier_distance_km": 16708.3, "second_furthest_km": 7026.4, "clarity_ratio": 2.38, "median_distance_km": 4791.1, "distances_to_centroid": { "Napier": 7026.4, "Eastwood": 4684.8, "Calamvale": 4791.1, "Caboolture": 4778.9, "Hutchinson": 16708.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Napier: (-39.49°, 176.91°)", " Eastwood: (-33.79°, 151.08°)", " Calamvale: (-27.62°, 153.05°)", " Caboolture: (-27.08°, 152.95°)", " Hutchinson: (38.06°, -97.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hutchinson: 16708.3 km from centroid", " Napier: 7026.4 km from centroid", " Calamvale: 4791.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hutchinson", "FINAL ANSWER: Hutchinson" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.98922, "lon": 9.57223, "name": "Lohr am Main" }, { "lat": 48.83864, "lon": 2.41579, "name": "Saint-Mandé" }, { "lat": 48.89148, "lon": 2.46451, "name": "Noisy-le-Sec" }, { "lat": 50.80019, "lon": 7.20769, "name": "Siegburg" }, { "lat": -27.64613, "lon": 152.85965, "name": "Redbank Plains" } ], "question": "Which location is the geographic outlier among: Lohr am Main, Saint-Mandé, Noisy-le-Sec, Siegburg, Redbank Plains?", "ground_truth": { "answer": "Redbank Plains", "outlier_distance_km": 14140.8, "second_furthest_km": 3123.5, "clarity_ratio": 4.53, "median_distance_km": 3122.1, "distances_to_centroid": { "Lohr am Main": 2708.2, "Saint-Mandé": 3123.5, "Noisy-le-Sec": 3122.1, "Siegburg": 2898.5, "Redbank Plains": 14140.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lohr am Main: (49.99°, 9.57°)", " Saint-Mandé: (48.84°, 2.42°)", " Noisy-le-Sec: (48.89°, 2.46°)", " Siegburg: (50.80°, 7.21°)", " Redbank Plains: (-27.65°, 152.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Redbank Plains: 14140.8 km from centroid", " Saint-Mandé: 3123.5 km from centroid", " Noisy-le-Sec: 3122.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Redbank Plains", "FINAL ANSWER: Redbank Plains" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.56188, "lon": 73.22317, "name": "Sāvli" }, { "lat": -6.8922, "lon": 109.619, "name": "Wiradesa" }, { "lat": 5.203, "lon": 96.7009, "name": "Bireun" }, { "lat": 21.3851, "lon": 78.92155, "name": "Saoner" }, { "lat": -36.84853, "lon": 174.76349, "name": "Auckland" } ], "question": "Which location is the geographic outlier among: Sāvli, Wiradesa, Bireun, Saoner, Auckland?", "ground_truth": { "answer": "Auckland", "outlier_distance_km": 8153.9, "second_furthest_km": 4329.4, "clarity_ratio": 1.88, "median_distance_km": 3758.3, "distances_to_centroid": { "Sāvli": 4329.4, "Wiradesa": 946.1, "Bireun": 1195.2, "Saoner": 3758.3, "Auckland": 8153.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sāvli: (22.56°, 73.22°)", " Wiradesa: (-6.89°, 109.62°)", " Bireun: (5.20°, 96.70°)", " Saoner: (21.39°, 78.92°)", " Auckland: (-36.85°, 174.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Auckland: 8153.9 km from centroid", " Sāvli: 4329.4 km from centroid", " Saoner: 3758.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Auckland", "FINAL ANSWER: Auckland" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.84711, "lon": -1.78785, "name": "Baildon" }, { "lat": 52.53711, "lon": 31.93659, "name": "Novozybkov" }, { "lat": 53.18463, "lon": 18.60466, "name": "Chełmża" }, { "lat": 53.5303, "lon": 49.3461, "name": "Tolyatti" }, { "lat": -24.50944, "lon": -50.41361, "name": "Tibagi" } ], "question": "Which location is the geographic outlier among: Baildon, Novozybkov, Chełmża, Tolyatti, Tibagi?", "ground_truth": { "answer": "Tibagi", "outlier_distance_km": 9327.0, "second_furthest_km": 3496.3, "clarity_ratio": 2.67, "median_distance_km": 2390.4, "distances_to_centroid": { "Baildon": 1991.3, "Novozybkov": 2390.4, "Chełmża": 1856.1, "Tolyatti": 3496.3, "Tibagi": 9327.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Baildon: (53.85°, -1.79°)", " Novozybkov: (52.54°, 31.94°)", " Chełmża: (53.18°, 18.60°)", " Tolyatti: (53.53°, 49.35°)", " Tibagi: (-24.51°, -50.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tibagi: 9327.0 km from centroid", " Tolyatti: 3496.3 km from centroid", " Novozybkov: 2390.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tibagi", "FINAL ANSWER: Tibagi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.0415, "lon": 8.24878, "name": "Biebrich" }, { "lat": 40.01131, "lon": 18.16237, "name": "Casarano" }, { "lat": 55.7, "lon": 37.5, "name": "Ramenki" }, { "lat": 53.9165, "lon": 15.20027, "name": "Gryfice" }, { "lat": -13.54639, "lon": -42.49139, "name": "Tanque Novo" } ], "question": "Which location is the geographic outlier among: Biebrich, Casarano, Ramenki, Gryfice, Tanque Novo?", "ground_truth": { "answer": "Tanque Novo", "outlier_distance_km": 7676.3, "second_furthest_km": 3049.0, "clarity_ratio": 2.52, "median_distance_km": 1951.8, "distances_to_centroid": { "Biebrich": 1427.1, "Casarano": 990.5, "Ramenki": 3049.0, "Gryfice": 1951.8, "Tanque Novo": 7676.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Biebrich: (50.04°, 8.25°)", " Casarano: (40.01°, 18.16°)", " Ramenki: (55.70°, 37.50°)", " Gryfice: (53.92°, 15.20°)", " Tanque Novo: (-13.55°, -42.49°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tanque Novo: 7676.3 km from centroid", " Ramenki: 3049.0 km from centroid", " Gryfice: 1951.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tanque Novo", "FINAL ANSWER: Tanque Novo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.14264, "lon": 19.13149, "name": "Lędziny" }, { "lat": 43.8245, "lon": 11.13027, "name": "Campi Bisenzio" }, { "lat": 52.15051, "lon": 21.05041, "name": "Ursynów" }, { "lat": 52.40881, "lon": 7.97288, "name": "Bramsche" }, { "lat": 20.67675, "lon": -101.35628, "name": "Irapuato" } ], "question": "Which location is the geographic outlier among: Lędziny, Campi Bisenzio, Ursynów, Bramsche, Irapuato?", "ground_truth": { "answer": "Irapuato", "outlier_distance_km": 8660.0, "second_furthest_km": 2358.5, "clarity_ratio": 3.67, "median_distance_km": 2188.9, "distances_to_centroid": { "Lędziny": 2188.9, "Campi Bisenzio": 1564.0, "Ursynów": 2358.5, "Bramsche": 1539.0, "Irapuato": 8660.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lędziny: (50.14°, 19.13°)", " Campi Bisenzio: (43.82°, 11.13°)", " Ursynów: (52.15°, 21.05°)", " Bramsche: (52.41°, 7.97°)", " Irapuato: (20.68°, -101.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Irapuato: 8660.0 km from centroid", " Ursynów: 2358.5 km from centroid", " Lędziny: 2188.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Irapuato", "FINAL ANSWER: Irapuato" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" }, { "lat": -27.62329, "lon": 153.04785, "name": "Calamvale" }, { "lat": -32.92953, "lon": 151.7801, "name": "Newcastle" }, { "lat": -38.38176, "lon": 142.48799, "name": "Warrnambool" }, { "lat": 48.93964, "lon": 9.25995, "name": "Marbach am Neckar" } ], "question": "Which location is the geographic outlier among: Mackay, Calamvale, Newcastle, Warrnambool, Marbach am Neckar?", "ground_truth": { "answer": "Marbach am Neckar", "outlier_distance_km": 12788.0, "second_furthest_km": 3727.4, "clarity_ratio": 3.43, "median_distance_km": 3617.3, "distances_to_centroid": { "Mackay": 3061.3, "Calamvale": 3617.3, "Newcastle": 3727.4, "Warrnambool": 3407.2, "Marbach am Neckar": 12788.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mackay: (-21.15°, 149.17°)", " Calamvale: (-27.62°, 153.05°)", " Newcastle: (-32.93°, 151.78°)", " Warrnambool: (-38.38°, 142.49°)", " Marbach am Neckar: (48.94°, 9.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Marbach am Neckar: 12788.0 km from centroid", " Newcastle: 3727.4 km from centroid", " Calamvale: 3617.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Marbach am Neckar", "FINAL ANSWER: Marbach am Neckar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.09639, "lon": -3.77786, "name": "Bailén" }, { "lat": 41.05562, "lon": 16.70321, "name": "Palo del Colle" }, { "lat": 50.06187, "lon": 43.23335, "name": "Mikhaylovka" }, { "lat": 37.32955, "lon": 14.74474, "name": "Palagonia" }, { "lat": -33.71816, "lon": 151.11561, "name": "Wahroonga" } ], "question": "Which location is the geographic outlier among: Bailén, Palo del Colle, Mikhaylovka, Palagonia, Wahroonga?", "ground_truth": { "answer": "Wahroonga", "outlier_distance_km": 13068.5, "second_furthest_km": 4650.0, "clarity_ratio": 2.81, "median_distance_km": 3027.2, "distances_to_centroid": { "Bailén": 4650.0, "Palo del Colle": 3003.9, "Mikhaylovka": 2614.6, "Palagonia": 3027.2, "Wahroonga": 13068.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bailén: (38.10°, -3.78°)", " Palo del Colle: (41.06°, 16.70°)", " Mikhaylovka: (50.06°, 43.23°)", " Palagonia: (37.33°, 14.74°)", " Wahroonga: (-33.72°, 151.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wahroonga: 13068.5 km from centroid", " Bailén: 4650.0 km from centroid", " Palagonia: 3027.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wahroonga", "FINAL ANSWER: Wahroonga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.58759, "lon": -72.59953, "name": "Greenfield" }, { "lat": 21.99631, "lon": -99.01093, "name": "Ciudad Valles" }, { "lat": 38.78928, "lon": -77.1872, "name": "Springfield" }, { "lat": 31.15013, "lon": -81.49147, "name": "Brunswick" }, { "lat": 7.85, "lon": 36.65, "name": "Āgaro" } ], "question": "Which location is the geographic outlier among: Greenfield, Ciudad Valles, Springfield, Brunswick, Āgaro?", "ground_truth": { "answer": "Āgaro", "outlier_distance_km": 10112.6, "second_furthest_km": 4096.2, "clarity_ratio": 2.47, "median_distance_km": 2212.3, "distances_to_centroid": { "Greenfield": 2003.9, "Ciudad Valles": 4096.2, "Springfield": 2051.8, "Brunswick": 2212.3, "Āgaro": 10112.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Greenfield: (42.59°, -72.60°)", " Ciudad Valles: (22.00°, -99.01°)", " Springfield: (38.79°, -77.19°)", " Brunswick: (31.15°, -81.49°)", " Āgaro: (7.85°, 36.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Āgaro: 10112.6 km from centroid", " Ciudad Valles: 4096.2 km from centroid", " Brunswick: 2212.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Āgaro", "FINAL ANSWER: Āgaro" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.19543, "lon": -79.46948, "name": "Pinehurst" }, { "lat": 21.14972, "lon": -101.6225, "name": "Medina" }, { "lat": 40.80482, "lon": -73.33623, "name": "Dix Hills" }, { "lat": 32.32931, "lon": -96.62527, "name": "Ennis" }, { "lat": -33.79176, "lon": 151.08057, "name": "Eastwood" } ], "question": "Which location is the geographic outlier among: Pinehurst, Medina, Dix Hills, Ennis, Eastwood?", "ground_truth": { "answer": "Eastwood", "outlier_distance_km": 18050.8, "second_furthest_km": 6396.1, "clarity_ratio": 2.82, "median_distance_km": 5792.3, "distances_to_centroid": { "Pinehurst": 4257.6, "Medina": 6396.1, "Dix Hills": 3974.5, "Ennis": 5792.3, "Eastwood": 18050.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pinehurst: (35.20°, -79.47°)", " Medina: (21.15°, -101.62°)", " Dix Hills: (40.80°, -73.34°)", " Ennis: (32.33°, -96.63°)", " Eastwood: (-33.79°, 151.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Eastwood: 18050.8 km from centroid", " Medina: 6396.1 km from centroid", " Ennis: 5792.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Eastwood", "FINAL ANSWER: Eastwood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.4279, "lon": 150.89268, "name": "Wollongong city centre" }, { "lat": -39.4926, "lon": 176.91233, "name": "Napier" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" }, { "lat": -34.91119, "lon": 138.70735, "name": "Adelaide Hills" }, { "lat": 12.45389, "lon": 4.1975, "name": "Birnin Kebbi" } ], "question": "Which location is the geographic outlier among: Wollongong city centre, Napier, Otara, Adelaide Hills, Birnin Kebbi?", "ground_truth": { "answer": "Birnin Kebbi", "outlier_distance_km": 14077.7, "second_furthest_km": 4617.2, "clarity_ratio": 3.05, "median_distance_km": 4427.7, "distances_to_centroid": { "Wollongong city centre": 2250.9, "Napier": 4617.2, "Otara": 4427.7, "Adelaide Hills": 1294.9, "Birnin Kebbi": 14077.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wollongong city centre: (-34.43°, 150.89°)", " Napier: (-39.49°, 176.91°)", " Otara: (-36.95°, 174.87°)", " Adelaide Hills: (-34.91°, 138.71°)", " Birnin Kebbi: (12.45°, 4.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Birnin Kebbi: 14077.7 km from centroid", " Napier: 4617.2 km from centroid", " Otara: 4427.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Birnin Kebbi", "FINAL ANSWER: Birnin Kebbi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.42412, "lon": -98.49363, "name": "San Antonio" }, { "lat": 26.2173, "lon": -80.22588, "name": "North Lauderdale" }, { "lat": 34.05195, "lon": -118.47397, "name": "Brentwood" }, { "lat": 17.06025, "lon": -96.72544, "name": "Oaxaca" }, { "lat": 2.67375, "lon": 101.8721, "name": "Bandar Sri Sendayan" } ], "question": "Which location is the geographic outlier among: San Antonio, North Lauderdale, Brentwood, Oaxaca, Bandar Sri Sendayan?", "ground_truth": { "answer": "Bandar Sri Sendayan", "outlier_distance_km": 16543.5, "second_furthest_km": 5968.3, "clarity_ratio": 2.77, "median_distance_km": 4083.8, "distances_to_centroid": { "San Antonio": 4083.8, "North Lauderdale": 2264.0, "Brentwood": 5968.3, "Oaxaca": 4042.3, "Bandar Sri Sendayan": 16543.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Antonio: (29.42°, -98.49°)", " North Lauderdale: (26.22°, -80.23°)", " Brentwood: (34.05°, -118.47°)", " Oaxaca: (17.06°, -96.73°)", " Bandar Sri Sendayan: (2.67°, 101.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bandar Sri Sendayan: 16543.5 km from centroid", " Brentwood: 5968.3 km from centroid", " San Antonio: 4083.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bandar Sri Sendayan", "FINAL ANSWER: Bandar Sri Sendayan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.77806, "lon": -45.35806, "name": "Ilhabela" }, { "lat": -16.08222, "lon": -48.50722, "name": "Alexânia" }, { "lat": -19.32556, "lon": -41.25528, "name": "Resplendor" }, { "lat": -7.60333, "lon": -35.23083, "name": "Aliança" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" } ], "question": "Which location is the geographic outlier among: Ilhabela, Alexânia, Resplendor, Aliança, Taylors Lakes?", "ground_truth": { "answer": "Taylors Lakes", "outlier_distance_km": 12778.7, "second_furthest_km": 4594.0, "clarity_ratio": 2.78, "median_distance_km": 4138.2, "distances_to_centroid": { "Ilhabela": 4138.2, "Alexânia": 4594.0, "Resplendor": 3770.0, "Aliança": 3556.6, "Taylors Lakes": 12778.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ilhabela: (-23.78°, -45.36°)", " Alexânia: (-16.08°, -48.51°)", " Resplendor: (-19.33°, -41.26°)", " Aliança: (-7.60°, -35.23°)", " Taylors Lakes: (-37.70°, 144.79°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Taylors Lakes: 12778.7 km from centroid", " Alexânia: 4594.0 km from centroid", " Ilhabela: 4138.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Taylors Lakes", "FINAL ANSWER: Taylors Lakes" ] }, { "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": 35.95633, "lon": 140.32356, "name": "Inashiki" }, { "lat": 12.79163, "lon": 78.71644, "name": "Ambur" }, { "lat": 8.24521, "lon": 77.301, "name": "Tiruvankod" }, { "lat": 27.29191, "lon": 81.11775, "name": "Mahmudābād" }, { "lat": -37.76667, "lon": 145.0, "name": "Northcote" } ], "question": "Which location is the geographic outlier among: Inashiki, Ambur, Tiruvankod, Mahmudābād, Northcote?", "ground_truth": { "answer": "Northcote", "outlier_distance_km": 6714.9, "second_furthest_km": 4675.8, "clarity_ratio": 1.44, "median_distance_km": 3164.6, "distances_to_centroid": { "Inashiki": 4675.8, "Ambur": 2838.2, "Tiruvankod": 2989.7, "Mahmudābād": 3164.6, "Northcote": 6714.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Inashiki: (35.96°, 140.32°)", " Ambur: (12.79°, 78.72°)", " Tiruvankod: (8.25°, 77.30°)", " Mahmudābād: (27.29°, 81.12°)", " Northcote: (-37.77°, 145.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Northcote: 6714.9 km from centroid", " Inashiki: 4675.8 km from centroid", " Mahmudābād: 3164.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Northcote", "FINAL ANSWER: Northcote" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81992, "lon": 145.0358, "name": "Hawthorn" }, { "lat": -33.28397, "lon": 149.10018, "name": "Orange" }, { "lat": -33.91972, "lon": 151.07592, "name": "Lakemba" }, { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" }, { "lat": 13.98411, "lon": 77.77224, "name": "Gorantla" } ], "question": "Which location is the geographic outlier among: Hawthorn, Orange, Lakemba, Hoppers Crossing, Gorantla?", "ground_truth": { "answer": "Gorantla", "outlier_distance_km": 7479.7, "second_furthest_km": 1914.2, "clarity_ratio": 3.91, "median_distance_km": 1720.9, "distances_to_centroid": { "Hawthorn": 1720.9, "Orange": 1718.4, "Lakemba": 1914.2, "Hoppers Crossing": 1706.5, "Gorantla": 7479.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hawthorn: (-37.82°, 145.04°)", " Orange: (-33.28°, 149.10°)", " Lakemba: (-33.92°, 151.08°)", " Hoppers Crossing: (-37.88°, 144.70°)", " Gorantla: (13.98°, 77.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gorantla: 7479.7 km from centroid", " Lakemba: 1914.2 km from centroid", " Hawthorn: 1720.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gorantla", "FINAL ANSWER: Gorantla" ] }, { "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": -26.22861, "lon": -52.67056, "name": "Pato Branco" }, { "lat": -7.09167, "lon": -39.68056, "name": "Nova Olinda" }, { "lat": -9.02306, "lon": -78.61556, "name": "Coishco" }, { "lat": -13.53306, "lon": -48.22, "name": "Minaçu" }, { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" } ], "question": "Which location is the geographic outlier among: Pato Branco, Nova Olinda, Coishco, Minaçu, Mackay?", "ground_truth": { "answer": "Mackay", "outlier_distance_km": 15554.3, "second_furthest_km": 7034.5, "clarity_ratio": 2.21, "median_distance_km": 4177.2, "distances_to_centroid": { "Pato Branco": 4177.2, "Nova Olinda": 2945.4, "Coishco": 7034.5, "Minaçu": 3686.1, "Mackay": 15554.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pato Branco: (-26.23°, -52.67°)", " Nova Olinda: (-7.09°, -39.68°)", " Coishco: (-9.02°, -78.62°)", " Minaçu: (-13.53°, -48.22°)", " Mackay: (-21.15°, 149.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mackay: 15554.3 km from centroid", " Coishco: 7034.5 km from centroid", " Pato Branco: 4177.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mackay", "FINAL ANSWER: Mackay" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 17.99913, "lon": -94.6359, "name": "Cosoleacaque" }, { "lat": 43.73917, "lon": -79.24576, "name": "Eglinton East" }, { "lat": 44.52358, "lon": -89.57456, "name": "Stevens Point" }, { "lat": 41.8092, "lon": -87.59755, "name": "Kenwood" }, { "lat": -33.22795, "lon": -60.32994, "name": "Villa Constitución" } ], "question": "Which location is the geographic outlier among: Cosoleacaque, Eglinton East, Stevens Point, Kenwood, Villa Constitución?", "ground_truth": { "answer": "Villa Constitución", "outlier_distance_km": 6667.8, "second_furthest_km": 2487.4, "clarity_ratio": 2.68, "median_distance_km": 2326.2, "distances_to_centroid": { "Cosoleacaque": 1400.2, "Eglinton East": 2326.2, "Stevens Point": 2487.4, "Kenwood": 2152.6, "Villa Constitución": 6667.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cosoleacaque: (18.00°, -94.64°)", " Eglinton East: (43.74°, -79.25°)", " Stevens Point: (44.52°, -89.57°)", " Kenwood: (41.81°, -87.60°)", " Villa Constitución: (-33.23°, -60.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Villa Constitución: 6667.8 km from centroid", " Stevens Point: 2487.4 km from centroid", " Eglinton East: 2326.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Villa Constitución", "FINAL ANSWER: Villa Constitución" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.2422, "lon": 12.45666, "name": "Ribnitz-Damgarten" }, { "lat": 61.09979, "lon": 72.60349, "name": "Nefteyugansk" }, { "lat": 37.38594, "lon": -6.05258, "name": "Castilleja de la Cuesta" }, { "lat": 50.81137, "lon": -0.54078, "name": "Littlehampton" }, { "lat": -38.18333, "lon": 145.08333, "name": "Mount Eliza" } ], "question": "Which location is the geographic outlier among: Ribnitz-Damgarten, Nefteyugansk, Castilleja de la Cuesta, Littlehampton, Mount Eliza?", "ground_truth": { "answer": "Mount Eliza", "outlier_distance_km": 13023.7, "second_furthest_km": 4580.5, "clarity_ratio": 2.84, "median_distance_km": 4145.0, "distances_to_centroid": { "Ribnitz-Damgarten": 3449.8, "Nefteyugansk": 3704.5, "Castilleja de la Cuesta": 4580.5, "Littlehampton": 4145.0, "Mount Eliza": 13023.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ribnitz-Damgarten: (54.24°, 12.46°)", " Nefteyugansk: (61.10°, 72.60°)", " Castilleja de la Cuesta: (37.39°, -6.05°)", " Littlehampton: (50.81°, -0.54°)", " Mount Eliza: (-38.18°, 145.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mount Eliza: 13023.7 km from centroid", " Castilleja de la Cuesta: 4580.5 km from centroid", " Littlehampton: 4145.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mount Eliza", "FINAL ANSWER: Mount Eliza" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.56523, "lon": -98.3364, "name": "Live Oak" }, { "lat": 42.16558, "lon": -88.29425, "name": "Algonquin" }, { "lat": 40.56233, "lon": -74.13986, "name": "Staten Island" }, { "lat": 39.07506, "lon": -84.44716, "name": "Fort Thomas" }, { "lat": -32.5269, "lon": 115.7217, "name": "Mandurah" } ], "question": "Which location is the geographic outlier among: Live Oak, Algonquin, Staten Island, Fort Thomas, Mandurah?", "ground_truth": { "answer": "Mandurah", "outlier_distance_km": 17971.2, "second_furthest_km": 5207.4, "clarity_ratio": 3.45, "median_distance_km": 4393.3, "distances_to_centroid": { "Live Oak": 5207.4, "Algonquin": 4393.3, "Staten Island": 3225.0, "Fort Thomas": 3995.6, "Mandurah": 17971.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Live Oak: (29.57°, -98.34°)", " Algonquin: (42.17°, -88.29°)", " Staten Island: (40.56°, -74.14°)", " Fort Thomas: (39.08°, -84.45°)", " Mandurah: (-32.53°, 115.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mandurah: 17971.2 km from centroid", " Live Oak: 5207.4 km from centroid", " Algonquin: 4393.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mandurah", "FINAL ANSWER: Mandurah" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.14477, "lon": -84.24244, "name": "Piqua" }, { "lat": 38.42102, "lon": -121.42384, "name": "Laguna" }, { "lat": 36.80553, "lon": -114.06719, "name": "Mesquite" }, { "lat": 40.7251, "lon": -73.24539, "name": "Bay Shore" }, { "lat": -23.98222, "lon": -48.87556, "name": "Itapeva" } ], "question": "Which location is the geographic outlier among: Piqua, Laguna, Mesquite, Bay Shore, Itapeva?", "ground_truth": { "answer": "Itapeva", "outlier_distance_km": 7030.0, "second_furthest_km": 3353.9, "clarity_ratio": 2.1, "median_distance_km": 2681.7, "distances_to_centroid": { "Piqua": 1572.8, "Laguna": 3353.9, "Mesquite": 2681.7, "Bay Shore": 2113.2, "Itapeva": 7030.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Piqua: (40.14°, -84.24°)", " Laguna: (38.42°, -121.42°)", " Mesquite: (36.81°, -114.07°)", " Bay Shore: (40.73°, -73.25°)", " Itapeva: (-23.98°, -48.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Itapeva: 7030.0 km from centroid", " Laguna: 3353.9 km from centroid", " Mesquite: 2681.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Itapeva", "FINAL ANSWER: Itapeva" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.86667, "lon": 145.28333, "name": "Boronia" }, { "lat": -34.424, "lon": 150.89345, "name": "Wollongong" }, { "lat": -27.10876, "lon": 152.94907, "name": "Morayfield" }, { "lat": -38.38176, "lon": 142.48799, "name": "Warrnambool" }, { "lat": 43.05923, "lon": -77.61222, "name": "Henrietta" } ], "question": "Which location is the geographic outlier among: Boronia, Wollongong, Morayfield, Warrnambool, Henrietta?", "ground_truth": { "answer": "Henrietta", "outlier_distance_km": 17333.4, "second_furthest_km": 5178.6, "clarity_ratio": 3.35, "median_distance_km": 5026.0, "distances_to_centroid": { "Boronia": 4605.1, "Wollongong": 5026.0, "Morayfield": 5178.6, "Warrnambool": 4387.1, "Henrietta": 17333.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Boronia: (-37.87°, 145.28°)", " Wollongong: (-34.42°, 150.89°)", " Morayfield: (-27.11°, 152.95°)", " Warrnambool: (-38.38°, 142.49°)", " Henrietta: (43.06°, -77.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Henrietta: 17333.4 km from centroid", " Morayfield: 5178.6 km from centroid", " Wollongong: 5026.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Henrietta", "FINAL ANSWER: Henrietta" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.48742, "lon": 28.97918, "name": "Mūţ" }, { "lat": 5.6698, "lon": -0.01657, "name": "Tema" }, { "lat": 8.58679, "lon": 39.12111, "name": "Mojo" }, { "lat": 9.6053, "lon": 3.94101, "name": "Kaiama" }, { "lat": -37.84205, "lon": 145.0694, "name": "Camberwell" } ], "question": "Which location is the geographic outlier among: Mūţ, Tema, Mojo, Kaiama, Camberwell?", "ground_truth": { "answer": "Camberwell", "outlier_distance_km": 11186.4, "second_furthest_km": 4831.4, "clarity_ratio": 2.32, "median_distance_km": 4437.0, "distances_to_centroid": { "Mūţ": 3006.0, "Tema": 4831.4, "Mojo": 845.3, "Kaiama": 4437.0, "Camberwell": 11186.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mūţ: (25.49°, 28.98°)", " Tema: (5.67°, -0.02°)", " Mojo: (8.59°, 39.12°)", " Kaiama: (9.61°, 3.94°)", " Camberwell: (-37.84°, 145.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Camberwell: 11186.4 km from centroid", " Tema: 4831.4 km from centroid", " Kaiama: 4437.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Camberwell", "FINAL ANSWER: Camberwell" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.88413, "lon": 144.78367, "name": "Altona Meadows" }, { "lat": -33.88374, "lon": 151.21282, "name": "Surry Hills" }, { "lat": -41.31667, "lon": 173.23333, "name": "Stoke" }, { "lat": -43.30437, "lon": 172.58356, "name": "Rangiora" }, { "lat": -22.18556, "lon": -47.39028, "name": "Leme" } ], "question": "Which location is the geographic outlier among: Altona Meadows, Surry Hills, Stoke, Rangiora, Leme?", "ground_truth": { "answer": "Leme", "outlier_distance_km": 13416.6, "second_furthest_km": 4692.1, "clarity_ratio": 2.86, "median_distance_km": 4602.8, "distances_to_centroid": { "Altona Meadows": 2311.1, "Surry Hills": 2945.6, "Stoke": 4692.1, "Rangiora": 4602.8, "Leme": 13416.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Altona Meadows: (-37.88°, 144.78°)", " Surry Hills: (-33.88°, 151.21°)", " Stoke: (-41.32°, 173.23°)", " Rangiora: (-43.30°, 172.58°)", " Leme: (-22.19°, -47.39°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Leme: 13416.6 km from centroid", " Stoke: 4692.1 km from centroid", " Rangiora: 4602.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Leme", "FINAL ANSWER: Leme" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.68104, "lon": -122.12441, "name": "San Lorenzo" }, { "lat": 32.73569, "lon": -97.10807, "name": "Arlington" }, { "lat": 49.68657, "lon": -124.9936, "name": "Courtenay" }, { "lat": 47.92526, "lon": -97.03285, "name": "Grand Forks" }, { "lat": 49.34449, "lon": 7.18045, "name": "Neunkirchen" } ], "question": "Which location is the geographic outlier among: San Lorenzo, Arlington, Courtenay, Grand Forks, Neunkirchen?", "ground_truth": { "answer": "Neunkirchen", "outlier_distance_km": 6752.2, "second_furthest_km": 3026.9, "clarity_ratio": 2.23, "median_distance_km": 2964.2, "distances_to_centroid": { "San Lorenzo": 3026.9, "Arlington": 1493.1, "Courtenay": 2964.2, "Grand Forks": 934.0, "Neunkirchen": 6752.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Lorenzo: (37.68°, -122.12°)", " Arlington: (32.74°, -97.11°)", " Courtenay: (49.69°, -124.99°)", " Grand Forks: (47.93°, -97.03°)", " Neunkirchen: (49.34°, 7.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Neunkirchen: 6752.2 km from centroid", " San Lorenzo: 3026.9 km from centroid", " Courtenay: 2964.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Neunkirchen", "FINAL ANSWER: Neunkirchen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": -32.24295, "lon": 148.60484, "name": "Dubbo" }, { "lat": -32.23013, "lon": 115.78128, "name": "Kwinana" }, { "lat": -37.74124, "lon": 144.73631, "name": "Caroline Springs" }, { "lat": 40.04837, "lon": -86.46917, "name": "Lebanon" } ], "question": "Which location is the geographic outlier among: Yarraville, Dubbo, Kwinana, Caroline Springs, Lebanon?", "ground_truth": { "answer": "Lebanon", "outlier_distance_km": 17785.4, "second_furthest_km": 5605.7, "clarity_ratio": 3.17, "median_distance_km": 5304.8, "distances_to_centroid": { "Yarraville": 5304.8, "Dubbo": 5605.7, "Kwinana": 2598.1, "Caroline Springs": 5289.5, "Lebanon": 17785.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yarraville: (-37.82°, 144.90°)", " Dubbo: (-32.24°, 148.60°)", " Kwinana: (-32.23°, 115.78°)", " Caroline Springs: (-37.74°, 144.74°)", " Lebanon: (40.05°, -86.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lebanon: 17785.4 km from centroid", " Dubbo: 5605.7 km from centroid", " Yarraville: 5304.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lebanon", "FINAL ANSWER: Lebanon" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.59412, "lon": -119.34095, "name": "Wasco" }, { "lat": 45.2333, "lon": -93.29134, "name": "Andover" }, { "lat": 37.22957, "lon": -80.41394, "name": "Blacksburg" }, { "lat": 16.84942, "lon": -99.90891, "name": "Acapulco de Juárez" }, { "lat": 8.13373, "lon": 4.24014, "name": "Ogbomoso" } ], "question": "Which location is the geographic outlier among: Wasco, Andover, Blacksburg, Acapulco de Juárez, Ogbomoso?", "ground_truth": { "answer": "Ogbomoso", "outlier_distance_km": 8796.5, "second_furthest_km": 3964.6, "clarity_ratio": 2.22, "median_distance_km": 2615.3, "distances_to_centroid": { "Wasco": 3964.6, "Andover": 2299.4, "Blacksburg": 990.4, "Acapulco de Juárez": 2615.3, "Ogbomoso": 8796.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wasco: (35.59°, -119.34°)", " Andover: (45.23°, -93.29°)", " Blacksburg: (37.23°, -80.41°)", " Acapulco de Juárez: (16.85°, -99.91°)", " Ogbomoso: (8.13°, 4.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ogbomoso: 8796.5 km from centroid", " Wasco: 3964.6 km from centroid", " Acapulco de Juárez: 2615.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ogbomoso", "FINAL ANSWER: Ogbomoso" ] }, { "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": 34.81282, "lon": 126.39181, "name": "Mokpo" }, { "lat": 26.75586, "lon": 83.12773, "name": "Maghar" }, { "lat": 6.08838, "lon": 100.39167, "name": "Kampung Alor Mengkudu" }, { "lat": 34.4, "lon": 132.45, "name": "Hiroshima" }, { "lat": -26.89778, "lon": -49.23167, "name": "Indaial" } ], "question": "Which location is the geographic outlier among: Mokpo, Maghar, Kampung Alor Mengkudu, Hiroshima, Indaial?", "ground_truth": { "answer": "Indaial", "outlier_distance_km": 14481.4, "second_furthest_km": 5772.1, "clarity_ratio": 2.51, "median_distance_km": 5234.5, "distances_to_centroid": { "Mokpo": 5234.5, "Maghar": 1384.6, "Kampung Alor Mengkudu": 2575.8, "Hiroshima": 5772.1, "Indaial": 14481.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mokpo: (34.81°, 126.39°)", " Maghar: (26.76°, 83.13°)", " Kampung Alor Mengkudu: (6.09°, 100.39°)", " Hiroshima: (34.40°, 132.45°)", " Indaial: (-26.90°, -49.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Indaial: 14481.4 km from centroid", " Hiroshima: 5772.1 km from centroid", " Mokpo: 5234.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Indaial", "FINAL ANSWER: Indaial" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.00845, "lon": -75.10879, "name": "Juniata Park" }, { "lat": 47.64995, "lon": -117.23991, "name": "Opportunity" }, { "lat": 33.77391, "lon": -117.94145, "name": "Garden Grove" }, { "lat": 42.15141, "lon": -87.95979, "name": "Buffalo Grove" }, { "lat": -36.90694, "lon": 174.68704, "name": "New Lynn" } ], "question": "Which location is the geographic outlier among: Juniata Park, Opportunity, Garden Grove, Buffalo Grove, New Lynn?", "ground_truth": { "answer": "New Lynn", "outlier_distance_km": 16082.1, "second_furthest_km": 7000.4, "clarity_ratio": 2.3, "median_distance_km": 6678.6, "distances_to_centroid": { "Juniata Park": 3255.9, "Opportunity": 6678.6, "Garden Grove": 7000.4, "Buffalo Grove": 4355.8, "New Lynn": 16082.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Juniata Park: (40.01°, -75.11°)", " Opportunity: (47.65°, -117.24°)", " Garden Grove: (33.77°, -117.94°)", " Buffalo Grove: (42.15°, -87.96°)", " New Lynn: (-36.91°, 174.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New Lynn: 16082.1 km from centroid", " Garden Grove: 7000.4 km from centroid", " Opportunity: 6678.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New Lynn", "FINAL ANSWER: New Lynn" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.95224, "lon": 115.8614, "name": "Perth" }, { "lat": -25.54073, "lon": 152.70493, "name": "Maryborough" }, { "lat": -30.29626, "lon": 153.11351, "name": "Coffs Harbour" }, { "lat": -33.90741, "lon": 151.15546, "name": "Marrickville" }, { "lat": 16.43425, "lon": 81.69845, "name": "Narasapur" } ], "question": "Which location is the geographic outlier among: Perth, Maryborough, Coffs Harbour, Marrickville, Narasapur?", "ground_truth": { "answer": "Narasapur", "outlier_distance_km": 6794.9, "second_furthest_km": 2448.2, "clarity_ratio": 2.78, "median_distance_km": 2445.3, "distances_to_centroid": { "Perth": 1922.5, "Maryborough": 2278.5, "Coffs Harbour": 2445.3, "Marrickville": 2448.2, "Narasapur": 6794.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Perth: (-31.95°, 115.86°)", " Maryborough: (-25.54°, 152.70°)", " Coffs Harbour: (-30.30°, 153.11°)", " Marrickville: (-33.91°, 151.16°)", " Narasapur: (16.43°, 81.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Narasapur: 6794.9 km from centroid", " Marrickville: 2448.2 km from centroid", " Coffs Harbour: 2445.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Narasapur", "FINAL ANSWER: Narasapur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -10.32, "lon": -36.57944, "name": "Neópolis" }, { "lat": -23.71636, "lon": -46.76872, "name": "Jardim Angela" }, { "lat": 4.03078, "lon": -74.9701, "name": "Guamo" }, { "lat": -19.82028, "lon": -40.27333, "name": "Aracruz" }, { "lat": 52.20024, "lon": 18.63865, "name": "Koło" } ], "question": "Which location is the geographic outlier among: Neópolis, Jardim Angela, Guamo, Aracruz, Koło?", "ground_truth": { "answer": "Koło", "outlier_distance_km": 7652.3, "second_furthest_km": 4348.1, "clarity_ratio": 1.76, "median_distance_km": 2931.0, "distances_to_centroid": { "Neópolis": 1202.1, "Jardim Angela": 2931.0, "Guamo": 4348.1, "Aracruz": 2304.5, "Koło": 7652.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Neópolis: (-10.32°, -36.58°)", " Jardim Angela: (-23.72°, -46.77°)", " Guamo: (4.03°, -74.97°)", " Aracruz: (-19.82°, -40.27°)", " Koło: (52.20°, 18.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Koło: 7652.3 km from centroid", " Guamo: 4348.1 km from centroid", " Jardim Angela: 2931.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Koło", "FINAL ANSWER: Koło" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -4.57444, "lon": -55.94361, "name": "Trairão" }, { "lat": -21.85389, "lon": -47.47917, "name": "Porto Ferreira" }, { "lat": 5.26667, "lon": -73.91667, "name": "La Mesa" }, { "lat": -19.75, "lon": -43.0375, "name": "Nova Era" }, { "lat": -39.4926, "lon": 176.91233, "name": "Napier" } ], "question": "Which location is the geographic outlier among: Trairão, Porto Ferreira, La Mesa, Nova Era, Napier?", "ground_truth": { "answer": "Napier", "outlier_distance_km": 13808.3, "second_furthest_km": 7554.8, "clarity_ratio": 1.83, "median_distance_km": 5310.6, "distances_to_centroid": { "Trairão": 5310.6, "Porto Ferreira": 4118.1, "La Mesa": 7554.8, "Nova Era": 3650.5, "Napier": 13808.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Trairão: (-4.57°, -55.94°)", " Porto Ferreira: (-21.85°, -47.48°)", " La Mesa: (5.27°, -73.92°)", " Nova Era: (-19.75°, -43.04°)", " Napier: (-39.49°, 176.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Napier: 13808.3 km from centroid", " La Mesa: 7554.8 km from centroid", " Trairão: 5310.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Napier", "FINAL ANSWER: Napier" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 56.11254, "lon": 69.48722, "name": "Ishim" }, { "lat": 36.643, "lon": -4.68728, "name": "Alhaurín el Grande" }, { "lat": 48.93564, "lon": 2.35387, "name": "Saint-Denis" }, { "lat": 47.51683, "lon": 40.80831, "name": "Semikarakorsk" }, { "lat": 19.44506, "lon": -99.14612, "name": "Cuauhtémoc" } ], "question": "Which location is the geographic outlier among: Ishim, Alhaurín el Grande, Saint-Denis, Semikarakorsk, Cuauhtémoc?", "ground_truth": { "answer": "Cuauhtémoc", "outlier_distance_km": 9443.6, "second_furthest_km": 4975.0, "clarity_ratio": 1.9, "median_distance_km": 3121.8, "distances_to_centroid": { "Ishim": 4975.0, "Alhaurín el Grande": 792.7, "Saint-Denis": 802.5, "Semikarakorsk": 3121.8, "Cuauhtémoc": 9443.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ishim: (56.11°, 69.49°)", " Alhaurín el Grande: (36.64°, -4.69°)", " Saint-Denis: (48.94°, 2.35°)", " Semikarakorsk: (47.52°, 40.81°)", " Cuauhtémoc: (19.45°, -99.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cuauhtémoc: 9443.6 km from centroid", " Ishim: 4975.0 km from centroid", " Semikarakorsk: 3121.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cuauhtémoc", "FINAL ANSWER: Cuauhtémoc" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.2, "lon": 174.95, "name": "Pukekohe East" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": -38.16667, "lon": 145.16667, "name": "Langwarrin" }, { "lat": -37.91806, "lon": 145.03544, "name": "Bentleigh" }, { "lat": -11.68472, "lon": -41.76889, "name": "Canarana" } ], "question": "Which location is the geographic outlier among: Pukekohe East, Cranbourne East, Langwarrin, Bentleigh, Canarana?", "ground_truth": { "answer": "Canarana", "outlier_distance_km": 14444.1, "second_furthest_km": 5508.2, "clarity_ratio": 2.62, "median_distance_km": 2911.7, "distances_to_centroid": { "Pukekohe East": 5508.2, "Cranbourne East": 2911.7, "Langwarrin": 2900.5, "Bentleigh": 2887.8, "Canarana": 14444.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pukekohe East: (-37.20°, 174.95°)", " Cranbourne East: (-38.12°, 145.30°)", " Langwarrin: (-38.17°, 145.17°)", " Bentleigh: (-37.92°, 145.04°)", " Canarana: (-11.68°, -41.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Canarana: 14444.1 km from centroid", " Pukekohe East: 5508.2 km from centroid", " Cranbourne East: 2911.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Canarana", "FINAL ANSWER: Canarana" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.53472, "lon": 135.70925, "name": "Kashiba" }, { "lat": 23.76571, "lon": 85.93864, "name": "Jāridih" }, { "lat": 36.83389, "lon": 118.89778, "name": "Daotian" }, { "lat": 3.4506, "lon": 102.4176, "name": "Temerluh" }, { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" } ], "question": "Which location is the geographic outlier among: Kashiba, Jāridih, Daotian, Temerluh, Saint Albans?", "ground_truth": { "answer": "Saint Albans", "outlier_distance_km": 6233.8, "second_furthest_km": 3572.9, "clarity_ratio": 1.74, "median_distance_km": 3089.8, "distances_to_centroid": { "Kashiba": 3089.8, "Jāridih": 3572.9, "Daotian": 2745.8, "Temerluh": 1927.2, "Saint Albans": 6233.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kashiba: (34.53°, 135.71°)", " Jāridih: (23.77°, 85.94°)", " Daotian: (36.83°, 118.90°)", " Temerluh: (3.45°, 102.42°)", " Saint Albans: (-37.73°, 144.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saint Albans: 6233.8 km from centroid", " Jāridih: 3572.9 km from centroid", " Kashiba: 3089.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saint Albans", "FINAL ANSWER: Saint Albans" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 59.83528, "lon": 30.14667, "name": "Sosnovaya Polyana" }, { "lat": 40.94223, "lon": 14.23476, "name": "Sant'Antimo" }, { "lat": 40.42478, "lon": -3.66379, "name": "Fuente del Berro" }, { "lat": 45.5305, "lon": 9.13954, "name": "Novate Milanese" }, { "lat": -37.91806, "lon": 145.03544, "name": "Bentleigh" } ], "question": "Which location is the geographic outlier among: Sosnovaya Polyana, Sant'Antimo, Fuente del Berro, Novate Milanese, Bentleigh?", "ground_truth": { "answer": "Bentleigh", "outlier_distance_km": 13302.9, "second_furthest_km": 4013.9, "clarity_ratio": 3.31, "median_distance_km": 3409.1, "distances_to_centroid": { "Sosnovaya Polyana": 3409.1, "Sant'Antimo": 2552.3, "Fuente del Berro": 4013.9, "Novate Milanese": 3129.6, "Bentleigh": 13302.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sosnovaya Polyana: (59.84°, 30.15°)", " Sant'Antimo: (40.94°, 14.23°)", " Fuente del Berro: (40.42°, -3.66°)", " Novate Milanese: (45.53°, 9.14°)", " Bentleigh: (-37.92°, 145.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bentleigh: 13302.9 km from centroid", " Fuente del Berro: 4013.9 km from centroid", " Sosnovaya Polyana: 3409.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bentleigh", "FINAL ANSWER: Bentleigh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.62201, "lon": 74.65699, "name": "Shrirampur" }, { "lat": 31.09407, "lon": 105.08731, "name": "Tongchuan" }, { "lat": 6.53995, "lon": 101.28128, "name": "Yala" }, { "lat": 29.95972, "lon": 107.20356, "name": "Shuanglong" }, { "lat": -16.68528, "lon": -44.365, "name": "Coração de Jesus" } ], "question": "Which location is the geographic outlier among: Shrirampur, Tongchuan, Yala, Shuanglong, Coração de Jesus?", "ground_truth": { "answer": "Coração de Jesus", "outlier_distance_km": 12874.9, "second_furthest_km": 4308.3, "clarity_ratio": 2.99, "median_distance_km": 4151.9, "distances_to_centroid": { "Shrirampur": 876.3, "Tongchuan": 4151.9, "Yala": 3650.1, "Shuanglong": 4308.3, "Coração de Jesus": 12874.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shrirampur: (19.62°, 74.66°)", " Tongchuan: (31.09°, 105.09°)", " Yala: (6.54°, 101.28°)", " Shuanglong: (29.96°, 107.20°)", " Coração de Jesus: (-16.69°, -44.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coração de Jesus: 12874.9 km from centroid", " Shuanglong: 4308.3 km from centroid", " Tongchuan: 4151.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coração de Jesus", "FINAL ANSWER: Coração de Jesus" ] }, { "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": -22.58056, "lon": -47.51861, "name": "Iracemápolis" }, { "lat": 3.40671, "lon": -76.34819, "name": "Candelaria" }, { "lat": -15.80976, "lon": -47.97202, "name": "Guará" }, { "lat": -15.94861, "lon": -44.86444, "name": "São Francisco" }, { "lat": 44.49381, "lon": 11.33875, "name": "Bologna" } ], "question": "Which location is the geographic outlier among: Iracemápolis, Candelaria, Guará, São Francisco, Bologna?", "ground_truth": { "answer": "Bologna", "outlier_distance_km": 7251.3, "second_furthest_km": 3955.2, "clarity_ratio": 1.83, "median_distance_km": 2468.0, "distances_to_centroid": { "Iracemápolis": 2468.0, "Candelaria": 3955.2, "Guará": 1783.2, "São Francisco": 1682.4, "Bologna": 7251.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Iracemápolis: (-22.58°, -47.52°)", " Candelaria: (3.41°, -76.35°)", " Guará: (-15.81°, -47.97°)", " São Francisco: (-15.95°, -44.86°)", " Bologna: (44.49°, 11.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bologna: 7251.3 km from centroid", " Candelaria: 3955.2 km from centroid", " Iracemápolis: 2468.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bologna", "FINAL ANSWER: Bologna" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.66354, "lon": 76.00326, "name": "Vadakkēkkād" }, { "lat": 29.15196, "lon": 108.74289, "name": "Apengjiang" }, { "lat": 20.43353, "lon": 99.87617, "name": "Mae Sai" }, { "lat": 14.05723, "lon": 78.75056, "name": "Rayachoti" }, { "lat": 38.95627, "lon": -5.86162, "name": "Don Benito" } ], "question": "Which location is the geographic outlier among: Vadakkēkkād, Apengjiang, Mae Sai, Rayachoti, Don Benito?", "ground_truth": { "answer": "Don Benito", "outlier_distance_km": 7391.8, "second_furthest_km": 3778.3, "clarity_ratio": 1.96, "median_distance_km": 2940.6, "distances_to_centroid": { "Vadakkēkkād": 1416.3, "Apengjiang": 3778.3, "Mae Sai": 2940.6, "Rayachoti": 1223.6, "Don Benito": 7391.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vadakkēkkād: (10.66°, 76.00°)", " Apengjiang: (29.15°, 108.74°)", " Mae Sai: (20.43°, 99.88°)", " Rayachoti: (14.06°, 78.75°)", " Don Benito: (38.96°, -5.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Don Benito: 7391.8 km from centroid", " Apengjiang: 3778.3 km from centroid", " Mae Sai: 2940.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Don Benito", "FINAL ANSWER: Don Benito" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.86414, "lon": -118.16341, "name": "Rosamond" }, { "lat": 41.76593, "lon": -72.23369, "name": "Mansfield City" }, { "lat": 45.16024, "lon": -93.08883, "name": "Lino Lakes" }, { "lat": 39.15017, "lon": -123.20778, "name": "Ukiah" }, { "lat": -37.83382, "lon": 144.93834, "name": "City of Port Phillip" } ], "question": "Which location is the geographic outlier among: Rosamond, Mansfield City, Lino Lakes, Ukiah, City of Port Phillip?", "ground_truth": { "answer": "City of Port Phillip", "outlier_distance_km": 17817.3, "second_furthest_km": 6714.1, "clarity_ratio": 2.65, "median_distance_km": 6344.7, "distances_to_centroid": { "Rosamond": 6344.7, "Mansfield City": 2643.5, "Lino Lakes": 4296.2, "Ukiah": 6714.1, "City of Port Phillip": 17817.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rosamond: (34.86°, -118.16°)", " Mansfield City: (41.77°, -72.23°)", " Lino Lakes: (45.16°, -93.09°)", " Ukiah: (39.15°, -123.21°)", " City of Port Phillip: (-37.83°, 144.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " City of Port Phillip: 17817.3 km from centroid", " Ukiah: 6714.1 km from centroid", " Rosamond: 6344.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: City of Port Phillip", "FINAL ANSWER: City of Port Phillip" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.99028, "lon": 139.07639, "name": "Chichibu" }, { "lat": 28.23995, "lon": 78.43994, "name": "Gunnaur" }, { "lat": 30.4225, "lon": 120.29722, "name": "Linping" }, { "lat": 36.93833, "lon": 114.50583, "name": "Shahecheng" }, { "lat": 53.42631, "lon": 11.84875, "name": "Parchim" } ], "question": "Which location is the geographic outlier among: Chichibu, Gunnaur, Linping, Shahecheng, Parchim?", "ground_truth": { "answer": "Parchim", "outlier_distance_km": 6236.7, "second_furthest_km": 4093.7, "clarity_ratio": 1.52, "median_distance_km": 2633.1, "distances_to_centroid": { "Chichibu": 4093.7, "Gunnaur": 1660.1, "Linping": 2633.1, "Shahecheng": 1921.1, "Parchim": 6236.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chichibu: (35.99°, 139.08°)", " Gunnaur: (28.24°, 78.44°)", " Linping: (30.42°, 120.30°)", " Shahecheng: (36.94°, 114.51°)", " Parchim: (53.43°, 11.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Parchim: 6236.7 km from centroid", " Chichibu: 4093.7 km from centroid", " Linping: 2633.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Parchim", "FINAL ANSWER: Parchim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.41278, "lon": -40.68306, "name": "Marechal Floriano" }, { "lat": -2.00082, "lon": -54.08102, "name": "Monte Alegre" }, { "lat": -12.43028, "lon": -39.25139, "name": "Santo Estêvão" }, { "lat": -3.76585, "lon": -49.67923, "name": "Tucuruí" }, { "lat": -33.41665, "lon": 149.5806, "name": "Bathurst" } ], "question": "Which location is the geographic outlier among: Marechal Floriano, Monte Alegre, Santo Estêvão, Tucuruí, Bathurst?", "ground_truth": { "answer": "Bathurst", "outlier_distance_km": 14137.9, "second_furthest_km": 5367.2, "clarity_ratio": 2.63, "median_distance_km": 4842.1, "distances_to_centroid": { "Marechal Floriano": 3647.3, "Monte Alegre": 5367.2, "Santo Estêvão": 3511.5, "Tucuruí": 4842.1, "Bathurst": 14137.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Marechal Floriano: (-20.41°, -40.68°)", " Monte Alegre: (-2.00°, -54.08°)", " Santo Estêvão: (-12.43°, -39.25°)", " Tucuruí: (-3.77°, -49.68°)", " Bathurst: (-33.42°, 149.58°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bathurst: 14137.9 km from centroid", " Monte Alegre: 5367.2 km from centroid", " Tucuruí: 4842.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bathurst", "FINAL ANSWER: Bathurst" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.38047, "lon": 145.39867, "name": "Shepparton" }, { "lat": -33.9681, "lon": 151.13564, "name": "Kogarah" }, { "lat": -19.30323, "lon": 146.72531, "name": "Kirwan" }, { "lat": -37.68333, "lon": 145.01667, "name": "Thomastown" }, { "lat": 49.34449, "lon": 7.18045, "name": "Neunkirchen" } ], "question": "Which location is the geographic outlier among: Shepparton, Kogarah, Kirwan, Thomastown, Neunkirchen?", "ground_truth": { "answer": "Neunkirchen", "outlier_distance_km": 12897.1, "second_furthest_km": 3800.0, "clarity_ratio": 3.39, "median_distance_km": 3535.7, "distances_to_centroid": { "Shepparton": 3478.4, "Kogarah": 3800.0, "Kirwan": 2956.9, "Thomastown": 3535.7, "Neunkirchen": 12897.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shepparton: (-36.38°, 145.40°)", " Kogarah: (-33.97°, 151.14°)", " Kirwan: (-19.30°, 146.73°)", " Thomastown: (-37.68°, 145.02°)", " Neunkirchen: (49.34°, 7.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Neunkirchen: 12897.1 km from centroid", " Kogarah: 3800.0 km from centroid", " Thomastown: 3535.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Neunkirchen", "FINAL ANSWER: Neunkirchen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.28374, "lon": 174.74141, "name": "Karori" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" }, { "lat": -27.49325, "lon": 153.05826, "name": "Coorparoo" }, { "lat": -33.2792, "lon": 115.71504, "name": "Australind" }, { "lat": -1.35528, "lon": -48.34194, "name": "Marituba" } ], "question": "Which location is the geographic outlier among: Karori, Launceston, Coorparoo, Australind, Marituba?", "ground_truth": { "answer": "Marituba", "outlier_distance_km": 15836.0, "second_furthest_km": 6034.0, "clarity_ratio": 2.62, "median_distance_km": 4346.1, "distances_to_centroid": { "Karori": 6034.0, "Launceston": 3739.9, "Coorparoo": 4346.1, "Australind": 840.0, "Marituba": 15836.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Karori: (-41.28°, 174.74°)", " Launceston: (-41.44°, 147.13°)", " Coorparoo: (-27.49°, 153.06°)", " Australind: (-33.28°, 115.72°)", " Marituba: (-1.36°, -48.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Marituba: 15836.0 km from centroid", " Karori: 6034.0 km from centroid", " Coorparoo: 4346.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Marituba", "FINAL ANSWER: Marituba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.08843, "lon": 31.28351, "name": "Ḩadā’iq al Qubbah" }, { "lat": 7.10168, "lon": 7.65945, "name": "Otukpa" }, { "lat": -25.47512, "lon": 30.96935, "name": "Mbombela" }, { "lat": -27.3887, "lon": 26.61701, "name": "Bothaville" }, { "lat": 17.83498, "lon": -93.38902, "name": "Huimanguillo" } ], "question": "Which location is the geographic outlier among: Ḩadā’iq al Qubbah, Otukpa, Mbombela, Bothaville, Huimanguillo?", "ground_truth": { "answer": "Huimanguillo", "outlier_distance_km": 10418.0, "second_furthest_km": 4622.9, "clarity_ratio": 2.25, "median_distance_km": 4349.7, "distances_to_centroid": { "Ḩadā’iq al Qubbah": 4622.9, "Otukpa": 1076.1, "Mbombela": 4349.7, "Bothaville": 4156.5, "Huimanguillo": 10418.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ḩadā’iq al Qubbah: (30.09°, 31.28°)", " Otukpa: (7.10°, 7.66°)", " Mbombela: (-25.48°, 30.97°)", " Bothaville: (-27.39°, 26.62°)", " Huimanguillo: (17.83°, -93.39°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Huimanguillo: 10418.0 km from centroid", " Ḩadā’iq al Qubbah: 4622.9 km from centroid", " Mbombela: 4349.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Huimanguillo", "FINAL ANSWER: Huimanguillo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.3, "lon": 139.11667, "name": "Tamamura" }, { "lat": 36.63246, "lon": 136.63726, "name": "Mukai-awagasaki" }, { "lat": 8.52218, "lon": 77.04001, "name": "Vilappil" }, { "lat": 29.48684, "lon": 105.58863, "name": "Guchang" }, { "lat": -37.71667, "lon": 145.0, "name": "Reservoir" } ], "question": "Which location is the geographic outlier among: Tamamura, Mukai-awagasaki, Vilappil, Guchang, Reservoir?", "ground_truth": { "answer": "Reservoir", "outlier_distance_km": 6352.5, "second_furthest_km": 4794.4, "clarity_ratio": 1.32, "median_distance_km": 3024.9, "distances_to_centroid": { "Tamamura": 3024.9, "Mukai-awagasaki": 2912.2, "Vilappil": 4794.4, "Guchang": 2262.5, "Reservoir": 6352.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tamamura: (36.30°, 139.12°)", " Mukai-awagasaki: (36.63°, 136.64°)", " Vilappil: (8.52°, 77.04°)", " Guchang: (29.49°, 105.59°)", " Reservoir: (-37.72°, 145.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Reservoir: 6352.5 km from centroid", " Vilappil: 4794.4 km from centroid", " Tamamura: 3024.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Reservoir", "FINAL ANSWER: Reservoir" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.88333, "lon": 151.1, "name": "Burwood" }, { "lat": -28.00029, "lon": 153.43088, "name": "Gold Coast" }, { "lat": -37.86667, "lon": 145.06667, "name": "Glen Iris" }, { "lat": -32.06003, "lon": 115.955, "name": "Thornlie" }, { "lat": 22.0, "lon": 103.13333, "name": "Mường Lay" } ], "question": "Which location is the geographic outlier among: Burwood, Gold Coast, Glen Iris, Thornlie, Mường Lay?", "ground_truth": { "answer": "Mường Lay", "outlier_distance_km": 5907.6, "second_furthest_km": 2154.7, "clarity_ratio": 2.74, "median_distance_km": 2092.3, "distances_to_centroid": { "Burwood": 2154.7, "Gold Coast": 2092.3, "Glen Iris": 2074.5, "Thornlie": 2084.3, "Mường Lay": 5907.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Burwood: (-33.88°, 151.10°)", " Gold Coast: (-28.00°, 153.43°)", " Glen Iris: (-37.87°, 145.07°)", " Thornlie: (-32.06°, 115.95°)", " Mường Lay: (22.00°, 103.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mường Lay: 5907.6 km from centroid", " Burwood: 2154.7 km from centroid", " Gold Coast: 2092.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mường Lay", "FINAL ANSWER: Mường Lay" ] }, { "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": -34.60251, "lon": 138.74902, "name": "Gawler" }, { "lat": -32.32889, "lon": 115.83047, "name": "Baldivis" }, { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" }, { "lat": -27.08465, "lon": 152.9511, "name": "Caboolture" }, { "lat": 40.75566, "lon": -73.58763, "name": "Westbury" } ], "question": "Which location is the geographic outlier among: Gawler, Baldivis, Carnegie, Caboolture, Westbury?", "ground_truth": { "answer": "Westbury", "outlier_distance_km": 17313.1, "second_furthest_km": 5898.8, "clarity_ratio": 2.94, "median_distance_km": 5231.7, "distances_to_centroid": { "Gawler": 4605.5, "Baldivis": 2544.0, "Carnegie": 5231.7, "Caboolture": 5898.8, "Westbury": 17313.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gawler: (-34.60°, 138.75°)", " Baldivis: (-32.33°, 115.83°)", " Carnegie: (-37.89°, 145.06°)", " Caboolture: (-27.08°, 152.95°)", " Westbury: (40.76°, -73.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Westbury: 17313.1 km from centroid", " Caboolture: 5898.8 km from centroid", " Carnegie: 5231.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Westbury", "FINAL ANSWER: Westbury" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.50291, "lon": -1.3458, "name": "Wath upon Dearne" }, { "lat": 51.14312, "lon": 23.4716, "name": "Chełm" }, { "lat": 57.41435, "lon": 56.97157, "name": "Kungur" }, { "lat": 44.10083, "lon": 39.08326, "name": "Tuapse" }, { "lat": -31.95224, "lon": 115.8614, "name": "Perth" } ], "question": "Which location is the geographic outlier among: Wath upon Dearne, Chełm, Kungur, Tuapse, Perth?", "ground_truth": { "answer": "Perth", "outlier_distance_km": 10347.8, "second_furthest_km": 4257.1, "clarity_ratio": 2.43, "median_distance_km": 2622.7, "distances_to_centroid": { "Wath upon Dearne": 4257.1, "Chełm": 2603.2, "Kungur": 2622.7, "Tuapse": 1223.3, "Perth": 10347.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wath upon Dearne: (53.50°, -1.35°)", " Chełm: (51.14°, 23.47°)", " Kungur: (57.41°, 56.97°)", " Tuapse: (44.10°, 39.08°)", " Perth: (-31.95°, 115.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Perth: 10347.8 km from centroid", " Wath upon Dearne: 4257.1 km from centroid", " Kungur: 2622.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Perth", "FINAL ANSWER: Perth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.75361, "lon": -47.41361, "name": "Santa Bárbara d'Oeste" }, { "lat": -6.45833, "lon": -37.09778, "name": "Caicó" }, { "lat": -25.59912, "lon": -54.57355, "name": "Puerto Iguazú" }, { "lat": -34.06863, "lon": -70.72747, "name": "Graneros" }, { "lat": 13.73058, "lon": 100.52388, "name": "Bang Rak" } ], "question": "Which location is the geographic outlier among: Santa Bárbara d'Oeste, Caicó, Puerto Iguazú, Graneros, Bang Rak?", "ground_truth": { "answer": "Bang Rak", "outlier_distance_km": 13825.2, "second_furthest_km": 5317.0, "clarity_ratio": 2.6, "median_distance_km": 3596.4, "distances_to_centroid": { "Santa Bárbara d'Oeste": 2817.6, "Caicó": 1916.8, "Puerto Iguazú": 3596.4, "Graneros": 5317.0, "Bang Rak": 13825.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Bárbara d'Oeste: (-22.75°, -47.41°)", " Caicó: (-6.46°, -37.10°)", " Puerto Iguazú: (-25.60°, -54.57°)", " Graneros: (-34.07°, -70.73°)", " Bang Rak: (13.73°, 100.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bang Rak: 13825.2 km from centroid", " Graneros: 5317.0 km from centroid", " Puerto Iguazú: 3596.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bang Rak", "FINAL ANSWER: Bang Rak" ] }, { "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": 17.48862, "lon": 78.60208, "name": "Nāgāvaram" }, { "lat": 1.72837, "lon": 128.00948, "name": "Tobelo" }, { "lat": 17.83564, "lon": 78.06811, "name": "Jogipet" }, { "lat": 14.55027, "lon": 121.03269, "name": "Makati City" }, { "lat": 10.53689, "lon": -2.70155, "name": "Jirapa" } ], "question": "Which location is the geographic outlier among: Nāgāvaram, Tobelo, Jogipet, Makati City, Jirapa?", "ground_truth": { "answer": "Jirapa", "outlier_distance_km": 9039.8, "second_furthest_km": 5354.6, "clarity_ratio": 1.69, "median_distance_km": 4372.6, "distances_to_centroid": { "Nāgāvaram": 602.3, "Tobelo": 5354.6, "Jogipet": 659.9, "Makati City": 4372.6, "Jirapa": 9039.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nāgāvaram: (17.49°, 78.60°)", " Tobelo: (1.73°, 128.01°)", " Jogipet: (17.84°, 78.07°)", " Makati City: (14.55°, 121.03°)", " Jirapa: (10.54°, -2.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jirapa: 9039.8 km from centroid", " Tobelo: 5354.6 km from centroid", " Makati City: 4372.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jirapa", "FINAL ANSWER: Jirapa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.80639, "lon": 145.03086, "name": "Kew" }, { "lat": -23.84852, "lon": 151.25775, "name": "Gladstone" }, { "lat": -38.14711, "lon": 144.36069, "name": "Geelong" }, { "lat": -33.91938, "lon": 150.92588, "name": "Liverpool" }, { "lat": 37.40458, "lon": 136.89912, "name": "Wajima" } ], "question": "Which location is the geographic outlier among: Kew, Gladstone, Geelong, Liverpool, Wajima?", "ground_truth": { "answer": "Wajima", "outlier_distance_km": 6368.2, "second_furthest_km": 2103.7, "clarity_ratio": 3.03, "median_distance_km": 2062.9, "distances_to_centroid": { "Kew": 2062.9, "Gladstone": 768.5, "Geelong": 2103.7, "Liverpool": 1709.9, "Wajima": 6368.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kew: (-37.81°, 145.03°)", " Gladstone: (-23.85°, 151.26°)", " Geelong: (-38.15°, 144.36°)", " Liverpool: (-33.92°, 150.93°)", " Wajima: (37.40°, 136.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wajima: 6368.2 km from centroid", " Geelong: 2103.7 km from centroid", " Kew: 2062.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wajima", "FINAL ANSWER: Wajima" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.98911, "lon": -97.87723, "name": "Kyle" }, { "lat": 42.12922, "lon": -80.08506, "name": "Erie" }, { "lat": 40.76844, "lon": -73.77708, "name": "Bayside" }, { "lat": 36.02153, "lon": -80.382, "name": "Clemmons" }, { "lat": -24.61778, "lon": -53.32, "name": "Cafelândia" } ], "question": "Which location is the geographic outlier among: Kyle, Erie, Bayside, Clemmons, Cafelândia?", "ground_truth": { "answer": "Cafelândia", "outlier_distance_km": 6067.2, "second_furthest_km": 2126.2, "clarity_ratio": 2.85, "median_distance_km": 1940.1, "distances_to_centroid": { "Kyle": 2126.2, "Erie": 1940.1, "Bayside": 1795.6, "Clemmons": 1280.6, "Cafelândia": 6067.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kyle: (29.99°, -97.88°)", " Erie: (42.13°, -80.09°)", " Bayside: (40.77°, -73.78°)", " Clemmons: (36.02°, -80.38°)", " Cafelândia: (-24.62°, -53.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cafelândia: 6067.2 km from centroid", " Kyle: 2126.2 km from centroid", " Erie: 1940.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cafelândia", "FINAL ANSWER: Cafelândia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.65333, "lon": 5.2875, "name": "Vught" }, { "lat": 54.83373, "lon": 37.61138, "name": "Pushchino" }, { "lat": 52.1653, "lon": 8.85996, "name": "Vlotho" }, { "lat": 49.98738, "lon": 20.06473, "name": "Wieliczka" }, { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" } ], "question": "Which location is the geographic outlier among: Vught, Pushchino, Vlotho, Wieliczka, Dianella?", "ground_truth": { "answer": "Dianella", "outlier_distance_km": 11067.4, "second_furthest_km": 3130.1, "clarity_ratio": 3.54, "median_distance_km": 2933.3, "distances_to_centroid": { "Vught": 3130.1, "Pushchino": 2166.5, "Vlotho": 2933.3, "Wieliczka": 2154.8, "Dianella": 11067.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vught: (51.65°, 5.29°)", " Pushchino: (54.83°, 37.61°)", " Vlotho: (52.17°, 8.86°)", " Wieliczka: (49.99°, 20.06°)", " Dianella: (-31.89°, 115.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dianella: 11067.4 km from centroid", " Vught: 3130.1 km from centroid", " Vlotho: 2933.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dianella", "FINAL ANSWER: Dianella" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 27.09978, "lon": -82.45426, "name": "Venice" }, { "lat": 20.3914, "lon": -101.19222, "name": "Valle de Santiago" }, { "lat": 44.79884, "lon": -68.77265, "name": "Bangor" }, { "lat": 22.18912, "lon": -100.93792, "name": "Soledad de Graciano Sánchez" }, { "lat": 20.81408, "lon": 77.98015, "name": "Chāndūr" } ], "question": "Which location is the geographic outlier among: Venice, Valle de Santiago, Bangor, Soledad de Graciano Sánchez, Chāndūr?", "ground_truth": { "answer": "Chāndūr", "outlier_distance_km": 12675.7, "second_furthest_km": 4727.2, "clarity_ratio": 2.68, "median_distance_km": 4642.6, "distances_to_centroid": { "Venice": 2705.2, "Valle de Santiago": 4727.2, "Bangor": 2319.1, "Soledad de Graciano Sánchez": 4642.6, "Chāndūr": 12675.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Venice: (27.10°, -82.45°)", " Valle de Santiago: (20.39°, -101.19°)", " Bangor: (44.80°, -68.77°)", " Soledad de Graciano Sánchez: (22.19°, -100.94°)", " Chāndūr: (20.81°, 77.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chāndūr: 12675.7 km from centroid", " Valle de Santiago: 4727.2 km from centroid", " Soledad de Graciano Sánchez: 4642.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chāndūr", "FINAL ANSWER: Chāndūr" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -43.58333, "lon": 172.38333, "name": "Rolleston" }, { "lat": -37.8318, "lon": 140.77919, "name": "Mount Gambier" }, { "lat": -37.91806, "lon": 145.03544, "name": "Bentleigh" }, { "lat": -41.05584, "lon": 145.90375, "name": "Burnie" }, { "lat": 5.71434, "lon": -72.93391, "name": "Sogamoso" } ], "question": "Which location is the geographic outlier among: Rolleston, Mount Gambier, Bentleigh, Burnie, Sogamoso?", "ground_truth": { "answer": "Sogamoso", "outlier_distance_km": 17209.3, "second_furthest_km": 5862.8, "clarity_ratio": 2.94, "median_distance_km": 3706.3, "distances_to_centroid": { "Rolleston": 5862.8, "Mount Gambier": 3241.8, "Bentleigh": 3615.5, "Burnie": 3706.3, "Sogamoso": 17209.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rolleston: (-43.58°, 172.38°)", " Mount Gambier: (-37.83°, 140.78°)", " Bentleigh: (-37.92°, 145.04°)", " Burnie: (-41.06°, 145.90°)", " Sogamoso: (5.71°, -72.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sogamoso: 17209.3 km from centroid", " Rolleston: 5862.8 km from centroid", " Burnie: 3706.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sogamoso", "FINAL ANSWER: Sogamoso" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -9.97472, "lon": -67.81, "name": "Rio Branco" }, { "lat": -24.24423, "lon": -49.70932, "name": "Jaguariaíva" }, { "lat": -6.495, "lon": -43.70222, "name": "São João dos Patos" }, { "lat": -6.26617, "lon": -35.20969, "name": "Goianinha" }, { "lat": 8.15, "lon": 39.35, "name": "Huruta" } ], "question": "Which location is the geographic outlier among: Rio Branco, Jaguariaíva, São João dos Patos, Goianinha, Huruta?", "ground_truth": { "answer": "Huruta", "outlier_distance_km": 8040.0, "second_furthest_km": 4004.0, "clarity_ratio": 2.01, "median_distance_km": 2673.0, "distances_to_centroid": { "Rio Branco": 4004.0, "Jaguariaíva": 2673.0, "São João dos Patos": 1362.9, "Goianinha": 450.6, "Huruta": 8040.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rio Branco: (-9.97°, -67.81°)", " Jaguariaíva: (-24.24°, -49.71°)", " São João dos Patos: (-6.50°, -43.70°)", " Goianinha: (-6.27°, -35.21°)", " Huruta: (8.15°, 39.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Huruta: 8040.0 km from centroid", " Rio Branco: 4004.0 km from centroid", " Jaguariaíva: 2673.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Huruta", "FINAL ANSWER: Huruta" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.84853, "lon": 174.76349, "name": "Auckland" }, { "lat": -36.84103, "lon": 174.65223, "name": "Te Atatu Peninsula" }, { "lat": -33.73333, "lon": 150.88333, "name": "Quakers Hill" }, { "lat": -37.9, "lon": 144.66667, "name": "Werribee" }, { "lat": -12.16028, "lon": -39.33167, "name": "Serra Preta" } ], "question": "Which location is the geographic outlier among: Auckland, Te Atatu Peninsula, Quakers Hill, Werribee, Serra Preta?", "ground_truth": { "answer": "Serra Preta", "outlier_distance_km": 14732.3, "second_furthest_km": 4906.1, "clarity_ratio": 3.0, "median_distance_km": 4896.4, "distances_to_centroid": { "Auckland": 4906.1, "Te Atatu Peninsula": 4896.4, "Quakers Hill": 2788.5, "Werribee": 2259.4, "Serra Preta": 14732.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Auckland: (-36.85°, 174.76°)", " Te Atatu Peninsula: (-36.84°, 174.65°)", " Quakers Hill: (-33.73°, 150.88°)", " Werribee: (-37.90°, 144.67°)", " Serra Preta: (-12.16°, -39.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Serra Preta: 14732.3 km from centroid", " Auckland: 4906.1 km from centroid", " Te Atatu Peninsula: 4896.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Serra Preta", "FINAL ANSWER: Serra Preta" ] }, { "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": 53.35934, "lon": -1.48759, "name": "Nether Edge" }, { "lat": 46.66817, "lon": 11.15953, "name": "Merano" }, { "lat": 40.38432, "lon": -3.74575, "name": "Vista Alegre" }, { "lat": 28.31122, "lon": -16.41276, "name": "Güimar" }, { "lat": 43.64111, "lon": 81.87, "name": "Kax" } ], "question": "Which location is the geographic outlier among: Nether Edge, Merano, Vista Alegre, Güimar, Kax?", "ground_truth": { "answer": "Kax", "outlier_distance_km": 5334.4, "second_furthest_km": 3171.1, "clarity_ratio": 1.68, "median_distance_km": 1679.7, "distances_to_centroid": { "Nether Edge": 1679.7, "Merano": 527.7, "Vista Alegre": 1517.4, "Güimar": 3171.1, "Kax": 5334.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nether Edge: (53.36°, -1.49°)", " Merano: (46.67°, 11.16°)", " Vista Alegre: (40.38°, -3.75°)", " Güimar: (28.31°, -16.41°)", " Kax: (43.64°, 81.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kax: 5334.4 km from centroid", " Güimar: 3171.1 km from centroid", " Nether Edge: 1679.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kax", "FINAL ANSWER: Kax" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -30.50123, "lon": 151.66553, "name": "Armidale" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" }, { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, { "lat": -32.32889, "lon": 115.83047, "name": "Baldivis" }, { "lat": 31.16757, "lon": 31.80125, "name": "Mīt Salsīl" } ], "question": "Which location is the geographic outlier among: Armidale, Launceston, Kallangur, Baldivis, Mīt Salsīl?", "ground_truth": { "answer": "Mīt Salsīl", "outlier_distance_km": 10971.5, "second_furthest_km": 3496.9, "clarity_ratio": 3.14, "median_distance_km": 3454.2, "distances_to_centroid": { "Armidale": 3385.1, "Launceston": 3496.9, "Kallangur": 3454.2, "Baldivis": 1421.4, "Mīt Salsīl": 10971.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Armidale: (-30.50°, 151.67°)", " Launceston: (-41.44°, 147.13°)", " Kallangur: (-27.25°, 152.99°)", " Baldivis: (-32.33°, 115.83°)", " Mīt Salsīl: (31.17°, 31.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mīt Salsīl: 10971.5 km from centroid", " Launceston: 3496.9 km from centroid", " Kallangur: 3454.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mīt Salsīl", "FINAL ANSWER: Mīt Salsīl" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.51603, "lon": 173.9528, "name": "Blenheim" }, { "lat": -36.88745, "lon": 174.77059, "name": "Epsom" }, { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" }, { "lat": -26.68443, "lon": 153.05705, "name": "Buderim" }, { "lat": 40.75566, "lon": -73.58763, "name": "Westbury" } ], "question": "Which location is the geographic outlier among: Blenheim, Epsom, Ashburton, Buderim, Westbury?", "ground_truth": { "answer": "Westbury", "outlier_distance_km": 17535.8, "second_furthest_km": 5498.8, "clarity_ratio": 3.19, "median_distance_km": 5466.8, "distances_to_centroid": { "Blenheim": 5466.8, "Epsom": 5498.8, "Ashburton": 5326.0, "Buderim": 3392.0, "Westbury": 17535.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Blenheim: (-41.52°, 173.95°)", " Epsom: (-36.89°, 174.77°)", " Ashburton: (-43.90°, 171.73°)", " Buderim: (-26.68°, 153.06°)", " Westbury: (40.76°, -73.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Westbury: 17535.8 km from centroid", " Epsom: 5498.8 km from centroid", " Blenheim: 5466.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Westbury", "FINAL ANSWER: Westbury" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 32.85727, "lon": -116.92225, "name": "Lakeside" }, { "lat": 46.74064, "lon": -71.45131, "name": "Saint-Augustin-de-Desmaures" }, { "lat": 41.52614, "lon": -87.88922, "name": "Mokena" }, { "lat": 39.18316, "lon": -76.64024, "name": "Ferndale" }, { "lat": 10.02737, "lon": 77.47815, "name": "Allinagaram" } ], "question": "Which location is the geographic outlier among: Lakeside, Saint-Augustin-de-Desmaures, Mokena, Ferndale, Allinagaram?", "ground_truth": { "answer": "Allinagaram", "outlier_distance_km": 13011.5, "second_furthest_km": 5646.1, "clarity_ratio": 2.3, "median_distance_km": 2979.3, "distances_to_centroid": { "Lakeside": 5646.1, "Saint-Augustin-de-Desmaures": 1968.8, "Mokena": 2979.3, "Ferndale": 2000.4, "Allinagaram": 13011.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lakeside: (32.86°, -116.92°)", " Saint-Augustin-de-Desmaures: (46.74°, -71.45°)", " Mokena: (41.53°, -87.89°)", " Ferndale: (39.18°, -76.64°)", " Allinagaram: (10.03°, 77.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Allinagaram: 13011.5 km from centroid", " Lakeside: 5646.1 km from centroid", " Mokena: 2979.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Allinagaram", "FINAL ANSWER: Allinagaram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.48178, "lon": 118.61119, "name": "Semporna" }, { "lat": 11.31984, "lon": 77.70971, "name": "Kāsipālaiyam" }, { "lat": 23.7, "lon": 113.03333, "name": "Qingyuan" }, { "lat": 22.36544, "lon": 88.4325, "name": "Baruipur" }, { "lat": 40.11059, "lon": -88.20727, "name": "Urbana" } ], "question": "Which location is the geographic outlier among: Semporna, Kāsipālaiyam, Qingyuan, Baruipur, Urbana?", "ground_truth": { "answer": "Urbana", "outlier_distance_km": 12608.9, "second_furthest_km": 6370.8, "clarity_ratio": 1.98, "median_distance_km": 5253.7, "distances_to_centroid": { "Semporna": 6370.8, "Kāsipālaiyam": 1965.6, "Qingyuan": 5253.7, "Baruipur": 2750.8, "Urbana": 12608.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Semporna: (4.48°, 118.61°)", " Kāsipālaiyam: (11.32°, 77.71°)", " Qingyuan: (23.70°, 113.03°)", " Baruipur: (22.37°, 88.43°)", " Urbana: (40.11°, -88.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Urbana: 12608.9 km from centroid", " Semporna: 6370.8 km from centroid", " Qingyuan: 5253.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Urbana", "FINAL ANSWER: Urbana" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.51801, "lon": -98.31612, "name": "Converse" }, { "lat": 37.05828, "lon": -120.84992, "name": "Los Banos" }, { "lat": 20.39833, "lon": -89.53541, "name": "Ticul" }, { "lat": 22.00554, "lon": -98.77972, "name": "Tamuín" }, { "lat": -26.26786, "lon": 28.12225, "name": "Alberton" } ], "question": "Which location is the geographic outlier among: Converse, Los Banos, Ticul, Tamuín, Alberton?", "ground_truth": { "answer": "Alberton", "outlier_distance_km": 12176.4, "second_furthest_km": 4953.0, "clarity_ratio": 2.46, "median_distance_km": 2704.0, "distances_to_centroid": { "Converse": 2704.0, "Los Banos": 4953.0, "Ticul": 1502.8, "Tamuín": 2477.1, "Alberton": 12176.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Converse: (29.52°, -98.32°)", " Los Banos: (37.06°, -120.85°)", " Ticul: (20.40°, -89.54°)", " Tamuín: (22.01°, -98.78°)", " Alberton: (-26.27°, 28.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alberton: 12176.4 km from centroid", " Los Banos: 4953.0 km from centroid", " Converse: 2704.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alberton", "FINAL ANSWER: Alberton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.41528, "lon": 128.16056, "name": "Sangju" }, { "lat": 16.8632, "lon": 120.7829, "name": "Mankayan" }, { "lat": 34.29341, "lon": 117.34436, "name": "Dahuangshan" }, { "lat": 16.22291, "lon": 74.3501, "name": "Gadhinglaj" }, { "lat": -43.58333, "lon": 172.38333, "name": "Rolleston" } ], "question": "Which location is the geographic outlier among: Sangju, Mankayan, Dahuangshan, Gadhinglaj, Rolleston?", "ground_truth": { "answer": "Rolleston", "outlier_distance_km": 7975.1, "second_furthest_km": 5212.8, "clarity_ratio": 1.53, "median_distance_km": 2766.7, "distances_to_centroid": { "Sangju": 2766.7, "Mankayan": 570.8, "Dahuangshan": 2530.8, "Gadhinglaj": 5212.8, "Rolleston": 7975.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sangju: (36.42°, 128.16°)", " Mankayan: (16.86°, 120.78°)", " Dahuangshan: (34.29°, 117.34°)", " Gadhinglaj: (16.22°, 74.35°)", " Rolleston: (-43.58°, 172.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rolleston: 7975.1 km from centroid", " Gadhinglaj: 5212.8 km from centroid", " Sangju: 2766.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rolleston", "FINAL ANSWER: Rolleston" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.4901, "lon": -71.31283, "name": "Newport" }, { "lat": 18.98196, "lon": -97.78363, "name": "Acatzingo" }, { "lat": 19.58867, "lon": -98.56972, "name": "Calpulalpan" }, { "lat": 35.22257, "lon": -97.43948, "name": "Norman" }, { "lat": 52.525, "lon": 5.71806, "name": "Dronten" } ], "question": "Which location is the geographic outlier among: Newport, Acatzingo, Calpulalpan, Norman, Dronten?", "ground_truth": { "answer": "Dronten", "outlier_distance_km": 6315.2, "second_furthest_km": 3061.5, "clarity_ratio": 2.06, "median_distance_km": 3035.6, "distances_to_centroid": { "Newport": 883.0, "Acatzingo": 3035.6, "Calpulalpan": 3061.5, "Norman": 2346.3, "Dronten": 6315.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Newport: (41.49°, -71.31°)", " Acatzingo: (18.98°, -97.78°)", " Calpulalpan: (19.59°, -98.57°)", " Norman: (35.22°, -97.44°)", " Dronten: (52.52°, 5.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dronten: 6315.2 km from centroid", " Calpulalpan: 3061.5 km from centroid", " Acatzingo: 3035.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dronten", "FINAL ANSWER: Dronten" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.22886, "lon": 31.48149, "name": "Al-'Ubūr" }, { "lat": 10.7, "lon": 37.26667, "name": "Finote Selam" }, { "lat": -26.33172, "lon": 26.32065, "name": "Coligny" }, { "lat": 6.01962, "lon": 6.91729, "name": "Nnewi" }, { "lat": 7.16083, "lon": 124.475, "name": "Malingao" } ], "question": "Which location is the geographic outlier among: Al-'Ubūr, Finote Selam, Coligny, Nnewi, Malingao?", "ground_truth": { "answer": "Malingao", "outlier_distance_km": 8741.6, "second_furthest_km": 4244.8, "clarity_ratio": 2.06, "median_distance_km": 4093.0, "distances_to_centroid": { "Al-'Ubūr": 3101.3, "Finote Selam": 1052.2, "Coligny": 4093.0, "Nnewi": 4244.8, "Malingao": 8741.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Al-'Ubūr: (30.23°, 31.48°)", " Finote Selam: (10.70°, 37.27°)", " Coligny: (-26.33°, 26.32°)", " Nnewi: (6.02°, 6.92°)", " Malingao: (7.16°, 124.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Malingao: 8741.6 km from centroid", " Nnewi: 4244.8 km from centroid", " Coligny: 4093.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Malingao", "FINAL ANSWER: Malingao" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.04439, "lon": 6.57089, "name": "Lapai" }, { "lat": 11.74697, "lon": 11.96083, "name": "Damaturu" }, { "lat": -33.92584, "lon": 18.42322, "name": "Cape Town" }, { "lat": 13.06269, "lon": 5.24322, "name": "Sokoto" }, { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" } ], "question": "Which location is the geographic outlier among: Lapai, Damaturu, Cape Town, Sokoto, Dianella?", "ground_truth": { "answer": "Dianella", "outlier_distance_km": 9091.8, "second_furthest_km": 3628.3, "clarity_ratio": 2.51, "median_distance_km": 3349.1, "distances_to_centroid": { "Lapai": 3263.3, "Damaturu": 2965.3, "Cape Town": 3349.1, "Sokoto": 3628.3, "Dianella": 9091.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lapai: (9.04°, 6.57°)", " Damaturu: (11.75°, 11.96°)", " Cape Town: (-33.93°, 18.42°)", " Sokoto: (13.06°, 5.24°)", " Dianella: (-31.89°, 115.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dianella: 9091.8 km from centroid", " Sokoto: 3628.3 km from centroid", " Cape Town: 3349.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dianella", "FINAL ANSWER: Dianella" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.07699, "lon": 1.17891, "name": "La Pineda" }, { "lat": 51.2504, "lon": 6.97536, "name": "Mettmann" }, { "lat": 41.11006, "lon": 16.69086, "name": "Bitonto" }, { "lat": 52.10387, "lon": 20.6337, "name": "Grodzisk Mazowiecki" }, { "lat": 35.49576, "lon": 135.74604, "name": "Obama" } ], "question": "Which location is the geographic outlier among: La Pineda, Mettmann, Bitonto, Grodzisk Mazowiecki, Obama?", "ground_truth": { "answer": "Obama", "outlier_distance_km": 8009.3, "second_furthest_km": 2867.2, "clarity_ratio": 2.79, "median_distance_km": 2306.6, "distances_to_centroid": { "La Pineda": 2867.2, "Mettmann": 2306.6, "Bitonto": 1631.5, "Grodzisk Mazowiecki": 1448.2, "Obama": 8009.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " La Pineda: (41.08°, 1.18°)", " Mettmann: (51.25°, 6.98°)", " Bitonto: (41.11°, 16.69°)", " Grodzisk Mazowiecki: (52.10°, 20.63°)", " Obama: (35.50°, 135.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Obama: 8009.3 km from centroid", " La Pineda: 2867.2 km from centroid", " Mettmann: 2306.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Obama", "FINAL ANSWER: Obama" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.8075, "lon": 115.86599, "name": "Landsdale" }, { "lat": -26.66008, "lon": 153.09953, "name": "Maroochydore" }, { "lat": -39.4926, "lon": 176.91233, "name": "Napier" }, { "lat": -31.91099, "lon": 152.45387, "name": "Taree" }, { "lat": 22.55213, "lon": 113.88288, "name": "Bao'an" } ], "question": "Which location is the geographic outlier among: Landsdale, Maroochydore, Napier, Taree, Bao'an?", "ground_truth": { "answer": "Bao'an", "outlier_distance_km": 5791.0, "second_furthest_km": 3828.6, "clarity_ratio": 1.51, "median_distance_km": 2870.9, "distances_to_centroid": { "Landsdale": 2870.9, "Maroochydore": 1225.9, "Napier": 3828.6, "Taree": 1527.5, "Bao'an": 5791.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Landsdale: (-31.81°, 115.87°)", " Maroochydore: (-26.66°, 153.10°)", " Napier: (-39.49°, 176.91°)", " Taree: (-31.91°, 152.45°)", " Bao'an: (22.55°, 113.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bao'an: 5791.0 km from centroid", " Napier: 3828.6 km from centroid", " Landsdale: 2870.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bao'an", "FINAL ANSWER: Bao'an" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.42505, "lon": -3.67442, "name": "Goya" }, { "lat": 43.32059, "lon": 45.04903, "name": "Sunzha" }, { "lat": 44.01759, "lon": 1.3542, "name": "Montauban" }, { "lat": 50.95572, "lon": 6.63986, "name": "Bergheim" }, { "lat": -38.99081, "lon": -64.09574, "name": "Río Colorado" } ], "question": "Which location is the geographic outlier among: Goya, Sunzha, Montauban, Bergheim, Río Colorado?", "ground_truth": { "answer": "Río Colorado", "outlier_distance_km": 9775.3, "second_furthest_km": 4589.0, "clarity_ratio": 2.13, "median_distance_km": 2682.4, "distances_to_centroid": { "Goya": 1389.3, "Sunzha": 4589.0, "Montauban": 1827.8, "Bergheim": 2682.4, "Río Colorado": 9775.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Goya: (40.43°, -3.67°)", " Sunzha: (43.32°, 45.05°)", " Montauban: (44.02°, 1.35°)", " Bergheim: (50.96°, 6.64°)", " Río Colorado: (-38.99°, -64.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Río Colorado: 9775.3 km from centroid", " Sunzha: 4589.0 km from centroid", " Bergheim: 2682.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Río Colorado", "FINAL ANSWER: Río Colorado" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 27.80058, "lon": -97.39638, "name": "Corpus Christi" }, { "lat": 49.10635, "lon": -122.82509, "name": "Surrey" }, { "lat": 33.43532, "lon": -112.35821, "name": "Goodyear" }, { "lat": 42.10482, "lon": -70.94532, "name": "Abington" }, { "lat": -27.96724, "lon": 153.39796, "name": "Southport" } ], "question": "Which location is the geographic outlier among: Corpus Christi, Surrey, Goodyear, Abington, Southport?", "ground_truth": { "answer": "Southport", "outlier_distance_km": 17661.6, "second_furthest_km": 6717.0, "clarity_ratio": 2.63, "median_distance_km": 6038.7, "distances_to_centroid": { "Corpus Christi": 4702.4, "Surrey": 6717.0, "Goodyear": 6038.7, "Abington": 2710.3, "Southport": 17661.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Corpus Christi: (27.80°, -97.40°)", " Surrey: (49.11°, -122.83°)", " Goodyear: (33.44°, -112.36°)", " Abington: (42.10°, -70.95°)", " Southport: (-27.97°, 153.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Southport: 17661.6 km from centroid", " Surrey: 6717.0 km from centroid", " Goodyear: 6038.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Southport", "FINAL ANSWER: Southport" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 47.60444, "lon": -122.03768, "name": "City of Sammamish" }, { "lat": 33.52253, "lon": -117.70755, "name": "Laguna Niguel" }, { "lat": 20.70551, "lon": -102.34514, "name": "Arandas" }, { "lat": 41.24006, "lon": -81.44067, "name": "Hudson" }, { "lat": -41.27078, "lon": 173.28404, "name": "Nelson" } ], "question": "Which location is the geographic outlier among: City of Sammamish, Laguna Niguel, Arandas, Hudson, Nelson?", "ground_truth": { "answer": "Nelson", "outlier_distance_km": 15334.3, "second_furthest_km": 7016.6, "clarity_ratio": 2.19, "median_distance_km": 6750.5, "distances_to_centroid": { "City of Sammamish": 7016.6, "Laguna Niguel": 6750.5, "Arandas": 5420.7, "Hudson": 3756.6, "Nelson": 15334.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " City of Sammamish: (47.60°, -122.04°)", " Laguna Niguel: (33.52°, -117.71°)", " Arandas: (20.71°, -102.35°)", " Hudson: (41.24°, -81.44°)", " Nelson: (-41.27°, 173.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nelson: 15334.3 km from centroid", " City of Sammamish: 7016.6 km from centroid", " Laguna Niguel: 6750.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nelson", "FINAL ANSWER: Nelson" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.74981, "lon": 144.9109, "name": "Essendon" }, { "lat": -33.78333, "lon": 150.93333, "name": "Seven Hills" }, { "lat": -37.74496, "lon": 144.80049, "name": "St Albans" }, { "lat": -37.94853, "lon": 145.15274, "name": "Springvale" }, { "lat": 37.28942, "lon": 13.52494, "name": "Porto Empedocle" } ], "question": "Which location is the geographic outlier among: Essendon, Seven Hills, St Albans, Springvale, Porto Empedocle?", "ground_truth": { "answer": "Porto Empedocle", "outlier_distance_km": 12870.3, "second_furthest_km": 3306.4, "clarity_ratio": 3.89, "median_distance_km": 2997.1, "distances_to_centroid": { "Essendon": 2967.8, "Seven Hills": 3306.4, "St Albans": 2959.0, "Springvale": 2997.1, "Porto Empedocle": 12870.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Essendon: (-37.75°, 144.91°)", " Seven Hills: (-33.78°, 150.93°)", " St Albans: (-37.74°, 144.80°)", " Springvale: (-37.95°, 145.15°)", " Porto Empedocle: (37.29°, 13.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Porto Empedocle: 12870.3 km from centroid", " Seven Hills: 3306.4 km from centroid", " Springvale: 2997.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Porto Empedocle", "FINAL ANSWER: Porto Empedocle" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.83333, "lon": 38.26667, "name": "Mertule Maryam" }, { "lat": 5.0847, "lon": -1.35093, "name": "Elmina" }, { "lat": 5.6698, "lon": -0.01657, "name": "Tema" }, { "lat": 6.17146, "lon": 7.00525, "name": "Enugu-Ukwu" }, { "lat": 10.53646, "lon": 76.98034, "name": "Kottur" } ], "question": "Which location is the geographic outlier among: Mertule Maryam, Elmina, Tema, Enugu-Ukwu, Kottur?", "ground_truth": { "answer": "Kottur", "outlier_distance_km": 5800.2, "second_furthest_km": 2835.0, "clarity_ratio": 2.05, "median_distance_km": 2680.7, "distances_to_centroid": { "Mertule Maryam": 1585.8, "Elmina": 2835.0, "Tema": 2680.7, "Enugu-Ukwu": 1902.6, "Kottur": 5800.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mertule Maryam: (10.83°, 38.27°)", " Elmina: (5.08°, -1.35°)", " Tema: (5.67°, -0.02°)", " Enugu-Ukwu: (6.17°, 7.01°)", " Kottur: (10.54°, 76.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kottur: 5800.2 km from centroid", " Elmina: 2835.0 km from centroid", " Tema: 2680.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kottur", "FINAL ANSWER: Kottur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.52579, "lon": -96.68451, "name": "Steinbach" }, { "lat": 38.58894, "lon": -89.99038, "name": "Fairview Heights" }, { "lat": 22.49396, "lon": -105.36369, "name": "Acaponeta" }, { "lat": 41.27954, "lon": -72.8151, "name": "Branford" }, { "lat": 11.48333, "lon": 37.58333, "name": "T’īs Isat" } ], "question": "Which location is the geographic outlier among: Steinbach, Fairview Heights, Acaponeta, Branford, T’īs Isat?", "ground_truth": { "answer": "T’īs Isat", "outlier_distance_km": 10508.9, "second_furthest_km": 4066.8, "clarity_ratio": 2.58, "median_distance_km": 3181.5, "distances_to_centroid": { "Steinbach": 3181.5, "Fairview Heights": 2305.0, "Acaponeta": 4066.8, "Branford": 1157.9, "T’īs Isat": 10508.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Steinbach: (49.53°, -96.68°)", " Fairview Heights: (38.59°, -89.99°)", " Acaponeta: (22.49°, -105.36°)", " Branford: (41.28°, -72.82°)", " T’īs Isat: (11.48°, 37.58°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " T’īs Isat: 10508.9 km from centroid", " Acaponeta: 4066.8 km from centroid", " Steinbach: 3181.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: T’īs Isat", "FINAL ANSWER: T’īs Isat" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.56822, "lon": 30.18618, "name": "Mpophomeni" }, { "lat": -29.82068, "lon": 30.88674, "name": "Pinetown" }, { "lat": -26.36094, "lon": 27.39767, "name": "Carletonville" }, { "lat": -33.963, "lon": 22.46173, "name": "George" }, { "lat": -18.72011, "lon": -39.85891, "name": "São Mateus" } ], "question": "Which location is the geographic outlier among: Mpophomeni, Pinetown, Carletonville, George, São Mateus?", "ground_truth": { "answer": "São Mateus", "outlier_distance_km": 5572.9, "second_furthest_km": 1641.0, "clarity_ratio": 3.4, "median_distance_km": 1571.5, "distances_to_centroid": { "Mpophomeni": 1571.5, "Pinetown": 1641.0, "Carletonville": 1313.5, "George": 1051.5, "São Mateus": 5572.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mpophomeni: (-29.57°, 30.19°)", " Pinetown: (-29.82°, 30.89°)", " Carletonville: (-26.36°, 27.40°)", " George: (-33.96°, 22.46°)", " São Mateus: (-18.72°, -39.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Mateus: 5572.9 km from centroid", " Pinetown: 1641.0 km from centroid", " Mpophomeni: 1571.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Mateus", "FINAL ANSWER: São Mateus" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -25.43321, "lon": 31.95478, "name": "Komatipoort" }, { "lat": -26.14095, "lon": 28.15247, "name": "Edenvale" }, { "lat": 27.06309, "lon": 31.34425, "name": "As Sāḩil" }, { "lat": -0.52731, "lon": 34.45714, "name": "Homa Bay" }, { "lat": 16.31281, "lon": -91.98224, "name": "Las Margaritas" } ], "question": "Which location is the geographic outlier among: Komatipoort, Edenvale, As Sāḩil, Homa Bay, Las Margaritas?", "ground_truth": { "answer": "Las Margaritas", "outlier_distance_km": 10997.6, "second_furthest_km": 4145.0, "clarity_ratio": 2.65, "median_distance_km": 3769.2, "distances_to_centroid": { "Komatipoort": 3769.2, "Edenvale": 3546.3, "As Sāḩil": 4145.0, "Homa Bay": 3079.3, "Las Margaritas": 10997.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Komatipoort: (-25.43°, 31.95°)", " Edenvale: (-26.14°, 28.15°)", " As Sāḩil: (27.06°, 31.34°)", " Homa Bay: (-0.53°, 34.46°)", " Las Margaritas: (16.31°, -91.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Las Margaritas: 10997.6 km from centroid", " As Sāḩil: 4145.0 km from centroid", " Komatipoort: 3769.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Las Margaritas", "FINAL ANSWER: Las Margaritas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.424, "lon": 150.89345, "name": "Wollongong" }, { "lat": -19.30323, "lon": 146.72531, "name": "Kirwan" }, { "lat": -37.69047, "lon": 144.74172, "name": "Hillside" }, { "lat": -34.28853, "lon": 146.05093, "name": "Griffith" }, { "lat": 43.25655, "lon": -79.08527, "name": "Niagara-on-the-Lake" } ], "question": "Which location is the geographic outlier among: Wollongong, Kirwan, Hillside, Griffith, Niagara-on-the-Lake?", "ground_truth": { "answer": "Niagara-on-the-Lake", "outlier_distance_km": 17037.4, "second_furthest_km": 5251.6, "clarity_ratio": 3.24, "median_distance_km": 4812.6, "distances_to_centroid": { "Wollongong": 5251.6, "Kirwan": 4744.4, "Hillside": 4797.8, "Griffith": 4812.6, "Niagara-on-the-Lake": 17037.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wollongong: (-34.42°, 150.89°)", " Kirwan: (-19.30°, 146.73°)", " Hillside: (-37.69°, 144.74°)", " Griffith: (-34.29°, 146.05°)", " Niagara-on-the-Lake: (43.26°, -79.09°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Niagara-on-the-Lake: 17037.4 km from centroid", " Wollongong: 5251.6 km from centroid", " Griffith: 4812.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Niagara-on-the-Lake", "FINAL ANSWER: Niagara-on-the-Lake" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.65825, "lon": -0.25223, "name": "Taifa" }, { "lat": 11.52351, "lon": 7.31174, "name": "Funtua" }, { "lat": -33.57565, "lon": 22.44391, "name": "Dysselsdorp" }, { "lat": -24.5878, "lon": 31.09467, "name": "Acornhoek" }, { "lat": -36.88041, "lon": 174.79819, "name": "Remuera" } ], "question": "Which location is the geographic outlier among: Taifa, Funtua, Dysselsdorp, Acornhoek, Remuera?", "ground_truth": { "answer": "Remuera", "outlier_distance_km": 12017.6, "second_furthest_km": 5720.7, "clarity_ratio": 2.1, "median_distance_km": 5313.8, "distances_to_centroid": { "Taifa": 5720.7, "Funtua": 5313.8, "Dysselsdorp": 3180.1, "Acornhoek": 1944.6, "Remuera": 12017.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taifa: (5.66°, -0.25°)", " Funtua: (11.52°, 7.31°)", " Dysselsdorp: (-33.58°, 22.44°)", " Acornhoek: (-24.59°, 31.09°)", " Remuera: (-36.88°, 174.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Remuera: 12017.6 km from centroid", " Taifa: 5720.7 km from centroid", " Funtua: 5313.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Remuera", "FINAL ANSWER: Remuera" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.68861, "lon": -51.46111, "name": "Montenegro" }, { "lat": -28.28389, "lon": -52.78639, "name": "Carazinho" }, { "lat": -18.97428, "lon": -49.46212, "name": "Ituiutaba" }, { "lat": -28.93611, "lon": -51.54944, "name": "Veranópolis" }, { "lat": 7.43383, "lon": 3.28788, "name": "Igbo-Ora" } ], "question": "Which location is the geographic outlier among: Montenegro, Carazinho, Ituiutaba, Veranópolis, Igbo-Ora?", "ground_truth": { "answer": "Igbo-Ora", "outlier_distance_km": 5652.4, "second_furthest_km": 1578.7, "clarity_ratio": 3.58, "median_distance_km": 1574.9, "distances_to_centroid": { "Montenegro": 1574.9, "Carazinho": 1578.7, "Ituiutaba": 954.7, "Veranópolis": 1526.3, "Igbo-Ora": 5652.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Montenegro: (-29.69°, -51.46°)", " Carazinho: (-28.28°, -52.79°)", " Ituiutaba: (-18.97°, -49.46°)", " Veranópolis: (-28.94°, -51.55°)", " Igbo-Ora: (7.43°, 3.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Igbo-Ora: 5652.4 km from centroid", " Carazinho: 1578.7 km from centroid", " Montenegro: 1574.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Igbo-Ora", "FINAL ANSWER: Igbo-Ora" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.34913, "lon": 127.38493, "name": "Daejeon" }, { "lat": 11.73559, "lon": 108.3733, "name": "Đưc Trọng" }, { "lat": 34.80361, "lon": 134.46806, "name": "Aioi" }, { "lat": 40.76432, "lon": 120.85327, "name": "Lianshan" }, { "lat": -37.96649, "lon": 145.2081, "name": "Dandenong North" } ], "question": "Which location is the geographic outlier among: Daejeon, Đưc Trọng, Aioi, Lianshan, Dandenong North?", "ground_truth": { "answer": "Dandenong North", "outlier_distance_km": 6407.9, "second_furthest_km": 2698.1, "clarity_ratio": 2.37, "median_distance_km": 2136.3, "distances_to_centroid": { "Daejeon": 2136.3, "Đưc Trọng": 2119.0, "Aioi": 2090.8, "Lianshan": 2698.1, "Dandenong North": 6407.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Daejeon: (36.35°, 127.38°)", " Đưc Trọng: (11.74°, 108.37°)", " Aioi: (34.80°, 134.47°)", " Lianshan: (40.76°, 120.85°)", " Dandenong North: (-37.97°, 145.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dandenong North: 6407.9 km from centroid", " Lianshan: 2698.1 km from centroid", " Daejeon: 2136.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dandenong North", "FINAL ANSWER: Dandenong North" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.11254, "lon": 6.0989, "name": "Drachten" }, { "lat": 49.98596, "lon": 6.89308, "name": "Wittlich" }, { "lat": 51.78333, "lon": 8.81683, "name": "Bad Lippspringe" }, { "lat": 50.82261, "lon": 9.01294, "name": "Stadtallendorf" }, { "lat": 7.95508, "lon": 98.28322, "name": "Ban Kamala" } ], "question": "Which location is the geographic outlier among: Drachten, Wittlich, Bad Lippspringe, Stadtallendorf, Ban Kamala?", "ground_truth": { "answer": "Ban Kamala", "outlier_distance_km": 7978.5, "second_furthest_km": 1858.1, "clarity_ratio": 4.29, "median_distance_km": 1654.8, "distances_to_centroid": { "Drachten": 1858.1, "Wittlich": 1654.8, "Bad Lippspringe": 1624.1, "Stadtallendorf": 1558.6, "Ban Kamala": 7978.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Drachten: (53.11°, 6.10°)", " Wittlich: (49.99°, 6.89°)", " Bad Lippspringe: (51.78°, 8.82°)", " Stadtallendorf: (50.82°, 9.01°)", " Ban Kamala: (7.96°, 98.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ban Kamala: 7978.5 km from centroid", " Drachten: 1858.1 km from centroid", " Wittlich: 1654.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ban Kamala", "FINAL ANSWER: Ban Kamala" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.78333, "lon": 150.93333, "name": "Seven Hills" }, { "lat": -33.80383, "lon": 150.98768, "name": "Westmead" }, { "lat": -36.88333, "lon": 174.7, "name": "Avondale" }, { "lat": -33.89743, "lon": 150.93446, "name": "Cabramatta" }, { "lat": 49.2846, "lon": -122.78217, "name": "Coquitlam" } ], "question": "Which location is the geographic outlier among: Seven Hills, Westmead, Avondale, Cabramatta, Coquitlam?", "ground_truth": { "answer": "Coquitlam", "outlier_distance_km": 14776.9, "second_furthest_km": 7408.1, "clarity_ratio": 1.99, "median_distance_km": 5257.6, "distances_to_centroid": { "Seven Hills": 5252.3, "Westmead": 5257.6, "Avondale": 7408.1, "Cabramatta": 5253.9, "Coquitlam": 14776.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Seven Hills: (-33.78°, 150.93°)", " Westmead: (-33.80°, 150.99°)", " Avondale: (-36.88°, 174.70°)", " Cabramatta: (-33.90°, 150.93°)", " Coquitlam: (49.28°, -122.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coquitlam: 14776.9 km from centroid", " Avondale: 7408.1 km from centroid", " Westmead: 5257.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coquitlam", "FINAL ANSWER: Coquitlam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.45, "lon": 135.35, "name": "Kaizuka" }, { "lat": 34.98975, "lon": 106.07205, "name": "Dayang" }, { "lat": 35.84373, "lon": 139.88347, "name": "Misato, Saitama" }, { "lat": 34.83475, "lon": 134.57803, "name": "Ikaruga" }, { "lat": 41.5931, "lon": -81.52679, "name": "Euclid" } ], "question": "Which location is the geographic outlier among: Kaizuka, Dayang, Misato, Saitama, Ikaruga, Euclid?", "ground_truth": { "answer": "Euclid", "outlier_distance_km": 11269.0, "second_furthest_km": 4701.4, "clarity_ratio": 2.4, "median_distance_km": 4352.8, "distances_to_centroid": { "Kaizuka": 4352.8, "Dayang": 1738.2, "Misato, Saitama": 4701.4, "Ikaruga": 4272.8, "Euclid": 11269.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kaizuka: (34.45°, 135.35°)", " Dayang: (34.99°, 106.07°)", " Misato, Saitama: (35.84°, 139.88°)", " Ikaruga: (34.83°, 134.58°)", " Euclid: (41.59°, -81.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Euclid: 11269.0 km from centroid", " Misato, Saitama: 4701.4 km from centroid", " Kaizuka: 4352.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Euclid", "FINAL ANSWER: Euclid" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -43.11819, "lon": -73.61661, "name": "Quellón" }, { "lat": -19.51889, "lon": -41.01583, "name": "Baixo Guandu" }, { "lat": -34.46971, "lon": -58.52111, "name": "San Isidro" }, { "lat": -11.73028, "lon": -40.55528, "name": "Piritiba" }, { "lat": -33.78269, "lon": 151.04888, "name": "Carlingford" } ], "question": "Which location is the geographic outlier among: Quellón, Baixo Guandu, San Isidro, Piritiba, Carlingford?", "ground_truth": { "answer": "Carlingford", "outlier_distance_km": 12874.4, "second_furthest_km": 5611.9, "clarity_ratio": 2.29, "median_distance_km": 4372.9, "distances_to_centroid": { "Quellón": 5611.9, "Baixo Guandu": 3052.1, "San Isidro": 4372.9, "Piritiba": 3455.4, "Carlingford": 12874.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Quellón: (-43.12°, -73.62°)", " Baixo Guandu: (-19.52°, -41.02°)", " San Isidro: (-34.47°, -58.52°)", " Piritiba: (-11.73°, -40.56°)", " Carlingford: (-33.78°, 151.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carlingford: 12874.4 km from centroid", " Quellón: 5611.9 km from centroid", " San Isidro: 4372.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carlingford", "FINAL ANSWER: Carlingford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.39317, "lon": 2.00689, "name": "Sant Vicenç dels Horts" }, { "lat": 54.03591, "lon": 19.0266, "name": "Malbork" }, { "lat": 52.99667, "lon": 6.5625, "name": "Assen" }, { "lat": 48.87563, "lon": 9.39819, "name": "Winnenden" }, { "lat": 32.97623, "lon": -96.59527, "name": "Sachse" } ], "question": "Which location is the geographic outlier among: Sant Vicenç dels Horts, Malbork, Assen, Winnenden, Sachse?", "ground_truth": { "answer": "Sachse", "outlier_distance_km": 7062.8, "second_furthest_km": 2357.8, "clarity_ratio": 3.0, "median_distance_km": 1627.3, "distances_to_centroid": { "Sant Vicenç dels Horts": 1231.1, "Malbork": 2357.8, "Assen": 1534.7, "Winnenden": 1627.3, "Sachse": 7062.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sant Vicenç dels Horts: (41.39°, 2.01°)", " Malbork: (54.04°, 19.03°)", " Assen: (53.00°, 6.56°)", " Winnenden: (48.88°, 9.40°)", " Sachse: (32.98°, -96.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sachse: 7062.8 km from centroid", " Malbork: 2357.8 km from centroid", " Winnenden: 1627.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sachse", "FINAL ANSWER: Sachse" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.10569, "lon": -75.39812, "name": "Chinú" }, { "lat": -13.11667, "lon": -60.54167, "name": "Colorado do Oeste" }, { "lat": -22.36611, "lon": -48.38028, "name": "Dois Córregos" }, { "lat": -1.81361, "lon": -49.79528, "name": "Curralinho" }, { "lat": 47.76316, "lon": -3.3393, "name": "Lanester" } ], "question": "Which location is the geographic outlier among: Chinú, Colorado do Oeste, Dois Córregos, Curralinho, Lanester?", "ground_truth": { "answer": "Lanester", "outlier_distance_km": 6435.8, "second_furthest_km": 3135.2, "clarity_ratio": 2.05, "median_distance_km": 2923.9, "distances_to_centroid": { "Chinú": 3135.2, "Colorado do Oeste": 2379.7, "Dois Córregos": 2923.9, "Curralinho": 686.5, "Lanester": 6435.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chinú: (9.11°, -75.40°)", " Colorado do Oeste: (-13.12°, -60.54°)", " Dois Córregos: (-22.37°, -48.38°)", " Curralinho: (-1.81°, -49.80°)", " Lanester: (47.76°, -3.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lanester: 6435.8 km from centroid", " Chinú: 3135.2 km from centroid", " Dois Córregos: 2923.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lanester", "FINAL ANSWER: Lanester" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.95, "lon": 151.13333, "name": "Rockdale" }, { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" }, { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" }, { "lat": -31.84062, "lon": 115.89549, "name": "Ballajura" }, { "lat": 7.3, "lon": 38.65, "name": "Kuyera" } ], "question": "Which location is the geographic outlier among: Rockdale, Lower Hutt, Dianella, Ballajura, Kuyera?", "ground_truth": { "answer": "Kuyera", "outlier_distance_km": 9444.8, "second_furthest_km": 5305.5, "clarity_ratio": 1.78, "median_distance_km": 3163.1, "distances_to_centroid": { "Rockdale": 3163.1, "Lower Hutt": 5305.5, "Dianella": 702.7, "Ballajura": 697.0, "Kuyera": 9444.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rockdale: (-33.95°, 151.13°)", " Lower Hutt: (-41.22°, 174.92°)", " Dianella: (-31.89°, 115.87°)", " Ballajura: (-31.84°, 115.90°)", " Kuyera: (7.30°, 38.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kuyera: 9444.8 km from centroid", " Lower Hutt: 5305.5 km from centroid", " Rockdale: 3163.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kuyera", "FINAL ANSWER: Kuyera" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.7706, "lon": -79.40148, "name": "Willowdale East" }, { "lat": 43.66294, "lon": -116.68736, "name": "Caldwell" }, { "lat": 20.28566, "lon": -103.42908, "name": "Jocotepec" }, { "lat": 41.88087, "lon": -87.70283, "name": "East Garfield Park" }, { "lat": -33.91972, "lon": 151.07592, "name": "Lakemba" } ], "question": "Which location is the geographic outlier among: Willowdale East, Caldwell, Jocotepec, East Garfield Park, Lakemba?", "ground_truth": { "answer": "Lakemba", "outlier_distance_km": 17867.6, "second_furthest_km": 6637.1, "clarity_ratio": 2.69, "median_distance_km": 5779.0, "distances_to_centroid": { "Willowdale East": 3725.1, "Caldwell": 6637.1, "Jocotepec": 5779.0, "East Garfield Park": 4275.7, "Lakemba": 17867.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Willowdale East: (43.77°, -79.40°)", " Caldwell: (43.66°, -116.69°)", " Jocotepec: (20.29°, -103.43°)", " East Garfield Park: (41.88°, -87.70°)", " Lakemba: (-33.92°, 151.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lakemba: 17867.6 km from centroid", " Caldwell: 6637.1 km from centroid", " Jocotepec: 5779.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lakemba", "FINAL ANSWER: Lakemba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.03867, "lon": -78.8642, "name": "North Tonawanda" }, { "lat": 37.5841, "lon": -122.36608, "name": "Burlingame" }, { "lat": 40.69538, "lon": -73.99375, "name": "Brooklyn Heights" }, { "lat": 43.61558, "lon": -84.24721, "name": "Midland" }, { "lat": -32.92953, "lon": 151.7801, "name": "Newcastle" } ], "question": "Which location is the geographic outlier among: North Tonawanda, Burlingame, Brooklyn Heights, Midland, Newcastle?", "ground_truth": { "answer": "Newcastle", "outlier_distance_km": 18539.4, "second_furthest_km": 7494.2, "clarity_ratio": 2.47, "median_distance_km": 4274.6, "distances_to_centroid": { "North Tonawanda": 3837.0, "Burlingame": 7494.2, "Brooklyn Heights": 3374.6, "Midland": 4274.6, "Newcastle": 18539.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " North Tonawanda: (43.04°, -78.86°)", " Burlingame: (37.58°, -122.37°)", " Brooklyn Heights: (40.70°, -73.99°)", " Midland: (43.62°, -84.25°)", " Newcastle: (-32.93°, 151.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Newcastle: 18539.4 km from centroid", " Burlingame: 7494.2 km from centroid", " Midland: 4274.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Newcastle", "FINAL ANSWER: Newcastle" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.08465, "lon": 152.9511, "name": "Caboolture" }, { "lat": -37.75, "lon": 145.35, "name": "Lilydale" }, { "lat": -39.4926, "lon": 176.91233, "name": "Napier" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" }, { "lat": 6.55504, "lon": 3.34363, "name": "Oshodi" } ], "question": "Which location is the geographic outlier among: Caboolture, Lilydale, Napier, New Plymouth, Oshodi?", "ground_truth": { "answer": "Oshodi", "outlier_distance_km": 13994.2, "second_furthest_km": 4457.0, "clarity_ratio": 3.14, "median_distance_km": 4210.9, "distances_to_centroid": { "Caboolture": 2214.3, "Lilydale": 1802.1, "Napier": 4457.0, "New Plymouth": 4210.9, "Oshodi": 13994.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caboolture: (-27.08°, 152.95°)", " Lilydale: (-37.75°, 145.35°)", " Napier: (-39.49°, 176.91°)", " New Plymouth: (-39.07°, 174.08°)", " Oshodi: (6.56°, 3.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Oshodi: 13994.2 km from centroid", " Napier: 4457.0 km from centroid", " New Plymouth: 4210.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Oshodi", "FINAL ANSWER: Oshodi" ] }, { "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": -33.55384, "lon": -71.60761, "name": "Cartagena" }, { "lat": -19.75, "lon": -43.0375, "name": "Nova Era" }, { "lat": -17.74431, "lon": -48.62789, "name": "Caldas Novas" }, { "lat": -18.37028, "lon": -40.21333, "name": "Pinheiros" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" } ], "question": "Which location is the geographic outlier among: Cartagena, Nova Era, Caldas Novas, Pinheiros, Launceston?", "ground_truth": { "answer": "Launceston", "outlier_distance_km": 12175.0, "second_furthest_km": 5796.1, "clarity_ratio": 2.1, "median_distance_km": 3950.3, "distances_to_centroid": { "Cartagena": 5796.1, "Nova Era": 3321.0, "Caldas Novas": 3950.3, "Pinheiros": 3094.2, "Launceston": 12175.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cartagena: (-33.55°, -71.61°)", " Nova Era: (-19.75°, -43.04°)", " Caldas Novas: (-17.74°, -48.63°)", " Pinheiros: (-18.37°, -40.21°)", " Launceston: (-41.44°, 147.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Launceston: 12175.0 km from centroid", " Cartagena: 5796.1 km from centroid", " Caldas Novas: 3950.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Launceston", "FINAL ANSWER: Launceston" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.6658, "lon": -0.16307, "name": "Medina Estates" }, { "lat": 10.28969, "lon": 11.16729, "name": "Gombe" }, { "lat": 26.87524, "lon": 31.32963, "name": "Al Ghanāyim" }, { "lat": 30.9128, "lon": 30.29019, "name": "Ḩawsh ‘Īsá" }, { "lat": 11.29811, "lon": 124.67895, "name": "Carigara" } ], "question": "Which location is the geographic outlier among: Medina Estates, Gombe, Al Ghanāyim, Ḩawsh ‘Īsá, Carigara?", "ground_truth": { "answer": "Carigara", "outlier_distance_km": 9141.8, "second_furthest_km": 4489.3, "clarity_ratio": 2.04, "median_distance_km": 3143.4, "distances_to_centroid": { "Medina Estates": 4489.3, "Gombe": 3143.4, "Al Ghanāyim": 1380.0, "Ḩawsh ‘Īsá": 1803.2, "Carigara": 9141.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Medina Estates: (5.67°, -0.16°)", " Gombe: (10.29°, 11.17°)", " Al Ghanāyim: (26.88°, 31.33°)", " Ḩawsh ‘Īsá: (30.91°, 30.29°)", " Carigara: (11.30°, 124.68°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carigara: 9141.8 km from centroid", " Medina Estates: 4489.3 km from centroid", " Gombe: 3143.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carigara", "FINAL ANSWER: Carigara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.26639, "lon": 146.80569, "name": "Townsville" }, { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" }, { "lat": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" }, { "lat": -31.76737, "lon": 115.96936, "name": "Ellenbrook" }, { "lat": -21.78778, "lon": -46.56139, "name": "Poços de Caldas" } ], "question": "Which location is the geographic outlier among: Townsville, Coogee, Bracken Ridge, Ellenbrook, Poços de Caldas?", "ground_truth": { "answer": "Poços de Caldas", "outlier_distance_km": 13756.2, "second_furthest_km": 4813.1, "clarity_ratio": 2.86, "median_distance_km": 4553.0, "distances_to_centroid": { "Townsville": 4428.9, "Coogee": 4553.0, "Bracken Ridge": 4813.1, "Ellenbrook": 1275.1, "Poços de Caldas": 13756.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Townsville: (-19.27°, 146.81°)", " Coogee: (-33.92°, 151.26°)", " Bracken Ridge: (-27.32°, 153.03°)", " Ellenbrook: (-31.77°, 115.97°)", " Poços de Caldas: (-21.79°, -46.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Poços de Caldas: 13756.2 km from centroid", " Bracken Ridge: 4813.1 km from centroid", " Coogee: 4553.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Poços de Caldas", "FINAL ANSWER: Poços de Caldas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.93333, "lon": -74.25, "name": "Huanta" }, { "lat": -19.96722, "lon": -43.80417, "name": "Raposos" }, { "lat": -15.3175, "lon": -49.1175, "name": "Goianésia" }, { "lat": -23.58581, "lon": -46.68241, "name": "Itaim Bibi" }, { "lat": 41.58948, "lon": -88.05784, "name": "Lockport" } ], "question": "Which location is the geographic outlier among: Huanta, Raposos, Goianésia, Itaim Bibi, Lockport?", "ground_truth": { "answer": "Lockport", "outlier_distance_km": 5996.6, "second_furthest_km": 2439.8, "clarity_ratio": 2.46, "median_distance_km": 2367.2, "distances_to_centroid": { "Huanta": 1702.0, "Raposos": 2367.2, "Goianésia": 1604.6, "Itaim Bibi": 2439.8, "Lockport": 5996.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Huanta: (-12.93°, -74.25°)", " Raposos: (-19.97°, -43.80°)", " Goianésia: (-15.32°, -49.12°)", " Itaim Bibi: (-23.59°, -46.68°)", " Lockport: (41.59°, -88.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lockport: 5996.6 km from centroid", " Itaim Bibi: 2439.8 km from centroid", " Raposos: 2367.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lockport", "FINAL ANSWER: Lockport" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.60333, "lon": -35.23083, "name": "Aliança" }, { "lat": -30.75482, "lon": -57.98196, "name": "Chajarí" }, { "lat": -22.58056, "lon": -47.51861, "name": "Iracemápolis" }, { "lat": 1.81611, "lon": -61.12806, "name": "Caracaraí" }, { "lat": 10.06667, "lon": 34.53333, "name": "Āsosa" } ], "question": "Which location is the geographic outlier among: Aliança, Chajarí, Iracemápolis, Caracaraí, Āsosa?", "ground_truth": { "answer": "Āsosa", "outlier_distance_km": 7840.1, "second_furthest_km": 3441.9, "clarity_ratio": 2.28, "median_distance_km": 3324.7, "distances_to_centroid": { "Aliança": 312.9, "Chajarí": 3441.9, "Iracemápolis": 2062.9, "Caracaraí": 3324.7, "Āsosa": 7840.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Aliança: (-7.60°, -35.23°)", " Chajarí: (-30.75°, -57.98°)", " Iracemápolis: (-22.58°, -47.52°)", " Caracaraí: (1.82°, -61.13°)", " Āsosa: (10.07°, 34.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Āsosa: 7840.1 km from centroid", " Chajarí: 3441.9 km from centroid", " Caracaraí: 3324.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Āsosa", "FINAL ANSWER: Āsosa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.94162, "lon": 31.29039, "name": "Aga" }, { "lat": 9.03528, "lon": 38.66083, "name": "Burayu" }, { "lat": 10.58964, "lon": 39.43767, "name": "Were Īlu" }, { "lat": 9.5725, "lon": 43.18139, "name": "Gedeb" }, { "lat": -38.03333, "lon": 145.35, "name": "Berwick" } ], "question": "Which location is the geographic outlier among: Aga, Burayu, Were Īlu, Gedeb, Berwick?", "ground_truth": { "answer": "Berwick", "outlier_distance_km": 9940.7, "second_furthest_km": 4177.6, "clarity_ratio": 2.38, "median_distance_km": 2366.0, "distances_to_centroid": { "Aga": 4177.6, "Burayu": 2366.0, "Were Īlu": 2323.2, "Gedeb": 1898.1, "Berwick": 9940.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Aga: (30.94°, 31.29°)", " Burayu: (9.04°, 38.66°)", " Were Īlu: (10.59°, 39.44°)", " Gedeb: (9.57°, 43.18°)", " Berwick: (-38.03°, 145.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Berwick: 9940.7 km from centroid", " Aga: 4177.6 km from centroid", " Burayu: 2366.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Berwick", "FINAL ANSWER: Berwick" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.08333, "lon": 38.03333, "name": "Kele" }, { "lat": 6.97198, "lon": 3.99938, "name": "Ijebu-Igbo" }, { "lat": -0.98169, "lon": 36.58642, "name": "Mai" }, { "lat": 6.70608, "lon": 37.76966, "name": "Tebela" }, { "lat": -25.21306, "lon": -50.97778, "name": "Prudentópolis" } ], "question": "Which location is the geographic outlier among: Kele, Ijebu-Igbo, Mai, Tebela, Prudentópolis?", "ground_truth": { "answer": "Prudentópolis", "outlier_distance_km": 7349.4, "second_furthest_km": 2888.7, "clarity_ratio": 2.54, "median_distance_km": 2880.3, "distances_to_centroid": { "Kele": 2888.7, "Ijebu-Igbo": 1363.5, "Mai": 2613.2, "Tebela": 2880.3, "Prudentópolis": 7349.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kele: (6.08°, 38.03°)", " Ijebu-Igbo: (6.97°, 4.00°)", " Mai: (-0.98°, 36.59°)", " Tebela: (6.71°, 37.77°)", " Prudentópolis: (-25.21°, -50.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Prudentópolis: 7349.4 km from centroid", " Kele: 2888.7 km from centroid", " Tebela: 2880.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Prudentópolis", "FINAL ANSWER: Prudentópolis" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -10.91111, "lon": -37.07167, "name": "Aracaju" }, { "lat": -6.60667, "lon": -39.06222, "name": "Cedro" }, { "lat": 8.09419, "lon": -74.77573, "name": "Nechí" }, { "lat": -33.02457, "lon": -71.55183, "name": "Viña del Mar" }, { "lat": 26.22375, "lon": 79.83739, "name": "Pukhrāyān" } ], "question": "Which location is the geographic outlier among: Aracaju, Cedro, Nechí, Viña del Mar, Pukhrāyān?", "ground_truth": { "answer": "Pukhrāyān", "outlier_distance_km": 11996.6, "second_furthest_km": 5559.7, "clarity_ratio": 2.16, "median_distance_km": 5282.1, "distances_to_centroid": { "Aracaju": 1270.7, "Cedro": 1225.6, "Nechí": 5282.1, "Viña del Mar": 5559.7, "Pukhrāyān": 11996.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Aracaju: (-10.91°, -37.07°)", " Cedro: (-6.61°, -39.06°)", " Nechí: (8.09°, -74.78°)", " Viña del Mar: (-33.02°, -71.55°)", " Pukhrāyān: (26.22°, 79.84°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pukhrāyān: 11996.6 km from centroid", " Viña del Mar: 5559.7 km from centroid", " Nechí: 5282.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pukhrāyān", "FINAL ANSWER: Pukhrāyān" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.74124, "lon": 144.73631, "name": "Caroline Springs" }, { "lat": -38.16604, "lon": 145.13643, "name": "Frankston South" }, { "lat": -34.75155, "lon": 149.72086, "name": "Goulburn" }, { "lat": -33.95, "lon": 151.23333, "name": "Maroubra" }, { "lat": 52.17333, "lon": 5.29167, "name": "Soest" } ], "question": "Which location is the geographic outlier among: Caroline Springs, Frankston South, Goulburn, Maroubra, Soest?", "ground_truth": { "answer": "Soest", "outlier_distance_km": 13243.8, "second_furthest_km": 3604.4, "clarity_ratio": 3.67, "median_distance_km": 3508.3, "distances_to_centroid": { "Caroline Springs": 3272.7, "Frankston South": 3328.2, "Goulburn": 3508.3, "Maroubra": 3604.4, "Soest": 13243.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caroline Springs: (-37.74°, 144.74°)", " Frankston South: (-38.17°, 145.14°)", " Goulburn: (-34.75°, 149.72°)", " Maroubra: (-33.95°, 151.23°)", " Soest: (52.17°, 5.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Soest: 13243.8 km from centroid", " Maroubra: 3604.4 km from centroid", " Goulburn: 3508.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Soest", "FINAL ANSWER: Soest" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.89138, "lon": 144.62368, "name": "Wyndham Vale" }, { "lat": -37.8, "lon": 145.28333, "name": "Croydon" }, { "lat": -37.88333, "lon": 145.21667, "name": "Wantirna South" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": 29.55605, "lon": 106.16002, "name": "Daxing" } ], "question": "Which location is the geographic outlier among: Wyndham Vale, Croydon, Wantirna South, Cranbourne East, Daxing?", "ground_truth": { "answer": "Daxing", "outlier_distance_km": 6862.9, "second_furthest_km": 1698.9, "clarity_ratio": 4.04, "median_distance_km": 1672.8, "distances_to_centroid": { "Wyndham Vale": 1649.3, "Croydon": 1667.6, "Wantirna South": 1672.8, "Cranbourne East": 1698.9, "Daxing": 6862.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wyndham Vale: (-37.89°, 144.62°)", " Croydon: (-37.80°, 145.28°)", " Wantirna South: (-37.88°, 145.22°)", " Cranbourne East: (-38.12°, 145.30°)", " Daxing: (29.56°, 106.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Daxing: 6862.9 km from centroid", " Cranbourne East: 1698.9 km from centroid", " Wantirna South: 1672.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Daxing", "FINAL ANSWER: Daxing" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -24.75722, "lon": -51.76139, "name": "Pitanga" }, { "lat": -20.28389, "lon": -50.24639, "name": "Fernandópolis" }, { "lat": -21.13361, "lon": -51.10167, "name": "Mirandópolis" }, { "lat": 10.02502, "lon": -74.62279, "name": "Chivolo" }, { "lat": 41.00954, "lon": -74.17292, "name": "Wyckoff" } ], "question": "Which location is the geographic outlier among: Pitanga, Fernandópolis, Mirandópolis, Chivolo, Wyckoff?", "ground_truth": { "answer": "Wyckoff", "outlier_distance_km": 5092.8, "second_furthest_km": 2586.7, "clarity_ratio": 1.97, "median_distance_km": 2249.8, "distances_to_centroid": { "Pitanga": 2586.7, "Fernandópolis": 2211.2, "Mirandópolis": 2249.8, "Chivolo": 2143.4, "Wyckoff": 5092.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pitanga: (-24.76°, -51.76°)", " Fernandópolis: (-20.28°, -50.25°)", " Mirandópolis: (-21.13°, -51.10°)", " Chivolo: (10.03°, -74.62°)", " Wyckoff: (41.01°, -74.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wyckoff: 5092.8 km from centroid", " Pitanga: 2586.7 km from centroid", " Mirandópolis: 2249.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wyckoff", "FINAL ANSWER: Wyckoff" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.73913, "lon": 13.951, "name": "Ischia Porto" }, { "lat": 43.64561, "lon": 0.58856, "name": "Auch" }, { "lat": 51.60794, "lon": 4.7915, "name": "Hoge Vucht" }, { "lat": 49.64868, "lon": -1.65306, "name": "Équeurdreville-Hainneville" }, { "lat": -27.42573, "lon": 29.16585, "name": "Vrede" } ], "question": "Which location is the geographic outlier among: Ischia Porto, Auch, Hoge Vucht, Équeurdreville-Hainneville, Vrede?", "ground_truth": { "answer": "Vrede", "outlier_distance_km": 6895.0, "second_furthest_km": 2251.2, "clarity_ratio": 3.06, "median_distance_km": 2202.1, "distances_to_centroid": { "Ischia Porto": 1091.4, "Auch": 1540.2, "Hoge Vucht": 2251.2, "Équeurdreville-Hainneville": 2202.1, "Vrede": 6895.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ischia Porto: (40.74°, 13.95°)", " Auch: (43.65°, 0.59°)", " Hoge Vucht: (51.61°, 4.79°)", " Équeurdreville-Hainneville: (49.65°, -1.65°)", " Vrede: (-27.43°, 29.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vrede: 6895.0 km from centroid", " Hoge Vucht: 2251.2 km from centroid", " Équeurdreville-Hainneville: 2202.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vrede", "FINAL ANSWER: Vrede" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.38047, "lon": 145.39867, "name": "Shepparton" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" }, { "lat": -38.1, "lon": 145.13333, "name": "Seaford" }, { "lat": -27.08465, "lon": 152.9511, "name": "Caboolture" }, { "lat": 8.91667, "lon": 38.61667, "name": "Sebeta" } ], "question": "Which location is the geographic outlier among: Shepparton, Otara, Seaford, Caboolture, Sebeta?", "ground_truth": { "answer": "Sebeta", "outlier_distance_km": 10714.9, "second_furthest_km": 4263.3, "clarity_ratio": 2.51, "median_distance_km": 2146.5, "distances_to_centroid": { "Shepparton": 1765.4, "Otara": 4263.3, "Seaford": 1869.9, "Caboolture": 2146.5, "Sebeta": 10714.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shepparton: (-36.38°, 145.40°)", " Otara: (-36.95°, 174.87°)", " Seaford: (-38.10°, 145.13°)", " Caboolture: (-27.08°, 152.95°)", " Sebeta: (8.92°, 38.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sebeta: 10714.9 km from centroid", " Otara: 4263.3 km from centroid", " Caboolture: 2146.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sebeta", "FINAL ANSWER: Sebeta" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.61025, "lon": 153.05388, "name": "Sunnybank Hills" }, { "lat": -46.4, "lon": 168.35, "name": "Invercargill" }, { "lat": -31.09048, "lon": 150.92905, "name": "Tamworth" }, { "lat": -33.9677, "lon": 151.10149, "name": "Hurstville" }, { "lat": 39.74595, "lon": -75.54659, "name": "Wilmington" } ], "question": "Which location is the geographic outlier among: Sunnybank Hills, Invercargill, Tamworth, Hurstville, Wilmington?", "ground_truth": { "answer": "Wilmington", "outlier_distance_km": 17750.8, "second_furthest_km": 6047.4, "clarity_ratio": 2.94, "median_distance_km": 4485.4, "distances_to_centroid": { "Sunnybank Hills": 4485.4, "Invercargill": 6047.4, "Tamworth": 4307.0, "Hurstville": 4370.1, "Wilmington": 17750.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunnybank Hills: (-27.61°, 153.05°)", " Invercargill: (-46.40°, 168.35°)", " Tamworth: (-31.09°, 150.93°)", " Hurstville: (-33.97°, 151.10°)", " Wilmington: (39.75°, -75.55°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wilmington: 17750.8 km from centroid", " Invercargill: 6047.4 km from centroid", " Sunnybank Hills: 4485.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wilmington", "FINAL ANSWER: Wilmington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.08339, "lon": -88.60005, "name": "Paducah" }, { "lat": 39.32796, "lon": -120.18325, "name": "Truckee" }, { "lat": 28.54944, "lon": -81.77285, "name": "Clermont" }, { "lat": 18.42131, "lon": -95.11398, "name": "Catemaco" }, { "lat": 26.26584, "lon": 78.67108, "name": "Mau" } ], "question": "Which location is the geographic outlier among: Paducah, Truckee, Clermont, Catemaco, Mau?", "ground_truth": { "answer": "Mau", "outlier_distance_km": 12457.6, "second_furthest_km": 5384.3, "clarity_ratio": 2.31, "median_distance_km": 3634.9, "distances_to_centroid": { "Paducah": 2633.8, "Truckee": 5384.3, "Clermont": 1980.1, "Catemaco": 3634.9, "Mau": 12457.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paducah: (37.08°, -88.60°)", " Truckee: (39.33°, -120.18°)", " Clermont: (28.55°, -81.77°)", " Catemaco: (18.42°, -95.11°)", " Mau: (26.27°, 78.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mau: 12457.6 km from centroid", " Truckee: 5384.3 km from centroid", " Catemaco: 3634.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mau", "FINAL ANSWER: Mau" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81992, "lon": 145.0358, "name": "Hawthorn" }, { "lat": -37.8149, "lon": 144.95052, "name": "Docklands" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" }, { "lat": -27.98941, "lon": 153.33633, "name": "Nerang" }, { "lat": 50.36463, "lon": 8.73859, "name": "Bad Nauheim" } ], "question": "Which location is the geographic outlier among: Hawthorn, Docklands, New Plymouth, Nerang, Bad Nauheim?", "ground_truth": { "answer": "Bad Nauheim", "outlier_distance_km": 13445.4, "second_furthest_km": 5207.2, "clarity_ratio": 2.58, "median_distance_km": 3052.0, "distances_to_centroid": { "Hawthorn": 2885.8, "Docklands": 2879.9, "New Plymouth": 5207.2, "Nerang": 3052.0, "Bad Nauheim": 13445.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hawthorn: (-37.82°, 145.04°)", " Docklands: (-37.81°, 144.95°)", " New Plymouth: (-39.07°, 174.08°)", " Nerang: (-27.99°, 153.34°)", " Bad Nauheim: (50.36°, 8.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bad Nauheim: 13445.4 km from centroid", " New Plymouth: 5207.2 km from centroid", " Nerang: 3052.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bad Nauheim", "FINAL ANSWER: Bad Nauheim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.34239, "lon": -102.0305, "name": "La Piedad" }, { "lat": 61.32139, "lon": -149.56778, "name": "Eagle River" }, { "lat": 44.15011, "lon": -79.86635, "name": "Alliston" }, { "lat": 35.97987, "lon": -78.50972, "name": "Wake Forest" }, { "lat": 45.39402, "lon": 9.29109, "name": "San Giuliano Milanese" } ], "question": "Which location is the geographic outlier among: La Piedad, Eagle River, Alliston, Wake Forest, San Giuliano Milanese?", "ground_truth": { "answer": "San Giuliano Milanese", "outlier_distance_km": 6843.8, "second_furthest_km": 5004.6, "clarity_ratio": 1.37, "median_distance_km": 3122.4, "distances_to_centroid": { "La Piedad": 3122.4, "Eagle River": 5004.6, "Alliston": 302.4, "Wake Forest": 623.0, "San Giuliano Milanese": 6843.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " La Piedad: (20.34°, -102.03°)", " Eagle River: (61.32°, -149.57°)", " Alliston: (44.15°, -79.87°)", " Wake Forest: (35.98°, -78.51°)", " San Giuliano Milanese: (45.39°, 9.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Giuliano Milanese: 6843.8 km from centroid", " Eagle River: 5004.6 km from centroid", " La Piedad: 3122.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Giuliano Milanese", "FINAL ANSWER: San Giuliano Milanese" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.55177, "lon": 7.48087, "name": "Eving" }, { "lat": 53.59245, "lon": -2.21941, "name": "Heywood" }, { "lat": 51.50896, "lon": -0.3713, "name": "Southall" }, { "lat": 51.62561, "lon": -0.05798, "name": "Edmonton" }, { "lat": 37.44882, "lon": -77.47353, "name": "Meadowbrook" } ], "question": "Which location is the geographic outlier among: Eving, Heywood, Southall, Edmonton, Meadowbrook?", "ground_truth": { "answer": "Meadowbrook", "outlier_distance_km": 5102.0, "second_furthest_km": 1578.2, "clarity_ratio": 3.23, "median_distance_km": 1060.4, "distances_to_centroid": { "Eving": 1578.2, "Heywood": 985.3, "Southall": 1036.9, "Edmonton": 1060.4, "Meadowbrook": 5102.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Eving: (51.55°, 7.48°)", " Heywood: (53.59°, -2.22°)", " Southall: (51.51°, -0.37°)", " Edmonton: (51.63°, -0.06°)", " Meadowbrook: (37.45°, -77.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Meadowbrook: 5102.0 km from centroid", " Eving: 1578.2 km from centroid", " Edmonton: 1060.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Meadowbrook", "FINAL ANSWER: Meadowbrook" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 7.95, "lon": 39.13333, "name": "Āsela" }, { "lat": 10.9992, "lon": 10.41062, "name": "Darazo" }, { "lat": -28.73226, "lon": 24.76232, "name": "Kimberley" }, { "lat": 7.7899, "lon": 5.7117, "name": "Ode" }, { "lat": 29.02582, "lon": -80.927, "name": "New Smyrna Beach" } ], "question": "Which location is the geographic outlier among: Āsela, Darazo, Kimberley, Ode, New Smyrna Beach?", "ground_truth": { "answer": "New Smyrna Beach", "outlier_distance_km": 8817.4, "second_furthest_km": 4640.6, "clarity_ratio": 1.9, "median_distance_km": 4349.6, "distances_to_centroid": { "Āsela": 4349.6, "Darazo": 1320.8, "Kimberley": 4640.6, "Ode": 702.8, "New Smyrna Beach": 8817.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Āsela: (7.95°, 39.13°)", " Darazo: (11.00°, 10.41°)", " Kimberley: (-28.73°, 24.76°)", " Ode: (7.79°, 5.71°)", " New Smyrna Beach: (29.03°, -80.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New Smyrna Beach: 8817.4 km from centroid", " Kimberley: 4640.6 km from centroid", " Āsela: 4349.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New Smyrna Beach", "FINAL ANSWER: New Smyrna Beach" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -6.23122, "lon": -42.68691, "name": "Regeneração" }, { "lat": -11.73028, "lon": -40.55528, "name": "Piritiba" }, { "lat": -5.89056, "lon": -38.62194, "name": "Jaguaribe" }, { "lat": -23.44361, "lon": -51.87389, "name": "Sarandi" }, { "lat": 0.53392, "lon": 38.51878, "name": "Garba Tula" } ], "question": "Which location is the geographic outlier among: Regeneração, Piritiba, Jaguaribe, Sarandi, Garba Tula?", "ground_truth": { "answer": "Garba Tula", "outlier_distance_km": 7339.3, "second_furthest_km": 3068.7, "clarity_ratio": 2.39, "median_distance_km": 1757.6, "distances_to_centroid": { "Regeneração": 1757.6, "Piritiba": 1500.3, "Jaguaribe": 1332.6, "Sarandi": 3068.7, "Garba Tula": 7339.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Regeneração: (-6.23°, -42.69°)", " Piritiba: (-11.73°, -40.56°)", " Jaguaribe: (-5.89°, -38.62°)", " Sarandi: (-23.44°, -51.87°)", " Garba Tula: (0.53°, 38.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Garba Tula: 7339.3 km from centroid", " Sarandi: 3068.7 km from centroid", " Regeneração: 1757.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Garba Tula", "FINAL ANSWER: Garba Tula" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.41687, "lon": -98.90202, "name": "Chicoloapan" }, { "lat": 47.67768, "lon": -116.78047, "name": "Coeur d'Alene" }, { "lat": 32.9029, "lon": -96.56388, "name": "Rowlett" }, { "lat": 49.8844, "lon": -97.14704, "name": "Winnipeg" }, { "lat": 46.12709, "lon": 3.42577, "name": "Vichy" } ], "question": "Which location is the geographic outlier among: Chicoloapan, Coeur d'Alene, Rowlett, Winnipeg, Vichy?", "ground_truth": { "answer": "Vichy", "outlier_distance_km": 6627.5, "second_furthest_km": 2993.5, "clarity_ratio": 2.21, "median_distance_km": 2779.4, "distances_to_centroid": { "Chicoloapan": 2779.4, "Coeur d'Alene": 2993.5, "Rowlett": 1546.3, "Winnipeg": 1728.1, "Vichy": 6627.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chicoloapan: (19.42°, -98.90°)", " Coeur d'Alene: (47.68°, -116.78°)", " Rowlett: (32.90°, -96.56°)", " Winnipeg: (49.88°, -97.15°)", " Vichy: (46.13°, 3.43°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vichy: 6627.5 km from centroid", " Coeur d'Alene: 2993.5 km from centroid", " Chicoloapan: 2779.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vichy", "FINAL ANSWER: Vichy" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.03427, "lon": 75.23779, "name": "Mādāyi" }, { "lat": 21.93053, "lon": 69.78081, "name": "Bhānvad" }, { "lat": 36.16167, "lon": 119.26306, "name": "Shiqiaozi" }, { "lat": 18.37725, "lon": 77.88007, "name": "Bānswāda" }, { "lat": -36.84853, "lon": 174.76349, "name": "Auckland" } ], "question": "Which location is the geographic outlier among: Mādāyi, Bhānvad, Shiqiaozi, Bānswāda, Auckland?", "ground_truth": { "answer": "Auckland", "outlier_distance_km": 9088.0, "second_furthest_km": 3803.1, "clarity_ratio": 2.39, "median_distance_km": 3287.7, "distances_to_centroid": { "Mādāyi": 3074.9, "Bhānvad": 3803.1, "Shiqiaozi": 3287.7, "Bānswāda": 2885.6, "Auckland": 9088.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mādāyi: (12.03°, 75.24°)", " Bhānvad: (21.93°, 69.78°)", " Shiqiaozi: (36.16°, 119.26°)", " Bānswāda: (18.38°, 77.88°)", " Auckland: (-36.85°, 174.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Auckland: 9088.0 km from centroid", " Bhānvad: 3803.1 km from centroid", " Shiqiaozi: 3287.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Auckland", "FINAL ANSWER: Auckland" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -9.645, "lon": -36.49722, "name": "Taquarana" }, { "lat": -15.88378, "lon": -48.01634, "name": "Riacho Fundo" }, { "lat": -14.07538, "lon": -75.73422, "name": "Ica" }, { "lat": 8.36361, "lon": -72.4063, "name": "Puerto Santander" }, { "lat": 26.34992, "lon": 84.87086, "name": "Kesariyā" } ], "question": "Which location is the geographic outlier among: Taquarana, Riacho Fundo, Ica, Puerto Santander, Kesariyā?", "ground_truth": { "answer": "Kesariyā", "outlier_distance_km": 12477.8, "second_furthest_km": 5280.9, "clarity_ratio": 2.36, "median_distance_km": 4861.2, "distances_to_centroid": { "Taquarana": 1232.1, "Riacho Fundo": 2616.1, "Ica": 5280.9, "Puerto Santander": 4861.2, "Kesariyā": 12477.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taquarana: (-9.64°, -36.50°)", " Riacho Fundo: (-15.88°, -48.02°)", " Ica: (-14.08°, -75.73°)", " Puerto Santander: (8.36°, -72.41°)", " Kesariyā: (26.35°, 84.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kesariyā: 12477.8 km from centroid", " Ica: 5280.9 km from centroid", " Puerto Santander: 4861.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kesariyā", "FINAL ANSWER: Kesariyā" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -35.81081, "lon": -61.89897, "name": "Pehuajó" }, { "lat": -3.22944, "lon": -40.125, "name": "Morrinhos" }, { "lat": -7.41028, "lon": -35.11278, "name": "Itambé" }, { "lat": -17.13806, "lon": -49.98806, "name": "Indiara" }, { "lat": -39.4926, "lon": 176.91233, "name": "Napier" } ], "question": "Which location is the geographic outlier among: Pehuajó, Morrinhos, Itambé, Indiara, Napier?", "ground_truth": { "answer": "Napier", "outlier_distance_km": 13330.4, "second_furthest_km": 6009.3, "clarity_ratio": 2.22, "median_distance_km": 5041.9, "distances_to_centroid": { "Pehuajó": 6009.3, "Morrinhos": 4552.5, "Itambé": 3846.7, "Indiara": 5041.9, "Napier": 13330.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pehuajó: (-35.81°, -61.90°)", " Morrinhos: (-3.23°, -40.12°)", " Itambé: (-7.41°, -35.11°)", " Indiara: (-17.14°, -49.99°)", " Napier: (-39.49°, 176.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Napier: 13330.4 km from centroid", " Pehuajó: 6009.3 km from centroid", " Indiara: 5041.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Napier", "FINAL ANSWER: Napier" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.41665, "lon": 149.5806, "name": "Bathurst" }, { "lat": -38.08333, "lon": 144.38333, "name": "Corio" }, { "lat": -28.00274, "lon": 153.42999, "name": "Surfers Paradise" }, { "lat": -33.65249, "lon": 115.3455, "name": "Busselton" }, { "lat": 49.28333, "lon": 120.73333, "name": "Yakeshi" } ], "question": "Which location is the geographic outlier among: Bathurst, Corio, Surfers Paradise, Busselton, Yakeshi?", "ground_truth": { "answer": "Yakeshi", "outlier_distance_km": 7512.2, "second_furthest_km": 2840.7, "clarity_ratio": 2.64, "median_distance_km": 2485.5, "distances_to_centroid": { "Bathurst": 2255.5, "Corio": 2485.5, "Surfers Paradise": 2121.8, "Busselton": 2840.7, "Yakeshi": 7512.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bathurst: (-33.42°, 149.58°)", " Corio: (-38.08°, 144.38°)", " Surfers Paradise: (-28.00°, 153.43°)", " Busselton: (-33.65°, 115.35°)", " Yakeshi: (49.28°, 120.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yakeshi: 7512.2 km from centroid", " Busselton: 2840.7 km from centroid", " Corio: 2485.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yakeshi", "FINAL ANSWER: Yakeshi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.55028, "lon": -55.13111, "name": "São Francisco de Assis" }, { "lat": 5.20856, "lon": -74.73584, "name": "Honda" }, { "lat": -21.28861, "lon": -50.34, "name": "Birigui" }, { "lat": -6.00306, "lon": -40.29278, "name": "Tauá" }, { "lat": 32.78306, "lon": -96.80667, "name": "Dallas" } ], "question": "Which location is the geographic outlier among: São Francisco de Assis, Honda, Birigui, Tauá, Dallas?", "ground_truth": { "answer": "Dallas", "outlier_distance_km": 5371.0, "second_furthest_km": 2998.0, "clarity_ratio": 1.79, "median_distance_km": 2578.5, "distances_to_centroid": { "São Francisco de Assis": 2998.0, "Honda": 1601.6, "Birigui": 2409.3, "Tauá": 2578.5, "Dallas": 5371.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Francisco de Assis: (-29.55°, -55.13°)", " Honda: (5.21°, -74.74°)", " Birigui: (-21.29°, -50.34°)", " Tauá: (-6.00°, -40.29°)", " Dallas: (32.78°, -96.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dallas: 5371.0 km from centroid", " São Francisco de Assis: 2998.0 km from centroid", " Tauá: 2578.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dallas", "FINAL ANSWER: Dallas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" }, { "lat": -33.71816, "lon": 151.11561, "name": "Wahroonga" }, { "lat": -46.4, "lon": 168.35, "name": "Invercargill" }, { "lat": -33.79176, "lon": 151.08057, "name": "Eastwood" }, { "lat": 50.23085, "lon": 7.58992, "name": "Boppard" } ], "question": "Which location is the geographic outlier among: Lower Hutt, Wahroonga, Invercargill, Eastwood, Boppard?", "ground_truth": { "answer": "Boppard", "outlier_distance_km": 14112.7, "second_furthest_km": 4714.0, "clarity_ratio": 2.99, "median_distance_km": 4423.6, "distances_to_centroid": { "Lower Hutt": 4714.0, "Wahroonga": 2463.3, "Invercargill": 4423.6, "Eastwood": 2464.6, "Boppard": 14112.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lower Hutt: (-41.22°, 174.92°)", " Wahroonga: (-33.72°, 151.12°)", " Invercargill: (-46.40°, 168.35°)", " Eastwood: (-33.79°, 151.08°)", " Boppard: (50.23°, 7.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Boppard: 14112.7 km from centroid", " Lower Hutt: 4714.0 km from centroid", " Invercargill: 4423.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Boppard", "FINAL ANSWER: Boppard" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.28333, "lon": -1.58333, "name": "Warwick" }, { "lat": 52.52437, "lon": 13.41053, "name": "Berlin" }, { "lat": 55.07108, "lon": 38.78399, "name": "Kolomna" }, { "lat": 36.71522, "lon": 15.09019, "name": "Pachino" }, { "lat": -32.22099, "lon": 116.009, "name": "Byford" } ], "question": "Which location is the geographic outlier among: Warwick, Berlin, Kolomna, Pachino, Byford?", "ground_truth": { "answer": "Byford", "outlier_distance_km": 11044.0, "second_furthest_km": 3716.0, "clarity_ratio": 2.97, "median_distance_km": 2853.2, "distances_to_centroid": { "Warwick": 3716.0, "Berlin": 2853.2, "Kolomna": 2475.5, "Pachino": 1982.6, "Byford": 11044.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Warwick: (52.28°, -1.58°)", " Berlin: (52.52°, 13.41°)", " Kolomna: (55.07°, 38.78°)", " Pachino: (36.72°, 15.09°)", " Byford: (-32.22°, 116.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Byford: 11044.0 km from centroid", " Warwick: 3716.0 km from centroid", " Berlin: 2853.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Byford", "FINAL ANSWER: Byford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.32643, "lon": 84.25983, "name": "Koāth" }, { "lat": 33.50528, "lon": 105.04782, "name": "Anhua" }, { "lat": 0.83194, "lon": 109.43589, "name": "Bengkayang" }, { "lat": 30.28757, "lon": 112.22979, "name": "Buhe" }, { "lat": -37.86667, "lon": 145.06667, "name": "Glen Iris" } ], "question": "Which location is the geographic outlier among: Koāth, Anhua, Bengkayang, Buhe, Glen Iris?", "ground_truth": { "answer": "Glen Iris", "outlier_distance_km": 6420.3, "second_furthest_km": 3287.4, "clarity_ratio": 1.95, "median_distance_km": 2643.2, "distances_to_centroid": { "Koāth": 3287.4, "Anhua": 2643.2, "Bengkayang": 1083.6, "Buhe": 2212.0, "Glen Iris": 6420.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Koāth: (25.33°, 84.26°)", " Anhua: (33.51°, 105.05°)", " Bengkayang: (0.83°, 109.44°)", " Buhe: (30.29°, 112.23°)", " Glen Iris: (-37.87°, 145.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glen Iris: 6420.3 km from centroid", " Koāth: 3287.4 km from centroid", " Anhua: 2643.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glen Iris", "FINAL ANSWER: Glen Iris" ] }, { "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": -33.79728, "lon": 150.7847, "name": "St Clair" }, { "lat": -36.8582, "lon": 174.62019, "name": "Lincoln" }, { "lat": -37.88214, "lon": 144.98215, "name": "Elwood" }, { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" }, { "lat": 5.35328, "lon": 5.50826, "name": "Burutu" } ], "question": "Which location is the geographic outlier among: St Clair, Lincoln, Elwood, Ashburton, Burutu?", "ground_truth": { "answer": "Burutu", "outlier_distance_km": 13574.0, "second_furthest_km": 4239.8, "clarity_ratio": 3.2, "median_distance_km": 4041.0, "distances_to_centroid": { "St Clair": 2067.3, "Lincoln": 4239.8, "Elwood": 1709.0, "Ashburton": 4041.0, "Burutu": 13574.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " St Clair: (-33.80°, 150.78°)", " Lincoln: (-36.86°, 174.62°)", " Elwood: (-37.88°, 144.98°)", " Ashburton: (-43.90°, 171.73°)", " Burutu: (5.35°, 5.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Burutu: 13574.0 km from centroid", " Lincoln: 4239.8 km from centroid", " Ashburton: 4041.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Burutu", "FINAL ANSWER: Burutu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.96667, "lon": 145.16667, "name": "Noble Park" }, { "lat": -38.21792, "lon": 145.03876, "name": "Mornington" }, { "lat": -40.91667, "lon": 175.01667, "name": "Paraparaumu" }, { "lat": -33.91667, "lon": 151.03333, "name": "Bankstown" }, { "lat": -19.88639, "lon": -43.80667, "name": "Sabará" } ], "question": "Which location is the geographic outlier among: Noble Park, Mornington, Paraparaumu, Bankstown, Sabará?", "ground_truth": { "answer": "Sabará", "outlier_distance_km": 13579.1, "second_furthest_km": 5282.2, "clarity_ratio": 2.57, "median_distance_km": 3348.6, "distances_to_centroid": { "Noble Park": 2776.2, "Mornington": 2764.9, "Paraparaumu": 5282.2, "Bankstown": 3348.6, "Sabará": 13579.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Noble Park: (-37.97°, 145.17°)", " Mornington: (-38.22°, 145.04°)", " Paraparaumu: (-40.92°, 175.02°)", " Bankstown: (-33.92°, 151.03°)", " Sabará: (-19.89°, -43.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sabará: 13579.1 km from centroid", " Paraparaumu: 5282.2 km from centroid", " Bankstown: 3348.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sabará", "FINAL ANSWER: Sabará" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.80047, "lon": -64.26285, "name": "Santiago del Estero" }, { "lat": -7.17697, "lon": -76.72774, "name": "Juanjuí" }, { "lat": -22.84694, "lon": -45.22972, "name": "Aparecida" }, { "lat": -5.70556, "lon": -35.30722, "name": "Extremoz" }, { "lat": 43.30664, "lon": 44.98395, "name": "Troitskaya" } ], "question": "Which location is the geographic outlier among: Santiago del Estero, Juanjuí, Aparecida, Extremoz, Troitskaya?", "ground_truth": { "answer": "Troitskaya", "outlier_distance_km": 9535.6, "second_furthest_km": 4595.1, "clarity_ratio": 2.08, "median_distance_km": 4046.6, "distances_to_centroid": { "Santiago del Estero": 4046.6, "Juanjuí": 4595.1, "Aparecida": 2347.3, "Extremoz": 184.7, "Troitskaya": 9535.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santiago del Estero: (-27.80°, -64.26°)", " Juanjuí: (-7.18°, -76.73°)", " Aparecida: (-22.85°, -45.23°)", " Extremoz: (-5.71°, -35.31°)", " Troitskaya: (43.31°, 44.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Troitskaya: 9535.6 km from centroid", " Juanjuí: 4595.1 km from centroid", " Santiago del Estero: 4046.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Troitskaya", "FINAL ANSWER: Troitskaya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.88145, "lon": -83.09296, "name": "Grove City" }, { "lat": 39.18361, "lon": -96.57167, "name": "Manhattan" }, { "lat": 48.41675, "lon": -71.06573, "name": "Saguenay" }, { "lat": 26.93022, "lon": -105.6664, "name": "Parral" }, { "lat": -24.73611, "lon": -48.12278, "name": "Cajati" } ], "question": "Which location is the geographic outlier among: Grove City, Manhattan, Saguenay, Parral, Cajati?", "ground_truth": { "answer": "Cajati", "outlier_distance_km": 6644.5, "second_furthest_km": 2642.2, "clarity_ratio": 2.51, "median_distance_km": 2464.2, "distances_to_centroid": { "Grove City": 1564.0, "Manhattan": 2073.9, "Saguenay": 2642.2, "Parral": 2464.2, "Cajati": 6644.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Grove City: (39.88°, -83.09°)", " Manhattan: (39.18°, -96.57°)", " Saguenay: (48.42°, -71.07°)", " Parral: (26.93°, -105.67°)", " Cajati: (-24.74°, -48.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cajati: 6644.5 km from centroid", " Saguenay: 2642.2 km from centroid", " Parral: 2464.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cajati", "FINAL ANSWER: Cajati" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.03333, "lon": 145.3, "name": "Narre Warren" }, { "lat": -41.28664, "lon": 174.77557, "name": "Wellington" }, { "lat": -28.00274, "lon": 153.42999, "name": "Surfers Paradise" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" }, { "lat": 7.15109, "lon": 35.81703, "name": "Wacha" } ], "question": "Which location is the geographic outlier among: Narre Warren, Wellington, Surfers Paradise, Otara, Wacha?", "ground_truth": { "answer": "Wacha", "outlier_distance_km": 11458.0, "second_furthest_km": 3770.4, "clarity_ratio": 3.04, "median_distance_km": 3705.2, "distances_to_centroid": { "Narre Warren": 1419.1, "Wellington": 3770.4, "Surfers Paradise": 1633.3, "Otara": 3705.2, "Wacha": 11458.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Narre Warren: (-38.03°, 145.30°)", " Wellington: (-41.29°, 174.78°)", " Surfers Paradise: (-28.00°, 153.43°)", " Otara: (-36.95°, 174.87°)", " Wacha: (7.15°, 35.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wacha: 11458.0 km from centroid", " Wellington: 3770.4 km from centroid", " Otara: 3705.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wacha", "FINAL ANSWER: Wacha" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 21.45713, "lon": 110.76591, "name": "Wuchuan" }, { "lat": 36.49889, "lon": 111.70472, "name": "Xinzhi" }, { "lat": 11.80388, "lon": 77.85673, "name": "Pottaneri Nallakavundanpatti" }, { "lat": 44.89334, "lon": 82.06993, "name": "Bole" }, { "lat": 31.72024, "lon": -106.46084, "name": "Ciudad Juárez" } ], "question": "Which location is the geographic outlier among: Wuchuan, Xinzhi, Pottaneri Nallakavundanpatti, Bole, Ciudad Juárez?", "ground_truth": { "answer": "Ciudad Juárez", "outlier_distance_km": 12961.0, "second_furthest_km": 5601.2, "clarity_ratio": 2.31, "median_distance_km": 5263.5, "distances_to_centroid": { "Wuchuan": 5601.2, "Xinzhi": 5263.5, "Pottaneri Nallakavundanpatti": 3045.5, "Bole": 2927.2, "Ciudad Juárez": 12961.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wuchuan: (21.46°, 110.77°)", " Xinzhi: (36.50°, 111.70°)", " Pottaneri Nallakavundanpatti: (11.80°, 77.86°)", " Bole: (44.89°, 82.07°)", " Ciudad Juárez: (31.72°, -106.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ciudad Juárez: 12961.0 km from centroid", " Wuchuan: 5601.2 km from centroid", " Xinzhi: 5263.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ciudad Juárez", "FINAL ANSWER: Ciudad Juárez" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.8382, "lon": 174.61019, "name": "Massey" }, { "lat": -34.60251, "lon": 138.74902, "name": "Gawler" }, { "lat": -23.84852, "lon": 151.25775, "name": "Gladstone" }, { "lat": -33.86785, "lon": 151.20732, "name": "Sydney" }, { "lat": 51.54048, "lon": 45.9901, "name": "Saratov" } ], "question": "Which location is the geographic outlier among: Massey, Gawler, Gladstone, Sydney, Saratov?", "ground_truth": { "answer": "Saratov", "outlier_distance_km": 11106.6, "second_furthest_km": 4781.9, "clarity_ratio": 2.32, "median_distance_km": 2780.0, "distances_to_centroid": { "Massey": 4781.9, "Gawler": 2215.4, "Gladstone": 2181.0, "Sydney": 2780.0, "Saratov": 11106.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Massey: (-36.84°, 174.61°)", " Gawler: (-34.60°, 138.75°)", " Gladstone: (-23.85°, 151.26°)", " Sydney: (-33.87°, 151.21°)", " Saratov: (51.54°, 45.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saratov: 11106.6 km from centroid", " Massey: 4781.9 km from centroid", " Sydney: 2780.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saratov", "FINAL ANSWER: Saratov" ] }, { "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": 32.7559, "lon": -111.55484, "name": "Eloy" }, { "lat": 19.61387, "lon": -98.9364, "name": "Tepexpan" }, { "lat": 41.64753, "lon": -88.08951, "name": "Romeoville" }, { "lat": 34.23676, "lon": -84.49076, "name": "Canton" }, { "lat": 14.46289, "lon": 78.81191, "name": "Chemmumiahpet" } ], "question": "Which location is the geographic outlier among: Eloy, Tepexpan, Romeoville, Canton, Chemmumiahpet?", "ground_truth": { "answer": "Chemmumiahpet", "outlier_distance_km": 13559.3, "second_furthest_km": 4827.3, "clarity_ratio": 2.81, "median_distance_km": 3973.7, "distances_to_centroid": { "Eloy": 4827.3, "Tepexpan": 3973.7, "Romeoville": 2856.3, "Canton": 2325.3, "Chemmumiahpet": 13559.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Eloy: (32.76°, -111.55°)", " Tepexpan: (19.61°, -98.94°)", " Romeoville: (41.65°, -88.09°)", " Canton: (34.24°, -84.49°)", " Chemmumiahpet: (14.46°, 78.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chemmumiahpet: 13559.3 km from centroid", " Eloy: 4827.3 km from centroid", " Tepexpan: 3973.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chemmumiahpet", "FINAL ANSWER: Chemmumiahpet" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.72371, "lon": -73.95097, "name": "Greenpoint" }, { "lat": 35.41968, "lon": -119.01955, "name": "Oildale" }, { "lat": 40.69983, "lon": -73.83125, "name": "Richmond Hill" }, { "lat": 33.53865, "lon": -112.18599, "name": "Glendale" }, { "lat": 10.61285, "lon": 12.19458, "name": "Biu" } ], "question": "Which location is the geographic outlier among: Greenpoint, Oildale, Richmond Hill, Glendale, Biu?", "ground_truth": { "answer": "Biu", "outlier_distance_km": 8966.8, "second_furthest_km": 4196.6, "clarity_ratio": 2.14, "median_distance_km": 3608.1, "distances_to_centroid": { "Greenpoint": 949.4, "Oildale": 4196.6, "Richmond Hill": 946.2, "Glendale": 3608.1, "Biu": 8966.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Greenpoint: (40.72°, -73.95°)", " Oildale: (35.42°, -119.02°)", " Richmond Hill: (40.70°, -73.83°)", " Glendale: (33.54°, -112.19°)", " Biu: (10.61°, 12.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Biu: 8966.8 km from centroid", " Oildale: 4196.6 km from centroid", " Glendale: 3608.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Biu", "FINAL ANSWER: Biu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.08889, "lon": 111.51889, "name": "Linfen" }, { "lat": 24.64648, "lon": 75.94325, "name": "Rāmganj Mandi" }, { "lat": 15.55877, "lon": 75.35305, "name": "Navalgund" }, { "lat": -7.73333, "lon": 110.36667, "name": "Melati" }, { "lat": 42.74702, "lon": -73.75901, "name": "Latham" } ], "question": "Which location is the geographic outlier among: Linfen, Rāmganj Mandi, Navalgund, Melati, Latham?", "ground_truth": { "answer": "Latham", "outlier_distance_km": 11368.0, "second_furthest_km": 6429.5, "clarity_ratio": 1.77, "median_distance_km": 5179.5, "distances_to_centroid": { "Linfen": 5179.5, "Rāmganj Mandi": 1658.4, "Navalgund": 1788.1, "Melati": 6429.5, "Latham": 11368.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Linfen: (36.09°, 111.52°)", " Rāmganj Mandi: (24.65°, 75.94°)", " Navalgund: (15.56°, 75.35°)", " Melati: (-7.73°, 110.37°)", " Latham: (42.75°, -73.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Latham: 11368.0 km from centroid", " Melati: 6429.5 km from centroid", " Linfen: 5179.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Latham", "FINAL ANSWER: Latham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.72816, "lon": -74.07764, "name": "Jersey City" }, { "lat": 47.02895, "lon": -65.50186, "name": "Miramichi" }, { "lat": 40.75982, "lon": -74.4171, "name": "Madison" }, { "lat": 33.85844, "lon": -84.3402, "name": "Brookhaven" }, { "lat": 12.45347, "lon": 10.04115, "name": "Hadejia" } ], "question": "Which location is the geographic outlier among: Jersey City, Miramichi, Madison, Brookhaven, Hadejia?", "ground_truth": { "answer": "Hadejia", "outlier_distance_km": 7195.2, "second_furthest_km": 2443.4, "clarity_ratio": 2.94, "median_distance_km": 1602.6, "distances_to_centroid": { "Jersey City": 1574.3, "Miramichi": 1492.3, "Madison": 1602.6, "Brookhaven": 2443.4, "Hadejia": 7195.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jersey City: (40.73°, -74.08°)", " Miramichi: (47.03°, -65.50°)", " Madison: (40.76°, -74.42°)", " Brookhaven: (33.86°, -84.34°)", " Hadejia: (12.45°, 10.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hadejia: 7195.2 km from centroid", " Brookhaven: 2443.4 km from centroid", " Madison: 1602.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hadejia", "FINAL ANSWER: Hadejia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.24444, "lon": -49.49583, "name": "Cametá" }, { "lat": 11.00703, "lon": -74.24765, "name": "Ciénaga" }, { "lat": -5.25806, "lon": -44.64889, "name": "Tuntum" }, { "lat": -26.23, "lon": -51.08639, "name": "União da Vitória" }, { "lat": 14.98333, "lon": 102.65, "name": "Ban Huai Thalaeng" } ], "question": "Which location is the geographic outlier among: Cametá, Ciénaga, Tuntum, União da Vitória, Ban Huai Thalaeng?", "ground_truth": { "answer": "Ban Huai Thalaeng", "outlier_distance_km": 13908.8, "second_furthest_km": 5796.1, "clarity_ratio": 2.4, "median_distance_km": 4038.6, "distances_to_centroid": { "Cametá": 2904.9, "Ciénaga": 5796.1, "Tuntum": 2397.7, "União da Vitória": 4038.6, "Ban Huai Thalaeng": 13908.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cametá: (-2.24°, -49.50°)", " Ciénaga: (11.01°, -74.25°)", " Tuntum: (-5.26°, -44.65°)", " União da Vitória: (-26.23°, -51.09°)", " Ban Huai Thalaeng: (14.98°, 102.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ban Huai Thalaeng: 13908.8 km from centroid", " Ciénaga: 5796.1 km from centroid", " União da Vitória: 4038.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ban Huai Thalaeng", "FINAL ANSWER: Ban Huai Thalaeng" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.86617, "lon": 101.36894, "name": "Yaring" }, { "lat": 35.59548, "lon": 139.66535, "name": "Den’enchōfu" }, { "lat": 27.91132, "lon": 116.77637, "name": "Xiugu" }, { "lat": 20.85865, "lon": 72.90648, "name": "Abrama" }, { "lat": 4.43573, "lon": -75.20289, "name": "Ibagué" } ], "question": "Which location is the geographic outlier among: Yaring, Den’enchōfu, Xiugu, Abrama, Ibagué?", "ground_truth": { "answer": "Ibagué", "outlier_distance_km": 15491.5, "second_furthest_km": 6879.0, "clarity_ratio": 2.25, "median_distance_km": 4730.4, "distances_to_centroid": { "Yaring": 3543.0, "Den’enchōfu": 6879.0, "Xiugu": 4730.4, "Abrama": 268.9, "Ibagué": 15491.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yaring: (6.87°, 101.37°)", " Den’enchōfu: (35.60°, 139.67°)", " Xiugu: (27.91°, 116.78°)", " Abrama: (20.86°, 72.91°)", " Ibagué: (4.44°, -75.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ibagué: 15491.5 km from centroid", " Den’enchōfu: 6879.0 km from centroid", " Xiugu: 4730.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ibagué", "FINAL ANSWER: Ibagué" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.76296, "lon": 11.10941, "name": "Grosseto" }, { "lat": 51.83537, "lon": 6.69602, "name": "Rhede" }, { "lat": 54.9198, "lon": 37.41618, "name": "Serpukhov" }, { "lat": 50.5752, "lon": 19.32461, "name": "Myszków" }, { "lat": -37.93333, "lon": 145.23333, "name": "Rowville" } ], "question": "Which location is the geographic outlier among: Grosseto, Rhede, Serpukhov, Myszków, Rowville?", "ground_truth": { "answer": "Rowville", "outlier_distance_km": 13051.9, "second_furthest_km": 3691.8, "clarity_ratio": 3.54, "median_distance_km": 3089.3, "distances_to_centroid": { "Grosseto": 3089.3, "Rhede": 3691.8, "Serpukhov": 2552.6, "Myszków": 2851.4, "Rowville": 13051.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Grosseto: (42.76°, 11.11°)", " Rhede: (51.84°, 6.70°)", " Serpukhov: (54.92°, 37.42°)", " Myszków: (50.58°, 19.32°)", " Rowville: (-37.93°, 145.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rowville: 13051.9 km from centroid", " Rhede: 3691.8 km from centroid", " Grosseto: 3089.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rowville", "FINAL ANSWER: Rowville" ] }, { "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": 28.98002, "lon": 77.70636, "name": "Meerut" }, { "lat": 16.07114, "lon": 80.54944, "name": "Ponnur" }, { "lat": 19.47506, "lon": 75.38558, "name": "Paithan" }, { "lat": 24.72094, "lon": 80.18772, "name": "Panna" }, { "lat": -7.94083, "lon": -34.87306, "name": "Paulista" } ], "question": "Which location is the geographic outlier among: Meerut, Ponnur, Paithan, Panna, Paulista?", "ground_truth": { "answer": "Paulista", "outlier_distance_km": 10324.4, "second_furthest_km": 2704.3, "clarity_ratio": 3.82, "median_distance_km": 2649.3, "distances_to_centroid": { "Meerut": 2649.3, "Ponnur": 2642.6, "Paithan": 2103.0, "Panna": 2704.3, "Paulista": 10324.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Meerut: (28.98°, 77.71°)", " Ponnur: (16.07°, 80.55°)", " Paithan: (19.48°, 75.39°)", " Panna: (24.72°, 80.19°)", " Paulista: (-7.94°, -34.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Paulista: 10324.4 km from centroid", " Panna: 2704.3 km from centroid", " Meerut: 2649.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Paulista", "FINAL ANSWER: Paulista" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.814, "lon": 144.96332, "name": "Melbourne" }, { "lat": -34.92873, "lon": 138.60334, "name": "Adelaide city centre" }, { "lat": -38.07018, "lon": 145.47411, "name": "Pakenham" }, { "lat": -33.95, "lon": 151.23333, "name": "Maroubra" }, { "lat": 50.61448, "lon": -2.45991, "name": "Weymouth" } ], "question": "Which location is the geographic outlier among: Melbourne, Adelaide city centre, Pakenham, Maroubra, Weymouth?", "ground_truth": { "answer": "Weymouth", "outlier_distance_km": 13578.6, "second_furthest_km": 3903.7, "clarity_ratio": 3.48, "median_distance_km": 3596.0, "distances_to_centroid": { "Melbourne": 3543.1, "Adelaide city centre": 2889.8, "Pakenham": 3596.0, "Maroubra": 3903.7, "Weymouth": 13578.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Melbourne: (-37.81°, 144.96°)", " Adelaide city centre: (-34.93°, 138.60°)", " Pakenham: (-38.07°, 145.47°)", " Maroubra: (-33.95°, 151.23°)", " Weymouth: (50.61°, -2.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Weymouth: 13578.6 km from centroid", " Maroubra: 3903.7 km from centroid", " Pakenham: 3596.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Weymouth", "FINAL ANSWER: Weymouth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.54594, "lon": -80.25599, "name": "Guelph" }, { "lat": 41.83892, "lon": -89.47955, "name": "Dixon" }, { "lat": 32.35126, "lon": -95.30106, "name": "Tyler" }, { "lat": 40.58654, "lon": -122.39168, "name": "Redding" }, { "lat": -24.95583, "lon": -53.45528, "name": "Cascavel" } ], "question": "Which location is the geographic outlier among: Guelph, Dixon, Tyler, Redding, Cascavel?", "ground_truth": { "answer": "Cascavel", "outlier_distance_km": 6843.4, "second_furthest_km": 3495.6, "clarity_ratio": 1.96, "median_distance_km": 2007.3, "distances_to_centroid": { "Guelph": 2007.3, "Dixon": 1690.5, "Tyler": 934.3, "Redding": 3495.6, "Cascavel": 6843.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Guelph: (43.55°, -80.26°)", " Dixon: (41.84°, -89.48°)", " Tyler: (32.35°, -95.30°)", " Redding: (40.59°, -122.39°)", " Cascavel: (-24.96°, -53.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cascavel: 6843.4 km from centroid", " Redding: 3495.6 km from centroid", " Guelph: 2007.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cascavel", "FINAL ANSWER: Cascavel" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.32127, "lon": 20.97204, "name": "Białołeka" }, { "lat": 45.19365, "lon": 11.30227, "name": "Legnago" }, { "lat": 51.31917, "lon": 5.35833, "name": "Bergeijk" }, { "lat": 45.55048, "lon": 9.07741, "name": "Arese" }, { "lat": -7.35833, "lon": -35.89833, "name": "Queimadas" } ], "question": "Which location is the geographic outlier among: Białołeka, Legnago, Bergeijk, Arese, Queimadas?", "ground_truth": { "answer": "Queimadas", "outlier_distance_km": 6354.4, "second_furthest_km": 2211.2, "clarity_ratio": 2.87, "median_distance_km": 1567.5, "distances_to_centroid": { "Białołeka": 2211.2, "Legnago": 1153.0, "Bergeijk": 1567.5, "Arese": 1072.4, "Queimadas": 6354.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Białołeka: (52.32°, 20.97°)", " Legnago: (45.19°, 11.30°)", " Bergeijk: (51.32°, 5.36°)", " Arese: (45.55°, 9.08°)", " Queimadas: (-7.36°, -35.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Queimadas: 6354.4 km from centroid", " Białołeka: 2211.2 km from centroid", " Bergeijk: 1567.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Queimadas", "FINAL ANSWER: Queimadas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.05523, "lon": -97.05214, "name": "Villa Independencia" }, { "lat": 21.36022, "lon": -157.91838, "name": "Aliamanu / Salt Lakes / Foster Village" }, { "lat": 37.80437, "lon": -122.2708, "name": "Oakland" }, { "lat": 19.06406, "lon": -98.30352, "name": "Cholula" }, { "lat": -38.13333, "lon": 145.13333, "name": "Frankston East" } ], "question": "Which location is the geographic outlier among: Villa Independencia, Aliamanu / Salt Lakes / Foster Village, Oakland, Cholula, Frankston East?", "ground_truth": { "answer": "Frankston East", "outlier_distance_km": 15775.4, "second_furthest_km": 9709.7, "clarity_ratio": 1.62, "median_distance_km": 6237.9, "distances_to_centroid": { "Villa Independencia": 3421.4, "Aliamanu / Salt Lakes / Foster Village": 9709.7, "Oakland": 6237.9, "Cholula": 3533.3, "Frankston East": 15775.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Villa Independencia: (20.06°, -97.05°)", " Aliamanu / Salt Lakes / Foster Village: (21.36°, -157.92°)", " Oakland: (37.80°, -122.27°)", " Cholula: (19.06°, -98.30°)", " Frankston East: (-38.13°, 145.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Frankston East: 15775.4 km from centroid", " Aliamanu / Salt Lakes / Foster Village: 9709.7 km from centroid", " Oakland: 6237.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Frankston East", "FINAL ANSWER: Frankston East" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.71399, "lon": 130.4313, "name": "Shingū" }, { "lat": 11.21259, "lon": 99.51167, "name": "Bang Saphan" }, { "lat": 10.55869, "lon": 77.36597, "name": "Madattukkulam" }, { "lat": 6.184, "lon": 100.37752, "name": "Anak Bukit" }, { "lat": 40.39003, "lon": -3.66787, "name": "San Diego" } ], "question": "Which location is the geographic outlier among: Shingū, Bang Saphan, Madattukkulam, Anak Bukit, San Diego?", "ground_truth": { "answer": "San Diego", "outlier_distance_km": 8101.3, "second_furthest_km": 5080.3, "clarity_ratio": 1.59, "median_distance_km": 2638.2, "distances_to_centroid": { "Shingū": 5080.3, "Bang Saphan": 2244.8, "Madattukkulam": 1155.7, "Anak Bukit": 2638.2, "San Diego": 8101.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shingū: (33.71°, 130.43°)", " Bang Saphan: (11.21°, 99.51°)", " Madattukkulam: (10.56°, 77.37°)", " Anak Bukit: (6.18°, 100.38°)", " San Diego: (40.39°, -3.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Diego: 8101.3 km from centroid", " Shingū: 5080.3 km from centroid", " Anak Bukit: 2638.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Diego", "FINAL ANSWER: San Diego" ] }, { "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": -28.872, "lon": 27.87506, "name": "Ficksburg" }, { "lat": 8.13373, "lon": 4.24014, "name": "Ogbomoso" }, { "lat": 7.15109, "lon": 35.81703, "name": "Wacha" }, { "lat": -25.7287, "lon": 27.87, "name": "Hartbeespoort" }, { "lat": 42.77424, "lon": -73.70012, "name": "Cohoes" } ], "question": "Which location is the geographic outlier among: Ficksburg, Ogbomoso, Wacha, Hartbeespoort, Cohoes?", "ground_truth": { "answer": "Cohoes", "outlier_distance_km": 8988.4, "second_furthest_km": 4126.7, "clarity_ratio": 2.18, "median_distance_km": 3869.5, "distances_to_centroid": { "Ficksburg": 4126.7, "Ogbomoso": 827.8, "Wacha": 3554.2, "Hartbeespoort": 3869.5, "Cohoes": 8988.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ficksburg: (-28.87°, 27.88°)", " Ogbomoso: (8.13°, 4.24°)", " Wacha: (7.15°, 35.82°)", " Hartbeespoort: (-25.73°, 27.87°)", " Cohoes: (42.77°, -73.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cohoes: 8988.4 km from centroid", " Ficksburg: 4126.7 km from centroid", " Hartbeespoort: 3869.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cohoes", "FINAL ANSWER: Cohoes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.8075, "lon": 115.86599, "name": "Landsdale" }, { "lat": -31.09048, "lon": 150.92905, "name": "Tamworth" }, { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, { "lat": -33.86785, "lon": 151.20732, "name": "Sydney" }, { "lat": 43.69468, "lon": -79.26509, "name": "Birchcliffe-Cliffside" } ], "question": "Which location is the geographic outlier among: Landsdale, Tamworth, Kallangur, Sydney, Birchcliffe-Cliffside?", "ground_truth": { "answer": "Birchcliffe-Cliffside", "outlier_distance_km": 16934.5, "second_furthest_km": 5738.7, "clarity_ratio": 2.95, "median_distance_km": 5616.5, "distances_to_centroid": { "Landsdale": 2489.8, "Tamworth": 5558.8, "Kallangur": 5738.7, "Sydney": 5616.5, "Birchcliffe-Cliffside": 16934.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Landsdale: (-31.81°, 115.87°)", " Tamworth: (-31.09°, 150.93°)", " Kallangur: (-27.25°, 152.99°)", " Sydney: (-33.87°, 151.21°)", " Birchcliffe-Cliffside: (43.69°, -79.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Birchcliffe-Cliffside: 16934.5 km from centroid", " Kallangur: 5738.7 km from centroid", " Sydney: 5616.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Birchcliffe-Cliffside", "FINAL ANSWER: Birchcliffe-Cliffside" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.6501, "lon": -63.91165, "name": "Río Segundo" }, { "lat": -27.17806, "lon": -51.50472, "name": "Joaçaba" }, { "lat": -6.05675, "lon": -77.16651, "name": "Rioja" }, { "lat": -15.79444, "lon": -48.77583, "name": "Cocalzinho de Goiás" }, { "lat": 39.09112, "lon": -94.41551, "name": "Independence" } ], "question": "Which location is the geographic outlier among: Río Segundo, Joaçaba, Rioja, Cocalzinho de Goiás, Independence?", "ground_truth": { "answer": "Independence", "outlier_distance_km": 5975.5, "second_furthest_km": 2666.6, "clarity_ratio": 2.24, "median_distance_km": 2616.1, "distances_to_centroid": { "Río Segundo": 2616.1, "Joaçaba": 2666.6, "Rioja": 1132.7, "Cocalzinho de Goiás": 2162.8, "Independence": 5975.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Río Segundo: (-31.65°, -63.91°)", " Joaçaba: (-27.18°, -51.50°)", " Rioja: (-6.06°, -77.17°)", " Cocalzinho de Goiás: (-15.79°, -48.78°)", " Independence: (39.09°, -94.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Independence: 5975.5 km from centroid", " Joaçaba: 2666.6 km from centroid", " Río Segundo: 2616.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Independence", "FINAL ANSWER: Independence" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.36301, "lon": 100.4667, "name": "Bukit Mertajam" }, { "lat": 28.77549, "lon": 108.54646, "name": "Dingshi" }, { "lat": 27.89196, "lon": 77.36744, "name": "Hodal" }, { "lat": -0.94734, "lon": 114.8962, "name": "Muara Teweh" }, { "lat": -7.19806, "lon": -37.92917, "name": "Piancó" } ], "question": "Which location is the geographic outlier among: Bukit Mertajam, Dingshi, Hodal, Muara Teweh, Piancó?", "ground_truth": { "answer": "Piancó", "outlier_distance_km": 12397.0, "second_furthest_km": 4847.5, "clarity_ratio": 2.56, "median_distance_km": 4228.6, "distances_to_centroid": { "Bukit Mertajam": 3117.2, "Dingshi": 4228.6, "Hodal": 1965.3, "Muara Teweh": 4847.5, "Piancó": 12397.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bukit Mertajam: (5.36°, 100.47°)", " Dingshi: (28.78°, 108.55°)", " Hodal: (27.89°, 77.37°)", " Muara Teweh: (-0.95°, 114.90°)", " Piancó: (-7.20°, -37.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Piancó: 12397.0 km from centroid", " Muara Teweh: 4847.5 km from centroid", " Dingshi: 4228.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Piancó", "FINAL ANSWER: Piancó" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.86333, "lon": 4.3625, "name": "Hoogvliet" }, { "lat": 51.71905, "lon": 8.75439, "name": "Paderborn" }, { "lat": 43.5283, "lon": 5.44973, "name": "Aix-en-Provence" }, { "lat": 50.27875, "lon": 3.97267, "name": "Maubeuge" }, { "lat": 48.26667, "lon": 126.6, "name": "Bei’an" } ], "question": "Which location is the geographic outlier among: Hoogvliet, Paderborn, Aix-en-Provence, Maubeuge, Bei’an?", "ground_truth": { "answer": "Bei’an", "outlier_distance_km": 6575.9, "second_furthest_km": 1962.6, "clarity_ratio": 3.35, "median_distance_km": 1854.3, "distances_to_centroid": { "Hoogvliet": 1817.0, "Paderborn": 1514.7, "Aix-en-Provence": 1962.6, "Maubeuge": 1854.3, "Bei’an": 6575.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hoogvliet: (51.86°, 4.36°)", " Paderborn: (51.72°, 8.75°)", " Aix-en-Provence: (43.53°, 5.45°)", " Maubeuge: (50.28°, 3.97°)", " Bei’an: (48.27°, 126.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bei’an: 6575.9 km from centroid", " Aix-en-Provence: 1962.6 km from centroid", " Maubeuge: 1854.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bei’an", "FINAL ANSWER: Bei’an" ] }, { "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": 40.70211, "lon": 14.48685, "name": "Castellammare di Stabia" }, { "lat": 51.48333, "lon": 0.08333, "name": "Plumstead" }, { "lat": 43.70853, "lon": 10.4036, "name": "Pisa" }, { "lat": 52.14, "lon": 5.58472, "name": "Barneveld" }, { "lat": 29.9, "lon": 31.25, "name": "Al Ḩawāmidīyah" } ], "question": "Which location is the geographic outlier among: Castellammare di Stabia, Plumstead, Pisa, Barneveld, Al Ḩawāmidīyah?", "ground_truth": { "answer": "Al Ḩawāmidīyah", "outlier_distance_km": 2259.1, "second_furthest_km": 1269.9, "clarity_ratio": 1.78, "median_distance_km": 1076.0, "distances_to_centroid": { "Castellammare di Stabia": 365.5, "Plumstead": 1269.9, "Pisa": 158.1, "Barneveld": 1076.0, "Al Ḩawāmidīyah": 2259.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Castellammare di Stabia: (40.70°, 14.49°)", " Plumstead: (51.48°, 0.08°)", " Pisa: (43.71°, 10.40°)", " Barneveld: (52.14°, 5.58°)", " Al Ḩawāmidīyah: (29.90°, 31.25°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Al Ḩawāmidīyah: 2259.1 km from centroid", " Plumstead: 1269.9 km from centroid", " Barneveld: 1076.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Al Ḩawāmidīyah", "FINAL ANSWER: Al Ḩawāmidīyah" ] }, { "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": 6.75, "lon": 38.41667, "name": "Yirga ‘Alem" }, { "lat": 5.85475, "lon": 6.85944, "name": "Ihiala" }, { "lat": 8.27338, "lon": 5.83526, "name": "Isanlu-Itedoijowa" }, { "lat": 29.03556, "lon": 31.11792, "name": "New Bani Sewif City" }, { "lat": 49.22219, "lon": -123.00588, "name": "Maywood" } ], "question": "Which location is the geographic outlier among: Yirga ‘Alem, Ihiala, Isanlu-Itedoijowa, New Bani Sewif City, Maywood?", "ground_truth": { "answer": "Maywood", "outlier_distance_km": 10016.2, "second_furthest_km": 5225.5, "clarity_ratio": 1.92, "median_distance_km": 4085.5, "distances_to_centroid": { "Yirga ‘Alem": 5225.5, "Ihiala": 2246.7, "Isanlu-Itedoijowa": 1979.4, "New Bani Sewif City": 4085.5, "Maywood": 10016.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yirga ‘Alem: (6.75°, 38.42°)", " Ihiala: (5.85°, 6.86°)", " Isanlu-Itedoijowa: (8.27°, 5.84°)", " New Bani Sewif City: (29.04°, 31.12°)", " Maywood: (49.22°, -123.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maywood: 10016.2 km from centroid", " Yirga ‘Alem: 5225.5 km from centroid", " New Bani Sewif City: 4085.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maywood", "FINAL ANSWER: Maywood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.36889, "lon": 19.31095, "name": "Ceres" }, { "lat": -23.88384, "lon": 29.70557, "name": "Mankweng" }, { "lat": 8.75225, "lon": 38.97846, "name": "Bishoftu" }, { "lat": 0.63513, "lon": 34.28165, "name": "Malaba" }, { "lat": 55.76273, "lon": 37.86303, "name": "Reutov" } ], "question": "Which location is the geographic outlier among: Ceres, Mankweng, Bishoftu, Malaba, Reutov?", "ground_truth": { "answer": "Reutov", "outlier_distance_km": 6047.8, "second_furthest_km": 4108.3, "clarity_ratio": 1.47, "median_distance_km": 2842.5, "distances_to_centroid": { "Ceres": 4108.3, "Mankweng": 2842.5, "Bishoftu": 1108.1, "Malaba": 271.7, "Reutov": 6047.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ceres: (-33.37°, 19.31°)", " Mankweng: (-23.88°, 29.71°)", " Bishoftu: (8.75°, 38.98°)", " Malaba: (0.64°, 34.28°)", " Reutov: (55.76°, 37.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Reutov: 6047.8 km from centroid", " Ceres: 4108.3 km from centroid", " Mankweng: 2842.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Reutov", "FINAL ANSWER: Reutov" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 0.04626, "lon": 37.65587, "name": "Meru" }, { "lat": 8.05627, "lon": -1.73058, "name": "Kintampo" }, { "lat": 7.94783, "lon": 4.78836, "name": "Otan Ayegbaju" }, { "lat": -34.05515, "lon": 18.47617, "name": "Retreat" }, { "lat": -19.30323, "lon": 146.72531, "name": "Kirwan" } ], "question": "Which location is the geographic outlier among: Meru, Kintampo, Otan Ayegbaju, Retreat, Kirwan?", "ground_truth": { "answer": "Kirwan", "outlier_distance_km": 11341.3, "second_furthest_km": 5060.2, "clarity_ratio": 2.24, "median_distance_km": 4383.3, "distances_to_centroid": { "Meru": 921.9, "Kintampo": 5060.2, "Otan Ayegbaju": 4383.3, "Retreat": 3763.6, "Kirwan": 11341.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Meru: (0.05°, 37.66°)", " Kintampo: (8.06°, -1.73°)", " Otan Ayegbaju: (7.95°, 4.79°)", " Retreat: (-34.06°, 18.48°)", " Kirwan: (-19.30°, 146.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kirwan: 11341.3 km from centroid", " Kintampo: 5060.2 km from centroid", " Otan Ayegbaju: 4383.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kirwan", "FINAL ANSWER: Kirwan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.46, "lon": 4.65, "name": "Velsen-Zuid" }, { "lat": 45.66019, "lon": 8.79164, "name": "Gallarate" }, { "lat": 49.24686, "lon": 7.36977, "name": "Zweibrücken" }, { "lat": 51.66667, "lon": -0.61667, "name": "Amersham" }, { "lat": 37.97353, "lon": -122.53109, "name": "San Rafael" } ], "question": "Which location is the geographic outlier among: Velsen-Zuid, Gallarate, Zweibrücken, Amersham, San Rafael?", "ground_truth": { "answer": "San Rafael", "outlier_distance_km": 7787.8, "second_furthest_km": 2233.3, "clarity_ratio": 3.49, "median_distance_km": 2056.6, "distances_to_centroid": { "Velsen-Zuid": 1872.8, "Gallarate": 2233.3, "Zweibrücken": 2056.6, "Amersham": 1503.4, "San Rafael": 7787.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Velsen-Zuid: (52.46°, 4.65°)", " Gallarate: (45.66°, 8.79°)", " Zweibrücken: (49.25°, 7.37°)", " Amersham: (51.67°, -0.62°)", " San Rafael: (37.97°, -122.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Rafael: 7787.8 km from centroid", " Gallarate: 2233.3 km from centroid", " Zweibrücken: 2056.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Rafael", "FINAL ANSWER: San Rafael" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.28764, "lon": 5.37918, "name": "Marseille 06" }, { "lat": 49.24686, "lon": 7.36977, "name": "Zweibrücken" }, { "lat": 52.49637, "lon": -0.68939, "name": "Corby" }, { "lat": 51.35, "lon": -0.2, "name": "Sutton" }, { "lat": 0.28422, "lon": 34.75229, "name": "Kakamega" } ], "question": "Which location is the geographic outlier among: Marseille 06, Zweibrücken, Corby, Sutton, Kakamega?", "ground_truth": { "answer": "Kakamega", "outlier_distance_km": 5052.6, "second_furthest_km": 1652.4, "clarity_ratio": 3.06, "median_distance_km": 1526.6, "distances_to_centroid": { "Marseille 06": 549.2, "Zweibrücken": 1113.2, "Corby": 1652.4, "Sutton": 1526.6, "Kakamega": 5052.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Marseille 06: (43.29°, 5.38°)", " Zweibrücken: (49.25°, 7.37°)", " Corby: (52.50°, -0.69°)", " Sutton: (51.35°, -0.20°)", " Kakamega: (0.28°, 34.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kakamega: 5052.6 km from centroid", " Corby: 1652.4 km from centroid", " Sutton: 1526.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kakamega", "FINAL ANSWER: Kakamega" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 31.09823, "lon": -97.34278, "name": "Temple" }, { "lat": 42.92924, "lon": -74.05207, "name": "Glenville" }, { "lat": 36.61033, "lon": -88.31476, "name": "Murray" }, { "lat": 41.08144, "lon": -81.51901, "name": "Akron" }, { "lat": 28.50254, "lon": 77.23117, "name": "Deoli" } ], "question": "Which location is the geographic outlier among: Temple, Glenville, Murray, Akron, Deoli?", "ground_truth": { "answer": "Deoli", "outlier_distance_km": 11136.3, "second_furthest_km": 4127.5, "clarity_ratio": 2.7, "median_distance_km": 3163.9, "distances_to_centroid": { "Temple": 4127.5, "Glenville": 1971.0, "Murray": 3163.9, "Akron": 2546.7, "Deoli": 11136.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Temple: (31.10°, -97.34°)", " Glenville: (42.93°, -74.05°)", " Murray: (36.61°, -88.31°)", " Akron: (41.08°, -81.52°)", " Deoli: (28.50°, 77.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Deoli: 11136.3 km from centroid", " Temple: 4127.5 km from centroid", " Murray: 3163.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Deoli", "FINAL ANSWER: Deoli" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.34881, "lon": 30.04074, "name": "Musina" }, { "lat": -28.33057, "lon": 28.99087, "name": "Tshiame" }, { "lat": -26.1844, "lon": 27.70203, "name": "Randfontein" }, { "lat": -24.88333, "lon": 28.28333, "name": "Bela Bela" }, { "lat": -8.75333, "lon": -37.33972, "name": "Tupanatinga" } ], "question": "Which location is the geographic outlier among: Musina, Tshiame, Randfontein, Bela Bela, Tupanatinga?", "ground_truth": { "answer": "Tupanatinga", "outlier_distance_km": 5828.2, "second_furthest_km": 1519.1, "clarity_ratio": 3.84, "median_distance_km": 1492.8, "distances_to_centroid": { "Musina": 1492.8, "Tshiame": 1519.1, "Randfontein": 1314.7, "Bela Bela": 1335.7, "Tupanatinga": 5828.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Musina: (-22.35°, 30.04°)", " Tshiame: (-28.33°, 28.99°)", " Randfontein: (-26.18°, 27.70°)", " Bela Bela: (-24.88°, 28.28°)", " Tupanatinga: (-8.75°, -37.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tupanatinga: 5828.2 km from centroid", " Tshiame: 1519.1 km from centroid", " Musina: 1492.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tupanatinga", "FINAL ANSWER: Tupanatinga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.29636, "lon": 31.74633, "name": "Al ‘Āshir min Ramaḑān" }, { "lat": -0.56333, "lon": 34.93583, "name": "Nyamira" }, { "lat": 28.92095, "lon": 30.85367, "name": "Sumusţā al Waqf" }, { "lat": 8.91667, "lon": 38.61667, "name": "Sebeta" }, { "lat": -21.03306, "lon": -44.75806, "name": "Bom Sucesso" } ], "question": "Which location is the geographic outlier among: Al ‘Āshir min Ramaḑān, Nyamira, Sumusţā al Waqf, Sebeta, Bom Sucesso?", "ground_truth": { "answer": "Bom Sucesso", "outlier_distance_km": 7664.1, "second_furthest_km": 2720.3, "clarity_ratio": 2.82, "median_distance_km": 2545.2, "distances_to_centroid": { "Al ‘Āshir min Ramaḑān": 2720.3, "Nyamira": 2146.3, "Sumusţā al Waqf": 2545.2, "Sebeta": 2233.0, "Bom Sucesso": 7664.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Al ‘Āshir min Ramaḑān: (30.30°, 31.75°)", " Nyamira: (-0.56°, 34.94°)", " Sumusţā al Waqf: (28.92°, 30.85°)", " Sebeta: (8.92°, 38.62°)", " Bom Sucesso: (-21.03°, -44.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bom Sucesso: 7664.1 km from centroid", " Al ‘Āshir min Ramaḑān: 2720.3 km from centroid", " Sumusţā al Waqf: 2545.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bom Sucesso", "FINAL ANSWER: Bom Sucesso" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 57.97729, "lon": 33.25153, "name": "Valday" }, { "lat": 55.90867, "lon": 53.93437, "name": "Agidel’" }, { "lat": 43.77925, "lon": 11.24626, "name": "Florence" }, { "lat": 45.35383, "lon": 40.69465, "name": "Gul’kevichi" }, { "lat": 30.04477, "lon": 107.9149, "name": "Longkong" } ], "question": "Which location is the geographic outlier among: Valday, Agidel’, Florence, Gul’kevichi, Longkong?", "ground_truth": { "answer": "Longkong", "outlier_distance_km": 5291.3, "second_furthest_km": 2977.4, "clarity_ratio": 1.78, "median_distance_km": 1665.9, "distances_to_centroid": { "Valday": 1665.9, "Agidel’": 1080.0, "Florence": 2977.4, "Gul’kevichi": 687.3, "Longkong": 5291.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Valday: (57.98°, 33.25°)", " Agidel’: (55.91°, 53.93°)", " Florence: (43.78°, 11.25°)", " Gul’kevichi: (45.35°, 40.69°)", " Longkong: (30.04°, 107.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Longkong: 5291.3 km from centroid", " Florence: 2977.4 km from centroid", " Valday: 1665.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Longkong", "FINAL ANSWER: Longkong" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.6, "lon": 145.15, "name": "Doreen" }, { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" }, { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" }, { "lat": -37.9, "lon": 145.18333, "name": "Wheelers Hill" }, { "lat": -7.23417, "lon": -39.40944, "name": "Crato" } ], "question": "Which location is the geographic outlier among: Doreen, Saint Albans, Carnegie, Wheelers Hill, Crato?", "ground_truth": { "answer": "Crato", "outlier_distance_km": 14486.0, "second_furthest_km": 3428.3, "clarity_ratio": 4.23, "median_distance_km": 3425.3, "distances_to_centroid": { "Doreen": 3425.3, "Saint Albans": 3394.6, "Carnegie": 3417.1, "Wheelers Hill": 3428.3, "Crato": 14486.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Doreen: (-37.60°, 145.15°)", " Saint Albans: (-37.73°, 144.80°)", " Carnegie: (-37.89°, 145.06°)", " Wheelers Hill: (-37.90°, 145.18°)", " Crato: (-7.23°, -39.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Crato: 14486.0 km from centroid", " Wheelers Hill: 3428.3 km from centroid", " Doreen: 3425.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Crato", "FINAL ANSWER: Crato" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.33361, "lon": -43.52833, "name": "São Benedito do Rio Preto" }, { "lat": -17.28556, "lon": -42.73, "name": "Turmalina" }, { "lat": -6.75472, "lon": -51.08389, "name": "Ourilândia do Norte" }, { "lat": -10.5075, "lon": -40.32139, "name": "Campo Formoso" }, { "lat": 46.86135, "lon": 124.442, "name": "Dorbod" } ], "question": "Which location is the geographic outlier among: São Benedito do Rio Preto, Turmalina, Ourilândia do Norte, Campo Formoso, Dorbod?", "ground_truth": { "answer": "Dorbod", "outlier_distance_km": 13060.9, "second_furthest_km": 4587.7, "clarity_ratio": 2.85, "median_distance_km": 4107.4, "distances_to_centroid": { "São Benedito do Rio Preto": 3699.2, "Turmalina": 4107.4, "Ourilândia do Norte": 4587.7, "Campo Formoso": 3557.3, "Dorbod": 13060.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Benedito do Rio Preto: (-3.33°, -43.53°)", " Turmalina: (-17.29°, -42.73°)", " Ourilândia do Norte: (-6.75°, -51.08°)", " Campo Formoso: (-10.51°, -40.32°)", " Dorbod: (46.86°, 124.44°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dorbod: 13060.9 km from centroid", " Ourilândia do Norte: 4587.7 km from centroid", " Turmalina: 4107.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dorbod", "FINAL ANSWER: Dorbod" ] }, { "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": -33.28397, "lon": 149.10018, "name": "Orange" }, { "lat": -36.99282, "lon": 174.87986, "name": "Manukau City" }, { "lat": -37.83834, "lon": 144.99149, "name": "South Yarra" }, { "lat": -27.63917, "lon": 153.10944, "name": "Logan City" }, { "lat": 31.01887, "lon": 75.79111, "name": "Phillaur" } ], "question": "Which location is the geographic outlier among: Orange, Manukau City, South Yarra, Logan City, Phillaur?", "ground_truth": { "answer": "Phillaur", "outlier_distance_km": 8923.4, "second_furthest_km": 3839.3, "clarity_ratio": 2.32, "median_distance_km": 1949.2, "distances_to_centroid": { "Orange": 1662.6, "Manukau City": 3839.3, "South Yarra": 1949.2, "Logan City": 1559.0, "Phillaur": 8923.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Orange: (-33.28°, 149.10°)", " Manukau City: (-36.99°, 174.88°)", " South Yarra: (-37.84°, 144.99°)", " Logan City: (-27.64°, 153.11°)", " Phillaur: (31.02°, 75.79°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Phillaur: 8923.4 km from centroid", " Manukau City: 3839.3 km from centroid", " South Yarra: 1949.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Phillaur", "FINAL ANSWER: Phillaur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.88384, "lon": 29.70557, "name": "Mankweng" }, { "lat": -32.90769, "lon": 27.50973, "name": "Ndevana" }, { "lat": 11.27727, "lon": 9.88385, "name": "Gwaram" }, { "lat": 8.25, "lon": 34.58333, "name": "Gambēla" }, { "lat": 41.68281, "lon": -88.35146, "name": "Oswego" } ], "question": "Which location is the geographic outlier among: Mankweng, Ndevana, Gwaram, Gambēla, Oswego?", "ground_truth": { "answer": "Oswego", "outlier_distance_km": 10026.7, "second_furthest_km": 4571.8, "clarity_ratio": 2.19, "median_distance_km": 4013.1, "distances_to_centroid": { "Mankweng": 4013.1, "Ndevana": 4571.8, "Gwaram": 1403.8, "Gambēla": 3628.6, "Oswego": 10026.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mankweng: (-23.88°, 29.71°)", " Ndevana: (-32.91°, 27.51°)", " Gwaram: (11.28°, 9.88°)", " Gambēla: (8.25°, 34.58°)", " Oswego: (41.68°, -88.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Oswego: 10026.7 km from centroid", " Ndevana: 4571.8 km from centroid", " Mankweng: 4013.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Oswego", "FINAL ANSWER: Oswego" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.9575, "lon": -36.20472, "name": "Santa Cruz do Capibaribe" }, { "lat": -7.65694, "lon": -35.32667, "name": "Vicência" }, { "lat": -17.28556, "lon": -42.73, "name": "Turmalina" }, { "lat": -16.06583, "lon": -47.97861, "name": "Valparaíso de Goiás" }, { "lat": 41.7658, "lon": 12.70188, "name": "Rocca di Papa" } ], "question": "Which location is the geographic outlier among: Santa Cruz do Capibaribe, Vicência, Turmalina, Valparaíso de Goiás, Rocca di Papa?", "ground_truth": { "answer": "Rocca di Papa", "outlier_distance_km": 6433.4, "second_furthest_km": 2562.3, "clarity_ratio": 2.51, "median_distance_km": 2251.6, "distances_to_centroid": { "Santa Cruz do Capibaribe": 1005.8, "Vicência": 915.6, "Turmalina": 2251.6, "Valparaíso de Goiás": 2562.3, "Rocca di Papa": 6433.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Cruz do Capibaribe: (-7.96°, -36.20°)", " Vicência: (-7.66°, -35.33°)", " Turmalina: (-17.29°, -42.73°)", " Valparaíso de Goiás: (-16.07°, -47.98°)", " Rocca di Papa: (41.77°, 12.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rocca di Papa: 6433.4 km from centroid", " Valparaíso de Goiás: 2562.3 km from centroid", " Turmalina: 2251.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rocca di Papa", "FINAL ANSWER: Rocca di Papa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.84853, "lon": 174.76349, "name": "Auckland" }, { "lat": -37.8149, "lon": 144.95052, "name": "Docklands" }, { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": 20.38897, "lon": -99.99637, "name": "San Juan del Río" } ], "question": "Which location is the geographic outlier among: Auckland, Docklands, Mackay, Cranbourne East, San Juan del Río?", "ground_truth": { "answer": "San Juan del Río", "outlier_distance_km": 17642.0, "second_furthest_km": 6958.5, "clarity_ratio": 2.54, "median_distance_km": 4762.5, "distances_to_centroid": { "Auckland": 6958.5, "Docklands": 4335.2, "Mackay": 4762.5, "Cranbourne East": 4371.3, "San Juan del Río": 17642.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Auckland: (-36.85°, 174.76°)", " Docklands: (-37.81°, 144.95°)", " Mackay: (-21.15°, 149.17°)", " Cranbourne East: (-38.12°, 145.30°)", " San Juan del Río: (20.39°, -100.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Juan del Río: 17642.0 km from centroid", " Auckland: 6958.5 km from centroid", " Mackay: 4762.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Juan del Río", "FINAL ANSWER: San Juan del Río" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" }, { "lat": -36.99282, "lon": 174.87986, "name": "Manukau City" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": -32.83211, "lon": 151.35623, "name": "Cessnock" }, { "lat": 43.65965, "lon": -79.37902, "name": "Church-Yonge Corridor" } ], "question": "Which location is the geographic outlier among: Carnegie, Manukau City, Cranbourne East, Cessnock, Church-Yonge Corridor?", "ground_truth": { "answer": "Church-Yonge Corridor", "outlier_distance_km": 17356.1, "second_furthest_km": 6691.9, "clarity_ratio": 2.59, "median_distance_km": 4541.4, "distances_to_centroid": { "Carnegie": 4097.3, "Manukau City": 6691.9, "Cranbourne East": 4125.0, "Cessnock": 4541.4, "Church-Yonge Corridor": 17356.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Carnegie: (-37.89°, 145.06°)", " Manukau City: (-36.99°, 174.88°)", " Cranbourne East: (-38.12°, 145.30°)", " Cessnock: (-32.83°, 151.36°)", " Church-Yonge Corridor: (43.66°, -79.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Church-Yonge Corridor: 17356.1 km from centroid", " Manukau City: 6691.9 km from centroid", " Cessnock: 4541.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Church-Yonge Corridor", "FINAL ANSWER: Church-Yonge Corridor" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.90107, "lon": 32.72392, "name": "Naqādah" }, { "lat": -27.8549, "lon": 26.36583, "name": "Wesselsbron" }, { "lat": 7.85868, "lon": 10.97187, "name": "Beli" }, { "lat": -1.48256, "lon": 40.03341, "name": "Hola" }, { "lat": -37.9, "lon": 144.66667, "name": "Werribee" } ], "question": "Which location is the geographic outlier among: Naqādah, Wesselsbron, Beli, Hola, Werribee?", "ground_truth": { "answer": "Werribee", "outlier_distance_km": 9874.7, "second_furthest_km": 4719.5, "clarity_ratio": 2.09, "median_distance_km": 4124.6, "distances_to_centroid": { "Naqādah": 4124.6, "Wesselsbron": 3498.7, "Beli": 4719.5, "Hola": 1342.2, "Werribee": 9874.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Naqādah: (25.90°, 32.72°)", " Wesselsbron: (-27.85°, 26.37°)", " Beli: (7.86°, 10.97°)", " Hola: (-1.48°, 40.03°)", " Werribee: (-37.90°, 144.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Werribee: 9874.7 km from centroid", " Beli: 4719.5 km from centroid", " Naqādah: 4124.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Werribee", "FINAL ANSWER: Werribee" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.73261, "lon": 144.86504, "name": "Keilor East" }, { "lat": -27.98941, "lon": 153.33633, "name": "Nerang" }, { "lat": -38.16604, "lon": 145.13643, "name": "Frankston South" }, { "lat": -26.65682, "lon": 153.07955, "name": "Sunshine Coast" }, { "lat": 17.48862, "lon": 78.60208, "name": "Nāgāvaram" } ], "question": "Which location is the geographic outlier among: Keilor East, Nerang, Frankston South, Sunshine Coast, Nāgāvaram?", "ground_truth": { "answer": "Nāgāvaram", "outlier_distance_km": 7581.4, "second_furthest_km": 1980.8, "clarity_ratio": 3.83, "median_distance_km": 1935.1, "distances_to_centroid": { "Keilor East": 1927.4, "Nerang": 1935.1, "Frankston South": 1980.8, "Sunshine Coast": 1879.7, "Nāgāvaram": 7581.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Keilor East: (-37.73°, 144.87°)", " Nerang: (-27.99°, 153.34°)", " Frankston South: (-38.17°, 145.14°)", " Sunshine Coast: (-26.66°, 153.08°)", " Nāgāvaram: (17.49°, 78.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nāgāvaram: 7581.4 km from centroid", " Frankston South: 1980.8 km from centroid", " Nerang: 1935.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nāgāvaram", "FINAL ANSWER: Nāgāvaram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.41028, "lon": -35.11278, "name": "Itambé" }, { "lat": 6.43809, "lon": -75.33136, "name": "Barbosa" }, { "lat": -10.73333, "lon": -37.49333, "name": "Campo do Brito" }, { "lat": -2.88, "lon": -52.01, "name": "Vitória do Xingu" }, { "lat": 50.72391, "lon": 3.16117, "name": "Tourcoing" } ], "question": "Which location is the geographic outlier among: Itambé, Barbosa, Campo do Brito, Vitória do Xingu, Tourcoing?", "ground_truth": { "answer": "Tourcoing", "outlier_distance_km": 6218.5, "second_furthest_km": 3971.7, "clarity_ratio": 1.57, "median_distance_km": 2007.8, "distances_to_centroid": { "Itambé": 1694.4, "Barbosa": 3971.7, "Campo do Brito": 2007.8, "Vitória do Xingu": 1798.5, "Tourcoing": 6218.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itambé: (-7.41°, -35.11°)", " Barbosa: (6.44°, -75.33°)", " Campo do Brito: (-10.73°, -37.49°)", " Vitória do Xingu: (-2.88°, -52.01°)", " Tourcoing: (50.72°, 3.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tourcoing: 6218.5 km from centroid", " Barbosa: 3971.7 km from centroid", " Campo do Brito: 2007.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tourcoing", "FINAL ANSWER: Tourcoing" ] }, { "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": 52.58514, "lon": -2.05934, "name": "Willenhall" }, { "lat": 50.3836, "lon": 8.0503, "name": "Limburg an der Lahn" }, { "lat": 52.6386, "lon": -1.13169, "name": "Leicester" }, { "lat": 42.88052, "lon": -8.54569, "name": "Santiago de Compostela" }, { "lat": -37.78247, "lon": 145.31682, "name": "Mooroolbark" } ], "question": "Which location is the geographic outlier among: Willenhall, Limburg an der Lahn, Leicester, Santiago de Compostela, Mooroolbark?", "ground_truth": { "answer": "Mooroolbark", "outlier_distance_km": 14347.0, "second_furthest_km": 3432.0, "clarity_ratio": 4.18, "median_distance_km": 3331.7, "distances_to_centroid": { "Willenhall": 3331.7, "Limburg an der Lahn": 2625.5, "Leicester": 3281.5, "Santiago de Compostela": 3432.0, "Mooroolbark": 14347.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Willenhall: (52.59°, -2.06°)", " Limburg an der Lahn: (50.38°, 8.05°)", " Leicester: (52.64°, -1.13°)", " Santiago de Compostela: (42.88°, -8.55°)", " Mooroolbark: (-37.78°, 145.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mooroolbark: 14347.0 km from centroid", " Santiago de Compostela: 3432.0 km from centroid", " Willenhall: 3331.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mooroolbark", "FINAL ANSWER: Mooroolbark" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.06611, "lon": -50.14722, "name": "Buritama" }, { "lat": -26.08111, "lon": -53.055, "name": "Francisco Beltrão" }, { "lat": -27.34361, "lon": -51.61194, "name": "Capinzal" }, { "lat": -27.48683, "lon": -55.11994, "name": "Oberá" }, { "lat": 51.61759, "lon": 15.31486, "name": "Żagań" } ], "question": "Which location is the geographic outlier among: Buritama, Francisco Beltrão, Capinzal, Oberá, Żagań?", "ground_truth": { "answer": "Żagań", "outlier_distance_km": 8593.2, "second_furthest_km": 2573.8, "clarity_ratio": 3.34, "median_distance_km": 2335.6, "distances_to_centroid": { "Buritama": 1712.9, "Francisco Beltrão": 2319.4, "Capinzal": 2335.6, "Oberá": 2573.8, "Żagań": 8593.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Buritama: (-21.07°, -50.15°)", " Francisco Beltrão: (-26.08°, -53.05°)", " Capinzal: (-27.34°, -51.61°)", " Oberá: (-27.49°, -55.12°)", " Żagań: (51.62°, 15.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Żagań: 8593.2 km from centroid", " Oberá: 2573.8 km from centroid", " Capinzal: 2335.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Żagań", "FINAL ANSWER: Żagań" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.41667, "lon": 36.91667, "name": "Gorod Shebekino" }, { "lat": 51.965, "lon": 6.28889, "name": "Doetinchem" }, { "lat": 55.72445, "lon": 38.20908, "name": "Elektrougli" }, { "lat": 37.37281, "lon": -6.04589, "name": "Tomares" }, { "lat": -37.90561, "lon": 145.00279, "name": "Brighton" } ], "question": "Which location is the geographic outlier among: Gorod Shebekino, Doetinchem, Elektrougli, Tomares, Brighton?", "ground_truth": { "answer": "Brighton", "outlier_distance_km": 12971.8, "second_furthest_km": 4588.3, "clarity_ratio": 2.83, "median_distance_km": 3805.7, "distances_to_centroid": { "Gorod Shebekino": 2183.5, "Doetinchem": 3805.7, "Elektrougli": 2730.8, "Tomares": 4588.3, "Brighton": 12971.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gorod Shebekino: (50.42°, 36.92°)", " Doetinchem: (51.97°, 6.29°)", " Elektrougli: (55.72°, 38.21°)", " Tomares: (37.37°, -6.05°)", " Brighton: (-37.91°, 145.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brighton: 12971.8 km from centroid", " Tomares: 4588.3 km from centroid", " Doetinchem: 3805.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brighton", "FINAL ANSWER: Brighton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.61025, "lon": 153.05388, "name": "Sunnybank Hills" }, { "lat": -38.14711, "lon": 144.36069, "name": "Geelong" }, { "lat": -41.28374, "lon": 174.74141, "name": "Karori" }, { "lat": -34.18551, "lon": 142.16251, "name": "Mildura" }, { "lat": 14.23333, "lon": 37.0, "name": "Abala" } ], "question": "Which location is the geographic outlier among: Sunnybank Hills, Geelong, Karori, Mildura, Abala?", "ground_truth": { "answer": "Abala", "outlier_distance_km": 11001.0, "second_furthest_km": 4434.9, "clarity_ratio": 2.48, "median_distance_km": 2277.9, "distances_to_centroid": { "Sunnybank Hills": 2277.9, "Geelong": 1940.9, "Karori": 4434.9, "Mildura": 1505.6, "Abala": 11001.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunnybank Hills: (-27.61°, 153.05°)", " Geelong: (-38.15°, 144.36°)", " Karori: (-41.28°, 174.74°)", " Mildura: (-34.19°, 142.16°)", " Abala: (14.23°, 37.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Abala: 11001.0 km from centroid", " Karori: 4434.9 km from centroid", " Sunnybank Hills: 2277.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Abala", "FINAL ANSWER: Abala" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.46113, "lon": 130.84185, "name": "Darwin" }, { "lat": -34.92866, "lon": 138.59863, "name": "Adelaide" }, { "lat": -37.68333, "lon": 145.01667, "name": "Thomastown" }, { "lat": -33.92893, "lon": 151.05111, "name": "Punchbowl" }, { "lat": 28.71448, "lon": 77.28489, "name": "Jīwanpur" } ], "question": "Which location is the geographic outlier among: Darwin, Adelaide, Thomastown, Punchbowl, Jīwanpur?", "ground_truth": { "answer": "Jīwanpur", "outlier_distance_km": 7574.2, "second_furthest_km": 2846.1, "clarity_ratio": 2.66, "median_distance_km": 2707.1, "distances_to_centroid": { "Darwin": 668.7, "Adelaide": 2122.4, "Thomastown": 2707.1, "Punchbowl": 2846.1, "Jīwanpur": 7574.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Darwin: (-12.46°, 130.84°)", " Adelaide: (-34.93°, 138.60°)", " Thomastown: (-37.68°, 145.02°)", " Punchbowl: (-33.93°, 151.05°)", " Jīwanpur: (28.71°, 77.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jīwanpur: 7574.2 km from centroid", " Punchbowl: 2846.1 km from centroid", " Thomastown: 2707.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jīwanpur", "FINAL ANSWER: Jīwanpur" ] }, { "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": 6.13833, "lon": -75.26417, "name": "Santuario" }, { "lat": 10.59181, "lon": -74.18983, "name": "Aracataca" }, { "lat": -40.57395, "lon": -73.13348, "name": "Osorno" }, { "lat": -21.75778, "lon": -48.82889, "name": "Ibitinga" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" } ], "question": "Which location is the geographic outlier among: Santuario, Aracataca, Osorno, Ibitinga, Otara?", "ground_truth": { "answer": "Otara", "outlier_distance_km": 13887.6, "second_furthest_km": 6745.5, "clarity_ratio": 2.06, "median_distance_km": 6647.4, "distances_to_centroid": { "Santuario": 6647.4, "Aracataca": 6745.5, "Osorno": 5789.9, "Ibitinga": 3150.4, "Otara": 13887.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santuario: (6.14°, -75.26°)", " Aracataca: (10.59°, -74.19°)", " Osorno: (-40.57°, -73.13°)", " Ibitinga: (-21.76°, -48.83°)", " Otara: (-36.95°, 174.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Otara: 13887.6 km from centroid", " Aracataca: 6745.5 km from centroid", " Santuario: 6647.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Otara", "FINAL ANSWER: Otara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.70791, "lon": 16.69937, "name": "Szczecinek" }, { "lat": 53.15145, "lon": 16.73782, "name": "Piła" }, { "lat": 51.65501, "lon": 17.80686, "name": "Ostrów Wielkopolski" }, { "lat": 48.92805, "lon": 2.39627, "name": "La Courneuve" }, { "lat": -40.95972, "lon": 175.6575, "name": "Masterton" } ], "question": "Which location is the geographic outlier among: Szczecinek, Piła, Ostrów Wielkopolski, La Courneuve, Masterton?", "ground_truth": { "answer": "Masterton", "outlier_distance_km": 15546.0, "second_furthest_km": 3965.7, "clarity_ratio": 3.92, "median_distance_km": 3226.1, "distances_to_centroid": { "Szczecinek": 3226.1, "Piła": 3190.7, "Ostrów Wielkopolski": 3041.7, "La Courneuve": 3965.7, "Masterton": 15546.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Szczecinek: (53.71°, 16.70°)", " Piła: (53.15°, 16.74°)", " Ostrów Wielkopolski: (51.66°, 17.81°)", " La Courneuve: (48.93°, 2.40°)", " Masterton: (-40.96°, 175.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Masterton: 15546.0 km from centroid", " La Courneuve: 3965.7 km from centroid", " Szczecinek: 3226.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Masterton", "FINAL ANSWER: Masterton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.27888, "lon": 28.49696, "name": "Frankfort" }, { "lat": -25.77507, "lon": 29.46482, "name": "Middelburg" }, { "lat": 3.11988, "lon": 35.59642, "name": "Lodwar" }, { "lat": -29.57366, "lon": 31.11552, "name": "Tongaat" }, { "lat": -21.06417, "lon": -41.36639, "name": "Mimoso do Sul" } ], "question": "Which location is the geographic outlier among: Frankfort, Middelburg, Lodwar, Tongaat, Mimoso do Sul?", "ground_truth": { "answer": "Mimoso do Sul", "outlier_distance_km": 6006.1, "second_furthest_km": 3308.5, "clarity_ratio": 1.82, "median_distance_km": 1795.4, "distances_to_centroid": { "Frankfort": 1443.3, "Middelburg": 1453.2, "Lodwar": 3308.5, "Tongaat": 1795.4, "Mimoso do Sul": 6006.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Frankfort: (-27.28°, 28.50°)", " Middelburg: (-25.78°, 29.46°)", " Lodwar: (3.12°, 35.60°)", " Tongaat: (-29.57°, 31.12°)", " Mimoso do Sul: (-21.06°, -41.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mimoso do Sul: 6006.1 km from centroid", " Lodwar: 3308.5 km from centroid", " Tongaat: 1795.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mimoso do Sul", "FINAL ANSWER: Mimoso do Sul" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.06564, "lon": 151.01266, "name": "Engadine" }, { "lat": -37.76667, "lon": 145.0, "name": "Northcote" }, { "lat": -37.8149, "lon": 144.95052, "name": "Docklands" }, { "lat": -37.9, "lon": 145.18333, "name": "Wheelers Hill" }, { "lat": 56.50328, "lon": 66.54672, "name": "Zavodoukovsk" } ], "question": "Which location is the geographic outlier among: Engadine, Northcote, Docklands, Wheelers Hill, Zavodoukovsk?", "ground_truth": { "answer": "Zavodoukovsk", "outlier_distance_km": 10203.2, "second_furthest_km": 2689.1, "clarity_ratio": 3.79, "median_distance_km": 2611.3, "distances_to_centroid": { "Engadine": 2689.1, "Northcote": 2589.8, "Docklands": 2591.5, "Wheelers Hill": 2611.3, "Zavodoukovsk": 10203.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Engadine: (-34.07°, 151.01°)", " Northcote: (-37.77°, 145.00°)", " Docklands: (-37.81°, 144.95°)", " Wheelers Hill: (-37.90°, 145.18°)", " Zavodoukovsk: (56.50°, 66.55°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zavodoukovsk: 10203.2 km from centroid", " Engadine: 2689.1 km from centroid", " Wheelers Hill: 2611.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zavodoukovsk", "FINAL ANSWER: Zavodoukovsk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.55968, "lon": 103.91413, "name": "Angarsk" }, { "lat": 50.72485, "lon": 1.61373, "name": "Boulogne-sur-Mer" }, { "lat": 55.78677, "lon": 37.80165, "name": "Izmaylovo" }, { "lat": 52.51167, "lon": 6.25694, "name": "Dalfsen" }, { "lat": -33.89743, "lon": 150.93446, "name": "Cabramatta" } ], "question": "Which location is the geographic outlier among: Angarsk, Boulogne-sur-Mer, Izmaylovo, Dalfsen, Cabramatta?", "ground_truth": { "answer": "Cabramatta", "outlier_distance_km": 12176.8, "second_furthest_km": 4894.1, "clarity_ratio": 2.49, "median_distance_km": 4572.1, "distances_to_centroid": { "Angarsk": 3899.2, "Boulogne-sur-Mer": 4894.1, "Izmaylovo": 2815.0, "Dalfsen": 4572.1, "Cabramatta": 12176.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Angarsk: (52.56°, 103.91°)", " Boulogne-sur-Mer: (50.72°, 1.61°)", " Izmaylovo: (55.79°, 37.80°)", " Dalfsen: (52.51°, 6.26°)", " Cabramatta: (-33.90°, 150.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cabramatta: 12176.8 km from centroid", " Boulogne-sur-Mer: 4894.1 km from centroid", " Dalfsen: 4572.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cabramatta", "FINAL ANSWER: Cabramatta" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.9488, "lon": 43.73709, "name": "Yelan’" }, { "lat": 45.51314, "lon": 9.14343, "name": "Quarto Oggiaro" }, { "lat": 40.86842, "lon": 14.40196, "name": "Sant'Anastasia" }, { "lat": 43.46589, "lon": -3.80493, "name": "Santander" }, { "lat": -35.28346, "lon": 149.12807, "name": "Canberra" } ], "question": "Which location is the geographic outlier among: Yelan’, Quarto Oggiaro, Sant'Anastasia, Santander, Canberra?", "ground_truth": { "answer": "Canberra", "outlier_distance_km": 13232.1, "second_furthest_km": 4383.4, "clarity_ratio": 3.02, "median_distance_km": 3433.3, "distances_to_centroid": { "Yelan’": 2431.3, "Quarto Oggiaro": 3433.3, "Sant'Anastasia": 2858.8, "Santander": 4383.4, "Canberra": 13232.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yelan’: (50.95°, 43.74°)", " Quarto Oggiaro: (45.51°, 9.14°)", " Sant'Anastasia: (40.87°, 14.40°)", " Santander: (43.47°, -3.80°)", " Canberra: (-35.28°, 149.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Canberra: 13232.1 km from centroid", " Santander: 4383.4 km from centroid", " Quarto Oggiaro: 3433.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Canberra", "FINAL ANSWER: Canberra" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": -27.10876, "lon": 152.94907, "name": "Morayfield" }, { "lat": -27.64613, "lon": 152.85965, "name": "Redbank Plains" }, { "lat": -37.83961, "lon": 144.94228, "name": "Port Melbourne" }, { "lat": 4.92675, "lon": 6.26764, "name": "Yenagoa" } ], "question": "Which location is the geographic outlier among: Yarraville, Morayfield, Redbank Plains, Port Melbourne, Yenagoa?", "ground_truth": { "answer": "Yenagoa", "outlier_distance_km": 12664.6, "second_furthest_km": 3250.5, "clarity_ratio": 3.9, "median_distance_km": 3238.6, "distances_to_centroid": { "Yarraville": 2708.9, "Morayfield": 3250.5, "Redbank Plains": 3238.6, "Port Melbourne": 2713.3, "Yenagoa": 12664.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yarraville: (-37.82°, 144.90°)", " Morayfield: (-27.11°, 152.95°)", " Redbank Plains: (-27.65°, 152.86°)", " Port Melbourne: (-37.84°, 144.94°)", " Yenagoa: (4.93°, 6.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yenagoa: 12664.6 km from centroid", " Morayfield: 3250.5 km from centroid", " Redbank Plains: 3238.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yenagoa", "FINAL ANSWER: Yenagoa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.8277, "lon": 39.59164, "name": "Weldiya" }, { "lat": -26.9033, "lon": 27.45727, "name": "Parys" }, { "lat": -26.36094, "lon": 27.39767, "name": "Carletonville" }, { "lat": 31.08898, "lon": 31.59478, "name": "Dikirnis" }, { "lat": -33.15365, "lon": -60.51168, "name": "Arroyo Seco" } ], "question": "Which location is the geographic outlier among: Weldiya, Parys, Carletonville, Dikirnis, Arroyo Seco?", "ground_truth": { "answer": "Arroyo Seco", "outlier_distance_km": 7958.3, "second_furthest_km": 4843.1, "clarity_ratio": 1.64, "median_distance_km": 3712.6, "distances_to_centroid": { "Weldiya": 3712.6, "Parys": 2525.6, "Carletonville": 2475.5, "Dikirnis": 4843.1, "Arroyo Seco": 7958.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Weldiya: (11.83°, 39.59°)", " Parys: (-26.90°, 27.46°)", " Carletonville: (-26.36°, 27.40°)", " Dikirnis: (31.09°, 31.59°)", " Arroyo Seco: (-33.15°, -60.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arroyo Seco: 7958.3 km from centroid", " Dikirnis: 4843.1 km from centroid", " Weldiya: 3712.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arroyo Seco", "FINAL ANSWER: Arroyo Seco" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.46687, "lon": 100.56248, "name": "Xiangcheng" }, { "lat": 26.72028, "lon": 108.12972, "name": "Kaitang" }, { "lat": 31.1245, "lon": 76.11613, "name": "Nawanshahr" }, { "lat": 22.34835, "lon": 73.13313, "name": "Undera" }, { "lat": 8.53333, "lon": 34.8, "name": "Dembī Dolo" } ], "question": "Which location is the geographic outlier among: Xiangcheng, Kaitang, Nawanshahr, Undera, Dembī Dolo?", "ground_truth": { "answer": "Dembī Dolo", "outlier_distance_km": 4923.4, "second_furthest_km": 3010.7, "clarity_ratio": 1.64, "median_distance_km": 2250.0, "distances_to_centroid": { "Xiangcheng": 2250.0, "Kaitang": 3010.7, "Nawanshahr": 952.2, "Undera": 558.6, "Dembī Dolo": 4923.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Xiangcheng: (25.47°, 100.56°)", " Kaitang: (26.72°, 108.13°)", " Nawanshahr: (31.12°, 76.12°)", " Undera: (22.35°, 73.13°)", " Dembī Dolo: (8.53°, 34.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dembī Dolo: 4923.4 km from centroid", " Kaitang: 3010.7 km from centroid", " Xiangcheng: 2250.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dembī Dolo", "FINAL ANSWER: Dembī Dolo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.91667, "lon": 151.03333, "name": "Bankstown" }, { "lat": -33.88096, "lon": 151.07986, "name": "Strathfield" }, { "lat": -36.84853, "lon": 174.76349, "name": "Auckland" }, { "lat": -35.13333, "lon": 138.51667, "name": "Morphett Vale" }, { "lat": 12.98417, "lon": 37.765, "name": "Dabat" } ], "question": "Which location is the geographic outlier among: Bankstown, Strathfield, Auckland, Morphett Vale, Dabat?", "ground_truth": { "answer": "Dabat", "outlier_distance_km": 10904.1, "second_furthest_km": 4349.7, "clarity_ratio": 2.51, "median_distance_km": 2186.4, "distances_to_centroid": { "Bankstown": 2183.8, "Strathfield": 2186.4, "Auckland": 4349.7, "Morphett Vale": 1323.6, "Dabat": 10904.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bankstown: (-33.92°, 151.03°)", " Strathfield: (-33.88°, 151.08°)", " Auckland: (-36.85°, 174.76°)", " Morphett Vale: (-35.13°, 138.52°)", " Dabat: (12.98°, 37.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dabat: 10904.1 km from centroid", " Auckland: 4349.7 km from centroid", " Strathfield: 2186.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dabat", "FINAL ANSWER: Dabat" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -17.18889, "lon": -41.69472, "name": "Caraí" }, { "lat": -8.87556, "lon": -36.36667, "name": "São João" }, { "lat": 4.30079, "lon": -74.80754, "name": "Girardot City" }, { "lat": -34.8969, "lon": -60.01909, "name": "Chivilcoy" }, { "lat": 30.35028, "lon": 112.19028, "name": "Jingzhou" } ], "question": "Which location is the geographic outlier among: Caraí, São João, Girardot City, Chivilcoy, Jingzhou?", "ground_truth": { "answer": "Jingzhou", "outlier_distance_km": 14308.8, "second_furthest_km": 6163.8, "clarity_ratio": 2.32, "median_distance_km": 5250.3, "distances_to_centroid": { "Caraí": 2694.6, "São João": 1834.8, "Girardot City": 6163.8, "Chivilcoy": 5250.3, "Jingzhou": 14308.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caraí: (-17.19°, -41.69°)", " São João: (-8.88°, -36.37°)", " Girardot City: (4.30°, -74.81°)", " Chivilcoy: (-34.90°, -60.02°)", " Jingzhou: (30.35°, 112.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jingzhou: 14308.8 km from centroid", " Girardot City: 6163.8 km from centroid", " Chivilcoy: 5250.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jingzhou", "FINAL ANSWER: Jingzhou" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.95672, "lon": -72.79456, "name": "Barrancas" }, { "lat": -22.52306, "lon": -44.10417, "name": "Volta Redonda" }, { "lat": 1.90999, "lon": -75.15931, "name": "Puerto Rico" }, { "lat": -23.4837, "lon": -46.41309, "name": "Jardim Helena" }, { "lat": 16.18673, "lon": 75.69614, "name": "Bagalkot" } ], "question": "Which location is the geographic outlier among: Barrancas, Volta Redonda, Puerto Rico, Jardim Helena, Bagalkot?", "ground_truth": { "answer": "Bagalkot", "outlier_distance_km": 12060.8, "second_furthest_km": 4771.8, "clarity_ratio": 2.53, "median_distance_km": 4729.5, "distances_to_centroid": { "Barrancas": 4729.5, "Volta Redonda": 2464.8, "Puerto Rico": 4771.8, "Jardim Helena": 2685.2, "Bagalkot": 12060.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Barrancas: (10.96°, -72.79°)", " Volta Redonda: (-22.52°, -44.10°)", " Puerto Rico: (1.91°, -75.16°)", " Jardim Helena: (-23.48°, -46.41°)", " Bagalkot: (16.19°, 75.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bagalkot: 12060.8 km from centroid", " Puerto Rico: 4771.8 km from centroid", " Barrancas: 4729.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bagalkot", "FINAL ANSWER: Bagalkot" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.37299, "lon": 14.2069, "name": "Gamboru" }, { "lat": 31.27133, "lon": 30.78617, "name": "Sīdī Sālim" }, { "lat": 7.81514, "lon": 5.06716, "name": "Ijero-Ekiti" }, { "lat": 11.48333, "lon": 37.58333, "name": "T’īs Isat" }, { "lat": 11.55051, "lon": 75.62887, "name": "Palayad" } ], "question": "Which location is the geographic outlier among: Gamboru, Sīdī Sālim, Ijero-Ekiti, T’īs Isat, Palayad?", "ground_truth": { "answer": "Palayad", "outlier_distance_km": 4659.9, "second_furthest_km": 3105.7, "clarity_ratio": 1.5, "median_distance_km": 2012.5, "distances_to_centroid": { "Gamboru": 2012.5, "Sīdī Sālim": 1830.5, "Ijero-Ekiti": 3105.7, "T’īs Isat": 654.9, "Palayad": 4659.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gamboru: (12.37°, 14.21°)", " Sīdī Sālim: (31.27°, 30.79°)", " Ijero-Ekiti: (7.82°, 5.07°)", " T’īs Isat: (11.48°, 37.58°)", " Palayad: (11.55°, 75.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palayad: 4659.9 km from centroid", " Ijero-Ekiti: 3105.7 km from centroid", " Gamboru: 2012.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palayad", "FINAL ANSWER: Palayad" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.78664, "lon": 20.12106, "name": "Montagu" }, { "lat": 7.2, "lon": 38.6, "name": "Shashamane" }, { "lat": -26.12516, "lon": 28.45472, "name": "Etwatwa" }, { "lat": -28.33392, "lon": 23.06541, "name": "Postmasburg" }, { "lat": 10.4242, "lon": 122.9212, "name": "La Carlota" } ], "question": "Which location is the geographic outlier among: Montagu, Shashamane, Etwatwa, Postmasburg, La Carlota?", "ground_truth": { "answer": "La Carlota", "outlier_distance_km": 8842.1, "second_furthest_km": 3449.9, "clarity_ratio": 2.56, "median_distance_km": 2899.6, "distances_to_centroid": { "Montagu": 3449.9, "Shashamane": 2531.4, "Etwatwa": 2315.3, "Postmasburg": 2899.6, "La Carlota": 8842.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Montagu: (-33.79°, 20.12°)", " Shashamane: (7.20°, 38.60°)", " Etwatwa: (-26.13°, 28.45°)", " Postmasburg: (-28.33°, 23.07°)", " La Carlota: (10.42°, 122.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " La Carlota: 8842.1 km from centroid", " Montagu: 3449.9 km from centroid", " Postmasburg: 2899.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: La Carlota", "FINAL ANSWER: La Carlota" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -6.33833, "lon": -47.39917, "name": "Porto Franco" }, { "lat": -1.35028, "lon": -47.57556, "name": "Santa Maria do Pará" }, { "lat": -11.57139, "lon": -77.26722, "name": "Chancay" }, { "lat": -4.25691, "lon": -80.88599, "name": "La Breita" }, { "lat": 10.65, "lon": 36.21667, "name": "Dibate" } ], "question": "Which location is the geographic outlier among: Porto Franco, Santa Maria do Pará, Chancay, La Breita, Dibate?", "ground_truth": { "answer": "Dibate", "outlier_distance_km": 8926.0, "second_furthest_km": 4166.6, "clarity_ratio": 2.14, "median_distance_km": 3866.0, "distances_to_centroid": { "Porto Franco": 611.1, "Santa Maria do Pará": 485.4, "Chancay": 3866.0, "La Breita": 4166.6, "Dibate": 8926.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Porto Franco: (-6.34°, -47.40°)", " Santa Maria do Pará: (-1.35°, -47.58°)", " Chancay: (-11.57°, -77.27°)", " La Breita: (-4.26°, -80.89°)", " Dibate: (10.65°, 36.22°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dibate: 8926.0 km from centroid", " La Breita: 4166.6 km from centroid", " Chancay: 3866.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dibate", "FINAL ANSWER: Dibate" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.52731, "lon": 34.45714, "name": "Homa Bay" }, { "lat": 6.01962, "lon": 6.91729, "name": "Nnewi" }, { "lat": 12.17024, "lon": 6.66412, "name": "Gusau" }, { "lat": -33.30422, "lon": 26.53276, "name": "Grahamstown" }, { "lat": -38.68333, "lon": 176.08333, "name": "Taupo" } ], "question": "Which location is the geographic outlier among: Homa Bay, Nnewi, Gusau, Grahamstown, Taupo?", "ground_truth": { "answer": "Taupo", "outlier_distance_km": 12165.5, "second_furthest_km": 5440.6, "clarity_ratio": 2.24, "median_distance_km": 5138.2, "distances_to_centroid": { "Homa Bay": 2078.5, "Nnewi": 5138.2, "Gusau": 5440.6, "Grahamstown": 3465.8, "Taupo": 12165.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Homa Bay: (-0.53°, 34.46°)", " Nnewi: (6.02°, 6.92°)", " Gusau: (12.17°, 6.66°)", " Grahamstown: (-33.30°, 26.53°)", " Taupo: (-38.68°, 176.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Taupo: 12165.5 km from centroid", " Gusau: 5440.6 km from centroid", " Nnewi: 5138.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Taupo", "FINAL ANSWER: Taupo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.62737, "lon": 37.85803, "name": "Dzerzhinsky" }, { "lat": 53.27096, "lon": 34.32143, "name": "Bryansk" }, { "lat": 41.99362, "lon": 12.72238, "name": "Guidonia Montecelio" }, { "lat": 54.39759, "lon": 53.25116, "name": "Bavly" }, { "lat": -28.28389, "lon": -52.78639, "name": "Carazinho" } ], "question": "Which location is the geographic outlier among: Dzerzhinsky, Bryansk, Guidonia Montecelio, Bavly, Carazinho?", "ground_truth": { "answer": "Carazinho", "outlier_distance_km": 10181.8, "second_furthest_km": 3485.5, "clarity_ratio": 2.92, "median_distance_km": 2748.4, "distances_to_centroid": { "Dzerzhinsky": 2748.4, "Bryansk": 2400.8, "Guidonia Montecelio": 824.3, "Bavly": 3485.5, "Carazinho": 10181.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dzerzhinsky: (55.63°, 37.86°)", " Bryansk: (53.27°, 34.32°)", " Guidonia Montecelio: (41.99°, 12.72°)", " Bavly: (54.40°, 53.25°)", " Carazinho: (-28.28°, -52.79°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carazinho: 10181.8 km from centroid", " Bavly: 3485.5 km from centroid", " Dzerzhinsky: 2748.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carazinho", "FINAL ANSWER: Carazinho" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 15.49574, "lon": 73.82624, "name": "Panjim" }, { "lat": 27.90354, "lon": 80.79754, "name": "Kheri" }, { "lat": 35.54651, "lon": 139.51723, "name": "Aobadai" }, { "lat": 36.52715, "lon": 138.08943, "name": "Chikuma" }, { "lat": -7.07694, "lon": -41.46694, "name": "Picos" } ], "question": "Which location is the geographic outlier among: Panjim, Kheri, Aobadai, Chikuma, Picos?", "ground_truth": { "answer": "Picos", "outlier_distance_km": 13352.9, "second_furthest_km": 6088.2, "clarity_ratio": 2.19, "median_distance_km": 5955.8, "distances_to_centroid": { "Panjim": 824.9, "Kheri": 741.7, "Aobadai": 6088.2, "Chikuma": 5955.8, "Picos": 13352.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Panjim: (15.50°, 73.83°)", " Kheri: (27.90°, 80.80°)", " Aobadai: (35.55°, 139.52°)", " Chikuma: (36.53°, 138.09°)", " Picos: (-7.08°, -41.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Picos: 13352.9 km from centroid", " Aobadai: 6088.2 km from centroid", " Chikuma: 5955.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Picos", "FINAL ANSWER: Picos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.18095, "lon": -96.1429, "name": "Veracruz" }, { "lat": 29.91465, "lon": -90.05396, "name": "Gretna" }, { "lat": 40.62122, "lon": -73.93486, "name": "Flatlands" }, { "lat": 42.88863, "lon": -88.03842, "name": "Franklin" }, { "lat": 44.0038, "lon": 10.10674, "name": "Marina di Massa" } ], "question": "Which location is the geographic outlier among: Veracruz, Gretna, Flatlands, Franklin, Marina di Massa?", "ground_truth": { "answer": "Marina di Massa", "outlier_distance_km": 6475.1, "second_furthest_km": 3323.4, "clarity_ratio": 1.95, "median_distance_km": 2180.6, "distances_to_centroid": { "Veracruz": 3323.4, "Gretna": 2180.6, "Flatlands": 808.5, "Franklin": 1946.2, "Marina di Massa": 6475.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Veracruz: (19.18°, -96.14°)", " Gretna: (29.91°, -90.05°)", " Flatlands: (40.62°, -73.93°)", " Franklin: (42.89°, -88.04°)", " Marina di Massa: (44.00°, 10.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Marina di Massa: 6475.1 km from centroid", " Veracruz: 3323.4 km from centroid", " Gretna: 2180.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Marina di Massa", "FINAL ANSWER: Marina di Massa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.26638, "lon": -6.94004, "name": "Huelva" }, { "lat": 54.00734, "lon": 37.50647, "name": "Shchëkino" }, { "lat": 40.15913, "lon": -3.62103, "name": "Ciempozuelos" }, { "lat": 48.47629, "lon": 8.93528, "name": "Rottenburg" }, { "lat": -27.31564, "lon": 25.99497, "name": "Makwassie" } ], "question": "Which location is the geographic outlier among: Huelva, Shchëkino, Ciempozuelos, Rottenburg, Makwassie?", "ground_truth": { "answer": "Makwassie", "outlier_distance_km": 6591.6, "second_furthest_km": 3295.0, "clarity_ratio": 2.0, "median_distance_km": 2017.9, "distances_to_centroid": { "Huelva": 1929.6, "Shchëkino": 3295.0, "Ciempozuelos": 1799.3, "Rottenburg": 2017.9, "Makwassie": 6591.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Huelva: (37.27°, -6.94°)", " Shchëkino: (54.01°, 37.51°)", " Ciempozuelos: (40.16°, -3.62°)", " Rottenburg: (48.48°, 8.94°)", " Makwassie: (-27.32°, 25.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Makwassie: 6591.6 km from centroid", " Shchëkino: 3295.0 km from centroid", " Rottenburg: 2017.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Makwassie", "FINAL ANSWER: Makwassie" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.85, "lon": 37.48333, "name": "Levoberezhnyy" }, { "lat": 57.00816, "lon": 61.46344, "name": "Asbest" }, { "lat": 52.85435, "lon": 11.1525, "name": "Salzwedel" }, { "lat": 56.50718, "lon": 56.07707, "name": "Chernushka" }, { "lat": 9.82564, "lon": 78.25795, "name": "Tiruppuvanam" } ], "question": "Which location is the geographic outlier among: Levoberezhnyy, Asbest, Salzwedel, Chernushka, Tiruppuvanam?", "ground_truth": { "answer": "Tiruppuvanam", "outlier_distance_km": 4926.2, "second_furthest_km": 2775.4, "clarity_ratio": 1.77, "median_distance_km": 1458.0, "distances_to_centroid": { "Levoberezhnyy": 1313.8, "Asbest": 1458.0, "Salzwedel": 2775.4, "Chernushka": 1226.8, "Tiruppuvanam": 4926.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Levoberezhnyy: (55.85°, 37.48°)", " Asbest: (57.01°, 61.46°)", " Salzwedel: (52.85°, 11.15°)", " Chernushka: (56.51°, 56.08°)", " Tiruppuvanam: (9.83°, 78.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tiruppuvanam: 4926.2 km from centroid", " Salzwedel: 2775.4 km from centroid", " Asbest: 1458.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tiruppuvanam", "FINAL ANSWER: Tiruppuvanam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 7.61667, "lon": 39.5, "name": "Gobēsa" }, { "lat": 6.41919, "lon": 45.85251, "name": "Raqo" }, { "lat": -26.12516, "lon": 28.45472, "name": "Etwatwa" }, { "lat": 5.10535, "lon": -1.2466, "name": "Cape Coast" }, { "lat": -46.4, "lon": 168.35, "name": "Invercargill" } ], "question": "Which location is the geographic outlier among: Gobēsa, Raqo, Etwatwa, Cape Coast, Invercargill?", "ground_truth": { "answer": "Invercargill", "outlier_distance_km": 10783.8, "second_furthest_km": 6594.6, "clarity_ratio": 1.64, "median_distance_km": 3379.8, "distances_to_centroid": { "Gobēsa": 2747.1, "Raqo": 2218.4, "Etwatwa": 3379.8, "Cape Coast": 6594.6, "Invercargill": 10783.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gobēsa: (7.62°, 39.50°)", " Raqo: (6.42°, 45.85°)", " Etwatwa: (-26.13°, 28.45°)", " Cape Coast: (5.11°, -1.25°)", " Invercargill: (-46.40°, 168.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Invercargill: 10783.8 km from centroid", " Cape Coast: 6594.6 km from centroid", " Etwatwa: 3379.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Invercargill", "FINAL ANSWER: Invercargill" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.22886, "lon": 31.48149, "name": "Al-'Ubūr" }, { "lat": 11.01537, "lon": 6.78036, "name": "Sofo-Birnin-Gwari" }, { "lat": 5.18194, "lon": 7.71481, "name": "Ikot Ekpene" }, { "lat": 7.28889, "lon": 36.24167, "name": "Bonga" }, { "lat": 39.88423, "lon": -82.7535, "name": "Pickerington" } ], "question": "Which location is the geographic outlier among: Al-'Ubūr, Sofo-Birnin-Gwari, Ikot Ekpene, Bonga, Pickerington?", "ground_truth": { "answer": "Pickerington", "outlier_distance_km": 8074.2, "second_furthest_km": 4127.6, "clarity_ratio": 1.96, "median_distance_km": 3428.7, "distances_to_centroid": { "Al-'Ubūr": 3428.7, "Sofo-Birnin-Gwari": 1131.7, "Ikot Ekpene": 1728.1, "Bonga": 4127.6, "Pickerington": 8074.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Al-'Ubūr: (30.23°, 31.48°)", " Sofo-Birnin-Gwari: (11.02°, 6.78°)", " Ikot Ekpene: (5.18°, 7.71°)", " Bonga: (7.29°, 36.24°)", " Pickerington: (39.88°, -82.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pickerington: 8074.2 km from centroid", " Bonga: 4127.6 km from centroid", " Al-'Ubūr: 3428.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pickerington", "FINAL ANSWER: Pickerington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.79025, "lon": 10.95509, "name": "Blankenburg" }, { "lat": 50.78773, "lon": -0.97697, "name": "South Hayling" }, { "lat": 52.5876, "lon": 39.55151, "name": "Lipetsk" }, { "lat": 39.08077, "lon": 17.12764, "name": "Crotone" }, { "lat": 8.58165, "lon": 76.92242, "name": "Uliyazhathura" } ], "question": "Which location is the geographic outlier among: Blankenburg, South Hayling, Lipetsk, Crotone, Uliyazhathura?", "ground_truth": { "answer": "Uliyazhathura", "outlier_distance_km": 5926.5, "second_furthest_km": 2548.3, "clarity_ratio": 2.33, "median_distance_km": 1842.4, "distances_to_centroid": { "Blankenburg": 1842.4, "South Hayling": 2548.3, "Lipetsk": 1568.7, "Crotone": 1002.6, "Uliyazhathura": 5926.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Blankenburg: (51.79°, 10.96°)", " South Hayling: (50.79°, -0.98°)", " Lipetsk: (52.59°, 39.55°)", " Crotone: (39.08°, 17.13°)", " Uliyazhathura: (8.58°, 76.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Uliyazhathura: 5926.5 km from centroid", " South Hayling: 2548.3 km from centroid", " Blankenburg: 1842.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Uliyazhathura", "FINAL ANSWER: Uliyazhathura" ] }, { "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": -9.29532, "lon": -75.99574, "name": "Tingo María" }, { "lat": -9.56722, "lon": -48.39167, "name": "Miracema do Tocantins" }, { "lat": -2.99, "lon": -65.10833, "name": "Uarini" }, { "lat": 8.27515, "lon": -76.37641, "name": "San Pedro de Urabá" }, { "lat": 41.90003, "lon": -87.6345, "name": "Near North Side" } ], "question": "Which location is the geographic outlier among: Tingo María, Miracema do Tocantins, Uarini, San Pedro de Urabá, Near North Side?", "ground_truth": { "answer": "Near North Side", "outlier_distance_km": 4363.5, "second_furthest_km": 2996.5, "clarity_ratio": 1.46, "median_distance_km": 1763.9, "distances_to_centroid": { "Tingo María": 1763.9, "Miracema do Tocantins": 2996.5, "Uarini": 1145.4, "San Pedro de Urabá": 690.3, "Near North Side": 4363.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tingo María: (-9.30°, -76.00°)", " Miracema do Tocantins: (-9.57°, -48.39°)", " Uarini: (-2.99°, -65.11°)", " San Pedro de Urabá: (8.28°, -76.38°)", " Near North Side: (41.90°, -87.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Near North Side: 4363.5 km from centroid", " Miracema do Tocantins: 2996.5 km from centroid", " Tingo María: 1763.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Near North Side", "FINAL ANSWER: Near North Side" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.31111, "lon": -46.04889, "name": "São Gotardo" }, { "lat": 9.23648, "lon": -75.8135, "name": "Lorica" }, { "lat": -24.00583, "lon": -46.40278, "name": "Praia Grande" }, { "lat": -22.76417, "lon": -43.39944, "name": "Belford Roxo" }, { "lat": 40.38524, "lon": -3.63726, "name": "Palomeras Sureste" } ], "question": "Which location is the geographic outlier among: São Gotardo, Lorica, Praia Grande, Belford Roxo, Palomeras Sureste?", "ground_truth": { "answer": "Palomeras Sureste", "outlier_distance_km": 6295.6, "second_furthest_km": 3887.7, "clarity_ratio": 1.62, "median_distance_km": 2331.1, "distances_to_centroid": { "São Gotardo": 1810.6, "Lorica": 3887.7, "Praia Grande": 2331.1, "Belford Roxo": 2165.5, "Palomeras Sureste": 6295.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Gotardo: (-19.31°, -46.05°)", " Lorica: (9.24°, -75.81°)", " Praia Grande: (-24.01°, -46.40°)", " Belford Roxo: (-22.76°, -43.40°)", " Palomeras Sureste: (40.39°, -3.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palomeras Sureste: 6295.6 km from centroid", " Lorica: 3887.7 km from centroid", " Praia Grande: 2331.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palomeras Sureste", "FINAL ANSWER: Palomeras Sureste" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.96669, "lon": 8.70632, "name": "Ikom" }, { "lat": 10.89469, "lon": -1.09083, "name": "Navrongo" }, { "lat": 27.04514, "lon": 31.31845, "name": "Abū Tīj" }, { "lat": 6.6584, "lon": 8.79923, "name": "Ogoja" }, { "lat": 13.9, "lon": 99.76667, "name": "Tha Maka" } ], "question": "Which location is the geographic outlier among: Ikom, Navrongo, Abū Tīj, Ogoja, Tha Maka?", "ground_truth": { "answer": "Tha Maka", "outlier_distance_km": 7571.6, "second_furthest_km": 3334.0, "clarity_ratio": 2.27, "median_distance_km": 2405.7, "distances_to_centroid": { "Ikom": 2405.7, "Navrongo": 3334.0, "Abū Tīj": 1585.0, "Ogoja": 2370.5, "Tha Maka": 7571.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ikom: (5.97°, 8.71°)", " Navrongo: (10.89°, -1.09°)", " Abū Tīj: (27.05°, 31.32°)", " Ogoja: (6.66°, 8.80°)", " Tha Maka: (13.90°, 99.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tha Maka: 7571.6 km from centroid", " Navrongo: 3334.0 km from centroid", " Ikom: 2405.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tha Maka", "FINAL ANSWER: Tha Maka" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 27.0631, "lon": 73.82304, "name": "Mūndwa" }, { "lat": 24.59916, "lon": 74.86261, "name": "Jāwad" }, { "lat": 8.88113, "lon": 76.58469, "name": "Kollam" }, { "lat": 27.55607, "lon": 77.78972, "name": "Rāya" }, { "lat": -22.45389, "lon": -43.46889, "name": "Miguel Pereira" } ], "question": "Which location is the geographic outlier among: Mūndwa, Jāwad, Kollam, Rāya, Miguel Pereira?", "ground_truth": { "answer": "Miguel Pereira", "outlier_distance_km": 11104.0, "second_furthest_km": 3127.2, "clarity_ratio": 3.55, "median_distance_km": 2754.8, "distances_to_centroid": { "Mūndwa": 2754.8, "Jāwad": 2724.1, "Kollam": 2732.0, "Rāya": 3127.2, "Miguel Pereira": 11104.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mūndwa: (27.06°, 73.82°)", " Jāwad: (24.60°, 74.86°)", " Kollam: (8.88°, 76.58°)", " Rāya: (27.56°, 77.79°)", " Miguel Pereira: (-22.45°, -43.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Miguel Pereira: 11104.0 km from centroid", " Rāya: 3127.2 km from centroid", " Mūndwa: 2754.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Miguel Pereira", "FINAL ANSWER: Miguel Pereira" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.47418, "lon": 100.12218, "name": "Suphan Buri" }, { "lat": 17.24767, "lon": 80.14368, "name": "Khammam" }, { "lat": -7.47056, "lon": 110.21778, "name": "Magelang" }, { "lat": 35.76666, "lon": 139.77137, "name": "Ōgi" }, { "lat": 6.41222, "lon": 4.0947, "name": "Lekki" } ], "question": "Which location is the geographic outlier among: Suphan Buri, Khammam, Magelang, Ōgi, Lekki?", "ground_truth": { "answer": "Lekki", "outlier_distance_km": 9065.7, "second_furthest_km": 5822.5, "clarity_ratio": 1.56, "median_distance_km": 3460.5, "distances_to_centroid": { "Suphan Buri": 1436.4, "Khammam": 845.2, "Magelang": 3460.5, "Ōgi": 5822.5, "Lekki": 9065.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Suphan Buri: (14.47°, 100.12°)", " Khammam: (17.25°, 80.14°)", " Magelang: (-7.47°, 110.22°)", " Ōgi: (35.77°, 139.77°)", " Lekki: (6.41°, 4.09°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lekki: 9065.7 km from centroid", " Ōgi: 5822.5 km from centroid", " Magelang: 3460.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lekki", "FINAL ANSWER: Lekki" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.30337, "lon": -0.61383, "name": "Mayenne" }, { "lat": 51.09954, "lon": 14.66738, "name": "Löbau" }, { "lat": 48.65412, "lon": 2.39343, "name": "Grigny" }, { "lat": 48.47629, "lon": 8.93528, "name": "Rottenburg" }, { "lat": 23.25469, "lon": 77.40289, "name": "Bhopal" } ], "question": "Which location is the geographic outlier among: Mayenne, Löbau, Grigny, Rottenburg, Bhopal?", "ground_truth": { "answer": "Bhopal", "outlier_distance_km": 5618.0, "second_furthest_km": 1695.2, "clarity_ratio": 3.31, "median_distance_km": 1485.3, "distances_to_centroid": { "Mayenne": 1695.2, "Löbau": 908.3, "Grigny": 1485.3, "Rottenburg": 1024.1, "Bhopal": 5618.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mayenne: (48.30°, -0.61°)", " Löbau: (51.10°, 14.67°)", " Grigny: (48.65°, 2.39°)", " Rottenburg: (48.48°, 8.94°)", " Bhopal: (23.25°, 77.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bhopal: 5618.0 km from centroid", " Mayenne: 1695.2 km from centroid", " Grigny: 1485.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bhopal", "FINAL ANSWER: Bhopal" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -4.57194, "lon": -44.62083, "name": "Trizidela do Vale" }, { "lat": -22.9527, "lon": -46.54418, "name": "Bragança Paulista" }, { "lat": -7.23056, "lon": -35.88111, "name": "Campina Grande" }, { "lat": 5.69188, "lon": -76.65835, "name": "Quibdó" }, { "lat": 26.65817, "lon": 31.67137, "name": "Sāqultah" } ], "question": "Which location is the geographic outlier among: Trizidela do Vale, Bragança Paulista, Campina Grande, Quibdó, Sāqultah?", "ground_truth": { "answer": "Sāqultah", "outlier_distance_km": 7670.8, "second_furthest_km": 4740.7, "clarity_ratio": 1.62, "median_distance_km": 2822.1, "distances_to_centroid": { "Trizidela do Vale": 1222.2, "Bragança Paulista": 2822.1, "Campina Grande": 768.1, "Quibdó": 4740.7, "Sāqultah": 7670.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Trizidela do Vale: (-4.57°, -44.62°)", " Bragança Paulista: (-22.95°, -46.54°)", " Campina Grande: (-7.23°, -35.88°)", " Quibdó: (5.69°, -76.66°)", " Sāqultah: (26.66°, 31.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sāqultah: 7670.8 km from centroid", " Quibdó: 4740.7 km from centroid", " Bragança Paulista: 2822.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sāqultah", "FINAL ANSWER: Sāqultah" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.00954, "lon": -74.17292, "name": "Wyckoff" }, { "lat": 30.00354, "lon": -91.81873, "name": "New Iberia" }, { "lat": 16.7075, "lon": -93.01216, "name": "Chiapa de Corzo" }, { "lat": 25.62177, "lon": -80.32477, "name": "Palmetto Bay" }, { "lat": 14.54519, "lon": 77.10552, "name": "Kalyandurg" } ], "question": "Which location is the geographic outlier among: Wyckoff, New Iberia, Chiapa de Corzo, Palmetto Bay, Kalyandurg?", "ground_truth": { "answer": "Kalyandurg", "outlier_distance_km": 12963.6, "second_furthest_km": 4303.7, "clarity_ratio": 3.01, "median_distance_km": 3885.5, "distances_to_centroid": { "Wyckoff": 2636.5, "New Iberia": 3885.5, "Chiapa de Corzo": 4303.7, "Palmetto Bay": 2790.6, "Kalyandurg": 12963.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wyckoff: (41.01°, -74.17°)", " New Iberia: (30.00°, -91.82°)", " Chiapa de Corzo: (16.71°, -93.01°)", " Palmetto Bay: (25.62°, -80.32°)", " Kalyandurg: (14.55°, 77.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kalyandurg: 12963.6 km from centroid", " Chiapa de Corzo: 4303.7 km from centroid", " New Iberia: 3885.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kalyandurg", "FINAL ANSWER: Kalyandurg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.37329, "lon": -119.01871, "name": "Bakersfield" }, { "lat": 42.50982, "lon": -70.94949, "name": "South Peabody" }, { "lat": 44.05207, "lon": -123.08675, "name": "Eugene" }, { "lat": 47.03426, "lon": -122.82319, "name": "Lacey" }, { "lat": -26.33172, "lon": 26.32065, "name": "Coligny" } ], "question": "Which location is the geographic outlier among: Bakersfield, South Peabody, Eugene, Lacey, Coligny?", "ground_truth": { "answer": "Coligny", "outlier_distance_km": 13039.9, "second_furthest_km": 4078.4, "clarity_ratio": 3.2, "median_distance_km": 4021.0, "distances_to_centroid": { "Bakersfield": 3561.2, "South Peabody": 1840.7, "Eugene": 4021.0, "Lacey": 4078.4, "Coligny": 13039.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bakersfield: (35.37°, -119.02°)", " South Peabody: (42.51°, -70.95°)", " Eugene: (44.05°, -123.09°)", " Lacey: (47.03°, -122.82°)", " Coligny: (-26.33°, 26.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coligny: 13039.9 km from centroid", " Lacey: 4078.4 km from centroid", " Eugene: 4021.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coligny", "FINAL ANSWER: Coligny" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.8162, "lon": 2.31393, "name": "Montrouge" }, { "lat": 40.46396, "lon": -3.63625, "name": "Canillas" }, { "lat": 53.26023, "lon": -2.12564, "name": "Macclesfield" }, { "lat": 43.18493, "lon": -2.47158, "name": "Eibar" }, { "lat": 35.74788, "lon": -95.36969, "name": "Muskogee" } ], "question": "Which location is the geographic outlier among: Montrouge, Canillas, Macclesfield, Eibar, Muskogee?", "ground_truth": { "answer": "Muskogee", "outlier_distance_km": 6241.9, "second_furthest_km": 1790.1, "clarity_ratio": 3.49, "median_distance_km": 1653.2, "distances_to_centroid": { "Montrouge": 1790.1, "Canillas": 1427.3, "Macclesfield": 1653.2, "Eibar": 1431.4, "Muskogee": 6241.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Montrouge: (48.82°, 2.31°)", " Canillas: (40.46°, -3.64°)", " Macclesfield: (53.26°, -2.13°)", " Eibar: (43.18°, -2.47°)", " Muskogee: (35.75°, -95.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Muskogee: 6241.9 km from centroid", " Montrouge: 1790.1 km from centroid", " Macclesfield: 1653.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Muskogee", "FINAL ANSWER: Muskogee" ] }, { "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": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" }, { "lat": -35.02692, "lon": 117.88369, "name": "Albany" }, { "lat": -28.00029, "lon": 153.43088, "name": "Gold Coast" }, { "lat": -27.49325, "lon": 153.05826, "name": "Coorparoo" }, { "lat": 10.98133, "lon": 8.05749, "name": "Soba" } ], "question": "Which location is the geographic outlier among: Bracken Ridge, Albany, Gold Coast, Coorparoo, Soba?", "ground_truth": { "answer": "Soba", "outlier_distance_km": 12405.6, "second_furthest_km": 3730.5, "clarity_ratio": 3.33, "median_distance_km": 3691.0, "distances_to_centroid": { "Bracken Ridge": 3687.5, "Albany": 1520.4, "Gold Coast": 3730.5, "Coorparoo": 3691.0, "Soba": 12405.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bracken Ridge: (-27.32°, 153.03°)", " Albany: (-35.03°, 117.88°)", " Gold Coast: (-28.00°, 153.43°)", " Coorparoo: (-27.49°, 153.06°)", " Soba: (10.98°, 8.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Soba: 12405.6 km from centroid", " Gold Coast: 3730.5 km from centroid", " Coorparoo: 3691.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Soba", "FINAL ANSWER: Soba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.61082, "lon": -58.481, "name": "Villa Santa Rita" }, { "lat": -21.12, "lon": -42.94278, "name": "Ubá" }, { "lat": -27.05452, "lon": -65.40189, "name": "Famaillá" }, { "lat": -8.28333, "lon": -35.97611, "name": "Caruaru" }, { "lat": 40.753, "lon": -73.2602, "name": "North Bay Shore" } ], "question": "Which location is the geographic outlier among: Villa Santa Rita, Ubá, Famaillá, Caruaru, North Bay Shore?", "ground_truth": { "answer": "North Bay Shore", "outlier_distance_km": 5946.6, "second_furthest_km": 2749.7, "clarity_ratio": 2.16, "median_distance_km": 2170.6, "distances_to_centroid": { "Villa Santa Rita": 2749.7, "Ubá": 1797.6, "Famaillá": 2170.6, "Caruaru": 2120.5, "North Bay Shore": 5946.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Villa Santa Rita: (-34.61°, -58.48°)", " Ubá: (-21.12°, -42.94°)", " Famaillá: (-27.05°, -65.40°)", " Caruaru: (-8.28°, -35.98°)", " North Bay Shore: (40.75°, -73.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Bay Shore: 5946.6 km from centroid", " Villa Santa Rita: 2749.7 km from centroid", " Famaillá: 2170.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Bay Shore", "FINAL ANSWER: North Bay Shore" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.2173, "lon": -80.22588, "name": "North Lauderdale" }, { "lat": 32.47098, "lon": -85.00077, "name": "Phenix City" }, { "lat": 39.83665, "lon": -105.0372, "name": "Westminster" }, { "lat": 42.29732, "lon": -71.43701, "name": "Framingham Center" }, { "lat": 50.17058, "lon": 12.13054, "name": "Selb" } ], "question": "Which location is the geographic outlier among: North Lauderdale, Phenix City, Westminster, Framingham Center, Selb?", "ground_truth": { "answer": "Selb", "outlier_distance_km": 6072.2, "second_furthest_km": 3357.9, "clarity_ratio": 1.81, "median_distance_km": 1889.7, "distances_to_centroid": { "North Lauderdale": 1889.7, "Phenix City": 1840.6, "Westminster": 3357.9, "Framingham Center": 653.5, "Selb": 6072.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " North Lauderdale: (26.22°, -80.23°)", " Phenix City: (32.47°, -85.00°)", " Westminster: (39.84°, -105.04°)", " Framingham Center: (42.30°, -71.44°)", " Selb: (50.17°, 12.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Selb: 6072.2 km from centroid", " Westminster: 3357.9 km from centroid", " North Lauderdale: 1889.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Selb", "FINAL ANSWER: Selb" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.9677, "lon": 151.10149, "name": "Hurstville" }, { "lat": -44.39672, "lon": 171.25364, "name": "Timaru" }, { "lat": -41.05584, "lon": 145.90375, "name": "Burnie" }, { "lat": -31.89578, "lon": 115.76431, "name": "Scarborough" }, { "lat": 10.85953, "lon": -74.77386, "name": "Malambo" } ], "question": "Which location is the geographic outlier among: Hurstville, Timaru, Burnie, Scarborough, Malambo?", "ground_truth": { "answer": "Malambo", "outlier_distance_km": 18066.9, "second_furthest_km": 6288.3, "clarity_ratio": 2.87, "median_distance_km": 4693.7, "distances_to_centroid": { "Hurstville": 4693.7, "Timaru": 6288.3, "Burnie": 4232.1, "Scarborough": 1403.9, "Malambo": 18066.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hurstville: (-33.97°, 151.10°)", " Timaru: (-44.40°, 171.25°)", " Burnie: (-41.06°, 145.90°)", " Scarborough: (-31.90°, 115.76°)", " Malambo: (10.86°, -74.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Malambo: 18066.9 km from centroid", " Timaru: 6288.3 km from centroid", " Hurstville: 4693.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Malambo", "FINAL ANSWER: Malambo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.60623, "lon": 135.04429, "name": "Kyōtango" }, { "lat": 34.50355, "lon": 109.50891, "name": "Weinan" }, { "lat": 45.40944, "lon": 141.67389, "name": "Wakkanai" }, { "lat": 38.04139, "lon": 114.47861, "name": "Shijiazhuang" }, { "lat": 53.14515, "lon": -2.36251, "name": "Sandbach" } ], "question": "Which location is the geographic outlier among: Kyōtango, Weinan, Wakkanai, Shijiazhuang, Sandbach?", "ground_truth": { "answer": "Sandbach", "outlier_distance_km": 7142.7, "second_furthest_km": 3386.0, "clarity_ratio": 2.11, "median_distance_km": 3122.3, "distances_to_centroid": { "Kyōtango": 3122.3, "Weinan": 1148.9, "Wakkanai": 3386.0, "Shijiazhuang": 1317.4, "Sandbach": 7142.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kyōtango: (35.61°, 135.04°)", " Weinan: (34.50°, 109.51°)", " Wakkanai: (45.41°, 141.67°)", " Shijiazhuang: (38.04°, 114.48°)", " Sandbach: (53.15°, -2.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sandbach: 7142.7 km from centroid", " Wakkanai: 3386.0 km from centroid", " Kyōtango: 3122.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sandbach", "FINAL ANSWER: Sandbach" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.41222, "lon": -42.19667, "name": "Miracema" }, { "lat": -37.71893, "lon": -72.24099, "name": "Mulchén" }, { "lat": -12.36333, "lon": -44.97333, "name": "São Desidério" }, { "lat": -21.83861, "lon": -44.80833, "name": "Cruzília" }, { "lat": 16.68393, "lon": -93.71814, "name": "Cintalapa de Figueroa" } ], "question": "Which location is the geographic outlier among: Miracema, Mulchén, São Desidério, Cruzília, Cintalapa de Figueroa?", "ground_truth": { "answer": "Cintalapa de Figueroa", "outlier_distance_km": 5166.6, "second_furthest_km": 2783.2, "clarity_ratio": 1.86, "median_distance_km": 1954.1, "distances_to_centroid": { "Miracema": 1954.1, "Mulchén": 2783.2, "São Desidério": 1611.5, "Cruzília": 1716.2, "Cintalapa de Figueroa": 5166.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Miracema: (-21.41°, -42.20°)", " Mulchén: (-37.72°, -72.24°)", " São Desidério: (-12.36°, -44.97°)", " Cruzília: (-21.84°, -44.81°)", " Cintalapa de Figueroa: (16.68°, -93.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cintalapa de Figueroa: 5166.6 km from centroid", " Mulchén: 2783.2 km from centroid", " Miracema: 1954.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cintalapa de Figueroa", "FINAL ANSWER: Cintalapa de Figueroa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.07222, "lon": 75.99607, "name": "Dirba" }, { "lat": 21.0, "lon": 105.83333, "name": "Trung Phụng" }, { "lat": 10.95818, "lon": 76.92013, "name": "Rāmachettipālaiyam" }, { "lat": 13.7775, "lon": 100.51977, "name": "Dusit" }, { "lat": -30.20672, "lon": 30.79641, "name": "eMkhomazi" } ], "question": "Which location is the geographic outlier among: Dirba, Trung Phụng, Rāmachettipālaiyam, Dusit, eMkhomazi?", "ground_truth": { "answer": "eMkhomazi", "outlier_distance_km": 6672.9, "second_furthest_km": 3258.4, "clarity_ratio": 2.05, "median_distance_km": 2505.5, "distances_to_centroid": { "Dirba": 2339.2, "Trung Phụng": 3258.4, "Rāmachettipālaiyam": 236.8, "Dusit": 2505.5, "eMkhomazi": 6672.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dirba: (30.07°, 76.00°)", " Trung Phụng: (21.00°, 105.83°)", " Rāmachettipālaiyam: (10.96°, 76.92°)", " Dusit: (13.78°, 100.52°)", " eMkhomazi: (-30.21°, 30.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " eMkhomazi: 6672.9 km from centroid", " Trung Phụng: 3258.4 km from centroid", " Dusit: 2505.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: eMkhomazi", "FINAL ANSWER: eMkhomazi" ] }, { "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": -26.65682, "lon": 153.07955, "name": "Sunshine Coast" }, { "lat": -37.83834, "lon": 144.99149, "name": "South Yarra" }, { "lat": -36.9682, "lon": 174.84019, "name": "Papatoetoe" }, { "lat": -38.19528, "lon": 146.5415, "name": "Traralgon" }, { "lat": 35.49527, "lon": 139.44279, "name": "Minamirinkan" } ], "question": "Which location is the geographic outlier among: Sunshine Coast, South Yarra, Papatoetoe, Traralgon, Minamirinkan?", "ground_truth": { "answer": "Minamirinkan", "outlier_distance_km": 6397.0, "second_furthest_km": 2859.8, "clarity_ratio": 2.24, "median_distance_km": 2000.6, "distances_to_centroid": { "Sunshine Coast": 661.0, "South Yarra": 2000.6, "Papatoetoe": 2859.8, "Traralgon": 1995.1, "Minamirinkan": 6397.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunshine Coast: (-26.66°, 153.08°)", " South Yarra: (-37.84°, 144.99°)", " Papatoetoe: (-36.97°, 174.84°)", " Traralgon: (-38.20°, 146.54°)", " Minamirinkan: (35.50°, 139.44°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Minamirinkan: 6397.0 km from centroid", " Papatoetoe: 2859.8 km from centroid", " South Yarra: 2000.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Minamirinkan", "FINAL ANSWER: Minamirinkan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.63333, "lon": -41.03333, "name": "Vera Cruz" }, { "lat": -4.39143, "lon": -59.58864, "name": "Borba" }, { "lat": -3.46056, "lon": -40.21222, "name": "Santana do Acaraú" }, { "lat": -16.36314, "lon": -72.1921, "name": "El Pedregal" }, { "lat": 7.65649, "lon": 4.92235, "name": "Efon-Alaaye" } ], "question": "Which location is the geographic outlier among: Vera Cruz, Borba, Santana do Acaraú, El Pedregal, Efon-Alaaye?", "ground_truth": { "answer": "Efon-Alaaye", "outlier_distance_km": 5376.2, "second_furthest_km": 3528.7, "clarity_ratio": 1.52, "median_distance_km": 1996.4, "distances_to_centroid": { "Vera Cruz": 758.3, "Borba": 1996.4, "Santana do Acaraú": 307.0, "El Pedregal": 3528.7, "Efon-Alaaye": 5376.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vera Cruz: (-12.63°, -41.03°)", " Borba: (-4.39°, -59.59°)", " Santana do Acaraú: (-3.46°, -40.21°)", " El Pedregal: (-16.36°, -72.19°)", " Efon-Alaaye: (7.66°, 4.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Efon-Alaaye: 5376.2 km from centroid", " El Pedregal: 3528.7 km from centroid", " Borba: 1996.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Efon-Alaaye", "FINAL ANSWER: Efon-Alaaye" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.54333, "lon": 153.20287, "name": "Capalaba" }, { "lat": -37.68333, "lon": 145.01667, "name": "Thomastown" }, { "lat": -37.81992, "lon": 145.0358, "name": "Hawthorn" }, { "lat": -36.99282, "lon": 174.87986, "name": "Manukau City" }, { "lat": 53.39808, "lon": 59.0066, "name": "Magnitogorsk" } ], "question": "Which location is the geographic outlier among: Capalaba, Thomastown, Hawthorn, Manukau City, Magnitogorsk?", "ground_truth": { "answer": "Magnitogorsk", "outlier_distance_km": 10680.8, "second_furthest_km": 4428.8, "clarity_ratio": 2.41, "median_distance_km": 2463.9, "distances_to_centroid": { "Capalaba": 2147.1, "Thomastown": 2449.4, "Hawthorn": 2463.9, "Manukau City": 4428.8, "Magnitogorsk": 10680.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Capalaba: (-27.54°, 153.20°)", " Thomastown: (-37.68°, 145.02°)", " Hawthorn: (-37.82°, 145.04°)", " Manukau City: (-36.99°, 174.88°)", " Magnitogorsk: (53.40°, 59.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Magnitogorsk: 10680.8 km from centroid", " Manukau City: 4428.8 km from centroid", " Hawthorn: 2463.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Magnitogorsk", "FINAL ANSWER: Magnitogorsk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.0775, "lon": 4.54444, "name": "Benthuizen" }, { "lat": 41.27733, "lon": 16.41011, "name": "Trani" }, { "lat": 50.80502, "lon": 23.89251, "name": "Hrubieszów" }, { "lat": 41.37263, "lon": 2.1546, "name": "Sants-Montjuïc" }, { "lat": -33.8, "lon": 151.18333, "name": "Chatswood" } ], "question": "Which location is the geographic outlier among: Benthuizen, Trani, Hrubieszów, Sants-Montjuïc, Chatswood?", "ground_truth": { "answer": "Chatswood", "outlier_distance_km": 13675.3, "second_furthest_km": 3740.8, "clarity_ratio": 3.66, "median_distance_km": 3560.8, "distances_to_centroid": { "Benthuizen": 3740.8, "Trani": 2410.2, "Hrubieszów": 2622.6, "Sants-Montjuïc": 3560.8, "Chatswood": 13675.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Benthuizen: (52.08°, 4.54°)", " Trani: (41.28°, 16.41°)", " Hrubieszów: (50.81°, 23.89°)", " Sants-Montjuïc: (41.37°, 2.15°)", " Chatswood: (-33.80°, 151.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chatswood: 13675.3 km from centroid", " Benthuizen: 3740.8 km from centroid", " Sants-Montjuïc: 3560.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chatswood", "FINAL ANSWER: Chatswood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.88461, "lon": 145.29539, "name": "Ferntree Gully" }, { "lat": -32.73308, "lon": 151.5574, "name": "Maitland" }, { "lat": -37.99116, "lon": 145.17385, "name": "Keysborough" }, { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -3.175, "lon": -41.86694, "name": "Buriti dos Lopes" } ], "question": "Which location is the geographic outlier among: Ferntree Gully, Maitland, Keysborough, Epping, Buriti dos Lopes?", "ground_truth": { "answer": "Buriti dos Lopes", "outlier_distance_km": 15210.4, "second_furthest_km": 4024.9, "clarity_ratio": 3.78, "median_distance_km": 3439.5, "distances_to_centroid": { "Ferntree Gully": 3439.5, "Maitland": 4024.9, "Keysborough": 3429.7, "Epping": 3414.7, "Buriti dos Lopes": 15210.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ferntree Gully: (-37.88°, 145.30°)", " Maitland: (-32.73°, 151.56°)", " Keysborough: (-37.99°, 145.17°)", " Epping: (-37.65°, 145.03°)", " Buriti dos Lopes: (-3.17°, -41.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Buriti dos Lopes: 15210.4 km from centroid", " Maitland: 4024.9 km from centroid", " Ferntree Gully: 3439.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Buriti dos Lopes", "FINAL ANSWER: Buriti dos Lopes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.05701, "lon": 103.83987, "name": "Lanzhou" }, { "lat": 24.0214, "lon": 76.3764, "name": "Jirapur" }, { "lat": 43.6475, "lon": 111.97667, "name": "Erenhot" }, { "lat": 24.9319, "lon": 98.6701, "name": "Mangbang" }, { "lat": 44.40854, "lon": 0.70415, "name": "Villeneuve-sur-Lot" } ], "question": "Which location is the geographic outlier among: Lanzhou, Jirapur, Erenhot, Mangbang, Villeneuve-sur-Lot?", "ground_truth": { "answer": "Villeneuve-sur-Lot", "outlier_distance_km": 6496.3, "second_furthest_km": 3047.9, "clarity_ratio": 2.13, "median_distance_km": 2314.5, "distances_to_centroid": { "Lanzhou": 2314.5, "Jirapur": 1192.6, "Erenhot": 3047.9, "Mangbang": 2234.0, "Villeneuve-sur-Lot": 6496.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lanzhou: (36.06°, 103.84°)", " Jirapur: (24.02°, 76.38°)", " Erenhot: (43.65°, 111.98°)", " Mangbang: (24.93°, 98.67°)", " Villeneuve-sur-Lot: (44.41°, 0.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Villeneuve-sur-Lot: 6496.3 km from centroid", " Erenhot: 3047.9 km from centroid", " Lanzhou: 2314.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Villeneuve-sur-Lot", "FINAL ANSWER: Villeneuve-sur-Lot" ] }, { "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": 7.35156, "lon": 4.18335, "name": "Apomu" }, { "lat": -33.58601, "lon": 26.88329, "name": "Port Alfred" }, { "lat": 11.11128, "lon": 7.7227, "name": "Zaria" }, { "lat": 6.20228, "lon": -1.66796, "name": "Obuase" }, { "lat": 16.98403, "lon": 98.51665, "name": "Mae Ramat" } ], "question": "Which location is the geographic outlier among: Apomu, Port Alfred, Zaria, Obuase, Mae Ramat?", "ground_truth": { "answer": "Mae Ramat", "outlier_distance_km": 7977.2, "second_furthest_km": 3914.0, "clarity_ratio": 2.04, "median_distance_km": 3234.0, "distances_to_centroid": { "Apomu": 2621.2, "Port Alfred": 3914.0, "Zaria": 2388.0, "Obuase": 3234.0, "Mae Ramat": 7977.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Apomu: (7.35°, 4.18°)", " Port Alfred: (-33.59°, 26.88°)", " Zaria: (11.11°, 7.72°)", " Obuase: (6.20°, -1.67°)", " Mae Ramat: (16.98°, 98.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mae Ramat: 7977.2 km from centroid", " Port Alfred: 3914.0 km from centroid", " Obuase: 3234.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mae Ramat", "FINAL ANSWER: Mae Ramat" ] }, { "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": -37.0182, "lon": 174.88019, "name": "Manurewa" }, { "lat": -37.87811, "lon": 145.16476, "name": "Glen Waverley" }, { "lat": -36.88745, "lon": 174.77059, "name": "Epsom" }, { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" }, { "lat": 40.68371, "lon": -73.51013, "name": "Wantagh" } ], "question": "Which location is the geographic outlier among: Manurewa, Glen Waverley, Epsom, Mackay, Wantagh?", "ground_truth": { "answer": "Wantagh", "outlier_distance_km": 17438.5, "second_furthest_km": 6219.1, "clarity_ratio": 2.8, "median_distance_km": 6208.9, "distances_to_centroid": { "Manurewa": 6219.1, "Glen Waverley": 3704.7, "Epsom": 6208.9, "Mackay": 3674.2, "Wantagh": 17438.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Manurewa: (-37.02°, 174.88°)", " Glen Waverley: (-37.88°, 145.16°)", " Epsom: (-36.89°, 174.77°)", " Mackay: (-21.15°, 149.17°)", " Wantagh: (40.68°, -73.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wantagh: 17438.5 km from centroid", " Manurewa: 6219.1 km from centroid", " Epsom: 6208.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wantagh", "FINAL ANSWER: Wantagh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8, "lon": 144.9, "name": "Footscray" }, { "lat": -20.72523, "lon": 139.49727, "name": "Mount Isa" }, { "lat": -24.86621, "lon": 152.3479, "name": "Bundaberg" }, { "lat": -28.00029, "lon": 153.43088, "name": "Gold Coast" }, { "lat": 36.52663, "lon": 118.99285, "name": "Yingqiu" } ], "question": "Which location is the geographic outlier among: Footscray, Mount Isa, Bundaberg, Gold Coast, Yingqiu?", "ground_truth": { "answer": "Yingqiu", "outlier_distance_km": 6208.0, "second_furthest_km": 2556.1, "clarity_ratio": 2.43, "median_distance_km": 1878.4, "distances_to_centroid": { "Footscray": 2556.1, "Mount Isa": 685.7, "Bundaberg": 1553.6, "Gold Coast": 1878.4, "Yingqiu": 6208.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Footscray: (-37.80°, 144.90°)", " Mount Isa: (-20.73°, 139.50°)", " Bundaberg: (-24.87°, 152.35°)", " Gold Coast: (-28.00°, 153.43°)", " Yingqiu: (36.53°, 118.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yingqiu: 6208.0 km from centroid", " Footscray: 2556.1 km from centroid", " Gold Coast: 1878.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yingqiu", "FINAL ANSWER: Yingqiu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.87905, "lon": -76.90133, "name": "Havelock" }, { "lat": 29.87522, "lon": -98.26251, "name": "Canyon Lake" }, { "lat": 42.97086, "lon": -82.42491, "name": "Port Huron" }, { "lat": 33.72672, "lon": -84.27246, "name": "Candler-McAfee" }, { "lat": 58.32582, "lon": 44.75881, "name": "Manturovo" } ], "question": "Which location is the geographic outlier among: Havelock, Canyon Lake, Port Huron, Candler-McAfee, Manturovo?", "ground_truth": { "answer": "Manturovo", "outlier_distance_km": 7048.5, "second_furthest_km": 3682.1, "clarity_ratio": 1.91, "median_distance_km": 2308.7, "distances_to_centroid": { "Havelock": 1640.4, "Canyon Lake": 3682.1, "Port Huron": 1939.7, "Candler-McAfee": 2308.7, "Manturovo": 7048.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Havelock: (34.88°, -76.90°)", " Canyon Lake: (29.88°, -98.26°)", " Port Huron: (42.97°, -82.42°)", " Candler-McAfee: (33.73°, -84.27°)", " Manturovo: (58.33°, 44.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Manturovo: 7048.5 km from centroid", " Canyon Lake: 3682.1 km from centroid", " Candler-McAfee: 2308.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Manturovo", "FINAL ANSWER: Manturovo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 28.38612, "lon": -80.742, "name": "Cocoa" }, { "lat": 42.56297, "lon": -114.46087, "name": "Twin Falls" }, { "lat": 40.13038, "lon": -75.51491, "name": "Phoenixville" }, { "lat": 21.93115, "lon": -99.99488, "name": "Rioverde" }, { "lat": 52.59841, "lon": 13.35766, "name": "Märkisches Viertel" } ], "question": "Which location is the geographic outlier among: Cocoa, Twin Falls, Phoenixville, Rioverde, Märkisches Viertel?", "ground_truth": { "answer": "Märkisches Viertel", "outlier_distance_km": 6500.5, "second_furthest_km": 3679.7, "clarity_ratio": 1.77, "median_distance_km": 3216.0, "distances_to_centroid": { "Cocoa": 1300.6, "Twin Falls": 3679.7, "Phoenixville": 485.0, "Rioverde": 3216.0, "Märkisches Viertel": 6500.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cocoa: (28.39°, -80.74°)", " Twin Falls: (42.56°, -114.46°)", " Phoenixville: (40.13°, -75.51°)", " Rioverde: (21.93°, -99.99°)", " Märkisches Viertel: (52.60°, 13.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Märkisches Viertel: 6500.5 km from centroid", " Twin Falls: 3679.7 km from centroid", " Rioverde: 3216.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Märkisches Viertel", "FINAL ANSWER: Märkisches Viertel" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.5427, "lon": -97.54667, "name": "Hutto" }, { "lat": 33.89205, "lon": -84.29881, "name": "Chamblee" }, { "lat": 28.90054, "lon": -81.26367, "name": "Deltona" }, { "lat": 35.53227, "lon": -97.95505, "name": "El Reno" }, { "lat": 40.40969, "lon": -3.73181, "name": "Puerta del Angel" } ], "question": "Which location is the geographic outlier among: Hutto, Chamblee, Deltona, El Reno, Puerta del Angel?", "ground_truth": { "answer": "Puerta del Angel", "outlier_distance_km": 6023.3, "second_furthest_km": 2336.9, "clarity_ratio": 2.58, "median_distance_km": 2286.7, "distances_to_centroid": { "Hutto": 2336.9, "Chamblee": 1046.4, "Deltona": 961.2, "El Reno": 2286.7, "Puerta del Angel": 6023.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hutto: (30.54°, -97.55°)", " Chamblee: (33.89°, -84.30°)", " Deltona: (28.90°, -81.26°)", " El Reno: (35.53°, -97.96°)", " Puerta del Angel: (40.41°, -3.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Puerta del Angel: 6023.3 km from centroid", " Hutto: 2336.9 km from centroid", " El Reno: 2286.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Puerta del Angel", "FINAL ANSWER: Puerta del Angel" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.74114, "lon": 8.28699, "name": "Dillenburg" }, { "lat": 51.8175, "lon": 4.63333, "name": "Zwijndrecht" }, { "lat": 53.31625, "lon": 13.86261, "name": "Prenzlau" }, { "lat": 52.32333, "lon": 9.20311, "name": "Stadthagen" }, { "lat": 30.81609, "lon": 108.26216, "name": "Lihe" } ], "question": "Which location is the geographic outlier among: Dillenburg, Zwijndrecht, Prenzlau, Stadthagen, Lihe?", "ground_truth": { "answer": "Lihe", "outlier_distance_km": 6777.8, "second_furthest_km": 1785.0, "clarity_ratio": 3.8, "median_distance_km": 1521.9, "distances_to_centroid": { "Dillenburg": 1521.9, "Zwijndrecht": 1785.0, "Prenzlau": 1219.9, "Stadthagen": 1484.1, "Lihe": 6777.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dillenburg: (50.74°, 8.29°)", " Zwijndrecht: (51.82°, 4.63°)", " Prenzlau: (53.32°, 13.86°)", " Stadthagen: (52.32°, 9.20°)", " Lihe: (30.82°, 108.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lihe: 6777.8 km from centroid", " Zwijndrecht: 1785.0 km from centroid", " Dillenburg: 1521.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lihe", "FINAL ANSWER: Lihe" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.7, "lon": 135.41667, "name": "Asso" }, { "lat": -2.6832, "lon": 111.6259, "name": "Pangkalanbuun" }, { "lat": 22.33971, "lon": 87.32501, "name": "Kharagpur" }, { "lat": 31.09023, "lon": 109.62397, "name": "Caotang" }, { "lat": -1.4563, "lon": 36.97826, "name": "Athi River" } ], "question": "Which location is the geographic outlier among: Asso, Pangkalanbuun, Kharagpur, Caotang, Athi River?", "ground_truth": { "answer": "Athi River", "outlier_distance_km": 6795.6, "second_furthest_km": 4346.7, "clarity_ratio": 1.56, "median_distance_km": 2732.9, "distances_to_centroid": { "Asso": 4346.7, "Pangkalanbuun": 2732.9, "Kharagpur": 1127.4, "Caotang": 2108.4, "Athi River": 6795.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Asso: (33.70°, 135.42°)", " Pangkalanbuun: (-2.68°, 111.63°)", " Kharagpur: (22.34°, 87.33°)", " Caotang: (31.09°, 109.62°)", " Athi River: (-1.46°, 36.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Athi River: 6795.6 km from centroid", " Asso: 4346.7 km from centroid", " Pangkalanbuun: 2732.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Athi River", "FINAL ANSWER: Athi River" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.2529, "lon": 8.87867, "name": "Sinsheim" }, { "lat": 53.7084, "lon": 37.29457, "name": "Plavsk" }, { "lat": 43.06425, "lon": 12.54612, "name": "Bastia umbra" }, { "lat": 51.24048, "lon": -0.17044, "name": "Redhill" }, { "lat": -1.69405, "lon": 40.17015, "name": "Masalani" } ], "question": "Which location is the geographic outlier among: Sinsheim, Plavsk, Bastia umbra, Redhill, Masalani?", "ground_truth": { "answer": "Masalani", "outlier_distance_km": 4994.5, "second_furthest_km": 2096.2, "clarity_ratio": 2.38, "median_distance_km": 2050.7, "distances_to_centroid": { "Sinsheim": 1418.8, "Plavsk": 2096.2, "Bastia umbra": 745.7, "Redhill": 2050.7, "Masalani": 4994.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sinsheim: (49.25°, 8.88°)", " Plavsk: (53.71°, 37.29°)", " Bastia umbra: (43.06°, 12.55°)", " Redhill: (51.24°, -0.17°)", " Masalani: (-1.69°, 40.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Masalani: 4994.5 km from centroid", " Plavsk: 2096.2 km from centroid", " Redhill: 2050.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Masalani", "FINAL ANSWER: Masalani" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 16.23557, "lon": -93.89972, "name": "Arriaga" }, { "lat": 44.87552, "lon": -91.91934, "name": "Menomonie" }, { "lat": 40.66205, "lon": -73.73541, "name": "Rosedale" }, { "lat": 46.64499, "lon": -80.9973, "name": "Valley East" }, { "lat": -5.57667, "lon": -36.90861, "name": "Açu" } ], "question": "Which location is the geographic outlier among: Arriaga, Menomonie, Rosedale, Valley East, Açu?", "ground_truth": { "answer": "Açu", "outlier_distance_km": 5609.3, "second_furthest_km": 2331.6, "clarity_ratio": 2.41, "median_distance_km": 2321.1, "distances_to_centroid": { "Arriaga": 2331.6, "Menomonie": 2321.1, "Rosedale": 1354.3, "Valley East": 2066.4, "Açu": 5609.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Arriaga: (16.24°, -93.90°)", " Menomonie: (44.88°, -91.92°)", " Rosedale: (40.66°, -73.74°)", " Valley East: (46.64°, -81.00°)", " Açu: (-5.58°, -36.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Açu: 5609.3 km from centroid", " Arriaga: 2331.6 km from centroid", " Menomonie: 2321.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Açu", "FINAL ANSWER: Açu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 21.89764, "lon": 83.3966, "name": "Raigarh" }, { "lat": 26.10224, "lon": 87.95534, "name": "Kishanganj" }, { "lat": 18.67337, "lon": 105.69232, "name": "Vinh" }, { "lat": 1.72837, "lon": 128.00948, "name": "Tobelo" }, { "lat": 32.7593, "lon": -97.79725, "name": "Weatherford" } ], "question": "Which location is the geographic outlier among: Raigarh, Kishanganj, Vinh, Tobelo, Weatherford?", "ground_truth": { "answer": "Weatherford", "outlier_distance_km": 13723.5, "second_furthest_km": 7499.8, "clarity_ratio": 1.83, "median_distance_km": 4628.1, "distances_to_centroid": { "Raigarh": 2282.7, "Kishanganj": 2781.5, "Vinh": 4628.1, "Tobelo": 7499.8, "Weatherford": 13723.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Raigarh: (21.90°, 83.40°)", " Kishanganj: (26.10°, 87.96°)", " Vinh: (18.67°, 105.69°)", " Tobelo: (1.73°, 128.01°)", " Weatherford: (32.76°, -97.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Weatherford: 13723.5 km from centroid", " Tobelo: 7499.8 km from centroid", " Vinh: 4628.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Weatherford", "FINAL ANSWER: Weatherford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.73583, "lon": 95.05841, "name": "Mon" }, { "lat": 29.84594, "lon": 105.87782, "name": "Pingtan" }, { "lat": 29.72235, "lon": 106.93206, "name": "Luoqi" }, { "lat": 18.08333, "lon": 73.41667, "name": "Mahād" }, { "lat": -10.43778, "lon": -39.33278, "name": "Monte Santo" } ], "question": "Which location is the geographic outlier among: Mon, Pingtan, Luoqi, Mahād, Monte Santo?", "ground_truth": { "answer": "Monte Santo", "outlier_distance_km": 12229.8, "second_furthest_km": 4070.5, "clarity_ratio": 3.0, "median_distance_km": 3972.1, "distances_to_centroid": { "Mon": 2866.8, "Pingtan": 3972.1, "Luoqi": 4070.5, "Mahād": 536.0, "Monte Santo": 12229.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mon: (26.74°, 95.06°)", " Pingtan: (29.85°, 105.88°)", " Luoqi: (29.72°, 106.93°)", " Mahād: (18.08°, 73.42°)", " Monte Santo: (-10.44°, -39.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Monte Santo: 12229.8 km from centroid", " Luoqi: 4070.5 km from centroid", " Pingtan: 3972.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Monte Santo", "FINAL ANSWER: Monte Santo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 24.355, "lon": 102.54222, "name": "Yuxi" }, { "lat": 36.24725, "lon": 118.83832, "name": "Wushan" }, { "lat": 16.57831, "lon": 100.30034, "name": "Bang Krathum" }, { "lat": 16.52539, "lon": 107.4755, "name": "Hương Trà" }, { "lat": 10.3121, "lon": 39.65888, "name": "Mehal Mēda" } ], "question": "Which location is the geographic outlier among: Yuxi, Wushan, Bang Krathum, Hương Trà, Mehal Mēda?", "ground_truth": { "answer": "Mehal Mēda", "outlier_distance_km": 5885.4, "second_furthest_km": 2976.4, "clarity_ratio": 1.98, "median_distance_km": 1520.1, "distances_to_centroid": { "Yuxi": 983.8, "Wushan": 2976.4, "Bang Krathum": 833.4, "Hương Trà": 1520.1, "Mehal Mēda": 5885.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yuxi: (24.36°, 102.54°)", " Wushan: (36.25°, 118.84°)", " Bang Krathum: (16.58°, 100.30°)", " Hương Trà: (16.53°, 107.48°)", " Mehal Mēda: (10.31°, 39.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mehal Mēda: 5885.4 km from centroid", " Wushan: 2976.4 km from centroid", " Hương Trà: 1520.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mehal Mēda", "FINAL ANSWER: Mehal Mēda" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.5441, "lon": 10.20048, "name": "Glinde" }, { "lat": 53.35, "lon": -3.01667, "name": "Bebington" }, { "lat": 59.8996, "lon": 29.08574, "name": "Sosnovyy Bor" }, { "lat": 40.40742, "lon": -3.64935, "name": "Moratalaz" }, { "lat": -9.47833, "lon": -35.85333, "name": "Rio Largo" } ], "question": "Which location is the geographic outlier among: Glinde, Bebington, Sosnovyy Bor, Moratalaz, Rio Largo?", "ground_truth": { "answer": "Rio Largo", "outlier_distance_km": 6548.7, "second_furthest_km": 3062.9, "clarity_ratio": 2.14, "median_distance_km": 1759.4, "distances_to_centroid": { "Glinde": 1759.4, "Bebington": 1545.6, "Sosnovyy Bor": 3062.9, "Moratalaz": 273.2, "Rio Largo": 6548.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Glinde: (53.54°, 10.20°)", " Bebington: (53.35°, -3.02°)", " Sosnovyy Bor: (59.90°, 29.09°)", " Moratalaz: (40.41°, -3.65°)", " Rio Largo: (-9.48°, -35.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rio Largo: 6548.7 km from centroid", " Sosnovyy Bor: 3062.9 km from centroid", " Glinde: 1759.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rio Largo", "FINAL ANSWER: Rio Largo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.71359, "lon": -79.28138, "name": "Clairlea-Birchmount" }, { "lat": 34.95537, "lon": -90.03481, "name": "Horn Lake" }, { "lat": 41.77982, "lon": -71.43728, "name": "Cranston" }, { "lat": 38.10409, "lon": -122.25664, "name": "Vallejo" }, { "lat": 24.20645, "lon": 84.87085, "name": "Chatrā" } ], "question": "Which location is the geographic outlier among: Clairlea-Birchmount, Horn Lake, Cranston, Vallejo, Chatrā?", "ground_truth": { "answer": "Chatrā", "outlier_distance_km": 12090.5, "second_furthest_km": 5761.1, "clarity_ratio": 2.1, "median_distance_km": 3093.4, "distances_to_centroid": { "Clairlea-Birchmount": 2153.4, "Horn Lake": 3093.4, "Cranston": 1478.9, "Vallejo": 5761.1, "Chatrā": 12090.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Clairlea-Birchmount: (43.71°, -79.28°)", " Horn Lake: (34.96°, -90.03°)", " Cranston: (41.78°, -71.44°)", " Vallejo: (38.10°, -122.26°)", " Chatrā: (24.21°, 84.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chatrā: 12090.5 km from centroid", " Vallejo: 5761.1 km from centroid", " Horn Lake: 3093.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chatrā", "FINAL ANSWER: Chatrā" ] }, { "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": 31.03637, "lon": 31.38069, "name": "Al Mansurah" }, { "lat": -26.18848, "lon": 28.32078, "name": "Benoni" }, { "lat": -26.33172, "lon": 26.32065, "name": "Coligny" }, { "lat": 30.60427, "lon": 32.27225, "name": "Ismailia" }, { "lat": -37.79117, "lon": 144.81637, "name": "Sunshine West" } ], "question": "Which location is the geographic outlier among: Al Mansurah, Benoni, Coligny, Ismailia, Sunshine West?", "ground_truth": { "answer": "Sunshine West", "outlier_distance_km": 9809.2, "second_furthest_km": 4670.4, "clarity_ratio": 2.1, "median_distance_km": 4584.5, "distances_to_centroid": { "Al Mansurah": 4670.4, "Benoni": 3438.7, "Coligny": 3609.5, "Ismailia": 4584.5, "Sunshine West": 9809.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Al Mansurah: (31.04°, 31.38°)", " Benoni: (-26.19°, 28.32°)", " Coligny: (-26.33°, 26.32°)", " Ismailia: (30.60°, 32.27°)", " Sunshine West: (-37.79°, 144.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sunshine West: 9809.2 km from centroid", " Al Mansurah: 4670.4 km from centroid", " Ismailia: 4584.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sunshine West", "FINAL ANSWER: Sunshine West" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.739, "lon": 30.949, "name": "Ntuzuma" }, { "lat": -29.19448, "lon": 27.45739, "name": "Ladybrand" }, { "lat": 10.40319, "lon": 5.4708, "name": "Kontagora" }, { "lat": -1.85238, "lon": 36.77683, "name": "Kajiado" }, { "lat": -12.78691, "lon": -74.97298, "name": "Huancavelica" } ], "question": "Which location is the geographic outlier among: Ntuzuma, Ladybrand, Kontagora, Kajiado, Huancavelica?", "ground_truth": { "answer": "Huancavelica", "outlier_distance_km": 8647.5, "second_furthest_km": 3684.5, "clarity_ratio": 2.35, "median_distance_km": 3269.0, "distances_to_centroid": { "Ntuzuma": 3269.0, "Ladybrand": 2950.1, "Kontagora": 2561.9, "Kajiado": 3684.5, "Huancavelica": 8647.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ntuzuma: (-29.74°, 30.95°)", " Ladybrand: (-29.19°, 27.46°)", " Kontagora: (10.40°, 5.47°)", " Kajiado: (-1.85°, 36.78°)", " Huancavelica: (-12.79°, -74.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Huancavelica: 8647.5 km from centroid", " Kajiado: 3684.5 km from centroid", " Ntuzuma: 3269.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Huancavelica", "FINAL ANSWER: Huancavelica" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.69946, "lon": -99.08148, "name": "Kearney" }, { "lat": 37.66243, "lon": -121.87468, "name": "Pleasanton" }, { "lat": 37.02089, "lon": -93.20602, "name": "Ozark" }, { "lat": 37.17526, "lon": -113.28995, "name": "Hurricane" }, { "lat": 30.54972, "lon": 31.24444, "name": "Kafr Shukr" } ], "question": "Which location is the geographic outlier among: Kearney, Pleasanton, Ozark, Hurricane, Kafr Shukr?", "ground_truth": { "answer": "Kafr Shukr", "outlier_distance_km": 9616.7, "second_furthest_km": 3747.7, "clarity_ratio": 2.57, "median_distance_km": 3011.9, "distances_to_centroid": { "Kearney": 1777.0, "Pleasanton": 3747.7, "Ozark": 1242.7, "Hurricane": 3011.9, "Kafr Shukr": 9616.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kearney: (40.70°, -99.08°)", " Pleasanton: (37.66°, -121.87°)", " Ozark: (37.02°, -93.21°)", " Hurricane: (37.18°, -113.29°)", " Kafr Shukr: (30.55°, 31.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kafr Shukr: 9616.7 km from centroid", " Pleasanton: 3747.7 km from centroid", " Hurricane: 3011.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kafr Shukr", "FINAL ANSWER: Kafr Shukr" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.48333, "lon": 13.31667, "name": "Wilmersdorf" }, { "lat": 49.32534, "lon": 12.1098, "name": "Schwandorf in Bayern" }, { "lat": 41.72748, "lon": 12.659, "name": "Albano Laziale" }, { "lat": 43.29789, "lon": 13.45293, "name": "Macerata" }, { "lat": -10.65167, "lon": -68.50444, "name": "Xapuri" } ], "question": "Which location is the geographic outlier among: Wilmersdorf, Schwandorf in Bayern, Albano Laziale, Macerata, Xapuri?", "ground_truth": { "answer": "Xapuri", "outlier_distance_km": 8521.2, "second_furthest_km": 2327.1, "clarity_ratio": 3.66, "median_distance_km": 2011.9, "distances_to_centroid": { "Wilmersdorf": 2327.1, "Schwandorf in Bayern": 2011.9, "Albano Laziale": 1569.1, "Macerata": 1700.1, "Xapuri": 8521.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wilmersdorf: (52.48°, 13.32°)", " Schwandorf in Bayern: (49.33°, 12.11°)", " Albano Laziale: (41.73°, 12.66°)", " Macerata: (43.30°, 13.45°)", " Xapuri: (-10.65°, -68.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Xapuri: 8521.2 km from centroid", " Wilmersdorf: 2327.1 km from centroid", " Schwandorf in Bayern: 2011.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Xapuri", "FINAL ANSWER: Xapuri" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.74255, "lon": -84.10523, "name": "Lima" }, { "lat": 38.93428, "lon": -77.17748, "name": "McLean" }, { "lat": 45.41679, "lon": -122.64009, "name": "Oak Grove" }, { "lat": 40.86649, "lon": -73.03566, "name": "Selden" }, { "lat": -33.90741, "lon": 151.15546, "name": "Marrickville" } ], "question": "Which location is the geographic outlier among: Lima, McLean, Oak Grove, Selden, Marrickville?", "ground_truth": { "answer": "Marrickville", "outlier_distance_km": 18568.8, "second_furthest_km": 7316.4, "clarity_ratio": 2.54, "median_distance_km": 4235.6, "distances_to_centroid": { "Lima": 4235.6, "McLean": 3618.1, "Oak Grove": 7316.4, "Selden": 3333.6, "Marrickville": 18568.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lima: (40.74°, -84.11°)", " McLean: (38.93°, -77.18°)", " Oak Grove: (45.42°, -122.64°)", " Selden: (40.87°, -73.04°)", " Marrickville: (-33.91°, 151.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Marrickville: 18568.8 km from centroid", " Oak Grove: 7316.4 km from centroid", " Lima: 4235.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Marrickville", "FINAL ANSWER: Marrickville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.53222, "lon": -44.1075, "name": "Paço do Lumiar" }, { "lat": -6.40111, "lon": -38.86222, "name": "Icó" }, { "lat": -28.71333, "lon": -49.3, "name": "Içara" }, { "lat": -0.97357, "lon": -62.9269, "name": "Barcelos" }, { "lat": 10.85, "lon": 36.88333, "name": "Gimja Bēt Maryam" } ], "question": "Which location is the geographic outlier among: Paço do Lumiar, Icó, Içara, Barcelos, Gimja Bēt Maryam?", "ground_truth": { "answer": "Gimja Bēt Maryam", "outlier_distance_km": 7802.0, "second_furthest_km": 3506.9, "clarity_ratio": 2.22, "median_distance_km": 3174.9, "distances_to_centroid": { "Paço do Lumiar": 1420.5, "Icó": 801.7, "Içara": 3174.9, "Barcelos": 3506.9, "Gimja Bēt Maryam": 7802.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paço do Lumiar: (-2.53°, -44.11°)", " Icó: (-6.40°, -38.86°)", " Içara: (-28.71°, -49.30°)", " Barcelos: (-0.97°, -62.93°)", " Gimja Bēt Maryam: (10.85°, 36.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gimja Bēt Maryam: 7802.0 km from centroid", " Barcelos: 3506.9 km from centroid", " Içara: 3174.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gimja Bēt Maryam", "FINAL ANSWER: Gimja Bēt Maryam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 23.74423, "lon": 84.49984, "name": "Lātehār" }, { "lat": 9.28358, "lon": 76.45519, "name": "Haripād" }, { "lat": 27.54566, "lon": 116.21456, "name": "Fenggang" }, { "lat": 23.02888, "lon": 79.48233, "name": "Gotegaon" }, { "lat": -33.9049, "lon": 151.01996, "name": "Yagoona" } ], "question": "Which location is the geographic outlier among: Lātehār, Haripād, Fenggang, Gotegaon, Yagoona?", "ground_truth": { "answer": "Yagoona", "outlier_distance_km": 7141.8, "second_furthest_km": 2758.8, "clarity_ratio": 2.59, "median_distance_km": 2749.9, "distances_to_centroid": { "Lātehār": 2370.8, "Haripād": 2749.9, "Fenggang": 2489.1, "Gotegaon": 2758.8, "Yagoona": 7141.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lātehār: (23.74°, 84.50°)", " Haripād: (9.28°, 76.46°)", " Fenggang: (27.55°, 116.21°)", " Gotegaon: (23.03°, 79.48°)", " Yagoona: (-33.90°, 151.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yagoona: 7141.8 km from centroid", " Gotegaon: 2758.8 km from centroid", " Haripād: 2749.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yagoona", "FINAL ANSWER: Yagoona" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.12914, "lon": 106.11377, "name": "Pangkalpinang" }, { "lat": 36.48, "lon": 102.41639, "name": "Nianbo" }, { "lat": 34.24643, "lon": 133.92296, "name": "Takinomiya" }, { "lat": 13.04603, "lon": 121.46205, "name": "Pinamalayan" }, { "lat": -28.88649, "lon": 31.4699, "name": "Eshowe" } ], "question": "Which location is the geographic outlier among: Pangkalpinang, Nianbo, Takinomiya, Pinamalayan, Eshowe?", "ground_truth": { "answer": "Eshowe", "outlier_distance_km": 8467.0, "second_furthest_km": 4408.6, "clarity_ratio": 1.92, "median_distance_km": 2902.6, "distances_to_centroid": { "Pangkalpinang": 1610.8, "Nianbo": 2902.6, "Takinomiya": 4408.6, "Pinamalayan": 2451.4, "Eshowe": 8467.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pangkalpinang: (-2.13°, 106.11°)", " Nianbo: (36.48°, 102.42°)", " Takinomiya: (34.25°, 133.92°)", " Pinamalayan: (13.05°, 121.46°)", " Eshowe: (-28.89°, 31.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Eshowe: 8467.0 km from centroid", " Takinomiya: 4408.6 km from centroid", " Nianbo: 2902.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Eshowe", "FINAL ANSWER: Eshowe" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 17.3381, "lon": 77.90441, "name": "Vikārābād" }, { "lat": 15.26349, "lon": 74.10875, "name": "Curchorem" }, { "lat": 12.11202, "lon": 78.15384, "name": "Lakkanahalli" }, { "lat": 3.61099, "lon": 125.4858, "name": "Tahuna" }, { "lat": -34.28853, "lon": 146.05093, "name": "Griffith" } ], "question": "Which location is the geographic outlier among: Vikārābād, Curchorem, Lakkanahalli, Tahuna, Griffith?", "ground_truth": { "answer": "Griffith", "outlier_distance_km": 6307.6, "second_furthest_km": 3190.3, "clarity_ratio": 1.98, "median_distance_km": 2933.7, "distances_to_centroid": { "Vikārābād": 2933.7, "Curchorem": 3190.3, "Lakkanahalli": 2653.1, "Tahuna": 2793.0, "Griffith": 6307.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vikārābād: (17.34°, 77.90°)", " Curchorem: (15.26°, 74.11°)", " Lakkanahalli: (12.11°, 78.15°)", " Tahuna: (3.61°, 125.49°)", " Griffith: (-34.29°, 146.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Griffith: 6307.6 km from centroid", " Curchorem: 3190.3 km from centroid", " Vikārābād: 2933.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Griffith", "FINAL ANSWER: Griffith" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -10.17611, "lon": -48.86667, "name": "Paraíso do Tocantins" }, { "lat": -7.93333, "lon": -39.29583, "name": "Serrita" }, { "lat": -7.36194, "lon": -46.61722, "name": "Riachão" }, { "lat": -3.3925, "lon": -44.35861, "name": "Itapecuru Mirim" }, { "lat": 44.77599, "lon": -63.67865, "name": "Lower Sackville" } ], "question": "Which location is the geographic outlier among: Paraíso do Tocantins, Serrita, Riachão, Itapecuru Mirim, Lower Sackville?", "ground_truth": { "answer": "Lower Sackville", "outlier_distance_km": 4855.7, "second_furthest_km": 1607.6, "clarity_ratio": 3.02, "median_distance_km": 1485.8, "distances_to_centroid": { "Paraíso do Tocantins": 1485.8, "Serrita": 1607.6, "Riachão": 1192.2, "Itapecuru Mirim": 867.7, "Lower Sackville": 4855.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paraíso do Tocantins: (-10.18°, -48.87°)", " Serrita: (-7.93°, -39.30°)", " Riachão: (-7.36°, -46.62°)", " Itapecuru Mirim: (-3.39°, -44.36°)", " Lower Sackville: (44.78°, -63.68°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lower Sackville: 4855.7 km from centroid", " Serrita: 1607.6 km from centroid", " Paraíso do Tocantins: 1485.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lower Sackville", "FINAL ANSWER: Lower Sackville" ] }, { "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": 35.15, "lon": 139.06667, "name": "Yugawara" }, { "lat": 20.92085, "lon": 74.76111, "name": "Walwadi" }, { "lat": 43.85037, "lon": 81.78308, "name": "Onyar" }, { "lat": 13.79284, "lon": 100.58298, "name": "Khetsamsenok" }, { "lat": 35.11859, "lon": -120.59073, "name": "Arroyo Grande" } ], "question": "Which location is the geographic outlier among: Yugawara, Walwadi, Onyar, Khetsamsenok, Arroyo Grande?", "ground_truth": { "answer": "Arroyo Grande", "outlier_distance_km": 12786.2, "second_furthest_km": 7656.7, "clarity_ratio": 1.67, "median_distance_km": 4980.9, "distances_to_centroid": { "Yugawara": 7656.7, "Walwadi": 2200.7, "Onyar": 2823.8, "Khetsamsenok": 4980.9, "Arroyo Grande": 12786.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yugawara: (35.15°, 139.07°)", " Walwadi: (20.92°, 74.76°)", " Onyar: (43.85°, 81.78°)", " Khetsamsenok: (13.79°, 100.58°)", " Arroyo Grande: (35.12°, -120.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arroyo Grande: 12786.2 km from centroid", " Yugawara: 7656.7 km from centroid", " Khetsamsenok: 4980.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arroyo Grande", "FINAL ANSWER: Arroyo Grande" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.5523, "lon": 37.70885, "name": "Vidnoye" }, { "lat": 51.86583, "lon": 4.66111, "name": "Alblasserdam" }, { "lat": 52.43022, "lon": 20.71652, "name": "Nowy Dwór Mazowiecki" }, { "lat": 45.76788, "lon": 4.85064, "name": "Lyon 06" }, { "lat": 27.13181, "lon": 81.95332, "name": "Gondā City" } ], "question": "Which location is the geographic outlier among: Vidnoye, Alblasserdam, Nowy Dwór Mazowiecki, Lyon 06, Gondā City?", "ground_truth": { "answer": "Gondā City", "outlier_distance_km": 4994.9, "second_furthest_km": 1929.1, "clarity_ratio": 2.59, "median_distance_km": 1920.5, "distances_to_centroid": { "Vidnoye": 1136.0, "Alblasserdam": 1920.5, "Nowy Dwór Mazowiecki": 934.1, "Lyon 06": 1929.1, "Gondā City": 4994.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vidnoye: (55.55°, 37.71°)", " Alblasserdam: (51.87°, 4.66°)", " Nowy Dwór Mazowiecki: (52.43°, 20.72°)", " Lyon 06: (45.77°, 4.85°)", " Gondā City: (27.13°, 81.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gondā City: 4994.9 km from centroid", " Lyon 06: 1929.1 km from centroid", " Alblasserdam: 1920.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gondā City", "FINAL ANSWER: Gondā City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.57583, "lon": 6.61944, "name": "Hardenberg" }, { "lat": 45.64498, "lon": 11.29886, "name": "Valdagno" }, { "lat": 54.84034, "lon": -1.46427, "name": "Houghton-Le-Spring" }, { "lat": 48.77275, "lon": 5.16108, "name": "Bar-le-Duc" }, { "lat": 17.98625, "lon": -92.93928, "name": "Villahermosa" } ], "question": "Which location is the geographic outlier among: Hardenberg, Valdagno, Houghton-Le-Spring, Bar-le-Duc, Villahermosa?", "ground_truth": { "answer": "Villahermosa", "outlier_distance_km": 7737.6, "second_furthest_km": 2016.8, "clarity_ratio": 3.84, "median_distance_km": 1808.3, "distances_to_centroid": { "Hardenberg": 1808.3, "Valdagno": 2016.8, "Houghton-Le-Spring": 1518.3, "Bar-le-Duc": 1578.2, "Villahermosa": 7737.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hardenberg: (52.58°, 6.62°)", " Valdagno: (45.64°, 11.30°)", " Houghton-Le-Spring: (54.84°, -1.46°)", " Bar-le-Duc: (48.77°, 5.16°)", " Villahermosa: (17.99°, -92.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Villahermosa: 7737.6 km from centroid", " Valdagno: 2016.8 km from centroid", " Hardenberg: 1808.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Villahermosa", "FINAL ANSWER: Villahermosa" ] }, { "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": -20.73722, "lon": -48.91472, "name": "Olímpia" }, { "lat": -4.77611, "lon": -48.06722, "name": "Rondon do Pará" }, { "lat": -11.61667, "lon": -38.8, "name": "Biritinga" }, { "lat": -0.7175, "lon": -47.69972, "name": "Marapanim" }, { "lat": 49.16638, "lon": -123.94003, "name": "Nanaimo" } ], "question": "Which location is the geographic outlier among: Olímpia, Rondon do Pará, Biritinga, Marapanim, Nanaimo?", "ground_truth": { "answer": "Nanaimo", "outlier_distance_km": 7851.3, "second_furthest_km": 2944.5, "clarity_ratio": 2.67, "median_distance_km": 2901.1, "distances_to_centroid": { "Olímpia": 2901.1, "Rondon do Pará": 1683.7, "Biritinga": 2944.5, "Marapanim": 1567.9, "Nanaimo": 7851.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Olímpia: (-20.74°, -48.91°)", " Rondon do Pará: (-4.78°, -48.07°)", " Biritinga: (-11.62°, -38.80°)", " Marapanim: (-0.72°, -47.70°)", " Nanaimo: (49.17°, -123.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nanaimo: 7851.3 km from centroid", " Biritinga: 2944.5 km from centroid", " Olímpia: 2901.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nanaimo", "FINAL ANSWER: Nanaimo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.36937, "lon": 105.88323, "name": "Zhuhai" }, { "lat": 16.18953, "lon": 100.85958, "name": "Chon Daen" }, { "lat": 15.46915, "lon": 73.83285, "name": "Taleigao" }, { "lat": 3.0693, "lon": 101.6074, "name": "Bandar Sunway" }, { "lat": -37.75405, "lon": 145.14864, "name": "Templestowe" } ], "question": "Which location is the geographic outlier among: Zhuhai, Chon Daen, Taleigao, Bandar Sunway, Templestowe?", "ground_truth": { "answer": "Templestowe", "outlier_distance_km": 6299.7, "second_furthest_km": 3635.0, "clarity_ratio": 1.73, "median_distance_km": 2680.2, "distances_to_centroid": { "Zhuhai": 2680.2, "Chon Daen": 1314.2, "Taleigao": 3635.0, "Bandar Sunway": 492.9, "Templestowe": 6299.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zhuhai: (29.37°, 105.88°)", " Chon Daen: (16.19°, 100.86°)", " Taleigao: (15.47°, 73.83°)", " Bandar Sunway: (3.07°, 101.61°)", " Templestowe: (-37.75°, 145.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Templestowe: 6299.7 km from centroid", " Taleigao: 3635.0 km from centroid", " Zhuhai: 2680.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Templestowe", "FINAL ANSWER: Templestowe" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.9417, "lon": 58.8083, "name": "Bakal" }, { "lat": 52.19166, "lon": -1.70734, "name": "Stratford-upon-Avon" }, { "lat": 56.90528, "lon": 59.94361, "name": "Pervouralsk" }, { "lat": 44.0038, "lon": 10.10674, "name": "Marina di Massa" }, { "lat": -36.88333, "lon": 174.7, "name": "Avondale" } ], "question": "Which location is the geographic outlier among: Bakal, Stratford-upon-Avon, Pervouralsk, Marina di Massa, Avondale?", "ground_truth": { "answer": "Avondale", "outlier_distance_km": 14187.9, "second_furthest_km": 5228.1, "clarity_ratio": 2.71, "median_distance_km": 4398.8, "distances_to_centroid": { "Bakal": 2306.0, "Stratford-upon-Avon": 5228.1, "Pervouralsk": 2521.4, "Marina di Massa": 4398.8, "Avondale": 14187.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bakal: (54.94°, 58.81°)", " Stratford-upon-Avon: (52.19°, -1.71°)", " Pervouralsk: (56.91°, 59.94°)", " Marina di Massa: (44.00°, 10.11°)", " Avondale: (-36.88°, 174.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Avondale: 14187.9 km from centroid", " Stratford-upon-Avon: 5228.1 km from centroid", " Marina di Massa: 4398.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Avondale", "FINAL ANSWER: Avondale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.56109, "lon": 8.50495, "name": "Wetzlar" }, { "lat": 59.63937, "lon": 33.52967, "name": "Tikhvin" }, { "lat": 49.20724, "lon": 2.58661, "name": "Senlis" }, { "lat": 56.19514, "lon": -3.17316, "name": "Glenrothes" }, { "lat": -21.205, "lon": -41.88778, "name": "Itaperuna" } ], "question": "Which location is the geographic outlier among: Wetzlar, Tikhvin, Senlis, Glenrothes, Itaperuna?", "ground_truth": { "answer": "Itaperuna", "outlier_distance_km": 7972.6, "second_furthest_km": 3294.3, "clarity_ratio": 2.42, "median_distance_km": 1938.8, "distances_to_centroid": { "Wetzlar": 1463.4, "Tikhvin": 3294.3, "Senlis": 1167.9, "Glenrothes": 1938.8, "Itaperuna": 7972.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wetzlar: (50.56°, 8.50°)", " Tikhvin: (59.64°, 33.53°)", " Senlis: (49.21°, 2.59°)", " Glenrothes: (56.20°, -3.17°)", " Itaperuna: (-21.20°, -41.89°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Itaperuna: 7972.6 km from centroid", " Tikhvin: 3294.3 km from centroid", " Glenrothes: 1938.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Itaperuna", "FINAL ANSWER: Itaperuna" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.44187, "lon": 152.93861, "name": "The Gap" }, { "lat": -38.17058, "lon": 144.3114, "name": "Highton" }, { "lat": -32.06003, "lon": 115.955, "name": "Thornlie" }, { "lat": -35.28346, "lon": 149.12807, "name": "Canberra" }, { "lat": 51.45342, "lon": 6.6326, "name": "Moers" } ], "question": "Which location is the geographic outlier among: The Gap, Highton, Thornlie, Canberra, Moers?", "ground_truth": { "answer": "Moers", "outlier_distance_km": 12601.4, "second_furthest_km": 4205.2, "clarity_ratio": 3.0, "median_distance_km": 4086.1, "distances_to_centroid": { "The Gap": 4205.2, "Highton": 3843.3, "Thornlie": 1765.9, "Canberra": 4086.1, "Moers": 12601.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " The Gap: (-27.44°, 152.94°)", " Highton: (-38.17°, 144.31°)", " Thornlie: (-32.06°, 115.95°)", " Canberra: (-35.28°, 149.13°)", " Moers: (51.45°, 6.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Moers: 12601.4 km from centroid", " The Gap: 4205.2 km from centroid", " Canberra: 4086.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Moers", "FINAL ANSWER: Moers" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.08297, "lon": 3.85196, "name": "Kisi" }, { "lat": 10.61285, "lon": 12.19458, "name": "Biu" }, { "lat": 5.10658, "lon": 7.36667, "name": "Aba" }, { "lat": 7.15571, "lon": 3.34509, "name": "Abeokuta" }, { "lat": 18.64813, "lon": 72.87579, "name": "Alībāg" } ], "question": "Which location is the geographic outlier among: Kisi, Biu, Aba, Abeokuta, Alībāg?", "ground_truth": { "answer": "Alībāg", "outlier_distance_km": 5761.6, "second_furthest_km": 1852.1, "clarity_ratio": 3.11, "median_distance_km": 1766.0, "distances_to_centroid": { "Kisi": 1766.0, "Biu": 847.5, "Aba": 1491.9, "Abeokuta": 1852.1, "Alībāg": 5761.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kisi: (9.08°, 3.85°)", " Biu: (10.61°, 12.19°)", " Aba: (5.11°, 7.37°)", " Abeokuta: (7.16°, 3.35°)", " Alībāg: (18.65°, 72.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alībāg: 5761.6 km from centroid", " Abeokuta: 1852.1 km from centroid", " Kisi: 1766.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alībāg", "FINAL ANSWER: Alībāg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.10461, "lon": 4.27557, "name": "Scheveningen" }, { "lat": 51.8289, "lon": 8.14724, "name": "Oelde" }, { "lat": 43.25347, "lon": -2.9161, "name": "Santutxu" }, { "lat": 52.92277, "lon": -1.47663, "name": "Derby" }, { "lat": -13.48694, "lon": -39.04389, "name": "Cairu" } ], "question": "Which location is the geographic outlier among: Scheveningen, Oelde, Santutxu, Derby, Cairu?", "ground_truth": { "answer": "Cairu", "outlier_distance_km": 6610.6, "second_furthest_km": 1965.3, "clarity_ratio": 3.36, "median_distance_km": 1835.9, "distances_to_centroid": { "Scheveningen": 1835.9, "Oelde": 1965.3, "Santutxu": 715.6, "Derby": 1772.7, "Cairu": 6610.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Scheveningen: (52.10°, 4.28°)", " Oelde: (51.83°, 8.15°)", " Santutxu: (43.25°, -2.92°)", " Derby: (52.92°, -1.48°)", " Cairu: (-13.49°, -39.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cairu: 6610.6 km from centroid", " Oelde: 1965.3 km from centroid", " Scheveningen: 1835.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cairu", "FINAL ANSWER: Cairu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.8844, "lon": -97.14704, "name": "Winnipeg" }, { "lat": 28.55778, "lon": -81.4534, "name": "Pine Hills" }, { "lat": 43.11682, "lon": -79.19958, "name": "Thorold" }, { "lat": 18.36759, "lon": -95.79857, "name": "Cosamaloapan" }, { "lat": 51.32997, "lon": -0.4113, "name": "Cobham" } ], "question": "Which location is the geographic outlier among: Winnipeg, Pine Hills, Thorold, Cosamaloapan, Cobham?", "ground_truth": { "answer": "Cobham", "outlier_distance_km": 5515.8, "second_furthest_km": 3277.4, "clarity_ratio": 1.68, "median_distance_km": 2451.0, "distances_to_centroid": { "Winnipeg": 2451.0, "Pine Hills": 1460.5, "Thorold": 890.4, "Cosamaloapan": 3277.4, "Cobham": 5515.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Winnipeg: (49.88°, -97.15°)", " Pine Hills: (28.56°, -81.45°)", " Thorold: (43.12°, -79.20°)", " Cosamaloapan: (18.37°, -95.80°)", " Cobham: (51.33°, -0.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cobham: 5515.8 km from centroid", " Cosamaloapan: 3277.4 km from centroid", " Winnipeg: 2451.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cobham", "FINAL ANSWER: Cobham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.09162, "lon": 6.89217, "name": "Monheim am Rhein" }, { "lat": 40.41189, "lon": -3.65682, "name": "Media Legua" }, { "lat": 45.42309, "lon": 9.10707, "name": "Romano Banco" }, { "lat": 52.9911, "lon": 22.88422, "name": "Łapy" }, { "lat": -37.80639, "lon": 145.03086, "name": "Kew" } ], "question": "Which location is the geographic outlier among: Monheim am Rhein, Media Legua, Romano Banco, Łapy, Kew?", "ground_truth": { "answer": "Kew", "outlier_distance_km": 13581.3, "second_furthest_km": 3730.9, "clarity_ratio": 3.64, "median_distance_km": 3323.5, "distances_to_centroid": { "Monheim am Rhein": 3323.5, "Media Legua": 3730.9, "Romano Banco": 2870.2, "Łapy": 2727.2, "Kew": 13581.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Monheim am Rhein: (51.09°, 6.89°)", " Media Legua: (40.41°, -3.66°)", " Romano Banco: (45.42°, 9.11°)", " Łapy: (52.99°, 22.88°)", " Kew: (-37.81°, 145.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kew: 13581.3 km from centroid", " Media Legua: 3730.9 km from centroid", " Monheim am Rhein: 3323.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kew", "FINAL ANSWER: Kew" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -18.41778, "lon": -46.41806, "name": "Presidente Olegário" }, { "lat": -23.39694, "lon": -47.00222, "name": "Pirapora do Bom Jesus" }, { "lat": 8.23773, "lon": -73.35604, "name": "Ocaña" }, { "lat": -5.70556, "lon": -35.30722, "name": "Extremoz" }, { "lat": 45.01052, "lon": -93.45551, "name": "Plymouth" } ], "question": "Which location is the geographic outlier among: Presidente Olegário, Pirapora do Bom Jesus, Ocaña, Extremoz, Plymouth?", "ground_truth": { "answer": "Plymouth", "outlier_distance_km": 5925.9, "second_furthest_km": 3026.8, "clarity_ratio": 1.96, "median_distance_km": 2750.4, "distances_to_centroid": { "Presidente Olegário": 2580.3, "Pirapora do Bom Jesus": 3026.8, "Ocaña": 1764.1, "Extremoz": 2750.4, "Plymouth": 5925.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Presidente Olegário: (-18.42°, -46.42°)", " Pirapora do Bom Jesus: (-23.40°, -47.00°)", " Ocaña: (8.24°, -73.36°)", " Extremoz: (-5.71°, -35.31°)", " Plymouth: (45.01°, -93.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Plymouth: 5925.9 km from centroid", " Pirapora do Bom Jesus: 3026.8 km from centroid", " Extremoz: 2750.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Plymouth", "FINAL ANSWER: Plymouth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.46498, "lon": 42.18447, "name": "Felana" }, { "lat": 8.55083, "lon": -0.51875, "name": "Salaga" }, { "lat": 9.08297, "lon": 3.85196, "name": "Kisi" }, { "lat": 8.85488, "lon": 0.05922, "name": "Bimbila" }, { "lat": -38.21792, "lon": 145.03876, "name": "Mornington" } ], "question": "Which location is the geographic outlier among: Felana, Salaga, Kisi, Bimbila, Mornington?", "ground_truth": { "answer": "Mornington", "outlier_distance_km": 11444.9, "second_furthest_km": 4396.6, "clarity_ratio": 2.6, "median_distance_km": 4341.1, "distances_to_centroid": { "Felana": 1191.0, "Salaga": 4396.6, "Kisi": 3940.5, "Bimbila": 4341.1, "Mornington": 11444.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Felana: (9.46°, 42.18°)", " Salaga: (8.55°, -0.52°)", " Kisi: (9.08°, 3.85°)", " Bimbila: (8.85°, 0.06°)", " Mornington: (-38.22°, 145.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mornington: 11444.9 km from centroid", " Salaga: 4396.6 km from centroid", " Bimbila: 4341.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mornington", "FINAL ANSWER: Mornington" ] }, { "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": -25.47288, "lon": 28.09919, "name": "Soshanguve" }, { "lat": -24.2957, "lon": 28.11415, "name": "Vaalwater" }, { "lat": 5.78009, "lon": 38.40887, "name": "Kercha" }, { "lat": 11.55965, "lon": 9.66407, "name": "Chakwama" }, { "lat": 24.68413, "lon": 113.59839, "name": "Maba" } ], "question": "Which location is the geographic outlier among: Soshanguve, Vaalwater, Kercha, Chakwama, Maba?", "ground_truth": { "answer": "Maba", "outlier_distance_km": 8072.7, "second_furthest_km": 4021.2, "clarity_ratio": 2.01, "median_distance_km": 3135.0, "distances_to_centroid": { "Soshanguve": 3135.0, "Vaalwater": 3026.9, "Kercha": 996.7, "Chakwama": 4021.2, "Maba": 8072.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Soshanguve: (-25.47°, 28.10°)", " Vaalwater: (-24.30°, 28.11°)", " Kercha: (5.78°, 38.41°)", " Chakwama: (11.56°, 9.66°)", " Maba: (24.68°, 113.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maba: 8072.7 km from centroid", " Chakwama: 4021.2 km from centroid", " Soshanguve: 3135.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maba", "FINAL ANSWER: Maba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.34361, "lon": -98.97472, "name": "Emiliano Zapata" }, { "lat": 42.26259, "lon": -71.80229, "name": "Worcester" }, { "lat": 40.9805, "lon": -111.88744, "name": "Farmington" }, { "lat": 37.96215, "lon": -122.34553, "name": "San Pablo" }, { "lat": -15.77972, "lon": -47.92972, "name": "Brasília" } ], "question": "Which location is the geographic outlier among: Emiliano Zapata, Worcester, Farmington, San Pablo, Brasília?", "ground_truth": { "answer": "Brasília", "outlier_distance_km": 6471.9, "second_furthest_km": 3319.4, "clarity_ratio": 1.95, "median_distance_km": 2655.6, "distances_to_centroid": { "Emiliano Zapata": 1065.0, "Worcester": 2582.4, "Farmington": 2655.6, "San Pablo": 3319.4, "Brasília": 6471.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Emiliano Zapata: (19.34°, -98.97°)", " Worcester: (42.26°, -71.80°)", " Farmington: (40.98°, -111.89°)", " San Pablo: (37.96°, -122.35°)", " Brasília: (-15.78°, -47.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brasília: 6471.9 km from centroid", " San Pablo: 3319.4 km from centroid", " Farmington: 2655.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brasília", "FINAL ANSWER: Brasília" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.11667, "lon": 79.73333, "name": "Kālpi" }, { "lat": 30.65622, "lon": 76.82093, "name": "Zerakpur" }, { "lat": 23.7, "lon": 113.03333, "name": "Qingyuan" }, { "lat": 13.00334, "lon": 80.19614, "name": "Saint Thomas Mount" }, { "lat": 41.80065, "lon": -73.12122, "name": "Torrington" } ], "question": "Which location is the geographic outlier among: Kālpi, Zerakpur, Qingyuan, Saint Thomas Mount, Torrington?", "ground_truth": { "answer": "Torrington", "outlier_distance_km": 10707.8, "second_furthest_km": 5758.7, "clarity_ratio": 1.86, "median_distance_km": 3021.3, "distances_to_centroid": { "Kālpi": 2424.8, "Zerakpur": 2127.2, "Qingyuan": 5758.7, "Saint Thomas Mount": 3021.3, "Torrington": 10707.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kālpi: (26.12°, 79.73°)", " Zerakpur: (30.66°, 76.82°)", " Qingyuan: (23.70°, 113.03°)", " Saint Thomas Mount: (13.00°, 80.20°)", " Torrington: (41.80°, -73.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Torrington: 10707.8 km from centroid", " Qingyuan: 5758.7 km from centroid", " Saint Thomas Mount: 3021.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Torrington", "FINAL ANSWER: Torrington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 27.14652, "lon": 83.75803, "name": "Siswā Bāzār" }, { "lat": 10.3239, "lon": 123.0215, "name": "La Castellana" }, { "lat": 11.40598, "lon": 77.77501, "name": "Elandakuttai" }, { "lat": 36.22309, "lon": 136.19236, "name": "Awara" }, { "lat": -38.99081, "lon": -64.09574, "name": "Río Colorado" } ], "question": "Which location is the geographic outlier among: Siswā Bāzār, La Castellana, Elandakuttai, Awara, Río Colorado?", "ground_truth": { "answer": "Río Colorado", "outlier_distance_km": 14493.3, "second_furthest_km": 7154.7, "clarity_ratio": 2.03, "median_distance_km": 5659.6, "distances_to_centroid": { "Siswā Bāzār": 2382.6, "La Castellana": 5659.6, "Elandakuttai": 745.7, "Awara": 7154.7, "Río Colorado": 14493.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Siswā Bāzār: (27.15°, 83.76°)", " La Castellana: (10.32°, 123.02°)", " Elandakuttai: (11.41°, 77.78°)", " Awara: (36.22°, 136.19°)", " Río Colorado: (-38.99°, -64.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Río Colorado: 14493.3 km from centroid", " Awara: 7154.7 km from centroid", " La Castellana: 5659.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Río Colorado", "FINAL ANSWER: Río Colorado" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.76667, "lon": 144.91667, "name": "Moonee Ponds" }, { "lat": -38.02388, "lon": 144.40617, "name": "Lara" }, { "lat": -45.87416, "lon": 170.50361, "name": "Dunedin" }, { "lat": -37.91806, "lon": 145.03544, "name": "Bentleigh" }, { "lat": 58.30194, "lon": -134.41972, "name": "Juneau" } ], "question": "Which location is the geographic outlier among: Moonee Ponds, Lara, Dunedin, Bentleigh, Juneau?", "ground_truth": { "answer": "Juneau", "outlier_distance_km": 14277.5, "second_furthest_km": 7372.3, "clarity_ratio": 1.94, "median_distance_km": 5251.8, "distances_to_centroid": { "Moonee Ponds": 5239.3, "Lara": 5198.5, "Dunedin": 7372.3, "Bentleigh": 5251.8, "Juneau": 14277.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Moonee Ponds: (-37.77°, 144.92°)", " Lara: (-38.02°, 144.41°)", " Dunedin: (-45.87°, 170.50°)", " Bentleigh: (-37.92°, 145.04°)", " Juneau: (58.30°, -134.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Juneau: 14277.5 km from centroid", " Dunedin: 7372.3 km from centroid", " Bentleigh: 5251.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Juneau", "FINAL ANSWER: Juneau" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -37.9, "lon": 144.66667, "name": "Werribee" }, { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": -27.50578, "lon": 153.10236, "name": "Carindale" }, { "lat": 4.0613, "lon": 98.3699, "name": "Tanjungtiram" } ], "question": "Which location is the geographic outlier among: Epping, Werribee, Yarraville, Carindale, Tanjungtiram?", "ground_truth": { "answer": "Tanjungtiram", "outlier_distance_km": 5437.0, "second_furthest_km": 1567.0, "clarity_ratio": 3.47, "median_distance_km": 1366.2, "distances_to_centroid": { "Epping": 1357.5, "Werribee": 1362.6, "Yarraville": 1366.2, "Carindale": 1567.0, "Tanjungtiram": 5437.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Epping: (-37.65°, 145.03°)", " Werribee: (-37.90°, 144.67°)", " Yarraville: (-37.82°, 144.90°)", " Carindale: (-27.51°, 153.10°)", " Tanjungtiram: (4.06°, 98.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tanjungtiram: 5437.0 km from centroid", " Carindale: 1567.0 km from centroid", " Yarraville: 1366.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tanjungtiram", "FINAL ANSWER: Tanjungtiram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.84447, "lon": -90.18874, "name": "Clinton" }, { "lat": 43.05285, "lon": -74.34375, "name": "Gloversville" }, { "lat": 40.87676, "lon": -73.32456, "name": "East Northport" }, { "lat": 33.40178, "lon": -86.95444, "name": "Bessemer" }, { "lat": 12.57513, "lon": 122.27081, "name": "Romblon" } ], "question": "Which location is the geographic outlier among: Clinton, Gloversville, East Northport, Bessemer, Romblon?", "ground_truth": { "answer": "Romblon", "outlier_distance_km": 14489.0, "second_furthest_km": 4364.5, "clarity_ratio": 3.32, "median_distance_km": 4251.0, "distances_to_centroid": { "Clinton": 4364.5, "Gloversville": 3067.5, "East Northport": 2961.5, "Bessemer": 4251.0, "Romblon": 14489.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Clinton: (41.84°, -90.19°)", " Gloversville: (43.05°, -74.34°)", " East Northport: (40.88°, -73.32°)", " Bessemer: (33.40°, -86.95°)", " Romblon: (12.58°, 122.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Romblon: 14489.0 km from centroid", " Clinton: 4364.5 km from centroid", " Bessemer: 4251.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Romblon", "FINAL ANSWER: Romblon" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.60855, "lon": 138.46473, "name": "Minamiarupusu" }, { "lat": -7.4737, "lon": 112.6505, "name": "Tulangan Utara" }, { "lat": 19.15516, "lon": 73.26553, "name": "Badlapur" }, { "lat": 9.81371, "lon": 105.82096, "name": "Ngã Bảy" }, { "lat": -7.09639, "lon": -35.23278, "name": "Sapé" } ], "question": "Which location is the geographic outlier among: Minamiarupusu, Tulangan Utara, Badlapur, Ngã Bảy, Sapé?", "ground_truth": { "answer": "Sapé", "outlier_distance_km": 12786.4, "second_furthest_km": 6613.9, "clarity_ratio": 1.93, "median_distance_km": 4203.0, "distances_to_centroid": { "Minamiarupusu": 6613.9, "Tulangan Utara": 4203.0, "Badlapur": 1189.5, "Ngã Bảy": 2937.8, "Sapé": 12786.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Minamiarupusu: (35.61°, 138.46°)", " Tulangan Utara: (-7.47°, 112.65°)", " Badlapur: (19.16°, 73.27°)", " Ngã Bảy: (9.81°, 105.82°)", " Sapé: (-7.10°, -35.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sapé: 12786.4 km from centroid", " Minamiarupusu: 6613.9 km from centroid", " Tulangan Utara: 4203.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sapé", "FINAL ANSWER: Sapé" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.91806, "lon": 145.03544, "name": "Bentleigh" }, { "lat": -37.69825, "lon": 145.05967, "name": "Bundoora" }, { "lat": -37.66667, "lon": 145.06667, "name": "Mill Park" }, { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, { "lat": 14.40076, "lon": 37.93399, "name": "Sheraro" } ], "question": "Which location is the geographic outlier among: Bentleigh, Bundoora, Mill Park, Kallangur, Sheraro?", "ground_truth": { "answer": "Sheraro", "outlier_distance_km": 10418.6, "second_furthest_km": 2773.7, "clarity_ratio": 3.76, "median_distance_km": 2340.0, "distances_to_centroid": { "Bentleigh": 2340.0, "Bundoora": 2329.2, "Mill Park": 2328.0, "Kallangur": 2773.7, "Sheraro": 10418.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bentleigh: (-37.92°, 145.04°)", " Bundoora: (-37.70°, 145.06°)", " Mill Park: (-37.67°, 145.07°)", " Kallangur: (-27.25°, 152.99°)", " Sheraro: (14.40°, 37.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sheraro: 10418.6 km from centroid", " Kallangur: 2773.7 km from centroid", " Bentleigh: 2340.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sheraro", "FINAL ANSWER: Sheraro" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.01384, "lon": -75.07859, "name": "Frankford" }, { "lat": 47.80527, "lon": -122.24064, "name": "Bothell West" }, { "lat": 38.71311, "lon": -90.42984, "name": "Maryland Heights" }, { "lat": 35.9987, "lon": -96.11417, "name": "Sapulpa" }, { "lat": 31.02543, "lon": 109.38562, "name": "Zhuyi" } ], "question": "Which location is the geographic outlier among: Frankford, Bothell West, Maryland Heights, Sapulpa, Zhuyi?", "ground_truth": { "answer": "Zhuyi", "outlier_distance_km": 12091.7, "second_furthest_km": 5370.9, "clarity_ratio": 2.25, "median_distance_km": 3625.0, "distances_to_centroid": { "Frankford": 1737.4, "Bothell West": 5370.9, "Maryland Heights": 3063.4, "Sapulpa": 3625.0, "Zhuyi": 12091.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Frankford: (40.01°, -75.08°)", " Bothell West: (47.81°, -122.24°)", " Maryland Heights: (38.71°, -90.43°)", " Sapulpa: (36.00°, -96.11°)", " Zhuyi: (31.03°, 109.39°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zhuyi: 12091.7 km from centroid", " Bothell West: 5370.9 km from centroid", " Sapulpa: 3625.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zhuyi", "FINAL ANSWER: Zhuyi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.0501, "lon": -72.58287, "name": "Longmeadow" }, { "lat": 35.96064, "lon": -83.92074, "name": "Knoxville" }, { "lat": 41.28899, "lon": -72.68176, "name": "Guilford" }, { "lat": 35.88264, "lon": -80.08199, "name": "Thomasville" }, { "lat": -0.24849, "lon": 35.73194, "name": "Molo" } ], "question": "Which location is the geographic outlier among: Longmeadow, Knoxville, Guilford, Thomasville, Molo?", "ground_truth": { "answer": "Molo", "outlier_distance_km": 10063.6, "second_furthest_km": 2754.7, "clarity_ratio": 3.65, "median_distance_km": 2409.4, "distances_to_centroid": { "Longmeadow": 2009.2, "Knoxville": 2754.7, "Guilford": 1972.8, "Thomasville": 2409.4, "Molo": 10063.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Longmeadow: (42.05°, -72.58°)", " Knoxville: (35.96°, -83.92°)", " Guilford: (41.29°, -72.68°)", " Thomasville: (35.88°, -80.08°)", " Molo: (-0.25°, 35.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Molo: 10063.6 km from centroid", " Knoxville: 2754.7 km from centroid", " Thomasville: 2409.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Molo", "FINAL ANSWER: Molo" ] }, { "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": -28.11694, "lon": 153.46584, "name": "Palm Beach" }, { "lat": -38.11342, "lon": 145.28326, "name": "Cranbourne" }, { "lat": -37.83834, "lon": 144.99149, "name": "South Yarra" }, { "lat": -40.35636, "lon": 175.61113, "name": "Palmerston North" }, { "lat": -8.66667, "lon": -35.71667, "name": "Catende" } ], "question": "Which location is the geographic outlier among: Palm Beach, Cranbourne, South Yarra, Palmerston North, Catende?", "ground_truth": { "answer": "Catende", "outlier_distance_km": 14749.8, "second_furthest_km": 5341.1, "clarity_ratio": 2.76, "median_distance_km": 3555.4, "distances_to_centroid": { "Palm Beach": 3555.4, "Cranbourne": 2737.7, "South Yarra": 2707.7, "Palmerston North": 5341.1, "Catende": 14749.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Palm Beach: (-28.12°, 153.47°)", " Cranbourne: (-38.11°, 145.28°)", " South Yarra: (-37.84°, 144.99°)", " Palmerston North: (-40.36°, 175.61°)", " Catende: (-8.67°, -35.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Catende: 14749.8 km from centroid", " Palmerston North: 5341.1 km from centroid", " Palm Beach: 3555.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Catende", "FINAL ANSWER: Catende" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.39733, "lon": 107.46953, "name": "Caohui" }, { "lat": 21.27851, "lon": 86.68833, "name": "Soro" }, { "lat": 28.71753, "lon": 77.26508, "name": "Dayal Pur" }, { "lat": 22.55213, "lon": 113.88288, "name": "Bao'an" }, { "lat": 7.43636, "lon": 5.45925, "name": "Emure-Ekiti" } ], "question": "Which location is the geographic outlier among: Caohui, Soro, Dayal Pur, Bao'an, Emure-Ekiti?", "ground_truth": { "answer": "Emure-Ekiti", "outlier_distance_km": 7918.9, "second_furthest_km": 3667.0, "clarity_ratio": 2.16, "median_distance_km": 3056.6, "distances_to_centroid": { "Caohui": 3056.6, "Soro": 886.3, "Dayal Pur": 743.8, "Bao'an": 3667.0, "Emure-Ekiti": 7918.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caohui: (30.40°, 107.47°)", " Soro: (21.28°, 86.69°)", " Dayal Pur: (28.72°, 77.27°)", " Bao'an: (22.55°, 113.88°)", " Emure-Ekiti: (7.44°, 5.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Emure-Ekiti: 7918.9 km from centroid", " Bao'an: 3667.0 km from centroid", " Caohui: 3056.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Emure-Ekiti", "FINAL ANSWER: Emure-Ekiti" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.22795, "lon": -60.32994, "name": "Villa Constitución" }, { "lat": -26.92617, "lon": -60.04852, "name": "Machagai" }, { "lat": -0.85833, "lon": -48.14167, "name": "Vigia" }, { "lat": -22.76417, "lon": -43.39944, "name": "Belford Roxo" }, { "lat": 8.74921, "lon": 4.13113, "name": "Igbeti" } ], "question": "Which location is the geographic outlier among: Villa Constitución, Machagai, Vigia, Belford Roxo, Igbeti?", "ground_truth": { "answer": "Igbeti", "outlier_distance_km": 5685.8, "second_furthest_km": 2771.4, "clarity_ratio": 2.05, "median_distance_km": 2328.1, "distances_to_centroid": { "Villa Constitución": 2771.4, "Machagai": 2328.1, "Vigia": 1731.3, "Belford Roxo": 884.2, "Igbeti": 5685.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Villa Constitución: (-33.23°, -60.33°)", " Machagai: (-26.93°, -60.05°)", " Vigia: (-0.86°, -48.14°)", " Belford Roxo: (-22.76°, -43.40°)", " Igbeti: (8.75°, 4.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Igbeti: 5685.8 km from centroid", " Villa Constitución: 2771.4 km from centroid", " Machagai: 2328.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Igbeti", "FINAL ANSWER: Igbeti" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.39879, "lon": 37.68336, "name": "Taveta" }, { "lat": 6.61012, "lon": 3.30968, "name": "Akowonjo" }, { "lat": 10.38584, "lon": 8.57286, "name": "Lere" }, { "lat": 11.21566, "lon": 38.36452, "name": "Wegeda" }, { "lat": 45.17191, "lon": -93.87469, "name": "Buffalo" } ], "question": "Which location is the geographic outlier among: Taveta, Akowonjo, Lere, Wegeda, Buffalo?", "ground_truth": { "answer": "Buffalo", "outlier_distance_km": 9116.0, "second_furthest_km": 4702.3, "clarity_ratio": 1.94, "median_distance_km": 4298.5, "distances_to_centroid": { "Taveta": 4702.3, "Akowonjo": 957.3, "Lere": 1134.2, "Wegeda": 4298.5, "Buffalo": 9116.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taveta: (-3.40°, 37.68°)", " Akowonjo: (6.61°, 3.31°)", " Lere: (10.39°, 8.57°)", " Wegeda: (11.22°, 38.36°)", " Buffalo: (45.17°, -93.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Buffalo: 9116.0 km from centroid", " Taveta: 4702.3 km from centroid", " Wegeda: 4298.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Buffalo", "FINAL ANSWER: Buffalo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.03672, "lon": -73.23558, "name": "Agustín Codazzi" }, { "lat": -9.30667, "lon": -35.94333, "name": "Murici" }, { "lat": -21.42917, "lon": -45.94722, "name": "Alfenas" }, { "lat": -21.41222, "lon": -42.19667, "name": "Miracema" }, { "lat": 41.78586, "lon": -88.14729, "name": "Naperville" } ], "question": "Which location is the geographic outlier among: Agustín Codazzi, Murici, Alfenas, Miracema, Naperville?", "ground_truth": { "answer": "Naperville", "outlier_distance_km": 5599.3, "second_furthest_km": 2872.0, "clarity_ratio": 1.95, "median_distance_km": 2665.9, "distances_to_centroid": { "Agustín Codazzi": 2109.6, "Murici": 2556.9, "Alfenas": 2665.9, "Miracema": 2872.0, "Naperville": 5599.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Agustín Codazzi: (10.04°, -73.24°)", " Murici: (-9.31°, -35.94°)", " Alfenas: (-21.43°, -45.95°)", " Miracema: (-21.41°, -42.20°)", " Naperville: (41.79°, -88.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Naperville: 5599.3 km from centroid", " Miracema: 2872.0 km from centroid", " Alfenas: 2665.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Naperville", "FINAL ANSWER: Naperville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.11342, "lon": 145.28326, "name": "Cranbourne" }, { "lat": -38.15912, "lon": 145.93118, "name": "Warragul" }, { "lat": -37.83382, "lon": 144.93834, "name": "City of Port Phillip" }, { "lat": -37.58333, "lon": 145.03333, "name": "Wollert" }, { "lat": -43.30031, "lon": -65.10564, "name": "Rawson" } ], "question": "Which location is the geographic outlier among: Cranbourne, Warragul, City of Port Phillip, Wollert, Rawson?", "ground_truth": { "answer": "Rawson", "outlier_distance_km": 10788.7, "second_furthest_km": 3679.7, "clarity_ratio": 2.93, "median_distance_km": 3626.3, "distances_to_centroid": { "Cranbourne": 3626.3, "Warragul": 3679.7, "City of Port Phillip": 3605.2, "Wollert": 3620.7, "Rawson": 10788.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cranbourne: (-38.11°, 145.28°)", " Warragul: (-38.16°, 145.93°)", " City of Port Phillip: (-37.83°, 144.94°)", " Wollert: (-37.58°, 145.03°)", " Rawson: (-43.30°, -65.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rawson: 10788.7 km from centroid", " Warragul: 3679.7 km from centroid", " Cranbourne: 3626.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rawson", "FINAL ANSWER: Rawson" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.94433, "lon": 28.01496, "name": "Gonubie" }, { "lat": 7.3, "lon": 38.65, "name": "Kuyera" }, { "lat": 0.02538, "lon": 36.40865, "name": "Mairo Inya" }, { "lat": 6.59651, "lon": 3.34205, "name": "Ikeja" }, { "lat": -41.28664, "lon": 174.77557, "name": "Wellington" } ], "question": "Which location is the geographic outlier among: Gonubie, Kuyera, Mairo Inya, Ikeja, Wellington?", "ground_truth": { "answer": "Wellington", "outlier_distance_km": 11376.1, "second_furthest_km": 6205.1, "clarity_ratio": 1.83, "median_distance_km": 3691.9, "distances_to_centroid": { "Gonubie": 3691.9, "Kuyera": 2901.2, "Mairo Inya": 2568.2, "Ikeja": 6205.1, "Wellington": 11376.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gonubie: (-32.94°, 28.01°)", " Kuyera: (7.30°, 38.65°)", " Mairo Inya: (0.03°, 36.41°)", " Ikeja: (6.60°, 3.34°)", " Wellington: (-41.29°, 174.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wellington: 11376.1 km from centroid", " Ikeja: 6205.1 km from centroid", " Gonubie: 3691.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wellington", "FINAL ANSWER: Wellington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.44187, "lon": 152.93861, "name": "The Gap" }, { "lat": -12.46113, "lon": 130.84185, "name": "Darwin" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": -27.35364, "lon": 152.96848, "name": "Albany Creek" }, { "lat": 36.48333, "lon": 139.0, "name": "Shibukawa" } ], "question": "Which location is the geographic outlier among: The Gap, Darwin, Taylors Lakes, Albany Creek, Shibukawa?", "ground_truth": { "answer": "Shibukawa", "outlier_distance_km": 5605.2, "second_furthest_km": 2670.0, "clarity_ratio": 2.1, "median_distance_km": 1782.2, "distances_to_centroid": { "The Gap": 1782.2, "Darwin": 1443.1, "Taylors Lakes": 2670.0, "Albany Creek": 1775.5, "Shibukawa": 5605.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " The Gap: (-27.44°, 152.94°)", " Darwin: (-12.46°, 130.84°)", " Taylors Lakes: (-37.70°, 144.79°)", " Albany Creek: (-27.35°, 152.97°)", " Shibukawa: (36.48°, 139.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shibukawa: 5605.2 km from centroid", " Taylors Lakes: 2670.0 km from centroid", " The Gap: 1782.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shibukawa", "FINAL ANSWER: Shibukawa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -35.03264, "lon": -63.01484, "name": "General Villegas" }, { "lat": -21.83222, "lon": -46.89361, "name": "Vargem Grande do Sul" }, { "lat": -16.525, "lon": -50.37222, "name": "São Luís de Montes Belos" }, { "lat": -21.97583, "lon": -51.65139, "name": "Santo Anastácio" }, { "lat": 25.67312, "lon": 78.45908, "name": "Datia" } ], "question": "Which location is the geographic outlier among: General Villegas, Vargem Grande do Sul, São Luís de Montes Belos, Santo Anastácio, Datia?", "ground_truth": { "answer": "Datia", "outlier_distance_km": 12170.6, "second_furthest_km": 4321.9, "clarity_ratio": 2.82, "median_distance_km": 2782.4, "distances_to_centroid": { "General Villegas": 4321.9, "Vargem Grande do Sul": 2307.6, "São Luís de Montes Belos": 2555.0, "Santo Anastácio": 2782.4, "Datia": 12170.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " General Villegas: (-35.03°, -63.01°)", " Vargem Grande do Sul: (-21.83°, -46.89°)", " São Luís de Montes Belos: (-16.52°, -50.37°)", " Santo Anastácio: (-21.98°, -51.65°)", " Datia: (25.67°, 78.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Datia: 12170.6 km from centroid", " General Villegas: 4321.9 km from centroid", " Santo Anastácio: 2782.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Datia", "FINAL ANSWER: Datia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.31157, "lon": 73.10087, "name": "Nandri" }, { "lat": 22.9757, "lon": 88.4337, "name": "Kalyani" }, { "lat": 26.94442, "lon": 84.5377, "name": "Chanpatia" }, { "lat": 30.26361, "lon": 78.00862, "name": "Clement Town" }, { "lat": 1.25744, "lon": -70.23551, "name": "Mitú" } ], "question": "Which location is the geographic outlier among: Nandri, Kalyani, Chanpatia, Clement Town, Mitú?", "ground_truth": { "answer": "Mitú", "outlier_distance_km": 13131.5, "second_furthest_km": 3868.6, "clarity_ratio": 3.39, "median_distance_km": 3465.3, "distances_to_centroid": { "Nandri": 2327.3, "Kalyani": 3868.6, "Chanpatia": 3465.3, "Clement Town": 2882.7, "Mitú": 13131.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nandri: (26.31°, 73.10°)", " Kalyani: (22.98°, 88.43°)", " Chanpatia: (26.94°, 84.54°)", " Clement Town: (30.26°, 78.01°)", " Mitú: (1.26°, -70.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mitú: 13131.5 km from centroid", " Kalyani: 3868.6 km from centroid", " Chanpatia: 3465.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mitú", "FINAL ANSWER: Mitú" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.41502, "lon": 2.88132, "name": "Badagry" }, { "lat": 7.13333, "lon": 37.95, "name": "Shonē" }, { "lat": 6.72556, "lon": 11.25652, "name": "Gembu" }, { "lat": 25.48742, "lon": 28.97918, "name": "Mūţ" }, { "lat": 35.52808, "lon": -108.74258, "name": "Gallup" } ], "question": "Which location is the geographic outlier among: Badagry, Shonē, Gembu, Mūţ, Gallup?", "ground_truth": { "answer": "Gallup", "outlier_distance_km": 10108.3, "second_furthest_km": 4832.0, "clarity_ratio": 2.09, "median_distance_km": 3717.7, "distances_to_centroid": { "Badagry": 1427.4, "Shonē": 4832.0, "Gembu": 2112.3, "Mūţ": 3717.7, "Gallup": 10108.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Badagry: (6.42°, 2.88°)", " Shonē: (7.13°, 37.95°)", " Gembu: (6.73°, 11.26°)", " Mūţ: (25.49°, 28.98°)", " Gallup: (35.53°, -108.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gallup: 10108.3 km from centroid", " Shonē: 4832.0 km from centroid", " Mūţ: 3717.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gallup", "FINAL ANSWER: Gallup" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.1525, "lon": 125.83278, "name": "Jiutai" }, { "lat": 16.28584, "lon": 81.25464, "name": "Kanuru" }, { "lat": 13.82609, "lon": 100.67933, "name": "Khan Na Yao" }, { "lat": 23.11147, "lon": 114.41523, "name": "Huizhou" }, { "lat": 48.96115, "lon": 2.06882, "name": "Achères" } ], "question": "Which location is the geographic outlier among: Jiutai, Kanuru, Khan Na Yao, Huizhou, Achères?", "ground_truth": { "answer": "Achères", "outlier_distance_km": 7099.8, "second_furthest_km": 3959.2, "clarity_ratio": 1.79, "median_distance_km": 3019.6, "distances_to_centroid": { "Jiutai": 3959.2, "Kanuru": 1489.5, "Khan Na Yao": 2366.9, "Huizhou": 3019.6, "Achères": 7099.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jiutai: (44.15°, 125.83°)", " Kanuru: (16.29°, 81.25°)", " Khan Na Yao: (13.83°, 100.68°)", " Huizhou: (23.11°, 114.42°)", " Achères: (48.96°, 2.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Achères: 7099.8 km from centroid", " Jiutai: 3959.2 km from centroid", " Huizhou: 3019.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Achères", "FINAL ANSWER: Achères" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -13.4425, "lon": -42.23889, "name": "Paramirim" }, { "lat": -20.39484, "lon": -43.50517, "name": "Ouro Preto" }, { "lat": -18.54861, "lon": -42.55694, "name": "Peçanha" }, { "lat": -20.795, "lon": -49.22028, "name": "Guapiaçu" }, { "lat": 6.10045, "lon": 7.061, "name": "Agulu" } ], "question": "Which location is the geographic outlier among: Paramirim, Ouro Preto, Peçanha, Guapiaçu, Agulu?", "ground_truth": { "answer": "Agulu", "outlier_distance_km": 5035.3, "second_furthest_km": 1803.4, "clarity_ratio": 2.79, "median_distance_km": 1266.2, "distances_to_centroid": { "Paramirim": 881.1, "Ouro Preto": 1266.2, "Peçanha": 1069.4, "Guapiaçu": 1803.4, "Agulu": 5035.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paramirim: (-13.44°, -42.24°)", " Ouro Preto: (-20.39°, -43.51°)", " Peçanha: (-18.55°, -42.56°)", " Guapiaçu: (-20.80°, -49.22°)", " Agulu: (6.10°, 7.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Agulu: 5035.3 km from centroid", " Guapiaçu: 1803.4 km from centroid", " Ouro Preto: 1266.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Agulu", "FINAL ANSWER: Agulu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.03634, "lon": 4.32501, "name": "Rijswijk" }, { "lat": 50.17103, "lon": 18.9041, "name": "Mikołów" }, { "lat": 53.4115, "lon": -2.83935, "name": "Huyton" }, { "lat": 54.35369, "lon": 41.91986, "name": "Sasovo" }, { "lat": -38.08333, "lon": 144.38333, "name": "Corio" } ], "question": "Which location is the geographic outlier among: Rijswijk, Mikołów, Huyton, Sasovo, Corio?", "ground_truth": { "answer": "Corio", "outlier_distance_km": 13306.0, "second_furthest_km": 4033.5, "clarity_ratio": 3.3, "median_distance_km": 3527.8, "distances_to_centroid": { "Rijswijk": 3527.8, "Mikołów": 2529.0, "Huyton": 4033.5, "Sasovo": 2221.7, "Corio": 13306.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rijswijk: (52.04°, 4.33°)", " Mikołów: (50.17°, 18.90°)", " Huyton: (53.41°, -2.84°)", " Sasovo: (54.35°, 41.92°)", " Corio: (-38.08°, 144.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Corio: 13306.0 km from centroid", " Huyton: 4033.5 km from centroid", " Rijswijk: 3527.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Corio", "FINAL ANSWER: Corio" ] }, { "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": 41.05, "lon": -0.13333, "name": "Alcañiz" }, { "lat": 52.1653, "lon": 8.85996, "name": "Vlotho" }, { "lat": 51.12753, "lon": 16.96186, "name": "Osiedle Kosmonautów" }, { "lat": 51.06358, "lon": 6.0998, "name": "Heinsberg" }, { "lat": 0.63513, "lon": 34.28165, "name": "Malaba" } ], "question": "Which location is the geographic outlier among: Alcañiz, Vlotho, Osiedle Kosmonautów, Heinsberg, Malaba?", "ground_truth": { "answer": "Malaba", "outlier_distance_km": 4793.8, "second_furthest_km": 1479.2, "clarity_ratio": 3.24, "median_distance_km": 1429.9, "distances_to_centroid": { "Alcañiz": 1151.9, "Vlotho": 1479.2, "Osiedle Kosmonautów": 1357.1, "Heinsberg": 1429.9, "Malaba": 4793.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Alcañiz: (41.05°, -0.13°)", " Vlotho: (52.17°, 8.86°)", " Osiedle Kosmonautów: (51.13°, 16.96°)", " Heinsberg: (51.06°, 6.10°)", " Malaba: (0.64°, 34.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Malaba: 4793.8 km from centroid", " Vlotho: 1479.2 km from centroid", " Heinsberg: 1429.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Malaba", "FINAL ANSWER: Malaba" ] }, { "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": 51.83149, "lon": 7.28075, "name": "Dülmen" }, { "lat": 52.47523, "lon": 1.75167, "name": "Lowestoft" }, { "lat": 56.90832, "lon": 62.03433, "name": "Sukhoy Log" }, { "lat": 51.40055, "lon": 6.71187, "name": "Rheinhausen" }, { "lat": 35.97113, "lon": 139.6491, "name": "Hasuda" } ], "question": "Which location is the geographic outlier among: Dülmen, Lowestoft, Sukhoy Log, Rheinhausen, Hasuda?", "ground_truth": { "answer": "Hasuda", "outlier_distance_km": 7441.9, "second_furthest_km": 2889.4, "clarity_ratio": 2.58, "median_distance_km": 2577.0, "distances_to_centroid": { "Dülmen": 2530.2, "Lowestoft": 2889.4, "Sukhoy Log": 1461.7, "Rheinhausen": 2577.0, "Hasuda": 7441.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dülmen: (51.83°, 7.28°)", " Lowestoft: (52.48°, 1.75°)", " Sukhoy Log: (56.91°, 62.03°)", " Rheinhausen: (51.40°, 6.71°)", " Hasuda: (35.97°, 139.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hasuda: 7441.9 km from centroid", " Lowestoft: 2889.4 km from centroid", " Rheinhausen: 2577.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hasuda", "FINAL ANSWER: Hasuda" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.01457, "lon": -97.09696, "name": "Flower Mound" }, { "lat": 31.85425, "lon": -110.9937, "name": "Green Valley" }, { "lat": 46.09454, "lon": -64.7965, "name": "Moncton" }, { "lat": 26.6359, "lon": -80.09615, "name": "Palm Springs" }, { "lat": -37.75, "lon": 145.01667, "name": "Preston" } ], "question": "Which location is the geographic outlier among: Flower Mound, Green Valley, Moncton, Palm Springs, Preston?", "ground_truth": { "answer": "Preston", "outlier_distance_km": 17937.4, "second_furthest_km": 6954.2, "clarity_ratio": 2.58, "median_distance_km": 5645.4, "distances_to_centroid": { "Flower Mound": 5645.4, "Green Valley": 6954.2, "Moncton": 3593.3, "Palm Springs": 3986.1, "Preston": 17937.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Flower Mound: (33.01°, -97.10°)", " Green Valley: (31.85°, -110.99°)", " Moncton: (46.09°, -64.80°)", " Palm Springs: (26.64°, -80.10°)", " Preston: (-37.75°, 145.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Preston: 17937.4 km from centroid", " Green Valley: 6954.2 km from centroid", " Flower Mound: 5645.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Preston", "FINAL ANSWER: Preston" ] }, { "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": 3.52973, "lon": -75.64525, "name": "Rioblanco" }, { "lat": -8.60111, "lon": -38.56861, "name": "Floresta" }, { "lat": -25.44472, "lon": -49.1925, "name": "Pinhais" }, { "lat": -20.07028, "lon": -44.30167, "name": "Igarapé" }, { "lat": 34.37803, "lon": 109.20892, "name": "Lintong" } ], "question": "Which location is the geographic outlier among: Rioblanco, Floresta, Pinhais, Igarapé, Lintong?", "ground_truth": { "answer": "Lintong", "outlier_distance_km": 13713.8, "second_furthest_km": 6262.6, "clarity_ratio": 2.19, "median_distance_km": 4002.9, "distances_to_centroid": { "Rioblanco": 6262.6, "Floresta": 2169.5, "Pinhais": 4002.9, "Igarapé": 3258.3, "Lintong": 13713.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rioblanco: (3.53°, -75.65°)", " Floresta: (-8.60°, -38.57°)", " Pinhais: (-25.44°, -49.19°)", " Igarapé: (-20.07°, -44.30°)", " Lintong: (34.38°, 109.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lintong: 13713.8 km from centroid", " Rioblanco: 6262.6 km from centroid", " Pinhais: 4002.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lintong", "FINAL ANSWER: Lintong" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.51278, "lon": -44.00056, "name": "Pinheiral" }, { "lat": -9.11694, "lon": -37.60222, "name": "Canapi" }, { "lat": -38.23291, "lon": -72.33292, "name": "Victoria" }, { "lat": -5.53778, "lon": -48.73333, "name": "São Domingos do Araguaia" }, { "lat": -27.56056, "lon": 151.95386, "name": "Toowoomba" } ], "question": "Which location is the geographic outlier among: Pinheiral, Canapi, Victoria, São Domingos do Araguaia, Toowoomba?", "ground_truth": { "answer": "Toowoomba", "outlier_distance_km": 14324.8, "second_furthest_km": 6215.2, "clarity_ratio": 2.3, "median_distance_km": 4485.6, "distances_to_centroid": { "Pinheiral": 3500.7, "Canapi": 3208.0, "Victoria": 6215.2, "São Domingos do Araguaia": 4485.6, "Toowoomba": 14324.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pinheiral: (-22.51°, -44.00°)", " Canapi: (-9.12°, -37.60°)", " Victoria: (-38.23°, -72.33°)", " São Domingos do Araguaia: (-5.54°, -48.73°)", " Toowoomba: (-27.56°, 151.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Toowoomba: 14324.8 km from centroid", " Victoria: 6215.2 km from centroid", " São Domingos do Araguaia: 4485.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Toowoomba", "FINAL ANSWER: Toowoomba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.436, "lon": 77.67603, "name": "Pudūr" }, { "lat": 36.91218, "lon": 119.5566, "name": "Buzhuang" }, { "lat": 36.59889, "lon": 109.49167, "name": "Yan’an" }, { "lat": 25.84664, "lon": 114.9326, "name": "Ganzhou" }, { "lat": 43.58127, "lon": 7.12487, "name": "Antibes" } ], "question": "Which location is the geographic outlier among: Pudūr, Buzhuang, Yan’an, Ganzhou, Antibes?", "ground_truth": { "answer": "Antibes", "outlier_distance_km": 6844.5, "second_furthest_km": 3173.8, "clarity_ratio": 2.16, "median_distance_km": 2900.4, "distances_to_centroid": { "Pudūr": 2316.1, "Buzhuang": 3173.8, "Yan’an": 2278.4, "Ganzhou": 2900.4, "Antibes": 6844.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pudūr: (11.44°, 77.68°)", " Buzhuang: (36.91°, 119.56°)", " Yan’an: (36.60°, 109.49°)", " Ganzhou: (25.85°, 114.93°)", " Antibes: (43.58°, 7.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Antibes: 6844.5 km from centroid", " Buzhuang: 3173.8 km from centroid", " Ganzhou: 2900.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Antibes", "FINAL ANSWER: Antibes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.97583, "lon": -51.65139, "name": "Santo Anastácio" }, { "lat": -21.97722, "lon": -44.9325, "name": "Caxambu" }, { "lat": -11.01611, "lon": -68.74806, "name": "Brasiléia" }, { "lat": -23.47544, "lon": -46.60609, "name": "Tucuruvi" }, { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" } ], "question": "Which location is the geographic outlier among: Santo Anastácio, Caxambu, Brasiléia, Tucuruvi, Coogee?", "ground_truth": { "answer": "Coogee", "outlier_distance_km": 13502.7, "second_furthest_km": 6126.5, "clarity_ratio": 2.2, "median_distance_km": 4055.8, "distances_to_centroid": { "Santo Anastácio": 4055.8, "Caxambu": 3369.5, "Brasiléia": 6126.5, "Tucuruvi": 3522.2, "Coogee": 13502.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santo Anastácio: (-21.98°, -51.65°)", " Caxambu: (-21.98°, -44.93°)", " Brasiléia: (-11.02°, -68.75°)", " Tucuruvi: (-23.48°, -46.61°)", " Coogee: (-33.92°, 151.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coogee: 13502.7 km from centroid", " Brasiléia: 6126.5 km from centroid", " Santo Anastácio: 4055.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coogee", "FINAL ANSWER: Coogee" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.93408, "lon": -40.40473, "name": "Fundão" }, { "lat": -5.87806, "lon": -46.69917, "name": "Sítio Novo" }, { "lat": -5.08917, "lon": -81.11444, "name": "Paita" }, { "lat": -1.02167, "lon": -46.635, "name": "Augusto Corrêa" }, { "lat": -37.88413, "lon": 144.78367, "name": "Altona Meadows" } ], "question": "Which location is the geographic outlier among: Fundão, Sítio Novo, Paita, Augusto Corrêa, Altona Meadows?", "ground_truth": { "answer": "Altona Meadows", "outlier_distance_km": 13840.1, "second_furthest_km": 7402.9, "clarity_ratio": 1.87, "median_distance_km": 3865.2, "distances_to_centroid": { "Fundão": 2880.9, "Sítio Novo": 3686.6, "Paita": 7402.9, "Augusto Corrêa": 3865.2, "Altona Meadows": 13840.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fundão: (-19.93°, -40.40°)", " Sítio Novo: (-5.88°, -46.70°)", " Paita: (-5.09°, -81.11°)", " Augusto Corrêa: (-1.02°, -46.63°)", " Altona Meadows: (-37.88°, 144.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Altona Meadows: 13840.1 km from centroid", " Paita: 7402.9 km from centroid", " Augusto Corrêa: 3865.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Altona Meadows", "FINAL ANSWER: Altona Meadows" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.06803, "lon": 134.35033, "name": "Kamojimachō-jōgejima" }, { "lat": 29.99152, "lon": 120.89845, "name": "Lianghu" }, { "lat": 30.30618, "lon": 107.41296, "name": "Changlong" }, { "lat": 12.50855, "lon": 80.14976, "name": "Pudupattanam" }, { "lat": -10.75, "lon": -77.76667, "name": "Barranca" } ], "question": "Which location is the geographic outlier among: Kamojimachō-jōgejima, Lianghu, Changlong, Pudupattanam, Barranca?", "ground_truth": { "answer": "Barranca", "outlier_distance_km": 16743.2, "second_furthest_km": 6224.0, "clarity_ratio": 2.69, "median_distance_km": 4950.6, "distances_to_centroid": { "Kamojimachō-jōgejima": 6224.0, "Lianghu": 4950.6, "Changlong": 3668.4, "Pudupattanam": 1067.8, "Barranca": 16743.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kamojimachō-jōgejima: (34.07°, 134.35°)", " Lianghu: (29.99°, 120.90°)", " Changlong: (30.31°, 107.41°)", " Pudupattanam: (12.51°, 80.15°)", " Barranca: (-10.75°, -77.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Barranca: 16743.2 km from centroid", " Kamojimachō-jōgejima: 6224.0 km from centroid", " Lianghu: 4950.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Barranca", "FINAL ANSWER: Barranca" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.74215, "lon": 7.08368, "name": "Okrika" }, { "lat": 30.35487, "lon": 31.20105, "name": "Ţūkh" }, { "lat": 30.85711, "lon": 32.31183, "name": "Al Qanţarah" }, { "lat": 7.53333, "lon": 39.25, "name": "Bek’ojī" }, { "lat": 20.67738, "lon": -103.34749, "name": "Guadalajara" } ], "question": "Which location is the geographic outlier among: Okrika, Ţūkh, Al Qanţarah, Bek’ojī, Guadalajara?", "ground_truth": { "answer": "Guadalajara", "outlier_distance_km": 10709.3, "second_furthest_km": 4285.1, "clarity_ratio": 2.5, "median_distance_km": 3387.8, "distances_to_centroid": { "Okrika": 1687.9, "Ţūkh": 3270.2, "Al Qanţarah": 3387.8, "Bek’ojī": 4285.1, "Guadalajara": 10709.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Okrika: (4.74°, 7.08°)", " Ţūkh: (30.35°, 31.20°)", " Al Qanţarah: (30.86°, 32.31°)", " Bek’ojī: (7.53°, 39.25°)", " Guadalajara: (20.68°, -103.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Guadalajara: 10709.3 km from centroid", " Bek’ojī: 4285.1 km from centroid", " Al Qanţarah: 3387.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Guadalajara", "FINAL ANSWER: Guadalajara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.27194, "lon": -101.98602, "name": "Loreto" }, { "lat": 42.26308, "lon": -88.00397, "name": "Mundelein" }, { "lat": 40.23384, "lon": -111.65853, "name": "Provo" }, { "lat": 21.03053, "lon": -102.40227, "name": "San Miguel el Alto" }, { "lat": 6.33815, "lon": 5.62575, "name": "Benin City" } ], "question": "Which location is the geographic outlier among: Loreto, Mundelein, Provo, San Miguel el Alto, Benin City?", "ground_truth": { "answer": "Benin City", "outlier_distance_km": 9229.0, "second_furthest_km": 3318.3, "clarity_ratio": 2.78, "median_distance_km": 2385.4, "distances_to_centroid": { "Loreto": 2302.8, "Mundelein": 1916.9, "Provo": 3318.3, "San Miguel el Alto": 2385.4, "Benin City": 9229.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Loreto: (22.27°, -101.99°)", " Mundelein: (42.26°, -88.00°)", " Provo: (40.23°, -111.66°)", " San Miguel el Alto: (21.03°, -102.40°)", " Benin City: (6.34°, 5.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Benin City: 9229.0 km from centroid", " Provo: 3318.3 km from centroid", " San Miguel el Alto: 2385.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Benin City", "FINAL ANSWER: Benin City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.68281, "lon": -88.35146, "name": "Oswego" }, { "lat": 34.06251, "lon": -118.12285, "name": "Monterey Park" }, { "lat": 33.8303, "lon": -116.54529, "name": "Palm Springs" }, { "lat": 19.25417, "lon": -99.62778, "name": "San Jorge Pueblo Nuevo" }, { "lat": -18.54778, "lon": -42.76333, "name": "São João Evangelista" } ], "question": "Which location is the geographic outlier among: Oswego, Monterey Park, Palm Springs, San Jorge Pueblo Nuevo, São João Evangelista?", "ground_truth": { "answer": "São João Evangelista", "outlier_distance_km": 7093.6, "second_furthest_km": 2785.1, "clarity_ratio": 2.55, "median_distance_km": 2641.0, "distances_to_centroid": { "Oswego": 2226.7, "Monterey Park": 2785.1, "Palm Springs": 2641.0, "San Jorge Pueblo Nuevo": 748.8, "São João Evangelista": 7093.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Oswego: (41.68°, -88.35°)", " Monterey Park: (34.06°, -118.12°)", " Palm Springs: (33.83°, -116.55°)", " San Jorge Pueblo Nuevo: (19.25°, -99.63°)", " São João Evangelista: (-18.55°, -42.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São João Evangelista: 7093.6 km from centroid", " Monterey Park: 2785.1 km from centroid", " Palm Springs: 2641.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São João Evangelista", "FINAL ANSWER: São João Evangelista" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.18856, "lon": -3.71887, "name": "Santafé" }, { "lat": 51.12645, "lon": 7.90333, "name": "Attendorn" }, { "lat": 43.37135, "lon": -8.396, "name": "A Coruña" }, { "lat": 41.07663, "lon": 1.14163, "name": "Salou" }, { "lat": -33.95, "lon": 151.23333, "name": "Maroubra" } ], "question": "Which location is the geographic outlier among: Santafé, Attendorn, A Coruña, Salou, Maroubra?", "ground_truth": { "answer": "Maroubra", "outlier_distance_km": 14471.9, "second_furthest_km": 3808.7, "clarity_ratio": 3.8, "median_distance_km": 3279.6, "distances_to_centroid": { "Santafé": 3279.6, "Attendorn": 3172.7, "A Coruña": 3808.7, "Salou": 2983.5, "Maroubra": 14471.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santafé: (37.19°, -3.72°)", " Attendorn: (51.13°, 7.90°)", " A Coruña: (43.37°, -8.40°)", " Salou: (41.08°, 1.14°)", " Maroubra: (-33.95°, 151.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maroubra: 14471.9 km from centroid", " A Coruña: 3808.7 km from centroid", " Santafé: 3279.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maroubra", "FINAL ANSWER: Maroubra" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -25.28762, "lon": 152.76936, "name": "Hervey Bay" }, { "lat": -38.03333, "lon": 145.25, "name": "Hampton Park" }, { "lat": -37.78247, "lon": 145.31682, "name": "Mooroolbark" }, { "lat": -37.814, "lon": 144.96332, "name": "Melbourne" }, { "lat": -22.28556, "lon": -46.61222, "name": "Jacutinga" } ], "question": "Which location is the geographic outlier among: Hervey Bay, Hampton Park, Mooroolbark, Melbourne, Jacutinga?", "ground_truth": { "answer": "Jacutinga", "outlier_distance_km": 13392.9, "second_furthest_km": 4368.5, "clarity_ratio": 3.07, "median_distance_km": 3401.1, "distances_to_centroid": { "Hervey Bay": 4368.5, "Hampton Park": 3394.9, "Mooroolbark": 3401.1, "Melbourne": 3370.0, "Jacutinga": 13392.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hervey Bay: (-25.29°, 152.77°)", " Hampton Park: (-38.03°, 145.25°)", " Mooroolbark: (-37.78°, 145.32°)", " Melbourne: (-37.81°, 144.96°)", " Jacutinga: (-22.29°, -46.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jacutinga: 13392.9 km from centroid", " Hervey Bay: 4368.5 km from centroid", " Mooroolbark: 3401.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jacutinga", "FINAL ANSWER: Jacutinga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.1691, "lon": -70.74053, "name": "Rancagua" }, { "lat": -9.97056, "lon": -37.00333, "name": "Traipu" }, { "lat": 6.15153, "lon": -75.61657, "name": "Sabaneta" }, { "lat": -22.73917, "lon": -47.33139, "name": "Americana" }, { "lat": 52.17333, "lon": 5.29167, "name": "Soest" } ], "question": "Which location is the geographic outlier among: Rancagua, Traipu, Sabaneta, Americana, Soest?", "ground_truth": { "answer": "Soest", "outlier_distance_km": 7610.7, "second_furthest_km": 4485.6, "clarity_ratio": 1.7, "median_distance_km": 3501.1, "distances_to_centroid": { "Rancagua": 4485.6, "Traipu": 1280.7, "Sabaneta": 3501.1, "Americana": 2350.9, "Soest": 7610.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rancagua: (-34.17°, -70.74°)", " Traipu: (-9.97°, -37.00°)", " Sabaneta: (6.15°, -75.62°)", " Americana: (-22.74°, -47.33°)", " Soest: (52.17°, 5.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Soest: 7610.7 km from centroid", " Rancagua: 4485.6 km from centroid", " Sabaneta: 3501.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Soest", "FINAL ANSWER: Soest" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.11639, "lon": -45.05444, "name": "São Lourenço" }, { "lat": 4.81367, "lon": -74.35453, "name": "Facatativá" }, { "lat": -23.64889, "lon": -47.57333, "name": "Salto de Pirapora" }, { "lat": -22.02861, "lon": -42.36083, "name": "Cordeiro" }, { "lat": -36.86472, "lon": 174.64768, "name": "Te Atatu South" } ], "question": "Which location is the geographic outlier among: São Lourenço, Facatativá, Salto de Pirapora, Cordeiro, Te Atatu South?", "ground_truth": { "answer": "Te Atatu South", "outlier_distance_km": 13693.3, "second_furthest_km": 7858.0, "clarity_ratio": 1.74, "median_distance_km": 4201.2, "distances_to_centroid": { "São Lourenço": 3952.7, "Facatativá": 7858.0, "Salto de Pirapora": 4201.2, "Cordeiro": 3676.2, "Te Atatu South": 13693.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Lourenço: (-22.12°, -45.05°)", " Facatativá: (4.81°, -74.35°)", " Salto de Pirapora: (-23.65°, -47.57°)", " Cordeiro: (-22.03°, -42.36°)", " Te Atatu South: (-36.86°, 174.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Te Atatu South: 13693.3 km from centroid", " Facatativá: 7858.0 km from centroid", " Salto de Pirapora: 4201.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Te Atatu South", "FINAL ANSWER: Te Atatu South" ] }, { "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": 41.83844, "lon": 15.56535, "name": "Sannicandro Garganico" }, { "lat": 50.30582, "lon": 18.9742, "name": "Chorzów" }, { "lat": 48.83669, "lon": 2.48255, "name": "Nogent-sur-Marne" }, { "lat": 39.46569, "lon": -0.46005, "name": "Aldaia" }, { "lat": 38.90015, "lon": -76.99587, "name": "H Street NE" } ], "question": "Which location is the geographic outlier among: Sannicandro Garganico, Chorzów, Nogent-sur-Marne, Aldaia, H Street NE?", "ground_truth": { "answer": "H Street NE", "outlier_distance_km": 5607.0, "second_furthest_km": 2155.9, "clarity_ratio": 2.6, "median_distance_km": 1934.5, "distances_to_centroid": { "Sannicandro Garganico": 1934.5, "Chorzów": 2155.9, "Nogent-sur-Marne": 980.0, "Aldaia": 800.1, "H Street NE": 5607.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sannicandro Garganico: (41.84°, 15.57°)", " Chorzów: (50.31°, 18.97°)", " Nogent-sur-Marne: (48.84°, 2.48°)", " Aldaia: (39.47°, -0.46°)", " H Street NE: (38.90°, -77.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " H Street NE: 5607.0 km from centroid", " Chorzów: 2155.9 km from centroid", " Sannicandro Garganico: 1934.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: H Street NE", "FINAL ANSWER: H Street NE" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.42497, "lon": -62.08404, "name": "San Francisco" }, { "lat": -7.22944, "lon": -44.55611, "name": "Uruçuí" }, { "lat": -9.89667, "lon": -39.02639, "name": "Canudos" }, { "lat": -23.52508, "lon": -46.63889, "name": "Bom Retiro" }, { "lat": -37.73261, "lon": 144.86504, "name": "Keilor East" } ], "question": "Which location is the geographic outlier among: San Francisco, Uruçuí, Canudos, Bom Retiro, Keilor East?", "ground_truth": { "answer": "Keilor East", "outlier_distance_km": 12856.0, "second_furthest_km": 5280.7, "clarity_ratio": 2.43, "median_distance_km": 4098.6, "distances_to_centroid": { "San Francisco": 5280.7, "Uruçuí": 4098.6, "Canudos": 3422.3, "Bom Retiro": 3803.2, "Keilor East": 12856.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Francisco: (-31.42°, -62.08°)", " Uruçuí: (-7.23°, -44.56°)", " Canudos: (-9.90°, -39.03°)", " Bom Retiro: (-23.53°, -46.64°)", " Keilor East: (-37.73°, 144.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Keilor East: 12856.0 km from centroid", " San Francisco: 5280.7 km from centroid", " Uruçuí: 4098.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Keilor East", "FINAL ANSWER: Keilor East" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.25451, "lon": 21.22407, "name": "Wesoła" }, { "lat": 28.68351, "lon": -17.76421, "name": "Santa Cruz de la Palma" }, { "lat": 45.53329, "lon": 9.22585, "name": "Sesto San Giovanni" }, { "lat": 53.33333, "lon": -2.9, "name": "Garston" }, { "lat": 6.245, "lon": -75.57151, "name": "Medellín" } ], "question": "Which location is the geographic outlier among: Wesoła, Santa Cruz de la Palma, Sesto San Giovanni, Garston, Medellín?", "ground_truth": { "answer": "Medellín", "outlier_distance_km": 7158.7, "second_furthest_km": 3145.8, "clarity_ratio": 2.28, "median_distance_km": 2074.9, "distances_to_centroid": { "Wesoła": 3145.8, "Santa Cruz de la Palma": 1040.6, "Sesto San Giovanni": 2074.9, "Garston": 1959.7, "Medellín": 7158.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wesoła: (52.25°, 21.22°)", " Santa Cruz de la Palma: (28.68°, -17.76°)", " Sesto San Giovanni: (45.53°, 9.23°)", " Garston: (53.33°, -2.90°)", " Medellín: (6.25°, -75.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Medellín: 7158.7 km from centroid", " Wesoła: 3145.8 km from centroid", " Sesto San Giovanni: 2074.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Medellín", "FINAL ANSWER: Medellín" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 31.22201, "lon": 109.71068, "name": "Futian" }, { "lat": 7.90963, "lon": 98.40248, "name": "Ban Ratsada" }, { "lat": 37.01083, "lon": 127.27028, "name": "Anseong" }, { "lat": 43.30667, "lon": 128.51139, "name": "Dashitou" }, { "lat": 40.8601, "lon": -73.9093, "name": "University Heights" } ], "question": "Which location is the geographic outlier among: Futian, Ban Ratsada, Anseong, Dashitou, University Heights?", "ground_truth": { "answer": "University Heights", "outlier_distance_km": 11408.7, "second_furthest_km": 4544.0, "clarity_ratio": 2.51, "median_distance_km": 4496.8, "distances_to_centroid": { "Futian": 2992.8, "Ban Ratsada": 3414.5, "Anseong": 4496.8, "Dashitou": 4544.0, "University Heights": 11408.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Futian: (31.22°, 109.71°)", " Ban Ratsada: (7.91°, 98.40°)", " Anseong: (37.01°, 127.27°)", " Dashitou: (43.31°, 128.51°)", " University Heights: (40.86°, -73.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " University Heights: 11408.7 km from centroid", " Dashitou: 4544.0 km from centroid", " Anseong: 4496.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: University Heights", "FINAL ANSWER: University Heights" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.17641, "lon": 36.7564, "name": "Karuri" }, { "lat": 5.70119, "lon": -1.28657, "name": "Foso" }, { "lat": 9.08569, "lon": 40.86708, "name": "Āsbe Teferī" }, { "lat": 30.63146, "lon": 31.93927, "name": "Aş Şāliḩīyah al Jadīdah" }, { "lat": -16.97278, "lon": -48.95333, "name": "Bela Vista de Goiás" } ], "question": "Which location is the geographic outlier among: Karuri, Foso, Āsbe Teferī, Aş Şāliḩīyah al Jadīdah, Bela Vista de Goiás?", "ground_truth": { "answer": "Bela Vista de Goiás", "outlier_distance_km": 7129.8, "second_furthest_km": 3498.8, "clarity_ratio": 2.04, "median_distance_km": 3223.3, "distances_to_centroid": { "Karuri": 2861.0, "Foso": 1455.6, "Āsbe Teferī": 3223.3, "Aş Şāliḩīyah al Jadīdah": 3498.8, "Bela Vista de Goiás": 7129.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Karuri: (-1.18°, 36.76°)", " Foso: (5.70°, -1.29°)", " Āsbe Teferī: (9.09°, 40.87°)", " Aş Şāliḩīyah al Jadīdah: (30.63°, 31.94°)", " Bela Vista de Goiás: (-16.97°, -48.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bela Vista de Goiás: 7129.8 km from centroid", " Aş Şāliḩīyah al Jadīdah: 3498.8 km from centroid", " Āsbe Teferī: 3223.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bela Vista de Goiás", "FINAL ANSWER: Bela Vista de Goiás" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.91667, "lon": 151.03333, "name": "Bankstown" }, { "lat": -33.80383, "lon": 150.98768, "name": "Westmead" }, { "lat": -33.76667, "lon": 150.81667, "name": "Mount Druitt" }, { "lat": -27.94402, "lon": 153.39815, "name": "Labrador" }, { "lat": 31.25861, "lon": 121.45972, "name": "Zhabei" } ], "question": "Which location is the geographic outlier among: Bankstown, Westmead, Mount Druitt, Labrador, Zhabei?", "ground_truth": { "answer": "Zhabei", "outlier_distance_km": 6215.3, "second_furthest_km": 1678.3, "clarity_ratio": 3.7, "median_distance_km": 1665.1, "distances_to_centroid": { "Bankstown": 1678.3, "Westmead": 1665.1, "Mount Druitt": 1655.8, "Labrador": 1221.1, "Zhabei": 6215.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bankstown: (-33.92°, 151.03°)", " Westmead: (-33.80°, 150.99°)", " Mount Druitt: (-33.77°, 150.82°)", " Labrador: (-27.94°, 153.40°)", " Zhabei: (31.26°, 121.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zhabei: 6215.3 km from centroid", " Bankstown: 1678.3 km from centroid", " Westmead: 1665.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zhabei", "FINAL ANSWER: Zhabei" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.13972, "lon": 110.405, "name": "Ungaran" }, { "lat": 39.04194, "lon": 106.39583, "name": "Dawukou" }, { "lat": 11.8049, "lon": 75.481, "name": "Pinarāyi" }, { "lat": 28.24737, "lon": 77.06544, "name": "Sohna" }, { "lat": -10.70833, "lon": -38.18333, "name": "Poço Verde" } ], "question": "Which location is the geographic outlier among: Ungaran, Dawukou, Pinarāyi, Sohna, Poço Verde?", "ground_truth": { "answer": "Poço Verde", "outlier_distance_km": 11805.5, "second_furthest_km": 5337.5, "clarity_ratio": 2.21, "median_distance_km": 4944.3, "distances_to_centroid": { "Ungaran": 5337.5, "Dawukou": 4944.3, "Pinarāyi": 1006.9, "Sohna": 2104.6, "Poço Verde": 11805.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ungaran: (-7.14°, 110.41°)", " Dawukou: (39.04°, 106.40°)", " Pinarāyi: (11.80°, 75.48°)", " Sohna: (28.25°, 77.07°)", " Poço Verde: (-10.71°, -38.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Poço Verde: 11805.5 km from centroid", " Ungaran: 5337.5 km from centroid", " Dawukou: 4944.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Poço Verde", "FINAL ANSWER: Poço Verde" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.04945, "lon": 13.92578, "name": "Sulmona" }, { "lat": 52.6069, "lon": 11.85867, "name": "Stendal" }, { "lat": 51.55306, "lon": -0.3023, "name": "Brent" }, { "lat": 39.59111, "lon": -0.46151, "name": "Bétera" }, { "lat": -25.40778, "lon": -52.41611, "name": "Laranjeiras do Sul" } ], "question": "Which location is the geographic outlier among: Sulmona, Stendal, Brent, Bétera, Laranjeiras do Sul?", "ground_truth": { "answer": "Laranjeiras do Sul", "outlier_distance_km": 8101.5, "second_furthest_km": 2675.3, "clarity_ratio": 3.03, "median_distance_km": 2206.2, "distances_to_centroid": { "Sulmona": 2040.4, "Stendal": 2675.3, "Brent": 2206.2, "Bétera": 949.5, "Laranjeiras do Sul": 8101.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sulmona: (42.05°, 13.93°)", " Stendal: (52.61°, 11.86°)", " Brent: (51.55°, -0.30°)", " Bétera: (39.59°, -0.46°)", " Laranjeiras do Sul: (-25.41°, -52.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Laranjeiras do Sul: 8101.5 km from centroid", " Stendal: 2675.3 km from centroid", " Brent: 2206.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Laranjeiras do Sul", "FINAL ANSWER: Laranjeiras do Sul" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.61448, "lon": -2.45991, "name": "Weymouth" }, { "lat": 52.48419, "lon": 13.53185, "name": "Karlshorst" }, { "lat": 53.01372, "lon": -1.35383, "name": "Heanor" }, { "lat": 44.13806, "lon": 4.81025, "name": "Orange" }, { "lat": -30.95619, "lon": -58.7797, "name": "Federal" } ], "question": "Which location is the geographic outlier among: Weymouth, Karlshorst, Heanor, Orange, Federal?", "ground_truth": { "answer": "Federal", "outlier_distance_km": 8907.3, "second_furthest_km": 2730.9, "clarity_ratio": 3.26, "median_distance_km": 2211.3, "distances_to_centroid": { "Weymouth": 1934.2, "Karlshorst": 2730.9, "Heanor": 2211.3, "Orange": 1639.0, "Federal": 8907.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Weymouth: (50.61°, -2.46°)", " Karlshorst: (52.48°, 13.53°)", " Heanor: (53.01°, -1.35°)", " Orange: (44.14°, 4.81°)", " Federal: (-30.96°, -58.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Federal: 8907.3 km from centroid", " Karlshorst: 2730.9 km from centroid", " Heanor: 2211.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Federal", "FINAL ANSWER: Federal" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.31056, "lon": -50.04833, "name": "Rio Maria" }, { "lat": -25.92842, "lon": -49.18008, "name": "Tijucas do Sul" }, { "lat": -21.27472, "lon": -43.17917, "name": "Rio Pomba" }, { "lat": -19.8, "lon": -41.43833, "name": "Mutum" }, { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" } ], "question": "Which location is the geographic outlier among: Rio Maria, Tijucas do Sul, Rio Pomba, Mutum, Hoppers Crossing?", "ground_truth": { "answer": "Hoppers Crossing", "outlier_distance_km": 12719.1, "second_furthest_km": 4817.2, "clarity_ratio": 2.64, "median_distance_km": 4195.4, "distances_to_centroid": { "Rio Maria": 4817.2, "Tijucas do Sul": 4195.4, "Rio Pomba": 3642.1, "Mutum": 3491.4, "Hoppers Crossing": 12719.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rio Maria: (-7.31°, -50.05°)", " Tijucas do Sul: (-25.93°, -49.18°)", " Rio Pomba: (-21.27°, -43.18°)", " Mutum: (-19.80°, -41.44°)", " Hoppers Crossing: (-37.88°, 144.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hoppers Crossing: 12719.1 km from centroid", " Rio Maria: 4817.2 km from centroid", " Tijucas do Sul: 4195.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hoppers Crossing", "FINAL ANSWER: Hoppers Crossing" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.71889, "lon": -46.60972, "name": "Passos" }, { "lat": -7.84472, "lon": -35.31972, "name": "Lagoa do Carro" }, { "lat": -14.75583, "lon": -43.93222, "name": "Manga" }, { "lat": -8.72028, "lon": -39.11389, "name": "Abaré" }, { "lat": 41.57337, "lon": -87.78449, "name": "Tinley Park" } ], "question": "Which location is the geographic outlier among: Passos, Lagoa do Carro, Manga, Abaré, Tinley Park?", "ground_truth": { "answer": "Tinley Park", "outlier_distance_km": 6135.8, "second_furthest_km": 2114.7, "clarity_ratio": 2.9, "median_distance_km": 1803.8, "distances_to_centroid": { "Passos": 2114.7, "Lagoa do Carro": 1803.8, "Manga": 1584.4, "Abaré": 1464.4, "Tinley Park": 6135.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Passos: (-20.72°, -46.61°)", " Lagoa do Carro: (-7.84°, -35.32°)", " Manga: (-14.76°, -43.93°)", " Abaré: (-8.72°, -39.11°)", " Tinley Park: (41.57°, -87.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tinley Park: 6135.8 km from centroid", " Passos: 2114.7 km from centroid", " Lagoa do Carro: 1803.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tinley Park", "FINAL ANSWER: Tinley Park" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.40116, "lon": -93.21406, "name": "Paraiso" }, { "lat": 36.03452, "lon": -89.38563, "name": "Dyersburg" }, { "lat": 18.14905, "lon": -94.4447, "name": "Coatzacoalcos" }, { "lat": 19.8173, "lon": -97.35992, "name": "Teziutlan" }, { "lat": 38.38008, "lon": 77.31324, "name": "Arele" } ], "question": "Which location is the geographic outlier among: Paraiso, Dyersburg, Coatzacoalcos, Teziutlan, Arele?", "ground_truth": { "answer": "Arele", "outlier_distance_km": 11542.8, "second_furthest_km": 3933.3, "clarity_ratio": 2.93, "median_distance_km": 3703.2, "distances_to_centroid": { "Paraiso": 3571.6, "Dyersburg": 3042.3, "Coatzacoalcos": 3703.2, "Teziutlan": 3933.3, "Arele": 11542.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paraiso: (18.40°, -93.21°)", " Dyersburg: (36.03°, -89.39°)", " Coatzacoalcos: (18.15°, -94.44°)", " Teziutlan: (19.82°, -97.36°)", " Arele: (38.38°, 77.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arele: 11542.8 km from centroid", " Teziutlan: 3933.3 km from centroid", " Coatzacoalcos: 3703.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arele", "FINAL ANSWER: Arele" ] }, { "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": 40.82649, "lon": -74.10681, "name": "Rutherford" }, { "lat": 39.61366, "lon": -86.10665, "name": "Greenwood" }, { "lat": 33.85455, "lon": -84.21714, "name": "Tucker" }, { "lat": 40.66871, "lon": -73.52707, "name": "Bellmore" }, { "lat": 9.99461, "lon": 39.89693, "name": "Robit" } ], "question": "Which location is the geographic outlier among: Rutherford, Greenwood, Tucker, Bellmore, Robit?", "ground_truth": { "answer": "Robit", "outlier_distance_km": 9910.7, "second_furthest_km": 2815.2, "clarity_ratio": 3.52, "median_distance_km": 2647.9, "distances_to_centroid": { "Rutherford": 1855.5, "Greenwood": 2815.2, "Tucker": 2647.9, "Bellmore": 1803.7, "Robit": 9910.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rutherford: (40.83°, -74.11°)", " Greenwood: (39.61°, -86.11°)", " Tucker: (33.85°, -84.22°)", " Bellmore: (40.67°, -73.53°)", " Robit: (9.99°, 39.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Robit: 9910.7 km from centroid", " Greenwood: 2815.2 km from centroid", " Tucker: 2647.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Robit", "FINAL ANSWER: Robit" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.88576, "lon": -122.11802, "name": "Lafayette" }, { "lat": 46.05007, "lon": -71.96579, "name": "Victoriaville" }, { "lat": 50.45008, "lon": -104.6178, "name": "Regina" }, { "lat": 45.40008, "lon": -73.58248, "name": "Sainte-Catherine" }, { "lat": -6.26083, "lon": -36.51778, "name": "Currais Novos" } ], "question": "Which location is the geographic outlier among: Lafayette, Victoriaville, Regina, Sainte-Catherine, Currais Novos?", "ground_truth": { "answer": "Currais Novos", "outlier_distance_km": 6573.4, "second_furthest_km": 3606.0, "clarity_ratio": 1.82, "median_distance_km": 2543.3, "distances_to_centroid": { "Lafayette": 3606.0, "Victoriaville": 1507.3, "Regina": 2543.3, "Sainte-Catherine": 1376.2, "Currais Novos": 6573.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lafayette: (37.89°, -122.12°)", " Victoriaville: (46.05°, -71.97°)", " Regina: (50.45°, -104.62°)", " Sainte-Catherine: (45.40°, -73.58°)", " Currais Novos: (-6.26°, -36.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Currais Novos: 6573.4 km from centroid", " Lafayette: 3606.0 km from centroid", " Regina: 2543.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Currais Novos", "FINAL ANSWER: Currais Novos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.94924, "lon": -0.28496, "name": "Hitchin" }, { "lat": 51.99417, "lon": 4.20972, "name": "Naaldwijk" }, { "lat": 52.05917, "lon": 1.15545, "name": "Ipswich" }, { "lat": 47.16878, "lon": -1.4729, "name": "Vertou" }, { "lat": 33.61153, "lon": 131.13002, "name": "Buzen" } ], "question": "Which location is the geographic outlier among: Hitchin, Naaldwijk, Ipswich, Vertou, Buzen?", "ground_truth": { "answer": "Buzen", "outlier_distance_km": 8272.6, "second_furthest_km": 2132.8, "clarity_ratio": 3.88, "median_distance_km": 2012.8, "distances_to_centroid": { "Hitchin": 2012.8, "Naaldwijk": 1707.3, "Ipswich": 1915.5, "Vertou": 2132.8, "Buzen": 8272.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hitchin: (51.95°, -0.28°)", " Naaldwijk: (51.99°, 4.21°)", " Ipswich: (52.06°, 1.16°)", " Vertou: (47.17°, -1.47°)", " Buzen: (33.61°, 131.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Buzen: 8272.6 km from centroid", " Vertou: 2132.8 km from centroid", " Hitchin: 2012.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Buzen", "FINAL ANSWER: Buzen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.78254, "lon": 138.61077, "name": "Parafield Gardens" }, { "lat": -37.7, "lon": 144.93333, "name": "Glenroy" }, { "lat": -27.66757, "lon": 152.92488, "name": "Springfield Lakes" }, { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" }, { "lat": 39.84395, "lon": -84.12466, "name": "Huber Heights" } ], "question": "Which location is the geographic outlier among: Parafield Gardens, Glenroy, Springfield Lakes, Palmerston, Huber Heights?", "ground_truth": { "answer": "Huber Heights", "outlier_distance_km": 17202.4, "second_furthest_km": 5964.6, "clarity_ratio": 2.88, "median_distance_km": 5385.6, "distances_to_centroid": { "Parafield Gardens": 4750.3, "Glenroy": 5385.6, "Springfield Lakes": 5964.6, "Palmerston": 3714.0, "Huber Heights": 17202.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parafield Gardens: (-34.78°, 138.61°)", " Glenroy: (-37.70°, 144.93°)", " Springfield Lakes: (-27.67°, 152.92°)", " Palmerston: (-12.49°, 130.98°)", " Huber Heights: (39.84°, -84.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Huber Heights: 17202.4 km from centroid", " Springfield Lakes: 5964.6 km from centroid", " Glenroy: 5385.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Huber Heights", "FINAL ANSWER: Huber Heights" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.05926, "lon": -0.24249, "name": "Bawku" }, { "lat": 7.40353, "lon": -2.46635, "name": "Nsoatre" }, { "lat": 26.23648, "lon": 32.00387, "name": "Al Balyanā" }, { "lat": -0.17344, "lon": 35.86313, "name": "Rongai" }, { "lat": -27.87683, "lon": 153.28572, "name": "Upper Coomera" } ], "question": "Which location is the geographic outlier among: Bawku, Nsoatre, Al Balyanā, Rongai, Upper Coomera?", "ground_truth": { "answer": "Upper Coomera", "outlier_distance_km": 12103.9, "second_furthest_km": 5127.4, "clarity_ratio": 2.36, "median_distance_km": 4916.3, "distances_to_centroid": { "Bawku": 4916.3, "Nsoatre": 5127.4, "Al Balyanā": 2835.5, "Rongai": 953.0, "Upper Coomera": 12103.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bawku: (11.06°, -0.24°)", " Nsoatre: (7.40°, -2.47°)", " Al Balyanā: (26.24°, 32.00°)", " Rongai: (-0.17°, 35.86°)", " Upper Coomera: (-27.88°, 153.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Upper Coomera: 12103.9 km from centroid", " Nsoatre: 5127.4 km from centroid", " Bawku: 4916.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Upper Coomera", "FINAL ANSWER: Upper Coomera" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.62512, "lon": 78.62434, "name": "Ilaiyankudi" }, { "lat": 35.50333, "lon": 119.17167, "name": "Sanzhuang" }, { "lat": 17.62477, "lon": 78.08669, "name": "Sangāreddi" }, { "lat": 43.95611, "lon": 125.46611, "name": "Xinglongshan" }, { "lat": 5.68476, "lon": -0.04011, "name": "Lashibi" } ], "question": "Which location is the geographic outlier among: Ilaiyankudi, Sanzhuang, Sangāreddi, Xinglongshan, Lashibi?", "ground_truth": { "answer": "Lashibi", "outlier_distance_km": 8771.7, "second_furthest_km": 4756.1, "clarity_ratio": 1.84, "median_distance_km": 4020.7, "distances_to_centroid": { "Ilaiyankudi": 1439.9, "Sanzhuang": 4020.7, "Sangāreddi": 585.6, "Xinglongshan": 4756.1, "Lashibi": 8771.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ilaiyankudi: (9.63°, 78.62°)", " Sanzhuang: (35.50°, 119.17°)", " Sangāreddi: (17.62°, 78.09°)", " Xinglongshan: (43.96°, 125.47°)", " Lashibi: (5.68°, -0.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lashibi: 8771.7 km from centroid", " Xinglongshan: 4756.1 km from centroid", " Sanzhuang: 4020.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lashibi", "FINAL ANSWER: Lashibi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.92675, "lon": 6.26764, "name": "Yenagoa" }, { "lat": 24.90652, "lon": 32.88563, "name": "Ar Radīsīyah Qiblī" }, { "lat": 31.03408, "lon": 30.46823, "name": "Damanhur" }, { "lat": 6.71667, "lon": 37.56667, "name": "Gasuba" }, { "lat": -12.15278, "lon": -44.99, "name": "Barreiras" } ], "question": "Which location is the geographic outlier among: Yenagoa, Ar Radīsīyah Qiblī, Damanhur, Gasuba, Barreiras?", "ground_truth": { "answer": "Barreiras", "outlier_distance_km": 6847.1, "second_furthest_km": 2892.2, "clarity_ratio": 2.37, "median_distance_km": 2801.5, "distances_to_centroid": { "Yenagoa": 964.6, "Ar Radīsīyah Qiblī": 2646.2, "Damanhur": 2892.2, "Gasuba": 2801.5, "Barreiras": 6847.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yenagoa: (4.93°, 6.27°)", " Ar Radīsīyah Qiblī: (24.91°, 32.89°)", " Damanhur: (31.03°, 30.47°)", " Gasuba: (6.72°, 37.57°)", " Barreiras: (-12.15°, -44.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Barreiras: 6847.1 km from centroid", " Damanhur: 2892.2 km from centroid", " Gasuba: 2801.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Barreiras", "FINAL ANSWER: Barreiras" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 13.15498, "lon": 10.63468, "name": "Kumagunnam" }, { "lat": -27.87394, "lon": 26.69072, "name": "Odendaalsrus" }, { "lat": 7.28889, "lon": 36.24167, "name": "Bonga" }, { "lat": 30.21035, "lon": 31.36812, "name": "Al Khānkah" }, { "lat": 33.72835, "lon": -117.14642, "name": "Menifee" } ], "question": "Which location is the geographic outlier among: Kumagunnam, Odendaalsrus, Bonga, Al Khānkah, Menifee?", "ground_truth": { "answer": "Menifee", "outlier_distance_km": 11499.4, "second_furthest_km": 5368.0, "clarity_ratio": 2.14, "median_distance_km": 4265.2, "distances_to_centroid": { "Kumagunnam": 1435.8, "Odendaalsrus": 5368.0, "Bonga": 4265.2, "Al Khānkah": 4070.7, "Menifee": 11499.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kumagunnam: (13.15°, 10.63°)", " Odendaalsrus: (-27.87°, 26.69°)", " Bonga: (7.29°, 36.24°)", " Al Khānkah: (30.21°, 31.37°)", " Menifee: (33.73°, -117.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Menifee: 11499.4 km from centroid", " Odendaalsrus: 5368.0 km from centroid", " Bonga: 4265.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Menifee", "FINAL ANSWER: Menifee" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.6835, "lon": -78.99837, "name": "Socastee" }, { "lat": 39.17316, "lon": -77.27165, "name": "Germantown" }, { "lat": 42.3501, "lon": -71.087, "name": "Back Bay" }, { "lat": 36.0397, "lon": -114.98194, "name": "Henderson" }, { "lat": -28.29917, "lon": -54.26306, "name": "Santo Ângelo" } ], "question": "Which location is the geographic outlier among: Socastee, Germantown, Back Bay, Henderson, Santo Ângelo?", "ground_truth": { "answer": "Santo Ângelo", "outlier_distance_km": 6463.6, "second_furthest_km": 3627.8, "clarity_ratio": 1.78, "median_distance_km": 2114.8, "distances_to_centroid": { "Socastee": 1011.7, "Germantown": 1633.0, "Back Bay": 2114.8, "Henderson": 3627.8, "Santo Ângelo": 6463.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Socastee: (33.68°, -79.00°)", " Germantown: (39.17°, -77.27°)", " Back Bay: (42.35°, -71.09°)", " Henderson: (36.04°, -114.98°)", " Santo Ângelo: (-28.30°, -54.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santo Ângelo: 6463.6 km from centroid", " Henderson: 3627.8 km from centroid", " Back Bay: 2114.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santo Ângelo", "FINAL ANSWER: Santo Ângelo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.17677, "lon": -77.19526, "name": "Montgomery Village" }, { "lat": 38.44957, "lon": -78.86892, "name": "Harrisonburg" }, { "lat": 16.09007, "lon": -93.7546, "name": "Tonalá" }, { "lat": 40.20148, "lon": -77.18887, "name": "Carlisle" }, { "lat": -1.76556, "lon": -55.86611, "name": "Oriximiná" } ], "question": "Which location is the geographic outlier among: Montgomery Village, Harrisonburg, Tonalá, Carlisle, Oriximiná?", "ground_truth": { "answer": "Oriximiná", "outlier_distance_km": 3843.2, "second_furthest_km": 2115.6, "clarity_ratio": 1.82, "median_distance_km": 1532.3, "distances_to_centroid": { "Montgomery Village": 1418.5, "Harrisonburg": 1353.6, "Tonalá": 2115.6, "Carlisle": 1532.3, "Oriximiná": 3843.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Montgomery Village: (39.18°, -77.20°)", " Harrisonburg: (38.45°, -78.87°)", " Tonalá: (16.09°, -93.75°)", " Carlisle: (40.20°, -77.19°)", " Oriximiná: (-1.77°, -55.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Oriximiná: 3843.2 km from centroid", " Tonalá: 2115.6 km from centroid", " Carlisle: 1532.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Oriximiná", "FINAL ANSWER: Oriximiná" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.40076, "lon": 37.93399, "name": "Sheraro" }, { "lat": 29.9, "lon": 31.25, "name": "Al Ḩawāmidīyah" }, { "lat": 25.87198, "lon": 32.75585, "name": "Jarājūs" }, { "lat": -29.01269, "lon": 29.86619, "name": "Estcourt" }, { "lat": -33.70244, "lon": 151.09931, "name": "Hornsby" } ], "question": "Which location is the geographic outlier among: Sheraro, Al Ḩawāmidīyah, Jarājūs, Estcourt, Hornsby?", "ground_truth": { "answer": "Hornsby", "outlier_distance_km": 10517.5, "second_furthest_km": 4425.7, "clarity_ratio": 2.38, "median_distance_km": 4139.3, "distances_to_centroid": { "Sheraro": 2501.6, "Al Ḩawāmidīyah": 4139.3, "Jarājūs": 3721.7, "Estcourt": 4425.7, "Hornsby": 10517.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sheraro: (14.40°, 37.93°)", " Al Ḩawāmidīyah: (29.90°, 31.25°)", " Jarājūs: (25.87°, 32.76°)", " Estcourt: (-29.01°, 29.87°)", " Hornsby: (-33.70°, 151.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hornsby: 10517.5 km from centroid", " Estcourt: 4425.7 km from centroid", " Al Ḩawāmidīyah: 4139.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hornsby", "FINAL ANSWER: Hornsby" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.29996, "lon": 36.99047, "name": "Githunguri" }, { "lat": 7.85, "lon": 36.65, "name": "Āgaro" }, { "lat": -26.37945, "lon": 28.92112, "name": "Lebohang" }, { "lat": -34.58301, "lon": 19.35048, "name": "Gansbaai" }, { "lat": -17.83917, "lon": -40.35389, "name": "Nanuque" } ], "question": "Which location is the geographic outlier among: Githunguri, Āgaro, Lebohang, Gansbaai, Nanuque?", "ground_truth": { "answer": "Nanuque", "outlier_distance_km": 6042.1, "second_furthest_km": 3343.8, "clarity_ratio": 1.81, "median_distance_km": 2702.0, "distances_to_centroid": { "Githunguri": 2702.0, "Āgaro": 3343.8, "Lebohang": 1864.5, "Gansbaai": 2259.3, "Nanuque": 6042.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Githunguri: (-1.30°, 36.99°)", " Āgaro: (7.85°, 36.65°)", " Lebohang: (-26.38°, 28.92°)", " Gansbaai: (-34.58°, 19.35°)", " Nanuque: (-17.84°, -40.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nanuque: 6042.1 km from centroid", " Āgaro: 3343.8 km from centroid", " Githunguri: 2702.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nanuque", "FINAL ANSWER: Nanuque" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.42103, "lon": -87.30747, "name": "Myrtle Grove" }, { "lat": 19.24473, "lon": -103.7127, "name": "Colima" }, { "lat": 40.66689, "lon": -111.88799, "name": "Murray" }, { "lat": 32.54487, "lon": -94.36742, "name": "Marshall" }, { "lat": -26.43138, "lon": 28.47713, "name": "Nigel" } ], "question": "Which location is the geographic outlier among: Myrtle Grove, Colima, Murray, Marshall, Nigel?", "ground_truth": { "answer": "Nigel", "outlier_distance_km": 12124.4, "second_furthest_km": 4323.5, "clarity_ratio": 2.8, "median_distance_km": 3140.1, "distances_to_centroid": { "Myrtle Grove": 1841.0, "Colima": 3140.1, "Murray": 4323.5, "Marshall": 2525.7, "Nigel": 12124.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Myrtle Grove: (30.42°, -87.31°)", " Colima: (19.24°, -103.71°)", " Murray: (40.67°, -111.89°)", " Marshall: (32.54°, -94.37°)", " Nigel: (-26.43°, 28.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nigel: 12124.4 km from centroid", " Murray: 4323.5 km from centroid", " Colima: 3140.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nigel", "FINAL ANSWER: Nigel" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.91449, "lon": -0.24186, "name": "Libourne" }, { "lat": 41.38125, "lon": 2.11744, "name": "la Maternitat i Sant Ramon" }, { "lat": 54.15077, "lon": 33.28151, "name": "Desnogorsk" }, { "lat": 51.9864, "lon": 22.78248, "name": "Międzyrzec Podlaski" }, { "lat": 5.35113, "lon": -0.62313, "name": "Winneba" } ], "question": "Which location is the geographic outlier among: Libourne, la Maternitat i Sant Ramon, Desnogorsk, Międzyrzec Podlaski, Winneba?", "ground_truth": { "answer": "Winneba", "outlier_distance_km": 3992.3, "second_furthest_km": 2302.7, "clarity_ratio": 1.73, "median_distance_km": 1633.1, "distances_to_centroid": { "Libourne": 1131.3, "la Maternitat i Sant Ramon": 815.7, "Desnogorsk": 2302.7, "Międzyrzec Podlaski": 1633.1, "Winneba": 3992.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Libourne: (44.91°, -0.24°)", " la Maternitat i Sant Ramon: (41.38°, 2.12°)", " Desnogorsk: (54.15°, 33.28°)", " Międzyrzec Podlaski: (51.99°, 22.78°)", " Winneba: (5.35°, -0.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Winneba: 3992.3 km from centroid", " Desnogorsk: 2302.7 km from centroid", " Międzyrzec Podlaski: 1633.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Winneba", "FINAL ANSWER: Winneba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.41278, "lon": -40.68306, "name": "Marechal Floriano" }, { "lat": -31.34582, "lon": -64.33849, "name": "La Calera" }, { "lat": 5.20087, "lon": -75.86865, "name": "Belén de Umbría" }, { "lat": -1.77111, "lon": -47.43806, "name": "Irituia" }, { "lat": 26.19401, "lon": 78.94137, "name": "Lahār" } ], "question": "Which location is the geographic outlier among: Marechal Floriano, La Calera, Belén de Umbría, Irituia, Lahār?", "ground_truth": { "answer": "Lahār", "outlier_distance_km": 12100.6, "second_furthest_km": 5218.8, "clarity_ratio": 2.32, "median_distance_km": 4679.0, "distances_to_centroid": { "Marechal Floriano": 2127.5, "La Calera": 4679.0, "Belén de Umbría": 5218.8, "Irituia": 1971.8, "Lahār": 12100.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Marechal Floriano: (-20.41°, -40.68°)", " La Calera: (-31.35°, -64.34°)", " Belén de Umbría: (5.20°, -75.87°)", " Irituia: (-1.77°, -47.44°)", " Lahār: (26.19°, 78.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lahār: 12100.6 km from centroid", " Belén de Umbría: 5218.8 km from centroid", " La Calera: 4679.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lahār", "FINAL ANSWER: Lahār" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.74845, "lon": 12.34726, "name": "Casal Palocco" }, { "lat": 40.44626, "lon": -3.68411, "name": "El Viso" }, { "lat": 48.9193, "lon": 2.54305, "name": "Livry-Gargan" }, { "lat": 53.13333, "lon": 46.58333, "name": "Zarechnyy" }, { "lat": 26.44467, "lon": 83.61302, "name": "Rūdarpur" } ], "question": "Which location is the geographic outlier among: Casal Palocco, El Viso, Livry-Gargan, Zarechnyy, Rūdarpur?", "ground_truth": { "answer": "Rūdarpur", "outlier_distance_km": 5274.4, "second_furthest_km": 2661.5, "clarity_ratio": 1.98, "median_distance_km": 2129.4, "distances_to_centroid": { "Casal Palocco": 1316.6, "El Viso": 2661.5, "Livry-Gargan": 2129.4, "Zarechnyy": 1827.6, "Rūdarpur": 5274.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Casal Palocco: (41.75°, 12.35°)", " El Viso: (40.45°, -3.68°)", " Livry-Gargan: (48.92°, 2.54°)", " Zarechnyy: (53.13°, 46.58°)", " Rūdarpur: (26.44°, 83.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rūdarpur: 5274.4 km from centroid", " El Viso: 2661.5 km from centroid", " Livry-Gargan: 2129.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rūdarpur", "FINAL ANSWER: Rūdarpur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.14458, "lon": 145.12291, "name": "Frankston" }, { "lat": -37.8318, "lon": 140.77919, "name": "Mount Gambier" }, { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" }, { "lat": -27.94402, "lon": 153.39815, "name": "Labrador" }, { "lat": 37.54174, "lon": 80.11735, "name": "Han’airike" } ], "question": "Which location is the geographic outlier among: Frankston, Mount Gambier, Hoppers Crossing, Labrador, Han’airike?", "ground_truth": { "answer": "Han’airike", "outlier_distance_km": 8515.5, "second_furthest_km": 2256.5, "clarity_ratio": 3.77, "median_distance_km": 2223.9, "distances_to_centroid": { "Frankston": 2256.5, "Mount Gambier": 2037.3, "Hoppers Crossing": 2211.4, "Labrador": 2223.9, "Han’airike": 8515.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Frankston: (-38.14°, 145.12°)", " Mount Gambier: (-37.83°, 140.78°)", " Hoppers Crossing: (-37.88°, 144.70°)", " Labrador: (-27.94°, 153.40°)", " Han’airike: (37.54°, 80.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Han’airike: 8515.5 km from centroid", " Frankston: 2256.5 km from centroid", " Labrador: 2223.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Han’airike", "FINAL ANSWER: Han’airike" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.68574, "lon": -121.08217, "name": "El Dorado Hills" }, { "lat": 40.85677, "lon": -74.12848, "name": "Passaic" }, { "lat": 34.01949, "lon": -118.49138, "name": "Santa Monica" }, { "lat": 20.06417, "lon": -98.71722, "name": "La Providencia Siglo XXI" }, { "lat": 46.63033, "lon": 38.66379, "name": "Staroshcherbinovskaya" } ], "question": "Which location is the geographic outlier among: El Dorado Hills, Passaic, Santa Monica, La Providencia Siglo XXI, Staroshcherbinovskaya?", "ground_truth": { "answer": "Staroshcherbinovskaya", "outlier_distance_km": 8677.9, "second_furthest_km": 4061.2, "clarity_ratio": 2.14, "median_distance_km": 3955.2, "distances_to_centroid": { "El Dorado Hills": 4061.2, "Passaic": 537.1, "Santa Monica": 3955.2, "La Providencia Siglo XXI": 2933.6, "Staroshcherbinovskaya": 8677.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " El Dorado Hills: (38.69°, -121.08°)", " Passaic: (40.86°, -74.13°)", " Santa Monica: (34.02°, -118.49°)", " La Providencia Siglo XXI: (20.06°, -98.72°)", " Staroshcherbinovskaya: (46.63°, 38.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Staroshcherbinovskaya: 8677.9 km from centroid", " El Dorado Hills: 4061.2 km from centroid", " Santa Monica: 3955.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Staroshcherbinovskaya", "FINAL ANSWER: Staroshcherbinovskaya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.47056, "lon": -47.73472, "name": "Capela do Alto" }, { "lat": -11.18143, "lon": -40.51372, "name": "Jacobina" }, { "lat": -2.97083, "lon": -44.31556, "name": "Bacabeira" }, { "lat": 7.97917, "lon": -75.4202, "name": "Montelíbano" }, { "lat": 18.57366, "lon": 83.35925, "name": "Bobbili" } ], "question": "Which location is the geographic outlier among: Capela do Alto, Jacobina, Bacabeira, Montelíbano, Bobbili?", "ground_truth": { "answer": "Bobbili", "outlier_distance_km": 12012.1, "second_furthest_km": 5713.2, "clarity_ratio": 2.1, "median_distance_km": 3408.3, "distances_to_centroid": { "Capela do Alto": 3408.3, "Jacobina": 1987.8, "Bacabeira": 2155.5, "Montelíbano": 5713.2, "Bobbili": 12012.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Capela do Alto: (-23.47°, -47.73°)", " Jacobina: (-11.18°, -40.51°)", " Bacabeira: (-2.97°, -44.32°)", " Montelíbano: (7.98°, -75.42°)", " Bobbili: (18.57°, 83.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bobbili: 12012.1 km from centroid", " Montelíbano: 5713.2 km from centroid", " Capela do Alto: 3408.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bobbili", "FINAL ANSWER: Bobbili" ] }, { "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": 36.07264, "lon": -79.79198, "name": "Greensboro" }, { "lat": 36.61774, "lon": -121.91662, "name": "Pacific Grove" }, { "lat": 39.50506, "lon": -76.31977, "name": "Bel Air South" }, { "lat": 36.09719, "lon": -115.14666, "name": "Paradise" }, { "lat": -1.19667, "lon": -46.14, "name": "Viseu" } ], "question": "Which location is the geographic outlier among: Greensboro, Pacific Grove, Bel Air South, Paradise, Viseu?", "ground_truth": { "answer": "Viseu", "outlier_distance_km": 5585.2, "second_furthest_km": 3256.0, "clarity_ratio": 1.72, "median_distance_km": 2647.2, "distances_to_centroid": { "Greensboro": 1056.1, "Pacific Grove": 3256.0, "Bel Air South": 1539.3, "Paradise": 2647.2, "Viseu": 5585.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Greensboro: (36.07°, -79.79°)", " Pacific Grove: (36.62°, -121.92°)", " Bel Air South: (39.51°, -76.32°)", " Paradise: (36.10°, -115.15°)", " Viseu: (-1.20°, -46.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Viseu: 5585.2 km from centroid", " Pacific Grove: 3256.0 km from centroid", " Paradise: 2647.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Viseu", "FINAL ANSWER: Viseu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 13.93714, "lon": 120.73224, "name": "Balayan" }, { "lat": 36.93333, "lon": 119.38333, "name": "Liutuan" }, { "lat": 29.21399, "lon": 78.95693, "name": "Kashipur" }, { "lat": 23.21667, "lon": 72.68333, "name": "Gandhinagar" }, { "lat": -37.71667, "lon": 145.0, "name": "Reservoir" } ], "question": "Which location is the geographic outlier among: Balayan, Liutuan, Kashipur, Gandhinagar, Reservoir?", "ground_truth": { "answer": "Reservoir", "outlier_distance_km": 6881.9, "second_furthest_km": 3819.6, "clarity_ratio": 1.8, "median_distance_km": 3430.1, "distances_to_centroid": { "Balayan": 1449.3, "Liutuan": 2906.3, "Kashipur": 3430.1, "Gandhinagar": 3819.6, "Reservoir": 6881.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Balayan: (13.94°, 120.73°)", " Liutuan: (36.93°, 119.38°)", " Kashipur: (29.21°, 78.96°)", " Gandhinagar: (23.22°, 72.68°)", " Reservoir: (-37.72°, 145.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Reservoir: 6881.9 km from centroid", " Gandhinagar: 3819.6 km from centroid", " Kashipur: 3430.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Reservoir", "FINAL ANSWER: Reservoir" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.60111, "lon": -38.56861, "name": "Floresta" }, { "lat": -34.47513, "lon": -58.75367, "name": "Tortuguitas" }, { "lat": -34.47775, "lon": -58.70652, "name": "Ingeniero Pablo Nogués" }, { "lat": -24.75722, "lon": -51.76139, "name": "Pitanga" }, { "lat": 15.34522, "lon": 76.15478, "name": "Koppal" } ], "question": "Which location is the geographic outlier among: Floresta, Tortuguitas, Ingeniero Pablo Nogués, Pitanga, Koppal?", "ground_truth": { "answer": "Koppal", "outlier_distance_km": 11802.3, "second_furthest_km": 3732.6, "clarity_ratio": 3.16, "median_distance_km": 3728.7, "distances_to_centroid": { "Floresta": 1646.4, "Tortuguitas": 3732.6, "Ingeniero Pablo Nogués": 3728.7, "Pitanga": 2757.9, "Koppal": 11802.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Floresta: (-8.60°, -38.57°)", " Tortuguitas: (-34.48°, -58.75°)", " Ingeniero Pablo Nogués: (-34.48°, -58.71°)", " Pitanga: (-24.76°, -51.76°)", " Koppal: (15.35°, 76.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Koppal: 11802.3 km from centroid", " Tortuguitas: 3732.6 km from centroid", " Ingeniero Pablo Nogués: 3728.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Koppal", "FINAL ANSWER: Koppal" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.205, "lon": -41.88778, "name": "Itaperuna" }, { "lat": -11.30417, "lon": -41.85583, "name": "Irecê" }, { "lat": -27.16944, "lon": -53.71222, "name": "Itapiranga" }, { "lat": -23.02972, "lon": -46.97528, "name": "Vinhedo" }, { "lat": 9.87342, "lon": 7.95407, "name": "Kachia" } ], "question": "Which location is the geographic outlier among: Itaperuna, Irecê, Itapiranga, Vinhedo, Kachia?", "ground_truth": { "answer": "Kachia", "outlier_distance_km": 5487.8, "second_furthest_km": 2366.4, "clarity_ratio": 2.32, "median_distance_km": 1546.9, "distances_to_centroid": { "Itaperuna": 1015.2, "Irecê": 798.1, "Itapiranga": 2366.4, "Vinhedo": 1546.9, "Kachia": 5487.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itaperuna: (-21.20°, -41.89°)", " Irecê: (-11.30°, -41.86°)", " Itapiranga: (-27.17°, -53.71°)", " Vinhedo: (-23.03°, -46.98°)", " Kachia: (9.87°, 7.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kachia: 5487.8 km from centroid", " Itapiranga: 2366.4 km from centroid", " Vinhedo: 1546.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kachia", "FINAL ANSWER: Kachia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.66181, "lon": 2.35338, "name": "Morsang-sur-Orge" }, { "lat": 54.06835, "lon": -2.86108, "name": "Morecambe" }, { "lat": 50.9803, "lon": 11.32903, "name": "Weimar" }, { "lat": 55.55487, "lon": 37.92566, "name": "Andreyevskoye" }, { "lat": 36.96667, "lon": 140.05, "name": "Kuroiso" } ], "question": "Which location is the geographic outlier among: Morsang-sur-Orge, Morecambe, Weimar, Andreyevskoye, Kuroiso?", "ground_truth": { "answer": "Kuroiso", "outlier_distance_km": 7766.8, "second_furthest_km": 2812.2, "clarity_ratio": 2.76, "median_distance_km": 2562.3, "distances_to_centroid": { "Morsang-sur-Orge": 2562.3, "Morecambe": 2812.2, "Weimar": 1884.2, "Andreyevskoye": 701.6, "Kuroiso": 7766.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Morsang-sur-Orge: (48.66°, 2.35°)", " Morecambe: (54.07°, -2.86°)", " Weimar: (50.98°, 11.33°)", " Andreyevskoye: (55.55°, 37.93°)", " Kuroiso: (36.97°, 140.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kuroiso: 7766.8 km from centroid", " Morecambe: 2812.2 km from centroid", " Morsang-sur-Orge: 2562.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kuroiso", "FINAL ANSWER: Kuroiso" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.10389, "lon": 5.25556, "name": "Rijau" }, { "lat": 28.92095, "lon": 30.85367, "name": "Sumusţā al Waqf" }, { "lat": 30.03, "lon": 31.47, "name": "New Cairo" }, { "lat": 30.6687, "lon": 30.07391, "name": "An Nūbārīyah" }, { "lat": -1.62667, "lon": -47.48333, "name": "São Miguel do Guamá" } ], "question": "Which location is the geographic outlier among: Rijau, Sumusţā al Waqf, New Cairo, An Nūbārīyah, São Miguel do Guamá?", "ground_truth": { "answer": "São Miguel do Guamá", "outlier_distance_km": 6705.4, "second_furthest_km": 2435.4, "clarity_ratio": 2.75, "median_distance_km": 2343.0, "distances_to_centroid": { "Rijau": 1095.8, "Sumusţā al Waqf": 2334.0, "New Cairo": 2435.4, "An Nūbārīyah": 2343.0, "São Miguel do Guamá": 6705.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rijau: (11.10°, 5.26°)", " Sumusţā al Waqf: (28.92°, 30.85°)", " New Cairo: (30.03°, 31.47°)", " An Nūbārīyah: (30.67°, 30.07°)", " São Miguel do Guamá: (-1.63°, -47.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Miguel do Guamá: 6705.4 km from centroid", " New Cairo: 2435.4 km from centroid", " An Nūbārīyah: 2343.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Miguel do Guamá", "FINAL ANSWER: São Miguel do Guamá" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.72976, "lon": 151.15977, "name": "Saint Ives" }, { "lat": -37.8228, "lon": 144.96434, "name": "Southbank" }, { "lat": -31.09048, "lon": 150.92905, "name": "Tamworth" }, { "lat": -37.71667, "lon": 145.0, "name": "Reservoir" }, { "lat": 34.05493, "lon": 134.13963, "name": "Mima" } ], "question": "Which location is the geographic outlier among: Saint Ives, Southbank, Tamworth, Reservoir, Mima?", "ground_truth": { "answer": "Mima", "outlier_distance_km": 6262.1, "second_furthest_km": 1841.8, "clarity_ratio": 3.4, "median_distance_km": 1829.9, "distances_to_centroid": { "Saint Ives": 1503.6, "Southbank": 1841.8, "Tamworth": 1231.1, "Reservoir": 1829.9, "Mima": 6262.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint Ives: (-33.73°, 151.16°)", " Southbank: (-37.82°, 144.96°)", " Tamworth: (-31.09°, 150.93°)", " Reservoir: (-37.72°, 145.00°)", " Mima: (34.05°, 134.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mima: 6262.1 km from centroid", " Southbank: 1841.8 km from centroid", " Reservoir: 1829.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mima", "FINAL ANSWER: Mima" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.61332, "lon": -105.01665, "name": "Littleton" }, { "lat": 40.6976, "lon": -74.2632, "name": "Union" }, { "lat": 34.07362, "lon": -118.40036, "name": "Beverly Hills" }, { "lat": 33.88946, "lon": -118.15979, "name": "Paramount" }, { "lat": -37.73333, "lon": 144.93333, "name": "Pascoe Vale" } ], "question": "Which location is the geographic outlier among: Littleton, Union, Beverly Hills, Paramount, Pascoe Vale?", "ground_truth": { "answer": "Pascoe Vale", "outlier_distance_km": 17492.7, "second_furthest_km": 6338.2, "clarity_ratio": 2.76, "median_distance_km": 6318.2, "distances_to_centroid": { "Littleton": 5149.8, "Union": 2797.7, "Beverly Hills": 6338.2, "Paramount": 6318.2, "Pascoe Vale": 17492.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Littleton: (39.61°, -105.02°)", " Union: (40.70°, -74.26°)", " Beverly Hills: (34.07°, -118.40°)", " Paramount: (33.89°, -118.16°)", " Pascoe Vale: (-37.73°, 144.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pascoe Vale: 17492.7 km from centroid", " Beverly Hills: 6338.2 km from centroid", " Paramount: 6318.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pascoe Vale", "FINAL ANSWER: Pascoe Vale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.73308, "lon": 151.5574, "name": "Maitland" }, { "lat": -38.65333, "lon": 178.00417, "name": "Gisborne" }, { "lat": -25.54073, "lon": 152.70493, "name": "Maryborough" }, { "lat": -37.76722, "lon": 144.76657, "name": "Deer Park" }, { "lat": 10.63111, "lon": 122.97889, "name": "Mansilingan" } ], "question": "Which location is the geographic outlier among: Maitland, Gisborne, Maryborough, Deer Park, Mansilingan?", "ground_truth": { "answer": "Mansilingan", "outlier_distance_km": 4911.4, "second_furthest_km": 3044.4, "clarity_ratio": 1.61, "median_distance_km": 1523.2, "distances_to_centroid": { "Maitland": 893.6, "Gisborne": 3044.4, "Maryborough": 283.7, "Deer Park": 1523.2, "Mansilingan": 4911.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maitland: (-32.73°, 151.56°)", " Gisborne: (-38.65°, 178.00°)", " Maryborough: (-25.54°, 152.70°)", " Deer Park: (-37.77°, 144.77°)", " Mansilingan: (10.63°, 122.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mansilingan: 4911.4 km from centroid", " Gisborne: 3044.4 km from centroid", " Deer Park: 1523.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mansilingan", "FINAL ANSWER: Mansilingan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.61841, "lon": -60.15478, "name": "Victoria" }, { "lat": -6.0, "lon": -40.28333, "name": "São João dos Inhamuns" }, { "lat": -3.98417, "lon": -38.62028, "name": "Pacatuba" }, { "lat": -3.89, "lon": -38.45056, "name": "Eusébio" }, { "lat": -41.51603, "lon": 173.9528, "name": "Blenheim" } ], "question": "Which location is the geographic outlier among: Victoria, São João dos Inhamuns, Pacatuba, Eusébio, Blenheim?", "ground_truth": { "answer": "Blenheim", "outlier_distance_km": 13418.6, "second_furthest_km": 6134.5, "clarity_ratio": 2.19, "median_distance_km": 4484.6, "distances_to_centroid": { "Victoria": 6134.5, "São João dos Inhamuns": 4484.6, "Pacatuba": 4396.0, "Eusébio": 4382.8, "Blenheim": 13418.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Victoria: (-32.62°, -60.15°)", " São João dos Inhamuns: (-6.00°, -40.28°)", " Pacatuba: (-3.98°, -38.62°)", " Eusébio: (-3.89°, -38.45°)", " Blenheim: (-41.52°, 173.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Blenheim: 13418.6 km from centroid", " Victoria: 6134.5 km from centroid", " São João dos Inhamuns: 4484.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Blenheim", "FINAL ANSWER: Blenheim" ] }, { "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": 23.74771, "lon": 86.78804, "name": "Chirkunda" }, { "lat": 30.19191, "lon": 106.0588, "name": "Longxing" }, { "lat": 12.94194, "lon": 80.19472, "name": "Kullattūr" }, { "lat": 15.6321, "lon": 121.1448, "name": "Bongabon" }, { "lat": -16.76769, "lon": -47.6153, "name": "Cristalina" } ], "question": "Which location is the geographic outlier among: Chirkunda, Longxing, Kullattūr, Bongabon, Cristalina?", "ground_truth": { "answer": "Cristalina", "outlier_distance_km": 13254.7, "second_furthest_km": 5576.0, "clarity_ratio": 2.38, "median_distance_km": 4216.7, "distances_to_centroid": { "Chirkunda": 2184.1, "Longxing": 4216.7, "Kullattūr": 1178.8, "Bongabon": 5576.0, "Cristalina": 13254.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chirkunda: (23.75°, 86.79°)", " Longxing: (30.19°, 106.06°)", " Kullattūr: (12.94°, 80.19°)", " Bongabon: (15.63°, 121.14°)", " Cristalina: (-16.77°, -47.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cristalina: 13254.7 km from centroid", " Bongabon: 5576.0 km from centroid", " Longxing: 4216.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cristalina", "FINAL ANSWER: Cristalina" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -5.7925, "lon": -37.55667, "name": "Caraúbas" }, { "lat": -26.96167, "lon": -52.53472, "name": "Xaxim" }, { "lat": 5.17282, "lon": -72.54706, "name": "Aguazul" }, { "lat": 6.04639, "lon": -75.90705, "name": "Concordia" }, { "lat": 9.31387, "lon": 42.11815, "name": "Harar" } ], "question": "Which location is the geographic outlier among: Caraúbas, Xaxim, Aguazul, Concordia, Harar?", "ground_truth": { "answer": "Harar", "outlier_distance_km": 9109.7, "second_furthest_km": 4174.5, "clarity_ratio": 2.18, "median_distance_km": 3790.5, "distances_to_centroid": { "Caraúbas": 418.8, "Xaxim": 3070.0, "Aguazul": 3790.5, "Concordia": 4174.5, "Harar": 9109.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caraúbas: (-5.79°, -37.56°)", " Xaxim: (-26.96°, -52.53°)", " Aguazul: (5.17°, -72.55°)", " Concordia: (6.05°, -75.91°)", " Harar: (9.31°, 42.12°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Harar: 9109.7 km from centroid", " Concordia: 4174.5 km from centroid", " Aguazul: 3790.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Harar", "FINAL ANSWER: Harar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.65995, "lon": -111.99633, "name": "Kearns" }, { "lat": 42.07225, "lon": -87.72284, "name": "Wilmette" }, { "lat": 29.08874, "lon": -110.96677, "name": "Hermosillo" }, { "lat": 41.59649, "lon": -72.8776, "name": "Southington" }, { "lat": 46.80714, "lon": 4.41632, "name": "Le Creusot" } ], "question": "Which location is the geographic outlier among: Kearns, Wilmette, Hermosillo, Southington, Le Creusot?", "ground_truth": { "answer": "Le Creusot", "outlier_distance_km": 6237.3, "second_furthest_km": 3413.5, "clarity_ratio": 1.83, "median_distance_km": 3043.7, "distances_to_centroid": { "Kearns": 3043.7, "Wilmette": 1021.4, "Hermosillo": 3413.5, "Southington": 302.4, "Le Creusot": 6237.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kearns: (40.66°, -112.00°)", " Wilmette: (42.07°, -87.72°)", " Hermosillo: (29.09°, -110.97°)", " Southington: (41.60°, -72.88°)", " Le Creusot: (46.81°, 4.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Le Creusot: 6237.3 km from centroid", " Hermosillo: 3413.5 km from centroid", " Kearns: 3043.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Le Creusot", "FINAL ANSWER: Le Creusot" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.06425, "lon": 12.54612, "name": "Bastia umbra" }, { "lat": 64.446, "lon": 40.6531, "name": "Isakogorka" }, { "lat": 55.14941, "lon": 124.73676, "name": "Tynda" }, { "lat": 39.94729, "lon": -0.06313, "name": "Almassora" }, { "lat": -36.75818, "lon": 144.28024, "name": "Bendigo" } ], "question": "Which location is the geographic outlier among: Bastia umbra, Isakogorka, Tynda, Almassora, Bendigo?", "ground_truth": { "answer": "Bendigo", "outlier_distance_km": 11350.5, "second_furthest_km": 5684.8, "clarity_ratio": 2.0, "median_distance_km": 5191.8, "distances_to_centroid": { "Bastia umbra": 4594.3, "Isakogorka": 3837.4, "Tynda": 5191.8, "Almassora": 5684.8, "Bendigo": 11350.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bastia umbra: (43.06°, 12.55°)", " Isakogorka: (64.45°, 40.65°)", " Tynda: (55.15°, 124.74°)", " Almassora: (39.95°, -0.06°)", " Bendigo: (-36.76°, 144.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bendigo: 11350.5 km from centroid", " Almassora: 5684.8 km from centroid", " Tynda: 5191.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bendigo", "FINAL ANSWER: Bendigo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.8282, "lon": 174.62019, "name": "Massey East" }, { "lat": -37.79798, "lon": 144.94512, "name": "North Melbourne" }, { "lat": -41.27078, "lon": 173.28404, "name": "Nelson" }, { "lat": -38.21792, "lon": 145.03876, "name": "Mornington" }, { "lat": 3.19698, "lon": -75.64506, "name": "Planadas" } ], "question": "Which location is the geographic outlier among: Massey East, North Melbourne, Nelson, Mornington, Planadas?", "ground_truth": { "answer": "Planadas", "outlier_distance_km": 16895.8, "second_furthest_km": 5711.4, "clarity_ratio": 2.96, "median_distance_km": 5514.2, "distances_to_centroid": { "Massey East": 5711.4, "North Melbourne": 3096.0, "Nelson": 5514.2, "Mornington": 3109.3, "Planadas": 16895.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Massey East: (-36.83°, 174.62°)", " North Melbourne: (-37.80°, 144.95°)", " Nelson: (-41.27°, 173.28°)", " Mornington: (-38.22°, 145.04°)", " Planadas: (3.20°, -75.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Planadas: 16895.8 km from centroid", " Massey East: 5711.4 km from centroid", " Nelson: 5514.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Planadas", "FINAL ANSWER: Planadas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.83039, "lon": -77.19637, "name": "Annandale" }, { "lat": 36.02153, "lon": -80.382, "name": "Clemmons" }, { "lat": 35.62246, "lon": -117.6709, "name": "Ridgecrest" }, { "lat": 46.60207, "lon": -120.5059, "name": "Yakima" }, { "lat": -15.91694, "lon": -46.10556, "name": "Arinos" } ], "question": "Which location is the geographic outlier among: Annandale, Clemmons, Ridgecrest, Yakima, Arinos?", "ground_truth": { "answer": "Arinos", "outlier_distance_km": 6691.8, "second_furthest_km": 3457.6, "clarity_ratio": 1.94, "median_distance_km": 2872.3, "distances_to_centroid": { "Annandale": 1566.5, "Clemmons": 1146.4, "Ridgecrest": 2872.3, "Yakima": 3457.6, "Arinos": 6691.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Annandale: (38.83°, -77.20°)", " Clemmons: (36.02°, -80.38°)", " Ridgecrest: (35.62°, -117.67°)", " Yakima: (46.60°, -120.51°)", " Arinos: (-15.92°, -46.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arinos: 6691.8 km from centroid", " Yakima: 3457.6 km from centroid", " Ridgecrest: 2872.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arinos", "FINAL ANSWER: Arinos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.41334, "lon": -0.36701, "name": "Hampton" }, { "lat": 55.86661, "lon": 48.35931, "name": "Volzhsk" }, { "lat": 50.61723, "lon": -3.40233, "name": "Exmouth" }, { "lat": 52.08868, "lon": 17.01508, "name": "Śrem" }, { "lat": -27.27611, "lon": -48.84944, "name": "São João Batista" } ], "question": "Which location is the geographic outlier among: Hampton, Volzhsk, Exmouth, Śrem, São João Batista?", "ground_truth": { "answer": "São João Batista", "outlier_distance_km": 8902.2, "second_furthest_km": 4023.9, "clarity_ratio": 2.21, "median_distance_km": 2068.3, "distances_to_centroid": { "Hampton": 1669.7, "Volzhsk": 4023.9, "Exmouth": 1635.6, "Śrem": 2068.3, "São João Batista": 8902.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hampton: (51.41°, -0.37°)", " Volzhsk: (55.87°, 48.36°)", " Exmouth: (50.62°, -3.40°)", " Śrem: (52.09°, 17.02°)", " São João Batista: (-27.28°, -48.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São João Batista: 8902.2 km from centroid", " Volzhsk: 4023.9 km from centroid", " Śrem: 2068.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São João Batista", "FINAL ANSWER: São João Batista" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.69662, "lon": -117.77668, "name": "El Camino Real" }, { "lat": 42.29171, "lon": -85.58723, "name": "Kalamazoo" }, { "lat": 39.48508, "lon": -80.14258, "name": "Fairmont" }, { "lat": 19.31777, "lon": -98.23846, "name": "Tlaxcala" }, { "lat": -8.16139, "lon": -70.76556, "name": "Tarauacá" } ], "question": "Which location is the geographic outlier among: El Camino Real, Kalamazoo, Fairmont, Tlaxcala, Tarauacá?", "ground_truth": { "answer": "Tarauacá", "outlier_distance_km": 4292.9, "second_furthest_km": 2788.5, "clarity_ratio": 1.54, "median_distance_km": 1939.5, "distances_to_centroid": { "El Camino Real": 2788.5, "Kalamazoo": 1939.5, "Fairmont": 1847.5, "Tlaxcala": 1038.5, "Tarauacá": 4292.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " El Camino Real: (33.70°, -117.78°)", " Kalamazoo: (42.29°, -85.59°)", " Fairmont: (39.49°, -80.14°)", " Tlaxcala: (19.32°, -98.24°)", " Tarauacá: (-8.16°, -70.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tarauacá: 4292.9 km from centroid", " El Camino Real: 2788.5 km from centroid", " Kalamazoo: 1939.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tarauacá", "FINAL ANSWER: Tarauacá" ] }, { "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": -28.07071, "lon": 153.39329, "name": "Robina" }, { "lat": -27.53221, "lon": 153.22889, "name": "Alexandra Hills" }, { "lat": -27.61025, "lon": 153.05388, "name": "Sunnybank Hills" }, { "lat": -37.68333, "lon": 145.01667, "name": "Thomastown" }, { "lat": -23.10083, "lon": -45.70694, "name": "Caçapava" } ], "question": "Which location is the geographic outlier among: Robina, Alexandra Hills, Sunnybank Hills, Thomastown, Caçapava?", "ground_truth": { "answer": "Caçapava", "outlier_distance_km": 13761.3, "second_furthest_km": 4047.0, "clarity_ratio": 3.4, "median_distance_km": 4043.2, "distances_to_centroid": { "Robina": 4047.0, "Alexandra Hills": 4043.2, "Sunnybank Hills": 4024.6, "Thomastown": 3224.0, "Caçapava": 13761.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Robina: (-28.07°, 153.39°)", " Alexandra Hills: (-27.53°, 153.23°)", " Sunnybank Hills: (-27.61°, 153.05°)", " Thomastown: (-37.68°, 145.02°)", " Caçapava: (-23.10°, -45.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Caçapava: 13761.3 km from centroid", " Robina: 4047.0 km from centroid", " Alexandra Hills: 4043.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Caçapava", "FINAL ANSWER: Caçapava" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.45049, "lon": -88.81961, "name": "Starkville" }, { "lat": 40.61872, "lon": -74.0332, "name": "Fort Hamilton" }, { "lat": 31.60351, "lon": -94.65549, "name": "Nacogdoches" }, { "lat": 31.65456, "lon": -106.30331, "name": "Socorro" }, { "lat": 34.67652, "lon": 138.94456, "name": "Shimoda" } ], "question": "Which location is the geographic outlier among: Starkville, Fort Hamilton, Nacogdoches, Socorro, Shimoda?", "ground_truth": { "answer": "Shimoda", "outlier_distance_km": 12323.2, "second_furthest_km": 5636.9, "clarity_ratio": 2.19, "median_distance_km": 4597.2, "distances_to_centroid": { "Starkville": 4014.8, "Fort Hamilton": 2641.5, "Nacogdoches": 4597.2, "Socorro": 5636.9, "Shimoda": 12323.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Starkville: (33.45°, -88.82°)", " Fort Hamilton: (40.62°, -74.03°)", " Nacogdoches: (31.60°, -94.66°)", " Socorro: (31.65°, -106.30°)", " Shimoda: (34.68°, 138.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shimoda: 12323.2 km from centroid", " Socorro: 5636.9 km from centroid", " Nacogdoches: 4597.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shimoda", "FINAL ANSWER: Shimoda" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.46427, "lon": 9.18951, "name": "Milan" }, { "lat": 45.55823, "lon": 9.21495, "name": "Cinisello Balsamo" }, { "lat": 41.52232, "lon": 1.75076, "name": "Piera" }, { "lat": 52.01246, "lon": 8.69834, "name": "Leopoldshöhe" }, { "lat": 33.11921, "lon": -117.08642, "name": "Escondido" } ], "question": "Which location is the geographic outlier among: Milan, Cinisello Balsamo, Piera, Leopoldshöhe, Escondido?", "ground_truth": { "answer": "Escondido", "outlier_distance_km": 8220.9, "second_furthest_km": 2166.6, "clarity_ratio": 3.79, "median_distance_km": 2130.5, "distances_to_centroid": { "Milan": 2129.2, "Cinisello Balsamo": 2130.5, "Piera": 1601.4, "Leopoldshöhe": 2166.6, "Escondido": 8220.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Milan: (45.46°, 9.19°)", " Cinisello Balsamo: (45.56°, 9.21°)", " Piera: (41.52°, 1.75°)", " Leopoldshöhe: (52.01°, 8.70°)", " Escondido: (33.12°, -117.09°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Escondido: 8220.9 km from centroid", " Leopoldshöhe: 2166.6 km from centroid", " Cinisello Balsamo: 2130.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Escondido", "FINAL ANSWER: Escondido" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.3475, "lon": 5.98333, "name": "Epe" }, { "lat": 48.81451, "lon": 3.08498, "name": "Coulommiers" }, { "lat": 47.99696, "lon": 2.73261, "name": "Montargis" }, { "lat": 60.01375, "lon": 30.39471, "name": "Akademicheskoe" }, { "lat": 37.11954, "lon": 140.26211, "name": "Shirakawa" } ], "question": "Which location is the geographic outlier among: Epe, Coulommiers, Montargis, Akademicheskoe, Shirakawa?", "ground_truth": { "answer": "Shirakawa", "outlier_distance_km": 7842.3, "second_furthest_km": 2464.4, "clarity_ratio": 3.18, "median_distance_km": 2415.8, "distances_to_centroid": { "Epe": 2154.7, "Coulommiers": 2415.8, "Montargis": 2464.4, "Akademicheskoe": 1257.4, "Shirakawa": 7842.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Epe: (52.35°, 5.98°)", " Coulommiers: (48.81°, 3.08°)", " Montargis: (48.00°, 2.73°)", " Akademicheskoe: (60.01°, 30.39°)", " Shirakawa: (37.12°, 140.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shirakawa: 7842.3 km from centroid", " Montargis: 2464.4 km from centroid", " Coulommiers: 2415.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shirakawa", "FINAL ANSWER: Shirakawa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.23282, "lon": -8.72264, "name": "Vigo" }, { "lat": 38.34511, "lon": -0.76721, "name": "Aspe" }, { "lat": 50.58727, "lon": 8.67554, "name": "Gießen" }, { "lat": 50.3836, "lon": 8.0503, "name": "Limburg an der Lahn" }, { "lat": -23.84852, "lon": 151.25775, "name": "Gladstone" } ], "question": "Which location is the geographic outlier among: Vigo, Aspe, Gießen, Limburg an der Lahn, Gladstone?", "ground_truth": { "answer": "Gladstone", "outlier_distance_km": 14075.8, "second_furthest_km": 3746.7, "clarity_ratio": 3.76, "median_distance_km": 3037.4, "distances_to_centroid": { "Vigo": 3746.7, "Aspe": 3037.4, "Gießen": 2841.9, "Limburg an der Lahn": 2862.3, "Gladstone": 14075.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vigo: (42.23°, -8.72°)", " Aspe: (38.35°, -0.77°)", " Gießen: (50.59°, 8.68°)", " Limburg an der Lahn: (50.38°, 8.05°)", " Gladstone: (-23.85°, 151.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gladstone: 14075.8 km from centroid", " Vigo: 3746.7 km from centroid", " Aspe: 3037.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gladstone", "FINAL ANSWER: Gladstone" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.41663, "lon": 29.08668, "name": "Kinross" }, { "lat": -29.47795, "lon": 30.23057, "name": "Howick" }, { "lat": 0.49194, "lon": 35.74303, "name": "Kabarnet" }, { "lat": 9.46498, "lon": 42.18447, "name": "Felana" }, { "lat": 6.28535, "lon": -75.33385, "name": "San Vicente" } ], "question": "Which location is the geographic outlier among: Kinross, Howick, Kabarnet, Felana, San Vicente?", "ground_truth": { "answer": "San Vicente", "outlier_distance_km": 9853.8, "second_furthest_km": 3825.7, "clarity_ratio": 2.58, "median_distance_km": 3035.6, "distances_to_centroid": { "Kinross": 2708.8, "Howick": 3035.6, "Kabarnet": 2753.8, "Felana": 3825.7, "San Vicente": 9853.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kinross: (-26.42°, 29.09°)", " Howick: (-29.48°, 30.23°)", " Kabarnet: (0.49°, 35.74°)", " Felana: (9.46°, 42.18°)", " San Vicente: (6.29°, -75.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Vicente: 9853.8 km from centroid", " Felana: 3825.7 km from centroid", " Howick: 3035.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Vicente", "FINAL ANSWER: San Vicente" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.86785, "lon": 94.78572, "name": "Kiphire" }, { "lat": 30.3531, "lon": 107.51289, "name": "Yong’an" }, { "lat": 25.57548, "lon": 83.98043, "name": "Buxar" }, { "lat": 34.43417, "lon": 117.29833, "name": "Liuquan" }, { "lat": 55.86667, "lon": 37.5, "name": "Novokhovrino" } ], "question": "Which location is the geographic outlier among: Kiphire, Yong’an, Buxar, Liuquan, Novokhovrino?", "ground_truth": { "answer": "Novokhovrino", "outlier_distance_km": 4498.0, "second_furthest_km": 2658.1, "clarity_ratio": 1.69, "median_distance_km": 1864.4, "distances_to_centroid": { "Kiphire": 1140.9, "Yong’an": 1864.4, "Buxar": 1064.3, "Liuquan": 2658.1, "Novokhovrino": 4498.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kiphire: (25.87°, 94.79°)", " Yong’an: (30.35°, 107.51°)", " Buxar: (25.58°, 83.98°)", " Liuquan: (34.43°, 117.30°)", " Novokhovrino: (55.87°, 37.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Novokhovrino: 4498.0 km from centroid", " Liuquan: 2658.1 km from centroid", " Yong’an: 1864.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Novokhovrino", "FINAL ANSWER: Novokhovrino" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.21792, "lon": 145.03876, "name": "Mornington" }, { "lat": -27.50578, "lon": 153.10236, "name": "Carindale" }, { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": -24.86621, "lon": 152.3479, "name": "Bundaberg" }, { "lat": 14.45506, "lon": 75.3952, "name": "Hirekerūr" } ], "question": "Which location is the geographic outlier among: Mornington, Carindale, Yarraville, Bundaberg, Hirekerūr?", "ground_truth": { "answer": "Hirekerūr", "outlier_distance_km": 7618.3, "second_furthest_km": 2003.9, "clarity_ratio": 3.8, "median_distance_km": 1975.3, "distances_to_centroid": { "Mornington": 2003.9, "Carindale": 1975.3, "Yarraville": 1960.2, "Bundaberg": 1863.2, "Hirekerūr": 7618.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mornington: (-38.22°, 145.04°)", " Carindale: (-27.51°, 153.10°)", " Yarraville: (-37.82°, 144.90°)", " Bundaberg: (-24.87°, 152.35°)", " Hirekerūr: (14.46°, 75.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hirekerūr: 7618.3 km from centroid", " Mornington: 2003.9 km from centroid", " Carindale: 1975.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hirekerūr", "FINAL ANSWER: Hirekerūr" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.42118, "lon": -79.7881, "name": "Monroeville" }, { "lat": 43.80486, "lon": -79.35442, "name": "Hillcrest Village" }, { "lat": 27.29393, "lon": -80.35033, "name": "Port Saint Lucie" }, { "lat": 44.78941, "lon": -93.60218, "name": "Chaska" }, { "lat": 52.14021, "lon": 8.48475, "name": "Spenge" } ], "question": "Which location is the geographic outlier among: Monroeville, Hillcrest Village, Port Saint Lucie, Chaska, Spenge?", "ground_truth": { "answer": "Spenge", "outlier_distance_km": 5449.2, "second_furthest_km": 2336.2, "clarity_ratio": 2.33, "median_distance_km": 2128.9, "distances_to_centroid": { "Monroeville": 1252.9, "Hillcrest Village": 1200.1, "Port Saint Lucie": 2128.9, "Chaska": 2336.2, "Spenge": 5449.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Monroeville: (40.42°, -79.79°)", " Hillcrest Village: (43.80°, -79.35°)", " Port Saint Lucie: (27.29°, -80.35°)", " Chaska: (44.79°, -93.60°)", " Spenge: (52.14°, 8.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Spenge: 5449.2 km from centroid", " Chaska: 2336.2 km from centroid", " Port Saint Lucie: 2128.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Spenge", "FINAL ANSWER: Spenge" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.57786, "lon": -101.85517, "name": "Lubbock" }, { "lat": 33.92427, "lon": -84.37854, "name": "Sandy Springs" }, { "lat": 41.01283, "lon": -81.60512, "name": "Barberton" }, { "lat": 45.27076, "lon": -66.05616, "name": "Saint John" }, { "lat": 16.06213, "lon": 76.0586, "name": "Hungund" } ], "question": "Which location is the geographic outlier among: Lubbock, Sandy Springs, Barberton, Saint John, Hungund?", "ground_truth": { "answer": "Hungund", "outlier_distance_km": 12163.3, "second_furthest_km": 4599.8, "clarity_ratio": 2.64, "median_distance_km": 3013.4, "distances_to_centroid": { "Lubbock": 4599.8, "Sandy Springs": 3013.4, "Barberton": 2748.0, "Saint John": 1760.8, "Hungund": 12163.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lubbock: (33.58°, -101.86°)", " Sandy Springs: (33.92°, -84.38°)", " Barberton: (41.01°, -81.61°)", " Saint John: (45.27°, -66.06°)", " Hungund: (16.06°, 76.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hungund: 12163.3 km from centroid", " Lubbock: 4599.8 km from centroid", " Sandy Springs: 3013.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hungund", "FINAL ANSWER: Hungund" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.26597, "lon": 105.77802, "name": "Laisu" }, { "lat": 28.88162, "lon": 120.03308, "name": "Guli" }, { "lat": 33.26611, "lon": 116.56605, "name": "Mengcheng Chengguanzhen" }, { "lat": 31.71194, "lon": 76.93273, "name": "Mandi" }, { "lat": -25.66756, "lon": 27.24208, "name": "Rustenburg" } ], "question": "Which location is the geographic outlier among: Laisu, Guli, Mengcheng Chengguanzhen, Mandi, Rustenburg?", "ground_truth": { "answer": "Rustenburg", "outlier_distance_km": 8374.9, "second_furthest_km": 3275.1, "clarity_ratio": 2.56, "median_distance_km": 3102.9, "distances_to_centroid": { "Laisu": 1987.1, "Guli": 3275.1, "Mengcheng Chengguanzhen": 3102.9, "Mandi": 1837.4, "Rustenburg": 8374.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Laisu: (29.27°, 105.78°)", " Guli: (28.88°, 120.03°)", " Mengcheng Chengguanzhen: (33.27°, 116.57°)", " Mandi: (31.71°, 76.93°)", " Rustenburg: (-25.67°, 27.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rustenburg: 8374.9 km from centroid", " Guli: 3275.1 km from centroid", " Mengcheng Chengguanzhen: 3102.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rustenburg", "FINAL ANSWER: Rustenburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.91018, "lon": 30.17438, "name": "Abū al Maţāmīr" }, { "lat": -0.98855, "lon": 36.58537, "name": "Maai Mahiu" }, { "lat": -26.10528, "lon": 28.09884, "name": "Alexandra" }, { "lat": 11.85172, "lon": 3.65478, "name": "Kamba" }, { "lat": -22.8375, "lon": -51.97306, "name": "Colorado" } ], "question": "Which location is the geographic outlier among: Abū al Maţāmīr, Maai Mahiu, Alexandra, Kamba, Colorado?", "ground_truth": { "answer": "Colorado", "outlier_distance_km": 7016.5, "second_furthest_km": 4219.3, "clarity_ratio": 1.66, "median_distance_km": 3401.0, "distances_to_centroid": { "Abū al Maţāmīr": 4219.3, "Maai Mahiu": 3032.8, "Alexandra": 3401.0, "Kamba": 1603.9, "Colorado": 7016.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Abū al Maţāmīr: (30.91°, 30.17°)", " Maai Mahiu: (-0.99°, 36.59°)", " Alexandra: (-26.11°, 28.10°)", " Kamba: (11.85°, 3.65°)", " Colorado: (-22.84°, -51.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Colorado: 7016.5 km from centroid", " Abū al Maţāmīr: 4219.3 km from centroid", " Alexandra: 3401.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Colorado", "FINAL ANSWER: Colorado" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 1.54631, "lon": 103.71829, "name": "Setia Tropika" }, { "lat": 2.5703, "lon": 101.833, "name": "Lukut" }, { "lat": 8.54884, "lon": 76.91716, "name": "Sreekaryam" }, { "lat": 11.11723, "lon": 77.37256, "name": "Mannarai" }, { "lat": 46.87497, "lon": -96.90036, "name": "West Fargo" } ], "question": "Which location is the geographic outlier among: Setia Tropika, Lukut, Sreekaryam, Mannarai, West Fargo?", "ground_truth": { "answer": "West Fargo", "outlier_distance_km": 12580.2, "second_furthest_km": 5788.1, "clarity_ratio": 2.17, "median_distance_km": 5554.8, "distances_to_centroid": { "Setia Tropika": 5788.1, "Lukut": 5554.8, "Sreekaryam": 2722.2, "Mannarai": 2708.7, "West Fargo": 12580.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Setia Tropika: (1.55°, 103.72°)", " Lukut: (2.57°, 101.83°)", " Sreekaryam: (8.55°, 76.92°)", " Mannarai: (11.12°, 77.37°)", " West Fargo: (46.87°, -96.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " West Fargo: 12580.2 km from centroid", " Setia Tropika: 5788.1 km from centroid", " Lukut: 5554.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: West Fargo", "FINAL ANSWER: West Fargo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.54409, "lon": 13.23743, "name": "Haselhorst" }, { "lat": 51.62202, "lon": -3.45544, "name": "Tonypandy" }, { "lat": 37.40202, "lon": -6.03314, "name": "Camas" }, { "lat": 51.0374, "lon": 21.07126, "name": "Starachowice" }, { "lat": -29.26737, "lon": 26.72595, "name": "Botshabelo" } ], "question": "Which location is the geographic outlier among: Haselhorst, Tonypandy, Camas, Starachowice, Botshabelo?", "ground_truth": { "answer": "Botshabelo", "outlier_distance_km": 7101.1, "second_furthest_km": 2384.6, "clarity_ratio": 2.98, "median_distance_km": 2223.2, "distances_to_centroid": { "Haselhorst": 2222.7, "Tonypandy": 2384.6, "Camas": 1575.7, "Starachowice": 2223.2, "Botshabelo": 7101.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Haselhorst: (52.54°, 13.24°)", " Tonypandy: (51.62°, -3.46°)", " Camas: (37.40°, -6.03°)", " Starachowice: (51.04°, 21.07°)", " Botshabelo: (-29.27°, 26.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Botshabelo: 7101.1 km from centroid", " Tonypandy: 2384.6 km from centroid", " Starachowice: 2223.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Botshabelo", "FINAL ANSWER: Botshabelo" ] }, { "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": -2.97083, "lon": -44.31556, "name": "Bacabeira" }, { "lat": -8.00222, "lon": -35.01833, "name": "São Lourenço da Mata" }, { "lat": -20.17944, "lon": -48.03194, "name": "Miguelópolis" }, { "lat": -31.63349, "lon": -71.16967, "name": "Illapel" }, { "lat": 41.13121, "lon": -74.36737, "name": "West Milford" } ], "question": "Which location is the geographic outlier among: Bacabeira, São Lourenço da Mata, Miguelópolis, Illapel, West Milford?", "ground_truth": { "answer": "West Milford", "outlier_distance_km": 5440.3, "second_furthest_km": 3495.1, "clarity_ratio": 1.56, "median_distance_km": 2200.3, "distances_to_centroid": { "Bacabeira": 1149.1, "São Lourenço da Mata": 2200.3, "Miguelópolis": 1899.5, "Illapel": 3495.1, "West Milford": 5440.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bacabeira: (-2.97°, -44.32°)", " São Lourenço da Mata: (-8.00°, -35.02°)", " Miguelópolis: (-20.18°, -48.03°)", " Illapel: (-31.63°, -71.17°)", " West Milford: (41.13°, -74.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " West Milford: 5440.3 km from centroid", " Illapel: 3495.1 km from centroid", " São Lourenço da Mata: 2200.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: West Milford", "FINAL ANSWER: West Milford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.94564, "lon": 30.48497, "name": "Thohoyandou" }, { "lat": 6.19824, "lon": 6.73187, "name": "Asaba" }, { "lat": 11.27727, "lon": 9.88385, "name": "Gwaram" }, { "lat": -30.69268, "lon": 28.5061, "name": "Tlokoeng" }, { "lat": 28.68012, "lon": 77.02975, "name": "Mūndka" } ], "question": "Which location is the geographic outlier among: Thohoyandou, Asaba, Gwaram, Tlokoeng, Mūndka?", "ground_truth": { "answer": "Mūndka", "outlier_distance_km": 5978.1, "second_furthest_km": 3253.4, "clarity_ratio": 1.84, "median_distance_km": 2776.8, "distances_to_centroid": { "Thohoyandou": 2385.0, "Asaba": 2776.8, "Gwaram": 2688.1, "Tlokoeng": 3253.4, "Mūndka": 5978.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Thohoyandou: (-22.95°, 30.48°)", " Asaba: (6.20°, 6.73°)", " Gwaram: (11.28°, 9.88°)", " Tlokoeng: (-30.69°, 28.51°)", " Mūndka: (28.68°, 77.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mūndka: 5978.1 km from centroid", " Tlokoeng: 3253.4 km from centroid", " Asaba: 2776.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mūndka", "FINAL ANSWER: Mūndka" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" }, { "lat": -36.84103, "lon": 174.65223, "name": "Te Atatu Peninsula" }, { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" }, { "lat": 52.50146, "lon": 13.4934, "name": "Rummelsburg" } ], "question": "Which location is the geographic outlier among: Hoppers Crossing, Cheltenham, Te Atatu Peninsula, Coogee, Rummelsburg?", "ground_truth": { "answer": "Rummelsburg", "outlier_distance_km": 13160.6, "second_furthest_km": 5136.8, "clarity_ratio": 2.56, "median_distance_km": 3024.6, "distances_to_centroid": { "Hoppers Crossing": 2799.2, "Cheltenham": 2827.9, "Te Atatu Peninsula": 5136.8, "Coogee": 3024.6, "Rummelsburg": 13160.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hoppers Crossing: (-37.88°, 144.70°)", " Cheltenham: (-37.97°, 145.05°)", " Te Atatu Peninsula: (-36.84°, 174.65°)", " Coogee: (-33.92°, 151.26°)", " Rummelsburg: (52.50°, 13.49°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rummelsburg: 13160.6 km from centroid", " Te Atatu Peninsula: 5136.8 km from centroid", " Coogee: 3024.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rummelsburg", "FINAL ANSWER: Rummelsburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.05456, "lon": -1.20763, "name": "Molina de Segura" }, { "lat": 52.02, "lon": 5.04306, "name": "IJsselstein" }, { "lat": 53.45131, "lon": -2.07943, "name": "Hyde" }, { "lat": 41.41109, "lon": 2.2026, "name": "Provenals del Poblenou" }, { "lat": 32.74255, "lon": -117.03142, "name": "Lemon Grove" } ], "question": "Which location is the geographic outlier among: Molina de Segura, IJsselstein, Hyde, Provenals del Poblenou, Lemon Grove?", "ground_truth": { "answer": "Lemon Grove", "outlier_distance_km": 7894.7, "second_furthest_km": 2253.7, "clarity_ratio": 3.5, "median_distance_km": 2041.4, "distances_to_centroid": { "Molina de Segura": 1895.9, "IJsselstein": 2253.7, "Hyde": 1861.2, "Provenals del Poblenou": 2041.4, "Lemon Grove": 7894.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Molina de Segura: (38.05°, -1.21°)", " IJsselstein: (52.02°, 5.04°)", " Hyde: (53.45°, -2.08°)", " Provenals del Poblenou: (41.41°, 2.20°)", " Lemon Grove: (32.74°, -117.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lemon Grove: 7894.7 km from centroid", " IJsselstein: 2253.7 km from centroid", " Provenals del Poblenou: 2041.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lemon Grove", "FINAL ANSWER: Lemon Grove" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 24.97024, "lon": 98.39368, "name": "Hehua" }, { "lat": 13.5926, "lon": 122.3215, "name": "Catanauan" }, { "lat": 21.93053, "lon": 69.78081, "name": "Bhānvad" }, { "lat": 27.66368, "lon": 80.47371, "name": "Maholi" }, { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" } ], "question": "Which location is the geographic outlier among: Hehua, Catanauan, Bhānvad, Maholi, Yarraville?", "ground_truth": { "answer": "Yarraville", "outlier_distance_km": 6866.3, "second_furthest_km": 3794.0, "clarity_ratio": 1.81, "median_distance_km": 3076.4, "distances_to_centroid": { "Hehua": 1732.3, "Catanauan": 2119.6, "Bhānvad": 3794.0, "Maholi": 3076.4, "Yarraville": 6866.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hehua: (24.97°, 98.39°)", " Catanauan: (13.59°, 122.32°)", " Bhānvad: (21.93°, 69.78°)", " Maholi: (27.66°, 80.47°)", " Yarraville: (-37.82°, 144.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yarraville: 6866.3 km from centroid", " Bhānvad: 3794.0 km from centroid", " Maholi: 3076.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yarraville", "FINAL ANSWER: Yarraville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.46146, "lon": -80.07282, "name": "Delray Beach" }, { "lat": 39.95238, "lon": -75.16362, "name": "Philadelphia" }, { "lat": 38.70446, "lon": -93.22826, "name": "Sedalia" }, { "lat": 42.28343, "lon": -71.3495, "name": "Natick" }, { "lat": 6.63105, "lon": 8.05814, "name": "Effium" } ], "question": "Which location is the geographic outlier among: Delray Beach, Philadelphia, Sedalia, Natick, Effium?", "ground_truth": { "answer": "Effium", "outlier_distance_km": 7762.1, "second_furthest_km": 2938.3, "clarity_ratio": 2.64, "median_distance_km": 1793.5, "distances_to_centroid": { "Delray Beach": 1793.5, "Philadelphia": 1540.9, "Sedalia": 2938.3, "Natick": 1506.2, "Effium": 7762.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Delray Beach: (26.46°, -80.07°)", " Philadelphia: (39.95°, -75.16°)", " Sedalia: (38.70°, -93.23°)", " Natick: (42.28°, -71.35°)", " Effium: (6.63°, 8.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Effium: 7762.1 km from centroid", " Sedalia: 2938.3 km from centroid", " Delray Beach: 1793.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Effium", "FINAL ANSWER: Effium" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 32.85791, "lon": -97.25474, "name": "Watauga" }, { "lat": 43.80136, "lon": -91.23958, "name": "La Crosse" }, { "lat": 40.78343, "lon": -73.96625, "name": "Manhattan" }, { "lat": 41.58337, "lon": -87.50004, "name": "Hammond" }, { "lat": 53.56047, "lon": -0.03225, "name": "Cleethorpes" } ], "question": "Which location is the geographic outlier among: Watauga, La Crosse, Manhattan, Hammond, Cleethorpes?", "ground_truth": { "answer": "Cleethorpes", "outlier_distance_km": 5123.8, "second_furthest_km": 2612.8, "clarity_ratio": 1.96, "median_distance_km": 1724.0, "distances_to_centroid": { "Watauga": 2612.8, "La Crosse": 1724.0, "Manhattan": 381.8, "Hammond": 1446.2, "Cleethorpes": 5123.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Watauga: (32.86°, -97.25°)", " La Crosse: (43.80°, -91.24°)", " Manhattan: (40.78°, -73.97°)", " Hammond: (41.58°, -87.50°)", " Cleethorpes: (53.56°, -0.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cleethorpes: 5123.8 km from centroid", " Watauga: 2612.8 km from centroid", " La Crosse: 1724.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cleethorpes", "FINAL ANSWER: Cleethorpes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 32.6518, "lon": -96.90834, "name": "Duncanville" }, { "lat": 20.03618, "lon": -98.35563, "name": "Santiago Tulantepec" }, { "lat": 34.61002, "lon": -112.31572, "name": "Prescott Valley" }, { "lat": 40.4167, "lon": -86.87529, "name": "Lafayette" }, { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" } ], "question": "Which location is the geographic outlier among: Duncanville, Santiago Tulantepec, Prescott Valley, Lafayette, Yarraville?", "ground_truth": { "answer": "Yarraville", "outlier_distance_km": 17380.3, "second_furthest_km": 6388.7, "clarity_ratio": 2.72, "median_distance_km": 5080.7, "distances_to_centroid": { "Duncanville": 4952.8, "Santiago Tulantepec": 5080.7, "Prescott Valley": 6388.7, "Lafayette": 4320.4, "Yarraville": 17380.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Duncanville: (32.65°, -96.91°)", " Santiago Tulantepec: (20.04°, -98.36°)", " Prescott Valley: (34.61°, -112.32°)", " Lafayette: (40.42°, -86.88°)", " Yarraville: (-37.82°, 144.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yarraville: 17380.3 km from centroid", " Prescott Valley: 6388.7 km from centroid", " Santiago Tulantepec: 5080.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yarraville", "FINAL ANSWER: Yarraville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.03333, "lon": 145.35, "name": "Berwick" }, { "lat": -36.88012, "lon": 174.61975, "name": "Henderson" }, { "lat": -31.09048, "lon": 150.92905, "name": "Tamworth" }, { "lat": -27.49325, "lon": 153.05826, "name": "Coorparoo" }, { "lat": -13.275, "lon": -50.16278, "name": "São Miguel do Araguaia" } ], "question": "Which location is the geographic outlier among: Berwick, Henderson, Tamworth, Coorparoo, São Miguel do Araguaia?", "ground_truth": { "answer": "São Miguel do Araguaia", "outlier_distance_km": 15006.2, "second_furthest_km": 5547.5, "clarity_ratio": 2.71, "median_distance_km": 3734.4, "distances_to_centroid": { "Berwick": 2974.2, "Henderson": 5547.5, "Tamworth": 3465.3, "Coorparoo": 3734.4, "São Miguel do Araguaia": 15006.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Berwick: (-38.03°, 145.35°)", " Henderson: (-36.88°, 174.62°)", " Tamworth: (-31.09°, 150.93°)", " Coorparoo: (-27.49°, 153.06°)", " São Miguel do Araguaia: (-13.28°, -50.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Miguel do Araguaia: 15006.2 km from centroid", " Henderson: 5547.5 km from centroid", " Coorparoo: 3734.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Miguel do Araguaia", "FINAL ANSWER: São Miguel do Araguaia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 16.52539, "lon": 107.4755, "name": "Hương Trà" }, { "lat": 9.68747, "lon": 76.77891, "name": "Erāttupetta" }, { "lat": 24.96899, "lon": 84.1964, "name": "Madhurampur Dehri" }, { "lat": 13.3622, "lon": 100.98345, "name": "Chon Buri" }, { "lat": -29.44931, "lon": 31.21532, "name": "Shakaskraal" } ], "question": "Which location is the geographic outlier among: Hương Trà, Erāttupetta, Madhurampur Dehri, Chon Buri, Shakaskraal?", "ground_truth": { "answer": "Shakaskraal", "outlier_distance_km": 6613.4, "second_furthest_km": 3154.1, "clarity_ratio": 2.1, "median_distance_km": 2387.1, "distances_to_centroid": { "Hương Trà": 3154.1, "Erāttupetta": 473.2, "Madhurampur Dehri": 2042.3, "Chon Buri": 2387.1, "Shakaskraal": 6613.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hương Trà: (16.53°, 107.48°)", " Erāttupetta: (9.69°, 76.78°)", " Madhurampur Dehri: (24.97°, 84.20°)", " Chon Buri: (13.36°, 100.98°)", " Shakaskraal: (-29.45°, 31.22°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shakaskraal: 6613.4 km from centroid", " Hương Trà: 3154.1 km from centroid", " Chon Buri: 2387.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shakaskraal", "FINAL ANSWER: Shakaskraal" ] }, { "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": 19.27127, "lon": -99.45787, "name": "Ocoyoacac" }, { "lat": 41.23922, "lon": -81.34594, "name": "Streetsboro" }, { "lat": 40.70911, "lon": -112.10161, "name": "Magna" }, { "lat": 40.93064, "lon": -73.10179, "name": "Setauket-East Setauket" }, { "lat": -37.97695, "lon": 145.25866, "name": "Endeavour Hills" } ], "question": "Which location is the geographic outlier among: Ocoyoacac, Streetsboro, Magna, Setauket-East Setauket, Endeavour Hills?", "ground_truth": { "answer": "Endeavour Hills", "outlier_distance_km": 17905.3, "second_furthest_km": 6687.0, "clarity_ratio": 2.68, "median_distance_km": 5750.8, "distances_to_centroid": { "Ocoyoacac": 5750.8, "Streetsboro": 4160.1, "Magna": 6687.0, "Setauket-East Setauket": 3524.1, "Endeavour Hills": 17905.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ocoyoacac: (19.27°, -99.46°)", " Streetsboro: (41.24°, -81.35°)", " Magna: (40.71°, -112.10°)", " Setauket-East Setauket: (40.93°, -73.10°)", " Endeavour Hills: (-37.98°, 145.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Endeavour Hills: 17905.3 km from centroid", " Magna: 6687.0 km from centroid", " Ocoyoacac: 5750.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Endeavour Hills", "FINAL ANSWER: Endeavour Hills" ] }, { "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": -22.665, "lon": -45.00944, "name": "Cachoeira Paulista" }, { "lat": -16.525, "lon": -50.37222, "name": "São Luís de Montes Belos" }, { "lat": -34.63333, "lon": -58.41667, "name": "Boedo" }, { "lat": -32.88341, "lon": -71.24882, "name": "Quillota" }, { "lat": 43.85495, "lon": 41.59019, "name": "Zelenchukskaya" } ], "question": "Which location is the geographic outlier among: Cachoeira Paulista, São Luís de Montes Belos, Boedo, Quillota, Zelenchukskaya?", "ground_truth": { "answer": "Zelenchukskaya", "outlier_distance_km": 10057.5, "second_furthest_km": 4171.5, "clarity_ratio": 2.41, "median_distance_km": 3288.4, "distances_to_centroid": { "Cachoeira Paulista": 1426.3, "São Luís de Montes Belos": 1536.2, "Boedo": 3288.4, "Quillota": 4171.5, "Zelenchukskaya": 10057.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cachoeira Paulista: (-22.66°, -45.01°)", " São Luís de Montes Belos: (-16.52°, -50.37°)", " Boedo: (-34.63°, -58.42°)", " Quillota: (-32.88°, -71.25°)", " Zelenchukskaya: (43.85°, 41.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zelenchukskaya: 10057.5 km from centroid", " Quillota: 4171.5 km from centroid", " Boedo: 3288.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zelenchukskaya", "FINAL ANSWER: Zelenchukskaya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.50153, "lon": 3.35808, "name": "Surulere" }, { "lat": 26.5622, "lon": 31.74566, "name": "Akhmīm" }, { "lat": -22.94564, "lon": 30.48497, "name": "Thohoyandou" }, { "lat": -26.33172, "lon": 26.32065, "name": "Coligny" }, { "lat": 21.85563, "lon": 111.96272, "name": "Yangjiang" } ], "question": "Which location is the geographic outlier among: Surulere, Akhmīm, Thohoyandou, Coligny, Yangjiang?", "ground_truth": { "answer": "Yangjiang", "outlier_distance_km": 8022.5, "second_furthest_km": 4192.2, "clarity_ratio": 1.91, "median_distance_km": 3424.7, "distances_to_centroid": { "Surulere": 4192.2, "Akhmīm": 2988.3, "Thohoyandou": 2899.5, "Coligny": 3424.7, "Yangjiang": 8022.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Surulere: (6.50°, 3.36°)", " Akhmīm: (26.56°, 31.75°)", " Thohoyandou: (-22.95°, 30.48°)", " Coligny: (-26.33°, 26.32°)", " Yangjiang: (21.86°, 111.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yangjiang: 8022.5 km from centroid", " Surulere: 4192.2 km from centroid", " Coligny: 3424.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yangjiang", "FINAL ANSWER: Yangjiang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.76616, "lon": 74.47738, "name": "Shirdi" }, { "lat": -7.45806, "lon": 109.28806, "name": "Sokaraja" }, { "lat": 30.54485, "lon": 119.9599, "name": "Deqing" }, { "lat": 18.78229, "lon": 109.5013, "name": "Wuzhishan" }, { "lat": 19.30653, "lon": -99.59279, "name": "Santa María Totoltepec" } ], "question": "Which location is the geographic outlier among: Shirdi, Sokaraja, Deqing, Wuzhishan, Santa María Totoltepec?", "ground_truth": { "answer": "Santa María Totoltepec", "outlier_distance_km": 15620.2, "second_furthest_km": 5992.4, "clarity_ratio": 2.61, "median_distance_km": 5758.8, "distances_to_centroid": { "Shirdi": 1304.5, "Sokaraja": 5758.8, "Deqing": 5992.4, "Wuzhishan": 4955.4, "Santa María Totoltepec": 15620.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shirdi: (19.77°, 74.48°)", " Sokaraja: (-7.46°, 109.29°)", " Deqing: (30.54°, 119.96°)", " Wuzhishan: (18.78°, 109.50°)", " Santa María Totoltepec: (19.31°, -99.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santa María Totoltepec: 15620.2 km from centroid", " Deqing: 5992.4 km from centroid", " Sokaraja: 5758.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santa María Totoltepec", "FINAL ANSWER: Santa María Totoltepec" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.91928, "lon": 145.05301, "name": "Bentleigh East" }, { "lat": -37.69047, "lon": 144.74172, "name": "Hillside" }, { "lat": -25.54073, "lon": 152.70493, "name": "Maryborough" }, { "lat": -40.63333, "lon": 175.275, "name": "Levin" }, { "lat": 33.68333, "lon": 135.35, "name": "Shirahama" } ], "question": "Which location is the geographic outlier among: Bentleigh East, Hillside, Maryborough, Levin, Shirahama?", "ground_truth": { "answer": "Shirahama", "outlier_distance_km": 6358.9, "second_furthest_km": 3137.7, "clarity_ratio": 2.03, "median_distance_km": 1889.5, "distances_to_centroid": { "Bentleigh East": 1889.5, "Hillside": 1874.1, "Maryborough": 484.7, "Levin": 3137.7, "Shirahama": 6358.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bentleigh East: (-37.92°, 145.05°)", " Hillside: (-37.69°, 144.74°)", " Maryborough: (-25.54°, 152.70°)", " Levin: (-40.63°, 175.28°)", " Shirahama: (33.68°, 135.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shirahama: 6358.9 km from centroid", " Levin: 3137.7 km from centroid", " Bentleigh East: 1889.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shirahama", "FINAL ANSWER: Shirahama" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.21003, "lon": -64.09965, "name": "Embarcación" }, { "lat": 10.59181, "lon": -74.18983, "name": "Aracataca" }, { "lat": -19.98639, "lon": -44.42778, "name": "Mateus Leme" }, { "lat": -30.78991, "lon": -60.59276, "name": "San Justo" }, { "lat": 52.64817, "lon": 19.0678, "name": "Włocławek" } ], "question": "Which location is the geographic outlier among: Embarcación, Aracataca, Mateus Leme, San Justo, Włocławek?", "ground_truth": { "answer": "Włocławek", "outlier_distance_km": 8484.7, "second_furthest_km": 3589.5, "clarity_ratio": 2.36, "median_distance_km": 3542.4, "distances_to_centroid": { "Embarcación": 3128.4, "Aracataca": 3542.4, "Mateus Leme": 1983.9, "San Justo": 3589.5, "Włocławek": 8484.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Embarcación: (-23.21°, -64.10°)", " Aracataca: (10.59°, -74.19°)", " Mateus Leme: (-19.99°, -44.43°)", " San Justo: (-30.79°, -60.59°)", " Włocławek: (52.65°, 19.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Włocławek: 8484.7 km from centroid", " San Justo: 3589.5 km from centroid", " Aracataca: 3542.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Włocławek", "FINAL ANSWER: Włocławek" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.01239, "lon": 76.32633, "name": "Vazhakkala" }, { "lat": 9.32439, "lon": 105.98006, "name": "Vĩnh Châu" }, { "lat": 29.10298, "lon": 75.17138, "name": "Bhādra" }, { "lat": 8.35983, "lon": 77.05253, "name": "Kanjiramkulam" }, { "lat": -33.9125, "lon": 151.10279, "name": "Campsie" } ], "question": "Which location is the geographic outlier among: Vazhakkala, Vĩnh Châu, Bhādra, Kanjiramkulam, Campsie?", "ground_truth": { "answer": "Campsie", "outlier_distance_km": 7090.8, "second_furthest_km": 3575.5, "clarity_ratio": 1.98, "median_distance_km": 2371.4, "distances_to_centroid": { "Vazhakkala": 2371.4, "Vĩnh Châu": 1110.4, "Bhādra": 3575.5, "Kanjiramkulam": 2256.9, "Campsie": 7090.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vazhakkala: (10.01°, 76.33°)", " Vĩnh Châu: (9.32°, 105.98°)", " Bhādra: (29.10°, 75.17°)", " Kanjiramkulam: (8.36°, 77.05°)", " Campsie: (-33.91°, 151.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Campsie: 7090.8 km from centroid", " Bhādra: 3575.5 km from centroid", " Vazhakkala: 2371.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Campsie", "FINAL ANSWER: Campsie" ] }, { "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": -38.26667, "lon": 145.01667, "name": "Mount Martha" }, { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" }, { "lat": -31.8075, "lon": 115.86599, "name": "Landsdale" }, { "lat": -37.73261, "lon": 144.86504, "name": "Keilor East" }, { "lat": 21.24757, "lon": 76.03509, "name": "Rāver" } ], "question": "Which location is the geographic outlier among: Mount Martha, Hoppers Crossing, Landsdale, Keilor East, Rāver?", "ground_truth": { "answer": "Rāver", "outlier_distance_km": 7391.0, "second_furthest_km": 2378.9, "clarity_ratio": 3.11, "median_distance_km": 2335.8, "distances_to_centroid": { "Mount Martha": 2378.9, "Hoppers Crossing": 2332.5, "Landsdale": 1200.5, "Keilor East": 2335.8, "Rāver": 7391.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mount Martha: (-38.27°, 145.02°)", " Hoppers Crossing: (-37.88°, 144.70°)", " Landsdale: (-31.81°, 115.87°)", " Keilor East: (-37.73°, 144.87°)", " Rāver: (21.25°, 76.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rāver: 7391.0 km from centroid", " Mount Martha: 2378.9 km from centroid", " Keilor East: 2335.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rāver", "FINAL ANSWER: Rāver" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.03483, "lon": -76.90747, "name": "Beltsville" }, { "lat": 38.93067, "lon": -77.04081, "name": "Mount Pleasant" }, { "lat": 25.49539, "lon": -80.42922, "name": "Leisure City" }, { "lat": 40.94926, "lon": -74.15375, "name": "Hawthorne" }, { "lat": 51.78826, "lon": 6.13865, "name": "Kleve" } ], "question": "Which location is the geographic outlier among: Beltsville, Mount Pleasant, Leisure City, Hawthorne, Kleve?", "ground_truth": { "answer": "Kleve", "outlier_distance_km": 5181.0, "second_furthest_km": 2408.1, "clarity_ratio": 2.15, "median_distance_km": 1427.9, "distances_to_centroid": { "Beltsville": 1415.2, "Mount Pleasant": 1427.9, "Leisure City": 2408.1, "Hawthorne": 1177.4, "Kleve": 5181.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Beltsville: (39.03°, -76.91°)", " Mount Pleasant: (38.93°, -77.04°)", " Leisure City: (25.50°, -80.43°)", " Hawthorne: (40.95°, -74.15°)", " Kleve: (51.79°, 6.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kleve: 5181.0 km from centroid", " Leisure City: 2408.1 km from centroid", " Mount Pleasant: 1427.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kleve", "FINAL ANSWER: Kleve" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.47241, "lon": 107.60326, "name": "Pushun" }, { "lat": 37.54, "lon": 127.20556, "name": "Hanam" }, { "lat": 9.5096, "lon": 78.09588, "name": "Aruppukkottai" }, { "lat": 36.05701, "lon": 103.83987, "name": "Lanzhou" }, { "lat": 4.23922, "lon": -75.23996, "name": "Rovira" } ], "question": "Which location is the geographic outlier among: Pushun, Hanam, Aruppukkottai, Lanzhou, Rovira?", "ground_truth": { "answer": "Rovira", "outlier_distance_km": 14998.2, "second_furthest_km": 5755.5, "clarity_ratio": 2.61, "median_distance_km": 3948.1, "distances_to_centroid": { "Pushun": 3948.1, "Hanam": 5755.5, "Aruppukkottai": 1877.5, "Lanzhou": 3674.0, "Rovira": 14998.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pushun: (30.47°, 107.60°)", " Hanam: (37.54°, 127.21°)", " Aruppukkottai: (9.51°, 78.10°)", " Lanzhou: (36.06°, 103.84°)", " Rovira: (4.24°, -75.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rovira: 14998.2 km from centroid", " Hanam: 5755.5 km from centroid", " Pushun: 3948.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rovira", "FINAL ANSWER: Rovira" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.19551, "lon": 9.46421, "name": "Bad Münder am Deister" }, { "lat": 52.62264, "lon": 10.08047, "name": "Celle" }, { "lat": 51.33678, "lon": -0.11201, "name": "Purley" }, { "lat": 44.98901, "lon": 38.94324, "name": "Yablonovskiy" }, { "lat": 32.08199, "lon": 131.39957, "name": "Saito" } ], "question": "Which location is the geographic outlier among: Bad Münder am Deister, Celle, Purley, Yablonovskiy, Saito?", "ground_truth": { "answer": "Saito", "outlier_distance_km": 7721.0, "second_furthest_km": 2793.2, "clarity_ratio": 2.76, "median_distance_km": 2135.5, "distances_to_centroid": { "Bad Münder am Deister": 2135.5, "Celle": 2099.2, "Purley": 2793.2, "Yablonovskiy": 199.4, "Saito": 7721.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bad Münder am Deister: (52.20°, 9.46°)", " Celle: (52.62°, 10.08°)", " Purley: (51.34°, -0.11°)", " Yablonovskiy: (44.99°, 38.94°)", " Saito: (32.08°, 131.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saito: 7721.0 km from centroid", " Purley: 2793.2 km from centroid", " Bad Münder am Deister: 2135.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saito", "FINAL ANSWER: Saito" ] }, { "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": -37.99116, "lon": 145.17385, "name": "Keysborough" }, { "lat": -37.79086, "lon": 145.09386, "name": "Balwyn North" }, { "lat": -38.18333, "lon": 145.08333, "name": "Mount Eliza" }, { "lat": -37.60075, "lon": 145.09555, "name": "Mernda" }, { "lat": -5.50361, "lon": -41.32333, "name": "São Miguel do Tapuio" } ], "question": "Which location is the geographic outlier among: Keysborough, Balwyn North, Mount Eliza, Mernda, São Miguel do Tapuio?", "ground_truth": { "answer": "São Miguel do Tapuio", "outlier_distance_km": 14765.4, "second_furthest_km": 3467.5, "clarity_ratio": 4.26, "median_distance_km": 3460.3, "distances_to_centroid": { "Keysborough": 3467.5, "Balwyn North": 3460.3, "Mount Eliza": 3460.0, "Mernda": 3460.3, "São Miguel do Tapuio": 14765.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Keysborough: (-37.99°, 145.17°)", " Balwyn North: (-37.79°, 145.09°)", " Mount Eliza: (-38.18°, 145.08°)", " Mernda: (-37.60°, 145.10°)", " São Miguel do Tapuio: (-5.50°, -41.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Miguel do Tapuio: 14765.4 km from centroid", " Keysborough: 3467.5 km from centroid", " Balwyn North: 3460.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Miguel do Tapuio", "FINAL ANSWER: São Miguel do Tapuio" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.91938, "lon": 150.92588, "name": "Liverpool" }, { "lat": -38.03333, "lon": 145.35, "name": "Berwick" }, { "lat": -32.5269, "lon": 115.7217, "name": "Mandurah" }, { "lat": -37.98333, "lon": 145.2, "name": "Dandenong" }, { "lat": 41.40634, "lon": 2.16503, "name": "el Camp d'en Grassot i Gràcia Nova" } ], "question": "Which location is the geographic outlier among: Liverpool, Berwick, Mandurah, Dandenong, el Camp d'en Grassot i Gràcia Nova?", "ground_truth": { "answer": "el Camp d'en Grassot i Gràcia Nova", "outlier_distance_km": 13094.9, "second_furthest_km": 4126.0, "clarity_ratio": 3.17, "median_distance_km": 3776.6, "distances_to_centroid": { "Liverpool": 4126.0, "Berwick": 3776.6, "Mandurah": 1421.8, "Dandenong": 3762.4, "el Camp d'en Grassot i Gràcia Nova": 13094.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Liverpool: (-33.92°, 150.93°)", " Berwick: (-38.03°, 145.35°)", " Mandurah: (-32.53°, 115.72°)", " Dandenong: (-37.98°, 145.20°)", " el Camp d'en Grassot i Gràcia Nova: (41.41°, 2.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " el Camp d'en Grassot i Gràcia Nova: 13094.9 km from centroid", " Liverpool: 4126.0 km from centroid", " Berwick: 3776.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: el Camp d'en Grassot i Gràcia Nova", "FINAL ANSWER: el Camp d'en Grassot i Gràcia Nova" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.11278, "lon": -51.53194, "name": "Jaguapitã" }, { "lat": -5.89222, "lon": -42.63611, "name": "Água Branca" }, { "lat": -11.51056, "lon": -38.15, "name": "Crisópolis" }, { "lat": -7.31111, "lon": -39.30417, "name": "Barbalha" }, { "lat": 36.41323, "lon": 139.86622, "name": "Shimotsuke" } ], "question": "Which location is the geographic outlier among: Jaguapitã, Água Branca, Crisópolis, Barbalha, Shimotsuke?", "ground_truth": { "answer": "Shimotsuke", "outlier_distance_km": 14876.5, "second_furthest_km": 5386.2, "clarity_ratio": 2.76, "median_distance_km": 4043.4, "distances_to_centroid": { "Jaguapitã": 5386.2, "Água Branca": 4043.4, "Crisópolis": 3652.7, "Barbalha": 3692.4, "Shimotsuke": 14876.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jaguapitã: (-23.11°, -51.53°)", " Água Branca: (-5.89°, -42.64°)", " Crisópolis: (-11.51°, -38.15°)", " Barbalha: (-7.31°, -39.30°)", " Shimotsuke: (36.41°, 139.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shimotsuke: 14876.5 km from centroid", " Jaguapitã: 5386.2 km from centroid", " Água Branca: 4043.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shimotsuke", "FINAL ANSWER: Shimotsuke" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.34491, "lon": -71.10017, "name": "Fenway/Kenmore" }, { "lat": 40.9126, "lon": -73.83708, "name": "Mount Vernon" }, { "lat": 27.48642, "lon": -109.94079, "name": "Ciudad Obregón" }, { "lat": 33.88835, "lon": -118.30896, "name": "Gardena" }, { "lat": -40.35636, "lon": 175.61113, "name": "Palmerston North" } ], "question": "Which location is the geographic outlier among: Fenway/Kenmore, Mount Vernon, Ciudad Obregón, Gardena, Palmerston North?", "ground_truth": { "answer": "Palmerston North", "outlier_distance_km": 16054.9, "second_furthest_km": 7734.5, "clarity_ratio": 2.08, "median_distance_km": 7090.4, "distances_to_centroid": { "Fenway/Kenmore": 3790.5, "Mount Vernon": 3922.4, "Ciudad Obregón": 7090.4, "Gardena": 7734.5, "Palmerston North": 16054.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fenway/Kenmore: (42.34°, -71.10°)", " Mount Vernon: (40.91°, -73.84°)", " Ciudad Obregón: (27.49°, -109.94°)", " Gardena: (33.89°, -118.31°)", " Palmerston North: (-40.36°, 175.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palmerston North: 16054.9 km from centroid", " Gardena: 7734.5 km from centroid", " Ciudad Obregón: 7090.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palmerston North", "FINAL ANSWER: Palmerston North" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81667, "lon": 145.23333, "name": "Ringwood" }, { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -37.91482, "lon": 144.75088, "name": "Point Cook" }, { "lat": -37.74124, "lon": 144.73631, "name": "Caroline Springs" }, { "lat": -27.14944, "lon": -52.31056, "name": "Seara" } ], "question": "Which location is the geographic outlier among: Ringwood, Epping, Point Cook, Caroline Springs, Seara?", "ground_truth": { "answer": "Seara", "outlier_distance_km": 12653.2, "second_furthest_km": 3523.2, "clarity_ratio": 3.59, "median_distance_km": 3508.6, "distances_to_centroid": { "Ringwood": 3523.2, "Epping": 3508.6, "Point Cook": 3479.7, "Caroline Springs": 3481.2, "Seara": 12653.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ringwood: (-37.82°, 145.23°)", " Epping: (-37.65°, 145.03°)", " Point Cook: (-37.91°, 144.75°)", " Caroline Springs: (-37.74°, 144.74°)", " Seara: (-27.15°, -52.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Seara: 12653.2 km from centroid", " Ringwood: 3523.2 km from centroid", " Epping: 3508.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Seara", "FINAL ANSWER: Seara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.65003, "lon": -0.2361, "name": "Dome" }, { "lat": 29.033, "lon": 31.11408, "name": "Banī Suwayf al Jadīdah" }, { "lat": 7.15571, "lon": 3.34509, "name": "Abeokuta" }, { "lat": 27.91582, "lon": 34.32995, "name": "Sharm el-Sheikh" }, { "lat": 47.50024, "lon": -111.30081, "name": "Great Falls" } ], "question": "Which location is the geographic outlier among: Dome, Banī Suwayf al Jadīdah, Abeokuta, Sharm el-Sheikh, Great Falls?", "ground_truth": { "answer": "Great Falls", "outlier_distance_km": 9005.6, "second_furthest_km": 4304.1, "clarity_ratio": 2.09, "median_distance_km": 3985.7, "distances_to_centroid": { "Dome": 2170.4, "Banī Suwayf al Jadīdah": 3985.7, "Abeokuta": 2212.9, "Sharm el-Sheikh": 4304.1, "Great Falls": 9005.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dome: (5.65°, -0.24°)", " Banī Suwayf al Jadīdah: (29.03°, 31.11°)", " Abeokuta: (7.16°, 3.35°)", " Sharm el-Sheikh: (27.92°, 34.33°)", " Great Falls: (47.50°, -111.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Great Falls: 9005.6 km from centroid", " Sharm el-Sheikh: 4304.1 km from centroid", " Banī Suwayf al Jadīdah: 3985.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Great Falls", "FINAL ANSWER: Great Falls" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" }, { "lat": -33.77271, "lon": 151.08184, "name": "Epping" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": -34.424, "lon": 150.89345, "name": "Wollongong" }, { "lat": 25.17555, "lon": 78.18863, "name": "Pichor" } ], "question": "Which location is the geographic outlier among: Saint Albans, Epping, Taylors Lakes, Wollongong, Pichor?", "ground_truth": { "answer": "Pichor", "outlier_distance_km": 8097.3, "second_furthest_km": 2029.0, "clarity_ratio": 3.99, "median_distance_km": 2007.1, "distances_to_centroid": { "Saint Albans": 1871.4, "Epping": 2007.1, "Taylors Lakes": 1867.6, "Wollongong": 2029.0, "Pichor": 8097.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint Albans: (-37.73°, 144.80°)", " Epping: (-33.77°, 151.08°)", " Taylors Lakes: (-37.70°, 144.79°)", " Wollongong: (-34.42°, 150.89°)", " Pichor: (25.18°, 78.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pichor: 8097.3 km from centroid", " Wollongong: 2029.0 km from centroid", " Epping: 2007.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pichor", "FINAL ANSWER: Pichor" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -28.00029, "lon": 153.43088, "name": "Gold Coast" }, { "lat": -33.76667, "lon": 150.91667, "name": "Blacktown" }, { "lat": -37.87709, "lon": 145.12939, "name": "Mount Waverley" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": 29.41345, "lon": 30.86579, "name": "Sinnūris" } ], "question": "Which location is the geographic outlier among: Gold Coast, Blacktown, Mount Waverley, Taylors Lakes, Sinnūris?", "ground_truth": { "answer": "Sinnūris", "outlier_distance_km": 11548.0, "second_furthest_km": 2947.2, "clarity_ratio": 3.92, "median_distance_km": 2875.0, "distances_to_centroid": { "Gold Coast": 2947.2, "Blacktown": 2875.0, "Mount Waverley": 2643.8, "Taylors Lakes": 2607.8, "Sinnūris": 11548.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gold Coast: (-28.00°, 153.43°)", " Blacktown: (-33.77°, 150.92°)", " Mount Waverley: (-37.88°, 145.13°)", " Taylors Lakes: (-37.70°, 144.79°)", " Sinnūris: (29.41°, 30.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sinnūris: 11548.0 km from centroid", " Gold Coast: 2947.2 km from centroid", " Blacktown: 2875.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sinnūris", "FINAL ANSWER: Sinnūris" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.95387, "lon": 32.86409, "name": "Roslavl’" }, { "lat": 51.47805, "lon": 6.8625, "name": "Oberhausen" }, { "lat": 43.56554, "lon": 1.29645, "name": "Plaisance-du-Touch" }, { "lat": 52.0825, "lon": 4.75, "name": "Bodegraven" }, { "lat": -9.89667, "lon": -39.02639, "name": "Canudos" } ], "question": "Which location is the geographic outlier among: Roslavl’, Oberhausen, Plaisance-du-Touch, Bodegraven, Canudos?", "ground_truth": { "answer": "Canudos", "outlier_distance_km": 6795.4, "second_furthest_km": 2953.7, "clarity_ratio": 2.3, "median_distance_km": 1562.1, "distances_to_centroid": { "Roslavl’": 2953.7, "Oberhausen": 1534.1, "Plaisance-du-Touch": 592.6, "Bodegraven": 1562.1, "Canudos": 6795.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Roslavl’: (53.95°, 32.86°)", " Oberhausen: (51.48°, 6.86°)", " Plaisance-du-Touch: (43.57°, 1.30°)", " Bodegraven: (52.08°, 4.75°)", " Canudos: (-9.90°, -39.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Canudos: 6795.4 km from centroid", " Roslavl’: 2953.7 km from centroid", " Bodegraven: 1562.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Canudos", "FINAL ANSWER: Canudos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.87167, "lon": 8.65027, "name": "Darmstadt" }, { "lat": 44.4115, "lon": 40.79281, "name": "Mostovskoy" }, { "lat": 55.58635, "lon": 37.67781, "name": "Biryulëvo" }, { "lat": 44.64671, "lon": 7.49309, "name": "Saluzzo" }, { "lat": -31.64978, "lon": -64.42972, "name": "Alta Gracia" } ], "question": "Which location is the geographic outlier among: Darmstadt, Mostovskoy, Biryulëvo, Saluzzo, Alta Gracia?", "ground_truth": { "answer": "Alta Gracia", "outlier_distance_km": 10279.3, "second_furthest_km": 3539.3, "clarity_ratio": 2.9, "median_distance_km": 3267.6, "distances_to_centroid": { "Darmstadt": 1935.6, "Mostovskoy": 3267.6, "Biryulëvo": 3539.3, "Saluzzo": 1348.4, "Alta Gracia": 10279.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Darmstadt: (49.87°, 8.65°)", " Mostovskoy: (44.41°, 40.79°)", " Biryulëvo: (55.59°, 37.68°)", " Saluzzo: (44.65°, 7.49°)", " Alta Gracia: (-31.65°, -64.43°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alta Gracia: 10279.3 km from centroid", " Biryulëvo: 3539.3 km from centroid", " Mostovskoy: 3267.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alta Gracia", "FINAL ANSWER: Alta Gracia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 46.74064, "lon": -71.45131, "name": "Saint-Augustin-de-Desmaures" }, { "lat": 40.97926, "lon": -74.11653, "name": "Ridgewood" }, { "lat": 40.80677, "lon": -74.18542, "name": "Bloomfield" }, { "lat": 33.99399, "lon": -96.37082, "name": "Durant" }, { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" } ], "question": "Which location is the geographic outlier among: Saint-Augustin-de-Desmaures, Ridgewood, Bloomfield, Durant, Carnegie?", "ground_truth": { "answer": "Carnegie", "outlier_distance_km": 18571.4, "second_furthest_km": 6012.4, "clarity_ratio": 3.09, "median_distance_km": 4084.2, "distances_to_centroid": { "Saint-Augustin-de-Desmaures": 4081.8, "Ridgewood": 4083.0, "Bloomfield": 4084.2, "Durant": 6012.4, "Carnegie": 18571.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint-Augustin-de-Desmaures: (46.74°, -71.45°)", " Ridgewood: (40.98°, -74.12°)", " Bloomfield: (40.81°, -74.19°)", " Durant: (33.99°, -96.37°)", " Carnegie: (-37.89°, 145.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carnegie: 18571.4 km from centroid", " Durant: 6012.4 km from centroid", " Bloomfield: 4084.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carnegie", "FINAL ANSWER: Carnegie" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.13053, "lon": 45.53791, "name": "Urus-Martan" }, { "lat": 49.21088, "lon": -0.30653, "name": "Hérouville-Saint-Clair" }, { "lat": 54.65455, "lon": 19.90929, "name": "Baltiysk" }, { "lat": 44.58014, "lon": 38.06646, "name": "Gelendzhik" }, { "lat": 33.03699, "lon": -117.29198, "name": "Encinitas" } ], "question": "Which location is the geographic outlier among: Urus-Martan, Hérouville-Saint-Clair, Baltiysk, Gelendzhik, Encinitas?", "ground_truth": { "answer": "Encinitas", "outlier_distance_km": 9118.7, "second_furthest_km": 3813.4, "clarity_ratio": 2.39, "median_distance_km": 3193.9, "distances_to_centroid": { "Urus-Martan": 3813.4, "Hérouville-Saint-Clair": 513.3, "Baltiysk": 1944.0, "Gelendzhik": 3193.9, "Encinitas": 9118.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Urus-Martan: (43.13°, 45.54°)", " Hérouville-Saint-Clair: (49.21°, -0.31°)", " Baltiysk: (54.65°, 19.91°)", " Gelendzhik: (44.58°, 38.07°)", " Encinitas: (33.04°, -117.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Encinitas: 9118.7 km from centroid", " Urus-Martan: 3813.4 km from centroid", " Gelendzhik: 3193.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Encinitas", "FINAL ANSWER: Encinitas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.55728, "lon": -0.1864, "name": "Osu" }, { "lat": 4.71131, "lon": 6.79084, "name": "Obonoma" }, { "lat": -23.65506, "lon": 27.62495, "name": "Marapong" }, { "lat": 12.11667, "lon": 37.78333, "name": "Ādīs Zemen" }, { "lat": 7.70611, "lon": 122.13528, "name": "Siocon" } ], "question": "Which location is the geographic outlier among: Osu, Obonoma, Marapong, Ādīs Zemen, Siocon?", "ground_truth": { "answer": "Siocon", "outlier_distance_km": 9250.8, "second_furthest_km": 4355.3, "clarity_ratio": 2.12, "median_distance_km": 3577.3, "distances_to_centroid": { "Osu": 4355.3, "Obonoma": 3577.3, "Marapong": 3026.4, "Ādīs Zemen": 1209.7, "Siocon": 9250.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Osu: (5.56°, -0.19°)", " Obonoma: (4.71°, 6.79°)", " Marapong: (-23.66°, 27.62°)", " Ādīs Zemen: (12.12°, 37.78°)", " Siocon: (7.71°, 122.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Siocon: 9250.8 km from centroid", " Osu: 4355.3 km from centroid", " Obonoma: 3577.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Siocon", "FINAL ANSWER: Siocon" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 17.05, "lon": 74.26667, "name": "Urun-Islāmpur" }, { "lat": 9.58509, "lon": 77.95787, "name": "Virudunagar" }, { "lat": 24.41667, "lon": 111.51667, "name": "Babu" }, { "lat": 31.20509, "lon": 108.50628, "name": "Houba" }, { "lat": -14.66972, "lon": -40.47111, "name": "Planalto" } ], "question": "Which location is the geographic outlier among: Urun-Islāmpur, Virudunagar, Babu, Houba, Planalto?", "ground_truth": { "answer": "Planalto", "outlier_distance_km": 12160.1, "second_furthest_km": 4878.4, "clarity_ratio": 2.49, "median_distance_km": 4722.3, "distances_to_centroid": { "Urun-Islāmpur": 934.9, "Virudunagar": 1337.2, "Babu": 4878.4, "Houba": 4722.3, "Planalto": 12160.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Urun-Islāmpur: (17.05°, 74.27°)", " Virudunagar: (9.59°, 77.96°)", " Babu: (24.42°, 111.52°)", " Houba: (31.21°, 108.51°)", " Planalto: (-14.67°, -40.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Planalto: 12160.1 km from centroid", " Babu: 4878.4 km from centroid", " Houba: 4722.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Planalto", "FINAL ANSWER: Planalto" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.03333, "lon": 145.3, "name": "Narre Warren" }, { "lat": -38.05916, "lon": 145.40947, "name": "Officer" }, { "lat": -37.75, "lon": 145.35, "name": "Lilydale" }, { "lat": -40.91667, "lon": 175.01667, "name": "Paraparaumu" }, { "lat": 8.75924, "lon": -76.52969, "name": "San Juan de Urabá" } ], "question": "Which location is the geographic outlier among: Narre Warren, Officer, Lilydale, Paraparaumu, San Juan de Urabá?", "ground_truth": { "answer": "San Juan de Urabá", "outlier_distance_km": 17714.0, "second_furthest_km": 6178.4, "clarity_ratio": 2.87, "median_distance_km": 3669.7, "distances_to_centroid": { "Narre Warren": 3659.9, "Officer": 3669.7, "Lilydale": 3662.2, "Paraparaumu": 6178.4, "San Juan de Urabá": 17714.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Narre Warren: (-38.03°, 145.30°)", " Officer: (-38.06°, 145.41°)", " Lilydale: (-37.75°, 145.35°)", " Paraparaumu: (-40.92°, 175.02°)", " San Juan de Urabá: (8.76°, -76.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Juan de Urabá: 17714.0 km from centroid", " Paraparaumu: 6178.4 km from centroid", " Officer: 3669.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Juan de Urabá", "FINAL ANSWER: San Juan de Urabá" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.47222, "lon": -51.19778, "name": "Anapu" }, { "lat": -14.2789, "lon": -38.99584, "name": "Itacaré" }, { "lat": -20.25333, "lon": -43.80139, "name": "Itabirito" }, { "lat": -16.82333, "lon": -49.24389, "name": "Aparecida de Goiânia" }, { "lat": 6.53891, "lon": 3.3742, "name": "Shomolu" } ], "question": "Which location is the geographic outlier among: Anapu, Itacaré, Itabirito, Aparecida de Goiânia, Shomolu?", "ground_truth": { "answer": "Shomolu", "outlier_distance_km": 4716.2, "second_furthest_km": 1816.2, "clarity_ratio": 2.6, "median_distance_km": 1641.5, "distances_to_centroid": { "Anapu": 1816.2, "Itacaré": 610.0, "Itabirito": 1446.7, "Aparecida de Goiânia": 1641.5, "Shomolu": 4716.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Anapu: (-3.47°, -51.20°)", " Itacaré: (-14.28°, -39.00°)", " Itabirito: (-20.25°, -43.80°)", " Aparecida de Goiânia: (-16.82°, -49.24°)", " Shomolu: (6.54°, 3.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shomolu: 4716.2 km from centroid", " Anapu: 1816.2 km from centroid", " Aparecida de Goiânia: 1641.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shomolu", "FINAL ANSWER: Shomolu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.25778, "lon": -73.81228, "name": "Chimichagua" }, { "lat": -23.62808, "lon": -46.66791, "name": "Campo Belo" }, { "lat": -23.60389, "lon": -46.91917, "name": "Cotia" }, { "lat": -14.79909, "lon": -39.03228, "name": "Ilhéus" }, { "lat": 30.96187, "lon": 108.24327, "name": "Nanmen" } ], "question": "Which location is the geographic outlier among: Chimichagua, Campo Belo, Cotia, Ilhéus, Nanmen?", "ground_truth": { "answer": "Nanmen", "outlier_distance_km": 13826.2, "second_furthest_km": 6191.6, "clarity_ratio": 2.23, "median_distance_km": 3624.3, "distances_to_centroid": { "Chimichagua": 6191.6, "Campo Belo": 3604.1, "Cotia": 3624.3, "Ilhéus": 2419.5, "Nanmen": 13826.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chimichagua: (9.26°, -73.81°)", " Campo Belo: (-23.63°, -46.67°)", " Cotia: (-23.60°, -46.92°)", " Ilhéus: (-14.80°, -39.03°)", " Nanmen: (30.96°, 108.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nanmen: 13826.2 km from centroid", " Chimichagua: 6191.6 km from centroid", " Cotia: 3624.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nanmen", "FINAL ANSWER: Nanmen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.18389, "lon": -44.53444, "name": "Cocos" }, { "lat": -6.55833, "lon": -35.74167, "name": "Araruna" }, { "lat": -3.45361, "lon": -44.78, "name": "Arari" }, { "lat": 9.24194, "lon": -74.42667, "name": "Mompós" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" } ], "question": "Which location is the geographic outlier among: Cocos, Araruna, Arari, Mompós, Launceston?", "ground_truth": { "answer": "Launceston", "outlier_distance_km": 13720.0, "second_furthest_km": 7430.4, "clarity_ratio": 1.85, "median_distance_km": 3878.4, "distances_to_centroid": { "Cocos": 3705.6, "Araruna": 2824.0, "Arari": 3878.4, "Mompós": 7430.4, "Launceston": 13720.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cocos: (-14.18°, -44.53°)", " Araruna: (-6.56°, -35.74°)", " Arari: (-3.45°, -44.78°)", " Mompós: (9.24°, -74.43°)", " Launceston: (-41.44°, 147.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Launceston: 13720.0 km from centroid", " Mompós: 7430.4 km from centroid", " Arari: 3878.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Launceston", "FINAL ANSWER: Launceston" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.35843, "lon": -71.12589, "name": "Allston" }, { "lat": 18.00011, "lon": -94.5569, "name": "Minatitlán" }, { "lat": 44.98595, "lon": -122.98287, "name": "Hayesville" }, { "lat": 35.44201, "lon": -97.44087, "name": "Del City" }, { "lat": 51.44083, "lon": 5.47778, "name": "Eindhoven" } ], "question": "Which location is the geographic outlier among: Allston, Minatitlán, Hayesville, Del City, Eindhoven?", "ground_truth": { "answer": "Eindhoven", "outlier_distance_km": 6240.0, "second_furthest_km": 3900.8, "clarity_ratio": 1.6, "median_distance_km": 2891.0, "distances_to_centroid": { "Allston": 606.9, "Minatitlán": 2891.0, "Hayesville": 3900.8, "Del City": 1919.0, "Eindhoven": 6240.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Allston: (42.36°, -71.13°)", " Minatitlán: (18.00°, -94.56°)", " Hayesville: (44.99°, -122.98°)", " Del City: (35.44°, -97.44°)", " Eindhoven: (51.44°, 5.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Eindhoven: 6240.0 km from centroid", " Hayesville: 3900.8 km from centroid", " Minatitlán: 2891.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Eindhoven", "FINAL ANSWER: Eindhoven" ] }, { "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": -1.29996, "lon": 36.99047, "name": "Githunguri" }, { "lat": 30.29735, "lon": 30.97641, "name": "Ashmūn" }, { "lat": 11.09596, "lon": 11.33261, "name": "Nafada" }, { "lat": 28.35831, "lon": 33.07829, "name": "Ras Gharib" }, { "lat": 21.35064, "lon": -98.2257, "name": "Tantoyuca" } ], "question": "Which location is the geographic outlier among: Githunguri, Ashmūn, Nafada, Ras Gharib, Tantoyuca?", "ground_truth": { "answer": "Tantoyuca", "outlier_distance_km": 10375.0, "second_furthest_km": 4308.1, "clarity_ratio": 2.41, "median_distance_km": 3289.9, "distances_to_centroid": { "Githunguri": 4308.1, "Ashmūn": 3156.1, "Nafada": 1191.2, "Ras Gharib": 3289.9, "Tantoyuca": 10375.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Githunguri: (-1.30°, 36.99°)", " Ashmūn: (30.30°, 30.98°)", " Nafada: (11.10°, 11.33°)", " Ras Gharib: (28.36°, 33.08°)", " Tantoyuca: (21.35°, -98.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tantoyuca: 10375.0 km from centroid", " Githunguri: 4308.1 km from centroid", " Ras Gharib: 3289.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tantoyuca", "FINAL ANSWER: Tantoyuca" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 17.80787, "lon": -97.77956, "name": "Ciudad de Huajuapan de León" }, { "lat": 40.41483, "lon": -74.36543, "name": "Old Bridge" }, { "lat": 32.56645, "lon": -115.35387, "name": "Puebla" }, { "lat": 41.52364, "lon": -90.57764, "name": "Davenport" }, { "lat": -21.61, "lon": -45.56528, "name": "Elói Mendes" } ], "question": "Which location is the geographic outlier among: Ciudad de Huajuapan de León, Old Bridge, Puebla, Davenport, Elói Mendes?", "ground_truth": { "answer": "Elói Mendes", "outlier_distance_km": 6457.0, "second_furthest_km": 3224.9, "clarity_ratio": 2.0, "median_distance_km": 2254.1, "distances_to_centroid": { "Ciudad de Huajuapan de León": 1445.8, "Old Bridge": 2254.1, "Puebla": 3224.9, "Davenport": 2223.6, "Elói Mendes": 6457.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ciudad de Huajuapan de León: (17.81°, -97.78°)", " Old Bridge: (40.41°, -74.37°)", " Puebla: (32.57°, -115.35°)", " Davenport: (41.52°, -90.58°)", " Elói Mendes: (-21.61°, -45.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Elói Mendes: 6457.0 km from centroid", " Puebla: 3224.9 km from centroid", " Old Bridge: 2254.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Elói Mendes", "FINAL ANSWER: Elói Mendes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 3.69637, "lon": -73.69957, "name": "San Martín" }, { "lat": -31.94504, "lon": -65.19025, "name": "Villa Dolores" }, { "lat": -27.48132, "lon": -58.93925, "name": "Barranqueras" }, { "lat": -19.225, "lon": -40.85139, "name": "Pancas" }, { "lat": 52.3025, "lon": 4.68889, "name": "Hoofddorp" } ], "question": "Which location is the geographic outlier among: San Martín, Villa Dolores, Barranqueras, Pancas, Hoofddorp?", "ground_truth": { "answer": "Hoofddorp", "outlier_distance_km": 7951.9, "second_furthest_km": 3600.8, "clarity_ratio": 2.21, "median_distance_km": 3125.5, "distances_to_centroid": { "San Martín": 3125.5, "Villa Dolores": 3600.8, "Barranqueras": 2858.0, "Pancas": 1756.7, "Hoofddorp": 7951.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Martín: (3.70°, -73.70°)", " Villa Dolores: (-31.95°, -65.19°)", " Barranqueras: (-27.48°, -58.94°)", " Pancas: (-19.23°, -40.85°)", " Hoofddorp: (52.30°, 4.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hoofddorp: 7951.9 km from centroid", " Villa Dolores: 3600.8 km from centroid", " San Martín: 3125.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hoofddorp", "FINAL ANSWER: Hoofddorp" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81819, "lon": 145.00176, "name": "Richmond" }, { "lat": -37.94853, "lon": 145.15274, "name": "Springvale" }, { "lat": -33.78269, "lon": 151.04888, "name": "Carlingford" }, { "lat": -27.94402, "lon": 153.39815, "name": "Labrador" }, { "lat": 48.72692, "lon": 2.28301, "name": "Massy" } ], "question": "Which location is the geographic outlier among: Richmond, Springvale, Carlingford, Labrador, Massy?", "ground_truth": { "answer": "Massy", "outlier_distance_km": 13456.5, "second_furthest_km": 3651.4, "clarity_ratio": 3.69, "median_distance_km": 3615.8, "distances_to_centroid": { "Richmond": 3345.0, "Springvale": 3364.1, "Carlingford": 3615.8, "Labrador": 3651.4, "Massy": 13456.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Richmond: (-37.82°, 145.00°)", " Springvale: (-37.95°, 145.15°)", " Carlingford: (-33.78°, 151.05°)", " Labrador: (-27.94°, 153.40°)", " Massy: (48.73°, 2.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Massy: 13456.5 km from centroid", " Labrador: 3651.4 km from centroid", " Carlingford: 3615.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Massy", "FINAL ANSWER: Massy" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.53891, "lon": 3.3742, "name": "Shomolu" }, { "lat": 30.61618, "lon": 31.73514, "name": "Al Qurayn" }, { "lat": 12.00012, "lon": 8.51672, "name": "Kano" }, { "lat": 9.67954, "lon": 39.53262, "name": "Debre Birhan" }, { "lat": 20.25809, "lon": 105.97965, "name": "Ninh Bình" } ], "question": "Which location is the geographic outlier among: Shomolu, Al Qurayn, Kano, Debre Birhan, Ninh Bình?", "ground_truth": { "answer": "Ninh Bình", "outlier_distance_km": 7173.6, "second_furthest_km": 3890.8, "clarity_ratio": 1.84, "median_distance_km": 3189.3, "distances_to_centroid": { "Shomolu": 3890.8, "Al Qurayn": 1758.3, "Kano": 3189.3, "Debre Birhan": 707.2, "Ninh Bình": 7173.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shomolu: (6.54°, 3.37°)", " Al Qurayn: (30.62°, 31.74°)", " Kano: (12.00°, 8.52°)", " Debre Birhan: (9.68°, 39.53°)", " Ninh Bình: (20.26°, 105.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ninh Bình: 7173.6 km from centroid", " Shomolu: 3890.8 km from centroid", " Kano: 3189.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ninh Bình", "FINAL ANSWER: Ninh Bình" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.21209, "lon": 36.27248, "name": "Upper Gilgil" }, { "lat": -0.50397, "lon": 36.31845, "name": "Gilgil" }, { "lat": 11.80937, "lon": 8.84422, "name": "Wudil" }, { "lat": 0.03813, "lon": 36.36339, "name": "Nyahururu" }, { "lat": -23.5275, "lon": -46.9025, "name": "Jandira" } ], "question": "Which location is the geographic outlier among: Upper Gilgil, Gilgil, Wudil, Nyahururu, Jandira?", "ground_truth": { "answer": "Jandira", "outlier_distance_km": 6960.7, "second_furthest_km": 2481.8, "clarity_ratio": 2.8, "median_distance_km": 2470.6, "distances_to_centroid": { "Upper Gilgil": 2468.7, "Gilgil": 2470.6, "Wudil": 1694.7, "Nyahururu": 2481.8, "Jandira": 6960.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Upper Gilgil: (-0.21°, 36.27°)", " Gilgil: (-0.50°, 36.32°)", " Wudil: (11.81°, 8.84°)", " Nyahururu: (0.04°, 36.36°)", " Jandira: (-23.53°, -46.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jandira: 6960.7 km from centroid", " Nyahururu: 2481.8 km from centroid", " Gilgil: 2470.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jandira", "FINAL ANSWER: Jandira" ] }, { "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": 33.86726, "lon": -112.14682, "name": "Anthem" }, { "lat": 33.70918, "lon": -117.95367, "name": "Fountain Valley" }, { "lat": 39.00178, "lon": -76.68747, "name": "Crofton" }, { "lat": 38.88101, "lon": -77.10428, "name": "Arlington" }, { "lat": -19.76694, "lon": -44.08667, "name": "Ribeirão das Neves" } ], "question": "Which location is the geographic outlier among: Anthem, Fountain Valley, Crofton, Arlington, Ribeirão das Neves?", "ground_truth": { "answer": "Ribeirão das Neves", "outlier_distance_km": 6713.5, "second_furthest_km": 3260.3, "clarity_ratio": 2.06, "median_distance_km": 2736.8, "distances_to_centroid": { "Anthem": 2736.8, "Fountain Valley": 3260.3, "Crofton": 1753.0, "Arlington": 1723.1, "Ribeirão das Neves": 6713.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Anthem: (33.87°, -112.15°)", " Fountain Valley: (33.71°, -117.95°)", " Crofton: (39.00°, -76.69°)", " Arlington: (38.88°, -77.10°)", " Ribeirão das Neves: (-19.77°, -44.09°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ribeirão das Neves: 6713.5 km from centroid", " Fountain Valley: 3260.3 km from centroid", " Anthem: 2736.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ribeirão das Neves", "FINAL ANSWER: Ribeirão das Neves" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.58333, "lon": 145.03333, "name": "Wollert" }, { "lat": -31.9652, "lon": 141.4512, "name": "Broken Hill" }, { "lat": -33.32711, "lon": 115.64137, "name": "Bunbury" }, { "lat": -37.96667, "lon": 145.16667, "name": "Noble Park" }, { "lat": 29.76416, "lon": 107.67834, "name": "Baoluan" } ], "question": "Which location is the geographic outlier among: Wollert, Broken Hill, Bunbury, Noble Park, Baoluan?", "ground_truth": { "answer": "Baoluan", "outlier_distance_km": 6294.9, "second_furthest_km": 2213.8, "clarity_ratio": 2.84, "median_distance_km": 2174.2, "distances_to_centroid": { "Wollert": 2174.2, "Broken Hill": 1497.2, "Bunbury": 1947.3, "Noble Park": 2213.8, "Baoluan": 6294.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wollert: (-37.58°, 145.03°)", " Broken Hill: (-31.97°, 141.45°)", " Bunbury: (-33.33°, 115.64°)", " Noble Park: (-37.97°, 145.17°)", " Baoluan: (29.76°, 107.68°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Baoluan: 6294.9 km from centroid", " Noble Park: 2213.8 km from centroid", " Wollert: 2174.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Baoluan", "FINAL ANSWER: Baoluan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.22316, "lon": 1.4028, "name": "Deal" }, { "lat": 53.07738, "lon": 7.40444, "name": "Papenburg" }, { "lat": 52.10577, "lon": 21.26129, "name": "Otwock" }, { "lat": 50.30582, "lon": 18.9742, "name": "Chorzów" }, { "lat": 9.24391, "lon": -75.14675, "name": "San Luis de Sincé" } ], "question": "Which location is the geographic outlier among: Deal, Papenburg, Otwock, Chorzów, San Luis de Sincé?", "ground_truth": { "answer": "San Luis de Sincé", "outlier_distance_km": 7682.2, "second_furthest_km": 2200.7, "clarity_ratio": 3.49, "median_distance_km": 1994.5, "distances_to_centroid": { "Deal": 1022.7, "Papenburg": 1440.1, "Otwock": 2200.7, "Chorzów": 1994.5, "San Luis de Sincé": 7682.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Deal: (51.22°, 1.40°)", " Papenburg: (53.08°, 7.40°)", " Otwock: (52.11°, 21.26°)", " Chorzów: (50.31°, 18.97°)", " San Luis de Sincé: (9.24°, -75.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Luis de Sincé: 7682.2 km from centroid", " Otwock: 2200.7 km from centroid", " Chorzów: 1994.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Luis de Sincé", "FINAL ANSWER: San Luis de Sincé" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.47056, "lon": 110.21778, "name": "Magelang" }, { "lat": 13.24025, "lon": 99.82428, "name": "Khao Yoi" }, { "lat": 25.91278, "lon": 109.31361, "name": "Shuikou" }, { "lat": 46.07622, "lon": 127.39369, "name": "Bayan" }, { "lat": -33.7061, "lon": 150.7094, "name": "Cranebrook" } ], "question": "Which location is the geographic outlier among: Magelang, Khao Yoi, Shuikou, Bayan, Cranebrook?", "ground_truth": { "answer": "Cranebrook", "outlier_distance_km": 5762.8, "second_furthest_km": 4211.8, "clarity_ratio": 1.37, "median_distance_km": 2201.4, "distances_to_centroid": { "Magelang": 2081.7, "Khao Yoi": 2201.4, "Shuikou": 2184.4, "Bayan": 4211.8, "Cranebrook": 5762.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Magelang: (-7.47°, 110.22°)", " Khao Yoi: (13.24°, 99.82°)", " Shuikou: (25.91°, 109.31°)", " Bayan: (46.08°, 127.39°)", " Cranebrook: (-33.71°, 150.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cranebrook: 5762.8 km from centroid", " Bayan: 4211.8 km from centroid", " Khao Yoi: 2201.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cranebrook", "FINAL ANSWER: Cranebrook" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.35335, "lon": 40.02095, "name": "Watamu" }, { "lat": 9.23478, "lon": 40.75593, "name": "Mī’ēso" }, { "lat": 30.71524, "lon": 31.2592, "name": "Mīt Ghamr" }, { "lat": -25.46279, "lon": 28.65041, "name": "Moloto South" }, { "lat": -37.83333, "lon": 145.05, "name": "Glenferrie" } ], "question": "Which location is the geographic outlier among: Watamu, Mī’ēso, Mīt Ghamr, Moloto South, Glenferrie?", "ground_truth": { "answer": "Glenferrie", "outlier_distance_km": 9459.9, "second_furthest_km": 4863.0, "clarity_ratio": 1.95, "median_distance_km": 3769.2, "distances_to_centroid": { "Watamu": 1911.6, "Mī’ēso": 2434.5, "Mīt Ghamr": 4863.0, "Moloto South": 3769.2, "Glenferrie": 9459.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Watamu: (-3.35°, 40.02°)", " Mī’ēso: (9.23°, 40.76°)", " Mīt Ghamr: (30.72°, 31.26°)", " Moloto South: (-25.46°, 28.65°)", " Glenferrie: (-37.83°, 145.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glenferrie: 9459.9 km from centroid", " Mīt Ghamr: 4863.0 km from centroid", " Moloto South: 3769.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glenferrie", "FINAL ANSWER: Glenferrie" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.74242, "lon": 139.42635, "name": "Musashimurayama" }, { "lat": 35.5, "lon": 133.68333, "name": "Yabase" }, { "lat": 10.82302, "lon": 106.62965, "name": "Ho Chi Minh City" }, { "lat": 42.83393, "lon": 93.50601, "name": "Hami" }, { "lat": 5.48956, "lon": 6.00407, "name": "Ughelli" } ], "question": "Which location is the geographic outlier among: Musashimurayama, Yabase, Ho Chi Minh City, Hami, Ughelli?", "ground_truth": { "answer": "Ughelli", "outlier_distance_km": 9724.2, "second_furthest_km": 4257.2, "clarity_ratio": 2.28, "median_distance_km": 3737.5, "distances_to_centroid": { "Musashimurayama": 4257.2, "Yabase": 3737.5, "Ho Chi Minh City": 2039.5, "Hami": 1875.3, "Ughelli": 9724.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Musashimurayama: (35.74°, 139.43°)", " Yabase: (35.50°, 133.68°)", " Ho Chi Minh City: (10.82°, 106.63°)", " Hami: (42.83°, 93.51°)", " Ughelli: (5.49°, 6.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ughelli: 9724.2 km from centroid", " Musashimurayama: 4257.2 km from centroid", " Yabase: 3737.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ughelli", "FINAL ANSWER: Ughelli" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.10247, "lon": 17.04827, "name": "Rejon ulicy Traugutta" }, { "lat": 46.46671, "lon": -0.80624, "name": "Fontenay-le-Comte" }, { "lat": 53.94646, "lon": 10.7312, "name": "Ratekau" }, { "lat": 53.16532, "lon": 8.68873, "name": "Burglesum" }, { "lat": -38.13333, "lon": 145.13333, "name": "Frankston East" } ], "question": "Which location is the geographic outlier among: Rejon ulicy Traugutta, Fontenay-le-Comte, Ratekau, Burglesum, Frankston East?", "ground_truth": { "answer": "Frankston East", "outlier_distance_km": 13739.5, "second_furthest_km": 3436.1, "clarity_ratio": 4.0, "median_distance_km": 3098.3, "distances_to_centroid": { "Rejon ulicy Traugutta": 2512.4, "Fontenay-le-Comte": 3436.1, "Ratekau": 3041.6, "Burglesum": 3098.3, "Frankston East": 13739.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rejon ulicy Traugutta: (51.10°, 17.05°)", " Fontenay-le-Comte: (46.47°, -0.81°)", " Ratekau: (53.95°, 10.73°)", " Burglesum: (53.17°, 8.69°)", " Frankston East: (-38.13°, 145.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Frankston East: 13739.5 km from centroid", " Fontenay-le-Comte: 3436.1 km from centroid", " Burglesum: 3098.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Frankston East", "FINAL ANSWER: Frankston East" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.72976, "lon": 151.15977, "name": "Saint Ives" }, { "lat": -33.79068, "lon": 150.6693, "name": "Glenmore Park" }, { "lat": -25.28762, "lon": 152.76936, "name": "Hervey Bay" }, { "lat": -37.75405, "lon": 145.14864, "name": "Templestowe" }, { "lat": -26.25028, "lon": -49.37861, "name": "São Bento do Sul" } ], "question": "Which location is the geographic outlier among: Saint Ives, Glenmore Park, Hervey Bay, Templestowe, São Bento do Sul?", "ground_truth": { "answer": "São Bento do Sul", "outlier_distance_km": 13247.6, "second_furthest_km": 4207.3, "clarity_ratio": 3.15, "median_distance_km": 3834.8, "distances_to_centroid": { "Saint Ives": 3834.8, "Glenmore Park": 3789.0, "Hervey Bay": 4207.3, "Templestowe": 3269.5, "São Bento do Sul": 13247.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint Ives: (-33.73°, 151.16°)", " Glenmore Park: (-33.79°, 150.67°)", " Hervey Bay: (-25.29°, 152.77°)", " Templestowe: (-37.75°, 145.15°)", " São Bento do Sul: (-26.25°, -49.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Bento do Sul: 13247.6 km from centroid", " Hervey Bay: 4207.3 km from centroid", " Saint Ives: 3834.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Bento do Sul", "FINAL ANSWER: São Bento do Sul" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.78254, "lon": 138.61077, "name": "Parafield Gardens" }, { "lat": -37.91667, "lon": 145.11667, "name": "Clayton" }, { "lat": -33.95222, "lon": 150.89949, "name": "Casula" }, { "lat": -33.79798, "lon": 151.28826, "name": "Manly" }, { "lat": 30.58768, "lon": 31.502, "name": "Zagazig" } ], "question": "Which location is the geographic outlier among: Parafield Gardens, Clayton, Casula, Manly, Zagazig?", "ground_truth": { "answer": "Zagazig", "outlier_distance_km": 11407.6, "second_furthest_km": 3019.2, "clarity_ratio": 3.78, "median_distance_km": 2990.8, "distances_to_centroid": { "Parafield Gardens": 2049.2, "Clayton": 2723.7, "Casula": 2990.8, "Manly": 3019.2, "Zagazig": 11407.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parafield Gardens: (-34.78°, 138.61°)", " Clayton: (-37.92°, 145.12°)", " Casula: (-33.95°, 150.90°)", " Manly: (-33.80°, 151.29°)", " Zagazig: (30.59°, 31.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zagazig: 11407.6 km from centroid", " Manly: 3019.2 km from centroid", " Casula: 2990.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zagazig", "FINAL ANSWER: Zagazig" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.05224, "lon": 8.39227, "name": "Bad Berleburg" }, { "lat": 53.55024, "lon": -2.77348, "name": "Skelmersdale" }, { "lat": 50.25937, "lon": 10.96384, "name": "Coburg" }, { "lat": 43.35982, "lon": 5.33421, "name": "Marseille 16" }, { "lat": 22.76843, "lon": -102.58141, "name": "Zacatecas" } ], "question": "Which location is the geographic outlier among: Bad Berleburg, Skelmersdale, Coburg, Marseille 16, Zacatecas?", "ground_truth": { "answer": "Zacatecas", "outlier_distance_km": 7994.4, "second_furthest_km": 2140.3, "clarity_ratio": 3.74, "median_distance_km": 1977.9, "distances_to_centroid": { "Bad Berleburg": 1977.9, "Skelmersdale": 1422.4, "Coburg": 2140.3, "Marseille 16": 1721.1, "Zacatecas": 7994.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bad Berleburg: (51.05°, 8.39°)", " Skelmersdale: (53.55°, -2.77°)", " Coburg: (50.26°, 10.96°)", " Marseille 16: (43.36°, 5.33°)", " Zacatecas: (22.77°, -102.58°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zacatecas: 7994.4 km from centroid", " Coburg: 2140.3 km from centroid", " Bad Berleburg: 1977.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zacatecas", "FINAL ANSWER: Zacatecas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.76667, "lon": 150.91667, "name": "Blacktown" }, { "lat": -32.06003, "lon": 115.955, "name": "Thornlie" }, { "lat": -40.63333, "lon": 175.275, "name": "Levin" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" }, { "lat": 40.4165, "lon": -3.70256, "name": "Madrid" } ], "question": "Which location is the geographic outlier among: Blacktown, Thornlie, Levin, Otara, Madrid?", "ground_truth": { "answer": "Madrid", "outlier_distance_km": 14521.1, "second_furthest_km": 5411.4, "clarity_ratio": 2.68, "median_distance_km": 5330.7, "distances_to_centroid": { "Blacktown": 3139.9, "Thornlie": 1438.2, "Levin": 5411.4, "Otara": 5330.7, "Madrid": 14521.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Blacktown: (-33.77°, 150.92°)", " Thornlie: (-32.06°, 115.95°)", " Levin: (-40.63°, 175.28°)", " Otara: (-36.95°, 174.87°)", " Madrid: (40.42°, -3.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Madrid: 14521.1 km from centroid", " Levin: 5411.4 km from centroid", " Otara: 5330.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Madrid", "FINAL ANSWER: Madrid" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.80293, "lon": 8.25341, "name": "Esuk Oron" }, { "lat": 10.53689, "lon": -2.70155, "name": "Jirapa" }, { "lat": -27.75431, "lon": 26.64382, "name": "Allanridge" }, { "lat": 31.5084, "lon": 31.84106, "name": "‘Izbat al Burj" }, { "lat": 33.97612, "lon": -117.90534, "name": "Rowland Heights" } ], "question": "Which location is the geographic outlier among: Esuk Oron, Jirapa, Allanridge, ‘Izbat al Burj, Rowland Heights?", "ground_truth": { "answer": "Rowland Heights", "outlier_distance_km": 10884.2, "second_furthest_km": 5867.4, "clarity_ratio": 1.86, "median_distance_km": 4950.9, "distances_to_centroid": { "Esuk Oron": 2192.8, "Jirapa": 882.4, "Allanridge": 5867.4, "‘Izbat al Burj": 4950.9, "Rowland Heights": 10884.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Esuk Oron: (4.80°, 8.25°)", " Jirapa: (10.54°, -2.70°)", " Allanridge: (-27.75°, 26.64°)", " ‘Izbat al Burj: (31.51°, 31.84°)", " Rowland Heights: (33.98°, -117.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rowland Heights: 10884.2 km from centroid", " Allanridge: 5867.4 km from centroid", " ‘Izbat al Burj: 4950.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rowland Heights", "FINAL ANSWER: Rowland Heights" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.85059, "lon": -87.79367, "name": "Berwyn" }, { "lat": 39.42734, "lon": -75.23408, "name": "Bridgeton" }, { "lat": 44.9483, "lon": -93.34801, "name": "Saint Louis Park" }, { "lat": 40.52467, "lon": -111.86382, "name": "Draper" }, { "lat": 14.5832, "lon": 121.0409, "name": "Mandaluyong City" } ], "question": "Which location is the geographic outlier among: Berwyn, Bridgeton, Saint Louis Park, Draper, Mandaluyong City?", "ground_truth": { "answer": "Mandaluyong City", "outlier_distance_km": 14273.0, "second_furthest_km": 5346.3, "clarity_ratio": 2.67, "median_distance_km": 3780.8, "distances_to_centroid": { "Berwyn": 3340.7, "Bridgeton": 2284.0, "Saint Louis Park": 3780.8, "Draper": 5346.3, "Mandaluyong City": 14273.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Berwyn: (41.85°, -87.79°)", " Bridgeton: (39.43°, -75.23°)", " Saint Louis Park: (44.95°, -93.35°)", " Draper: (40.52°, -111.86°)", " Mandaluyong City: (14.58°, 121.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mandaluyong City: 14273.0 km from centroid", " Draper: 5346.3 km from centroid", " Saint Louis Park: 3780.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mandaluyong City", "FINAL ANSWER: Mandaluyong City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.89405, "lon": 5.67666, "name": "Sapele" }, { "lat": -22.97111, "lon": 30.67361, "name": "Malamulele" }, { "lat": 0.17124, "lon": 34.59466, "name": "Khwisero" }, { "lat": 0.6004, "lon": 34.77119, "name": "Webuye" }, { "lat": 46.31836, "lon": -72.56632, "name": "Sainte-Catherine" } ], "question": "Which location is the geographic outlier among: Sapele, Malamulele, Khwisero, Webuye, Sainte-Catherine?", "ground_truth": { "answer": "Sainte-Catherine", "outlier_distance_km": 8696.2, "second_furthest_km": 4148.4, "clarity_ratio": 2.1, "median_distance_km": 3179.9, "distances_to_centroid": { "Sapele": 106.1, "Malamulele": 4148.4, "Khwisero": 3170.6, "Webuye": 3179.9, "Sainte-Catherine": 8696.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sapele: (5.89°, 5.68°)", " Malamulele: (-22.97°, 30.67°)", " Khwisero: (0.17°, 34.59°)", " Webuye: (0.60°, 34.77°)", " Sainte-Catherine: (46.32°, -72.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sainte-Catherine: 8696.2 km from centroid", " Malamulele: 4148.4 km from centroid", " Webuye: 3179.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sainte-Catherine", "FINAL ANSWER: Sainte-Catherine" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.88775, "lon": 115.9099, "name": "Morley" }, { "lat": -33.80383, "lon": 150.98768, "name": "Westmead" }, { "lat": -33.8406, "lon": 151.00748, "name": "Granville" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": 49.97078, "lon": 8.05883, "name": "Ingelheim am Rhein" } ], "question": "Which location is the geographic outlier among: Morley, Westmead, Granville, Melbourne City Centre, Ingelheim am Rhein?", "ground_truth": { "answer": "Ingelheim am Rhein", "outlier_distance_km": 12631.8, "second_furthest_km": 4084.5, "clarity_ratio": 3.09, "median_distance_km": 4081.5, "distances_to_centroid": { "Morley": 1611.9, "Westmead": 4081.5, "Granville": 4084.5, "Melbourne City Centre": 3752.5, "Ingelheim am Rhein": 12631.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Morley: (-31.89°, 115.91°)", " Westmead: (-33.80°, 150.99°)", " Granville: (-33.84°, 151.01°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Ingelheim am Rhein: (49.97°, 8.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ingelheim am Rhein: 12631.8 km from centroid", " Granville: 4084.5 km from centroid", " Westmead: 4081.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ingelheim am Rhein", "FINAL ANSWER: Ingelheim am Rhein" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.94175, "lon": 123.50266, "name": "Hushitai" }, { "lat": 22.55213, "lon": 113.88288, "name": "Bao'an" }, { "lat": 24.28859, "lon": 116.11768, "name": "Meizhou" }, { "lat": 10.24026, "lon": 76.171, "name": "Edavilangu" }, { "lat": 45.10359, "lon": 7.76803, "name": "San Mauro Torinese" } ], "question": "Which location is the geographic outlier among: Hushitai, Bao'an, Meizhou, Edavilangu, San Mauro Torinese?", "ground_truth": { "answer": "San Mauro Torinese", "outlier_distance_km": 7020.3, "second_furthest_km": 3542.4, "clarity_ratio": 1.98, "median_distance_km": 2884.6, "distances_to_centroid": { "Hushitai": 3542.4, "Bao'an": 2728.8, "Meizhou": 2884.6, "Edavilangu": 2379.0, "San Mauro Torinese": 7020.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hushitai: (41.94°, 123.50°)", " Bao'an: (22.55°, 113.88°)", " Meizhou: (24.29°, 116.12°)", " Edavilangu: (10.24°, 76.17°)", " San Mauro Torinese: (45.10°, 7.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Mauro Torinese: 7020.3 km from centroid", " Hushitai: 3542.4 km from centroid", " Meizhou: 2884.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Mauro Torinese", "FINAL ANSWER: San Mauro Torinese" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.43158, "lon": -0.55239, "name": "Egham" }, { "lat": 36.75793, "lon": -3.95233, "name": "Torrox" }, { "lat": 48.83732, "lon": 2.35823, "name": "Salpêtrière" }, { "lat": 50.84048, "lon": 10.95198, "name": "Arnstadt" }, { "lat": -6.2375, "lon": 106.69556, "name": "Ciputat" } ], "question": "Which location is the geographic outlier among: Egham, Torrox, Salpêtrière, Arnstadt, Ciputat?", "ground_truth": { "answer": "Ciputat", "outlier_distance_km": 9848.4, "second_furthest_km": 2512.3, "clarity_ratio": 3.92, "median_distance_km": 2409.2, "distances_to_centroid": { "Egham": 2512.3, "Torrox": 2409.2, "Salpêtrière": 2182.7, "Arnstadt": 1881.9, "Ciputat": 9848.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Egham: (51.43°, -0.55°)", " Torrox: (36.76°, -3.95°)", " Salpêtrière: (48.84°, 2.36°)", " Arnstadt: (50.84°, 10.95°)", " Ciputat: (-6.24°, 106.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ciputat: 9848.4 km from centroid", " Egham: 2512.3 km from centroid", " Torrox: 2409.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ciputat", "FINAL ANSWER: Ciputat" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.14701, "lon": 105.83481, "name": "Bắc Kạn" }, { "lat": 10.99175, "lon": 77.28633, "name": "Palladam" }, { "lat": 31.98333, "lon": 131.33333, "name": "Honjō" }, { "lat": 21.48815, "lon": 70.07576, "name": "Bāntva" }, { "lat": 23.63138, "lon": -103.64134, "name": "Sombrerete" } ], "question": "Which location is the geographic outlier among: Bắc Kạn, Palladam, Honjō, Bāntva, Sombrerete?", "ground_truth": { "answer": "Sombrerete", "outlier_distance_km": 14486.6, "second_furthest_km": 7384.1, "clarity_ratio": 1.96, "median_distance_km": 5091.8, "distances_to_centroid": { "Bắc Kạn": 5091.8, "Palladam": 2559.4, "Honjō": 7384.1, "Bāntva": 1436.0, "Sombrerete": 14486.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bắc Kạn: (22.15°, 105.83°)", " Palladam: (10.99°, 77.29°)", " Honjō: (31.98°, 131.33°)", " Bāntva: (21.49°, 70.08°)", " Sombrerete: (23.63°, -103.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sombrerete: 14486.6 km from centroid", " Honjō: 7384.1 km from centroid", " Bắc Kạn: 5091.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sombrerete", "FINAL ANSWER: Sombrerete" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.32127, "lon": 20.97204, "name": "Białołeka" }, { "lat": 52.53048, "lon": 13.29371, "name": "Charlottenburg-Nord" }, { "lat": 52.91149, "lon": -0.64184, "name": "Grantham" }, { "lat": 42.03565, "lon": 0.12686, "name": "Barbastro" }, { "lat": 42.16558, "lon": -88.29425, "name": "Algonquin" } ], "question": "Which location is the geographic outlier among: Białołeka, Charlottenburg-Nord, Grantham, Barbastro, Algonquin?", "ground_truth": { "answer": "Algonquin", "outlier_distance_km": 5832.5, "second_furthest_km": 2284.0, "clarity_ratio": 2.55, "median_distance_km": 1764.6, "distances_to_centroid": { "Białołeka": 2284.0, "Charlottenburg-Nord": 1764.6, "Grantham": 879.8, "Barbastro": 1114.8, "Algonquin": 5832.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Białołeka: (52.32°, 20.97°)", " Charlottenburg-Nord: (52.53°, 13.29°)", " Grantham: (52.91°, -0.64°)", " Barbastro: (42.04°, 0.13°)", " Algonquin: (42.17°, -88.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Algonquin: 5832.5 km from centroid", " Białołeka: 2284.0 km from centroid", " Charlottenburg-Nord: 1764.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Algonquin", "FINAL ANSWER: Algonquin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.5144, "lon": -0.13535, "name": "Soho" }, { "lat": 50.59034, "lon": 12.70657, "name": "Aue" }, { "lat": 52.79886, "lon": 18.26387, "name": "Inowrocław" }, { "lat": 51.10286, "lon": 17.03006, "name": "Wrocław" }, { "lat": 5.58385, "lon": -0.27787, "name": "Awoshi" } ], "question": "Which location is the geographic outlier among: Soho, Aue, Inowrocław, Wrocław, Awoshi?", "ground_truth": { "answer": "Awoshi", "outlier_distance_km": 4197.6, "second_furthest_km": 1335.3, "clarity_ratio": 3.14, "median_distance_km": 1256.0, "distances_to_centroid": { "Soho": 1256.0, "Aue": 951.5, "Inowrocław": 1335.3, "Wrocław": 1131.0, "Awoshi": 4197.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Soho: (51.51°, -0.14°)", " Aue: (50.59°, 12.71°)", " Inowrocław: (52.80°, 18.26°)", " Wrocław: (51.10°, 17.03°)", " Awoshi: (5.58°, -0.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Awoshi: 4197.6 km from centroid", " Inowrocław: 1335.3 km from centroid", " Soho: 1256.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Awoshi", "FINAL ANSWER: Awoshi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.86893, "lon": 10.68729, "name": "Lübeck" }, { "lat": 53.1235, "lon": 18.00762, "name": "Bydgoszcz" }, { "lat": 40.73757, "lon": 13.86003, "name": "Forio" }, { "lat": 49.04353, "lon": 2.12134, "name": "Saint-Ouen-l'Aumône" }, { "lat": -20.41639, "lon": -42.90861, "name": "Ponte Nova" } ], "question": "Which location is the geographic outlier among: Lübeck, Bydgoszcz, Forio, Saint-Ouen-l'Aumône, Ponte Nova?", "ground_truth": { "answer": "Ponte Nova", "outlier_distance_km": 7690.3, "second_furthest_km": 2419.0, "clarity_ratio": 3.18, "median_distance_km": 2218.7, "distances_to_centroid": { "Lübeck": 2218.7, "Bydgoszcz": 2419.0, "Forio": 1328.3, "Saint-Ouen-l'Aumône": 1538.2, "Ponte Nova": 7690.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lübeck: (53.87°, 10.69°)", " Bydgoszcz: (53.12°, 18.01°)", " Forio: (40.74°, 13.86°)", " Saint-Ouen-l'Aumône: (49.04°, 2.12°)", " Ponte Nova: (-20.42°, -42.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ponte Nova: 7690.3 km from centroid", " Bydgoszcz: 2419.0 km from centroid", " Lübeck: 2218.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ponte Nova", "FINAL ANSWER: Ponte Nova" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.52297, "lon": -87.90333, "name": "Fairhope" }, { "lat": 18.98856, "lon": -97.44643, "name": "Ciudad Serdán" }, { "lat": 41.50948, "lon": -90.57875, "name": "Rock Island" }, { "lat": 40.88149, "lon": -74.1132, "name": "Garfield" }, { "lat": -0.90833, "lon": 119.87083, "name": "Palu" } ], "question": "Which location is the geographic outlier among: Fairhope, Ciudad Serdán, Rock Island, Garfield, Palu?", "ground_truth": { "answer": "Palu", "outlier_distance_km": 16823.8, "second_furthest_km": 5305.5, "clarity_ratio": 3.17, "median_distance_km": 4393.7, "distances_to_centroid": { "Fairhope": 4101.8, "Ciudad Serdán": 5305.5, "Rock Island": 4393.7, "Garfield": 3051.1, "Palu": 16823.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fairhope: (30.52°, -87.90°)", " Ciudad Serdán: (18.99°, -97.45°)", " Rock Island: (41.51°, -90.58°)", " Garfield: (40.88°, -74.11°)", " Palu: (-0.91°, 119.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palu: 16823.8 km from centroid", " Ciudad Serdán: 5305.5 km from centroid", " Rock Island: 4393.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palu", "FINAL ANSWER: Palu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -30.54389, "lon": -52.52194, "name": "Encruzilhada do Sul" }, { "lat": -23.11694, "lon": -46.55028, "name": "Atibaia" }, { "lat": -12.13556, "lon": -38.41917, "name": "Alagoinhas" }, { "lat": -9.37833, "lon": -37.24528, "name": "Santana do Ipanema" }, { "lat": 42.55843, "lon": -70.88005, "name": "Beverly" } ], "question": "Which location is the geographic outlier among: Encruzilhada do Sul, Atibaia, Alagoinhas, Santana do Ipanema, Beverly?", "ground_truth": { "answer": "Beverly", "outlier_distance_km": 5885.1, "second_furthest_km": 2694.4, "clarity_ratio": 2.18, "median_distance_km": 1865.6, "distances_to_centroid": { "Encruzilhada do Sul": 2694.4, "Atibaia": 1865.6, "Alagoinhas": 1329.5, "Santana do Ipanema": 1345.9, "Beverly": 5885.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Encruzilhada do Sul: (-30.54°, -52.52°)", " Atibaia: (-23.12°, -46.55°)", " Alagoinhas: (-12.14°, -38.42°)", " Santana do Ipanema: (-9.38°, -37.25°)", " Beverly: (42.56°, -70.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Beverly: 5885.1 km from centroid", " Encruzilhada do Sul: 2694.4 km from centroid", " Atibaia: 1865.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Beverly", "FINAL ANSWER: Beverly" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.88101, "lon": -77.10428, "name": "Arlington" }, { "lat": 46.82666, "lon": -100.88958, "name": "Mandan" }, { "lat": 33.66808, "lon": -117.32726, "name": "Lake Elsinore" }, { "lat": 53.63344, "lon": -113.63533, "name": "St. Albert" }, { "lat": -9.52614, "lon": -77.52869, "name": "Huaraz" } ], "question": "Which location is the geographic outlier among: Arlington, Mandan, Lake Elsinore, St. Albert, Huaraz?", "ground_truth": { "answer": "Huaraz", "outlier_distance_km": 5141.8, "second_furthest_km": 2664.3, "clarity_ratio": 1.93, "median_distance_km": 1941.7, "distances_to_centroid": { "Arlington": 1941.7, "Mandan": 1600.5, "Lake Elsinore": 1864.3, "St. Albert": 2664.3, "Huaraz": 5141.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Arlington: (38.88°, -77.10°)", " Mandan: (46.83°, -100.89°)", " Lake Elsinore: (33.67°, -117.33°)", " St. Albert: (53.63°, -113.64°)", " Huaraz: (-9.53°, -77.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Huaraz: 5141.8 km from centroid", " St. Albert: 2664.3 km from centroid", " Arlington: 1941.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Huaraz", "FINAL ANSWER: Huaraz" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.31062, "lon": -69.77949, "name": "Augusta" }, { "lat": 33.76696, "lon": -118.18923, "name": "Long Beach" }, { "lat": 42.03725, "lon": -88.28119, "name": "Elgin" }, { "lat": 40.9304, "lon": -73.89789, "name": "Yonkers" }, { "lat": 26.04259, "lon": 74.02373, "name": "Raipur" } ], "question": "Which location is the geographic outlier among: Augusta, Long Beach, Elgin, Yonkers, Raipur?", "ground_truth": { "answer": "Raipur", "outlier_distance_km": 11191.1, "second_furthest_km": 5600.8, "clarity_ratio": 2.0, "median_distance_km": 2854.9, "distances_to_centroid": { "Augusta": 1440.9, "Long Beach": 5600.8, "Elgin": 2854.9, "Yonkers": 1652.9, "Raipur": 11191.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Augusta: (44.31°, -69.78°)", " Long Beach: (33.77°, -118.19°)", " Elgin: (42.04°, -88.28°)", " Yonkers: (40.93°, -73.90°)", " Raipur: (26.04°, 74.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Raipur: 11191.1 km from centroid", " Long Beach: 5600.8 km from centroid", " Elgin: 2854.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Raipur", "FINAL ANSWER: Raipur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 28.83826, "lon": -105.91214, "name": "Aldama" }, { "lat": 36.72836, "lon": -76.58496, "name": "Suffolk" }, { "lat": 40.98065, "lon": -73.68374, "name": "Rye" }, { "lat": 34.25807, "lon": -88.70464, "name": "Tupelo" }, { "lat": 7.77104, "lon": 4.55698, "name": "Osogbo" } ], "question": "Which location is the geographic outlier among: Aldama, Suffolk, Rye, Tupelo, Osogbo?", "ground_truth": { "answer": "Osogbo", "outlier_distance_km": 7905.2, "second_furthest_km": 3655.5, "clarity_ratio": 2.16, "median_distance_km": 2007.0, "distances_to_centroid": { "Aldama": 3655.5, "Suffolk": 1110.8, "Rye": 1351.5, "Tupelo": 2007.0, "Osogbo": 7905.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Aldama: (28.84°, -105.91°)", " Suffolk: (36.73°, -76.58°)", " Rye: (40.98°, -73.68°)", " Tupelo: (34.26°, -88.70°)", " Osogbo: (7.77°, 4.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Osogbo: 7905.2 km from centroid", " Aldama: 3655.5 km from centroid", " Tupelo: 2007.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Osogbo", "FINAL ANSWER: Osogbo" ] }, { "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": 32.68222, "lon": 112.08194, "name": "Dengzhou" }, { "lat": 19.74276, "lon": 109.34492, "name": "Zhonghe" }, { "lat": 18.61867, "lon": 73.80375, "name": "Pimpri-Chinchwad" }, { "lat": 30.60369, "lon": 109.72333, "name": "Yezhou" }, { "lat": 5.35113, "lon": -0.62313, "name": "Winneba" } ], "question": "Which location is the geographic outlier among: Dengzhou, Zhonghe, Pimpri-Chinchwad, Yezhou, Winneba?", "ground_truth": { "answer": "Winneba", "outlier_distance_km": 8911.3, "second_furthest_km": 3320.6, "clarity_ratio": 2.68, "median_distance_km": 3049.5, "distances_to_centroid": { "Dengzhou": 3320.6, "Zhonghe": 2966.5, "Pimpri-Chinchwad": 799.9, "Yezhou": 3049.5, "Winneba": 8911.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dengzhou: (32.68°, 112.08°)", " Zhonghe: (19.74°, 109.34°)", " Pimpri-Chinchwad: (18.62°, 73.80°)", " Yezhou: (30.60°, 109.72°)", " Winneba: (5.35°, -0.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Winneba: 8911.3 km from centroid", " Dengzhou: 3320.6 km from centroid", " Yezhou: 3049.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Winneba", "FINAL ANSWER: Winneba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.36471, "lon": 5.5856, "name": "Voiron" }, { "lat": 50.78314, "lon": 16.03037, "name": "Kamienna Góra" }, { "lat": 50.72485, "lon": 1.61373, "name": "Boulogne-sur-Mer" }, { "lat": 53.87561, "lon": -1.71232, "name": "Guiseley" }, { "lat": 41.91419, "lon": -88.30869, "name": "St. Charles" } ], "question": "Which location is the geographic outlier among: Voiron, Kamienna Góra, Boulogne-sur-Mer, Guiseley, St. Charles?", "ground_truth": { "answer": "St. Charles", "outlier_distance_km": 5677.5, "second_furthest_km": 2116.0, "clarity_ratio": 2.68, "median_distance_km": 1476.3, "distances_to_centroid": { "Voiron": 1476.3, "Kamienna Góra": 2116.0, "Boulogne-sur-Mer": 1103.5, "Guiseley": 1003.6, "St. Charles": 5677.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Voiron: (45.36°, 5.59°)", " Kamienna Góra: (50.78°, 16.03°)", " Boulogne-sur-Mer: (50.72°, 1.61°)", " Guiseley: (53.88°, -1.71°)", " St. Charles: (41.91°, -88.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " St. Charles: 5677.5 km from centroid", " Kamienna Góra: 2116.0 km from centroid", " Voiron: 1476.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: St. Charles", "FINAL ANSWER: St. Charles" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 13.82735, "lon": 100.55531, "name": "Chatuchak subdistrict" }, { "lat": 35.48778, "lon": 119.34583, "name": "Nanhu" }, { "lat": 22.61198, "lon": 70.94379, "name": "Wānkāner" }, { "lat": 21.02115, "lon": 105.85231, "name": "Cửa Nam" }, { "lat": 11.55684, "lon": 8.58065, "name": "Rano" } ], "question": "Which location is the geographic outlier among: Chatuchak subdistrict, Nanhu, Wānkāner, Cửa Nam, Rano?", "ground_truth": { "answer": "Rano", "outlier_distance_km": 7749.3, "second_furthest_km": 4055.6, "clarity_ratio": 1.91, "median_distance_km": 2572.2, "distances_to_centroid": { "Chatuchak subdistrict": 2211.5, "Nanhu": 4055.6, "Wānkāner": 1061.2, "Cửa Nam": 2572.2, "Rano": 7749.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chatuchak subdistrict: (13.83°, 100.56°)", " Nanhu: (35.49°, 119.35°)", " Wānkāner: (22.61°, 70.94°)", " Cửa Nam: (21.02°, 105.85°)", " Rano: (11.56°, 8.58°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rano: 7749.3 km from centroid", " Nanhu: 4055.6 km from centroid", " Cửa Nam: 2572.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rano", "FINAL ANSWER: Rano" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.50506, "lon": -76.31977, "name": "Bel Air South" }, { "lat": 19.22906, "lon": -98.92504, "name": "San Mateo Huitzilzingo" }, { "lat": 31.11712, "lon": -97.7278, "name": "Killeen" }, { "lat": 34.02316, "lon": -84.36159, "name": "Roswell" }, { "lat": 5.2236, "lon": 100.69262, "name": "Selama" } ], "question": "Which location is the geographic outlier among: Bel Air South, San Mateo Huitzilzingo, Killeen, Roswell, Selama?", "ground_truth": { "answer": "Selama", "outlier_distance_km": 15429.9, "second_furthest_km": 4917.6, "clarity_ratio": 3.14, "median_distance_km": 4541.2, "distances_to_centroid": { "Bel Air South": 2775.8, "San Mateo Huitzilzingo": 4917.6, "Killeen": 4541.2, "Roswell": 3295.6, "Selama": 15429.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bel Air South: (39.51°, -76.32°)", " San Mateo Huitzilzingo: (19.23°, -98.93°)", " Killeen: (31.12°, -97.73°)", " Roswell: (34.02°, -84.36°)", " Selama: (5.22°, 100.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Selama: 15429.9 km from centroid", " San Mateo Huitzilzingo: 4917.6 km from centroid", " Killeen: 4541.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Selama", "FINAL ANSWER: Selama" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.56338, "lon": -46.63228, "name": "Liberdade" }, { "lat": -19.86028, "lon": -44.60833, "name": "Pará de Minas" }, { "lat": -0.15491, "lon": -50.0615, "name": "Tucumã" }, { "lat": -16.02028, "lon": -49.81028, "name": "Itaberaí" }, { "lat": 39.70471, "lon": -105.08137, "name": "Lakewood" } ], "question": "Which location is the geographic outlier among: Liberdade, Pará de Minas, Tucumã, Itaberaí, Lakewood?", "ground_truth": { "answer": "Lakewood", "outlier_distance_km": 6742.6, "second_furthest_km": 2564.0, "clarity_ratio": 2.63, "median_distance_km": 2373.4, "distances_to_centroid": { "Liberdade": 2564.0, "Pará de Minas": 2373.4, "Tucumã": 1104.7, "Itaberaí": 1689.5, "Lakewood": 6742.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Liberdade: (-23.56°, -46.63°)", " Pará de Minas: (-19.86°, -44.61°)", " Tucumã: (-0.15°, -50.06°)", " Itaberaí: (-16.02°, -49.81°)", " Lakewood: (39.70°, -105.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lakewood: 6742.6 km from centroid", " Liberdade: 2564.0 km from centroid", " Pará de Minas: 2373.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lakewood", "FINAL ANSWER: Lakewood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.08371, "lon": 18.22572, "name": "Solec Kujawski" }, { "lat": 43.32059, "lon": 45.04903, "name": "Sunzha" }, { "lat": 56.02714, "lon": 37.46793, "name": "Lobnya" }, { "lat": 53.56321, "lon": 9.94257, "name": "Altona-Nord" }, { "lat": 23.1749, "lon": -102.86785, "name": "Fresnillo" } ], "question": "Which location is the geographic outlier among: Solec Kujawski, Sunzha, Lobnya, Altona-Nord, Fresnillo?", "ground_truth": { "answer": "Fresnillo", "outlier_distance_km": 9224.1, "second_furthest_km": 3412.9, "clarity_ratio": 2.7, "median_distance_km": 2720.0, "distances_to_centroid": { "Solec Kujawski": 1443.7, "Sunzha": 3412.9, "Lobnya": 2720.0, "Altona-Nord": 1048.1, "Fresnillo": 9224.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Solec Kujawski: (53.08°, 18.23°)", " Sunzha: (43.32°, 45.05°)", " Lobnya: (56.03°, 37.47°)", " Altona-Nord: (53.56°, 9.94°)", " Fresnillo: (23.17°, -102.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fresnillo: 9224.1 km from centroid", " Sunzha: 3412.9 km from centroid", " Lobnya: 2720.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fresnillo", "FINAL ANSWER: Fresnillo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.38032, "lon": 150.50595, "name": "Rockhampton" }, { "lat": -32.06003, "lon": 115.955, "name": "Thornlie" }, { "lat": -31.91099, "lon": 152.45387, "name": "Taree" }, { "lat": -37.78761, "lon": 145.14888, "name": "Doncaster East" }, { "lat": 41.82186, "lon": -71.50675, "name": "Johnston" } ], "question": "Which location is the geographic outlier among: Rockhampton, Thornlie, Taree, Doncaster East, Johnston?", "ground_truth": { "answer": "Johnston", "outlier_distance_km": 17059.8, "second_furthest_km": 5663.4, "clarity_ratio": 3.01, "median_distance_km": 5455.5, "distances_to_centroid": { "Rockhampton": 5455.5, "Thornlie": 2453.3, "Taree": 5663.4, "Doncaster East": 5107.2, "Johnston": 17059.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rockhampton: (-23.38°, 150.51°)", " Thornlie: (-32.06°, 115.95°)", " Taree: (-31.91°, 152.45°)", " Doncaster East: (-37.79°, 145.15°)", " Johnston: (41.82°, -71.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Johnston: 17059.8 km from centroid", " Taree: 5663.4 km from centroid", " Rockhampton: 5455.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Johnston", "FINAL ANSWER: Johnston" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.65, "lon": -2.61667, "name": "Chorley" }, { "lat": 41.41803, "lon": 2.18596, "name": "Navas" }, { "lat": 50.91877, "lon": -1.49037, "name": "Totton" }, { "lat": 52.49376, "lon": 13.44469, "name": "Treptow" }, { "lat": 21.08242, "lon": 106.5138, "name": "Thị Trấn Đông Triều" } ], "question": "Which location is the geographic outlier among: Chorley, Navas, Totton, Treptow, Thị Trấn Đông Triều?", "ground_truth": { "answer": "Thị Trấn Đông Triều", "outlier_distance_km": 7848.1, "second_furthest_km": 2187.3, "clarity_ratio": 3.59, "median_distance_km": 2030.2, "distances_to_centroid": { "Chorley": 2187.3, "Navas": 1768.2, "Totton": 2030.2, "Treptow": 1213.2, "Thị Trấn Đông Triều": 7848.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chorley: (53.65°, -2.62°)", " Navas: (41.42°, 2.19°)", " Totton: (50.92°, -1.49°)", " Treptow: (52.49°, 13.44°)", " Thị Trấn Đông Triều: (21.08°, 106.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Thị Trấn Đông Triều: 7848.1 km from centroid", " Chorley: 2187.3 km from centroid", " Totton: 2030.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Thị Trấn Đông Triều", "FINAL ANSWER: Thị Trấn Đông Triều" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.46667, "lon": 101.43333, "name": "Qingshizui" }, { "lat": 35.61143, "lon": 139.71736, "name": "Togoshi" }, { "lat": 35.49333, "lon": 128.74889, "name": "Miryang" }, { "lat": 23.75644, "lon": 86.0051, "name": "Phusro" }, { "lat": -33.96109, "lon": 25.61494, "name": "Port Elizabeth" } ], "question": "Which location is the geographic outlier among: Qingshizui, Togoshi, Miryang, Phusro, Port Elizabeth?", "ground_truth": { "answer": "Port Elizabeth", "outlier_distance_km": 9559.9, "second_furthest_km": 4584.1, "clarity_ratio": 2.09, "median_distance_km": 3624.9, "distances_to_centroid": { "Qingshizui": 2040.0, "Togoshi": 4584.1, "Miryang": 3624.9, "Phusro": 1156.2, "Port Elizabeth": 9559.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Qingshizui: (37.47°, 101.43°)", " Togoshi: (35.61°, 139.72°)", " Miryang: (35.49°, 128.75°)", " Phusro: (23.76°, 86.01°)", " Port Elizabeth: (-33.96°, 25.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Port Elizabeth: 9559.9 km from centroid", " Togoshi: 4584.1 km from centroid", " Miryang: 3624.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Port Elizabeth", "FINAL ANSWER: Port Elizabeth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.42118, "lon": 130.6136, "name": "Yamaguma" }, { "lat": 22.29161, "lon": 70.79322, "name": "Rājkot" }, { "lat": 15.1773, "lon": 73.99392, "name": "Cuncolim" }, { "lat": 35.37111, "lon": 139.22361, "name": "Hadano" }, { "lat": -20.23389, "lon": -41.51056, "name": "Ibatiba" } ], "question": "Which location is the geographic outlier among: Yamaguma, Rājkot, Cuncolim, Hadano, Ibatiba?", "ground_truth": { "answer": "Ibatiba", "outlier_distance_km": 13322.0, "second_furthest_km": 6632.4, "clarity_ratio": 2.01, "median_distance_km": 5836.9, "distances_to_centroid": { "Yamaguma": 5836.9, "Rājkot": 693.1, "Cuncolim": 235.3, "Hadano": 6632.4, "Ibatiba": 13322.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yamaguma: (33.42°, 130.61°)", " Rājkot: (22.29°, 70.79°)", " Cuncolim: (15.18°, 73.99°)", " Hadano: (35.37°, 139.22°)", " Ibatiba: (-20.23°, -41.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ibatiba: 13322.0 km from centroid", " Hadano: 6632.4 km from centroid", " Yamaguma: 5836.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ibatiba", "FINAL ANSWER: Ibatiba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.37814, "lon": -3.70712, "name": "Pradolongo" }, { "lat": 53.65, "lon": -2.61667, "name": "Chorley" }, { "lat": 49.7685, "lon": 4.72487, "name": "Charleville-Mézières" }, { "lat": 44.03837, "lon": 10.04142, "name": "Marina di Carrara" }, { "lat": 5.62657, "lon": -0.25807, "name": "New Achimota" } ], "question": "Which location is the geographic outlier among: Pradolongo, Chorley, Charleville-Mézières, Marina di Carrara, New Achimota?", "ground_truth": { "answer": "New Achimota", "outlier_distance_km": 3681.7, "second_furthest_km": 1694.4, "clarity_ratio": 2.17, "median_distance_km": 1255.7, "distances_to_centroid": { "Pradolongo": 495.0, "Chorley": 1694.4, "Charleville-Mézières": 1255.7, "Marina di Carrara": 918.6, "New Achimota": 3681.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pradolongo: (40.38°, -3.71°)", " Chorley: (53.65°, -2.62°)", " Charleville-Mézières: (49.77°, 4.72°)", " Marina di Carrara: (44.04°, 10.04°)", " New Achimota: (5.63°, -0.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New Achimota: 3681.7 km from centroid", " Chorley: 1694.4 km from centroid", " Charleville-Mézières: 1255.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New Achimota", "FINAL ANSWER: New Achimota" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.47389, "lon": -48.45972, "name": "Niquelândia" }, { "lat": -9.335, "lon": -50.35, "name": "Santana do Araguaia" }, { "lat": -23.41778, "lon": -49.09056, "name": "Itaí" }, { "lat": -4.90389, "lon": -80.68528, "name": "Sullana" }, { "lat": -27.53221, "lon": 153.22889, "name": "Alexandra Hills" } ], "question": "Which location is the geographic outlier among: Niquelândia, Santana do Araguaia, Itaí, Sullana, Alexandra Hills?", "ground_truth": { "answer": "Alexandra Hills", "outlier_distance_km": 15020.1, "second_furthest_km": 7252.8, "clarity_ratio": 2.07, "median_distance_km": 3892.1, "distances_to_centroid": { "Niquelândia": 3582.6, "Santana do Araguaia": 3892.1, "Itaí": 3648.5, "Sullana": 7252.8, "Alexandra Hills": 15020.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Niquelândia: (-14.47°, -48.46°)", " Santana do Araguaia: (-9.34°, -50.35°)", " Itaí: (-23.42°, -49.09°)", " Sullana: (-4.90°, -80.69°)", " Alexandra Hills: (-27.53°, 153.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alexandra Hills: 15020.1 km from centroid", " Sullana: 7252.8 km from centroid", " Santana do Araguaia: 3892.1 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": 42.32226, "lon": -83.17631, "name": "Dearborn" }, { "lat": 40.02233, "lon": -75.06323, "name": "Wissinoming" }, { "lat": 18.91614, "lon": -103.87713, "name": "Tecomán" }, { "lat": 18.88352, "lon": -97.73344, "name": "Tecamachalco" }, { "lat": 27.04514, "lon": 31.31845, "name": "Abū Tīj" } ], "question": "Which location is the geographic outlier among: Dearborn, Wissinoming, Tecomán, Tecamachalco, Abū Tīj?", "ground_truth": { "answer": "Abū Tīj", "outlier_distance_km": 9185.9, "second_furthest_km": 4024.6, "clarity_ratio": 2.28, "median_distance_km": 3440.9, "distances_to_centroid": { "Dearborn": 2120.5, "Wissinoming": 1452.8, "Tecomán": 4024.6, "Tecamachalco": 3440.9, "Abū Tīj": 9185.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dearborn: (42.32°, -83.18°)", " Wissinoming: (40.02°, -75.06°)", " Tecomán: (18.92°, -103.88°)", " Tecamachalco: (18.88°, -97.73°)", " Abū Tīj: (27.05°, 31.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Abū Tīj: 9185.9 km from centroid", " Tecomán: 4024.6 km from centroid", " Tecamachalco: 3440.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Abū Tīj", "FINAL ANSWER: Abū Tīj" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.83643, "lon": 139.79957, "name": "Sōka" }, { "lat": 22.50143, "lon": 70.04363, "name": "Bedi" }, { "lat": 34.58167, "lon": 119.12889, "name": "Haizhou" }, { "lat": 30.90343, "lon": 109.46682, "name": "Xinmin" }, { "lat": -23.62808, "lon": -46.66791, "name": "Campo Belo" } ], "question": "Which location is the geographic outlier among: Sōka, Bedi, Haizhou, Xinmin, Campo Belo?", "ground_truth": { "answer": "Campo Belo", "outlier_distance_km": 14360.3, "second_furthest_km": 6184.8, "clarity_ratio": 2.32, "median_distance_km": 4305.3, "distances_to_centroid": { "Sōka": 6184.8, "Bedi": 903.4, "Haizhou": 4305.3, "Xinmin": 3334.6, "Campo Belo": 14360.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sōka: (35.84°, 139.80°)", " Bedi: (22.50°, 70.04°)", " Haizhou: (34.58°, 119.13°)", " Xinmin: (30.90°, 109.47°)", " Campo Belo: (-23.63°, -46.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Campo Belo: 14360.3 km from centroid", " Sōka: 6184.8 km from centroid", " Haizhou: 4305.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Campo Belo", "FINAL ANSWER: Campo Belo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.90561, "lon": 145.00279, "name": "Brighton" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" }, { "lat": -38.04369, "lon": 145.2923, "name": "Narre Warren South" }, { "lat": -36.75818, "lon": 144.28024, "name": "Bendigo" }, { "lat": 28.41866, "lon": 30.77861, "name": "Maţāy" } ], "question": "Which location is the geographic outlier among: Brighton, Launceston, Narre Warren South, Bendigo, Maţāy?", "ground_truth": { "answer": "Maţāy", "outlier_distance_km": 11460.6, "second_furthest_km": 2901.7, "clarity_ratio": 3.95, "median_distance_km": 2580.5, "distances_to_centroid": { "Brighton": 2550.9, "Launceston": 2901.7, "Narre Warren South": 2580.5, "Bendigo": 2436.7, "Maţāy": 11460.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Brighton: (-37.91°, 145.00°)", " Launceston: (-41.44°, 147.13°)", " Narre Warren South: (-38.04°, 145.29°)", " Bendigo: (-36.76°, 144.28°)", " Maţāy: (28.42°, 30.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maţāy: 11460.6 km from centroid", " Launceston: 2901.7 km from centroid", " Narre Warren South: 2580.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maţāy", "FINAL ANSWER: Maţāy" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.84382, "lon": 6.85774, "name": "Borken" }, { "lat": 51.7836, "lon": -1.4854, "name": "Witney" }, { "lat": 51.24053, "lon": 6.18376, "name": "Brüggen" }, { "lat": 48.22786, "lon": 9.87874, "name": "Laupheim" }, { "lat": 33.01457, "lon": -97.09696, "name": "Flower Mound" } ], "question": "Which location is the geographic outlier among: Borken, Witney, Brüggen, Laupheim, Flower Mound?", "ground_truth": { "answer": "Flower Mound", "outlier_distance_km": 6821.3, "second_furthest_km": 1865.9, "clarity_ratio": 3.66, "median_distance_km": 1660.6, "distances_to_centroid": { "Borken": 1660.6, "Witney": 1106.0, "Brüggen": 1604.5, "Laupheim": 1865.9, "Flower Mound": 6821.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Borken: (51.84°, 6.86°)", " Witney: (51.78°, -1.49°)", " Brüggen: (51.24°, 6.18°)", " Laupheim: (48.23°, 9.88°)", " Flower Mound: (33.01°, -97.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Flower Mound: 6821.3 km from centroid", " Laupheim: 1865.9 km from centroid", " Borken: 1660.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Flower Mound", "FINAL ANSWER: Flower Mound" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.09408, "lon": -0.25913, "name": "Koforidua" }, { "lat": -31.49285, "lon": 25.00633, "name": "Middelburg" }, { "lat": 10.48536, "lon": 5.14501, "name": "Ibeto" }, { "lat": 31.16844, "lon": 31.7655, "name": "Kafr al Kurdī" }, { "lat": 48.44963, "lon": -123.50261, "name": "Langford" } ], "question": "Which location is the geographic outlier among: Koforidua, Middelburg, Ibeto, Kafr al Kurdī, Langford?", "ground_truth": { "answer": "Langford", "outlier_distance_km": 10425.0, "second_furthest_km": 6347.3, "clarity_ratio": 1.64, "median_distance_km": 4937.6, "distances_to_centroid": { "Koforidua": 1530.0, "Middelburg": 6347.3, "Ibeto": 1925.9, "Kafr al Kurdī": 4937.6, "Langford": 10425.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Koforidua: (6.09°, -0.26°)", " Middelburg: (-31.49°, 25.01°)", " Ibeto: (10.49°, 5.15°)", " Kafr al Kurdī: (31.17°, 31.77°)", " Langford: (48.45°, -123.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Langford: 10425.0 km from centroid", " Middelburg: 6347.3 km from centroid", " Kafr al Kurdī: 4937.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Langford", "FINAL ANSWER: Langford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.49755, "lon": -2.16889, "name": "Kingswinford" }, { "lat": 51.55237, "lon": -0.12497, "name": "Holloway" }, { "lat": 38.27559, "lon": -3.61535, "name": "La Carolina" }, { "lat": 40.38644, "lon": -3.79818, "name": "Campamento" }, { "lat": 9.8857, "lon": 76.37328, "name": "Manakunnam" } ], "question": "Which location is the geographic outlier among: Kingswinford, Holloway, La Carolina, Campamento, Manakunnam?", "ground_truth": { "answer": "Manakunnam", "outlier_distance_km": 6988.3, "second_furthest_km": 1959.8, "clarity_ratio": 3.57, "median_distance_km": 1787.9, "distances_to_centroid": { "Kingswinford": 1959.8, "Holloway": 1787.9, "La Carolina": 1475.1, "Campamento": 1483.1, "Manakunnam": 6988.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kingswinford: (52.50°, -2.17°)", " Holloway: (51.55°, -0.12°)", " La Carolina: (38.28°, -3.62°)", " Campamento: (40.39°, -3.80°)", " Manakunnam: (9.89°, 76.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Manakunnam: 6988.3 km from centroid", " Kingswinford: 1959.8 km from centroid", " Holloway: 1787.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Manakunnam", "FINAL ANSWER: Manakunnam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -39.6381, "lon": 176.84918, "name": "Hastings" }, { "lat": -36.96807, "lon": 174.79875, "name": "Mangere" }, { "lat": -23.84852, "lon": 151.25775, "name": "Gladstone" }, { "lat": -33.88374, "lon": 151.21282, "name": "Surry Hills" }, { "lat": 32.76397, "lon": -116.96877, "name": "Casa de Oro-Mount Helix" } ], "question": "Which location is the geographic outlier among: Hastings, Mangere, Gladstone, Surry Hills, Casa de Oro-Mount Helix?", "ground_truth": { "answer": "Casa de Oro-Mount Helix", "outlier_distance_km": 15423.4, "second_furthest_km": 6851.6, "clarity_ratio": 2.25, "median_distance_km": 6693.0, "distances_to_centroid": { "Hastings": 6851.6, "Mangere": 6693.0, "Gladstone": 4515.6, "Surry Hills": 4550.0, "Casa de Oro-Mount Helix": 15423.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hastings: (-39.64°, 176.85°)", " Mangere: (-36.97°, 174.80°)", " Gladstone: (-23.85°, 151.26°)", " Surry Hills: (-33.88°, 151.21°)", " Casa de Oro-Mount Helix: (32.76°, -116.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Casa de Oro-Mount Helix: 15423.4 km from centroid", " Hastings: 6851.6 km from centroid", " Mangere: 6693.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Casa de Oro-Mount Helix", "FINAL ANSWER: Casa de Oro-Mount Helix" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.40076, "lon": 1.04582, "name": "Le Grand-Quevilly" }, { "lat": 51.59231, "lon": 7.6638, "name": "Kamen" }, { "lat": 52.56014, "lon": 13.0927, "name": "Falkensee" }, { "lat": 51.38678, "lon": -0.41319, "name": "Walton-on-Thames" }, { "lat": -23.38032, "lon": 150.50595, "name": "Rockhampton" } ], "question": "Which location is the geographic outlier among: Le Grand-Quevilly, Kamen, Falkensee, Walton-on-Thames, Rockhampton?", "ground_truth": { "answer": "Rockhampton", "outlier_distance_km": 13799.8, "second_furthest_km": 3210.6, "clarity_ratio": 4.3, "median_distance_km": 3047.6, "distances_to_centroid": { "Le Grand-Quevilly": 3047.6, "Kamen": 2705.0, "Falkensee": 2455.5, "Walton-on-Thames": 3210.6, "Rockhampton": 13799.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Le Grand-Quevilly: (49.40°, 1.05°)", " Kamen: (51.59°, 7.66°)", " Falkensee: (52.56°, 13.09°)", " Walton-on-Thames: (51.39°, -0.41°)", " Rockhampton: (-23.38°, 150.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rockhampton: 13799.8 km from centroid", " Walton-on-Thames: 3210.6 km from centroid", " Le Grand-Quevilly: 3047.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rockhampton", "FINAL ANSWER: Rockhampton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.81, "lon": -43.17361, "name": "João Monlevade" }, { "lat": -20.91806, "lon": -49.44528, "name": "Bady Bassitt" }, { "lat": -17.345, "lon": -44.94194, "name": "Pirapora" }, { "lat": -6.80306, "lon": -35.08056, "name": "Rio Tinto" }, { "lat": 50.85162, "lon": -1.17929, "name": "Fareham" } ], "question": "Which location is the geographic outlier among: João Monlevade, Bady Bassitt, Pirapora, Rio Tinto, Fareham?", "ground_truth": { "answer": "Fareham", "outlier_distance_km": 6764.3, "second_furthest_km": 2566.0, "clarity_ratio": 2.64, "median_distance_km": 2099.8, "distances_to_centroid": { "João Monlevade": 2099.8, "Bady Bassitt": 2566.0, "Pirapora": 1961.7, "Rio Tinto": 446.0, "Fareham": 6764.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " João Monlevade: (-19.81°, -43.17°)", " Bady Bassitt: (-20.92°, -49.45°)", " Pirapora: (-17.34°, -44.94°)", " Rio Tinto: (-6.80°, -35.08°)", " Fareham: (50.85°, -1.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fareham: 6764.3 km from centroid", " Bady Bassitt: 2566.0 km from centroid", " João Monlevade: 2099.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fareham", "FINAL ANSWER: Fareham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.58412, "lon": 3.98336, "name": "Epe" }, { "lat": -32.72173, "lon": 25.58804, "name": "Somerset East" }, { "lat": 25.48742, "lon": 28.97918, "name": "Mūţ" }, { "lat": -34.08401, "lon": 18.82113, "name": "Somerset West" }, { "lat": 20.43108, "lon": -101.72261, "name": "Pénjamo" } ], "question": "Which location is the geographic outlier among: Epe, Somerset East, Mūţ, Somerset West, Pénjamo?", "ground_truth": { "answer": "Pénjamo", "outlier_distance_km": 10832.3, "second_furthest_km": 4819.4, "clarity_ratio": 2.25, "median_distance_km": 4592.2, "distances_to_centroid": { "Epe": 1438.4, "Somerset East": 4592.2, "Mūţ": 4819.4, "Somerset West": 4251.9, "Pénjamo": 10832.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Epe: (6.58°, 3.98°)", " Somerset East: (-32.72°, 25.59°)", " Mūţ: (25.49°, 28.98°)", " Somerset West: (-34.08°, 18.82°)", " Pénjamo: (20.43°, -101.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pénjamo: 10832.3 km from centroid", " Mūţ: 4819.4 km from centroid", " Somerset East: 4592.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pénjamo", "FINAL ANSWER: Pénjamo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -4.75181, "lon": -44.94385, "name": "Poção de Pedras" }, { "lat": -11.6725, "lon": -61.19361, "name": "Pimenta Bueno" }, { "lat": 0.71333, "lon": -51.41333, "name": "Porto Grande" }, { "lat": -8.11599, "lon": -79.02998, "name": "Trujillo" }, { "lat": 38.94312, "lon": -84.54411, "name": "Independence" } ], "question": "Which location is the geographic outlier among: Poção de Pedras, Pimenta Bueno, Porto Grande, Trujillo, Independence?", "ground_truth": { "answer": "Independence", "outlier_distance_km": 4492.6, "second_furthest_km": 2310.0, "clarity_ratio": 1.94, "median_distance_km": 2056.8, "distances_to_centroid": { "Poção de Pedras": 2310.0, "Pimenta Bueno": 1668.1, "Porto Grande": 1446.7, "Trujillo": 2056.8, "Independence": 4492.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Poção de Pedras: (-4.75°, -44.94°)", " Pimenta Bueno: (-11.67°, -61.19°)", " Porto Grande: (0.71°, -51.41°)", " Trujillo: (-8.12°, -79.03°)", " Independence: (38.94°, -84.54°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Independence: 4492.6 km from centroid", " Poção de Pedras: 2310.0 km from centroid", " Trujillo: 2056.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Independence", "FINAL ANSWER: Independence" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.8075, "lon": 115.86599, "name": "Landsdale" }, { "lat": -34.92866, "lon": 138.59863, "name": "Adelaide" }, { "lat": -33.95222, "lon": 150.89949, "name": "Casula" }, { "lat": -33.95, "lon": 151.23333, "name": "Maroubra" }, { "lat": 9.99461, "lon": 39.89693, "name": "Robit" } ], "question": "Which location is the geographic outlier among: Landsdale, Adelaide, Casula, Maroubra, Robit?", "ground_truth": { "answer": "Robit", "outlier_distance_km": 9426.3, "second_furthest_km": 3235.7, "clarity_ratio": 2.91, "median_distance_km": 3205.3, "distances_to_centroid": { "Landsdale": 835.2, "Adelaide": 2160.9, "Casula": 3205.3, "Maroubra": 3235.7, "Robit": 9426.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Landsdale: (-31.81°, 115.87°)", " Adelaide: (-34.93°, 138.60°)", " Casula: (-33.95°, 150.90°)", " Maroubra: (-33.95°, 151.23°)", " Robit: (9.99°, 39.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Robit: 9426.3 km from centroid", " Maroubra: 3235.7 km from centroid", " Casula: 3205.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Robit", "FINAL ANSWER: Robit" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.39559, "lon": -97.87839, "name": "Enid" }, { "lat": 40.30428, "lon": -74.10042, "name": "Tinton Falls" }, { "lat": 19.44999, "lon": -98.87274, "name": "San Miguel Coatlinchán" }, { "lat": 43.04946, "lon": -88.00759, "name": "Wauwatosa" }, { "lat": 22.6305, "lon": 110.14686, "name": "Yulin" } ], "question": "Which location is the geographic outlier among: Enid, Tinton Falls, San Miguel Coatlinchán, Wauwatosa, Yulin?", "ground_truth": { "answer": "Yulin", "outlier_distance_km": 13537.1, "second_furthest_km": 5072.8, "clarity_ratio": 2.67, "median_distance_km": 4394.7, "distances_to_centroid": { "Enid": 4394.7, "Tinton Falls": 2344.0, "San Miguel Coatlinchán": 5072.8, "Wauwatosa": 3534.0, "Yulin": 13537.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Enid: (36.40°, -97.88°)", " Tinton Falls: (40.30°, -74.10°)", " San Miguel Coatlinchán: (19.45°, -98.87°)", " Wauwatosa: (43.05°, -88.01°)", " Yulin: (22.63°, 110.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yulin: 13537.1 km from centroid", " San Miguel Coatlinchán: 5072.8 km from centroid", " Enid: 4394.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yulin", "FINAL ANSWER: Yulin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.79224, "lon": -118.31507, "name": "Lomita" }, { "lat": 30.28604, "lon": -97.73889, "name": "University of Texas" }, { "lat": 28.26701, "lon": -105.48093, "name": "Meoqui" }, { "lat": 19.71288, "lon": -98.96895, "name": "Tecámac" }, { "lat": -38.17058, "lon": 144.3114, "name": "Highton" } ], "question": "Which location is the geographic outlier among: Lomita, University of Texas, Meoqui, Tecámac, Highton?", "ground_truth": { "answer": "Highton", "outlier_distance_km": 16782.0, "second_furthest_km": 6629.5, "clarity_ratio": 2.53, "median_distance_km": 5368.9, "distances_to_centroid": { "Lomita": 6629.5, "University of Texas": 4659.9, "Meoqui": 5368.9, "Tecámac": 4664.1, "Highton": 16782.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lomita: (33.79°, -118.32°)", " University of Texas: (30.29°, -97.74°)", " Meoqui: (28.27°, -105.48°)", " Tecámac: (19.71°, -98.97°)", " Highton: (-38.17°, 144.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Highton: 16782.0 km from centroid", " Lomita: 6629.5 km from centroid", " Meoqui: 5368.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Highton", "FINAL ANSWER: Highton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -39.64355, "lon": -72.33269, "name": "Panguipulli" }, { "lat": -21.31806, "lon": -49.05444, "name": "Itajobi" }, { "lat": -40.80255, "lon": -62.98349, "name": "Carmen de Patagones" }, { "lat": -3.33361, "lon": -43.52833, "name": "São Benedito do Rio Preto" }, { "lat": -41.13333, "lon": 174.85, "name": "Porirua" } ], "question": "Which location is the geographic outlier among: Panguipulli, Itajobi, Carmen de Patagones, São Benedito do Rio Preto, Porirua?", "ground_truth": { "answer": "Porirua", "outlier_distance_km": 12169.1, "second_furthest_km": 5665.4, "clarity_ratio": 2.15, "median_distance_km": 4863.7, "distances_to_centroid": { "Panguipulli": 5665.4, "Itajobi": 3946.2, "Carmen de Patagones": 4863.7, "São Benedito do Rio Preto": 4511.2, "Porirua": 12169.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Panguipulli: (-39.64°, -72.33°)", " Itajobi: (-21.32°, -49.05°)", " Carmen de Patagones: (-40.80°, -62.98°)", " São Benedito do Rio Preto: (-3.33°, -43.53°)", " Porirua: (-41.13°, 174.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Porirua: 12169.1 km from centroid", " Panguipulli: 5665.4 km from centroid", " Carmen de Patagones: 4863.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Porirua", "FINAL ANSWER: Porirua" ] }, { "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": 49.75787, "lon": 0.37457, "name": "Fécamp" }, { "lat": 48.15, "lon": 11.35, "name": "Puchheim" }, { "lat": 51.56844, "lon": 0.45782, "name": "Basildon" }, { "lat": 44.83061, "lon": -0.52675, "name": "Floirac" }, { "lat": 18.61472, "lon": -99.18028, "name": "Jojutla" } ], "question": "Which location is the geographic outlier among: Fécamp, Puchheim, Basildon, Floirac, Jojutla?", "ground_truth": { "answer": "Jojutla", "outlier_distance_km": 7952.3, "second_furthest_km": 2322.3, "clarity_ratio": 3.42, "median_distance_km": 1680.2, "distances_to_centroid": { "Fécamp": 1585.3, "Puchheim": 2322.3, "Basildon": 1680.2, "Floirac": 1384.7, "Jojutla": 7952.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fécamp: (49.76°, 0.37°)", " Puchheim: (48.15°, 11.35°)", " Basildon: (51.57°, 0.46°)", " Floirac: (44.83°, -0.53°)", " Jojutla: (18.61°, -99.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jojutla: 7952.3 km from centroid", " Puchheim: 2322.3 km from centroid", " Basildon: 1680.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jojutla", "FINAL ANSWER: Jojutla" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" }, { "lat": -33.71816, "lon": 151.11561, "name": "Wahroonga" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": -37.96667, "lon": 145.16667, "name": "Noble Park" }, { "lat": 36.94589, "lon": 118.58864, "name": "Hualong" } ], "question": "Which location is the geographic outlier among: Saint Albans, Wahroonga, Taylors Lakes, Noble Park, Hualong?", "ground_truth": { "answer": "Hualong", "outlier_distance_km": 6962.8, "second_furthest_km": 1818.2, "clarity_ratio": 3.83, "median_distance_km": 1785.4, "distances_to_centroid": { "Saint Albans": 1785.4, "Wahroonga": 1640.4, "Taylors Lakes": 1781.3, "Noble Park": 1818.2, "Hualong": 6962.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint Albans: (-37.73°, 144.80°)", " Wahroonga: (-33.72°, 151.12°)", " Taylors Lakes: (-37.70°, 144.79°)", " Noble Park: (-37.97°, 145.17°)", " Hualong: (36.95°, 118.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hualong: 6962.8 km from centroid", " Noble Park: 1818.2 km from centroid", " Saint Albans: 1785.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hualong", "FINAL ANSWER: Hualong" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" }, { "lat": -37.88461, "lon": 145.29539, "name": "Ferntree Gully" }, { "lat": -34.78254, "lon": 138.61077, "name": "Parafield Gardens" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" }, { "lat": 21.23695, "lon": 105.70483, "name": "Phúc Yên" } ], "question": "Which location is the geographic outlier among: Palmerston, Ferntree Gully, Parafield Gardens, Otara, Phúc Yên?", "ground_truth": { "answer": "Phúc Yên", "outlier_distance_km": 5863.0, "second_furthest_km": 3927.9, "clarity_ratio": 1.49, "median_distance_km": 2058.3, "distances_to_centroid": { "Palmerston": 1215.7, "Ferntree Gully": 2058.3, "Parafield Gardens": 1625.2, "Otara": 3927.9, "Phúc Yên": 5863.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Palmerston: (-12.49°, 130.98°)", " Ferntree Gully: (-37.88°, 145.30°)", " Parafield Gardens: (-34.78°, 138.61°)", " Otara: (-36.95°, 174.87°)", " Phúc Yên: (21.24°, 105.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Phúc Yên: 5863.0 km from centroid", " Otara: 3927.9 km from centroid", " Ferntree Gully: 2058.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Phúc Yên", "FINAL ANSWER: Phúc Yên" ] }, { "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": 40.57788, "lon": -73.99403, "name": "Coney Island" }, { "lat": 38.5767, "lon": -92.17352, "name": "Jefferson City" }, { "lat": 40.91677, "lon": -74.17181, "name": "Paterson" }, { "lat": 25.18909, "lon": -99.82865, "name": "Montemorelos" }, { "lat": 44.10083, "lon": 39.08326, "name": "Tuapse" } ], "question": "Which location is the geographic outlier among: Coney Island, Jefferson City, Paterson, Montemorelos, Tuapse?", "ground_truth": { "answer": "Tuapse", "outlier_distance_km": 7827.0, "second_furthest_km": 3975.2, "clarity_ratio": 1.97, "median_distance_km": 2778.5, "distances_to_centroid": { "Coney Island": 1222.9, "Jefferson City": 2778.5, "Paterson": 1244.5, "Montemorelos": 3975.2, "Tuapse": 7827.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Coney Island: (40.58°, -73.99°)", " Jefferson City: (38.58°, -92.17°)", " Paterson: (40.92°, -74.17°)", " Montemorelos: (25.19°, -99.83°)", " Tuapse: (44.10°, 39.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tuapse: 7827.0 km from centroid", " Montemorelos: 3975.2 km from centroid", " Jefferson City: 2778.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tuapse", "FINAL ANSWER: Tuapse" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.84222, "lon": 38.56686, "name": "Il’skiy" }, { "lat": 27.99243, "lon": -15.41915, "name": "Telde" }, { "lat": 51.3281, "lon": 8.00369, "name": "Sundern" }, { "lat": 53.42519, "lon": -2.32443, "name": "Sale" }, { "lat": 45.56839, "lon": -73.20568, "name": "Beloeil" } ], "question": "Which location is the geographic outlier among: Il’skiy, Telde, Sundern, Sale, Beloeil?", "ground_truth": { "answer": "Beloeil", "outlier_distance_km": 4909.6, "second_furthest_km": 3692.8, "clarity_ratio": 1.33, "median_distance_km": 1939.2, "distances_to_centroid": { "Il’skiy": 3692.8, "Telde": 1939.2, "Sundern": 1455.4, "Sale": 1087.2, "Beloeil": 4909.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Il’skiy: (44.84°, 38.57°)", " Telde: (27.99°, -15.42°)", " Sundern: (51.33°, 8.00°)", " Sale: (53.43°, -2.32°)", " Beloeil: (45.57°, -73.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Beloeil: 4909.6 km from centroid", " Il’skiy: 3692.8 km from centroid", " Telde: 1939.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Beloeil", "FINAL ANSWER: Beloeil" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.50525, "lon": -43.8588, "name": "Congonhas" }, { "lat": -23.74417, "lon": -46.39833, "name": "Rio Grande da Serra" }, { "lat": 6.17591, "lon": -75.59174, "name": "Envigado" }, { "lat": -34.65187, "lon": -71.19724, "name": "Nancagua" }, { "lat": 48.78889, "lon": 2.27078, "name": "Le Plessis-Robinson" } ], "question": "Which location is the geographic outlier among: Congonhas, Rio Grande da Serra, Envigado, Nancagua, Le Plessis-Robinson?", "ground_truth": { "answer": "Le Plessis-Robinson", "outlier_distance_km": 7620.4, "second_furthest_km": 4153.4, "clarity_ratio": 1.83, "median_distance_km": 3404.8, "distances_to_centroid": { "Congonhas": 1779.5, "Rio Grande da Serra": 2108.8, "Envigado": 3404.8, "Nancagua": 4153.4, "Le Plessis-Robinson": 7620.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Congonhas: (-20.51°, -43.86°)", " Rio Grande da Serra: (-23.74°, -46.40°)", " Envigado: (6.18°, -75.59°)", " Nancagua: (-34.65°, -71.20°)", " Le Plessis-Robinson: (48.79°, 2.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Le Plessis-Robinson: 7620.4 km from centroid", " Nancagua: 4153.4 km from centroid", " Envigado: 3404.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Le Plessis-Robinson", "FINAL ANSWER: Le Plessis-Robinson" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.71877, "lon": 120.24233, "name": "Zhuji" }, { "lat": 35.68917, "lon": 139.83282, "name": "Ōjima" }, { "lat": 22.8774, "lon": 88.75479, "name": "Gobārdānga" }, { "lat": 33.39471, "lon": 133.29128, "name": "Susaki" }, { "lat": 51.0344, "lon": 2.37681, "name": "Dunkerque" } ], "question": "Which location is the geographic outlier among: Zhuji, Ōjima, Gobārdānga, Susaki, Dunkerque?", "ground_truth": { "answer": "Dunkerque", "outlier_distance_km": 7385.6, "second_furthest_km": 3875.6, "clarity_ratio": 1.91, "median_distance_km": 3340.2, "distances_to_centroid": { "Zhuji": 2256.9, "Ōjima": 3875.6, "Gobārdānga": 1519.6, "Susaki": 3340.2, "Dunkerque": 7385.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zhuji: (29.72°, 120.24°)", " Ōjima: (35.69°, 139.83°)", " Gobārdānga: (22.88°, 88.75°)", " Susaki: (33.39°, 133.29°)", " Dunkerque: (51.03°, 2.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dunkerque: 7385.6 km from centroid", " Ōjima: 3875.6 km from centroid", " Susaki: 3340.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dunkerque", "FINAL ANSWER: Dunkerque" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.43997, "lon": -76.61099, "name": "Lutherville-Timonium" }, { "lat": 38.77144, "lon": -90.37095, "name": "Hazelwood" }, { "lat": 45.4002, "lon": -75.80644, "name": "Aylmer" }, { "lat": 41.53311, "lon": -81.57901, "name": "East Cleveland" }, { "lat": 48.97374, "lon": 1.70253, "name": "Mantes-la-Ville" } ], "question": "Which location is the geographic outlier among: Lutherville-Timonium, Hazelwood, Aylmer, East Cleveland, Mantes-la-Ville?", "ground_truth": { "answer": "Mantes-la-Ville", "outlier_distance_km": 5006.4, "second_furthest_km": 2211.9, "clarity_ratio": 2.26, "median_distance_km": 1409.5, "distances_to_centroid": { "Lutherville-Timonium": 1078.0, "Hazelwood": 2211.9, "Aylmer": 943.6, "East Cleveland": 1409.5, "Mantes-la-Ville": 5006.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lutherville-Timonium: (39.44°, -76.61°)", " Hazelwood: (38.77°, -90.37°)", " Aylmer: (45.40°, -75.81°)", " East Cleveland: (41.53°, -81.58°)", " Mantes-la-Ville: (48.97°, 1.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mantes-la-Ville: 5006.4 km from centroid", " Hazelwood: 2211.9 km from centroid", " East Cleveland: 1409.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mantes-la-Ville", "FINAL ANSWER: Mantes-la-Ville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 7.20556, "lon": 37.77778, "name": "Shinshicho" }, { "lat": -26.41663, "lon": 29.08668, "name": "Kinross" }, { "lat": -30.64966, "lon": 24.0123, "name": "De Aar" }, { "lat": -27.38985, "lon": 30.95469, "name": "Frischgewaagd" }, { "lat": 26.74134, "lon": 83.88689, "name": "Kushinagar" } ], "question": "Which location is the geographic outlier among: Shinshicho, Kinross, De Aar, Frischgewaagd, Kushinagar?", "ground_truth": { "answer": "Kushinagar", "outlier_distance_km": 6168.5, "second_furthest_km": 2891.0, "clarity_ratio": 2.13, "median_distance_km": 2212.9, "distances_to_centroid": { "Shinshicho": 1960.3, "Kinross": 2212.9, "De Aar": 2891.0, "Frischgewaagd": 2198.7, "Kushinagar": 6168.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shinshicho: (7.21°, 37.78°)", " Kinross: (-26.42°, 29.09°)", " De Aar: (-30.65°, 24.01°)", " Frischgewaagd: (-27.39°, 30.95°)", " Kushinagar: (26.74°, 83.89°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kushinagar: 6168.5 km from centroid", " De Aar: 2891.0 km from centroid", " Kinross: 2212.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kushinagar", "FINAL ANSWER: Kushinagar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.0646, "lon": 174.94212, "name": "Papakura" }, { "lat": -31.95224, "lon": 115.8614, "name": "Perth" }, { "lat": -37.69047, "lon": 144.74172, "name": "Hillside" }, { "lat": -36.88158, "lon": 174.76204, "name": "Mount Eden" }, { "lat": 31.02795, "lon": 30.71493, "name": "Shubrākhīt" } ], "question": "Which location is the geographic outlier among: Papakura, Perth, Hillside, Mount Eden, Shubrākhīt?", "ground_truth": { "answer": "Shubrākhīt", "outlier_distance_km": 11952.4, "second_furthest_km": 4738.1, "clarity_ratio": 2.52, "median_distance_km": 4720.0, "distances_to_centroid": { "Papakura": 4738.1, "Perth": 1607.4, "Hillside": 2311.9, "Mount Eden": 4720.0, "Shubrākhīt": 11952.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Papakura: (-37.06°, 174.94°)", " Perth: (-31.95°, 115.86°)", " Hillside: (-37.69°, 144.74°)", " Mount Eden: (-36.88°, 174.76°)", " Shubrākhīt: (31.03°, 30.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shubrākhīt: 11952.4 km from centroid", " Papakura: 4738.1 km from centroid", " Mount Eden: 4720.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shubrākhīt", "FINAL ANSWER: Shubrākhīt" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.17697, "lon": -76.72774, "name": "Juanjuí" }, { "lat": -23.55083, "lon": -51.46083, "name": "Apucarana" }, { "lat": 10.88606, "lon": -72.8487, "name": "Fonseca" }, { "lat": -29.02889, "lon": -51.18167, "name": "Flores da Cunha" }, { "lat": -37.0182, "lon": 174.88019, "name": "Manurewa" } ], "question": "Which location is the geographic outlier among: Juanjuí, Apucarana, Fonseca, Flores da Cunha, Manurewa?", "ground_truth": { "answer": "Manurewa", "outlier_distance_km": 13891.8, "second_furthest_km": 7034.1, "clarity_ratio": 1.97, "median_distance_km": 6725.4, "distances_to_centroid": { "Juanjuí": 6725.4, "Apucarana": 3808.1, "Fonseca": 7034.1, "Flores da Cunha": 3864.7, "Manurewa": 13891.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Juanjuí: (-7.18°, -76.73°)", " Apucarana: (-23.55°, -51.46°)", " Fonseca: (10.89°, -72.85°)", " Flores da Cunha: (-29.03°, -51.18°)", " Manurewa: (-37.02°, 174.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Manurewa: 13891.8 km from centroid", " Fonseca: 7034.1 km from centroid", " Juanjuí: 6725.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Manurewa", "FINAL ANSWER: Manurewa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.53284, "lon": 108.42504, "name": "Yushan" }, { "lat": 30.08963, "lon": 105.85665, "name": "Tianjia" }, { "lat": 14.23976, "lon": 75.64507, "name": "Honnāli" }, { "lat": 27.99486, "lon": 74.95628, "name": "Fatehpur" }, { "lat": 39.02861, "lon": -96.8314, "name": "Junction City" } ], "question": "Which location is the geographic outlier among: Yushan, Tianjia, Honnāli, Fatehpur, Junction City?", "ground_truth": { "answer": "Junction City", "outlier_distance_km": 11937.4, "second_furthest_km": 5289.5, "clarity_ratio": 2.26, "median_distance_km": 5034.2, "distances_to_centroid": { "Yushan": 5289.5, "Tianjia": 5034.2, "Honnāli": 2752.0, "Fatehpur": 2091.4, "Junction City": 11937.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yushan: (29.53°, 108.43°)", " Tianjia: (30.09°, 105.86°)", " Honnāli: (14.24°, 75.65°)", " Fatehpur: (27.99°, 74.96°)", " Junction City: (39.03°, -96.83°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Junction City: 11937.4 km from centroid", " Yushan: 5289.5 km from centroid", " Tianjia: 5034.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Junction City", "FINAL ANSWER: Junction City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.31168, "lon": 41.44301, "name": "Deder" }, { "lat": 7.55632, "lon": 3.44107, "name": "Orita-Eruwa" }, { "lat": 5.61411, "lon": -1.5502, "name": "Twifu Praso" }, { "lat": -26.10528, "lon": 28.09884, "name": "Alexandra" }, { "lat": 19.23502, "lon": -101.45824, "name": "Tacámbaro de Codallos" } ], "question": "Which location is the geographic outlier among: Deder, Orita-Eruwa, Twifu Praso, Alexandra, Tacámbaro de Codallos?", "ground_truth": { "answer": "Tacámbaro de Codallos", "outlier_distance_km": 10464.4, "second_furthest_km": 5285.4, "clarity_ratio": 1.98, "median_distance_km": 4900.4, "distances_to_centroid": { "Deder": 5285.4, "Orita-Eruwa": 1155.9, "Twifu Praso": 566.3, "Alexandra": 4900.4, "Tacámbaro de Codallos": 10464.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Deder: (9.31°, 41.44°)", " Orita-Eruwa: (7.56°, 3.44°)", " Twifu Praso: (5.61°, -1.55°)", " Alexandra: (-26.11°, 28.10°)", " Tacámbaro de Codallos: (19.24°, -101.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tacámbaro de Codallos: 10464.4 km from centroid", " Deder: 5285.4 km from centroid", " Alexandra: 4900.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tacámbaro de Codallos", "FINAL ANSWER: Tacámbaro de Codallos" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.88374, "lon": 151.21282, "name": "Surry Hills" }, { "lat": -37.76722, "lon": 144.76657, "name": "Deer Park" }, { "lat": -33.8406, "lon": 151.00748, "name": "Granville" }, { "lat": -38.02388, "lon": 144.40617, "name": "Lara" }, { "lat": 23.87968, "lon": 115.72546, "name": "Hengbei" } ], "question": "Which location is the geographic outlier among: Surry Hills, Deer Park, Granville, Lara, Hengbei?", "ground_truth": { "answer": "Hengbei", "outlier_distance_km": 5995.3, "second_furthest_km": 1592.8, "clarity_ratio": 3.76, "median_distance_km": 1571.4, "distances_to_centroid": { "Surry Hills": 1459.0, "Deer Park": 1571.4, "Granville": 1442.6, "Lara": 1592.8, "Hengbei": 5995.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Surry Hills: (-33.88°, 151.21°)", " Deer Park: (-37.77°, 144.77°)", " Granville: (-33.84°, 151.01°)", " Lara: (-38.02°, 144.41°)", " Hengbei: (23.88°, 115.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hengbei: 5995.3 km from centroid", " Lara: 1592.8 km from centroid", " Deer Park: 1571.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hengbei", "FINAL ANSWER: Hengbei" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81819, "lon": 145.00176, "name": "Richmond" }, { "lat": -37.70988, "lon": 144.75483, "name": "Taylors Hill" }, { "lat": -33.86482, "lon": 151.20773, "name": "Sydney Central Business District" }, { "lat": -28.21298, "lon": 153.53634, "name": "Banora Point" }, { "lat": 42.03336, "lon": -88.08341, "name": "Schaumburg" } ], "question": "Which location is the geographic outlier among: Richmond, Taylors Hill, Sydney Central Business District, Banora Point, Schaumburg?", "ground_truth": { "answer": "Schaumburg", "outlier_distance_km": 17317.6, "second_furthest_km": 5376.8, "clarity_ratio": 3.22, "median_distance_km": 5177.4, "distances_to_centroid": { "Richmond": 4697.7, "Taylors Hill": 4673.8, "Sydney Central Business District": 5177.4, "Banora Point": 5376.8, "Schaumburg": 17317.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Richmond: (-37.82°, 145.00°)", " Taylors Hill: (-37.71°, 144.75°)", " Sydney Central Business District: (-33.86°, 151.21°)", " Banora Point: (-28.21°, 153.54°)", " Schaumburg: (42.03°, -88.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Schaumburg: 17317.6 km from centroid", " Banora Point: 5376.8 km from centroid", " Sydney Central Business District: 5177.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Schaumburg", "FINAL ANSWER: Schaumburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.18833, "lon": -39.73694, "name": "Santana do Cariri" }, { "lat": -1.35028, "lon": -47.57556, "name": "Santa Maria do Pará" }, { "lat": 2.89583, "lon": -61.4975, "name": "Alto Alegre" }, { "lat": -14.75583, "lon": -43.93222, "name": "Manga" }, { "lat": 46.0693, "lon": 13.23715, "name": "Udine" } ], "question": "Which location is the geographic outlier among: Santana do Cariri, Santa Maria do Pará, Alto Alegre, Manga, Udine?", "ground_truth": { "answer": "Udine", "outlier_distance_km": 6549.4, "second_furthest_km": 2849.8, "clarity_ratio": 2.3, "median_distance_km": 2382.3, "distances_to_centroid": { "Santana do Cariri": 1434.8, "Santa Maria do Pará": 1483.7, "Alto Alegre": 2849.8, "Manga": 2382.3, "Udine": 6549.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santana do Cariri: (-7.19°, -39.74°)", " Santa Maria do Pará: (-1.35°, -47.58°)", " Alto Alegre: (2.90°, -61.50°)", " Manga: (-14.76°, -43.93°)", " Udine: (46.07°, 13.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Udine: 6549.4 km from centroid", " Alto Alegre: 2849.8 km from centroid", " Manga: 2382.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Udine", "FINAL ANSWER: Udine" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.77884, "lon": 124.09545, "name": "Changtu" }, { "lat": 23.4871, "lon": 80.10404, "name": "Sihorā" }, { "lat": 10.79832, "lon": 105.23887, "name": "Tân Châu" }, { "lat": 35.40056, "lon": 116.96556, "name": "Zoucheng" }, { "lat": 20.56444, "lon": -103.30222, "name": "Las Pintitas" } ], "question": "Which location is the geographic outlier among: Changtu, Sihorā, Tân Châu, Zoucheng, Las Pintitas?", "ground_truth": { "answer": "Las Pintitas", "outlier_distance_km": 14610.8, "second_furthest_km": 5603.7, "clarity_ratio": 2.61, "median_distance_km": 5025.7, "distances_to_centroid": { "Changtu": 5603.7, "Sihorā": 1596.7, "Tân Châu": 4599.0, "Zoucheng": 5025.7, "Las Pintitas": 14610.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Changtu: (42.78°, 124.10°)", " Sihorā: (23.49°, 80.10°)", " Tân Châu: (10.80°, 105.24°)", " Zoucheng: (35.40°, 116.97°)", " Las Pintitas: (20.56°, -103.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Las Pintitas: 14610.8 km from centroid", " Changtu: 5603.7 km from centroid", " Zoucheng: 5025.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Las Pintitas", "FINAL ANSWER: Las Pintitas" ] }, { "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": -25.81015, "lon": 28.74248, "name": "Bronkhorstspruit" }, { "lat": 7.62329, "lon": 5.22087, "name": "Ado-Ekiti" }, { "lat": -33.30422, "lon": 26.53276, "name": "Grahamstown" }, { "lat": -26.67313, "lon": 27.92615, "name": "Vereeniging" }, { "lat": 26.17231, "lon": -80.13199, "name": "Oakland Park" } ], "question": "Which location is the geographic outlier among: Bronkhorstspruit, Ado-Ekiti, Grahamstown, Vereeniging, Oakland Park?", "ground_truth": { "answer": "Oakland Park", "outlier_distance_km": 9711.5, "second_furthest_km": 3596.1, "clarity_ratio": 2.7, "median_distance_km": 3324.2, "distances_to_centroid": { "Bronkhorstspruit": 3324.2, "Ado-Ekiti": 2042.4, "Grahamstown": 3596.1, "Vereeniging": 3295.6, "Oakland Park": 9711.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bronkhorstspruit: (-25.81°, 28.74°)", " Ado-Ekiti: (7.62°, 5.22°)", " Grahamstown: (-33.30°, 26.53°)", " Vereeniging: (-26.67°, 27.93°)", " Oakland Park: (26.17°, -80.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Oakland Park: 9711.5 km from centroid", " Grahamstown: 3596.1 km from centroid", " Bronkhorstspruit: 3324.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Oakland Park", "FINAL ANSWER: Oakland Park" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 1.09667, "lon": 36.69806, "name": "Maralal" }, { "lat": 13.06269, "lon": 5.24322, "name": "Sokoto" }, { "lat": 7.23333, "lon": 37.88333, "name": "Duramē" }, { "lat": 28.82306, "lon": 30.89903, "name": "Al Fashn" }, { "lat": 8.94417, "lon": 125.50194, "name": "Libertad" } ], "question": "Which location is the geographic outlier among: Maralal, Sokoto, Duramē, Al Fashn, Libertad?", "ground_truth": { "answer": "Libertad", "outlier_distance_km": 8537.8, "second_furthest_km": 4557.6, "clarity_ratio": 1.87, "median_distance_km": 2538.1, "distances_to_centroid": { "Maralal": 1667.0, "Sokoto": 4557.6, "Duramē": 1146.6, "Al Fashn": 2538.1, "Libertad": 8537.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maralal: (1.10°, 36.70°)", " Sokoto: (13.06°, 5.24°)", " Duramē: (7.23°, 37.88°)", " Al Fashn: (28.82°, 30.90°)", " Libertad: (8.94°, 125.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Libertad: 8537.8 km from centroid", " Sokoto: 4557.6 km from centroid", " Al Fashn: 2538.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Libertad", "FINAL ANSWER: Libertad" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.30664, "lon": 44.98395, "name": "Troitskaya" }, { "lat": 53.96796, "lon": 38.33151, "name": "Donskoy" }, { "lat": 50.95843, "lon": -0.13287, "name": "Burgess Hill" }, { "lat": 45.80463, "lon": 13.53292, "name": "Monfalcone" }, { "lat": 8.35983, "lon": 77.05253, "name": "Kanjiramkulam" } ], "question": "Which location is the geographic outlier among: Troitskaya, Donskoy, Burgess Hill, Monfalcone, Kanjiramkulam?", "ground_truth": { "answer": "Kanjiramkulam", "outlier_distance_km": 5491.1, "second_furthest_km": 2913.9, "clarity_ratio": 1.88, "median_distance_km": 1814.2, "distances_to_centroid": { "Troitskaya": 902.5, "Donskoy": 1523.5, "Burgess Hill": 2913.9, "Monfalcone": 1814.2, "Kanjiramkulam": 5491.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Troitskaya: (43.31°, 44.98°)", " Donskoy: (53.97°, 38.33°)", " Burgess Hill: (50.96°, -0.13°)", " Monfalcone: (45.80°, 13.53°)", " Kanjiramkulam: (8.36°, 77.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kanjiramkulam: 5491.1 km from centroid", " Burgess Hill: 2913.9 km from centroid", " Monfalcone: 1814.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kanjiramkulam", "FINAL ANSWER: Kanjiramkulam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.81509, "lon": -92.22432, "name": "Sherwood" }, { "lat": 41.73392, "lon": -87.7795, "name": "Burbank" }, { "lat": 45.38401, "lon": -122.76399, "name": "Tualatin" }, { "lat": 42.29593, "lon": -71.71285, "name": "Shrewsbury" }, { "lat": -37.79798, "lon": 144.94512, "name": "North Melbourne" } ], "question": "Which location is the geographic outlier among: Sherwood, Burbank, Tualatin, Shrewsbury, North Melbourne?", "ground_truth": { "answer": "North Melbourne", "outlier_distance_km": 18287.8, "second_furthest_km": 7044.8, "clarity_ratio": 2.6, "median_distance_km": 4540.9, "distances_to_centroid": { "Sherwood": 4540.9, "Burbank": 4238.2, "Tualatin": 7044.8, "Shrewsbury": 3022.5, "North Melbourne": 18287.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sherwood: (34.82°, -92.22°)", " Burbank: (41.73°, -87.78°)", " Tualatin: (45.38°, -122.76°)", " Shrewsbury: (42.30°, -71.71°)", " North Melbourne: (-37.80°, 144.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Melbourne: 18287.8 km from centroid", " Tualatin: 7044.8 km from centroid", " Sherwood: 4540.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Melbourne", "FINAL ANSWER: North Melbourne" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.56414, "lon": 13.27532, "name": "Neubrandenburg" }, { "lat": 45.07073, "lon": 7.51465, "name": "Rivoli" }, { "lat": 52.18661, "lon": 7.86043, "name": "Lengerich" }, { "lat": 51.40944, "lon": 46.04833, "name": "Privolzhskiy" }, { "lat": -23.26917, "lon": -51.04806, "name": "Ibiporã" } ], "question": "Which location is the geographic outlier among: Neubrandenburg, Rivoli, Lengerich, Privolzhskiy, Ibiporã?", "ground_truth": { "answer": "Ibiporã", "outlier_distance_km": 8802.4, "second_furthest_km": 3687.4, "clarity_ratio": 2.39, "median_distance_km": 2084.9, "distances_to_centroid": { "Neubrandenburg": 2084.9, "Rivoli": 1058.1, "Lengerich": 1839.6, "Privolzhskiy": 3687.4, "Ibiporã": 8802.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Neubrandenburg: (53.56°, 13.28°)", " Rivoli: (45.07°, 7.51°)", " Lengerich: (52.19°, 7.86°)", " Privolzhskiy: (51.41°, 46.05°)", " Ibiporã: (-23.27°, -51.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ibiporã: 8802.4 km from centroid", " Privolzhskiy: 3687.4 km from centroid", " Neubrandenburg: 2084.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ibiporã", "FINAL ANSWER: Ibiporã" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 24.8, "lon": 113.58333, "name": "Shaoguan" }, { "lat": -8.31667, "lon": 114.23333, "name": "Singojuruh" }, { "lat": 29.82739, "lon": 106.43645, "name": "Beibei" }, { "lat": 21.85523, "lon": 70.24791, "name": "Bhāyāvadar" }, { "lat": 29.5294, "lon": -95.20104, "name": "Friendswood" } ], "question": "Which location is the geographic outlier among: Shaoguan, Singojuruh, Beibei, Bhāyāvadar, Friendswood?", "ground_truth": { "answer": "Friendswood", "outlier_distance_km": 14030.5, "second_furthest_km": 6516.6, "clarity_ratio": 2.15, "median_distance_km": 5327.9, "distances_to_centroid": { "Shaoguan": 5327.9, "Singojuruh": 6516.6, "Beibei": 4616.9, "Bhāyāvadar": 909.5, "Friendswood": 14030.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shaoguan: (24.80°, 113.58°)", " Singojuruh: (-8.32°, 114.23°)", " Beibei: (29.83°, 106.44°)", " Bhāyāvadar: (21.86°, 70.25°)", " Friendswood: (29.53°, -95.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Friendswood: 14030.5 km from centroid", " Singojuruh: 6516.6 km from centroid", " Shaoguan: 5327.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Friendswood", "FINAL ANSWER: Friendswood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.67873, "lon": 6.15895, "name": "Goch" }, { "lat": 36.643, "lon": -4.68728, "name": "Alhaurín el Grande" }, { "lat": 55.65, "lon": 37.7, "name": "Kur’yanovo" }, { "lat": 40.46276, "lon": -3.67813, "name": "Nueva España" }, { "lat": 41.18806, "lon": 122.04944, "name": "Panshan" } ], "question": "Which location is the geographic outlier among: Goch, Alhaurín el Grande, Kur’yanovo, Nueva España, Panshan?", "ground_truth": { "answer": "Panshan", "outlier_distance_km": 6950.4, "second_furthest_km": 3155.9, "clarity_ratio": 2.2, "median_distance_km": 2893.8, "distances_to_centroid": { "Goch": 1995.7, "Alhaurín el Grande": 3155.9, "Kur’yanovo": 1248.8, "Nueva España": 2893.8, "Panshan": 6950.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Goch: (51.68°, 6.16°)", " Alhaurín el Grande: (36.64°, -4.69°)", " Kur’yanovo: (55.65°, 37.70°)", " Nueva España: (40.46°, -3.68°)", " Panshan: (41.19°, 122.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Panshan: 6950.4 km from centroid", " Alhaurín el Grande: 3155.9 km from centroid", " Nueva España: 2893.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Panshan", "FINAL ANSWER: Panshan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.97438, "lon": -93.9924, "name": "Nederland" }, { "lat": 38.67852, "lon": -121.7733, "name": "Woodland" }, { "lat": 43.75386, "lon": -79.28215, "name": "Dorset Park" }, { "lat": 28.01057, "lon": -82.57732, "name": "Town 'n' Country" }, { "lat": 29.64885, "lon": 94.35509, "name": "Nyingchi" } ], "question": "Which location is the geographic outlier among: Nederland, Woodland, Dorset Park, Town 'n' Country, Nyingchi?", "ground_truth": { "answer": "Nyingchi", "outlier_distance_km": 12308.8, "second_furthest_km": 5732.0, "clarity_ratio": 2.15, "median_distance_km": 3530.3, "distances_to_centroid": { "Nederland": 3530.3, "Woodland": 5732.0, "Dorset Park": 2227.6, "Town 'n' Country": 2551.3, "Nyingchi": 12308.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nederland: (29.97°, -93.99°)", " Woodland: (38.68°, -121.77°)", " Dorset Park: (43.75°, -79.28°)", " Town 'n' Country: (28.01°, -82.58°)", " Nyingchi: (29.65°, 94.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nyingchi: 12308.8 km from centroid", " Woodland: 5732.0 km from centroid", " Nederland: 3530.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nyingchi", "FINAL ANSWER: Nyingchi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.80168, "lon": -74.39304, "name": "Nueva Granada" }, { "lat": -23.52806, "lon": -46.34472, "name": "Poá" }, { "lat": -27.59667, "lon": -48.54917, "name": "Florianópolis" }, { "lat": -27.57679, "lon": -60.71114, "name": "Villa Ángela" }, { "lat": -6.47472, "lon": 108.31528, "name": "Jatibarang" } ], "question": "Which location is the geographic outlier among: Nueva Granada, Poá, Florianópolis, Villa Ángela, Jatibarang?", "ground_truth": { "answer": "Jatibarang", "outlier_distance_km": 14274.0, "second_furthest_km": 6169.7, "clarity_ratio": 2.31, "median_distance_km": 3997.5, "distances_to_centroid": { "Nueva Granada": 6169.7, "Poá": 2489.5, "Florianópolis": 2859.8, "Villa Ángela": 3997.5, "Jatibarang": 14274.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nueva Granada: (9.80°, -74.39°)", " Poá: (-23.53°, -46.34°)", " Florianópolis: (-27.60°, -48.55°)", " Villa Ángela: (-27.58°, -60.71°)", " Jatibarang: (-6.47°, 108.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jatibarang: 14274.0 km from centroid", " Nueva Granada: 6169.7 km from centroid", " Villa Ángela: 3997.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jatibarang", "FINAL ANSWER: Jatibarang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -30.50123, "lon": 151.66553, "name": "Armidale" }, { "lat": -36.84103, "lon": 174.65223, "name": "Te Atatu Peninsula" }, { "lat": -31.09048, "lon": 150.92905, "name": "Tamworth" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": 7.55632, "lon": 3.44107, "name": "Orita-Eruwa" } ], "question": "Which location is the geographic outlier among: Armidale, Te Atatu Peninsula, Tamworth, Melbourne City Centre, Orita-Eruwa?", "ground_truth": { "answer": "Orita-Eruwa", "outlier_distance_km": 13537.9, "second_furthest_km": 4809.2, "clarity_ratio": 2.81, "median_distance_km": 2649.1, "distances_to_centroid": { "Armidale": 2649.1, "Te Atatu Peninsula": 4809.2, "Tamworth": 2585.8, "Melbourne City Centre": 2298.1, "Orita-Eruwa": 13537.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Armidale: (-30.50°, 151.67°)", " Te Atatu Peninsula: (-36.84°, 174.65°)", " Tamworth: (-31.09°, 150.93°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Orita-Eruwa: (7.56°, 3.44°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Orita-Eruwa: 13537.9 km from centroid", " Te Atatu Peninsula: 4809.2 km from centroid", " Armidale: 2649.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Orita-Eruwa", "FINAL ANSWER: Orita-Eruwa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.96807, "lon": 174.79875, "name": "Mangere" }, { "lat": -27.61025, "lon": 153.05388, "name": "Sunnybank Hills" }, { "lat": -33.7511, "lon": 151.28886, "name": "Dee Why" }, { "lat": -36.93754, "lon": 174.65584, "name": "Titirangi" }, { "lat": 49.97078, "lon": 8.05883, "name": "Ingelheim am Rhein" } ], "question": "Which location is the geographic outlier among: Mangere, Sunnybank Hills, Dee Why, Titirangi, Ingelheim am Rhein?", "ground_truth": { "answer": "Ingelheim am Rhein", "outlier_distance_km": 13881.2, "second_furthest_km": 4698.0, "clarity_ratio": 2.95, "median_distance_km": 4684.9, "distances_to_centroid": { "Mangere": 4698.0, "Sunnybank Hills": 2423.9, "Dee Why": 2646.9, "Titirangi": 4684.9, "Ingelheim am Rhein": 13881.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mangere: (-36.97°, 174.80°)", " Sunnybank Hills: (-27.61°, 153.05°)", " Dee Why: (-33.75°, 151.29°)", " Titirangi: (-36.94°, 174.66°)", " Ingelheim am Rhein: (49.97°, 8.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ingelheim am Rhein: 13881.2 km from centroid", " Mangere: 4698.0 km from centroid", " Titirangi: 4684.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ingelheim am Rhein", "FINAL ANSWER: Ingelheim am Rhein" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.45361, "lon": -44.78, "name": "Arari" }, { "lat": -35.57681, "lon": -58.01215, "name": "Chascomús" }, { "lat": -20.15139, "lon": -41.62278, "name": "Lajinha" }, { "lat": -34.71247, "lon": -71.0434, "name": "Chimbarongo" }, { "lat": 39.95238, "lon": -75.16362, "name": "Philadelphia" } ], "question": "Which location is the geographic outlier among: Arari, Chascomús, Lajinha, Chimbarongo, Philadelphia?", "ground_truth": { "answer": "Philadelphia", "outlier_distance_km": 5909.6, "second_furthest_km": 2965.0, "clarity_ratio": 1.99, "median_distance_km": 2756.4, "distances_to_centroid": { "Arari": 1682.2, "Chascomús": 2756.4, "Lajinha": 2049.7, "Chimbarongo": 2965.0, "Philadelphia": 5909.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Arari: (-3.45°, -44.78°)", " Chascomús: (-35.58°, -58.01°)", " Lajinha: (-20.15°, -41.62°)", " Chimbarongo: (-34.71°, -71.04°)", " Philadelphia: (39.95°, -75.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Philadelphia: 5909.6 km from centroid", " Chimbarongo: 2965.0 km from centroid", " Chascomús: 2756.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Philadelphia", "FINAL ANSWER: Philadelphia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 27.55642, "lon": 30.81057, "name": "Dayrūţ" }, { "lat": 30.575, "lon": 30.71111, "name": "Badr" }, { "lat": 9.86709, "lon": 11.22594, "name": "Biliri" }, { "lat": -26.95659, "lon": 24.7284, "name": "Vryburg" }, { "lat": -32.03077, "lon": -60.30619, "name": "Crespo" } ], "question": "Which location is the geographic outlier among: Dayrūţ, Badr, Biliri, Vryburg, Crespo?", "ground_truth": { "answer": "Crespo", "outlier_distance_km": 8037.6, "second_furthest_km": 4030.3, "clarity_ratio": 1.99, "median_distance_km": 3793.2, "distances_to_centroid": { "Dayrūţ": 3793.2, "Badr": 4030.3, "Biliri": 989.9, "Vryburg": 3696.2, "Crespo": 8037.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dayrūţ: (27.56°, 30.81°)", " Badr: (30.57°, 30.71°)", " Biliri: (9.87°, 11.23°)", " Vryburg: (-26.96°, 24.73°)", " Crespo: (-32.03°, -60.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Crespo: 8037.6 km from centroid", " Badr: 4030.3 km from centroid", " Dayrūţ: 3793.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Crespo", "FINAL ANSWER: Crespo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.98037, "lon": 18.95382, "name": "Pszczyna" }, { "lat": 55.66853, "lon": 39.87488, "name": "Roshal’" }, { "lat": 53.53333, "lon": -1.15, "name": "Bentley" }, { "lat": 55.81667, "lon": -4.01667, "name": "Bellshill" }, { "lat": 30.43826, "lon": -84.28073, "name": "Tallahassee" } ], "question": "Which location is the geographic outlier among: Pszczyna, Roshal’, Bentley, Bellshill, Tallahassee?", "ground_truth": { "answer": "Tallahassee", "outlier_distance_km": 6681.0, "second_furthest_km": 3144.7, "clarity_ratio": 2.12, "median_distance_km": 1804.0, "distances_to_centroid": { "Pszczyna": 1804.0, "Roshal’": 3144.7, "Bentley": 602.9, "Bellshill": 761.7, "Tallahassee": 6681.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pszczyna: (49.98°, 18.95°)", " Roshal’: (55.67°, 39.87°)", " Bentley: (53.53°, -1.15°)", " Bellshill: (55.82°, -4.02°)", " Tallahassee: (30.44°, -84.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tallahassee: 6681.0 km from centroid", " Roshal’: 3144.7 km from centroid", " Pszczyna: 1804.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tallahassee", "FINAL ANSWER: Tallahassee" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.0393, "lon": 174.92815, "name": "Takanini" }, { "lat": -33.92399, "lon": 151.22749, "name": "Kingsford" }, { "lat": -37.76667, "lon": 144.91667, "name": "Moonee Ponds" }, { "lat": -33.78333, "lon": 150.93333, "name": "Seven Hills" }, { "lat": 43.80136, "lon": -91.23958, "name": "La Crosse" } ], "question": "Which location is the geographic outlier among: Takanini, Kingsford, Moonee Ponds, Seven Hills, La Crosse?", "ground_truth": { "answer": "La Crosse", "outlier_distance_km": 16889.7, "second_furthest_km": 6850.7, "clarity_ratio": 2.47, "median_distance_km": 4699.5, "distances_to_centroid": { "Takanini": 6850.7, "Kingsford": 4699.5, "Moonee Ponds": 4235.4, "Seven Hills": 4670.5, "La Crosse": 16889.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Takanini: (-37.04°, 174.93°)", " Kingsford: (-33.92°, 151.23°)", " Moonee Ponds: (-37.77°, 144.92°)", " Seven Hills: (-33.78°, 150.93°)", " La Crosse: (43.80°, -91.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " La Crosse: 16889.7 km from centroid", " Takanini: 6850.7 km from centroid", " Kingsford: 4699.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: La Crosse", "FINAL ANSWER: La Crosse" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.10771, "lon": 10.646, "name": "Bad Langensalza" }, { "lat": 41.78333, "lon": 3.03333, "name": "Sant Feliu de Guíxols" }, { "lat": 51.92917, "lon": 4.57778, "name": "Capelle aan den IJssel" }, { "lat": 48.76476, "lon": 2.3503, "name": "Chevilly-Larue" }, { "lat": 39.00862, "lon": -94.46356, "name": "Raytown" } ], "question": "Which location is the geographic outlier among: Bad Langensalza, Sant Feliu de Guíxols, Capelle aan den IJssel, Chevilly-Larue, Raytown?", "ground_truth": { "answer": "Raytown", "outlier_distance_km": 6279.0, "second_furthest_km": 1919.1, "clarity_ratio": 3.27, "median_distance_km": 1522.6, "distances_to_centroid": { "Bad Langensalza": 1919.1, "Sant Feliu de Guíxols": 1510.9, "Capelle aan den IJssel": 1522.6, "Chevilly-Larue": 1303.9, "Raytown": 6279.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bad Langensalza: (51.11°, 10.65°)", " Sant Feliu de Guíxols: (41.78°, 3.03°)", " Capelle aan den IJssel: (51.93°, 4.58°)", " Chevilly-Larue: (48.76°, 2.35°)", " Raytown: (39.01°, -94.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Raytown: 6279.0 km from centroid", " Bad Langensalza: 1919.1 km from centroid", " Capelle aan den IJssel: 1522.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Raytown", "FINAL ANSWER: Raytown" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.58531, "lon": 86.47682, "name": "Ghātsīla" }, { "lat": 36.31667, "lon": 138.43333, "name": "Komoro" }, { "lat": 34.59882, "lon": 138.21934, "name": "Omaezaki" }, { "lat": 36.77957, "lon": 137.07576, "name": "Nishishinminato" }, { "lat": -26.67313, "lon": 27.92615, "name": "Vereeniging" } ], "question": "Which location is the geographic outlier among: Ghātsīla, Komoro, Omaezaki, Nishishinminato, Vereeniging?", "ground_truth": { "answer": "Vereeniging", "outlier_distance_km": 9885.1, "second_furthest_km": 3618.7, "clarity_ratio": 2.73, "median_distance_km": 3540.0, "distances_to_centroid": { "Ghātsīla": 1988.5, "Komoro": 3618.7, "Omaezaki": 3540.0, "Nishishinminato": 3523.4, "Vereeniging": 9885.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ghātsīla: (22.59°, 86.48°)", " Komoro: (36.32°, 138.43°)", " Omaezaki: (34.60°, 138.22°)", " Nishishinminato: (36.78°, 137.08°)", " Vereeniging: (-26.67°, 27.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vereeniging: 9885.1 km from centroid", " Komoro: 3618.7 km from centroid", " Omaezaki: 3540.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vereeniging", "FINAL ANSWER: Vereeniging" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.07082, "lon": -97.06078, "name": "Martínez de la Torre" }, { "lat": 42.86509, "lon": -71.4934, "name": "Merrimack" }, { "lat": 43.76481, "lon": -79.45606, "name": "Bathurst Manor" }, { "lat": 32.61574, "lon": -83.62664, "name": "Warner Robins" }, { "lat": 32.30173, "lon": 130.50376, "name": "Sashiki" } ], "question": "Which location is the geographic outlier among: Martínez de la Torre, Merrimack, Bathurst Manor, Warner Robins, Sashiki?", "ground_truth": { "answer": "Sashiki", "outlier_distance_km": 12543.5, "second_furthest_km": 5764.2, "clarity_ratio": 2.18, "median_distance_km": 3999.4, "distances_to_centroid": { "Martínez de la Torre": 5764.2, "Merrimack": 2859.0, "Bathurst Manor": 3510.1, "Warner Robins": 3999.4, "Sashiki": 12543.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Martínez de la Torre: (20.07°, -97.06°)", " Merrimack: (42.87°, -71.49°)", " Bathurst Manor: (43.76°, -79.46°)", " Warner Robins: (32.62°, -83.63°)", " Sashiki: (32.30°, 130.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sashiki: 12543.5 km from centroid", " Martínez de la Torre: 5764.2 km from centroid", " Warner Robins: 3999.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sashiki", "FINAL ANSWER: Sashiki" ] }, { "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": 39.95622, "lon": -75.05795, "name": "Pennsauken" }, { "lat": 42.63342, "lon": -71.31617, "name": "Lowell" }, { "lat": 42.45008, "lon": -73.24538, "name": "Pittsfield" }, { "lat": 40.63371, "lon": -74.40737, "name": "Plainfield" }, { "lat": 51.93333, "lon": 7.35, "name": "Nottuln" } ], "question": "Which location is the geographic outlier among: Pennsauken, Lowell, Pittsfield, Plainfield, Nottuln?", "ground_truth": { "answer": "Nottuln", "outlier_distance_km": 4763.0, "second_furthest_km": 1519.7, "clarity_ratio": 3.13, "median_distance_km": 1442.3, "distances_to_centroid": { "Pennsauken": 1519.7, "Lowell": 1138.5, "Pittsfield": 1297.6, "Plainfield": 1442.3, "Nottuln": 4763.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pennsauken: (39.96°, -75.06°)", " Lowell: (42.63°, -71.32°)", " Pittsfield: (42.45°, -73.25°)", " Plainfield: (40.63°, -74.41°)", " Nottuln: (51.93°, 7.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nottuln: 4763.0 km from centroid", " Pennsauken: 1519.7 km from centroid", " Plainfield: 1442.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nottuln", "FINAL ANSWER: Nottuln" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -11.79667, "lon": -49.52889, "name": "Formoso do Araguaia" }, { "lat": -2.52972, "lon": -44.30278, "name": "São Luís" }, { "lat": -1.19667, "lon": -46.14, "name": "Viseu" }, { "lat": -23.15306, "lon": -47.05778, "name": "Itupeva" }, { "lat": 22.1752, "lon": 88.42008, "name": "Jaynagar Majilpur" } ], "question": "Which location is the geographic outlier among: Formoso do Araguaia, São Luís, Viseu, Itupeva, Jaynagar Majilpur?", "ground_truth": { "answer": "Jaynagar Majilpur", "outlier_distance_km": 12012.9, "second_furthest_km": 3676.5, "clarity_ratio": 3.27, "median_distance_km": 3415.1, "distances_to_centroid": { "Formoso do Araguaia": 3415.1, "São Luís": 2731.0, "Viseu": 2944.4, "Itupeva": 3676.5, "Jaynagar Majilpur": 12012.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Formoso do Araguaia: (-11.80°, -49.53°)", " São Luís: (-2.53°, -44.30°)", " Viseu: (-1.20°, -46.14°)", " Itupeva: (-23.15°, -47.06°)", " Jaynagar Majilpur: (22.18°, 88.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jaynagar Majilpur: 12012.9 km from centroid", " Itupeva: 3676.5 km from centroid", " Formoso do Araguaia: 3415.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jaynagar Majilpur", "FINAL ANSWER: Jaynagar Majilpur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8739, "lon": 145.02485, "name": "Caulfield North" }, { "lat": -37.95855, "lon": 176.98545, "name": "Whakatane" }, { "lat": -38.18333, "lon": 145.08333, "name": "Mount Eliza" }, { "lat": -37.98333, "lon": 145.2, "name": "Dandenong" }, { "lat": 34.09668, "lon": -117.71978, "name": "Claremont" } ], "question": "Which location is the geographic outlier among: Caulfield North, Whakatane, Mount Eliza, Dandenong, Claremont?", "ground_truth": { "answer": "Claremont", "outlier_distance_km": 16283.1, "second_furthest_km": 7417.5, "clarity_ratio": 2.2, "median_distance_km": 4648.6, "distances_to_centroid": { "Caulfield North": 4632.0, "Whakatane": 7417.5, "Mount Eliza": 4641.0, "Dandenong": 4648.6, "Claremont": 16283.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caulfield North: (-37.87°, 145.02°)", " Whakatane: (-37.96°, 176.99°)", " Mount Eliza: (-38.18°, 145.08°)", " Dandenong: (-37.98°, 145.20°)", " Claremont: (34.10°, -117.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Claremont: 16283.1 km from centroid", " Whakatane: 7417.5 km from centroid", " Dandenong: 4648.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Claremont", "FINAL ANSWER: Claremont" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -30.31002, "lon": 30.66275, "name": "eMuziwezinto" }, { "lat": 6.55459, "lon": 45.38992, "name": "Neefkuceliye" }, { "lat": -33.64651, "lon": 19.44852, "name": "Worcester" }, { "lat": 8.22542, "lon": -0.64889, "name": "Yegyi" }, { "lat": 34.12828, "lon": 134.534, "name": "Takabō" } ], "question": "Which location is the geographic outlier among: eMuziwezinto, Neefkuceliye, Worcester, Yegyi, Takabō?", "ground_truth": { "answer": "Takabō", "outlier_distance_km": 10071.8, "second_furthest_km": 5308.5, "clarity_ratio": 1.9, "median_distance_km": 4373.1, "distances_to_centroid": { "eMuziwezinto": 3431.8, "Neefkuceliye": 1064.9, "Worcester": 4373.1, "Yegyi": 5308.5, "Takabō": 10071.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " eMuziwezinto: (-30.31°, 30.66°)", " Neefkuceliye: (6.55°, 45.39°)", " Worcester: (-33.65°, 19.45°)", " Yegyi: (8.23°, -0.65°)", " Takabō: (34.13°, 134.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Takabō: 10071.8 km from centroid", " Yegyi: 5308.5 km from centroid", " Worcester: 4373.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Takabō", "FINAL ANSWER: Takabō" ] }, { "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": 22.00554, "lon": -98.77972, "name": "Tamuín" }, { "lat": 20.05523, "lon": -97.05214, "name": "Villa Independencia" }, { "lat": 39.10816, "lon": -76.99775, "name": "Cloverly" }, { "lat": 42.54648, "lon": -71.17367, "name": "Wilmington" }, { "lat": 27.2127, "lon": 116.53008, "name": "Qincheng" } ], "question": "Which location is the geographic outlier among: Tamuín, Villa Independencia, Cloverly, Wilmington, Qincheng?", "ground_truth": { "answer": "Qincheng", "outlier_distance_km": 13352.8, "second_furthest_km": 5351.2, "clarity_ratio": 2.5, "median_distance_km": 5267.3, "distances_to_centroid": { "Tamuín": 5351.2, "Villa Independencia": 5267.3, "Cloverly": 3029.7, "Wilmington": 2662.8, "Qincheng": 13352.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tamuín: (22.01°, -98.78°)", " Villa Independencia: (20.06°, -97.05°)", " Cloverly: (39.11°, -77.00°)", " Wilmington: (42.55°, -71.17°)", " Qincheng: (27.21°, 116.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Qincheng: 13352.8 km from centroid", " Tamuín: 5351.2 km from centroid", " Villa Independencia: 5267.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Qincheng", "FINAL ANSWER: Qincheng" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.9652, "lon": 141.4512, "name": "Broken Hill" }, { "lat": -41.13333, "lon": 174.85, "name": "Porirua" }, { "lat": -37.62581, "lon": 144.92555, "name": "Roxburgh Park" }, { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" }, { "lat": 41.5067, "lon": -90.51513, "name": "Moline" } ], "question": "Which location is the geographic outlier among: Broken Hill, Porirua, Roxburgh Park, Ashburton, Moline?", "ground_truth": { "answer": "Moline", "outlier_distance_km": 17268.5, "second_furthest_km": 6435.2, "clarity_ratio": 2.68, "median_distance_km": 6173.1, "distances_to_centroid": { "Broken Hill": 3403.4, "Porirua": 6435.2, "Roxburgh Park": 3848.9, "Ashburton": 6173.1, "Moline": 17268.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Broken Hill: (-31.97°, 141.45°)", " Porirua: (-41.13°, 174.85°)", " Roxburgh Park: (-37.63°, 144.93°)", " Ashburton: (-43.90°, 171.73°)", " Moline: (41.51°, -90.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Moline: 17268.5 km from centroid", " Porirua: 6435.2 km from centroid", " Ashburton: 6173.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Moline", "FINAL ANSWER: Moline" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 15.65995, "lon": -92.14111, "name": "Comalapa" }, { "lat": 39.9936, "lon": -105.08971, "name": "Lafayette" }, { "lat": 41.03399, "lon": -73.76291, "name": "White Plains" }, { "lat": 33.96358, "lon": -117.56418, "name": "Eastvale" }, { "lat": 8.27911, "lon": 77.30958, "name": "Kothanallur" } ], "question": "Which location is the geographic outlier among: Comalapa, Lafayette, White Plains, Eastvale, Kothanallur?", "ground_truth": { "answer": "Kothanallur", "outlier_distance_km": 14100.7, "second_furthest_km": 5260.9, "clarity_ratio": 2.68, "median_distance_km": 4135.8, "distances_to_centroid": { "Comalapa": 3356.9, "Lafayette": 4135.8, "White Plains": 1809.0, "Eastvale": 5260.9, "Kothanallur": 14100.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Comalapa: (15.66°, -92.14°)", " Lafayette: (39.99°, -105.09°)", " White Plains: (41.03°, -73.76°)", " Eastvale: (33.96°, -117.56°)", " Kothanallur: (8.28°, 77.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kothanallur: 14100.7 km from centroid", " Eastvale: 5260.9 km from centroid", " Lafayette: 4135.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kothanallur", "FINAL ANSWER: Kothanallur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.10816, "lon": -76.99775, "name": "Cloverly" }, { "lat": 32.75957, "lon": -97.45835, "name": "White Settlement" }, { "lat": 18.36663, "lon": -99.87185, "name": "Teloloapan" }, { "lat": 40.71816, "lon": -73.35429, "name": "West Babylon" }, { "lat": -36.88745, "lon": 174.77059, "name": "Epsom" } ], "question": "Which location is the geographic outlier among: Cloverly, White Settlement, Teloloapan, West Babylon, Epsom?", "ground_truth": { "answer": "Epsom", "outlier_distance_km": 16522.4, "second_furthest_km": 6838.5, "clarity_ratio": 2.42, "median_distance_km": 6392.8, "distances_to_centroid": { "Cloverly": 4646.0, "White Settlement": 6392.8, "Teloloapan": 6838.5, "West Babylon": 4411.3, "Epsom": 16522.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cloverly: (39.11°, -77.00°)", " White Settlement: (32.76°, -97.46°)", " Teloloapan: (18.37°, -99.87°)", " West Babylon: (40.72°, -73.35°)", " Epsom: (-36.89°, 174.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Epsom: 16522.4 km from centroid", " Teloloapan: 6838.5 km from centroid", " White Settlement: 6392.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Epsom", "FINAL ANSWER: Epsom" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.9133, "lon": -93.50329, "name": "Minnetonka" }, { "lat": 42.7262, "lon": -71.19089, "name": "Methuen" }, { "lat": 41.82649, "lon": -72.73009, "name": "Bloomfield" }, { "lat": 40.37637, "lon": -104.69219, "name": "Evans" }, { "lat": -0.52731, "lon": 34.45714, "name": "Homa Bay" } ], "question": "Which location is the geographic outlier among: Minnetonka, Methuen, Bloomfield, Evans, Homa Bay?", "ground_truth": { "answer": "Homa Bay", "outlier_distance_km": 10593.0, "second_furthest_km": 3855.6, "clarity_ratio": 2.75, "median_distance_km": 2984.6, "distances_to_centroid": { "Minnetonka": 2984.6, "Methuen": 1295.0, "Bloomfield": 1321.1, "Evans": 3855.6, "Homa Bay": 10593.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Minnetonka: (44.91°, -93.50°)", " Methuen: (42.73°, -71.19°)", " Bloomfield: (41.83°, -72.73°)", " Evans: (40.38°, -104.69°)", " Homa Bay: (-0.53°, 34.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Homa Bay: 10593.0 km from centroid", " Evans: 3855.6 km from centroid", " Minnetonka: 2984.6 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": 34.58277, "lon": -117.40922, "name": "Adelanto" }, { "lat": 30.69436, "lon": -88.04305, "name": "Mobile" }, { "lat": 15.13924, "lon": -92.4634, "name": "Huixtla" }, { "lat": 41.8501, "lon": -71.46617, "name": "North Providence" }, { "lat": 51.80917, "lon": 5.725, "name": "Wijchen" } ], "question": "Which location is the geographic outlier among: Adelanto, Mobile, Huixtla, North Providence, Wijchen?", "ground_truth": { "answer": "Wijchen", "outlier_distance_km": 6295.0, "second_furthest_km": 4049.6, "clarity_ratio": 1.55, "median_distance_km": 2944.6, "distances_to_centroid": { "Adelanto": 4049.6, "Mobile": 1501.5, "Huixtla": 2944.6, "North Providence": 790.0, "Wijchen": 6295.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Adelanto: (34.58°, -117.41°)", " Mobile: (30.69°, -88.04°)", " Huixtla: (15.14°, -92.46°)", " North Providence: (41.85°, -71.47°)", " Wijchen: (51.81°, 5.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wijchen: 6295.0 km from centroid", " Adelanto: 4049.6 km from centroid", " Huixtla: 2944.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wijchen", "FINAL ANSWER: Wijchen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.89578, "lon": 115.76431, "name": "Scarborough" }, { "lat": -33.7457, "lon": 151.04764, "name": "West Pennant Hills" }, { "lat": -33.91667, "lon": 151.03333, "name": "Bankstown" }, { "lat": -33.7511, "lon": 151.28886, "name": "Dee Why" }, { "lat": 31.39798, "lon": 109.57063, "name": "Chengxiang" } ], "question": "Which location is the geographic outlier among: Scarborough, West Pennant Hills, Bankstown, Dee Why, Chengxiang?", "ground_truth": { "answer": "Chengxiang", "outlier_distance_km": 6398.6, "second_furthest_km": 2363.2, "clarity_ratio": 2.71, "median_distance_km": 2134.9, "distances_to_centroid": { "Scarborough": 2363.2, "West Pennant Hills": 2117.5, "Bankstown": 2128.9, "Dee Why": 2134.9, "Chengxiang": 6398.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Scarborough: (-31.90°, 115.76°)", " West Pennant Hills: (-33.75°, 151.05°)", " Bankstown: (-33.92°, 151.03°)", " Dee Why: (-33.75°, 151.29°)", " Chengxiang: (31.40°, 109.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chengxiang: 6398.6 km from centroid", " Scarborough: 2363.2 km from centroid", " Dee Why: 2134.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chengxiang", "FINAL ANSWER: Chengxiang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.92665, "lon": -0.98577, "name": "Akim Oda" }, { "lat": -33.75562, "lon": 25.40074, "name": "Kariega" }, { "lat": -26.1625, "lon": 27.8725, "name": "Roodepoort" }, { "lat": -23.83322, "lon": 30.16351, "name": "Tzaneen" }, { "lat": 43.78609, "lon": -79.33502, "name": "Pleasant View" } ], "question": "Which location is the geographic outlier among: Akim Oda, Kariega, Roodepoort, Tzaneen, Pleasant View?", "ground_truth": { "answer": "Pleasant View", "outlier_distance_km": 9733.7, "second_furthest_km": 3933.1, "clarity_ratio": 2.47, "median_distance_km": 3676.0, "distances_to_centroid": { "Akim Oda": 1427.2, "Kariega": 3933.1, "Roodepoort": 3599.7, "Tzaneen": 3676.0, "Pleasant View": 9733.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Akim Oda: (5.93°, -0.99°)", " Kariega: (-33.76°, 25.40°)", " Roodepoort: (-26.16°, 27.87°)", " Tzaneen: (-23.83°, 30.16°)", " Pleasant View: (43.79°, -79.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pleasant View: 9733.7 km from centroid", " Kariega: 3933.1 km from centroid", " Tzaneen: 3676.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pleasant View", "FINAL ANSWER: Pleasant View" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.88333, "lon": 38.08333, "name": "Yabēlo" }, { "lat": 10.9992, "lon": 10.41062, "name": "Darazo" }, { "lat": 30.72816, "lon": 31.79697, "name": "Fāqūs" }, { "lat": 9.08044, "lon": 6.0099, "name": "Bida" }, { "lat": 21.03929, "lon": 105.76659, "name": "Cầu Diễn" } ], "question": "Which location is the geographic outlier among: Yabēlo, Darazo, Fāqūs, Bida, Cầu Diễn?", "ground_truth": { "answer": "Cầu Diễn", "outlier_distance_km": 7093.7, "second_furthest_km": 3585.7, "clarity_ratio": 1.98, "median_distance_km": 3067.7, "distances_to_centroid": { "Yabēlo": 1164.0, "Darazo": 3067.7, "Fāqūs": 1838.4, "Bida": 3585.7, "Cầu Diễn": 7093.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yabēlo: (4.88°, 38.08°)", " Darazo: (11.00°, 10.41°)", " Fāqūs: (30.73°, 31.80°)", " Bida: (9.08°, 6.01°)", " Cầu Diễn: (21.04°, 105.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cầu Diễn: 7093.7 km from centroid", " Bida: 3585.7 km from centroid", " Darazo: 3067.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cầu Diễn", "FINAL ANSWER: Cầu Diễn" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.88335, "lon": 19.49292, "name": "Wadowice" }, { "lat": 39.98567, "lon": -0.04935, "name": "Castelló de la Plana" }, { "lat": 49.12426, "lon": 8.59804, "name": "Bruchsal" }, { "lat": 47.61497, "lon": 7.66457, "name": "Lörrach" }, { "lat": 45.5608, "lon": -94.16249, "name": "Saint Cloud" } ], "question": "Which location is the geographic outlier among: Wadowice, Castelló de la Plana, Bruchsal, Lörrach, Saint Cloud?", "ground_truth": { "answer": "Saint Cloud", "outlier_distance_km": 6061.2, "second_furthest_km": 2327.2, "clarity_ratio": 2.6, "median_distance_km": 1540.4, "distances_to_centroid": { "Wadowice": 2327.2, "Castelló de la Plana": 1183.0, "Bruchsal": 1540.4, "Lörrach": 1469.2, "Saint Cloud": 6061.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wadowice: (49.88°, 19.49°)", " Castelló de la Plana: (39.99°, -0.05°)", " Bruchsal: (49.12°, 8.60°)", " Lörrach: (47.61°, 7.66°)", " Saint Cloud: (45.56°, -94.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saint Cloud: 6061.2 km from centroid", " Wadowice: 2327.2 km from centroid", " Bruchsal: 1540.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saint Cloud", "FINAL ANSWER: Saint Cloud" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 7.84468, "lon": 98.33897, "name": "Ban Chalong" }, { "lat": -7.75, "lon": 110.49417, "name": "Candi Prambanan" }, { "lat": 31.70472, "lon": 112.25611, "name": "Yicheng" }, { "lat": 14.72526, "lon": 100.79536, "name": "Phra Phutthabat" }, { "lat": 54.8951, "lon": -2.9382, "name": "Carlisle" } ], "question": "Which location is the geographic outlier among: Ban Chalong, Candi Prambanan, Yicheng, Phra Phutthabat, Carlisle?", "ground_truth": { "answer": "Carlisle", "outlier_distance_km": 7969.9, "second_furthest_km": 4271.6, "clarity_ratio": 1.87, "median_distance_km": 3103.0, "distances_to_centroid": { "Ban Chalong": 2089.0, "Candi Prambanan": 4271.6, "Yicheng": 3103.0, "Phra Phutthabat": 1905.0, "Carlisle": 7969.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ban Chalong: (7.84°, 98.34°)", " Candi Prambanan: (-7.75°, 110.49°)", " Yicheng: (31.70°, 112.26°)", " Phra Phutthabat: (14.73°, 100.80°)", " Carlisle: (54.90°, -2.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carlisle: 7969.9 km from centroid", " Candi Prambanan: 4271.6 km from centroid", " Yicheng: 3103.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carlisle", "FINAL ANSWER: Carlisle" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.49586, "lon": -42.56198, "name": "Santa Quitéria do Maranhão" }, { "lat": -15.10222, "lon": -44.09194, "name": "Itacarambi" }, { "lat": -27.36737, "lon": -70.33219, "name": "Copiapó" }, { "lat": -9.31833, "lon": -35.56111, "name": "São Luís do Quitunde" }, { "lat": 35.75118, "lon": -86.93, "name": "Spring Hill" } ], "question": "Which location is the geographic outlier among: Santa Quitéria do Maranhão, Itacarambi, Copiapó, São Luís do Quitunde, Spring Hill?", "ground_truth": { "answer": "Spring Hill", "outlier_distance_km": 5466.2, "second_furthest_km": 3025.4, "clarity_ratio": 1.81, "median_distance_km": 2324.3, "distances_to_centroid": { "Santa Quitéria do Maranhão": 1480.2, "Itacarambi": 1794.3, "Copiapó": 3025.4, "São Luís do Quitunde": 2324.3, "Spring Hill": 5466.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Quitéria do Maranhão: (-3.50°, -42.56°)", " Itacarambi: (-15.10°, -44.09°)", " Copiapó: (-27.37°, -70.33°)", " São Luís do Quitunde: (-9.32°, -35.56°)", " Spring Hill: (35.75°, -86.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Spring Hill: 5466.2 km from centroid", " Copiapó: 3025.4 km from centroid", " São Luís do Quitunde: 2324.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Spring Hill", "FINAL ANSWER: Spring Hill" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.8178, "lon": 151.00348, "name": "Parramatta" }, { "lat": -33.91439, "lon": 151.24895, "name": "Randwick" }, { "lat": -28.07071, "lon": 153.39329, "name": "Robina" }, { "lat": -33.86436, "lon": 151.0397, "name": "Lidcombe" }, { "lat": 26.96637, "lon": 31.37953, "name": "Şidfā" } ], "question": "Which location is the geographic outlier among: Parramatta, Randwick, Robina, Lidcombe, Şidfā?", "ground_truth": { "answer": "Şidfā", "outlier_distance_km": 11615.6, "second_furthest_km": 2759.0, "clarity_ratio": 4.21, "median_distance_km": 2739.2, "distances_to_centroid": { "Parramatta": 2733.9, "Randwick": 2759.0, "Robina": 2736.9, "Lidcombe": 2739.2, "Şidfā": 11615.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parramatta: (-33.82°, 151.00°)", " Randwick: (-33.91°, 151.25°)", " Robina: (-28.07°, 153.39°)", " Lidcombe: (-33.86°, 151.04°)", " Şidfā: (26.97°, 31.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Şidfā: 11615.6 km from centroid", " Randwick: 2759.0 km from centroid", " Lidcombe: 2739.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Şidfā", "FINAL ANSWER: Şidfā" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.9005, "lon": -4.45028, "name": "Erskine" }, { "lat": 51.12382, "lon": -0.0061, "name": "East Grinstead" }, { "lat": 49.74657, "lon": 8.11513, "name": "Alzey" }, { "lat": 52.54833, "lon": 4.66944, "name": "Castricum" }, { "lat": -26.89972, "lon": -48.82722, "name": "Ilhota" } ], "question": "Which location is the geographic outlier among: Erskine, East Grinstead, Alzey, Castricum, Ilhota?", "ground_truth": { "answer": "Ilhota", "outlier_distance_km": 8236.8, "second_furthest_km": 2176.5, "clarity_ratio": 3.78, "median_distance_km": 2046.3, "distances_to_centroid": { "Erskine": 2176.5, "East Grinstead": 1750.1, "Alzey": 1968.1, "Castricum": 2046.3, "Ilhota": 8236.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Erskine: (55.90°, -4.45°)", " East Grinstead: (51.12°, -0.01°)", " Alzey: (49.75°, 8.12°)", " Castricum: (52.55°, 4.67°)", " Ilhota: (-26.90°, -48.83°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ilhota: 8236.8 km from centroid", " Erskine: 2176.5 km from centroid", " Castricum: 2046.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ilhota", "FINAL ANSWER: Ilhota" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.18333, "lon": 145.08333, "name": "Mount Eliza" }, { "lat": -31.91099, "lon": 152.45387, "name": "Taree" }, { "lat": -37.81992, "lon": 145.0358, "name": "Hawthorn" }, { "lat": -41.05584, "lon": 145.90375, "name": "Burnie" }, { "lat": 11.07937, "lon": 77.03709, "name": "Kālappatti" } ], "question": "Which location is the geographic outlier among: Mount Eliza, Taree, Hawthorn, Burnie, Kālappatti?", "ground_truth": { "answer": "Kālappatti", "outlier_distance_km": 7409.2, "second_furthest_km": 1926.4, "clarity_ratio": 3.85, "median_distance_km": 1900.2, "distances_to_centroid": { "Mount Eliza": 1622.6, "Taree": 1926.4, "Hawthorn": 1592.2, "Burnie": 1900.2, "Kālappatti": 7409.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mount Eliza: (-38.18°, 145.08°)", " Taree: (-31.91°, 152.45°)", " Hawthorn: (-37.82°, 145.04°)", " Burnie: (-41.06°, 145.90°)", " Kālappatti: (11.08°, 77.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kālappatti: 7409.2 km from centroid", " Taree: 1926.4 km from centroid", " Burnie: 1900.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kālappatti", "FINAL ANSWER: Kālappatti" ] }, { "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": -23.11694, "lon": -46.55028, "name": "Atibaia" }, { "lat": -8.02861, "lon": -50.03139, "name": "Redenção" }, { "lat": -25.76889, "lon": -53.5325, "name": "Realeza" }, { "lat": -29.51694, "lon": -50.77778, "name": "Três Coroas" }, { "lat": 48.8262, "lon": 2.35986, "name": "Paris 13e Arrondissement" } ], "question": "Which location is the geographic outlier among: Atibaia, Redenção, Realeza, Três Coroas, Paris 13e Arrondissement?", "ground_truth": { "answer": "Paris 13e Arrondissement", "outlier_distance_km": 7482.7, "second_furthest_km": 2705.9, "clarity_ratio": 2.77, "median_distance_km": 2502.5, "distances_to_centroid": { "Atibaia": 1882.0, "Redenção": 1138.9, "Realeza": 2502.5, "Três Coroas": 2705.9, "Paris 13e Arrondissement": 7482.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Atibaia: (-23.12°, -46.55°)", " Redenção: (-8.03°, -50.03°)", " Realeza: (-25.77°, -53.53°)", " Três Coroas: (-29.52°, -50.78°)", " Paris 13e Arrondissement: (48.83°, 2.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Paris 13e Arrondissement: 7482.7 km from centroid", " Três Coroas: 2705.9 km from centroid", " Realeza: 2502.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Paris 13e Arrondissement", "FINAL ANSWER: Paris 13e Arrondissement" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 17.5242, "lon": 78.32273, "name": "Amīnpur" }, { "lat": 35.16278, "lon": 112.865, "name": "Xixiang" }, { "lat": 35.65, "lon": 140.31667, "name": "Yachimata" }, { "lat": 21.88868, "lon": 71.87935, "name": "Valabhīpur" }, { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" } ], "question": "Which location is the geographic outlier among: Amīnpur, Xixiang, Yachimata, Valabhīpur, Lower Hutt?", "ground_truth": { "answer": "Lower Hutt", "outlier_distance_km": 8618.9, "second_furthest_km": 4704.4, "clarity_ratio": 1.83, "median_distance_km": 4012.7, "distances_to_centroid": { "Amīnpur": 4012.7, "Xixiang": 2391.7, "Yachimata": 3458.7, "Valabhīpur": 4704.4, "Lower Hutt": 8618.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Amīnpur: (17.52°, 78.32°)", " Xixiang: (35.16°, 112.86°)", " Yachimata: (35.65°, 140.32°)", " Valabhīpur: (21.89°, 71.88°)", " Lower Hutt: (-41.22°, 174.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lower Hutt: 8618.9 km from centroid", " Valabhīpur: 4704.4 km from centroid", " Amīnpur: 4012.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lower Hutt", "FINAL ANSWER: Lower Hutt" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.81144, "lon": -89.95316, "name": "Edwardsville" }, { "lat": 33.96057, "lon": -118.18535, "name": "Cudahy" }, { "lat": 26.16647, "lon": -80.20838, "name": "Lauderdale Lakes" }, { "lat": 20.12571, "lon": -101.19208, "name": "Moroleón" }, { "lat": 31.13159, "lon": 33.79844, "name": "Arīsh" } ], "question": "Which location is the geographic outlier among: Edwardsville, Cudahy, Lauderdale Lakes, Moroleón, Arīsh?", "ground_truth": { "answer": "Arīsh", "outlier_distance_km": 9576.0, "second_furthest_km": 4418.6, "clarity_ratio": 2.17, "median_distance_km": 3208.3, "distances_to_centroid": { "Edwardsville": 1975.8, "Cudahy": 4418.6, "Lauderdale Lakes": 987.0, "Moroleón": 3208.3, "Arīsh": 9576.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Edwardsville: (38.81°, -89.95°)", " Cudahy: (33.96°, -118.19°)", " Lauderdale Lakes: (26.17°, -80.21°)", " Moroleón: (20.13°, -101.19°)", " Arīsh: (31.13°, 33.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arīsh: 9576.0 km from centroid", " Cudahy: 4418.6 km from centroid", " Moroleón: 3208.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arīsh", "FINAL ANSWER: Arīsh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.75818, "lon": 144.28024, "name": "Bendigo" }, { "lat": -41.28664, "lon": 174.77557, "name": "Wellington" }, { "lat": -37.83834, "lon": 144.99149, "name": "South Yarra" }, { "lat": -31.83291, "lon": 115.7759, "name": "Duncraig" }, { "lat": 2.2958, "lon": 102.2537, "name": "Kampung Kerubong" } ], "question": "Which location is the geographic outlier among: Bendigo, Wellington, South Yarra, Duncraig, Kampung Kerubong?", "ground_truth": { "answer": "Kampung Kerubong", "outlier_distance_km": 5040.1, "second_furthest_km": 3704.6, "clarity_ratio": 1.36, "median_distance_km": 1998.6, "distances_to_centroid": { "Bendigo": 1124.7, "Wellington": 3704.6, "South Yarra": 1255.9, "Duncraig": 1998.6, "Kampung Kerubong": 5040.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bendigo: (-36.76°, 144.28°)", " Wellington: (-41.29°, 174.78°)", " South Yarra: (-37.84°, 144.99°)", " Duncraig: (-31.83°, 115.78°)", " Kampung Kerubong: (2.30°, 102.25°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kampung Kerubong: 5040.1 km from centroid", " Wellington: 3704.6 km from centroid", " Duncraig: 1998.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kampung Kerubong", "FINAL ANSWER: Kampung Kerubong" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.63526, "lon": -70.92701, "name": "New Bedford" }, { "lat": 33.01457, "lon": -97.09696, "name": "Flower Mound" }, { "lat": 34.28556, "lon": -118.88204, "name": "Moorpark" }, { "lat": 42.96336, "lon": -85.66809, "name": "Grand Rapids" }, { "lat": 53.9, "lon": 53.93333, "name": "Priyutovo" } ], "question": "Which location is the geographic outlier among: New Bedford, Flower Mound, Moorpark, Grand Rapids, Priyutovo?", "ground_truth": { "answer": "Priyutovo", "outlier_distance_km": 7892.9, "second_furthest_km": 4829.5, "clarity_ratio": 1.63, "median_distance_km": 3074.0, "distances_to_centroid": { "New Bedford": 602.6, "Flower Mound": 3074.0, "Moorpark": 4829.5, "Grand Rapids": 1817.1, "Priyutovo": 7892.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " New Bedford: (41.64°, -70.93°)", " Flower Mound: (33.01°, -97.10°)", " Moorpark: (34.29°, -118.88°)", " Grand Rapids: (42.96°, -85.67°)", " Priyutovo: (53.90°, 53.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Priyutovo: 7892.9 km from centroid", " Moorpark: 4829.5 km from centroid", " Flower Mound: 3074.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Priyutovo", "FINAL ANSWER: Priyutovo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -25.73271, "lon": -59.10989, "name": "Pirané" }, { "lat": -20.61444, "lon": -42.14861, "name": "Divino" }, { "lat": -24.23127, "lon": -64.86614, "name": "San Pedro de Jujuy" }, { "lat": -22.84278, "lon": -45.25139, "name": "Potim" }, { "lat": 28.02224, "lon": -81.73286, "name": "Winter Haven" } ], "question": "Which location is the geographic outlier among: Pirané, Divino, San Pedro de Jujuy, Potim, Winter Haven?", "ground_truth": { "answer": "Winter Haven", "outlier_distance_km": 5204.1, "second_furthest_km": 1941.1, "clarity_ratio": 2.68, "median_distance_km": 1780.8, "distances_to_centroid": { "Pirané": 1407.9, "Divino": 1941.1, "San Pedro de Jujuy": 1403.0, "Potim": 1780.8, "Winter Haven": 5204.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pirané: (-25.73°, -59.11°)", " Divino: (-20.61°, -42.15°)", " San Pedro de Jujuy: (-24.23°, -64.87°)", " Potim: (-22.84°, -45.25°)", " Winter Haven: (28.02°, -81.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Winter Haven: 5204.1 km from centroid", " Divino: 1941.1 km from centroid", " Potim: 1780.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Winter Haven", "FINAL ANSWER: Winter Haven" ] }, { "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": 35.71091, "lon": 139.6372, "name": "Asagayakita" }, { "lat": 50.24413, "lon": 127.49016, "name": "Heihe" }, { "lat": 35.02269, "lon": 136.90887, "name": "Tōkai" }, { "lat": 26.59048, "lon": 86.13791, "name": "Jainagar" }, { "lat": -37.92845, "lon": 145.17708, "name": "Mulgrave" } ], "question": "Which location is the geographic outlier among: Asagayakita, Heihe, Tōkai, Jainagar, Mulgrave?", "ground_truth": { "answer": "Mulgrave", "outlier_distance_km": 6919.6, "second_furthest_km": 4164.5, "clarity_ratio": 1.66, "median_distance_km": 3148.8, "distances_to_centroid": { "Asagayakita": 1957.7, "Heihe": 3148.8, "Tōkai": 1742.6, "Jainagar": 4164.5, "Mulgrave": 6919.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Asagayakita: (35.71°, 139.64°)", " Heihe: (50.24°, 127.49°)", " Tōkai: (35.02°, 136.91°)", " Jainagar: (26.59°, 86.14°)", " Mulgrave: (-37.93°, 145.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mulgrave: 6919.6 km from centroid", " Jainagar: 4164.5 km from centroid", " Heihe: 3148.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mulgrave", "FINAL ANSWER: Mulgrave" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.17058, "lon": 144.3114, "name": "Highton" }, { "lat": -33.94185, "lon": 150.8717, "name": "Prestons" }, { "lat": -34.18551, "lon": 142.16251, "name": "Mildura" }, { "lat": -37.70988, "lon": 144.75483, "name": "Taylors Hill" }, { "lat": 38.81144, "lon": -90.85291, "name": "Wentzville" } ], "question": "Which location is the geographic outlier among: Highton, Prestons, Mildura, Taylors Hill, Wentzville?", "ground_truth": { "answer": "Wentzville", "outlier_distance_km": 17855.9, "second_furthest_km": 5325.6, "clarity_ratio": 3.35, "median_distance_km": 4814.4, "distances_to_centroid": { "Highton": 4784.6, "Prestons": 5325.6, "Mildura": 4527.8, "Taylors Hill": 4814.4, "Wentzville": 17855.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Highton: (-38.17°, 144.31°)", " Prestons: (-33.94°, 150.87°)", " Mildura: (-34.19°, 142.16°)", " Taylors Hill: (-37.71°, 144.75°)", " Wentzville: (38.81°, -90.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wentzville: 17855.9 km from centroid", " Prestons: 5325.6 km from centroid", " Taylors Hill: 4814.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wentzville", "FINAL ANSWER: Wentzville" ] }, { "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": 28.88305, "lon": -81.30868, "name": "DeBary" }, { "lat": 38.47005, "lon": -90.30456, "name": "Oakville" }, { "lat": 41.92337, "lon": -87.69922, "name": "Logan Square" }, { "lat": 20.38897, "lon": -99.99637, "name": "San Juan del Río" }, { "lat": 36.52672, "lon": -6.2891, "name": "Cadiz" } ], "question": "Which location is the geographic outlier among: DeBary, Oakville, Logan Square, San Juan del Río, Cadiz?", "ground_truth": { "answer": "Cadiz", "outlier_distance_km": 5981.6, "second_furthest_km": 3012.6, "clarity_ratio": 1.99, "median_distance_km": 1651.3, "distances_to_centroid": { "DeBary": 917.7, "Oakville": 1651.3, "Logan Square": 1603.5, "San Juan del Río": 3012.6, "Cadiz": 5981.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " DeBary: (28.88°, -81.31°)", " Oakville: (38.47°, -90.30°)", " Logan Square: (41.92°, -87.70°)", " San Juan del Río: (20.39°, -100.00°)", " Cadiz: (36.53°, -6.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cadiz: 5981.6 km from centroid", " San Juan del Río: 3012.6 km from centroid", " Oakville: 1651.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cadiz", "FINAL ANSWER: Cadiz" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -13.41316, "lon": -41.28572, "name": "Ibicoara" }, { "lat": -26.96167, "lon": -52.53472, "name": "Xaxim" }, { "lat": -16.43085, "lon": -71.52921, "name": "Ciudad Satelite" }, { "lat": 5.13278, "lon": -74.15977, "name": "Pacho" }, { "lat": 0.05196, "lon": 35.72734, "name": "Eldama Ravine" } ], "question": "Which location is the geographic outlier among: Ibicoara, Xaxim, Ciudad Satelite, Pacho, Eldama Ravine?", "ground_truth": { "answer": "Eldama Ravine", "outlier_distance_km": 8530.5, "second_furthest_km": 4078.8, "clarity_ratio": 2.09, "median_distance_km": 3393.5, "distances_to_centroid": { "Ibicoara": 348.3, "Xaxim": 2224.3, "Ciudad Satelite": 3393.5, "Pacho": 4078.8, "Eldama Ravine": 8530.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ibicoara: (-13.41°, -41.29°)", " Xaxim: (-26.96°, -52.53°)", " Ciudad Satelite: (-16.43°, -71.53°)", " Pacho: (5.13°, -74.16°)", " Eldama Ravine: (0.05°, 35.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Eldama Ravine: 8530.5 km from centroid", " Pacho: 4078.8 km from centroid", " Ciudad Satelite: 3393.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Eldama Ravine", "FINAL ANSWER: Eldama Ravine" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.91694, "lon": -46.99139, "name": "São Sebastião do Paraíso" }, { "lat": -38.96667, "lon": -68.23333, "name": "Plottier" }, { "lat": -5.84426, "lon": -40.70195, "name": "Quiterianópolis" }, { "lat": -1.94167, "lon": -54.73833, "name": "Alenquer" }, { "lat": 0.46005, "lon": 34.11169, "name": "Busia" } ], "question": "Which location is the geographic outlier among: São Sebastião do Paraíso, Plottier, Quiterianópolis, Alenquer, Busia?", "ground_truth": { "answer": "Busia", "outlier_distance_km": 7797.5, "second_furthest_km": 4297.9, "clarity_ratio": 1.81, "median_distance_km": 2490.2, "distances_to_centroid": { "São Sebastião do Paraíso": 1492.4, "Plottier": 4297.9, "Quiterianópolis": 1030.8, "Alenquer": 2490.2, "Busia": 7797.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Sebastião do Paraíso: (-20.92°, -46.99°)", " Plottier: (-38.97°, -68.23°)", " Quiterianópolis: (-5.84°, -40.70°)", " Alenquer: (-1.94°, -54.74°)", " Busia: (0.46°, 34.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Busia: 7797.5 km from centroid", " Plottier: 4297.9 km from centroid", " Alenquer: 2490.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Busia", "FINAL ANSWER: Busia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.7449, "lon": 116.8532, "name": "Taliwang" }, { "lat": 27.42752, "lon": 83.41789, "name": "Nautanwa" }, { "lat": 34.81667, "lon": 137.4, "name": "Toyokawa" }, { "lat": 34.76667, "lon": 138.01667, "name": "Kakegawa" }, { "lat": 34.77405, "lon": -79.46282, "name": "Laurinburg" } ], "question": "Which location is the geographic outlier among: Taliwang, Nautanwa, Toyokawa, Kakegawa, Laurinburg?", "ground_truth": { "answer": "Laurinburg", "outlier_distance_km": 13040.9, "second_furthest_km": 5709.0, "clarity_ratio": 2.28, "median_distance_km": 5652.4, "distances_to_centroid": { "Taliwang": 5511.5, "Nautanwa": 521.6, "Toyokawa": 5652.4, "Kakegawa": 5709.0, "Laurinburg": 13040.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taliwang: (-8.74°, 116.85°)", " Nautanwa: (27.43°, 83.42°)", " Toyokawa: (34.82°, 137.40°)", " Kakegawa: (34.77°, 138.02°)", " Laurinburg: (34.77°, -79.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Laurinburg: 13040.9 km from centroid", " Kakegawa: 5709.0 km from centroid", " Toyokawa: 5652.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Laurinburg", "FINAL ANSWER: Laurinburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.27668, "lon": 131.15628, "name": "Tsukawaki" }, { "lat": 30.13894, "lon": 107.20487, "name": "Yuntai" }, { "lat": 12.37169, "lon": 123.62494, "name": "Masbate" }, { "lat": 24.26667, "lon": 98.28333, "name": "Zhefang" }, { "lat": 41.5501, "lon": -71.46617, "name": "North Kingstown" } ], "question": "Which location is the geographic outlier among: Tsukawaki, Yuntai, Masbate, Zhefang, North Kingstown?", "ground_truth": { "answer": "North Kingstown", "outlier_distance_km": 11626.4, "second_furthest_km": 5075.1, "clarity_ratio": 2.29, "median_distance_km": 5063.8, "distances_to_centroid": { "Tsukawaki": 5075.1, "Yuntai": 2856.4, "Masbate": 5063.8, "Zhefang": 2092.1, "North Kingstown": 11626.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tsukawaki: (33.28°, 131.16°)", " Yuntai: (30.14°, 107.20°)", " Masbate: (12.37°, 123.62°)", " Zhefang: (24.27°, 98.28°)", " North Kingstown: (41.55°, -71.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Kingstown: 11626.4 km from centroid", " Tsukawaki: 5075.1 km from centroid", " Masbate: 5063.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Kingstown", "FINAL ANSWER: North Kingstown" ] }, { "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": 53.09787, "lon": -2.44161, "name": "Crewe" }, { "lat": 44.3496, "lon": 9.22796, "name": "Rapallo" }, { "lat": 49.71443, "lon": 7.30776, "name": "Idar-Oberstein" }, { "lat": 36.67777, "lon": -5.446, "name": "Ubrique" }, { "lat": -38.68333, "lon": 176.08333, "name": "Taupo" } ], "question": "Which location is the geographic outlier among: Crewe, Rapallo, Idar-Oberstein, Ubrique, Taupo?", "ground_truth": { "answer": "Taupo", "outlier_distance_km": 16127.1, "second_furthest_km": 4164.9, "clarity_ratio": 3.87, "median_distance_km": 4016.6, "distances_to_centroid": { "Crewe": 4164.9, "Rapallo": 2978.1, "Idar-Oberstein": 3392.1, "Ubrique": 4016.6, "Taupo": 16127.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Crewe: (53.10°, -2.44°)", " Rapallo: (44.35°, 9.23°)", " Idar-Oberstein: (49.71°, 7.31°)", " Ubrique: (36.68°, -5.45°)", " Taupo: (-38.68°, 176.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Taupo: 16127.1 km from centroid", " Crewe: 4164.9 km from centroid", " Ubrique: 4016.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Taupo", "FINAL ANSWER: Taupo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.6554, "lon": 52.442, "name": "Buguruslan" }, { "lat": 51.58417, "lon": 4.31944, "name": "Steenbergen" }, { "lat": 41.45152, "lon": 2.2081, "name": "Santa Coloma de Gramenet" }, { "lat": 46.49067, "lon": 11.33982, "name": "Bolzano" }, { "lat": 28.58, "lon": 77.33, "name": "Noida" } ], "question": "Which location is the geographic outlier among: Buguruslan, Steenbergen, Santa Coloma de Gramenet, Bolzano, Noida?", "ground_truth": { "answer": "Noida", "outlier_distance_km": 4544.5, "second_furthest_km": 2237.9, "clarity_ratio": 2.03, "median_distance_km": 2028.7, "distances_to_centroid": { "Buguruslan": 1952.5, "Steenbergen": 2028.7, "Santa Coloma de Gramenet": 2237.9, "Bolzano": 1436.0, "Noida": 4544.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Buguruslan: (53.66°, 52.44°)", " Steenbergen: (51.58°, 4.32°)", " Santa Coloma de Gramenet: (41.45°, 2.21°)", " Bolzano: (46.49°, 11.34°)", " Noida: (28.58°, 77.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Noida: 4544.5 km from centroid", " Santa Coloma de Gramenet: 2237.9 km from centroid", " Steenbergen: 2028.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Noida", "FINAL ANSWER: Noida" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.55874, "lon": 7.63359, "name": "Bende" }, { "lat": 12.01667, "lon": 39.63333, "name": "Robīt" }, { "lat": 5.55728, "lon": -0.1864, "name": "Osu" }, { "lat": -33.78664, "lon": 20.12106, "name": "Montagu" }, { "lat": -37.79117, "lon": 144.81637, "name": "Sunshine West" } ], "question": "Which location is the geographic outlier among: Bende, Robīt, Osu, Montagu, Sunshine West?", "ground_truth": { "answer": "Sunshine West", "outlier_distance_km": 10417.6, "second_furthest_km": 5013.7, "clarity_ratio": 2.08, "median_distance_km": 4208.7, "distances_to_centroid": { "Bende": 4208.7, "Robīt": 2432.9, "Osu": 5013.7, "Montagu": 3514.4, "Sunshine West": 10417.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bende: (5.56°, 7.63°)", " Robīt: (12.02°, 39.63°)", " Osu: (5.56°, -0.19°)", " Montagu: (-33.79°, 20.12°)", " Sunshine West: (-37.79°, 144.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sunshine West: 10417.6 km from centroid", " Osu: 5013.7 km from centroid", " Bende: 4208.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sunshine West", "FINAL ANSWER: Sunshine West" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.23922, "lon": -81.34594, "name": "Streetsboro" }, { "lat": 58.30194, "lon": -134.41972, "name": "Juneau" }, { "lat": 43.16547, "lon": -77.70066, "name": "Gates-North Gates" }, { "lat": 40.16523, "lon": -111.61075, "name": "Springville" }, { "lat": 14.7451, "lon": 79.06288, "name": "Badvel" } ], "question": "Which location is the geographic outlier among: Streetsboro, Juneau, Gates-North Gates, Springville, Badvel?", "ground_truth": { "answer": "Badvel", "outlier_distance_km": 12935.4, "second_furthest_km": 5197.5, "clarity_ratio": 2.49, "median_distance_km": 3916.6, "distances_to_centroid": { "Streetsboro": 1378.6, "Juneau": 5197.5, "Gates-North Gates": 1117.8, "Springville": 3916.6, "Badvel": 12935.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Streetsboro: (41.24°, -81.35°)", " Juneau: (58.30°, -134.42°)", " Gates-North Gates: (43.17°, -77.70°)", " Springville: (40.17°, -111.61°)", " Badvel: (14.75°, 79.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Badvel: 12935.4 km from centroid", " Juneau: 5197.5 km from centroid", " Springville: 3916.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Badvel", "FINAL ANSWER: Badvel" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.05159, "lon": 12.61969, "name": "Monterotondo" }, { "lat": 54.90395, "lon": 52.31793, "name": "Al’met’yevsk" }, { "lat": 40.81249, "lon": 0.5216, "name": "Tortosa" }, { "lat": 48.77275, "lon": 5.16108, "name": "Bar-le-Duc" }, { "lat": 31.80921, "lon": 75.20294, "name": "Batāla" } ], "question": "Which location is the geographic outlier among: Monterotondo, Al’met’yevsk, Tortosa, Bar-le-Duc, Batāla?", "ground_truth": { "answer": "Batāla", "outlier_distance_km": 4197.9, "second_furthest_km": 2367.2, "clarity_ratio": 1.77, "median_distance_km": 2076.7, "distances_to_centroid": { "Monterotondo": 1358.2, "Al’met’yevsk": 2076.7, "Tortosa": 2367.2, "Bar-le-Duc": 1922.6, "Batāla": 4197.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Monterotondo: (42.05°, 12.62°)", " Al’met’yevsk: (54.90°, 52.32°)", " Tortosa: (40.81°, 0.52°)", " Bar-le-Duc: (48.77°, 5.16°)", " Batāla: (31.81°, 75.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Batāla: 4197.9 km from centroid", " Tortosa: 2367.2 km from centroid", " Al’met’yevsk: 2076.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Batāla", "FINAL ANSWER: Batāla" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.55308, "lon": -87.93341, "name": "Pleasant Prairie" }, { "lat": 21.88262, "lon": -102.2843, "name": "Aguascalientes" }, { "lat": 34.00288, "lon": -84.14464, "name": "Duluth" }, { "lat": 34.57943, "lon": -118.11646, "name": "Palmdale" }, { "lat": -34.63364, "lon": -58.57047, "name": "Villa Sarmiento" } ], "question": "Which location is the geographic outlier among: Pleasant Prairie, Aguascalientes, Duluth, Palmdale, Villa Sarmiento?", "ground_truth": { "answer": "Villa Sarmiento", "outlier_distance_km": 6903.0, "second_furthest_km": 3203.7, "clarity_ratio": 2.15, "median_distance_km": 2552.7, "distances_to_centroid": { "Pleasant Prairie": 2552.7, "Aguascalientes": 1278.6, "Duluth": 1701.8, "Palmdale": 3203.7, "Villa Sarmiento": 6903.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pleasant Prairie: (42.55°, -87.93°)", " Aguascalientes: (21.88°, -102.28°)", " Duluth: (34.00°, -84.14°)", " Palmdale: (34.58°, -118.12°)", " Villa Sarmiento: (-34.63°, -58.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Villa Sarmiento: 6903.0 km from centroid", " Palmdale: 3203.7 km from centroid", " Pleasant Prairie: 2552.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Villa Sarmiento", "FINAL ANSWER: Villa Sarmiento" ] }, { "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": 41.47892, "lon": -87.45476, "name": "Schererville" }, { "lat": 41.34559, "lon": -88.84258, "name": "Ottawa" }, { "lat": 43.91452, "lon": -69.96533, "name": "Brunswick" }, { "lat": 34.73706, "lon": -82.25428, "name": "Simpsonville" }, { "lat": 27.2146, "lon": 78.23683, "name": "Tūndla" } ], "question": "Which location is the geographic outlier among: Schererville, Ottawa, Brunswick, Simpsonville, Tūndla?", "ground_truth": { "answer": "Tūndla", "outlier_distance_km": 11004.8, "second_furthest_km": 3322.1, "clarity_ratio": 3.31, "median_distance_km": 3205.5, "distances_to_centroid": { "Schererville": 3205.5, "Ottawa": 3322.1, "Brunswick": 1804.7, "Simpsonville": 2892.7, "Tūndla": 11004.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Schererville: (41.48°, -87.45°)", " Ottawa: (41.35°, -88.84°)", " Brunswick: (43.91°, -69.97°)", " Simpsonville: (34.74°, -82.25°)", " Tūndla: (27.21°, 78.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tūndla: 11004.8 km from centroid", " Ottawa: 3322.1 km from centroid", " Schererville: 3205.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tūndla", "FINAL ANSWER: Tūndla" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.50306, "lon": -80.27306, "name": "Zarumilla" }, { "lat": -17.56944, "lon": -52.55111, "name": "Mineiros" }, { "lat": -16.58197, "lon": -39.78117, "name": "Guaratinga" }, { "lat": -24.50944, "lon": -50.41361, "name": "Tibagi" }, { "lat": 38.78928, "lon": -77.1872, "name": "Springfield" } ], "question": "Which location is the geographic outlier among: Zarumilla, Mineiros, Guaratinga, Tibagi, Springfield?", "ground_truth": { "answer": "Springfield", "outlier_distance_km": 5144.8, "second_furthest_km": 2575.7, "clarity_ratio": 2.0, "median_distance_km": 2434.0, "distances_to_centroid": { "Zarumilla": 2247.6, "Mineiros": 1649.4, "Guaratinga": 2575.7, "Tibagi": 2434.0, "Springfield": 5144.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zarumilla: (-3.50°, -80.27°)", " Mineiros: (-17.57°, -52.55°)", " Guaratinga: (-16.58°, -39.78°)", " Tibagi: (-24.51°, -50.41°)", " Springfield: (38.79°, -77.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Springfield: 5144.8 km from centroid", " Guaratinga: 2575.7 km from centroid", " Tibagi: 2434.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Springfield", "FINAL ANSWER: Springfield" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 1.15284, "lon": -76.65208, "name": "Mocoa" }, { "lat": -12.16028, "lon": -39.33167, "name": "Serra Preta" }, { "lat": 7.07993, "lon": -74.6989, "name": "Segovia" }, { "lat": -4.00092, "lon": -49.5068, "name": "Breu Branco" }, { "lat": -27.19354, "lon": 153.02631, "name": "Deception Bay" } ], "question": "Which location is the geographic outlier among: Mocoa, Serra Preta, Segovia, Breu Branco, Deception Bay?", "ground_truth": { "answer": "Deception Bay", "outlier_distance_km": 16074.0, "second_furthest_km": 6632.3, "clarity_ratio": 2.42, "median_distance_km": 6542.1, "distances_to_centroid": { "Mocoa": 6632.3, "Serra Preta": 2466.7, "Segovia": 6542.1, "Breu Branco": 3565.0, "Deception Bay": 16074.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mocoa: (1.15°, -76.65°)", " Serra Preta: (-12.16°, -39.33°)", " Segovia: (7.08°, -74.70°)", " Breu Branco: (-4.00°, -49.51°)", " Deception Bay: (-27.19°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Deception Bay: 16074.0 km from centroid", " Mocoa: 6632.3 km from centroid", " Segovia: 6542.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Deception Bay", "FINAL ANSWER: Deception Bay" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.91756, "lon": -82.07842, "name": "Punta Gorda Isles" }, { "lat": 18.82776, "lon": -97.16311, "name": "Nogales" }, { "lat": 28.0199, "lon": -82.77323, "name": "Dunedin" }, { "lat": 19.10446, "lon": -99.5898, "name": "Tenango de Arista" }, { "lat": 25.19407, "lon": 75.07215, "name": "Māndalgarh" } ], "question": "Which location is the geographic outlier among: Punta Gorda Isles, Nogales, Dunedin, Tenango de Arista, Māndalgarh?", "ground_truth": { "answer": "Māndalgarh", "outlier_distance_km": 12548.4, "second_furthest_km": 4392.0, "clarity_ratio": 2.86, "median_distance_km": 4152.4, "distances_to_centroid": { "Punta Gorda Isles": 2513.9, "Nogales": 4152.4, "Dunedin": 2590.8, "Tenango de Arista": 4392.0, "Māndalgarh": 12548.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Punta Gorda Isles: (26.92°, -82.08°)", " Nogales: (18.83°, -97.16°)", " Dunedin: (28.02°, -82.77°)", " Tenango de Arista: (19.10°, -99.59°)", " Māndalgarh: (25.19°, 75.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Māndalgarh: 12548.4 km from centroid", " Tenango de Arista: 4392.0 km from centroid", " Nogales: 4152.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Māndalgarh", "FINAL ANSWER: Māndalgarh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.51103, "lon": -46.74713, "name": "Jaguara" }, { "lat": -16.20639, "lon": -44.43333, "name": "Brasília de Minas" }, { "lat": 10.39817, "lon": -75.49328, "name": "Cartagena" }, { "lat": -4.49083, "lon": -38.59667, "name": "Ocara" }, { "lat": 18.9378, "lon": -103.96417, "name": "Ciudad de Armería" } ], "question": "Which location is the geographic outlier among: Jaguara, Brasília de Minas, Cartagena, Ocara, Ciudad de Armería?", "ground_truth": { "answer": "Ciudad de Armería", "outlier_distance_km": 5210.1, "second_furthest_km": 2802.1, "clarity_ratio": 1.86, "median_distance_km": 2585.2, "distances_to_centroid": { "Jaguara": 2802.1, "Brasília de Minas": 2406.6, "Cartagena": 2119.8, "Ocara": 2585.2, "Ciudad de Armería": 5210.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jaguara: (-23.51°, -46.75°)", " Brasília de Minas: (-16.21°, -44.43°)", " Cartagena: (10.40°, -75.49°)", " Ocara: (-4.49°, -38.60°)", " Ciudad de Armería: (18.94°, -103.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ciudad de Armería: 5210.1 km from centroid", " Jaguara: 2802.1 km from centroid", " Ocara: 2585.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ciudad de Armería", "FINAL ANSWER: Ciudad de Armería" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.99389, "lon": 119.65028, "name": "Linjiacun" }, { "lat": 33.52111, "lon": 130.42444, "name": "Katanawa" }, { "lat": 33.96389, "lon": 117.96944, "name": "Liangji" }, { "lat": 26.34197, "lon": 89.21555, "name": "Mātābhānga" }, { "lat": 49.69925, "lon": -123.15631, "name": "Squamish" } ], "question": "Which location is the geographic outlier among: Linjiacun, Katanawa, Liangji, Mātābhānga, Squamish?", "ground_truth": { "answer": "Squamish", "outlier_distance_km": 10445.8, "second_furthest_km": 5713.9, "clarity_ratio": 1.83, "median_distance_km": 4694.4, "distances_to_centroid": { "Linjiacun": 4694.4, "Katanawa": 5713.9, "Liangji": 4613.7, "Mātābhānga": 2374.3, "Squamish": 10445.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Linjiacun: (35.99°, 119.65°)", " Katanawa: (33.52°, 130.42°)", " Liangji: (33.96°, 117.97°)", " Mātābhānga: (26.34°, 89.22°)", " Squamish: (49.70°, -123.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Squamish: 10445.8 km from centroid", " Katanawa: 5713.9 km from centroid", " Linjiacun: 4694.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Squamish", "FINAL ANSWER: Squamish" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.54647, "lon": 9.12054, "name": "Bollate" }, { "lat": 48.81642, "lon": 2.49366, "name": "Champigny-sur-Marne" }, { "lat": 42.5114, "lon": 14.14507, "name": "Montesilvano Marina" }, { "lat": 40.50024, "lon": -3.67877, "name": "Valverde" }, { "lat": -10.46139, "lon": -40.18944, "name": "Senhor do Bonfim" } ], "question": "Which location is the geographic outlier among: Bollate, Champigny-sur-Marne, Montesilvano Marina, Valverde, Senhor do Bonfim?", "ground_truth": { "answer": "Senhor do Bonfim", "outlier_distance_km": 6223.9, "second_furthest_km": 1853.5, "clarity_ratio": 3.36, "median_distance_km": 1789.5, "distances_to_centroid": { "Bollate": 1735.0, "Champigny-sur-Marne": 1789.5, "Montesilvano Marina": 1853.5, "Valverde": 791.5, "Senhor do Bonfim": 6223.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bollate: (45.55°, 9.12°)", " Champigny-sur-Marne: (48.82°, 2.49°)", " Montesilvano Marina: (42.51°, 14.15°)", " Valverde: (40.50°, -3.68°)", " Senhor do Bonfim: (-10.46°, -40.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Senhor do Bonfim: 6223.9 km from centroid", " Montesilvano Marina: 1853.5 km from centroid", " Champigny-sur-Marne: 1789.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Senhor do Bonfim", "FINAL ANSWER: Senhor do Bonfim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.76952, "lon": 30.79165, "name": "Vryheid" }, { "lat": 1.23889, "lon": 35.11194, "name": "Kapenguria" }, { "lat": 8.72851, "lon": 5.75561, "name": "Patigi" }, { "lat": -0.36774, "lon": 35.28314, "name": "Kericho" }, { "lat": -36.84103, "lon": 174.65223, "name": "Te Atatu Peninsula" } ], "question": "Which location is the geographic outlier among: Vryheid, Kapenguria, Patigi, Kericho, Te Atatu Peninsula?", "ground_truth": { "answer": "Te Atatu Peninsula", "outlier_distance_km": 11672.8, "second_furthest_km": 6007.8, "clarity_ratio": 1.94, "median_distance_km": 3249.9, "distances_to_centroid": { "Vryheid": 3249.9, "Kapenguria": 2711.3, "Patigi": 6007.8, "Kericho": 2607.5, "Te Atatu Peninsula": 11672.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vryheid: (-27.77°, 30.79°)", " Kapenguria: (1.24°, 35.11°)", " Patigi: (8.73°, 5.76°)", " Kericho: (-0.37°, 35.28°)", " Te Atatu Peninsula: (-36.84°, 174.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Te Atatu Peninsula: 11672.8 km from centroid", " Patigi: 6007.8 km from centroid", " Vryheid: 3249.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Te Atatu Peninsula", "FINAL ANSWER: Te Atatu Peninsula" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" }, { "lat": -20.72523, "lon": 139.49727, "name": "Mount Isa" }, { "lat": -31.83291, "lon": 115.7759, "name": "Duncraig" }, { "lat": -32.24295, "lon": 148.60484, "name": "Dubbo" }, { "lat": 43.41727, "lon": 5.21462, "name": "Marignane" } ], "question": "Which location is the geographic outlier among: Coogee, Mount Isa, Duncraig, Dubbo, Marignane?", "ground_truth": { "answer": "Marignane", "outlier_distance_km": 12504.5, "second_furthest_km": 4447.2, "clarity_ratio": 2.81, "median_distance_km": 4153.9, "distances_to_centroid": { "Coogee": 4447.2, "Mount Isa": 2965.7, "Duncraig": 1902.5, "Dubbo": 4153.9, "Marignane": 12504.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Coogee: (-33.92°, 151.26°)", " Mount Isa: (-20.73°, 139.50°)", " Duncraig: (-31.83°, 115.78°)", " Dubbo: (-32.24°, 148.60°)", " Marignane: (43.42°, 5.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Marignane: 12504.5 km from centroid", " Coogee: 4447.2 km from centroid", " Dubbo: 4153.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Marignane", "FINAL ANSWER: Marignane" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.44623, "lon": -122.63926, "name": "Milwaukie" }, { "lat": 33.836, "lon": -79.04781, "name": "Conway" }, { "lat": 34.93873, "lon": -82.22706, "name": "Greer" }, { "lat": 40.39162, "lon": -111.85077, "name": "Lehi" }, { "lat": -40.91667, "lon": 175.01667, "name": "Paraparaumu" } ], "question": "Which location is the geographic outlier among: Milwaukie, Conway, Greer, Lehi, Paraparaumu?", "ground_truth": { "answer": "Paraparaumu", "outlier_distance_km": 15846.9, "second_furthest_km": 7354.0, "clarity_ratio": 2.15, "median_distance_km": 6545.8, "distances_to_centroid": { "Milwaukie": 7354.0, "Conway": 3612.1, "Greer": 3921.0, "Lehi": 6545.8, "Paraparaumu": 15846.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Milwaukie: (45.45°, -122.64°)", " Conway: (33.84°, -79.05°)", " Greer: (34.94°, -82.23°)", " Lehi: (40.39°, -111.85°)", " Paraparaumu: (-40.92°, 175.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Paraparaumu: 15846.9 km from centroid", " Milwaukie: 7354.0 km from centroid", " Lehi: 6545.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Paraparaumu", "FINAL ANSWER: Paraparaumu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.77993, "lon": -121.97802, "name": "San Ramon" }, { "lat": 38.597, "lon": -90.50929, "name": "Manchester" }, { "lat": 17.17291, "lon": -92.33392, "name": "Yajalón" }, { "lat": 34.15917, "lon": -118.50119, "name": "Encino" }, { "lat": -36.88158, "lon": 174.76204, "name": "Mount Eden" } ], "question": "Which location is the geographic outlier among: San Ramon, Manchester, Yajalón, Encino, Mount Eden?", "ground_truth": { "answer": "Mount Eden", "outlier_distance_km": 15215.7, "second_furthest_km": 7247.9, "clarity_ratio": 2.1, "median_distance_km": 6965.7, "distances_to_centroid": { "San Ramon": 7247.9, "Manchester": 4540.0, "Yajalón": 4506.9, "Encino": 6965.7, "Mount Eden": 15215.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Ramon: (37.78°, -121.98°)", " Manchester: (38.60°, -90.51°)", " Yajalón: (17.17°, -92.33°)", " Encino: (34.16°, -118.50°)", " Mount Eden: (-36.88°, 174.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mount Eden: 15215.7 km from centroid", " San Ramon: 7247.9 km from centroid", " Encino: 6965.7 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": -20.54139, "lon": -44.635, "name": "Carmópolis de Minas" }, { "lat": -20.97194, "lon": -46.11889, "name": "Carmo do Rio Claro" }, { "lat": -4.85889, "lon": -43.35611, "name": "Caxias" }, { "lat": -22.23333, "lon": -53.34306, "name": "Nova Andradina" }, { "lat": 29.41386, "lon": 77.4689, "name": "Sisauli" } ], "question": "Which location is the geographic outlier among: Carmópolis de Minas, Carmo do Rio Claro, Caxias, Nova Andradina, Sisauli?", "ground_truth": { "answer": "Sisauli", "outlier_distance_km": 11348.3, "second_furthest_km": 3714.9, "clarity_ratio": 3.05, "median_distance_km": 2973.2, "distances_to_centroid": { "Carmópolis de Minas": 2813.7, "Carmo do Rio Claro": 2973.2, "Caxias": 2383.2, "Nova Andradina": 3714.9, "Sisauli": 11348.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Carmópolis de Minas: (-20.54°, -44.63°)", " Carmo do Rio Claro: (-20.97°, -46.12°)", " Caxias: (-4.86°, -43.36°)", " Nova Andradina: (-22.23°, -53.34°)", " Sisauli: (29.41°, 77.47°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sisauli: 11348.3 km from centroid", " Nova Andradina: 3714.9 km from centroid", " Carmo do Rio Claro: 2973.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sisauli", "FINAL ANSWER: Sisauli" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.77778, "lon": -38.91944, "name": "Maragogipe" }, { "lat": -29.35622, "lon": -50.81357, "name": "Canela" }, { "lat": -7.24972, "lon": -39.14306, "name": "Missão Velha" }, { "lat": -7.51556, "lon": -34.90833, "name": "Caaporã" }, { "lat": 42.09869, "lon": -75.91797, "name": "Binghamton" } ], "question": "Which location is the geographic outlier among: Maragogipe, Canela, Missão Velha, Caaporã, Binghamton?", "ground_truth": { "answer": "Binghamton", "outlier_distance_km": 5748.8, "second_furthest_km": 2950.8, "clarity_ratio": 1.95, "median_distance_km": 1529.0, "distances_to_centroid": { "Maragogipe": 1475.3, "Canela": 2950.8, "Missão Velha": 1084.6, "Caaporã": 1529.0, "Binghamton": 5748.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maragogipe: (-12.78°, -38.92°)", " Canela: (-29.36°, -50.81°)", " Missão Velha: (-7.25°, -39.14°)", " Caaporã: (-7.52°, -34.91°)", " Binghamton: (42.10°, -75.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Binghamton: 5748.8 km from centroid", " Canela: 2950.8 km from centroid", " Caaporã: 1529.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Binghamton", "FINAL ANSWER: Binghamton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.39759, "lon": 107.3895, "name": "Xinmin" }, { "lat": 27.57429, "lon": 81.59474, "name": "Bahraigh" }, { "lat": 38.51473, "lon": 114.9868, "name": "Dingzhou" }, { "lat": 16.05025, "lon": 75.78997, "name": "Guledagudda" }, { "lat": 39.02756, "lon": -84.72411, "name": "Burlington" } ], "question": "Which location is the geographic outlier among: Xinmin, Bahraigh, Dingzhou, Guledagudda, Burlington?", "ground_truth": { "answer": "Burlington", "outlier_distance_km": 11439.5, "second_furthest_km": 5136.5, "clarity_ratio": 2.23, "median_distance_km": 4605.2, "distances_to_centroid": { "Xinmin": 4605.2, "Bahraigh": 2215.1, "Dingzhou": 5136.5, "Guledagudda": 2330.5, "Burlington": 11439.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Xinmin: (30.40°, 107.39°)", " Bahraigh: (27.57°, 81.59°)", " Dingzhou: (38.51°, 114.99°)", " Guledagudda: (16.05°, 75.79°)", " Burlington: (39.03°, -84.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Burlington: 11439.5 km from centroid", " Dingzhou: 5136.5 km from centroid", " Xinmin: 4605.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Burlington", "FINAL ANSWER: Burlington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.56222, "lon": -38.50889, "name": "Conceição" }, { "lat": -16.62306, "lon": -54.47389, "name": "Pedra Preta" }, { "lat": -19.00917, "lon": -57.65333, "name": "Corumbá" }, { "lat": -10.70778, "lon": -43.63056, "name": "Buritirama" }, { "lat": 44.55468, "lon": 4.75469, "name": "Montélimar" } ], "question": "Which location is the geographic outlier among: Conceição, Pedra Preta, Corumbá, Buritirama, Montélimar?", "ground_truth": { "answer": "Montélimar", "outlier_distance_km": 6665.2, "second_furthest_km": 2873.5, "clarity_ratio": 2.32, "median_distance_km": 2445.1, "distances_to_centroid": { "Conceição": 636.6, "Pedra Preta": 2445.1, "Corumbá": 2873.5, "Buritirama": 1168.7, "Montélimar": 6665.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Conceição: (-7.56°, -38.51°)", " Pedra Preta: (-16.62°, -54.47°)", " Corumbá: (-19.01°, -57.65°)", " Buritirama: (-10.71°, -43.63°)", " Montélimar: (44.55°, 4.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Montélimar: 6665.2 km from centroid", " Corumbá: 2873.5 km from centroid", " Pedra Preta: 2445.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Montélimar", "FINAL ANSWER: Montélimar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.92893, "lon": 151.05111, "name": "Punchbowl" }, { "lat": -33.83902, "lon": 151.23956, "name": "Mosman" }, { "lat": -37.97695, "lon": 145.25866, "name": "Endeavour Hills" }, { "lat": -36.9382, "lon": 174.84019, "name": "Otahuhu" }, { "lat": 51.84417, "lon": 4.63889, "name": "Hendrik-Ido-Ambacht" } ], "question": "Which location is the geographic outlier among: Punchbowl, Mosman, Endeavour Hills, Otahuhu, Hendrik-Ido-Ambacht?", "ground_truth": { "answer": "Hendrik-Ido-Ambacht", "outlier_distance_km": 13683.2, "second_furthest_km": 5232.7, "clarity_ratio": 2.61, "median_distance_km": 3099.7, "distances_to_centroid": { "Punchbowl": 3089.0, "Mosman": 3099.7, "Endeavour Hills": 2926.9, "Otahuhu": 5232.7, "Hendrik-Ido-Ambacht": 13683.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Punchbowl: (-33.93°, 151.05°)", " Mosman: (-33.84°, 151.24°)", " Endeavour Hills: (-37.98°, 145.26°)", " Otahuhu: (-36.94°, 174.84°)", " Hendrik-Ido-Ambacht: (51.84°, 4.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hendrik-Ido-Ambacht: 13683.2 km from centroid", " Otahuhu: 5232.7 km from centroid", " Mosman: 3099.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hendrik-Ido-Ambacht", "FINAL ANSWER: Hendrik-Ido-Ambacht" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.32711, "lon": 115.64137, "name": "Bunbury" }, { "lat": -38.09968, "lon": 145.17248, "name": "Carrum Downs" }, { "lat": -33.86436, "lon": 151.0397, "name": "Lidcombe" }, { "lat": -37.83634, "lon": 144.65952, "name": "Tarneit" }, { "lat": 11.73292, "lon": 41.082, "name": "Dubti" } ], "question": "Which location is the geographic outlier among: Bunbury, Carrum Downs, Lidcombe, Tarneit, Dubti?", "ground_truth": { "answer": "Dubti", "outlier_distance_km": 9459.3, "second_furthest_km": 3134.5, "clarity_ratio": 3.02, "median_distance_km": 2735.3, "distances_to_centroid": { "Bunbury": 868.2, "Carrum Downs": 2735.3, "Lidcombe": 3134.5, "Tarneit": 2682.8, "Dubti": 9459.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bunbury: (-33.33°, 115.64°)", " Carrum Downs: (-38.10°, 145.17°)", " Lidcombe: (-33.86°, 151.04°)", " Tarneit: (-37.84°, 144.66°)", " Dubti: (11.73°, 41.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dubti: 9459.3 km from centroid", " Lidcombe: 3134.5 km from centroid", " Carrum Downs: 2735.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dubti", "FINAL ANSWER: Dubti" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.00204, "lon": -118.29896, "name": "Vermont Square" }, { "lat": 44.64024, "lon": -93.14355, "name": "Farmington" }, { "lat": 41.50087, "lon": -90.4443, "name": "East Moline" }, { "lat": 19.12384, "lon": -98.76649, "name": "Amecameca" }, { "lat": 49.03333, "lon": 2.03333, "name": "Vauréal" } ], "question": "Which location is the geographic outlier among: Vermont Square, Farmington, East Moline, Amecameca, Vauréal?", "ground_truth": { "answer": "Vauréal", "outlier_distance_km": 6405.4, "second_furthest_km": 3476.8, "clarity_ratio": 1.84, "median_distance_km": 2766.5, "distances_to_centroid": { "Vermont Square": 3476.8, "Farmington": 1362.8, "East Moline": 1012.2, "Amecameca": 2766.5, "Vauréal": 6405.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Vermont Square: (34.00°, -118.30°)", " Farmington: (44.64°, -93.14°)", " East Moline: (41.50°, -90.44°)", " Amecameca: (19.12°, -98.77°)", " Vauréal: (49.03°, 2.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vauréal: 6405.4 km from centroid", " Vermont Square: 3476.8 km from centroid", " Amecameca: 2766.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vauréal", "FINAL ANSWER: Vauréal" ] }, { "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": 7.93333, "lon": 38.71667, "name": "Ziway" }, { "lat": 29.30995, "lon": 30.8418, "name": "Al Fayyum" }, { "lat": 25.75089, "lon": 32.6776, "name": "Az Zaynīyah Qiblī" }, { "lat": 26.99306, "lon": 31.41605, "name": "Al Badārī" }, { "lat": 6.76667, "lon": 125.18333, "name": "Magsaysay" } ], "question": "Which location is the geographic outlier among: Ziway, Al Fayyum, Az Zaynīyah Qiblī, Al Badārī, Magsaysay?", "ground_truth": { "answer": "Magsaysay", "outlier_distance_km": 8023.2, "second_furthest_km": 2386.3, "clarity_ratio": 3.36, "median_distance_km": 2243.4, "distances_to_centroid": { "Ziway": 1895.3, "Al Fayyum": 2386.3, "Az Zaynīyah Qiblī": 2082.8, "Al Badārī": 2243.4, "Magsaysay": 8023.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ziway: (7.93°, 38.72°)", " Al Fayyum: (29.31°, 30.84°)", " Az Zaynīyah Qiblī: (25.75°, 32.68°)", " Al Badārī: (26.99°, 31.42°)", " Magsaysay: (6.77°, 125.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Magsaysay: 8023.2 km from centroid", " Al Fayyum: 2386.3 km from centroid", " Al Badārī: 2243.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Magsaysay", "FINAL ANSWER: Magsaysay" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.74124, "lon": 144.73631, "name": "Caroline Springs" }, { "lat": -38.09968, "lon": 145.17248, "name": "Carrum Downs" }, { "lat": -37.68611, "lon": 176.16667, "name": "Tauranga" }, { "lat": -36.84853, "lon": 174.76349, "name": "Auckland" }, { "lat": -1.28333, "lon": 36.81667, "name": "Nairobi" } ], "question": "Which location is the geographic outlier among: Caroline Springs, Carrum Downs, Tauranga, Auckland, Nairobi?", "ground_truth": { "answer": "Nairobi", "outlier_distance_km": 10770.2, "second_furthest_km": 3803.0, "clarity_ratio": 2.83, "median_distance_km": 3679.0, "distances_to_centroid": { "Caroline Springs": 1181.3, "Carrum Downs": 1236.3, "Tauranga": 3803.0, "Auckland": 3679.0, "Nairobi": 10770.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caroline Springs: (-37.74°, 144.74°)", " Carrum Downs: (-38.10°, 145.17°)", " Tauranga: (-37.69°, 176.17°)", " Auckland: (-36.85°, 174.76°)", " Nairobi: (-1.28°, 36.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nairobi: 10770.2 km from centroid", " Tauranga: 3803.0 km from centroid", " Auckland: 3679.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nairobi", "FINAL ANSWER: Nairobi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.07294, "lon": 36.56828, "name": "May Cadera" }, { "lat": -0.93605, "lon": 38.05955, "name": "Mwingi" }, { "lat": 6.84684, "lon": -1.39612, "name": "Effiduase" }, { "lat": -27.42573, "lon": 29.16585, "name": "Vrede" }, { "lat": -23.77806, "lon": -45.35806, "name": "Ilhabela" } ], "question": "Which location is the geographic outlier among: May Cadera, Mwingi, Effiduase, Vrede, Ilhabela?", "ground_truth": { "answer": "Ilhabela", "outlier_distance_km": 6355.0, "second_furthest_km": 3579.2, "clarity_ratio": 1.78, "median_distance_km": 3014.9, "distances_to_centroid": { "May Cadera": 3579.2, "Mwingi": 3014.9, "Effiduase": 2034.0, "Vrede": 3010.8, "Ilhabela": 6355.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " May Cadera: (14.07°, 36.57°)", " Mwingi: (-0.94°, 38.06°)", " Effiduase: (6.85°, -1.40°)", " Vrede: (-27.43°, 29.17°)", " Ilhabela: (-23.78°, -45.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ilhabela: 6355.0 km from centroid", " May Cadera: 3579.2 km from centroid", " Mwingi: 3014.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ilhabela", "FINAL ANSWER: Ilhabela" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -5.7925, "lon": -37.55667, "name": "Caraúbas" }, { "lat": -9.40917, "lon": -59.025, "name": "Colniza" }, { "lat": -31.25285, "lon": -61.49078, "name": "Rafaela" }, { "lat": -35.44394, "lon": -60.88463, "name": "Nueve de Julio" }, { "lat": 7.91283, "lon": 4.66741, "name": "Ikirun" } ], "question": "Which location is the geographic outlier among: Caraúbas, Colniza, Rafaela, Nueve de Julio, Ikirun?", "ground_truth": { "answer": "Ikirun", "outlier_distance_km": 5815.8, "second_furthest_km": 2915.5, "clarity_ratio": 1.99, "median_distance_km": 2634.5, "distances_to_centroid": { "Caraúbas": 1156.8, "Colniza": 1856.1, "Rafaela": 2634.5, "Nueve de Julio": 2915.5, "Ikirun": 5815.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caraúbas: (-5.79°, -37.56°)", " Colniza: (-9.41°, -59.02°)", " Rafaela: (-31.25°, -61.49°)", " Nueve de Julio: (-35.44°, -60.88°)", " Ikirun: (7.91°, 4.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ikirun: 5815.8 km from centroid", " Nueve de Julio: 2915.5 km from centroid", " Rafaela: 2634.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ikirun", "FINAL ANSWER: Ikirun" ] }, { "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": -28.41098, "lon": 26.70107, "name": "Theunissen" }, { "lat": 9.4025, "lon": 42.3175, "name": "Funyan Bīra" }, { "lat": 9.39334, "lon": 42.00967, "name": "‘Alemaya" }, { "lat": -26.36737, "lon": 28.9189, "name": "Leslie" }, { "lat": -28.21298, "lon": 153.53634, "name": "Banora Point" } ], "question": "Which location is the geographic outlier among: Theunissen, Funyan Bīra, ‘Alemaya, Leslie, Banora Point?", "ground_truth": { "answer": "Banora Point", "outlier_distance_km": 9800.0, "second_furthest_km": 3735.0, "clarity_ratio": 2.62, "median_distance_km": 3450.3, "distances_to_centroid": { "Theunissen": 3735.0, "Funyan Bīra": 3064.1, "‘Alemaya": 3083.5, "Leslie": 3450.3, "Banora Point": 9800.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Theunissen: (-28.41°, 26.70°)", " Funyan Bīra: (9.40°, 42.32°)", " ‘Alemaya: (9.39°, 42.01°)", " Leslie: (-26.37°, 28.92°)", " Banora Point: (-28.21°, 153.54°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Banora Point: 9800.0 km from centroid", " Theunissen: 3735.0 km from centroid", " Leslie: 3450.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Banora Point", "FINAL ANSWER: Banora Point" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.15667, "lon": -49.57944, "name": "Balneário Gaivota" }, { "lat": -11.54722, "lon": -41.9775, "name": "Ibititá" }, { "lat": -24.08204, "lon": -54.24622, "name": "Guaíra" }, { "lat": -29.95111, "lon": -51.09389, "name": "Cachoeirinha" }, { "lat": 43.71619, "lon": -79.59636, "name": "West Humber-Clairville" } ], "question": "Which location is the geographic outlier among: Balneário Gaivota, Ibititá, Guaíra, Cachoeirinha, West Humber-Clairville?", "ground_truth": { "answer": "West Humber-Clairville", "outlier_distance_km": 6479.5, "second_furthest_km": 2238.6, "clarity_ratio": 2.89, "median_distance_km": 2189.8, "distances_to_centroid": { "Balneário Gaivota": 2189.8, "Ibititá": 1462.1, "Guaíra": 1547.2, "Cachoeirinha": 2238.6, "West Humber-Clairville": 6479.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Balneário Gaivota: (-29.16°, -49.58°)", " Ibititá: (-11.55°, -41.98°)", " Guaíra: (-24.08°, -54.25°)", " Cachoeirinha: (-29.95°, -51.09°)", " West Humber-Clairville: (43.72°, -79.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " West Humber-Clairville: 6479.5 km from centroid", " Cachoeirinha: 2238.6 km from centroid", " Balneário Gaivota: 2189.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: West Humber-Clairville", "FINAL ANSWER: West Humber-Clairville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.13389, "lon": -35.85639, "name": "Riacho das Almas" }, { "lat": -27.14944, "lon": -52.31056, "name": "Seara" }, { "lat": -4.88583, "lon": -46.005, "name": "Arame" }, { "lat": 4.56639, "lon": -75.75111, "name": "Montenegro" }, { "lat": 5.82917, "lon": 7.35056, "name": "Okigwe" } ], "question": "Which location is the geographic outlier among: Riacho das Almas, Seara, Arame, Montenegro, Okigwe?", "ground_truth": { "answer": "Okigwe", "outlier_distance_km": 5472.0, "second_furthest_km": 4083.5, "clarity_ratio": 1.34, "median_distance_km": 2666.8, "distances_to_centroid": { "Riacho das Almas": 568.3, "Seara": 2666.8, "Arame": 619.3, "Montenegro": 4083.5, "Okigwe": 5472.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Riacho das Almas: (-8.13°, -35.86°)", " Seara: (-27.15°, -52.31°)", " Arame: (-4.89°, -46.01°)", " Montenegro: (4.57°, -75.75°)", " Okigwe: (5.83°, 7.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Okigwe: 5472.0 km from centroid", " Montenegro: 4083.5 km from centroid", " Seara: 2666.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Okigwe", "FINAL ANSWER: Okigwe" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" }, { "lat": -32.5269, "lon": 115.7217, "name": "Mandurah" }, { "lat": -32.27682, "lon": 115.72978, "name": "Rockingham" }, { "lat": -38.38176, "lon": 142.48799, "name": "Warrnambool" }, { "lat": 40.1215, "lon": -75.3399, "name": "Norristown" } ], "question": "Which location is the geographic outlier among: Kallangur, Mandurah, Rockingham, Warrnambool, Norristown?", "ground_truth": { "answer": "Norristown", "outlier_distance_km": 17202.8, "second_furthest_km": 6448.9, "clarity_ratio": 2.67, "median_distance_km": 5502.8, "distances_to_centroid": { "Kallangur": 6448.9, "Mandurah": 3005.1, "Rockingham": 2993.7, "Warrnambool": 5502.8, "Norristown": 17202.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kallangur: (-27.25°, 152.99°)", " Mandurah: (-32.53°, 115.72°)", " Rockingham: (-32.28°, 115.73°)", " Warrnambool: (-38.38°, 142.49°)", " Norristown: (40.12°, -75.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Norristown: 17202.8 km from centroid", " Kallangur: 6448.9 km from centroid", " Warrnambool: 5502.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Norristown", "FINAL ANSWER: Norristown" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.92953, "lon": 151.7801, "name": "Newcastle" }, { "lat": -37.75819, "lon": 145.00583, "name": "Thornbury" }, { "lat": -37.81819, "lon": 145.00176, "name": "Richmond" }, { "lat": -33.91439, "lon": 151.24895, "name": "Randwick" }, { "lat": -26.25, "lon": 29.26, "name": "Kriel" } ], "question": "Which location is the geographic outlier among: Newcastle, Thornbury, Richmond, Randwick, Kriel?", "ground_truth": { "answer": "Kriel", "outlier_distance_km": 8867.2, "second_furthest_km": 2532.4, "clarity_ratio": 3.5, "median_distance_km": 2467.7, "distances_to_centroid": { "Newcastle": 2532.4, "Thornbury": 1903.2, "Richmond": 1903.7, "Randwick": 2467.7, "Kriel": 8867.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Newcastle: (-32.93°, 151.78°)", " Thornbury: (-37.76°, 145.01°)", " Richmond: (-37.82°, 145.00°)", " Randwick: (-33.91°, 151.25°)", " Kriel: (-26.25°, 29.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kriel: 8867.2 km from centroid", " Newcastle: 2532.4 km from centroid", " Randwick: 2467.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kriel", "FINAL ANSWER: Kriel" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -9.62361, "lon": -37.75667, "name": "Piranhas" }, { "lat": -23.5702, "lon": -46.72628, "name": "Butanta" }, { "lat": -3.10222, "lon": -67.93972, "name": "Santo Antônio do Içá" }, { "lat": -3.57972, "lon": -59.13056, "name": "Autazes" }, { "lat": 5.63418, "lon": 38.23603, "name": "Hagere Maryam" } ], "question": "Which location is the geographic outlier among: Piranhas, Butanta, Santo Antônio do Içá, Autazes, Hagere Maryam?", "ground_truth": { "answer": "Hagere Maryam", "outlier_distance_km": 8207.2, "second_furthest_km": 3708.6, "clarity_ratio": 2.21, "median_distance_km": 2733.1, "distances_to_centroid": { "Piranhas": 459.4, "Butanta": 2262.2, "Santo Antônio do Içá": 3708.6, "Autazes": 2733.1, "Hagere Maryam": 8207.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Piranhas: (-9.62°, -37.76°)", " Butanta: (-23.57°, -46.73°)", " Santo Antônio do Içá: (-3.10°, -67.94°)", " Autazes: (-3.58°, -59.13°)", " Hagere Maryam: (5.63°, 38.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hagere Maryam: 8207.2 km from centroid", " Santo Antônio do Içá: 3708.6 km from centroid", " Autazes: 2733.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hagere Maryam", "FINAL ANSWER: Hagere Maryam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.58601, "lon": 26.88329, "name": "Port Alfred" }, { "lat": -30.29831, "lon": 29.93772, "name": "Clydesdale" }, { "lat": 7.25256, "lon": 5.19312, "name": "Akure" }, { "lat": -27.03026, "lon": 28.60061, "name": "Villiers" }, { "lat": 59.59737, "lon": 60.58608, "name": "Serov" } ], "question": "Which location is the geographic outlier among: Port Alfred, Clydesdale, Akure, Villiers, Serov?", "ground_truth": { "answer": "Serov", "outlier_distance_km": 7642.0, "second_furthest_km": 3218.2, "clarity_ratio": 2.37, "median_distance_km": 3086.2, "distances_to_centroid": { "Port Alfred": 3218.2, "Clydesdale": 2834.0, "Akure": 3086.2, "Villiers": 2476.6, "Serov": 7642.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Port Alfred: (-33.59°, 26.88°)", " Clydesdale: (-30.30°, 29.94°)", " Akure: (7.25°, 5.19°)", " Villiers: (-27.03°, 28.60°)", " Serov: (59.60°, 60.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Serov: 7642.0 km from centroid", " Port Alfred: 3218.2 km from centroid", " Akure: 3086.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Serov", "FINAL ANSWER: Serov" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.74761, "lon": -77.08303, "name": "Hybla Valley" }, { "lat": 23.77846, "lon": -105.36038, "name": "El Salto" }, { "lat": 41.4501, "lon": -71.4495, "name": "Narragansett" }, { "lat": 39.06387, "lon": -108.55065, "name": "Grand Junction" }, { "lat": -21.23342, "lon": -45.23488, "name": "Nepomuceno" } ], "question": "Which location is the geographic outlier among: Hybla Valley, El Salto, Narragansett, Grand Junction, Nepomuceno?", "ground_truth": { "answer": "Nepomuceno", "outlier_distance_km": 6411.6, "second_furthest_km": 3015.2, "clarity_ratio": 2.13, "median_distance_km": 2416.7, "distances_to_centroid": { "Hybla Valley": 1653.8, "El Salto": 2416.7, "Narragansett": 2117.0, "Grand Junction": 3015.2, "Nepomuceno": 6411.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hybla Valley: (38.75°, -77.08°)", " El Salto: (23.78°, -105.36°)", " Narragansett: (41.45°, -71.45°)", " Grand Junction: (39.06°, -108.55°)", " Nepomuceno: (-21.23°, -45.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nepomuceno: 6411.6 km from centroid", " Grand Junction: 3015.2 km from centroid", " El Salto: 2416.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nepomuceno", "FINAL ANSWER: Nepomuceno" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.91928, "lon": 145.05301, "name": "Bentleigh East" }, { "lat": -39.93333, "lon": 175.05, "name": "Whanganui" }, { "lat": -41.26667, "lon": 174.95, "name": "Wainuiomata" }, { "lat": -28.00274, "lon": 153.42999, "name": "Surfers Paradise" }, { "lat": 27.43137, "lon": 80.53157, "name": "Misrikh" } ], "question": "Which location is the geographic outlier among: Bentleigh East, Whanganui, Wainuiomata, Surfers Paradise, Misrikh?", "ground_truth": { "answer": "Misrikh", "outlier_distance_km": 9032.6, "second_furthest_km": 3315.5, "clarity_ratio": 2.72, "median_distance_km": 3259.7, "distances_to_centroid": { "Bentleigh East": 1556.3, "Whanganui": 3259.7, "Wainuiomata": 3315.5, "Surfers Paradise": 886.0, "Misrikh": 9032.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bentleigh East: (-37.92°, 145.05°)", " Whanganui: (-39.93°, 175.05°)", " Wainuiomata: (-41.27°, 174.95°)", " Surfers Paradise: (-28.00°, 153.43°)", " Misrikh: (27.43°, 80.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Misrikh: 9032.6 km from centroid", " Wainuiomata: 3315.5 km from centroid", " Whanganui: 3259.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Misrikh", "FINAL ANSWER: Misrikh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 32.01667, "lon": 130.2, "name": "Akune" }, { "lat": 21.0028, "lon": 105.8151, "name": "Vinhomes Royal City" }, { "lat": 30.83424, "lon": 76.57677, "name": "Kūrāli" }, { "lat": 13.71466, "lon": 100.43691, "name": "Phasi Charoen" }, { "lat": -11.33333, "lon": -38.96667, "name": "Araci" } ], "question": "Which location is the geographic outlier among: Akune, Vinhomes Royal City, Kūrāli, Phasi Charoen, Araci?", "ground_truth": { "answer": "Araci", "outlier_distance_km": 12880.7, "second_furthest_km": 5770.0, "clarity_ratio": 2.23, "median_distance_km": 3278.6, "distances_to_centroid": { "Akune": 5770.0, "Vinhomes Royal City": 3278.6, "Kūrāli": 1521.3, "Phasi Charoen": 2771.7, "Araci": 12880.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Akune: (32.02°, 130.20°)", " Vinhomes Royal City: (21.00°, 105.82°)", " Kūrāli: (30.83°, 76.58°)", " Phasi Charoen: (13.71°, 100.44°)", " Araci: (-11.33°, -38.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Araci: 12880.7 km from centroid", " Akune: 5770.0 km from centroid", " Vinhomes Royal City: 3278.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Araci", "FINAL ANSWER: Araci" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.76667, "lon": 150.91667, "name": "Blacktown" }, { "lat": -37.8739, "lon": 145.02485, "name": "Caulfield North" }, { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" }, { "lat": -33.88834, "lon": 151.12274, "name": "Ashfield" }, { "lat": 7.75537, "lon": -0.98085, "name": "Atebubu" } ], "question": "Which location is the geographic outlier among: Blacktown, Caulfield North, Palmerston, Ashfield, Atebubu?", "ground_truth": { "answer": "Atebubu", "outlier_distance_km": 13045.1, "second_furthest_km": 3722.8, "clarity_ratio": 3.5, "median_distance_km": 3701.5, "distances_to_centroid": { "Blacktown": 3701.5, "Caulfield North": 3329.0, "Palmerston": 1963.4, "Ashfield": 3722.8, "Atebubu": 13045.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Blacktown: (-33.77°, 150.92°)", " Caulfield North: (-37.87°, 145.02°)", " Palmerston: (-12.49°, 130.98°)", " Ashfield: (-33.89°, 151.12°)", " Atebubu: (7.76°, -0.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Atebubu: 13045.1 km from centroid", " Ashfield: 3722.8 km from centroid", " Blacktown: 3701.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Atebubu", "FINAL ANSWER: Atebubu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.277, "lon": 39.462, "name": "Ādīgrat" }, { "lat": 7.06273, "lon": -1.4001, "name": "Mampong" }, { "lat": 30.75438, "lon": 31.44016, "name": "Diyarb Najm" }, { "lat": -22.34881, "lon": 30.04074, "name": "Musina" }, { "lat": 42.96339, "lon": -78.80392, "name": "Eggertsville" } ], "question": "Which location is the geographic outlier among: Ādīgrat, Mampong, Diyarb Najm, Musina, Eggertsville?", "ground_truth": { "answer": "Eggertsville", "outlier_distance_km": 8344.8, "second_furthest_km": 4978.5, "clarity_ratio": 1.68, "median_distance_km": 3799.5, "distances_to_centroid": { "Ādīgrat": 3799.5, "Mampong": 1028.7, "Diyarb Najm": 3315.3, "Musina": 4978.5, "Eggertsville": 8344.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ādīgrat: (14.28°, 39.46°)", " Mampong: (7.06°, -1.40°)", " Diyarb Najm: (30.75°, 31.44°)", " Musina: (-22.35°, 30.04°)", " Eggertsville: (42.96°, -78.80°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Eggertsville: 8344.8 km from centroid", " Musina: 4978.5 km from centroid", " Ādīgrat: 3799.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Eggertsville", "FINAL ANSWER: Eggertsville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.98333, "lon": 145.2, "name": "Dandenong" }, { "lat": -37.70462, "lon": 145.10302, "name": "Greensborough" }, { "lat": -38.04369, "lon": 145.2923, "name": "Narre Warren South" }, { "lat": -33.70244, "lon": 151.09931, "name": "Hornsby" }, { "lat": -21.8025, "lon": -49.61, "name": "Cafelândia" } ], "question": "Which location is the geographic outlier among: Dandenong, Greensborough, Narre Warren South, Hornsby, Cafelândia?", "ground_truth": { "answer": "Cafelândia", "outlier_distance_km": 13366.2, "second_furthest_km": 4006.1, "clarity_ratio": 3.34, "median_distance_km": 3417.6, "distances_to_centroid": { "Dandenong": 3410.0, "Greensborough": 3403.8, "Narre Warren South": 3417.6, "Hornsby": 4006.1, "Cafelândia": 13366.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dandenong: (-37.98°, 145.20°)", " Greensborough: (-37.70°, 145.10°)", " Narre Warren South: (-38.04°, 145.29°)", " Hornsby: (-33.70°, 151.10°)", " Cafelândia: (-21.80°, -49.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cafelândia: 13366.2 km from centroid", " Hornsby: 4006.1 km from centroid", " Narre Warren South: 3417.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cafelândia", "FINAL ANSWER: Cafelândia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.02366, "lon": 39.10436, "name": "Pashkovskiy" }, { "lat": 55.66977, "lon": 37.27716, "name": "Odintsovo" }, { "lat": 45.08201, "lon": 7.66485, "name": "San Donato" }, { "lat": 38.09519, "lon": -3.63602, "name": "Linares" }, { "lat": -38.09968, "lon": 145.17248, "name": "Carrum Downs" } ], "question": "Which location is the geographic outlier among: Pashkovskiy, Odintsovo, San Donato, Linares, Carrum Downs?", "ground_truth": { "answer": "Carrum Downs", "outlier_distance_km": 12773.2, "second_furthest_km": 4568.8, "clarity_ratio": 2.8, "median_distance_km": 3718.0, "distances_to_centroid": { "Pashkovskiy": 1842.1, "Odintsovo": 3013.4, "San Donato": 3718.0, "Linares": 4568.8, "Carrum Downs": 12773.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pashkovskiy: (45.02°, 39.10°)", " Odintsovo: (55.67°, 37.28°)", " San Donato: (45.08°, 7.66°)", " Linares: (38.10°, -3.64°)", " Carrum Downs: (-38.10°, 145.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carrum Downs: 12773.2 km from centroid", " Linares: 4568.8 km from centroid", " San Donato: 3718.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carrum Downs", "FINAL ANSWER: Carrum Downs" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.10482, "lon": -70.94532, "name": "Abington" }, { "lat": 44.08385, "lon": -93.22604, "name": "Owatonna" }, { "lat": 28.05502, "lon": -82.60982, "name": "Westchase" }, { "lat": 33.93113, "lon": -117.54866, "name": "Norco" }, { "lat": 53.14657, "lon": 140.72287, "name": "Nikolayevsk-on-Amure" } ], "question": "Which location is the geographic outlier among: Abington, Owatonna, Westchase, Norco, Nikolayevsk-on-Amure?", "ground_truth": { "answer": "Nikolayevsk-on-Amure", "outlier_distance_km": 9615.1, "second_furthest_km": 6314.8, "clarity_ratio": 1.52, "median_distance_km": 3961.6, "distances_to_centroid": { "Abington": 2195.4, "Owatonna": 3961.6, "Westchase": 3707.1, "Norco": 6314.8, "Nikolayevsk-on-Amure": 9615.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Abington: (42.10°, -70.95°)", " Owatonna: (44.08°, -93.23°)", " Westchase: (28.06°, -82.61°)", " Norco: (33.93°, -117.55°)", " Nikolayevsk-on-Amure: (53.15°, 140.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nikolayevsk-on-Amure: 9615.1 km from centroid", " Norco: 6314.8 km from centroid", " Owatonna: 3961.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nikolayevsk-on-Amure", "FINAL ANSWER: Nikolayevsk-on-Amure" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 3.10591, "lon": 101.68683, "name": "Taman Desa" }, { "lat": 30.60369, "lon": 109.72333, "name": "Yezhou" }, { "lat": 6.6925, "lon": 124.67639, "name": "Tacurong" }, { "lat": 27.43818, "lon": 78.03758, "name": "Sadābād" }, { "lat": 19.13325, "lon": -97.64167, "name": "San Salvador El Seco" } ], "question": "Which location is the geographic outlier among: Taman Desa, Yezhou, Tacurong, Sadābād, San Salvador El Seco?", "ground_truth": { "answer": "San Salvador El Seco", "outlier_distance_km": 15450.5, "second_furthest_km": 6753.6, "clarity_ratio": 2.29, "median_distance_km": 4901.8, "distances_to_centroid": { "Taman Desa": 4477.4, "Yezhou": 4901.8, "Tacurong": 6753.6, "Sadābād": 1879.5, "San Salvador El Seco": 15450.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taman Desa: (3.11°, 101.69°)", " Yezhou: (30.60°, 109.72°)", " Tacurong: (6.69°, 124.68°)", " Sadābād: (27.44°, 78.04°)", " San Salvador El Seco: (19.13°, -97.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Salvador El Seco: 15450.5 km from centroid", " Tacurong: 6753.6 km from centroid", " Yezhou: 4901.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Salvador El Seco", "FINAL ANSWER: San Salvador El Seco" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.56667, "lon": 105.68333, "name": "Hồng Lĩnh" }, { "lat": 19.61186, "lon": 76.6874, "name": "Jintūr" }, { "lat": 16.36389, "lon": 120.67694, "name": "Itogon" }, { "lat": 35.75264, "lon": 139.73348, "name": "Kita" }, { "lat": -43.24895, "lon": -65.30505, "name": "Trelew" } ], "question": "Which location is the geographic outlier among: Hồng Lĩnh, Jintūr, Itogon, Kita, Trelew?", "ground_truth": { "answer": "Trelew", "outlier_distance_km": 14675.6, "second_furthest_km": 7080.1, "clarity_ratio": 2.07, "median_distance_km": 4948.0, "distances_to_centroid": { "Hồng Lĩnh": 3406.6, "Jintūr": 1141.7, "Itogon": 4948.0, "Kita": 7080.1, "Trelew": 14675.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hồng Lĩnh: (18.57°, 105.68°)", " Jintūr: (19.61°, 76.69°)", " Itogon: (16.36°, 120.68°)", " Kita: (35.75°, 139.73°)", " Trelew: (-43.25°, -65.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Trelew: 14675.6 km from centroid", " Kita: 7080.1 km from centroid", " Itogon: 4948.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Trelew", "FINAL ANSWER: Trelew" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -11.51056, "lon": -38.15, "name": "Crisópolis" }, { "lat": -23.54476, "lon": -46.64105, "name": "Republica" }, { "lat": -9.70926, "lon": -36.44785, "name": "Cajueiro" }, { "lat": -6.0, "lon": -40.28333, "name": "São João dos Inhamuns" }, { "lat": 17.4, "lon": 73.76667, "name": "Koynanagar" } ], "question": "Which location is the geographic outlier among: Crisópolis, Republica, Cajueiro, São João dos Inhamuns, Koynanagar?", "ground_truth": { "answer": "Koynanagar", "outlier_distance_km": 10368.0, "second_furthest_km": 3629.1, "clarity_ratio": 2.86, "median_distance_km": 2513.2, "distances_to_centroid": { "Crisópolis": 2323.8, "Republica": 3629.1, "Cajueiro": 2106.6, "São João dos Inhamuns": 2513.2, "Koynanagar": 10368.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Crisópolis: (-11.51°, -38.15°)", " Republica: (-23.54°, -46.64°)", " Cajueiro: (-9.71°, -36.45°)", " São João dos Inhamuns: (-6.00°, -40.28°)", " Koynanagar: (17.40°, 73.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Koynanagar: 10368.0 km from centroid", " Republica: 3629.1 km from centroid", " São João dos Inhamuns: 2513.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Koynanagar", "FINAL ANSWER: Koynanagar" ] }, { "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": -9.40917, "lon": -59.025, "name": "Colniza" }, { "lat": -15.74333, "lon": -43.02833, "name": "Porteirinha" }, { "lat": 4.53656, "lon": -75.67263, "name": "Armenia" }, { "lat": -23.60389, "lon": -46.91917, "name": "Cotia" }, { "lat": -33.85, "lon": 151.03333, "name": "Auburn" } ], "question": "Which location is the geographic outlier among: Colniza, Porteirinha, Armenia, Cotia, Auburn?", "ground_truth": { "answer": "Auburn", "outlier_distance_km": 14311.5, "second_furthest_km": 7070.1, "clarity_ratio": 2.02, "median_distance_km": 4849.9, "distances_to_centroid": { "Colniza": 4849.9, "Porteirinha": 3028.1, "Armenia": 7070.1, "Cotia": 3478.9, "Auburn": 14311.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Colniza: (-9.41°, -59.02°)", " Porteirinha: (-15.74°, -43.03°)", " Armenia: (4.54°, -75.67°)", " Cotia: (-23.60°, -46.92°)", " Auburn: (-33.85°, 151.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Auburn: 14311.5 km from centroid", " Armenia: 7070.1 km from centroid", " Colniza: 4849.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Auburn", "FINAL ANSWER: Auburn" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.54389, "lon": -45.77546, "name": "Santa Luzia do Paruá" }, { "lat": -12.60139, "lon": -38.96576, "name": "Cachoeira" }, { "lat": -6.89028, "lon": -38.55528, "name": "Cajazeiras" }, { "lat": -16.25, "lon": -69.08333, "name": "Yunguyo" }, { "lat": 26.61708, "lon": -80.07231, "name": "Lake Worth Beach" } ], "question": "Which location is the geographic outlier among: Santa Luzia do Paruá, Cachoeira, Cajazeiras, Yunguyo, Lake Worth Beach?", "ground_truth": { "answer": "Lake Worth Beach", "outlier_distance_km": 4231.0, "second_furthest_km": 2223.7, "clarity_ratio": 1.9, "median_distance_km": 2055.4, "distances_to_centroid": { "Santa Luzia do Paruá": 968.5, "Cachoeira": 2055.4, "Cajazeiras": 1836.9, "Yunguyo": 2223.7, "Lake Worth Beach": 4231.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Luzia do Paruá: (-2.54°, -45.78°)", " Cachoeira: (-12.60°, -38.97°)", " Cajazeiras: (-6.89°, -38.56°)", " Yunguyo: (-16.25°, -69.08°)", " Lake Worth Beach: (26.62°, -80.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lake Worth Beach: 4231.0 km from centroid", " Yunguyo: 2223.7 km from centroid", " Cachoeira: 2055.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lake Worth Beach", "FINAL ANSWER: Lake Worth Beach" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.88384, "lon": 29.70557, "name": "Mankweng" }, { "lat": 5.01806, "lon": -1.66437, "name": "Shama Junction" }, { "lat": -27.00805, "lon": 27.3646, "name": "Vredefort" }, { "lat": -0.75675, "lon": 34.59833, "name": "Rongo" }, { "lat": 54.91443, "lon": 85.63971, "name": "Promyshlennaya" } ], "question": "Which location is the geographic outlier among: Mankweng, Shama Junction, Vredefort, Rongo, Promyshlennaya?", "ground_truth": { "answer": "Promyshlennaya", "outlier_distance_km": 7461.8, "second_furthest_km": 4100.5, "clarity_ratio": 1.82, "median_distance_km": 3294.2, "distances_to_centroid": { "Mankweng": 2899.9, "Shama Junction": 4100.5, "Vredefort": 3294.2, "Rongo": 274.8, "Promyshlennaya": 7461.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mankweng: (-23.88°, 29.71°)", " Shama Junction: (5.02°, -1.66°)", " Vredefort: (-27.01°, 27.36°)", " Rongo: (-0.76°, 34.60°)", " Promyshlennaya: (54.91°, 85.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Promyshlennaya: 7461.8 km from centroid", " Shama Junction: 4100.5 km from centroid", " Vredefort: 3294.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Promyshlennaya", "FINAL ANSWER: Promyshlennaya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.54783, "lon": -104.0461, "name": "Ameca" }, { "lat": 43.1859, "lon": -76.17243, "name": "Clay" }, { "lat": 44.29496, "lon": -93.26883, "name": "Faribault" }, { "lat": 20.21081, "lon": -101.13212, "name": "Yuriria" }, { "lat": 44.12489, "lon": 4.08082, "name": "Alès" } ], "question": "Which location is the geographic outlier among: Ameca, Clay, Faribault, Yuriria, Alès?", "ground_truth": { "answer": "Alès", "outlier_distance_km": 6559.3, "second_furthest_km": 3315.7, "clarity_ratio": 1.98, "median_distance_km": 3089.5, "distances_to_centroid": { "Ameca": 3315.7, "Clay": 985.1, "Faribault": 1968.3, "Yuriria": 3089.5, "Alès": 6559.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ameca: (20.55°, -104.05°)", " Clay: (43.19°, -76.17°)", " Faribault: (44.29°, -93.27°)", " Yuriria: (20.21°, -101.13°)", " Alès: (44.12°, 4.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alès: 6559.3 km from centroid", " Ameca: 3315.7 km from centroid", " Yuriria: 3089.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alès", "FINAL ANSWER: Alès" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -4.05466, "lon": 39.66359, "name": "Mombasa" }, { "lat": 7.1962, "lon": 5.58681, "name": "Owo" }, { "lat": -28.01274, "lon": 27.08234, "name": "Phomolong" }, { "lat": 5.31667, "lon": 39.58333, "name": "Negēlē" }, { "lat": -38.02388, "lon": 144.40617, "name": "Lara" } ], "question": "Which location is the geographic outlier among: Mombasa, Owo, Phomolong, Negēlē, Lara?", "ground_truth": { "answer": "Lara", "outlier_distance_km": 9493.0, "second_furthest_km": 5464.0, "clarity_ratio": 1.74, "median_distance_km": 3113.8, "distances_to_centroid": { "Mombasa": 1522.9, "Owo": 5464.0, "Phomolong": 3113.8, "Negēlē": 2274.4, "Lara": 9493.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mombasa: (-4.05°, 39.66°)", " Owo: (7.20°, 5.59°)", " Phomolong: (-28.01°, 27.08°)", " Negēlē: (5.32°, 39.58°)", " Lara: (-38.02°, 144.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lara: 9493.0 km from centroid", " Owo: 5464.0 km from centroid", " Phomolong: 3113.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lara", "FINAL ANSWER: Lara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.18333, "lon": 145.08333, "name": "Mount Eliza" }, { "lat": -35.73167, "lon": 174.32391, "name": "Whangarei" }, { "lat": -30.29626, "lon": 153.11351, "name": "Coffs Harbour" }, { "lat": -37.76722, "lon": 144.76657, "name": "Deer Park" }, { "lat": -27.03026, "lon": 28.60061, "name": "Villiers" } ], "question": "Which location is the geographic outlier among: Mount Eliza, Whangarei, Coffs Harbour, Deer Park, Villiers?", "ground_truth": { "answer": "Villiers", "outlier_distance_km": 9260.7, "second_furthest_km": 4092.9, "clarity_ratio": 2.26, "median_distance_km": 2284.0, "distances_to_centroid": { "Mount Eliza": 1509.3, "Whangarei": 4092.9, "Coffs Harbour": 2284.0, "Deer Park": 1471.6, "Villiers": 9260.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mount Eliza: (-38.18°, 145.08°)", " Whangarei: (-35.73°, 174.32°)", " Coffs Harbour: (-30.30°, 153.11°)", " Deer Park: (-37.77°, 144.77°)", " Villiers: (-27.03°, 28.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Villiers: 9260.7 km from centroid", " Whangarei: 4092.9 km from centroid", " Coffs Harbour: 2284.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Villiers", "FINAL ANSWER: Villiers" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.79176, "lon": 151.08057, "name": "Eastwood" }, { "lat": -38.07018, "lon": 145.47411, "name": "Pakenham" }, { "lat": -37.96667, "lon": 145.16667, "name": "Noble Park" }, { "lat": -33.9677, "lon": 151.10149, "name": "Hurstville" }, { "lat": 10.38584, "lon": 8.57286, "name": "Lere" } ], "question": "Which location is the geographic outlier among: Eastwood, Pakenham, Noble Park, Hurstville, Lere?", "ground_truth": { "answer": "Lere", "outlier_distance_km": 12671.1, "second_furthest_km": 3054.4, "clarity_ratio": 4.15, "median_distance_km": 3050.1, "distances_to_centroid": { "Eastwood": 3050.1, "Pakenham": 2671.1, "Noble Park": 2641.8, "Hurstville": 3054.4, "Lere": 12671.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Eastwood: (-33.79°, 151.08°)", " Pakenham: (-38.07°, 145.47°)", " Noble Park: (-37.97°, 145.17°)", " Hurstville: (-33.97°, 151.10°)", " Lere: (10.39°, 8.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lere: 12671.1 km from centroid", " Hurstville: 3054.4 km from centroid", " Eastwood: 3050.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lere", "FINAL ANSWER: Lere" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.92598, "lon": 151.19347, "name": "Mascot" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" }, { "lat": -33.8178, "lon": 151.00348, "name": "Parramatta" }, { "lat": -41.13333, "lon": 174.85, "name": "Porirua" }, { "lat": 45.94541, "lon": -66.66558, "name": "Fredericton" } ], "question": "Which location is the geographic outlier among: Mascot, New Plymouth, Parramatta, Porirua, Fredericton?", "ground_truth": { "answer": "Fredericton", "outlier_distance_km": 17156.0, "second_furthest_km": 5877.2, "clarity_ratio": 2.92, "median_distance_km": 5795.6, "distances_to_centroid": { "Mascot": 3688.8, "New Plymouth": 5795.6, "Parramatta": 3668.7, "Porirua": 5877.2, "Fredericton": 17156.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mascot: (-33.93°, 151.19°)", " New Plymouth: (-39.07°, 174.08°)", " Parramatta: (-33.82°, 151.00°)", " Porirua: (-41.13°, 174.85°)", " Fredericton: (45.95°, -66.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fredericton: 17156.0 km from centroid", " Porirua: 5877.2 km from centroid", " New Plymouth: 5795.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fredericton", "FINAL ANSWER: Fredericton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.09086, "lon": -45.78501, "name": "Luis Eduardo Magalhães" }, { "lat": -10.74167, "lon": -40.36083, "name": "Pindobaçu" }, { "lat": 5.01789, "lon": -72.74675, "name": "Tauramena" }, { "lat": -38.90056, "lon": -70.06674, "name": "Zapala" }, { "lat": -37.8739, "lon": 145.02485, "name": "Caulfield North" } ], "question": "Which location is the geographic outlier among: Luis Eduardo Magalhães, Pindobaçu, Tauramena, Zapala, Caulfield North?", "ground_truth": { "answer": "Caulfield North", "outlier_distance_km": 13420.0, "second_furthest_km": 6677.9, "clarity_ratio": 2.01, "median_distance_km": 5551.5, "distances_to_centroid": { "Luis Eduardo Magalhães": 3193.9, "Pindobaçu": 2688.6, "Tauramena": 6677.9, "Zapala": 5551.5, "Caulfield North": 13420.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Luis Eduardo Magalhães: (-12.09°, -45.79°)", " Pindobaçu: (-10.74°, -40.36°)", " Tauramena: (5.02°, -72.75°)", " Zapala: (-38.90°, -70.07°)", " Caulfield North: (-37.87°, 145.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Caulfield North: 13420.0 km from centroid", " Tauramena: 6677.9 km from centroid", " Zapala: 5551.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Caulfield North", "FINAL ANSWER: Caulfield North" ] }, { "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": 19.28431, "lon": -98.43885, "name": "San Martin Texmelucan de Labastida" }, { "lat": 25.79698, "lon": -100.31791, "name": "Ciudad General Escobedo" }, { "lat": 30.60353, "lon": -87.9036, "name": "Daphne" }, { "lat": 15.13924, "lon": -92.4634, "name": "Huixtla" }, { "lat": -7.0868, "lon": 110.9158, "name": "Purwodadi" } ], "question": "Which location is the geographic outlier among: San Martin Texmelucan de Labastida, Ciudad General Escobedo, Daphne, Huixtla, Purwodadi?", "ground_truth": { "answer": "Purwodadi", "outlier_distance_km": 18023.0, "second_furthest_km": 4914.6, "clarity_ratio": 3.67, "median_distance_km": 4732.7, "distances_to_centroid": { "San Martin Texmelucan de Labastida": 4732.7, "Ciudad General Escobedo": 4914.6, "Daphne": 3793.8, "Huixtla": 4148.2, "Purwodadi": 18023.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Martin Texmelucan de Labastida: (19.28°, -98.44°)", " Ciudad General Escobedo: (25.80°, -100.32°)", " Daphne: (30.60°, -87.90°)", " Huixtla: (15.14°, -92.46°)", " Purwodadi: (-7.09°, 110.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Purwodadi: 18023.0 km from centroid", " Ciudad General Escobedo: 4914.6 km from centroid", " San Martin Texmelucan de Labastida: 4732.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Purwodadi", "FINAL ANSWER: Purwodadi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.20333, "lon": -52.20639, "name": "Altamira" }, { "lat": 4.9825, "lon": -75.60361, "name": "Chinchiná" }, { "lat": -17.74431, "lon": -48.62789, "name": "Caldas Novas" }, { "lat": -23.56675, "lon": -46.66439, "name": "Jardim Paulista" }, { "lat": 28.55023, "lon": 79.31761, "name": "Shāhi" } ], "question": "Which location is the geographic outlier among: Altamira, Chinchiná, Caldas Novas, Jardim Paulista, Shāhi?", "ground_truth": { "answer": "Shāhi", "outlier_distance_km": 11886.3, "second_furthest_km": 5264.9, "clarity_ratio": 2.26, "median_distance_km": 3059.8, "distances_to_centroid": { "Altamira": 2606.9, "Chinchiná": 5264.9, "Caldas Novas": 2773.3, "Jardim Paulista": 3059.8, "Shāhi": 11886.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Altamira: (-3.20°, -52.21°)", " Chinchiná: (4.98°, -75.60°)", " Caldas Novas: (-17.74°, -48.63°)", " Jardim Paulista: (-23.57°, -46.66°)", " Shāhi: (28.55°, 79.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shāhi: 11886.3 km from centroid", " Chinchiná: 5264.9 km from centroid", " Jardim Paulista: 3059.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shāhi", "FINAL ANSWER: Shāhi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.69689, "lon": 7.46809, "name": "Selm" }, { "lat": 55.52771, "lon": 45.45679, "name": "Sergach" }, { "lat": 52.25443, "lon": 21.03472, "name": "Praga Północ" }, { "lat": 53.27096, "lon": 34.32143, "name": "Bryansk" }, { "lat": -0.56333, "lon": 34.93583, "name": "Nyamira" } ], "question": "Which location is the geographic outlier among: Selm, Sergach, Praga Północ, Bryansk, Nyamira?", "ground_truth": { "answer": "Nyamira", "outlier_distance_km": 4822.8, "second_furthest_km": 1895.1, "clarity_ratio": 2.54, "median_distance_km": 1893.5, "distances_to_centroid": { "Selm": 1895.1, "Sergach": 1893.5, "Praga Północ": 1231.4, "Bryansk": 1276.0, "Nyamira": 4822.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Selm: (51.70°, 7.47°)", " Sergach: (55.53°, 45.46°)", " Praga Północ: (52.25°, 21.03°)", " Bryansk: (53.27°, 34.32°)", " Nyamira: (-0.56°, 34.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nyamira: 4822.8 km from centroid", " Selm: 1895.1 km from centroid", " Sergach: 1893.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nyamira", "FINAL ANSWER: Nyamira" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -18.16583, "lon": -47.94639, "name": "Catalão" }, { "lat": -16.32667, "lon": -48.95278, "name": "Anápolis" }, { "lat": -11.6725, "lon": -61.19361, "name": "Pimenta Bueno" }, { "lat": -19.22444, "lon": -44.93528, "name": "Pompéu" }, { "lat": -45.87416, "lon": 170.50361, "name": "Dunedin" } ], "question": "Which location is the geographic outlier among: Catalão, Anápolis, Pimenta Bueno, Pompéu, Dunedin?", "ground_truth": { "answer": "Dunedin", "outlier_distance_km": 12433.7, "second_furthest_km": 5903.6, "clarity_ratio": 2.11, "median_distance_km": 4489.2, "distances_to_centroid": { "Catalão": 4335.2, "Anápolis": 4489.2, "Pimenta Bueno": 5903.6, "Pompéu": 4000.1, "Dunedin": 12433.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Catalão: (-18.17°, -47.95°)", " Anápolis: (-16.33°, -48.95°)", " Pimenta Bueno: (-11.67°, -61.19°)", " Pompéu: (-19.22°, -44.94°)", " Dunedin: (-45.87°, 170.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dunedin: 12433.7 km from centroid", " Pimenta Bueno: 5903.6 km from centroid", " Anápolis: 4489.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dunedin", "FINAL ANSWER: Dunedin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.27519, "lon": -89.78117, "name": "Slidell" }, { "lat": 42.33437, "lon": -71.10845, "name": "Mission Hill" }, { "lat": 33.93196, "lon": -117.94617, "name": "La Habra" }, { "lat": 37.29347, "lon": -80.05476, "name": "Salem" }, { "lat": -36.96587, "lon": 174.82389, "name": "Mangere East" } ], "question": "Which location is the geographic outlier among: Slidell, Mission Hill, La Habra, Salem, Mangere East?", "ground_truth": { "answer": "Mangere East", "outlier_distance_km": 16512.3, "second_furthest_km": 7915.3, "clarity_ratio": 2.09, "median_distance_km": 5346.3, "distances_to_centroid": { "Slidell": 5346.3, "Mission Hill": 3947.1, "La Habra": 7915.3, "Salem": 4502.5, "Mangere East": 16512.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Slidell: (30.28°, -89.78°)", " Mission Hill: (42.33°, -71.11°)", " La Habra: (33.93°, -117.95°)", " Salem: (37.29°, -80.05°)", " Mangere East: (-36.97°, 174.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mangere East: 16512.3 km from centroid", " La Habra: 7915.3 km from centroid", " Slidell: 5346.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mangere East", "FINAL ANSWER: Mangere East" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.7457, "lon": 151.04764, "name": "West Pennant Hills" }, { "lat": -37.82289, "lon": 147.61041, "name": "Bairnsdale" }, { "lat": -37.98333, "lon": 145.2, "name": "Dandenong" }, { "lat": -33.86482, "lon": 151.20773, "name": "Sydney Central Business District" }, { "lat": 42.3751, "lon": -71.10561, "name": "Cambridge" } ], "question": "Which location is the geographic outlier among: West Pennant Hills, Bairnsdale, Dandenong, Sydney Central Business District, Cambridge?", "ground_truth": { "answer": "Cambridge", "outlier_distance_km": 17520.4, "second_furthest_km": 4796.7, "clarity_ratio": 3.65, "median_distance_km": 4780.6, "distances_to_centroid": { "West Pennant Hills": 4780.6, "Bairnsdale": 4550.6, "Dandenong": 4350.1, "Sydney Central Business District": 4796.7, "Cambridge": 17520.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " West Pennant Hills: (-33.75°, 151.05°)", " Bairnsdale: (-37.82°, 147.61°)", " Dandenong: (-37.98°, 145.20°)", " Sydney Central Business District: (-33.86°, 151.21°)", " Cambridge: (42.38°, -71.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cambridge: 17520.4 km from centroid", " Sydney Central Business District: 4796.7 km from centroid", " West Pennant Hills: 4780.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cambridge", "FINAL ANSWER: Cambridge" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.83333, "lon": 145.05, "name": "Glenferrie" }, { "lat": -27.46794, "lon": 153.02809, "name": "Brisbane" }, { "lat": -36.88041, "lon": 174.79819, "name": "Remuera" }, { "lat": -33.95, "lon": 151.13333, "name": "Rockdale" }, { "lat": 46.57472, "lon": 131.39318, "name": "Baoshan" } ], "question": "Which location is the geographic outlier among: Glenferrie, Brisbane, Remuera, Rockdale, Baoshan?", "ground_truth": { "answer": "Baoshan", "outlier_distance_km": 7437.8, "second_furthest_km": 3134.3, "clarity_ratio": 2.37, "median_distance_km": 2291.7, "distances_to_centroid": { "Glenferrie": 2291.7, "Brisbane": 1081.2, "Remuera": 3134.3, "Rockdale": 1783.4, "Baoshan": 7437.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Glenferrie: (-37.83°, 145.05°)", " Brisbane: (-27.47°, 153.03°)", " Remuera: (-36.88°, 174.80°)", " Rockdale: (-33.95°, 151.13°)", " Baoshan: (46.57°, 131.39°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Baoshan: 7437.8 km from centroid", " Remuera: 3134.3 km from centroid", " Glenferrie: 2291.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Baoshan", "FINAL ANSWER: Baoshan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 27.3126, "lon": 30.96987, "name": "Manfalūţ" }, { "lat": 7.94783, "lon": 4.78836, "name": "Otan Ayegbaju" }, { "lat": 29.30995, "lon": 30.8418, "name": "Al Fayyum" }, { "lat": -28.70025, "lon": 26.4581, "name": "Winnie Mandela" }, { "lat": 29.42412, "lon": -98.49363, "name": "San Antonio" } ], "question": "Which location is the geographic outlier among: Manfalūţ, Otan Ayegbaju, Al Fayyum, Winnie Mandela, San Antonio?", "ground_truth": { "answer": "San Antonio", "outlier_distance_km": 9997.2, "second_furthest_km": 5507.1, "clarity_ratio": 1.82, "median_distance_km": 3752.1, "distances_to_centroid": { "Manfalūţ": 3686.2, "Otan Ayegbaju": 857.5, "Al Fayyum": 3752.1, "Winnie Mandela": 5507.1, "San Antonio": 9997.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Manfalūţ: (27.31°, 30.97°)", " Otan Ayegbaju: (7.95°, 4.79°)", " Al Fayyum: (29.31°, 30.84°)", " Winnie Mandela: (-28.70°, 26.46°)", " San Antonio: (29.42°, -98.49°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Antonio: 9997.2 km from centroid", " Winnie Mandela: 5507.1 km from centroid", " Al Fayyum: 3752.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Antonio", "FINAL ANSWER: San Antonio" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.26667, "lon": -73.91667, "name": "La Mesa" }, { "lat": -6.45833, "lon": -37.09778, "name": "Caicó" }, { "lat": -7.16378, "lon": -78.50027, "name": "Cajamarca" }, { "lat": -22.76111, "lon": -47.15417, "name": "Paulínia" }, { "lat": 34.76062, "lon": 127.66215, "name": "Yeosu" } ], "question": "Which location is the geographic outlier among: La Mesa, Caicó, Cajamarca, Paulínia, Yeosu?", "ground_truth": { "answer": "Yeosu", "outlier_distance_km": 14950.2, "second_furthest_km": 6349.6, "clarity_ratio": 2.35, "median_distance_km": 5806.9, "distances_to_centroid": { "La Mesa": 5806.9, "Caicó": 1876.3, "Cajamarca": 6349.6, "Paulínia": 3788.7, "Yeosu": 14950.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " La Mesa: (5.27°, -73.92°)", " Caicó: (-6.46°, -37.10°)", " Cajamarca: (-7.16°, -78.50°)", " Paulínia: (-22.76°, -47.15°)", " Yeosu: (34.76°, 127.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yeosu: 14950.2 km from centroid", " Cajamarca: 6349.6 km from centroid", " La Mesa: 5806.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yeosu", "FINAL ANSWER: Yeosu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.46579, "lon": 9.84344, "name": "Neugraben-Fischbek" }, { "lat": 37.33791, "lon": -5.83951, "name": "Alcalá de Guadaira" }, { "lat": 48.80263, "lon": 44.47491, "name": "Gorodishche" }, { "lat": 47.19058, "lon": -1.56885, "name": "Rezé" }, { "lat": 10.9499, "lon": 79.35607, "name": "Dārāsuram" } ], "question": "Which location is the geographic outlier among: Neugraben-Fischbek, Alcalá de Guadaira, Gorodishche, Rezé, Dārāsuram?", "ground_truth": { "answer": "Dārāsuram", "outlier_distance_km": 6183.5, "second_furthest_km": 2705.5, "clarity_ratio": 2.29, "median_distance_km": 2314.3, "distances_to_centroid": { "Neugraben-Fischbek": 1936.8, "Alcalá de Guadaira": 2705.5, "Gorodishche": 1838.0, "Rezé": 2314.3, "Dārāsuram": 6183.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Neugraben-Fischbek: (53.47°, 9.84°)", " Alcalá de Guadaira: (37.34°, -5.84°)", " Gorodishche: (48.80°, 44.47°)", " Rezé: (47.19°, -1.57°)", " Dārāsuram: (10.95°, 79.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dārāsuram: 6183.5 km from centroid", " Alcalá de Guadaira: 2705.5 km from centroid", " Rezé: 2314.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dārāsuram", "FINAL ANSWER: Dārāsuram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.87394, "lon": 26.69072, "name": "Odendaalsrus" }, { "lat": 10.08333, "lon": 39.03333, "name": "‘Alem Ketema" }, { "lat": 6.73156, "lon": -1.6137, "name": "Tafo" }, { "lat": 5.96667, "lon": 41.03333, "name": "Ara Ali" }, { "lat": -3.78514, "lon": 103.54279, "name": "Lahat" } ], "question": "Which location is the geographic outlier among: Odendaalsrus, ‘Alem Ketema, Tafo, Ara Ali, Lahat?", "ground_truth": { "answer": "Lahat", "outlier_distance_km": 6866.8, "second_furthest_km": 4903.3, "clarity_ratio": 1.4, "median_distance_km": 3313.8, "distances_to_centroid": { "Odendaalsrus": 3313.8, "‘Alem Ketema": 1352.2, "Tafo": 4903.3, "Ara Ali": 864.4, "Lahat": 6866.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Odendaalsrus: (-27.87°, 26.69°)", " ‘Alem Ketema: (10.08°, 39.03°)", " Tafo: (6.73°, -1.61°)", " Ara Ali: (5.97°, 41.03°)", " Lahat: (-3.79°, 103.54°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lahat: 6866.8 km from centroid", " Tafo: 4903.3 km from centroid", " Odendaalsrus: 3313.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lahat", "FINAL ANSWER: Lahat" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -6.18667, "lon": -35.09194, "name": "Tibau do Sul" }, { "lat": -13.94697, "lon": -39.10257, "name": "Camamu" }, { "lat": -18.91806, "lon": -54.84417, "name": "Rio Verde de Mato Grosso" }, { "lat": -29.98972, "lon": -52.37806, "name": "Rio Pardo" }, { "lat": 48.78716, "lon": 2.40332, "name": "Vitry-sur-Seine" } ], "question": "Which location is the geographic outlier among: Tibau do Sul, Camamu, Rio Verde de Mato Grosso, Rio Pardo, Vitry-sur-Seine?", "ground_truth": { "answer": "Vitry-sur-Seine", "outlier_distance_km": 6938.6, "second_furthest_km": 3369.7, "clarity_ratio": 2.06, "median_distance_km": 2647.5, "distances_to_centroid": { "Tibau do Sul": 250.2, "Camamu": 1158.4, "Rio Verde de Mato Grosso": 2647.5, "Rio Pardo": 3369.7, "Vitry-sur-Seine": 6938.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tibau do Sul: (-6.19°, -35.09°)", " Camamu: (-13.95°, -39.10°)", " Rio Verde de Mato Grosso: (-18.92°, -54.84°)", " Rio Pardo: (-29.99°, -52.38°)", " Vitry-sur-Seine: (48.79°, 2.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vitry-sur-Seine: 6938.6 km from centroid", " Rio Pardo: 3369.7 km from centroid", " Rio Verde de Mato Grosso: 2647.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vitry-sur-Seine", "FINAL ANSWER: Vitry-sur-Seine" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.41944, "lon": -51.42444, "name": "Arapongas" }, { "lat": -17.84222, "lon": -42.07667, "name": "Malacacheta" }, { "lat": 11.23855, "lon": -74.19427, "name": "Santa Marta" }, { "lat": -24.00028, "lon": -51.31944, "name": "Faxinal" }, { "lat": 15.2921, "lon": 120.65498, "name": "San Vicente" } ], "question": "Which location is the geographic outlier among: Arapongas, Malacacheta, Santa Marta, Faxinal, San Vicente?", "ground_truth": { "answer": "San Vicente", "outlier_distance_km": 15618.8, "second_furthest_km": 6390.0, "clarity_ratio": 2.44, "median_distance_km": 3821.7, "distances_to_centroid": { "Arapongas": 3806.8, "Malacacheta": 2672.3, "Santa Marta": 6390.0, "Faxinal": 3821.7, "San Vicente": 15618.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Arapongas: (-23.42°, -51.42°)", " Malacacheta: (-17.84°, -42.08°)", " Santa Marta: (11.24°, -74.19°)", " Faxinal: (-24.00°, -51.32°)", " San Vicente: (15.29°, 120.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Vicente: 15618.8 km from centroid", " Santa Marta: 6390.0 km from centroid", " Faxinal: 3821.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Vicente", "FINAL ANSWER: San Vicente" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -5.19889, "lon": -35.46083, "name": "Touros" }, { "lat": -6.87444, "lon": -39.875, "name": "Assaré" }, { "lat": -39.28569, "lon": -72.2279, "name": "Villarrica" }, { "lat": -12.89444, "lon": -38.32722, "name": "Lauro de Freitas" }, { "lat": -33.78333, "lon": 150.93333, "name": "Seven Hills" } ], "question": "Which location is the geographic outlier among: Touros, Assaré, Villarrica, Lauro de Freitas, Seven Hills?", "ground_truth": { "answer": "Seven Hills", "outlier_distance_km": 13633.9, "second_furthest_km": 6539.3, "clarity_ratio": 2.08, "median_distance_km": 3820.1, "distances_to_centroid": { "Touros": 3472.5, "Assaré": 3820.1, "Villarrica": 6539.3, "Lauro de Freitas": 3421.8, "Seven Hills": 13633.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Touros: (-5.20°, -35.46°)", " Assaré: (-6.87°, -39.88°)", " Villarrica: (-39.29°, -72.23°)", " Lauro de Freitas: (-12.89°, -38.33°)", " Seven Hills: (-33.78°, 150.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Seven Hills: 13633.9 km from centroid", " Villarrica: 6539.3 km from centroid", " Assaré: 3820.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Seven Hills", "FINAL ANSWER: Seven Hills" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.19361, "lon": -49.38389, "name": "Piraju" }, { "lat": -12.05354, "lon": -77.09802, "name": "Carmen De La Legua Reynoso" }, { "lat": 9.24391, "lon": -75.14675, "name": "San Luis de Sincé" }, { "lat": -22.41139, "lon": -47.56139, "name": "Rio Claro" }, { "lat": 51.48167, "lon": 5.66111, "name": "Helmond" } ], "question": "Which location is the geographic outlier among: Piraju, Carmen De La Legua Reynoso, San Luis de Sincé, Rio Claro, Helmond?", "ground_truth": { "answer": "Helmond", "outlier_distance_km": 7584.8, "second_furthest_km": 3436.3, "clarity_ratio": 2.21, "median_distance_km": 3079.5, "distances_to_centroid": { "Piraju": 2648.2, "Carmen De La Legua Reynoso": 3436.3, "San Luis de Sincé": 3079.5, "Rio Claro": 2563.2, "Helmond": 7584.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Piraju: (-23.19°, -49.38°)", " Carmen De La Legua Reynoso: (-12.05°, -77.10°)", " San Luis de Sincé: (9.24°, -75.15°)", " Rio Claro: (-22.41°, -47.56°)", " Helmond: (51.48°, 5.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Helmond: 7584.8 km from centroid", " Carmen De La Legua Reynoso: 3436.3 km from centroid", " San Luis de Sincé: 3079.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Helmond", "FINAL ANSWER: Helmond" ] }, { "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": 29.35896, "lon": 30.68061, "name": "Ibshawāy" }, { "lat": 10.71668, "lon": 39.86997, "name": "Kemisē" }, { "lat": -32.78749, "lon": 26.8344, "name": "Alice" }, { "lat": 7.12294, "lon": 40.00412, "name": "Bale Robe" }, { "lat": 41.44144, "lon": -81.8643, "name": "Fairview Park" } ], "question": "Which location is the geographic outlier among: Ibshawāy, Kemisē, Alice, Bale Robe, Fairview Park?", "ground_truth": { "answer": "Fairview Park", "outlier_distance_km": 9432.6, "second_furthest_km": 5165.2, "clarity_ratio": 1.83, "median_distance_km": 3202.8, "distances_to_centroid": { "Ibshawāy": 2864.5, "Kemisē": 3139.5, "Alice": 5165.2, "Bale Robe": 3202.8, "Fairview Park": 9432.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ibshawāy: (29.36°, 30.68°)", " Kemisē: (10.72°, 39.87°)", " Alice: (-32.79°, 26.83°)", " Bale Robe: (7.12°, 40.00°)", " Fairview Park: (41.44°, -81.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fairview Park: 9432.6 km from centroid", " Alice: 5165.2 km from centroid", " Bale Robe: 3202.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fairview Park", "FINAL ANSWER: Fairview Park" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.28861, "lon": -50.34, "name": "Birigui" }, { "lat": -23.69389, "lon": -46.565, "name": "São Bernardo do Campo" }, { "lat": -3.6707, "lon": -45.84749, "name": "Alto Alegre do Pindaré" }, { "lat": -26.74056, "lon": -49.17694, "name": "Pomerode" }, { "lat": 5.6, "lon": 100.65, "name": "Kuala Ketil" } ], "question": "Which location is the geographic outlier among: Birigui, São Bernardo do Campo, Alto Alegre do Pindaré, Pomerode, Kuala Ketil?", "ground_truth": { "answer": "Kuala Ketil", "outlier_distance_km": 13273.0, "second_furthest_km": 3509.9, "clarity_ratio": 3.78, "median_distance_km": 3489.4, "distances_to_centroid": { "Birigui": 3489.4, "São Bernardo do Campo": 3162.4, "Alto Alegre do Pindaré": 3235.7, "Pomerode": 3509.9, "Kuala Ketil": 13273.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Birigui: (-21.29°, -50.34°)", " São Bernardo do Campo: (-23.69°, -46.56°)", " Alto Alegre do Pindaré: (-3.67°, -45.85°)", " Pomerode: (-26.74°, -49.18°)", " Kuala Ketil: (5.60°, 100.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kuala Ketil: 13273.0 km from centroid", " Pomerode: 3509.9 km from centroid", " Birigui: 3489.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kuala Ketil", "FINAL ANSWER: Kuala Ketil" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.64621, "lon": -73.97069, "name": "Kensington" }, { "lat": 35.59412, "lon": -119.34095, "name": "Wasco" }, { "lat": 39.58471, "lon": -104.90109, "name": "Castlewood" }, { "lat": 18.83036, "lon": -97.156, "name": "Río Blanco" }, { "lat": 43.83125, "lon": 5.03586, "name": "Cavaillon" } ], "question": "Which location is the geographic outlier among: Kensington, Wasco, Castlewood, Río Blanco, Cavaillon?", "ground_truth": { "answer": "Cavaillon", "outlier_distance_km": 6858.1, "second_furthest_km": 3701.3, "clarity_ratio": 1.85, "median_distance_km": 2650.3, "distances_to_centroid": { "Kensington": 656.3, "Wasco": 3701.3, "Castlewood": 2392.7, "Río Blanco": 2650.3, "Cavaillon": 6858.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kensington: (40.65°, -73.97°)", " Wasco: (35.59°, -119.34°)", " Castlewood: (39.58°, -104.90°)", " Río Blanco: (18.83°, -97.16°)", " Cavaillon: (43.83°, 5.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cavaillon: 6858.1 km from centroid", " Wasco: 3701.3 km from centroid", " Río Blanco: 2650.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cavaillon", "FINAL ANSWER: Cavaillon" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.93537, "lon": -89.01802, "name": "Izamal" }, { "lat": 41.75003, "lon": -87.80422, "name": "Bridgeview" }, { "lat": 19.02867, "lon": -98.27698, "name": "San Bernardino Tlaxcalancingo" }, { "lat": 40.84954, "lon": -73.90569, "name": "Tremont" }, { "lat": -37.81667, "lon": 144.75, "name": "Truganina" } ], "question": "Which location is the geographic outlier among: Izamal, Bridgeview, San Bernardino Tlaxcalancingo, Tremont, Truganina?", "ground_truth": { "answer": "Truganina", "outlier_distance_km": 17631.1, "second_furthest_km": 6050.7, "clarity_ratio": 2.91, "median_distance_km": 5232.6, "distances_to_centroid": { "Izamal": 5067.1, "Bridgeview": 5232.6, "San Bernardino Tlaxcalancingo": 6050.7, "Tremont": 4130.0, "Truganina": 17631.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Izamal: (20.94°, -89.02°)", " Bridgeview: (41.75°, -87.80°)", " San Bernardino Tlaxcalancingo: (19.03°, -98.28°)", " Tremont: (40.85°, -73.91°)", " Truganina: (-37.82°, 144.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Truganina: 17631.1 km from centroid", " San Bernardino Tlaxcalancingo: 6050.7 km from centroid", " Bridgeview: 5232.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Truganina", "FINAL ANSWER: Truganina" ] }, { "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": -36.88333, "lon": 174.7, "name": "Avondale" }, { "lat": -31.84062, "lon": 115.89549, "name": "Ballajura" }, { "lat": -27.94402, "lon": 153.39815, "name": "Labrador" }, { "lat": -36.8, "lon": 174.75, "name": "North Shore" }, { "lat": -34.15152, "lon": 19.01509, "name": "Grabouw" } ], "question": "Which location is the geographic outlier among: Avondale, Ballajura, Labrador, North Shore, Grabouw?", "ground_truth": { "answer": "Grabouw", "outlier_distance_km": 9428.8, "second_furthest_km": 4262.7, "clarity_ratio": 2.21, "median_distance_km": 4256.7, "distances_to_centroid": { "Avondale": 4256.7, "Ballajura": 1106.2, "Labrador": 2539.7, "North Shore": 4262.7, "Grabouw": 9428.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Avondale: (-36.88°, 174.70°)", " Ballajura: (-31.84°, 115.90°)", " Labrador: (-27.94°, 153.40°)", " North Shore: (-36.80°, 174.75°)", " Grabouw: (-34.15°, 19.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Grabouw: 9428.8 km from centroid", " North Shore: 4262.7 km from centroid", " Avondale: 4256.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Grabouw", "FINAL ANSWER: Grabouw" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.34772, "lon": -120.60908, "name": "Atwater" }, { "lat": 41.93808, "lon": -88.40452, "name": "Wasco" }, { "lat": 33.74021, "lon": -86.64938, "name": "Dixiana" }, { "lat": 34.01434, "lon": -86.00639, "name": "Gadsden" }, { "lat": -43.30437, "lon": 172.58356, "name": "Rangiora" } ], "question": "Which location is the geographic outlier among: Atwater, Wasco, Dixiana, Gadsden, Rangiora?", "ground_truth": { "answer": "Rangiora", "outlier_distance_km": 15963.1, "second_furthest_km": 7665.4, "clarity_ratio": 2.08, "median_distance_km": 4933.9, "distances_to_centroid": { "Atwater": 7665.4, "Wasco": 4933.9, "Dixiana": 4621.5, "Gadsden": 4566.1, "Rangiora": 15963.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Atwater: (37.35°, -120.61°)", " Wasco: (41.94°, -88.40°)", " Dixiana: (33.74°, -86.65°)", " Gadsden: (34.01°, -86.01°)", " Rangiora: (-43.30°, 172.58°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rangiora: 15963.1 km from centroid", " Atwater: 7665.4 km from centroid", " Wasco: 4933.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rangiora", "FINAL ANSWER: Rangiora" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" }, { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" }, { "lat": -37.86667, "lon": 145.28333, "name": "Boronia" }, { "lat": -38.18333, "lon": 145.08333, "name": "Mount Eliza" }, { "lat": 48.7, "lon": 9.01667, "name": "Sindelfingen" } ], "question": "Which location is the geographic outlier among: Dianella, Lower Hutt, Boronia, Mount Eliza, Sindelfingen?", "ground_truth": { "answer": "Sindelfingen", "outlier_distance_km": 13053.2, "second_furthest_km": 5809.1, "clarity_ratio": 2.25, "median_distance_km": 3287.3, "distances_to_centroid": { "Dianella": 1329.4, "Lower Hutt": 5809.1, "Boronia": 3285.1, "Mount Eliza": 3287.3, "Sindelfingen": 13053.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dianella: (-31.89°, 115.87°)", " Lower Hutt: (-41.22°, 174.92°)", " Boronia: (-37.87°, 145.28°)", " Mount Eliza: (-38.18°, 145.08°)", " Sindelfingen: (48.70°, 9.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sindelfingen: 13053.2 km from centroid", " Lower Hutt: 5809.1 km from centroid", " Mount Eliza: 3287.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sindelfingen", "FINAL ANSWER: Sindelfingen" ] }, { "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": 26.45352, "lon": 87.02744, "name": "Bhawanipur" }, { "lat": 10.77269, "lon": 79.6368, "name": "Thiruvarur" }, { "lat": 11.23725, "lon": 79.73585, "name": "Sīrkāzhi" }, { "lat": 9.04298, "lon": 76.52297, "name": "Ayanavelikulangara Vadakku" }, { "lat": 7.60039, "lon": 4.19264, "name": "Olupona" } ], "question": "Which location is the geographic outlier among: Bhawanipur, Thiruvarur, Sīrkāzhi, Ayanavelikulangara Vadakku, Olupona?", "ground_truth": { "answer": "Olupona", "outlier_distance_km": 6711.4, "second_furthest_km": 2702.6, "clarity_ratio": 2.48, "median_distance_km": 1568.3, "distances_to_centroid": { "Bhawanipur": 2702.6, "Thiruvarur": 1566.3, "Sīrkāzhi": 1568.3, "Ayanavelikulangara Vadakku": 1289.4, "Olupona": 6711.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bhawanipur: (26.45°, 87.03°)", " Thiruvarur: (10.77°, 79.64°)", " Sīrkāzhi: (11.24°, 79.74°)", " Ayanavelikulangara Vadakku: (9.04°, 76.52°)", " Olupona: (7.60°, 4.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Olupona: 6711.4 km from centroid", " Bhawanipur: 2702.6 km from centroid", " Sīrkāzhi: 1568.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Olupona", "FINAL ANSWER: Olupona" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 32.93429, "lon": -97.07807, "name": "Grapevine" }, { "lat": 41.45532, "lon": -81.91792, "name": "Westlake" }, { "lat": 31.31716, "lon": -113.53799, "name": "Puerto Peñasco" }, { "lat": 33.44179, "lon": -94.03769, "name": "Texarkana" }, { "lat": -12.36333, "lon": -44.97333, "name": "São Desidério" } ], "question": "Which location is the geographic outlier among: Grapevine, Westlake, Puerto Peñasco, Texarkana, São Desidério?", "ground_truth": { "answer": "São Desidério", "outlier_distance_km": 6135.1, "second_furthest_km": 2738.3, "clarity_ratio": 2.24, "median_distance_km": 1835.2, "distances_to_centroid": { "Grapevine": 1341.6, "Westlake": 1835.2, "Puerto Peñasco": 2738.3, "Texarkana": 1169.1, "São Desidério": 6135.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Grapevine: (32.93°, -97.08°)", " Westlake: (41.46°, -81.92°)", " Puerto Peñasco: (31.32°, -113.54°)", " Texarkana: (33.44°, -94.04°)", " São Desidério: (-12.36°, -44.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São Desidério: 6135.1 km from centroid", " Puerto Peñasco: 2738.3 km from centroid", " Westlake: 1835.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São Desidério", "FINAL ANSWER: São Desidério" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.97549, "lon": 75.36453, "name": "Kalliyasshēri" }, { "lat": 22.69385, "lon": 72.86157, "name": "Nadiād" }, { "lat": 25.44126, "lon": 74.56979, "name": "Māndal" }, { "lat": 37.84608, "lon": 139.23039, "name": "Suibara" }, { "lat": -37.76667, "lon": 144.91667, "name": "Moonee Ponds" } ], "question": "Which location is the geographic outlier among: Kalliyasshēri, Nadiād, Māndal, Suibara, Moonee Ponds?", "ground_truth": { "answer": "Moonee Ponds", "outlier_distance_km": 7155.8, "second_furthest_km": 4720.4, "clarity_ratio": 1.52, "median_distance_km": 3243.1, "distances_to_centroid": { "Kalliyasshēri": 2829.4, "Nadiād": 3243.1, "Māndal": 3183.0, "Suibara": 4720.4, "Moonee Ponds": 7155.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kalliyasshēri: (11.98°, 75.36°)", " Nadiād: (22.69°, 72.86°)", " Māndal: (25.44°, 74.57°)", " Suibara: (37.85°, 139.23°)", " Moonee Ponds: (-37.77°, 144.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Moonee Ponds: 7155.8 km from centroid", " Suibara: 4720.4 km from centroid", " Nadiād: 3243.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Moonee Ponds", "FINAL ANSWER: Moonee Ponds" ] }, { "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": 52.58501, "lon": 32.76314, "name": "Starodub" }, { "lat": 53.61122, "lon": -0.96308, "name": "Thorne" }, { "lat": 43.30621, "lon": 10.51729, "name": "Cecina" }, { "lat": 53.3613, "lon": 13.07292, "name": "Neustrelitz" }, { "lat": -7.35889, "lon": 109.90306, "name": "Wonosobo" } ], "question": "Which location is the geographic outlier among: Starodub, Thorne, Cecina, Neustrelitz, Wonosobo?", "ground_truth": { "answer": "Wonosobo", "outlier_distance_km": 9405.3, "second_furthest_km": 3026.2, "clarity_ratio": 3.11, "median_distance_km": 2193.8, "distances_to_centroid": { "Starodub": 1499.5, "Thorne": 3026.2, "Cecina": 1936.4, "Neustrelitz": 2193.8, "Wonosobo": 9405.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Starodub: (52.59°, 32.76°)", " Thorne: (53.61°, -0.96°)", " Cecina: (43.31°, 10.52°)", " Neustrelitz: (53.36°, 13.07°)", " Wonosobo: (-7.36°, 109.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wonosobo: 9405.3 km from centroid", " Thorne: 3026.2 km from centroid", " Neustrelitz: 2193.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wonosobo", "FINAL ANSWER: Wonosobo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.83868, "lon": 7.21399, "name": "Lohmar" }, { "lat": 45.85589, "lon": 9.39704, "name": "Lecco" }, { "lat": 50.93182, "lon": 6.99469, "name": "Humboldtkolonie" }, { "lat": 54.35, "lon": -6.28333, "name": "Banbridge" }, { "lat": -33.92019, "lon": 151.22241, "name": "Kensington" } ], "question": "Which location is the geographic outlier among: Lohmar, Lecco, Humboldtkolonie, Banbridge, Kensington?", "ground_truth": { "answer": "Kensington", "outlier_distance_km": 14334.6, "second_furthest_km": 3863.6, "clarity_ratio": 3.71, "median_distance_km": 2893.5, "distances_to_centroid": { "Lohmar": 2874.9, "Lecco": 2469.5, "Humboldtkolonie": 2893.5, "Banbridge": 3863.6, "Kensington": 14334.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lohmar: (50.84°, 7.21°)", " Lecco: (45.86°, 9.40°)", " Humboldtkolonie: (50.93°, 6.99°)", " Banbridge: (54.35°, -6.28°)", " Kensington: (-33.92°, 151.22°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kensington: 14334.6 km from centroid", " Banbridge: 3863.6 km from centroid", " Humboldtkolonie: 2893.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kensington", "FINAL ANSWER: Kensington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.88822, "lon": 115.87186, "name": "Dianella" }, { "lat": -27.62329, "lon": 153.04785, "name": "Calamvale" }, { "lat": -37.8, "lon": 145.28333, "name": "Croydon" }, { "lat": -37.66667, "lon": 145.01667, "name": "Lalor" }, { "lat": 8.53417, "lon": 37.96515, "name": "Waliso" } ], "question": "Which location is the geographic outlier among: Dianella, Calamvale, Croydon, Lalor, Waliso?", "ground_truth": { "answer": "Waliso", "outlier_distance_km": 9566.3, "second_furthest_km": 3345.9, "clarity_ratio": 2.86, "median_distance_km": 2802.7, "distances_to_centroid": { "Dianella": 812.0, "Calamvale": 3345.9, "Croydon": 2802.7, "Lalor": 2775.4, "Waliso": 9566.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dianella: (-31.89°, 115.87°)", " Calamvale: (-27.62°, 153.05°)", " Croydon: (-37.80°, 145.28°)", " Lalor: (-37.67°, 145.02°)", " Waliso: (8.53°, 37.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Waliso: 9566.3 km from centroid", " Calamvale: 3345.9 km from centroid", " Croydon: 2802.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Waliso", "FINAL ANSWER: Waliso" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.4647, "lon": -98.48648, "name": "Aberdeen" }, { "lat": 33.60002, "lon": -117.672, "name": "Mission Viejo" }, { "lat": 50.03928, "lon": -110.67661, "name": "Medicine Hat" }, { "lat": 41.82371, "lon": -72.6212, "name": "South Windsor" }, { "lat": 12.87398, "lon": 11.04057, "name": "Gashua" } ], "question": "Which location is the geographic outlier among: Aberdeen, Mission Viejo, Medicine Hat, South Windsor, Gashua?", "ground_truth": { "answer": "Gashua", "outlier_distance_km": 9043.5, "second_furthest_km": 3625.0, "clarity_ratio": 2.49, "median_distance_km": 3012.4, "distances_to_centroid": { "Aberdeen": 1985.1, "Mission Viejo": 3625.0, "Medicine Hat": 3012.4, "South Windsor": 711.6, "Gashua": 9043.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Aberdeen: (45.46°, -98.49°)", " Mission Viejo: (33.60°, -117.67°)", " Medicine Hat: (50.04°, -110.68°)", " South Windsor: (41.82°, -72.62°)", " Gashua: (12.87°, 11.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gashua: 9043.5 km from centroid", " Mission Viejo: 3625.0 km from centroid", " Medicine Hat: 3012.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gashua", "FINAL ANSWER: Gashua" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.66667, "lon": 145.01667, "name": "Lalor" }, { "lat": -37.88333, "lon": 145.21667, "name": "Wantirna South" }, { "lat": -33.73333, "lon": 151.0, "name": "Castle Hill" }, { "lat": -37.90561, "lon": 145.00279, "name": "Brighton" }, { "lat": 43.47064, "lon": 11.14804, "name": "Poggibonsi" } ], "question": "Which location is the geographic outlier among: Lalor, Wantirna South, Castle Hill, Brighton, Poggibonsi?", "ground_truth": { "answer": "Poggibonsi", "outlier_distance_km": 13032.1, "second_furthest_km": 3416.3, "clarity_ratio": 3.81, "median_distance_km": 3121.5, "distances_to_centroid": { "Lalor": 3094.2, "Wantirna South": 3121.5, "Castle Hill": 3416.3, "Brighton": 3106.6, "Poggibonsi": 13032.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lalor: (-37.67°, 145.02°)", " Wantirna South: (-37.88°, 145.22°)", " Castle Hill: (-33.73°, 151.00°)", " Brighton: (-37.91°, 145.00°)", " Poggibonsi: (43.47°, 11.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Poggibonsi: 13032.1 km from centroid", " Castle Hill: 3416.3 km from centroid", " Wantirna South: 3121.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Poggibonsi", "FINAL ANSWER: Poggibonsi" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 23.09714, "lon": 86.22292, "name": "Balarāmpur" }, { "lat": 25.33218, "lon": 84.40454, "name": "Piro" }, { "lat": 28.41124, "lon": 77.31316, "name": "Faridabad" }, { "lat": 16.61667, "lon": 74.40442, "name": "Hupari" }, { "lat": 37.35411, "lon": -121.95524, "name": "Santa Clara" } ], "question": "Which location is the geographic outlier among: Balarāmpur, Piro, Faridabad, Hupari, Santa Clara?", "ground_truth": { "answer": "Santa Clara", "outlier_distance_km": 12707.0, "second_furthest_km": 4652.7, "clarity_ratio": 2.73, "median_distance_km": 4418.5, "distances_to_centroid": { "Balarāmpur": 4652.7, "Piro": 4418.5, "Faridabad": 3673.7, "Hupari": 3696.3, "Santa Clara": 12707.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Balarāmpur: (23.10°, 86.22°)", " Piro: (25.33°, 84.40°)", " Faridabad: (28.41°, 77.31°)", " Hupari: (16.62°, 74.40°)", " Santa Clara: (37.35°, -121.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santa Clara: 12707.0 km from centroid", " Balarāmpur: 4652.7 km from centroid", " Piro: 4418.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santa Clara", "FINAL ANSWER: Santa Clara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.06611, "lon": -50.14722, "name": "Buritama" }, { "lat": -13.03667, "lon": -46.77167, "name": "Campos Belos" }, { "lat": -17.7425, "lon": -46.1725, "name": "João Pinheiro" }, { "lat": 1.21456, "lon": -77.27846, "name": "Pasto" }, { "lat": 13.2997, "lon": 123.4386, "name": "Libon" } ], "question": "Which location is the geographic outlier among: Buritama, Campos Belos, João Pinheiro, Pasto, Libon?", "ground_truth": { "answer": "Libon", "outlier_distance_km": 15902.0, "second_furthest_km": 6492.7, "clarity_ratio": 2.45, "median_distance_km": 3632.8, "distances_to_centroid": { "Buritama": 3632.8, "Campos Belos": 3057.7, "João Pinheiro": 3117.9, "Pasto": 6492.7, "Libon": 15902.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Buritama: (-21.07°, -50.15°)", " Campos Belos: (-13.04°, -46.77°)", " João Pinheiro: (-17.74°, -46.17°)", " Pasto: (1.21°, -77.28°)", " Libon: (13.30°, 123.44°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Libon: 15902.0 km from centroid", " Pasto: 6492.7 km from centroid", " Buritama: 3632.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Libon", "FINAL ANSWER: Libon" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": -33.80383, "lon": 150.98768, "name": "Westmead" }, { "lat": -31.83291, "lon": 115.7759, "name": "Duncraig" }, { "lat": -27.53221, "lon": 153.22889, "name": "Alexandra Hills" }, { "lat": -22.28306, "lon": -46.36889, "name": "Ouro Fino" } ], "question": "Which location is the geographic outlier among: Yarraville, Westmead, Duncraig, Alexandra Hills, Ouro Fino?", "ground_truth": { "answer": "Ouro Fino", "outlier_distance_km": 13318.1, "second_furthest_km": 4786.0, "clarity_ratio": 2.78, "median_distance_km": 4422.6, "distances_to_centroid": { "Yarraville": 3837.9, "Westmead": 4422.6, "Duncraig": 1154.4, "Alexandra Hills": 4786.0, "Ouro Fino": 13318.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yarraville: (-37.82°, 144.90°)", " Westmead: (-33.80°, 150.99°)", " Duncraig: (-31.83°, 115.78°)", " Alexandra Hills: (-27.53°, 153.23°)", " Ouro Fino: (-22.28°, -46.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ouro Fino: 13318.1 km from centroid", " Alexandra Hills: 4786.0 km from centroid", " Westmead: 4422.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ouro Fino", "FINAL ANSWER: Ouro Fino" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.06982, "lon": -77.04495, "name": "Jesus Maria" }, { "lat": -34.57365, "lon": -58.44924, "name": "Colegiales" }, { "lat": -23.40472, "lon": -46.75472, "name": "Perus" }, { "lat": -23.71694, "lon": -46.84917, "name": "Itapecerica da Serra" }, { "lat": 19.9855, "lon": -102.28387, "name": "Zamora" } ], "question": "Which location is the geographic outlier among: Jesus Maria, Colegiales, Perus, Itapecerica da Serra, Zamora?", "ground_truth": { "answer": "Zamora", "outlier_distance_km": 5515.4, "second_furthest_km": 2339.1, "clarity_ratio": 2.36, "median_distance_km": 2266.5, "distances_to_centroid": { "Jesus Maria": 1202.2, "Colegiales": 2339.1, "Perus": 2262.3, "Itapecerica da Serra": 2266.5, "Zamora": 5515.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jesus Maria: (-12.07°, -77.04°)", " Colegiales: (-34.57°, -58.45°)", " Perus: (-23.40°, -46.75°)", " Itapecerica da Serra: (-23.72°, -46.85°)", " Zamora: (19.99°, -102.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zamora: 5515.4 km from centroid", " Colegiales: 2339.1 km from centroid", " Itapecerica da Serra: 2266.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zamora", "FINAL ANSWER: Zamora" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.26667, "lon": 174.95, "name": "Wainuiomata" }, { "lat": -41.27078, "lon": 173.28404, "name": "Nelson" }, { "lat": -31.91099, "lon": 152.45387, "name": "Taree" }, { "lat": -36.8, "lon": 174.75, "name": "North Shore" }, { "lat": 36.09005, "lon": 136.35994, "name": "Iijima" } ], "question": "Which location is the geographic outlier among: Wainuiomata, Nelson, Taree, North Shore, Iijima?", "ground_truth": { "answer": "Iijima", "outlier_distance_km": 7119.4, "second_furthest_km": 2342.8, "clarity_ratio": 3.04, "median_distance_km": 2269.4, "distances_to_centroid": { "Wainuiomata": 2342.8, "Nelson": 2269.4, "Taree": 1387.8, "North Shore": 1937.7, "Iijima": 7119.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wainuiomata: (-41.27°, 174.95°)", " Nelson: (-41.27°, 173.28°)", " Taree: (-31.91°, 152.45°)", " North Shore: (-36.80°, 174.75°)", " Iijima: (36.09°, 136.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Iijima: 7119.4 km from centroid", " Wainuiomata: 2342.8 km from centroid", " Nelson: 2269.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Iijima", "FINAL ANSWER: Iijima" ] }, { "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": 38.97789, "lon": -77.00748, "name": "Takoma Park" }, { "lat": 19.6927, "lon": -100.55445, "name": "Ciudad Hidalgo" }, { "lat": 43.64801, "lon": -93.36827, "name": "Albert Lea" }, { "lat": 40.9276, "lon": -73.99736, "name": "Bergenfield" }, { "lat": -6.96333, "lon": -35.69167, "name": "Areia" } ], "question": "Which location is the geographic outlier among: Takoma Park, Ciudad Hidalgo, Albert Lea, Bergenfield, Areia?", "ground_truth": { "answer": "Areia", "outlier_distance_km": 5778.2, "second_furthest_km": 2624.3, "clarity_ratio": 2.2, "median_distance_km": 2390.3, "distances_to_centroid": { "Takoma Park": 1305.9, "Ciudad Hidalgo": 2624.3, "Albert Lea": 2390.3, "Bergenfield": 1532.6, "Areia": 5778.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Takoma Park: (38.98°, -77.01°)", " Ciudad Hidalgo: (19.69°, -100.55°)", " Albert Lea: (43.65°, -93.37°)", " Bergenfield: (40.93°, -74.00°)", " Areia: (-6.96°, -35.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Areia: 5778.2 km from centroid", " Ciudad Hidalgo: 2624.3 km from centroid", " Albert Lea: 2390.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Areia", "FINAL ANSWER: Areia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.06889, "lon": 34.29891, "name": "Kirov" }, { "lat": 50.2813, "lon": 19.56503, "name": "Olkusz" }, { "lat": 44.02556, "lon": 43.05028, "name": "Svobody" }, { "lat": 51.48158, "lon": 11.97947, "name": "Halle (Saale)" }, { "lat": -19.26639, "lon": 146.80569, "name": "Townsville" } ], "question": "Which location is the geographic outlier among: Kirov, Olkusz, Svobody, Halle (Saale), Townsville?", "ground_truth": { "answer": "Townsville", "outlier_distance_km": 11747.9, "second_furthest_km": 3519.4, "clarity_ratio": 3.34, "median_distance_km": 2971.6, "distances_to_centroid": { "Kirov": 2380.7, "Olkusz": 2971.6, "Svobody": 1115.5, "Halle (Saale)": 3519.4, "Townsville": 11747.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kirov: (54.07°, 34.30°)", " Olkusz: (50.28°, 19.57°)", " Svobody: (44.03°, 43.05°)", " Halle (Saale): (51.48°, 11.98°)", " Townsville: (-19.27°, 146.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Townsville: 11747.9 km from centroid", " Halle (Saale): 3519.4 km from centroid", " Olkusz: 2971.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Townsville", "FINAL ANSWER: Townsville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -15.54667, "lon": -55.16889, "name": "Campo Verde" }, { "lat": -26.40843, "lon": -54.69463, "name": "Puerto Eldorado" }, { "lat": -22.42313, "lon": -42.96612, "name": "São Pedro" }, { "lat": -2.64528, "lon": -44.895, "name": "Palmeirândia" }, { "lat": 27.05715, "lon": 78.68661, "name": "Sirsāganj" } ], "question": "Which location is the geographic outlier among: Campo Verde, Puerto Eldorado, São Pedro, Palmeirândia, Sirsāganj?", "ground_truth": { "answer": "Sirsāganj", "outlier_distance_km": 11644.0, "second_furthest_km": 3848.8, "clarity_ratio": 3.03, "median_distance_km": 3511.2, "distances_to_centroid": { "Campo Verde": 3511.2, "Puerto Eldorado": 3848.8, "São Pedro": 2602.0, "Palmeirândia": 2408.3, "Sirsāganj": 11644.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Campo Verde: (-15.55°, -55.17°)", " Puerto Eldorado: (-26.41°, -54.69°)", " São Pedro: (-22.42°, -42.97°)", " Palmeirândia: (-2.65°, -44.90°)", " Sirsāganj: (27.06°, 78.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sirsāganj: 11644.0 km from centroid", " Puerto Eldorado: 3848.8 km from centroid", " Campo Verde: 3511.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sirsāganj", "FINAL ANSWER: Sirsāganj" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -25.46279, "lon": 28.65041, "name": "Moloto South" }, { "lat": 11.73292, "lon": 41.082, "name": "Dubti" }, { "lat": -24.78864, "lon": 31.07938, "name": "Mafemani" }, { "lat": 8.66667, "lon": 39.43333, "name": "Welench’ītī" }, { "lat": -33.91439, "lon": 151.24895, "name": "Randwick" } ], "question": "Which location is the geographic outlier among: Moloto South, Dubti, Mafemani, Welench’ītī, Randwick?", "ground_truth": { "answer": "Randwick", "outlier_distance_km": 9487.7, "second_furthest_km": 3409.2, "clarity_ratio": 2.78, "median_distance_km": 3319.9, "distances_to_centroid": { "Moloto South": 3409.2, "Dubti": 3319.9, "Mafemani": 3153.7, "Welench’ītī": 3164.8, "Randwick": 9487.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Moloto South: (-25.46°, 28.65°)", " Dubti: (11.73°, 41.08°)", " Mafemani: (-24.79°, 31.08°)", " Welench’ītī: (8.67°, 39.43°)", " Randwick: (-33.91°, 151.25°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Randwick: 9487.7 km from centroid", " Moloto South: 3409.2 km from centroid", " Dubti: 3319.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Randwick", "FINAL ANSWER: Randwick" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.84205, "lon": 145.0694, "name": "Camberwell" }, { "lat": -37.66667, "lon": 145.01667, "name": "Lalor" }, { "lat": -33.91667, "lon": 151.03333, "name": "Bankstown" }, { "lat": -37.86667, "lon": 145.06667, "name": "Glen Iris" }, { "lat": 53.69803, "lon": -2.46494, "name": "Darwen" } ], "question": "Which location is the geographic outlier among: Camberwell, Lalor, Bankstown, Glen Iris, Darwen?", "ground_truth": { "answer": "Darwen", "outlier_distance_km": 13583.4, "second_furthest_km": 3787.5, "clarity_ratio": 3.59, "median_distance_km": 3471.7, "distances_to_centroid": { "Camberwell": 3470.5, "Lalor": 3456.8, "Bankstown": 3787.5, "Glen Iris": 3471.7, "Darwen": 13583.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Camberwell: (-37.84°, 145.07°)", " Lalor: (-37.67°, 145.02°)", " Bankstown: (-33.92°, 151.03°)", " Glen Iris: (-37.87°, 145.07°)", " Darwen: (53.70°, -2.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Darwen: 13583.4 km from centroid", " Bankstown: 3787.5 km from centroid", " Glen Iris: 3471.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Darwen", "FINAL ANSWER: Darwen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.77271, "lon": 151.08184, "name": "Epping" }, { "lat": -37.74496, "lon": 144.80049, "name": "St Albans" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" }, { "lat": -16.92366, "lon": 145.76613, "name": "Cairns" }, { "lat": 40.6851, "lon": -73.7018, "name": "North Valley Stream" } ], "question": "Which location is the geographic outlier among: Epping, St Albans, New Plymouth, Cairns, North Valley Stream?", "ground_truth": { "answer": "North Valley Stream", "outlier_distance_km": 17414.1, "second_furthest_km": 6720.9, "clarity_ratio": 2.59, "median_distance_km": 4612.3, "distances_to_centroid": { "Epping": 4612.3, "St Albans": 4202.7, "New Plymouth": 6720.9, "Cairns": 3963.6, "North Valley Stream": 17414.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Epping: (-33.77°, 151.08°)", " St Albans: (-37.74°, 144.80°)", " New Plymouth: (-39.07°, 174.08°)", " Cairns: (-16.92°, 145.77°)", " North Valley Stream: (40.69°, -73.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Valley Stream: 17414.1 km from centroid", " New Plymouth: 6720.9 km from centroid", " Epping: 4612.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: North Valley Stream", "FINAL ANSWER: North Valley Stream" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.4759, "lon": 4.51294, "name": "Saint-Chamond" }, { "lat": 48.56067, "lon": 11.26071, "name": "Schrobenhausen" }, { "lat": 43.14322, "lon": -2.96204, "name": "Laudio / Llodio" }, { "lat": 53.55024, "lon": -2.77348, "name": "Skelmersdale" }, { "lat": -3.22028, "lon": -45.00361, "name": "Viana" } ], "question": "Which location is the geographic outlier among: Saint-Chamond, Schrobenhausen, Laudio / Llodio, Skelmersdale, Viana?", "ground_truth": { "answer": "Viana", "outlier_distance_km": 5988.0, "second_furthest_km": 1918.3, "clarity_ratio": 3.12, "median_distance_km": 1813.7, "distances_to_centroid": { "Saint-Chamond": 1303.2, "Schrobenhausen": 1918.3, "Laudio / Llodio": 714.1, "Skelmersdale": 1813.7, "Viana": 5988.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint-Chamond: (45.48°, 4.51°)", " Schrobenhausen: (48.56°, 11.26°)", " Laudio / Llodio: (43.14°, -2.96°)", " Skelmersdale: (53.55°, -2.77°)", " Viana: (-3.22°, -45.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Viana: 5988.0 km from centroid", " Schrobenhausen: 1918.3 km from centroid", " Skelmersdale: 1813.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Viana", "FINAL ANSWER: Viana" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.91119, "lon": 138.70735, "name": "Adelaide Hills" }, { "lat": -33.77271, "lon": 151.08184, "name": "Epping" }, { "lat": -41.13333, "lon": 174.85, "name": "Porirua" }, { "lat": -38.04369, "lon": 145.2923, "name": "Narre Warren South" }, { "lat": 39.94845, "lon": -75.17212, "name": "Rittenhouse" } ], "question": "Which location is the geographic outlier among: Adelaide Hills, Epping, Porirua, Narre Warren South, Rittenhouse?", "ground_truth": { "answer": "Rittenhouse", "outlier_distance_km": 17963.0, "second_furthest_km": 6631.2, "clarity_ratio": 2.71, "median_distance_km": 4514.3, "distances_to_centroid": { "Adelaide Hills": 3425.4, "Epping": 4514.3, "Porirua": 6631.2, "Narre Warren South": 4088.3, "Rittenhouse": 17963.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Adelaide Hills: (-34.91°, 138.71°)", " Epping: (-33.77°, 151.08°)", " Porirua: (-41.13°, 174.85°)", " Narre Warren South: (-38.04°, 145.29°)", " Rittenhouse: (39.95°, -75.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rittenhouse: 17963.0 km from centroid", " Porirua: 6631.2 km from centroid", " Epping: 4514.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rittenhouse", "FINAL ANSWER: Rittenhouse" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.65, "lon": 36.21667, "name": "Dibate" }, { "lat": -27.1974, "lon": 25.98311, "name": "Wolmaransstad" }, { "lat": 7.61667, "lon": 39.5, "name": "Gobēsa" }, { "lat": 9.50619, "lon": 42.60938, "name": "Chinahsen" }, { "lat": 39.55388, "lon": -104.96943, "name": "Highlands Ranch" } ], "question": "Which location is the geographic outlier among: Dibate, Wolmaransstad, Gobēsa, Chinahsen, Highlands Ranch?", "ground_truth": { "answer": "Highlands Ranch", "outlier_distance_km": 11338.6, "second_furthest_km": 4375.8, "clarity_ratio": 2.59, "median_distance_km": 3820.0, "distances_to_centroid": { "Dibate": 3123.0, "Wolmaransstad": 4375.8, "Gobēsa": 3484.0, "Chinahsen": 3820.0, "Highlands Ranch": 11338.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dibate: (10.65°, 36.22°)", " Wolmaransstad: (-27.20°, 25.98°)", " Gobēsa: (7.62°, 39.50°)", " Chinahsen: (9.51°, 42.61°)", " Highlands Ranch: (39.55°, -104.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Highlands Ranch: 11338.6 km from centroid", " Wolmaransstad: 4375.8 km from centroid", " Chinahsen: 3820.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Highlands Ranch", "FINAL ANSWER: Highlands Ranch" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -6.2349, "lon": 106.9896, "name": "Bekasi" }, { "lat": 16.16901, "lon": 74.82393, "name": "Gokak" }, { "lat": 5.3473, "lon": 115.7455, "name": "Beaufort" }, { "lat": -7.1955, "lon": 107.4313, "name": "Banjar" }, { "lat": 41.64662, "lon": 2.74135, "name": "Malgrat de Mar" } ], "question": "Which location is the geographic outlier among: Bekasi, Gokak, Beaufort, Banjar, Malgrat de Mar?", "ground_truth": { "answer": "Malgrat de Mar", "outlier_distance_km": 8347.1, "second_furthest_km": 3801.4, "clarity_ratio": 2.2, "median_distance_km": 3442.5, "distances_to_centroid": { "Bekasi": 3343.6, "Gokak": 1004.2, "Beaufort": 3801.4, "Banjar": 3442.5, "Malgrat de Mar": 8347.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bekasi: (-6.23°, 106.99°)", " Gokak: (16.17°, 74.82°)", " Beaufort: (5.35°, 115.75°)", " Banjar: (-7.20°, 107.43°)", " Malgrat de Mar: (41.65°, 2.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Malgrat de Mar: 8347.1 km from centroid", " Beaufort: 3801.4 km from centroid", " Banjar: 3442.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Malgrat de Mar", "FINAL ANSWER: Malgrat de Mar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -30.30225, "lon": 27.08395, "name": "Zastron" }, { "lat": 27.26881, "lon": 31.15232, "name": "Abnūb" }, { "lat": 12.11667, "lon": 37.78333, "name": "Ādīs Zemen" }, { "lat": 10.65, "lon": 36.21667, "name": "Dibate" }, { "lat": -2.895, "lon": -40.44917, "name": "Jijoca de Jericoacoara" } ], "question": "Which location is the geographic outlier among: Zastron, Abnūb, Ādīs Zemen, Dibate, Jijoca de Jericoacoara?", "ground_truth": { "answer": "Jijoca de Jericoacoara", "outlier_distance_km": 6572.6, "second_furthest_km": 3857.1, "clarity_ratio": 1.7, "median_distance_km": 2985.3, "distances_to_centroid": { "Zastron": 3857.1, "Abnūb": 2985.3, "Ādīs Zemen": 2348.9, "Dibate": 2129.5, "Jijoca de Jericoacoara": 6572.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zastron: (-30.30°, 27.08°)", " Abnūb: (27.27°, 31.15°)", " Ādīs Zemen: (12.12°, 37.78°)", " Dibate: (10.65°, 36.22°)", " Jijoca de Jericoacoara: (-2.90°, -40.45°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jijoca de Jericoacoara: 6572.6 km from centroid", " Zastron: 3857.1 km from centroid", " Abnūb: 2985.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jijoca de Jericoacoara", "FINAL ANSWER: Jijoca de Jericoacoara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.86472, "lon": 174.64768, "name": "Te Atatu South" }, { "lat": -38.21792, "lon": 145.03876, "name": "Mornington" }, { "lat": -31.95224, "lon": 115.8614, "name": "Perth" }, { "lat": -37.97695, "lon": 145.25866, "name": "Endeavour Hills" }, { "lat": 17.99913, "lon": -94.6359, "name": "Cosoleacaque" } ], "question": "Which location is the geographic outlier among: Te Atatu South, Mornington, Perth, Endeavour Hills, Cosoleacaque?", "ground_truth": { "answer": "Cosoleacaque", "outlier_distance_km": 18539.4, "second_furthest_km": 7282.2, "clarity_ratio": 2.55, "median_distance_km": 4698.2, "distances_to_centroid": { "Te Atatu South": 7282.2, "Mornington": 4680.4, "Perth": 1954.2, "Endeavour Hills": 4698.2, "Cosoleacaque": 18539.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Te Atatu South: (-36.86°, 174.65°)", " Mornington: (-38.22°, 145.04°)", " Perth: (-31.95°, 115.86°)", " Endeavour Hills: (-37.98°, 145.26°)", " Cosoleacaque: (18.00°, -94.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cosoleacaque: 18539.4 km from centroid", " Te Atatu South: 7282.2 km from centroid", " Endeavour Hills: 4698.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cosoleacaque", "FINAL ANSWER: Cosoleacaque" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.28316, "lon": 36.84725, "name": "Pumwani" }, { "lat": -0.30719, "lon": 36.07225, "name": "Nakuru" }, { "lat": -32.83483, "lon": 27.21742, "name": "Dimbaza" }, { "lat": 29.03556, "lon": 31.11792, "name": "New Bani Sewif City" }, { "lat": 28.29675, "lon": 108.95841, "name": "Zhongling" } ], "question": "Which location is the geographic outlier among: Pumwani, Nakuru, Dimbaza, New Bani Sewif City, Zhongling?", "ground_truth": { "answer": "Zhongling", "outlier_distance_km": 6929.9, "second_furthest_km": 4704.6, "clarity_ratio": 1.47, "median_distance_km": 3251.8, "distances_to_centroid": { "Pumwani": 1404.4, "Nakuru": 1436.5, "Dimbaza": 4704.6, "New Bani Sewif City": 3251.8, "Zhongling": 6929.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pumwani: (-1.28°, 36.85°)", " Nakuru: (-0.31°, 36.07°)", " Dimbaza: (-32.83°, 27.22°)", " New Bani Sewif City: (29.04°, 31.12°)", " Zhongling: (28.30°, 108.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Zhongling: 6929.9 km from centroid", " Dimbaza: 4704.6 km from centroid", " New Bani Sewif City: 3251.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Zhongling", "FINAL ANSWER: Zhongling" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.73333, "lon": 139.16667, "name": "Gosen" }, { "lat": 36.45556, "lon": 127.12472, "name": "Gongju" }, { "lat": 16.7262, "lon": 121.3589, "name": "Diadi" }, { "lat": 22.75278, "lon": 88.34222, "name": "Shrīrāmpur" }, { "lat": -35.13333, "lon": 138.51667, "name": "Morphett Vale" } ], "question": "Which location is the geographic outlier among: Gosen, Gongju, Diadi, Shrīrāmpur, Morphett Vale?", "ground_truth": { "answer": "Morphett Vale", "outlier_distance_km": 5888.4, "second_furthest_km": 3703.0, "clarity_ratio": 1.59, "median_distance_km": 2923.7, "distances_to_centroid": { "Gosen": 2923.7, "Gongju": 2344.7, "Diadi": 200.0, "Shrīrāmpur": 3703.0, "Morphett Vale": 5888.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gosen: (37.73°, 139.17°)", " Gongju: (36.46°, 127.12°)", " Diadi: (16.73°, 121.36°)", " Shrīrāmpur: (22.75°, 88.34°)", " Morphett Vale: (-35.13°, 138.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Morphett Vale: 5888.4 km from centroid", " Shrīrāmpur: 3703.0 km from centroid", " Gosen: 2923.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Morphett Vale", "FINAL ANSWER: Morphett Vale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.002, "lon": 29.034, "name": "Phola" }, { "lat": -32.33083, "lon": 28.14981, "name": "Butterworth" }, { "lat": -28.17827, "lon": 30.14702, "name": "Glencoe" }, { "lat": 7.25256, "lon": 5.19312, "name": "Akure" }, { "lat": -25.59912, "lon": -54.57355, "name": "Puerto Iguazú" } ], "question": "Which location is the geographic outlier among: Phola, Butterworth, Glencoe, Akure, Puerto Iguazú?", "ground_truth": { "answer": "Puerto Iguazú", "outlier_distance_km": 6313.6, "second_furthest_km": 3149.3, "clarity_ratio": 2.0, "median_distance_km": 2412.9, "distances_to_centroid": { "Phola": 2254.3, "Butterworth": 2395.2, "Glencoe": 2412.9, "Akure": 3149.3, "Puerto Iguazú": 6313.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Phola: (-26.00°, 29.03°)", " Butterworth: (-32.33°, 28.15°)", " Glencoe: (-28.18°, 30.15°)", " Akure: (7.25°, 5.19°)", " Puerto Iguazú: (-25.60°, -54.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Puerto Iguazú: 6313.6 km from centroid", " Akure: 3149.3 km from centroid", " Glencoe: 2412.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Puerto Iguazú", "FINAL ANSWER: Puerto Iguazú" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.13278, "lon": -74.15977, "name": "Pacho" }, { "lat": 2.64644, "lon": -75.97269, "name": "Belalcázar" }, { "lat": -36.77803, "lon": -59.85848, "name": "Azul" }, { "lat": 7.00621, "lon": -73.90972, "name": "Yondó" }, { "lat": 17.87445, "lon": 76.94972, "name": "Basavakalyan" } ], "question": "Which location is the geographic outlier among: Pacho, Belalcázar, Azul, Yondó, Basavakalyan?", "ground_truth": { "answer": "Basavakalyan", "outlier_distance_km": 13025.3, "second_furthest_km": 4426.0, "clarity_ratio": 2.94, "median_distance_km": 3863.6, "distances_to_centroid": { "Pacho": 3699.3, "Belalcázar": 3863.6, "Azul": 4426.0, "Yondó": 3711.3, "Basavakalyan": 13025.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pacho: (5.13°, -74.16°)", " Belalcázar: (2.65°, -75.97°)", " Azul: (-36.78°, -59.86°)", " Yondó: (7.01°, -73.91°)", " Basavakalyan: (17.87°, 76.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Basavakalyan: 13025.3 km from centroid", " Azul: 4426.0 km from centroid", " Belalcázar: 3863.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Basavakalyan", "FINAL ANSWER: Basavakalyan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.18307, "lon": 22.14605, "name": "Mossel Bay" }, { "lat": -31.87101, "lon": 26.97862, "name": "Queensdale" }, { "lat": 12.6, "lon": 37.46667, "name": "Gonder" }, { "lat": 10.9992, "lon": 10.41062, "name": "Darazo" }, { "lat": -27.46794, "lon": 153.02809, "name": "Brisbane" } ], "question": "Which location is the geographic outlier among: Mossel Bay, Queensdale, Gonder, Darazo, Brisbane?", "ground_truth": { "answer": "Brisbane", "outlier_distance_km": 10534.0, "second_furthest_km": 5174.7, "clarity_ratio": 2.04, "median_distance_km": 3589.2, "distances_to_centroid": { "Mossel Bay": 3589.2, "Queensdale": 3071.7, "Gonder": 3263.0, "Darazo": 5174.7, "Brisbane": 10534.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mossel Bay: (-34.18°, 22.15°)", " Queensdale: (-31.87°, 26.98°)", " Gonder: (12.60°, 37.47°)", " Darazo: (11.00°, 10.41°)", " Brisbane: (-27.47°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brisbane: 10534.0 km from centroid", " Darazo: 5174.7 km from centroid", " Mossel Bay: 3589.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brisbane", "FINAL ANSWER: Brisbane" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.88333, "lon": 37.58333, "name": "Altuf’yevskiy" }, { "lat": 52.20197, "lon": 8.33826, "name": "Melle" }, { "lat": 50.3425, "lon": -4.77442, "name": "St Austell" }, { "lat": 41.03288, "lon": 13.94354, "name": "Castel Volturno" }, { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" } ], "question": "Which location is the geographic outlier among: Altuf’yevskiy, Melle, St Austell, Castel Volturno, Carnegie?", "ground_truth": { "answer": "Carnegie", "outlier_distance_km": 13352.4, "second_furthest_km": 4160.6, "clarity_ratio": 3.21, "median_distance_km": 3372.6, "distances_to_centroid": { "Altuf’yevskiy": 2627.7, "Melle": 3372.6, "St Austell": 4160.6, "Castel Volturno": 2508.1, "Carnegie": 13352.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Altuf’yevskiy: (55.88°, 37.58°)", " Melle: (52.20°, 8.34°)", " St Austell: (50.34°, -4.77°)", " Castel Volturno: (41.03°, 13.94°)", " Carnegie: (-37.89°, 145.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carnegie: 13352.4 km from centroid", " St Austell: 4160.6 km from centroid", " Melle: 3372.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carnegie", "FINAL ANSWER: Carnegie" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.83417, "lon": 76.45924, "name": "Nāndūra" }, { "lat": 23.53798, "lon": 93.3732, "name": "Ngūr" }, { "lat": 19.71664, "lon": 74.48109, "name": "Rahata" }, { "lat": 2.6931, "lon": 101.7498, "name": "Sepang" }, { "lat": 42.74698, "lon": -84.40108, "name": "Haslett" } ], "question": "Which location is the geographic outlier among: Nāndūra, Ngūr, Rahata, Sepang, Haslett?", "ground_truth": { "answer": "Haslett", "outlier_distance_km": 11570.7, "second_furthest_km": 5743.4, "clarity_ratio": 2.01, "median_distance_km": 4199.0, "distances_to_centroid": { "Nāndūra": 2498.6, "Ngūr": 4199.0, "Rahata": 2312.9, "Sepang": 5743.4, "Haslett": 11570.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nāndūra: (20.83°, 76.46°)", " Ngūr: (23.54°, 93.37°)", " Rahata: (19.72°, 74.48°)", " Sepang: (2.69°, 101.75°)", " Haslett: (42.75°, -84.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Haslett: 11570.7 km from centroid", " Sepang: 5743.4 km from centroid", " Ngūr: 4199.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Haslett", "FINAL ANSWER: Haslett" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -5.68167, "lon": -43.09333, "name": "Parnarama" }, { "lat": 0.71333, "lon": -51.41333, "name": "Porto Grande" }, { "lat": -3.96333, "lon": -45.65833, "name": "Santa Luzia" }, { "lat": 6.96321, "lon": -75.41738, "name": "Yarumal" }, { "lat": 40.81232, "lon": -73.07844, "name": "Holbrook" } ], "question": "Which location is the geographic outlier among: Parnarama, Porto Grande, Santa Luzia, Yarumal, Holbrook?", "ground_truth": { "answer": "Holbrook", "outlier_distance_km": 3975.8, "second_furthest_km": 2207.6, "clarity_ratio": 1.8, "median_distance_km": 1952.2, "distances_to_centroid": { "Parnarama": 2207.6, "Porto Grande": 1051.6, "Santa Luzia": 1869.8, "Yarumal": 1952.2, "Holbrook": 3975.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Parnarama: (-5.68°, -43.09°)", " Porto Grande: (0.71°, -51.41°)", " Santa Luzia: (-3.96°, -45.66°)", " Yarumal: (6.96°, -75.42°)", " Holbrook: (40.81°, -73.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Holbrook: 3975.8 km from centroid", " Parnarama: 2207.6 km from centroid", " Yarumal: 1952.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Holbrook", "FINAL ANSWER: Holbrook" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.65003, "lon": -0.2361, "name": "Dome" }, { "lat": 12.416, "lon": 39.55971, "name": "Alamata" }, { "lat": -24.95775, "lon": 27.26543, "name": "Northam" }, { "lat": -28.41098, "lon": 26.70107, "name": "Theunissen" }, { "lat": 7.06528, "lon": -73.85472, "name": "Barrancabermeja" } ], "question": "Which location is the geographic outlier among: Dome, Alamata, Northam, Theunissen, Barrancabermeja?", "ground_truth": { "answer": "Barrancabermeja", "outlier_distance_km": 8740.4, "second_furthest_km": 4424.9, "clarity_ratio": 1.98, "median_distance_km": 3490.5, "distances_to_centroid": { "Dome": 1337.0, "Alamata": 4424.9, "Northam": 3289.1, "Theunissen": 3490.5, "Barrancabermeja": 8740.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dome: (5.65°, -0.24°)", " Alamata: (12.42°, 39.56°)", " Northam: (-24.96°, 27.27°)", " Theunissen: (-28.41°, 26.70°)", " Barrancabermeja: (7.07°, -73.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Barrancabermeja: 8740.4 km from centroid", " Alamata: 4424.9 km from centroid", " Theunissen: 3490.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Barrancabermeja", "FINAL ANSWER: Barrancabermeja" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.61835, "lon": -1.17904, "name": "Braunstone" }, { "lat": 54.03481, "lon": 38.40172, "name": "Severo-Zadonsk" }, { "lat": 50.24962, "lon": 8.64281, "name": "Friedrichsdorf" }, { "lat": 56.04284, "lon": 37.85153, "name": "Zavety Il’icha" }, { "lat": 10.04807, "lon": 11.21055, "name": "Kumo" } ], "question": "Which location is the geographic outlier among: Braunstone, Severo-Zadonsk, Friedrichsdorf, Zavety Il’icha, Kumo?", "ground_truth": { "answer": "Kumo", "outlier_distance_km": 3913.7, "second_furthest_km": 1836.2, "clarity_ratio": 2.13, "median_distance_km": 1745.9, "distances_to_centroid": { "Braunstone": 1721.3, "Severo-Zadonsk": 1745.9, "Friedrichsdorf": 998.6, "Zavety Il’icha": 1836.2, "Kumo": 3913.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Braunstone: (52.62°, -1.18°)", " Severo-Zadonsk: (54.03°, 38.40°)", " Friedrichsdorf: (50.25°, 8.64°)", " Zavety Il’icha: (56.04°, 37.85°)", " Kumo: (10.05°, 11.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kumo: 3913.7 km from centroid", " Zavety Il’icha: 1836.2 km from centroid", " Severo-Zadonsk: 1745.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kumo", "FINAL ANSWER: Kumo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.39528, "lon": -54.56639, "name": "São Gabriel do Oeste" }, { "lat": -23.05056, "lon": -50.22889, "name": "Andirá" }, { "lat": -29.16806, "lon": -51.17944, "name": "Caxias do Sul" }, { "lat": -31.34582, "lon": -64.33849, "name": "La Calera" }, { "lat": 41.41533, "lon": -81.56596, "name": "Maple Heights" } ], "question": "Which location is the geographic outlier among: São Gabriel do Oeste, Andirá, Caxias do Sul, La Calera, Maple Heights?", "ground_truth": { "answer": "Maple Heights", "outlier_distance_km": 6357.1, "second_furthest_km": 2155.4, "clarity_ratio": 2.95, "median_distance_km": 2102.2, "distances_to_centroid": { "São Gabriel do Oeste": 1003.2, "Andirá": 1605.5, "Caxias do Sul": 2102.2, "La Calera": 2155.4, "Maple Heights": 6357.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " São Gabriel do Oeste: (-19.40°, -54.57°)", " Andirá: (-23.05°, -50.23°)", " Caxias do Sul: (-29.17°, -51.18°)", " La Calera: (-31.35°, -64.34°)", " Maple Heights: (41.42°, -81.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maple Heights: 6357.1 km from centroid", " La Calera: 2155.4 km from centroid", " Caxias do Sul: 2102.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maple Heights", "FINAL ANSWER: Maple Heights" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -6.0144, "lon": 106.0542, "name": "Cilegon" }, { "lat": 35.1, "lon": 138.86667, "name": "Numazu" }, { "lat": 33.28662, "lon": 134.16832, "name": "Muroto-misakicho" }, { "lat": 35.46667, "lon": 133.9, "name": "Matsuzaki" }, { "lat": -12.60139, "lon": -38.96576, "name": "Cachoeira" } ], "question": "Which location is the geographic outlier among: Cilegon, Numazu, Muroto-misakicho, Matsuzaki, Cachoeira?", "ground_truth": { "answer": "Cachoeira", "outlier_distance_km": 15032.0, "second_furthest_km": 4787.9, "clarity_ratio": 3.14, "median_distance_km": 4364.1, "distances_to_centroid": { "Cilegon": 2846.9, "Numazu": 4787.9, "Muroto-misakicho": 4319.9, "Matsuzaki": 4364.1, "Cachoeira": 15032.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cilegon: (-6.01°, 106.05°)", " Numazu: (35.10°, 138.87°)", " Muroto-misakicho: (33.29°, 134.17°)", " Matsuzaki: (35.47°, 133.90°)", " Cachoeira: (-12.60°, -38.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cachoeira: 15032.0 km from centroid", " Numazu: 4787.9 km from centroid", " Matsuzaki: 4364.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cachoeira", "FINAL ANSWER: Cachoeira" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.52306, "lon": -44.10417, "name": "Volta Redonda" }, { "lat": -15.32333, "lon": -58.00361, "name": "Lambari d'Oeste" }, { "lat": -23.53194, "lon": -46.44417, "name": "Itaquera" }, { "lat": -23.43088, "lon": -46.79295, "name": "Anhanguera" }, { "lat": 8.11667, "lon": 38.36667, "name": "Butajīra" } ], "question": "Which location is the geographic outlier among: Volta Redonda, Lambari d'Oeste, Itaquera, Anhanguera, Butajīra?", "ground_truth": { "answer": "Butajīra", "outlier_distance_km": 8113.7, "second_furthest_km": 2851.6, "clarity_ratio": 2.85, "median_distance_km": 1846.7, "distances_to_centroid": { "Volta Redonda": 1556.0, "Lambari d'Oeste": 2851.6, "Itaquera": 1820.1, "Anhanguera": 1846.7, "Butajīra": 8113.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Volta Redonda: (-22.52°, -44.10°)", " Lambari d'Oeste: (-15.32°, -58.00°)", " Itaquera: (-23.53°, -46.44°)", " Anhanguera: (-23.43°, -46.79°)", " Butajīra: (8.12°, 38.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Butajīra: 8113.7 km from centroid", " Lambari d'Oeste: 2851.6 km from centroid", " Anhanguera: 1846.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Butajīra", "FINAL ANSWER: Butajīra" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.68095, "lon": 101.25798, "name": "Rayong" }, { "lat": 22.60777, "lon": 73.46272, "name": "Kālol" }, { "lat": 22.69881, "lon": 73.11561, "name": "Umreth" }, { "lat": -7.74306, "lon": 110.57944, "name": "Wedi" }, { "lat": 29.71106, "lon": -95.59633, "name": "Alief" } ], "question": "Which location is the geographic outlier among: Rayong, Kālol, Umreth, Wedi, Alief?", "ground_truth": { "answer": "Alief", "outlier_distance_km": 13893.0, "second_furthest_km": 6908.8, "clarity_ratio": 2.01, "median_distance_km": 5247.6, "distances_to_centroid": { "Rayong": 5247.6, "Kālol": 2310.5, "Umreth": 2278.8, "Wedi": 6908.8, "Alief": 13893.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rayong: (12.68°, 101.26°)", " Kālol: (22.61°, 73.46°)", " Umreth: (22.70°, 73.12°)", " Wedi: (-7.74°, 110.58°)", " Alief: (29.71°, -95.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alief: 13893.0 km from centroid", " Wedi: 6908.8 km from centroid", " Rayong: 5247.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alief", "FINAL ANSWER: Alief" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.52066, "lon": -74.18504, "name": "Fundación" }, { "lat": -7.09829, "lon": -49.9435, "name": "Xinguara" }, { "lat": -2.76194, "lon": -42.27444, "name": "Tutóia" }, { "lat": -26.74056, "lon": -49.17694, "name": "Pomerode" }, { "lat": 47.62621, "lon": -122.52124, "name": "Bainbridge Island" } ], "question": "Which location is the geographic outlier among: Fundación, Xinguara, Tutóia, Pomerode, Bainbridge Island?", "ground_truth": { "answer": "Bainbridge Island", "outlier_distance_km": 7091.2, "second_furthest_km": 3981.7, "clarity_ratio": 1.78, "median_distance_km": 2924.0, "distances_to_centroid": { "Fundación": 1000.2, "Xinguara": 2336.1, "Tutóia": 2924.0, "Pomerode": 3981.7, "Bainbridge Island": 7091.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fundación: (10.52°, -74.19°)", " Xinguara: (-7.10°, -49.94°)", " Tutóia: (-2.76°, -42.27°)", " Pomerode: (-26.74°, -49.18°)", " Bainbridge Island: (47.63°, -122.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bainbridge Island: 7091.2 km from centroid", " Pomerode: 3981.7 km from centroid", " Tutóia: 2924.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bainbridge Island", "FINAL ANSWER: Bainbridge Island" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 28.80055, "lon": -81.27312, "name": "Sanford" }, { "lat": 44.05817, "lon": -121.31531, "name": "Bend" }, { "lat": 42.13919, "lon": -87.92896, "name": "Wheeling" }, { "lat": 44.64969, "lon": -93.24272, "name": "Lakeville" }, { "lat": -38.04369, "lon": 145.2923, "name": "Narre Warren South" } ], "question": "Which location is the geographic outlier among: Sanford, Bend, Wheeling, Lakeville, Narre Warren South?", "ground_truth": { "answer": "Narre Warren South", "outlier_distance_km": 18056.2, "second_furthest_km": 6882.7, "clarity_ratio": 2.62, "median_distance_km": 4667.5, "distances_to_centroid": { "Sanford": 3365.6, "Bend": 6882.7, "Wheeling": 4182.3, "Lakeville": 4667.5, "Narre Warren South": 18056.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sanford: (28.80°, -81.27°)", " Bend: (44.06°, -121.32°)", " Wheeling: (42.14°, -87.93°)", " Lakeville: (44.65°, -93.24°)", " Narre Warren South: (-38.04°, 145.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Narre Warren South: 18056.2 km from centroid", " Bend: 6882.7 km from centroid", " Lakeville: 4667.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Narre Warren South", "FINAL ANSWER: Narre Warren South" ] }, { "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": 30.43046, "lon": 31.03679, "name": "Al Bājūr" }, { "lat": 30.79336, "lon": 31.62575, "name": "Kafr Şaqr" }, { "lat": 12.87398, "lon": 11.04057, "name": "Gashua" }, { "lat": 13.15498, "lon": 10.63468, "name": "Kumagunnam" }, { "lat": 36.35, "lon": 138.63333, "name": "Karuizawa" } ], "question": "Which location is the geographic outlier among: Al Bājūr, Kafr Şaqr, Gashua, Kumagunnam, Karuizawa?", "ground_truth": { "answer": "Karuizawa", "outlier_distance_km": 8748.5, "second_furthest_km": 3783.0, "clarity_ratio": 2.31, "median_distance_km": 3756.6, "distances_to_centroid": { "Al Bājūr": 1477.9, "Kafr Şaqr": 1442.3, "Gashua": 3756.6, "Kumagunnam": 3783.0, "Karuizawa": 8748.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Al Bājūr: (30.43°, 31.04°)", " Kafr Şaqr: (30.79°, 31.63°)", " Gashua: (12.87°, 11.04°)", " Kumagunnam: (13.15°, 10.63°)", " Karuizawa: (36.35°, 138.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Karuizawa: 8748.5 km from centroid", " Kumagunnam: 3783.0 km from centroid", " Gashua: 3756.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Karuizawa", "FINAL ANSWER: Karuizawa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -25.40778, "lon": -52.41611, "name": "Laranjeiras do Sul" }, { "lat": -2.52139, "lon": -45.0825, "name": "Pinheiro" }, { "lat": -23.58481, "lon": -46.40084, "name": "Cidade Tiradentes" }, { "lat": -4.13873, "lon": -45.11881, "name": "Olho d’Água das Cunhãs" }, { "lat": 7.25256, "lon": 5.19312, "name": "Akure" } ], "question": "Which location is the geographic outlier among: Laranjeiras do Sul, Pinheiro, Cidade Tiradentes, Olho d’Água das Cunhãs, Akure?", "ground_truth": { "answer": "Akure", "outlier_distance_km": 5014.2, "second_furthest_km": 2405.8, "clarity_ratio": 2.08, "median_distance_km": 1854.1, "distances_to_centroid": { "Laranjeiras do Sul": 2405.8, "Pinheiro": 1215.8, "Cidade Tiradentes": 1854.1, "Olho d’Água das Cunhãs": 1108.7, "Akure": 5014.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Laranjeiras do Sul: (-25.41°, -52.42°)", " Pinheiro: (-2.52°, -45.08°)", " Cidade Tiradentes: (-23.58°, -46.40°)", " Olho d’Água das Cunhãs: (-4.14°, -45.12°)", " Akure: (7.25°, 5.19°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Akure: 5014.2 km from centroid", " Laranjeiras do Sul: 2405.8 km from centroid", " Cidade Tiradentes: 1854.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Akure", "FINAL ANSWER: Akure" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.78941, "lon": -93.60218, "name": "Chaska" }, { "lat": 19.55793, "lon": -99.25675, "name": "Ciudad López Mateos" }, { "lat": 20.21081, "lon": -101.13212, "name": "Yuriria" }, { "lat": 44.40011, "lon": -79.66634, "name": "Barrie" }, { "lat": 47.95013, "lon": 1.87601, "name": "Saran" } ], "question": "Which location is the geographic outlier among: Chaska, Ciudad López Mateos, Yuriria, Barrie, Saran?", "ground_truth": { "answer": "Saran", "outlier_distance_km": 6221.3, "second_furthest_km": 3111.2, "clarity_ratio": 2.0, "median_distance_km": 3006.7, "distances_to_centroid": { "Chaska": 1935.4, "Ciudad López Mateos": 3006.7, "Yuriria": 3111.2, "Barrie": 1099.8, "Saran": 6221.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chaska: (44.79°, -93.60°)", " Ciudad López Mateos: (19.56°, -99.26°)", " Yuriria: (20.21°, -101.13°)", " Barrie: (44.40°, -79.67°)", " Saran: (47.95°, 1.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saran: 6221.3 km from centroid", " Yuriria: 3111.2 km from centroid", " Ciudad López Mateos: 3006.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saran", "FINAL ANSWER: Saran" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -31.84062, "lon": 115.89549, "name": "Ballajura" }, { "lat": -33.90034, "lon": 151.05563, "name": "Greenacre" }, { "lat": -28.00029, "lon": 153.43088, "name": "Gold Coast" }, { "lat": -39.6381, "lon": 176.84918, "name": "Hastings" }, { "lat": 41.80753, "lon": -87.65644, "name": "New City" } ], "question": "Which location is the geographic outlier among: Ballajura, Greenacre, Gold Coast, Hastings, New City?", "ground_truth": { "answer": "New City", "outlier_distance_km": 17249.6, "second_furthest_km": 7451.7, "clarity_ratio": 2.31, "median_distance_km": 5337.2, "distances_to_centroid": { "Ballajura": 2056.1, "Greenacre": 5149.5, "Gold Coast": 5337.2, "Hastings": 7451.7, "New City": 17249.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ballajura: (-31.84°, 115.90°)", " Greenacre: (-33.90°, 151.06°)", " Gold Coast: (-28.00°, 153.43°)", " Hastings: (-39.64°, 176.85°)", " New City: (41.81°, -87.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New City: 17249.6 km from centroid", " Hastings: 7451.7 km from centroid", " Gold Coast: 5337.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New City", "FINAL ANSWER: New City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.73308, "lon": 151.5574, "name": "Maitland" }, { "lat": -27.10876, "lon": 152.94907, "name": "Morayfield" }, { "lat": -34.92866, "lon": 138.59863, "name": "Adelaide" }, { "lat": -33.85, "lon": 151.03333, "name": "Auburn" }, { "lat": -23.57381, "lon": -46.51561, "name": "Aricanduva" } ], "question": "Which location is the geographic outlier among: Maitland, Morayfield, Adelaide, Auburn, Aricanduva?", "ground_truth": { "answer": "Aricanduva", "outlier_distance_km": 13487.9, "second_furthest_km": 4223.0, "clarity_ratio": 3.19, "median_distance_km": 3963.6, "distances_to_centroid": { "Maitland": 3963.6, "Morayfield": 4223.0, "Adelaide": 2756.4, "Auburn": 3900.2, "Aricanduva": 13487.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maitland: (-32.73°, 151.56°)", " Morayfield: (-27.11°, 152.95°)", " Adelaide: (-34.93°, 138.60°)", " Auburn: (-33.85°, 151.03°)", " Aricanduva: (-23.57°, -46.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Aricanduva: 13487.9 km from centroid", " Morayfield: 4223.0 km from centroid", " Maitland: 3963.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Aricanduva", "FINAL ANSWER: Aricanduva" ] }, { "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": -29.04912, "lon": 29.78232, "name": "Wembesi" }, { "lat": 31.58229, "lon": 30.98095, "name": "Al Burj" }, { "lat": 11.35599, "lon": 36.95449, "name": "Gurbetē" }, { "lat": -0.98855, "lon": 36.58537, "name": "Maai Mahiu" }, { "lat": -27.80047, "lon": -64.26285, "name": "Santiago del Estero" } ], "question": "Which location is the geographic outlier among: Wembesi, Al Burj, Gurbetē, Maai Mahiu, Santiago del Estero?", "ground_truth": { "answer": "Santiago del Estero", "outlier_distance_km": 8699.8, "second_furthest_km": 4241.5, "clarity_ratio": 2.05, "median_distance_km": 3344.0, "distances_to_centroid": { "Wembesi": 3344.0, "Al Burj": 4241.5, "Gurbetē": 2997.0, "Maai Mahiu": 2518.6, "Santiago del Estero": 8699.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Wembesi: (-29.05°, 29.78°)", " Al Burj: (31.58°, 30.98°)", " Gurbetē: (11.36°, 36.95°)", " Maai Mahiu: (-0.99°, 36.59°)", " Santiago del Estero: (-27.80°, -64.26°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santiago del Estero: 8699.8 km from centroid", " Al Burj: 4241.5 km from centroid", " Wembesi: 3344.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santiago del Estero", "FINAL ANSWER: Santiago del Estero" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.33971, "lon": 87.32501, "name": "Kharagpur" }, { "lat": 33.51003, "lon": 105.1812, "name": "Yulong" }, { "lat": 10.93314, "lon": 108.28327, "name": "Mui Ne" }, { "lat": 13.95114, "lon": 101.71769, "name": "Kabin Buri" }, { "lat": 31.76212, "lon": -95.63079, "name": "Palestine" } ], "question": "Which location is the geographic outlier among: Kharagpur, Yulong, Mui Ne, Kabin Buri, Palestine?", "ground_truth": { "answer": "Palestine", "outlier_distance_km": 13504.0, "second_furthest_km": 5135.9, "clarity_ratio": 2.63, "median_distance_km": 4436.3, "distances_to_centroid": { "Kharagpur": 2664.1, "Yulong": 4436.3, "Mui Ne": 5135.9, "Kabin Buri": 4351.6, "Palestine": 13504.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kharagpur: (22.34°, 87.33°)", " Yulong: (33.51°, 105.18°)", " Mui Ne: (10.93°, 108.28°)", " Kabin Buri: (13.95°, 101.72°)", " Palestine: (31.76°, -95.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palestine: 13504.0 km from centroid", " Mui Ne: 5135.9 km from centroid", " Yulong: 4436.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palestine", "FINAL ANSWER: Palestine" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.44722, "lon": -40.77111, "name": "Dormentes" }, { "lat": -3.14306, "lon": -58.44417, "name": "Itacoatiara" }, { "lat": -22.84278, "lon": -45.25139, "name": "Potim" }, { "lat": -29.51694, "lon": -50.77778, "name": "Três Coroas" }, { "lat": -32.05251, "lon": 115.88782, "name": "Willetton" } ], "question": "Which location is the geographic outlier among: Dormentes, Itacoatiara, Potim, Três Coroas, Willetton?", "ground_truth": { "answer": "Willetton", "outlier_distance_km": 12343.8, "second_furthest_km": 4955.5, "clarity_ratio": 2.49, "median_distance_km": 3700.8, "distances_to_centroid": { "Dormentes": 2937.0, "Itacoatiara": 4955.5, "Potim": 3071.2, "Três Coroas": 3700.8, "Willetton": 12343.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dormentes: (-8.45°, -40.77°)", " Itacoatiara: (-3.14°, -58.44°)", " Potim: (-22.84°, -45.25°)", " Três Coroas: (-29.52°, -50.78°)", " Willetton: (-32.05°, 115.89°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Willetton: 12343.8 km from centroid", " Itacoatiara: 4955.5 km from centroid", " Três Coroas: 3700.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Willetton", "FINAL ANSWER: Willetton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.90012, "lon": -78.93286, "name": "Fort Erie" }, { "lat": 45.49452, "lon": -73.82419, "name": "Dollard-Des Ormeaux" }, { "lat": 42.86947, "lon": -85.64475, "name": "Kentwood" }, { "lat": 25.7065, "lon": -80.4388, "name": "Kendall West" }, { "lat": -31.8075, "lon": 115.86599, "name": "Landsdale" } ], "question": "Which location is the geographic outlier among: Fort Erie, Dollard-Des Ormeaux, Kentwood, Kendall West, Landsdale?", "ground_truth": { "answer": "Landsdale", "outlier_distance_km": 17598.9, "second_furthest_km": 4536.5, "clarity_ratio": 3.88, "median_distance_km": 4007.0, "distances_to_centroid": { "Fort Erie": 4007.0, "Dollard-Des Ormeaux": 3734.7, "Kentwood": 4536.5, "Kendall West": 3988.4, "Landsdale": 17598.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fort Erie: (42.90°, -78.93°)", " Dollard-Des Ormeaux: (45.49°, -73.82°)", " Kentwood: (42.87°, -85.64°)", " Kendall West: (25.71°, -80.44°)", " Landsdale: (-31.81°, 115.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Landsdale: 17598.9 km from centroid", " Kentwood: 4536.5 km from centroid", " Fort Erie: 4007.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Landsdale", "FINAL ANSWER: Landsdale" ] }, { "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": -36.88041, "lon": 174.79819, "name": "Remuera" }, { "lat": -39.6381, "lon": 176.84918, "name": "Hastings" }, { "lat": -34.28853, "lon": 146.05093, "name": "Griffith" }, { "lat": -37.65, "lon": 145.1, "name": "South Morang" }, { "lat": 7.83793, "lon": -72.5037, "name": "Los Patios" } ], "question": "Which location is the geographic outlier among: Remuera, Hastings, Griffith, South Morang, Los Patios?", "ground_truth": { "answer": "Los Patios", "outlier_distance_km": 17656.4, "second_furthest_km": 5817.7, "clarity_ratio": 3.03, "median_distance_km": 5684.1, "distances_to_centroid": { "Remuera": 5684.1, "Hastings": 5817.7, "Griffith": 3105.3, "South Morang": 3068.8, "Los Patios": 17656.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Remuera: (-36.88°, 174.80°)", " Hastings: (-39.64°, 176.85°)", " Griffith: (-34.29°, 146.05°)", " South Morang: (-37.65°, 145.10°)", " Los Patios: (7.84°, -72.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Los Patios: 17656.4 km from centroid", " Hastings: 5817.7 km from centroid", " Remuera: 5684.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Los Patios", "FINAL ANSWER: Los Patios" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.51716, "lon": 83.20548, "name": "Sālūr" }, { "lat": 40.54139, "lon": 110.51083, "name": "Salaqi" }, { "lat": 30.66134, "lon": 117.47783, "name": "Chizhou" }, { "lat": 38.71528, "lon": 112.7575, "name": "Yuanping" }, { "lat": -22.14583, "lon": -51.17083, "name": "Martinópolis" } ], "question": "Which location is the geographic outlier among: Sālūr, Salaqi, Chizhou, Yuanping, Martinópolis?", "ground_truth": { "answer": "Martinópolis", "outlier_distance_km": 14438.2, "second_furthest_km": 4389.0, "clarity_ratio": 3.29, "median_distance_km": 4118.7, "distances_to_centroid": { "Sālūr": 954.2, "Salaqi": 4003.6, "Chizhou": 4389.0, "Yuanping": 4118.7, "Martinópolis": 14438.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sālūr: (18.52°, 83.21°)", " Salaqi: (40.54°, 110.51°)", " Chizhou: (30.66°, 117.48°)", " Yuanping: (38.72°, 112.76°)", " Martinópolis: (-22.15°, -51.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Martinópolis: 14438.2 km from centroid", " Chizhou: 4389.0 km from centroid", " Yuanping: 4118.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Martinópolis", "FINAL ANSWER: Martinópolis" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.69572, "lon": 2.18727, "name": "Orsay" }, { "lat": 51.57141, "lon": 34.68324, "name": "Ryl’sk" }, { "lat": 45.76873, "lon": 4.95883, "name": "Décines-Charpieu" }, { "lat": 54.51889, "lon": 18.53188, "name": "Gdynia" }, { "lat": 38.62083, "lon": 115.39639, "name": "Beiwangli" } ], "question": "Which location is the geographic outlier among: Orsay, Ryl’sk, Décines-Charpieu, Gdynia, Beiwangli?", "ground_truth": { "answer": "Beiwangli", "outlier_distance_km": 6285.8, "second_furthest_km": 2422.8, "clarity_ratio": 2.59, "median_distance_km": 2294.8, "distances_to_centroid": { "Orsay": 2422.8, "Ryl’sk": 416.8, "Décines-Charpieu": 2294.8, "Gdynia": 1371.2, "Beiwangli": 6285.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Orsay: (48.70°, 2.19°)", " Ryl’sk: (51.57°, 34.68°)", " Décines-Charpieu: (45.77°, 4.96°)", " Gdynia: (54.52°, 18.53°)", " Beiwangli: (38.62°, 115.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Beiwangli: 6285.8 km from centroid", " Orsay: 2422.8 km from centroid", " Décines-Charpieu: 2294.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Beiwangli", "FINAL ANSWER: Beiwangli" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.7, "lon": 37.8, "name": "Kuz’minki" }, { "lat": 58.28731, "lon": 59.74751, "name": "Kushva" }, { "lat": 55.50194, "lon": 36.02722, "name": "Mozhaysk" }, { "lat": 45.37411, "lon": 44.2198, "name": "Arzgir" }, { "lat": -5.1075, "lon": -36.32028, "name": "Guamaré" } ], "question": "Which location is the geographic outlier among: Kuz’minki, Kushva, Mozhaysk, Arzgir, Guamaré?", "ground_truth": { "answer": "Guamaré", "outlier_distance_km": 8344.7, "second_furthest_km": 2841.3, "clarity_ratio": 2.94, "median_distance_km": 1676.1, "distances_to_centroid": { "Kuz’minki": 1676.1, "Kushva": 2841.3, "Mozhaysk": 1607.6, "Arzgir": 1333.8, "Guamaré": 8344.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kuz’minki: (55.70°, 37.80°)", " Kushva: (58.29°, 59.75°)", " Mozhaysk: (55.50°, 36.03°)", " Arzgir: (45.37°, 44.22°)", " Guamaré: (-5.11°, -36.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Guamaré: 8344.7 km from centroid", " Kushva: 2841.3 km from centroid", " Kuz’minki: 1676.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Guamaré", "FINAL ANSWER: Guamaré" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.42833, "lon": -47.82417, "name": "Guará" }, { "lat": -13.18222, "lon": -39.425, "name": "Laje" }, { "lat": -18.37333, "lon": -40.83056, "name": "Ecoporanga" }, { "lat": -21.23342, "lon": -45.23488, "name": "Nepomuceno" }, { "lat": -23.69748, "lon": 133.88362, "name": "Alice Springs" } ], "question": "Which location is the geographic outlier among: Guará, Laje, Ecoporanga, Nepomuceno, Alice Springs?", "ground_truth": { "answer": "Alice Springs", "outlier_distance_km": 13680.8, "second_furthest_km": 4166.9, "clarity_ratio": 3.28, "median_distance_km": 3891.4, "distances_to_centroid": { "Guará": 4166.9, "Laje": 3430.8, "Ecoporanga": 3462.8, "Nepomuceno": 3891.4, "Alice Springs": 13680.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Guará: (-20.43°, -47.82°)", " Laje: (-13.18°, -39.42°)", " Ecoporanga: (-18.37°, -40.83°)", " Nepomuceno: (-21.23°, -45.23°)", " Alice Springs: (-23.70°, 133.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alice Springs: 13680.8 km from centroid", " Guará: 4166.9 km from centroid", " Nepomuceno: 3891.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alice Springs", "FINAL ANSWER: Alice Springs" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.0182, "lon": 174.88019, "name": "Manurewa" }, { "lat": -33.72197, "lon": 151.04607, "name": "Cherrybrook" }, { "lat": -37.79798, "lon": 144.94512, "name": "North Melbourne" }, { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" }, { "lat": 28.47112, "lon": -81.42452, "name": "Oak Ridge" } ], "question": "Which location is the geographic outlier among: Manurewa, Cherrybrook, North Melbourne, Lower Hutt, Oak Ridge?", "ground_truth": { "answer": "Oak Ridge", "outlier_distance_km": 18516.8, "second_furthest_km": 5994.8, "clarity_ratio": 3.09, "median_distance_km": 5969.7, "distances_to_centroid": { "Manurewa": 5994.8, "Cherrybrook": 3835.2, "North Melbourne": 3383.6, "Lower Hutt": 5969.7, "Oak Ridge": 18516.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Manurewa: (-37.02°, 174.88°)", " Cherrybrook: (-33.72°, 151.05°)", " North Melbourne: (-37.80°, 144.95°)", " Lower Hutt: (-41.22°, 174.92°)", " Oak Ridge: (28.47°, -81.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Oak Ridge: 18516.8 km from centroid", " Manurewa: 5994.8 km from centroid", " Lower Hutt: 5969.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Oak Ridge", "FINAL ANSWER: Oak Ridge" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.01114, "lon": -87.84062, "name": "Park Ridge" }, { "lat": 40.78955, "lon": -74.05653, "name": "Secaucus" }, { "lat": 41.05899, "lon": -74.02181, "name": "Pearl River" }, { "lat": 47.64177, "lon": -122.0804, "name": "Sammamish" }, { "lat": -26.65682, "lon": 153.07955, "name": "Sunshine Coast" } ], "question": "Which location is the geographic outlier among: Park Ridge, Secaucus, Pearl River, Sammamish, Sunshine Coast?", "ground_truth": { "answer": "Sunshine Coast", "outlier_distance_km": 18609.2, "second_furthest_km": 7040.0, "clarity_ratio": 2.64, "median_distance_km": 4421.7, "distances_to_centroid": { "Park Ridge": 4421.7, "Secaucus": 3265.8, "Pearl River": 3269.9, "Sammamish": 7040.0, "Sunshine Coast": 18609.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Park Ridge: (42.01°, -87.84°)", " Secaucus: (40.79°, -74.06°)", " Pearl River: (41.06°, -74.02°)", " Sammamish: (47.64°, -122.08°)", " Sunshine Coast: (-26.66°, 153.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sunshine Coast: 18609.2 km from centroid", " Sammamish: 7040.0 km from centroid", " Park Ridge: 4421.7 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": -37.73261, "lon": 144.86504, "name": "Keilor East" }, { "lat": -35.41647, "lon": 149.06954, "name": "Tuggeranong Administrative District" }, { "lat": -33.78333, "lon": 150.93333, "name": "Seven Hills" }, { "lat": -37.80639, "lon": 145.03086, "name": "Kew" }, { "lat": -29.2975, "lon": -51.50361, "name": "Carlos Barbosa" } ], "question": "Which location is the geographic outlier among: Keilor East, Tuggeranong Administrative District, Seven Hills, Kew, Carlos Barbosa?", "ground_truth": { "answer": "Carlos Barbosa", "outlier_distance_km": 12559.8, "second_furthest_km": 3943.9, "clarity_ratio": 3.18, "median_distance_km": 3737.5, "distances_to_centroid": { "Keilor East": 3327.7, "Tuggeranong Administrative District": 3737.5, "Seven Hills": 3943.9, "Kew": 3341.3, "Carlos Barbosa": 12559.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Keilor East: (-37.73°, 144.87°)", " Tuggeranong Administrative District: (-35.42°, 149.07°)", " Seven Hills: (-33.78°, 150.93°)", " Kew: (-37.81°, 145.03°)", " Carlos Barbosa: (-29.30°, -51.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carlos Barbosa: 12559.8 km from centroid", " Seven Hills: 3943.9 km from centroid", " Tuggeranong Administrative District: 3737.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carlos Barbosa", "FINAL ANSWER: Carlos Barbosa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 28.30468, "lon": -81.41667, "name": "Kissimmee" }, { "lat": 36.74731, "lon": -95.98082, "name": "Bartlesville" }, { "lat": 19.70186, "lon": -99.14485, "name": "Melchor Ocampo" }, { "lat": 32.85727, "lon": -116.92225, "name": "Lakeside" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" } ], "question": "Which location is the geographic outlier among: Kissimmee, Bartlesville, Melchor Ocampo, Lakeside, Cheltenham?", "ground_truth": { "answer": "Cheltenham", "outlier_distance_km": 17170.9, "second_furthest_km": 6952.1, "clarity_ratio": 2.47, "median_distance_km": 5235.4, "distances_to_centroid": { "Kissimmee": 3532.4, "Bartlesville": 5098.2, "Melchor Ocampo": 5235.4, "Lakeside": 6952.1, "Cheltenham": 17170.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kissimmee: (28.30°, -81.42°)", " Bartlesville: (36.75°, -95.98°)", " Melchor Ocampo: (19.70°, -99.14°)", " Lakeside: (32.86°, -116.92°)", " Cheltenham: (-37.97°, 145.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cheltenham: 17170.9 km from centroid", " Lakeside: 6952.1 km from centroid", " Melchor Ocampo: 5235.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cheltenham", "FINAL ANSWER: Cheltenham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.64082, "lon": 79.43229, "name": "Rānikhet" }, { "lat": 13.79425, "lon": 100.50447, "name": "Bang Phlat" }, { "lat": 12.66621, "lon": 76.4877, "name": "Krishnarājpet" }, { "lat": 10.96464, "lon": 79.4293, "name": "Tirunāgeswaram" }, { "lat": 32.72541, "lon": -97.32085, "name": "Fort Worth" } ], "question": "Which location is the geographic outlier among: Rānikhet, Bang Phlat, Krishnarājpet, Tirunāgeswaram, Fort Worth?", "ground_truth": { "answer": "Fort Worth", "outlier_distance_km": 13077.5, "second_furthest_km": 5638.2, "clarity_ratio": 2.32, "median_distance_km": 3536.6, "distances_to_centroid": { "Rānikhet": 3365.6, "Bang Phlat": 5638.2, "Krishnarājpet": 3171.7, "Tirunāgeswaram": 3536.6, "Fort Worth": 13077.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rānikhet: (29.64°, 79.43°)", " Bang Phlat: (13.79°, 100.50°)", " Krishnarājpet: (12.67°, 76.49°)", " Tirunāgeswaram: (10.96°, 79.43°)", " Fort Worth: (32.73°, -97.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fort Worth: 13077.5 km from centroid", " Bang Phlat: 5638.2 km from centroid", " Tirunāgeswaram: 3536.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fort Worth", "FINAL ANSWER: Fort Worth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.60004, "lon": 126.91699, "name": "Jeongeup" }, { "lat": 2.08333, "lon": 111.61667, "name": "Maradong" }, { "lat": 13.80349, "lon": 100.60749, "name": "Lat Phrao" }, { "lat": 39.07167, "lon": 141.71667, "name": "Ōfunato" }, { "lat": -21.76417, "lon": -43.35028, "name": "Juiz de Fora" } ], "question": "Which location is the geographic outlier among: Jeongeup, Maradong, Lat Phrao, Ōfunato, Juiz de Fora?", "ground_truth": { "answer": "Juiz de Fora", "outlier_distance_km": 14756.2, "second_furthest_km": 5980.4, "clarity_ratio": 2.47, "median_distance_km": 4618.1, "distances_to_centroid": { "Jeongeup": 4618.1, "Maradong": 2951.5, "Lat Phrao": 1415.2, "Ōfunato": 5980.4, "Juiz de Fora": 14756.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jeongeup: (35.60°, 126.92°)", " Maradong: (2.08°, 111.62°)", " Lat Phrao: (13.80°, 100.61°)", " Ōfunato: (39.07°, 141.72°)", " Juiz de Fora: (-21.76°, -43.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Juiz de Fora: 14756.2 km from centroid", " Ōfunato: 5980.4 km from centroid", " Jeongeup: 4618.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Juiz de Fora", "FINAL ANSWER: Juiz de Fora" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 14.71694, "lon": 120.95806, "name": "Malanday" }, { "lat": 20.53917, "lon": 85.91512, "name": "Choudwar" }, { "lat": 5.41123, "lon": 100.33543, "name": "George Town" }, { "lat": 28.63406, "lon": 77.05771, "name": "Hashtsāl" }, { "lat": -27.46794, "lon": 153.02809, "name": "Brisbane" } ], "question": "Which location is the geographic outlier among: Malanday, Choudwar, George Town, Hashtsāl, Brisbane?", "ground_truth": { "answer": "Brisbane", "outlier_distance_km": 6317.1, "second_furthest_km": 3896.9, "clarity_ratio": 1.62, "median_distance_km": 2680.5, "distances_to_centroid": { "Malanday": 1630.5, "Choudwar": 2680.5, "George Town": 852.2, "Hashtsāl": 3896.9, "Brisbane": 6317.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Malanday: (14.72°, 120.96°)", " Choudwar: (20.54°, 85.92°)", " George Town: (5.41°, 100.34°)", " Hashtsāl: (28.63°, 77.06°)", " Brisbane: (-27.47°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brisbane: 6317.1 km from centroid", " Hashtsāl: 3896.9 km from centroid", " Choudwar: 2680.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brisbane", "FINAL ANSWER: Brisbane" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -15.83326, "lon": -48.05506, "name": "Taguatinga" }, { "lat": -21.27528, "lon": -47.30417, "name": "Cajuru" }, { "lat": -5.25806, "lon": -44.64889, "name": "Tuntum" }, { "lat": -27.36737, "lon": -70.33219, "name": "Copiapó" }, { "lat": 51.43158, "lon": -0.55239, "name": "Egham" } ], "question": "Which location is the geographic outlier among: Taguatinga, Cajuru, Tuntum, Copiapó, Egham?", "ground_truth": { "answer": "Egham", "outlier_distance_km": 7280.0, "second_furthest_km": 3984.1, "clarity_ratio": 1.83, "median_distance_km": 2035.5, "distances_to_centroid": { "Taguatinga": 1498.4, "Cajuru": 2035.5, "Tuntum": 326.4, "Copiapó": 3984.1, "Egham": 7280.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taguatinga: (-15.83°, -48.06°)", " Cajuru: (-21.28°, -47.30°)", " Tuntum: (-5.26°, -44.65°)", " Copiapó: (-27.37°, -70.33°)", " Egham: (51.43°, -0.55°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Egham: 7280.0 km from centroid", " Copiapó: 3984.1 km from centroid", " Cajuru: 2035.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Egham", "FINAL ANSWER: Egham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 41.38364, "lon": 2.17628, "name": "Barri Gòtic" }, { "lat": 41.32879, "lon": 15.70994, "name": "Orta Nova" }, { "lat": 47.85775, "lon": 11.48054, "name": "Geretsried" }, { "lat": 39.07195, "lon": -0.26623, "name": "Tavernes de la Valldigna" }, { "lat": -21.19361, "lon": -48.16389, "name": "Barrinha" } ], "question": "Which location is the geographic outlier among: Barri Gòtic, Orta Nova, Geretsried, Tavernes de la Valldigna, Barrinha?", "ground_truth": { "answer": "Barrinha", "outlier_distance_km": 7385.0, "second_furthest_km": 2406.5, "clarity_ratio": 3.07, "median_distance_km": 2181.8, "distances_to_centroid": { "Barri Gòtic": 1407.8, "Orta Nova": 2181.8, "Geretsried": 2406.5, "Tavernes de la Valldigna": 1092.6, "Barrinha": 7385.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Barri Gòtic: (41.38°, 2.18°)", " Orta Nova: (41.33°, 15.71°)", " Geretsried: (47.86°, 11.48°)", " Tavernes de la Valldigna: (39.07°, -0.27°)", " Barrinha: (-21.19°, -48.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Barrinha: 7385.0 km from centroid", " Geretsried: 2406.5 km from centroid", " Orta Nova: 2181.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Barrinha", "FINAL ANSWER: Barrinha" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.86, "lon": 37.76159, "name": "Sodo" }, { "lat": -29.20824, "lon": 29.9946, "name": "Mooi River" }, { "lat": -33.96109, "lon": 25.61494, "name": "Port Elizabeth" }, { "lat": 5.63418, "lon": 38.23603, "name": "Hagere Maryam" }, { "lat": -28.84556, "lon": -51.89028, "name": "Guaporé" } ], "question": "Which location is the geographic outlier among: Sodo, Mooi River, Port Elizabeth, Hagere Maryam, Guaporé?", "ground_truth": { "answer": "Guaporé", "outlier_distance_km": 7033.5, "second_furthest_km": 3489.6, "clarity_ratio": 2.02, "median_distance_km": 3428.8, "distances_to_centroid": { "Sodo": 3489.6, "Mooi River": 2062.7, "Port Elizabeth": 2229.1, "Hagere Maryam": 3428.8, "Guaporé": 7033.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sodo: (6.86°, 37.76°)", " Mooi River: (-29.21°, 29.99°)", " Port Elizabeth: (-33.96°, 25.61°)", " Hagere Maryam: (5.63°, 38.24°)", " Guaporé: (-28.85°, -51.89°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Guaporé: 7033.5 km from centroid", " Sodo: 3489.6 km from centroid", " Hagere Maryam: 3428.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Guaporé", "FINAL ANSWER: Guaporé" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.66008, "lon": 153.09953, "name": "Maroochydore" }, { "lat": -33.90034, "lon": 151.05563, "name": "Greenacre" }, { "lat": -27.98941, "lon": 153.33633, "name": "Nerang" }, { "lat": -38.15912, "lon": 145.93118, "name": "Warragul" }, { "lat": 6.70608, "lon": 37.76966, "name": "Tebela" } ], "question": "Which location is the geographic outlier among: Maroochydore, Greenacre, Nerang, Warragul, Tebela?", "ground_truth": { "answer": "Tebela", "outlier_distance_km": 10357.6, "second_furthest_km": 2542.6, "clarity_ratio": 4.07, "median_distance_km": 2512.1, "distances_to_centroid": { "Maroochydore": 2512.1, "Greenacre": 2470.1, "Nerang": 2542.6, "Warragul": 2298.1, "Tebela": 10357.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maroochydore: (-26.66°, 153.10°)", " Greenacre: (-33.90°, 151.06°)", " Nerang: (-27.99°, 153.34°)", " Warragul: (-38.16°, 145.93°)", " Tebela: (6.71°, 37.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tebela: 10357.6 km from centroid", " Nerang: 2542.6 km from centroid", " Maroochydore: 2512.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tebela", "FINAL ANSWER: Tebela" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.36, "lon": 28.129, "name": "Tokoza" }, { "lat": -29.06415, "lon": 30.59279, "name": "Greytown" }, { "lat": -1.17641, "lon": 36.7564, "name": "Karuri" }, { "lat": 12.416, "lon": 39.55971, "name": "Alamata" }, { "lat": -24.70806, "lon": -47.55528, "name": "Iguape" } ], "question": "Which location is the geographic outlier among: Tokoza, Greytown, Karuri, Alamata, Iguape?", "ground_truth": { "answer": "Iguape", "outlier_distance_km": 6877.9, "second_furthest_km": 3794.2, "clarity_ratio": 1.81, "median_distance_km": 2540.2, "distances_to_centroid": { "Tokoza": 1784.1, "Greytown": 2170.2, "Karuri": 2540.2, "Alamata": 3794.2, "Iguape": 6877.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tokoza: (-26.36°, 28.13°)", " Greytown: (-29.06°, 30.59°)", " Karuri: (-1.18°, 36.76°)", " Alamata: (12.42°, 39.56°)", " Iguape: (-24.71°, -47.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Iguape: 6877.9 km from centroid", " Alamata: 3794.2 km from centroid", " Karuri: 2540.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Iguape", "FINAL ANSWER: Iguape" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.01028, "lon": -42.84056, "name": "Visconde do Rio Branco" }, { "lat": -14.54114, "lon": -52.79508, "name": "Campinápolis" }, { "lat": -28.4602, "lon": -62.83354, "name": "Añatuya" }, { "lat": -19.86028, "lon": -44.60833, "name": "Pará de Minas" }, { "lat": -37.90232, "lon": 145.01734, "name": "Brighton East" } ], "question": "Which location is the geographic outlier among: Visconde do Rio Branco, Campinápolis, Añatuya, Pará de Minas, Brighton East?", "ground_truth": { "answer": "Brighton East", "outlier_distance_km": 12674.8, "second_furthest_km": 5084.0, "clarity_ratio": 2.49, "median_distance_km": 4436.2, "distances_to_centroid": { "Visconde do Rio Branco": 3218.7, "Campinápolis": 4436.2, "Añatuya": 5084.0, "Pará de Minas": 3427.7, "Brighton East": 12674.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Visconde do Rio Branco: (-21.01°, -42.84°)", " Campinápolis: (-14.54°, -52.80°)", " Añatuya: (-28.46°, -62.83°)", " Pará de Minas: (-19.86°, -44.61°)", " Brighton East: (-37.90°, 145.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brighton East: 12674.8 km from centroid", " Añatuya: 5084.0 km from centroid", " Campinápolis: 4436.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brighton East", "FINAL ANSWER: Brighton East" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.08639, "lon": 106.98722, "name": "Nanping" }, { "lat": 33.27668, "lon": 131.15628, "name": "Tsukawaki" }, { "lat": 31.17664, "lon": 108.13155, "name": "Zhonghe" }, { "lat": 36.43351, "lon": 129.057, "name": "Cheongsong gun" }, { "lat": 42.48509, "lon": -71.43284, "name": "Acton" } ], "question": "Which location is the geographic outlier among: Nanping, Tsukawaki, Zhonghe, Cheongsong gun, Acton?", "ground_truth": { "answer": "Acton", "outlier_distance_km": 11000.7, "second_furthest_km": 4603.0, "clarity_ratio": 2.39, "median_distance_km": 4331.7, "distances_to_centroid": { "Nanping": 2541.0, "Tsukawaki": 4603.0, "Zhonghe": 2574.0, "Cheongsong gun": 4331.7, "Acton": 11000.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nanping: (29.09°, 106.99°)", " Tsukawaki: (33.28°, 131.16°)", " Zhonghe: (31.18°, 108.13°)", " Cheongsong gun: (36.43°, 129.06°)", " Acton: (42.49°, -71.43°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Acton: 11000.7 km from centroid", " Tsukawaki: 4603.0 km from centroid", " Cheongsong gun: 4331.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Acton", "FINAL ANSWER: Acton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.90694, "lon": 174.68704, "name": "New Lynn" }, { "lat": -43.58333, "lon": 172.38333, "name": "Rolleston" }, { "lat": -41.05584, "lon": 145.90375, "name": "Burnie" }, { "lat": -37.89138, "lon": 144.62368, "name": "Wyndham Vale" }, { "lat": 46.21125, "lon": -119.13723, "name": "Kennewick" } ], "question": "Which location is the geographic outlier among: New Lynn, Rolleston, Burnie, Wyndham Vale, Kennewick?", "ground_truth": { "answer": "Kennewick", "outlier_distance_km": 15375.2, "second_furthest_km": 6879.2, "clarity_ratio": 2.24, "median_distance_km": 6609.9, "distances_to_centroid": { "New Lynn": 6879.2, "Rolleston": 6609.9, "Burnie": 4425.0, "Wyndham Vale": 4238.7, "Kennewick": 15375.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " New Lynn: (-36.91°, 174.69°)", " Rolleston: (-43.58°, 172.38°)", " Burnie: (-41.06°, 145.90°)", " Wyndham Vale: (-37.89°, 144.62°)", " Kennewick: (46.21°, -119.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kennewick: 15375.2 km from centroid", " New Lynn: 6879.2 km from centroid", " Rolleston: 6609.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kennewick", "FINAL ANSWER: Kennewick" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 28.35748, "lon": 78.26914, "name": "Anūpshahr" }, { "lat": -6.82222, "lon": 107.13944, "name": "Cianjur" }, { "lat": 36.77083, "lon": 119.21083, "name": "Hanting" }, { "lat": 4.66115, "lon": 119.39647, "name": "Sitangkai" }, { "lat": 40.66312, "lon": -73.76221, "name": "Springfield Gardens" } ], "question": "Which location is the geographic outlier among: Anūpshahr, Cianjur, Hanting, Sitangkai, Springfield Gardens?", "ground_truth": { "answer": "Springfield Gardens", "outlier_distance_km": 12231.3, "second_furthest_km": 5615.4, "clarity_ratio": 2.18, "median_distance_km": 5078.6, "distances_to_centroid": { "Anūpshahr": 1187.1, "Cianjur": 5078.6, "Hanting": 5051.5, "Sitangkai": 5615.4, "Springfield Gardens": 12231.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Anūpshahr: (28.36°, 78.27°)", " Cianjur: (-6.82°, 107.14°)", " Hanting: (36.77°, 119.21°)", " Sitangkai: (4.66°, 119.40°)", " Springfield Gardens: (40.66°, -73.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Springfield Gardens: 12231.3 km from centroid", " Sitangkai: 5615.4 km from centroid", " Cianjur: 5078.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Springfield Gardens", "FINAL ANSWER: Springfield Gardens" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.80139, "lon": -45.68556, "name": "Luz" }, { "lat": -19.69194, "lon": -43.92333, "name": "Vespasiano" }, { "lat": -2.04278, "lon": -45.95917, "name": "Maracaçumé" }, { "lat": 5.13278, "lon": -74.15977, "name": "Pacho" }, { "lat": 51.86583, "lon": 4.66111, "name": "Alblasserdam" } ], "question": "Which location is the geographic outlier among: Luz, Vespasiano, Maracaçumé, Pacho, Alblasserdam?", "ground_truth": { "answer": "Alblasserdam", "outlier_distance_km": 6866.6, "second_furthest_km": 3682.7, "clarity_ratio": 1.86, "median_distance_km": 2596.3, "distances_to_centroid": { "Luz": 2596.3, "Vespasiano": 2553.4, "Maracaçumé": 792.6, "Pacho": 3682.7, "Alblasserdam": 6866.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Luz: (-19.80°, -45.69°)", " Vespasiano: (-19.69°, -43.92°)", " Maracaçumé: (-2.04°, -45.96°)", " Pacho: (5.13°, -74.16°)", " Alblasserdam: (51.87°, 4.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Alblasserdam: 6866.6 km from centroid", " Pacho: 3682.7 km from centroid", " Luz: 2596.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Alblasserdam", "FINAL ANSWER: Alblasserdam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.20087, "lon": -75.86865, "name": "Belén de Umbría" }, { "lat": -1.05361, "lon": -46.76556, "name": "Bragança" }, { "lat": -20.76361, "lon": -41.53306, "name": "Alegre" }, { "lat": -23.785, "lon": -53.07333, "name": "Cruzeiro do Oeste" }, { "lat": 22.00853, "lon": 81.23148, "name": "Kawardha" } ], "question": "Which location is the geographic outlier among: Belén de Umbría, Bragança, Alegre, Cruzeiro do Oeste, Kawardha?", "ground_truth": { "answer": "Kawardha", "outlier_distance_km": 12059.9, "second_furthest_km": 5494.9, "clarity_ratio": 2.19, "median_distance_km": 3564.4, "distances_to_centroid": { "Belén de Umbría": 5494.9, "Bragança": 2192.8, "Alegre": 2452.3, "Cruzeiro do Oeste": 3564.4, "Kawardha": 12059.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Belén de Umbría: (5.20°, -75.87°)", " Bragança: (-1.05°, -46.77°)", " Alegre: (-20.76°, -41.53°)", " Cruzeiro do Oeste: (-23.79°, -53.07°)", " Kawardha: (22.01°, 81.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kawardha: 12059.9 km from centroid", " Belén de Umbría: 5494.9 km from centroid", " Cruzeiro do Oeste: 3564.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kawardha", "FINAL ANSWER: Kawardha" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.33611, "lon": -43.77361, "name": "Malhada" }, { "lat": -20.26871, "lon": -70.1049, "name": "Alto Hospicio" }, { "lat": -22.61222, "lon": -46.70056, "name": "Serra Negra" }, { "lat": -27.28278, "lon": -50.58444, "name": "Curitibanos" }, { "lat": -37.8318, "lon": 140.77919, "name": "Mount Gambier" } ], "question": "Which location is the geographic outlier among: Malhada, Alto Hospicio, Serra Negra, Curitibanos, Mount Gambier?", "ground_truth": { "answer": "Mount Gambier", "outlier_distance_km": 12606.7, "second_furthest_km": 5742.2, "clarity_ratio": 2.2, "median_distance_km": 3653.2, "distances_to_centroid": { "Malhada": 3303.1, "Alto Hospicio": 5742.2, "Serra Negra": 3324.5, "Curitibanos": 3653.2, "Mount Gambier": 12606.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Malhada: (-14.34°, -43.77°)", " Alto Hospicio: (-20.27°, -70.10°)", " Serra Negra: (-22.61°, -46.70°)", " Curitibanos: (-27.28°, -50.58°)", " Mount Gambier: (-37.83°, 140.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mount Gambier: 12606.7 km from centroid", " Alto Hospicio: 5742.2 km from centroid", " Curitibanos: 3653.2 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": 4.775, "lon": 103.4162, "name": "Dungun" }, { "lat": 7.36194, "lon": 125.85528, "name": "Maco" }, { "lat": 32.45993, "lon": 130.16713, "name": "Hondomachi-hondo" }, { "lat": 32.31625, "lon": 75.60741, "name": "Sujānpur" }, { "lat": 4.64231, "lon": 7.92438, "name": "Eket" } ], "question": "Which location is the geographic outlier among: Dungun, Maco, Hondomachi-hondo, Sujānpur, Eket?", "ground_truth": { "answer": "Eket", "outlier_distance_km": 8868.6, "second_furthest_km": 4541.0, "clarity_ratio": 1.95, "median_distance_km": 4167.8, "distances_to_centroid": { "Dungun": 2064.1, "Maco": 4167.8, "Hondomachi-hondo": 4541.0, "Sujānpur": 2209.0, "Eket": 8868.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dungun: (4.78°, 103.42°)", " Maco: (7.36°, 125.86°)", " Hondomachi-hondo: (32.46°, 130.17°)", " Sujānpur: (32.32°, 75.61°)", " Eket: (4.64°, 7.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Eket: 8868.6 km from centroid", " Hondomachi-hondo: 4541.0 km from centroid", " Maco: 4167.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Eket", "FINAL ANSWER: Eket" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.60822, "lon": -74.51803, "name": "Warren Township" }, { "lat": 35.14953, "lon": -90.04898, "name": "Memphis" }, { "lat": 34.41333, "lon": -119.86097, "name": "Isla Vista" }, { "lat": 34.09751, "lon": -117.64839, "name": "Upland" }, { "lat": -26.55, "lon": 29.16667, "name": "Secunda" } ], "question": "Which location is the geographic outlier among: Warren Township, Memphis, Isla Vista, Upland, Secunda?", "ground_truth": { "answer": "Secunda", "outlier_distance_km": 12445.9, "second_furthest_km": 4527.6, "clarity_ratio": 2.75, "median_distance_km": 4322.5, "distances_to_centroid": { "Warren Township": 1897.5, "Memphis": 1973.5, "Isla Vista": 4527.6, "Upland": 4322.5, "Secunda": 12445.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Warren Township: (40.61°, -74.52°)", " Memphis: (35.15°, -90.05°)", " Isla Vista: (34.41°, -119.86°)", " Upland: (34.10°, -117.65°)", " Secunda: (-26.55°, 29.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Secunda: 12445.9 km from centroid", " Isla Vista: 4527.6 km from centroid", " Upland: 4322.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Secunda", "FINAL ANSWER: Secunda" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -11.34484, "lon": -41.66317, "name": "João Dourado" }, { "lat": 0.82501, "lon": -77.63966, "name": "Ipiales" }, { "lat": -17.79806, "lon": -50.92806, "name": "Rio Verde" }, { "lat": -7.57611, "lon": -40.49833, "name": "Araripina" }, { "lat": 40.01499, "lon": -105.27055, "name": "Boulder" } ], "question": "Which location is the geographic outlier among: João Dourado, Ipiales, Rio Verde, Araripina, Boulder?", "ground_truth": { "answer": "Boulder", "outlier_distance_km": 6083.5, "second_furthest_km": 2737.7, "clarity_ratio": 2.22, "median_distance_km": 2685.3, "distances_to_centroid": { "João Dourado": 2737.7, "Ipiales": 1605.5, "Rio Verde": 2468.2, "Araripina": 2685.3, "Boulder": 6083.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " João Dourado: (-11.34°, -41.66°)", " Ipiales: (0.83°, -77.64°)", " Rio Verde: (-17.80°, -50.93°)", " Araripina: (-7.58°, -40.50°)", " Boulder: (40.01°, -105.27°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Boulder: 6083.5 km from centroid", " João Dourado: 2737.7 km from centroid", " Araripina: 2685.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Boulder", "FINAL ANSWER: Boulder" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.66877, "lon": -46.78051, "name": "Capao Redondo" }, { "lat": -8.4325, "lon": -35.80444, "name": "São Joaquim do Monte" }, { "lat": -14.26722, "lon": -43.16194, "name": "Palmas de Monte Alto" }, { "lat": 10.8293, "lon": -75.03346, "name": "Juan de Acosta" }, { "lat": 55.63794, "lon": 51.81502, "name": "Nizhnekamsk" } ], "question": "Which location is the geographic outlier among: Capao Redondo, São Joaquim do Monte, Palmas de Monte Alto, Juan de Acosta, Nizhnekamsk?", "ground_truth": { "answer": "Nizhnekamsk", "outlier_distance_km": 9112.4, "second_furthest_km": 5040.1, "clarity_ratio": 1.81, "median_distance_km": 3587.3, "distances_to_centroid": { "Capao Redondo": 3587.3, "São Joaquim do Monte": 1536.7, "Palmas de Monte Alto": 2511.5, "Juan de Acosta": 5040.1, "Nizhnekamsk": 9112.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Capao Redondo: (-23.67°, -46.78°)", " São Joaquim do Monte: (-8.43°, -35.80°)", " Palmas de Monte Alto: (-14.27°, -43.16°)", " Juan de Acosta: (10.83°, -75.03°)", " Nizhnekamsk: (55.64°, 51.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nizhnekamsk: 9112.4 km from centroid", " Juan de Acosta: 5040.1 km from centroid", " Capao Redondo: 3587.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nizhnekamsk", "FINAL ANSWER: Nizhnekamsk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 39.934, "lon": -74.891, "name": "Mount Laurel" }, { "lat": 34.00946, "lon": -118.10535, "name": "Montebello" }, { "lat": 19.26174, "lon": -98.89775, "name": "Chalco" }, { "lat": 36.48847, "lon": -79.7667, "name": "Eden" }, { "lat": -12.48602, "lon": 130.9833, "name": "Palmerston" } ], "question": "Which location is the geographic outlier among: Mount Laurel, Montebello, Chalco, Eden, Palmerston?", "ground_truth": { "answer": "Palmerston", "outlier_distance_km": 18793.3, "second_furthest_km": 6796.1, "clarity_ratio": 2.77, "median_distance_km": 5251.5, "distances_to_centroid": { "Mount Laurel": 3105.4, "Montebello": 6796.1, "Chalco": 5251.5, "Eden": 3353.9, "Palmerston": 18793.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mount Laurel: (39.93°, -74.89°)", " Montebello: (34.01°, -118.11°)", " Chalco: (19.26°, -98.90°)", " Eden: (36.49°, -79.77°)", " Palmerston: (-12.49°, 130.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Palmerston: 18793.3 km from centroid", " Montebello: 6796.1 km from centroid", " Chalco: 5251.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Palmerston", "FINAL ANSWER: Palmerston" ] }, { "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": -22.65278, "lon": -43.04056, "name": "Magé" }, { "lat": -20.42833, "lon": -47.82417, "name": "Guará" }, { "lat": -25.42861, "lon": -48.71194, "name": "Antonina" }, { "lat": -23.4837, "lon": -46.41309, "name": "Jardim Helena" }, { "lat": -29.20932, "lon": 26.83898, "name": "Thaba Nchu" } ], "question": "Which location is the geographic outlier among: Magé, Guará, Antonina, Jardim Helena, Thaba Nchu?", "ground_truth": { "answer": "Thaba Nchu", "outlier_distance_km": 5793.9, "second_furthest_km": 1707.5, "clarity_ratio": 3.39, "median_distance_km": 1697.6, "distances_to_centroid": { "Magé": 1156.8, "Guará": 1697.6, "Antonina": 1707.5, "Jardim Helena": 1484.7, "Thaba Nchu": 5793.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Magé: (-22.65°, -43.04°)", " Guará: (-20.43°, -47.82°)", " Antonina: (-25.43°, -48.71°)", " Jardim Helena: (-23.48°, -46.41°)", " Thaba Nchu: (-29.21°, 26.84°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Thaba Nchu: 5793.9 km from centroid", " Antonina: 1707.5 km from centroid", " Guará: 1697.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Thaba Nchu", "FINAL ANSWER: Thaba Nchu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.10417, "lon": -55.22583, "name": "Amambai" }, { "lat": -21.42917, "lon": -45.94722, "name": "Alfenas" }, { "lat": -22.665, "lon": -45.00944, "name": "Cachoeira Paulista" }, { "lat": -2.94722, "lon": -48.95306, "name": "Tailândia" }, { "lat": 13.9, "lon": 99.76667, "name": "Tha Maka" } ], "question": "Which location is the geographic outlier among: Amambai, Alfenas, Cachoeira Paulista, Tailândia, Tha Maka?", "ground_truth": { "answer": "Tha Maka", "outlier_distance_km": 13388.5, "second_furthest_km": 4046.7, "clarity_ratio": 3.31, "median_distance_km": 3420.3, "distances_to_centroid": { "Amambai": 4046.7, "Alfenas": 3076.4, "Cachoeira Paulista": 3029.4, "Tailândia": 3420.3, "Tha Maka": 13388.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Amambai: (-23.10°, -55.23°)", " Alfenas: (-21.43°, -45.95°)", " Cachoeira Paulista: (-22.66°, -45.01°)", " Tailândia: (-2.95°, -48.95°)", " Tha Maka: (13.90°, 99.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tha Maka: 13388.5 km from centroid", " Amambai: 4046.7 km from centroid", " Tailândia: 3420.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tha Maka", "FINAL ANSWER: Tha Maka" ] }, { "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": -22.61222, "lon": -46.70056, "name": "Serra Negra" }, { "lat": -16.25, "lon": -69.08333, "name": "Yunguyo" }, { "lat": -29.68861, "lon": -51.46111, "name": "Montenegro" }, { "lat": -1.19667, "lon": -46.14, "name": "Viseu" }, { "lat": -27.62329, "lon": 153.04785, "name": "Calamvale" } ], "question": "Which location is the geographic outlier among: Serra Negra, Yunguyo, Montenegro, Viseu, Calamvale?", "ground_truth": { "answer": "Calamvale", "outlier_distance_km": 14538.4, "second_furthest_km": 6018.2, "clarity_ratio": 2.42, "median_distance_km": 4228.3, "distances_to_centroid": { "Serra Negra": 3603.2, "Yunguyo": 6018.2, "Montenegro": 4120.2, "Viseu": 4228.3, "Calamvale": 14538.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Serra Negra: (-22.61°, -46.70°)", " Yunguyo: (-16.25°, -69.08°)", " Montenegro: (-29.69°, -51.46°)", " Viseu: (-1.20°, -46.14°)", " Calamvale: (-27.62°, 153.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Calamvale: 14538.4 km from centroid", " Yunguyo: 6018.2 km from centroid", " Viseu: 4228.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Calamvale", "FINAL ANSWER: Calamvale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.55329, "lon": 34.99684, "name": "Gagarin" }, { "lat": 40.41409, "lon": -3.66553, "name": "Estrella" }, { "lat": 50.95572, "lon": 6.63986, "name": "Bergheim" }, { "lat": 41.3845, "lon": 2.18152, "name": "Sant Pere, Santa Caterina i La Ribera" }, { "lat": -37.94853, "lon": 145.15274, "name": "Springvale" } ], "question": "Which location is the geographic outlier among: Gagarin, Estrella, Bergheim, Sant Pere, Santa Caterina i La Ribera, Springvale?", "ground_truth": { "answer": "Springvale", "outlier_distance_km": 13492.0, "second_furthest_km": 3835.5, "clarity_ratio": 3.52, "median_distance_km": 3421.1, "distances_to_centroid": { "Gagarin": 2838.1, "Estrella": 3835.5, "Bergheim": 3421.1, "Sant Pere, Santa Caterina i La Ribera": 3362.5, "Springvale": 13492.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gagarin: (55.55°, 35.00°)", " Estrella: (40.41°, -3.67°)", " Bergheim: (50.96°, 6.64°)", " Sant Pere, Santa Caterina i La Ribera: (41.38°, 2.18°)", " Springvale: (-37.95°, 145.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Springvale: 13492.0 km from centroid", " Estrella: 3835.5 km from centroid", " Bergheim: 3421.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Springvale", "FINAL ANSWER: Springvale" ] }, { "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": 47.75935, "lon": 8.8403, "name": "Singen" }, { "lat": 59.37627, "lon": 28.61409, "name": "Kingisepp" }, { "lat": 40.05, "lon": 0.06667, "name": "Benicàssim" }, { "lat": 51.55797, "lon": -1.78116, "name": "Swindon" }, { "lat": -33.79798, "lon": 151.28826, "name": "Manly" } ], "question": "Which location is the geographic outlier among: Singen, Kingisepp, Benicàssim, Swindon, Manly?", "ground_truth": { "answer": "Manly", "outlier_distance_km": 13989.3, "second_furthest_km": 3762.2, "clarity_ratio": 3.72, "median_distance_km": 3401.4, "distances_to_centroid": { "Singen": 2898.0, "Kingisepp": 3005.3, "Benicàssim": 3401.4, "Swindon": 3762.2, "Manly": 13989.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Singen: (47.76°, 8.84°)", " Kingisepp: (59.38°, 28.61°)", " Benicàssim: (40.05°, 0.07°)", " Swindon: (51.56°, -1.78°)", " Manly: (-33.80°, 151.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Manly: 13989.3 km from centroid", " Swindon: 3762.2 km from centroid", " Benicàssim: 3401.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Manly", "FINAL ANSWER: Manly" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.45, "lon": 115.65, "name": "Shangqiu" }, { "lat": 21.6281, "lon": 81.70376, "name": "Simga" }, { "lat": 19.56784, "lon": 74.21154, "name": "Sangamner" }, { "lat": 2.5703, "lon": 101.833, "name": "Lukut" }, { "lat": 33.01512, "lon": -96.61305, "name": "Murphy" } ], "question": "Which location is the geographic outlier among: Shangqiu, Simga, Sangamner, Lukut, Murphy?", "ground_truth": { "answer": "Murphy", "outlier_distance_km": 13188.5, "second_furthest_km": 5968.1, "clarity_ratio": 2.21, "median_distance_km": 5468.1, "distances_to_centroid": { "Shangqiu": 5968.1, "Simga": 2714.9, "Sangamner": 1979.6, "Lukut": 5468.1, "Murphy": 13188.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shangqiu: (34.45°, 115.65°)", " Simga: (21.63°, 81.70°)", " Sangamner: (19.57°, 74.21°)", " Lukut: (2.57°, 101.83°)", " Murphy: (33.02°, -96.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Murphy: 13188.5 km from centroid", " Shangqiu: 5968.1 km from centroid", " Lukut: 5468.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Murphy", "FINAL ANSWER: Murphy" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.23656, "lon": 28.36938, "name": "Brakpan" }, { "lat": 9.99461, "lon": 39.89693, "name": "Robit" }, { "lat": 0.52036, "lon": 35.26993, "name": "Eldoret" }, { "lat": 0.00624, "lon": 37.07398, "name": "Nanyuki" }, { "lat": -33.79068, "lon": 150.6693, "name": "Glenmore Park" } ], "question": "Which location is the geographic outlier among: Brakpan, Robit, Eldoret, Nanyuki, Glenmore Park?", "ground_truth": { "answer": "Glenmore Park", "outlier_distance_km": 9617.7, "second_furthest_km": 3628.8, "clarity_ratio": 2.65, "median_distance_km": 3003.3, "distances_to_centroid": { "Brakpan": 3628.8, "Robit": 3003.3, "Eldoret": 2795.2, "Nanyuki": 2589.5, "Glenmore Park": 9617.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Brakpan: (-26.24°, 28.37°)", " Robit: (9.99°, 39.90°)", " Eldoret: (0.52°, 35.27°)", " Nanyuki: (0.01°, 37.07°)", " Glenmore Park: (-33.79°, 150.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Glenmore Park: 9617.7 km from centroid", " Brakpan: 3628.8 km from centroid", " Robit: 3003.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Glenmore Park", "FINAL ANSWER: Glenmore Park" ] }, { "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": -33.94185, "lon": 150.8717, "name": "Prestons" }, { "lat": -34.03857, "lon": 151.10005, "name": "Miranda" }, { "lat": -33.79068, "lon": 150.6693, "name": "Glenmore Park" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" }, { "lat": 41.45282, "lon": -82.18237, "name": "Lorain" } ], "question": "Which location is the geographic outlier among: Prestons, Miranda, Glenmore Park, Cheltenham, Lorain?", "ground_truth": { "answer": "Lorain", "outlier_distance_km": 17540.6, "second_furthest_km": 4973.3, "clarity_ratio": 3.53, "median_distance_km": 4951.2, "distances_to_centroid": { "Prestons": 4951.2, "Miranda": 4973.3, "Glenmore Park": 4930.9, "Cheltenham": 4515.9, "Lorain": 17540.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Prestons: (-33.94°, 150.87°)", " Miranda: (-34.04°, 151.10°)", " Glenmore Park: (-33.79°, 150.67°)", " Cheltenham: (-37.97°, 145.05°)", " Lorain: (41.45°, -82.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lorain: 17540.6 km from centroid", " Miranda: 4973.3 km from centroid", " Prestons: 4951.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lorain", "FINAL ANSWER: Lorain" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.60252, "lon": 4.68815, "name": "Heiloo" }, { "lat": 38.22008, "lon": 15.24023, "name": "Milazzo" }, { "lat": 40.38524, "lon": -3.63726, "name": "Palomeras Sureste" }, { "lat": 51.36969, "lon": -0.36693, "name": "Esher" }, { "lat": -38.14711, "lon": 144.36069, "name": "Geelong" } ], "question": "Which location is the geographic outlier among: Heiloo, Milazzo, Palomeras Sureste, Esher, Geelong?", "ground_truth": { "answer": "Geelong", "outlier_distance_km": 13792.2, "second_furthest_km": 3668.2, "clarity_ratio": 3.76, "median_distance_km": 3478.2, "distances_to_centroid": { "Heiloo": 3461.2, "Milazzo": 1867.6, "Palomeras Sureste": 3478.2, "Esher": 3668.2, "Geelong": 13792.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Heiloo: (52.60°, 4.69°)", " Milazzo: (38.22°, 15.24°)", " Palomeras Sureste: (40.39°, -3.64°)", " Esher: (51.37°, -0.37°)", " Geelong: (-38.15°, 144.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Geelong: 13792.2 km from centroid", " Esher: 3668.2 km from centroid", " Palomeras Sureste: 3478.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Geelong", "FINAL ANSWER: Geelong" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 25.98507, "lon": -98.08964, "name": "Ciudad Río Bravo" }, { "lat": 37.83615, "lon": -87.59001, "name": "Henderson" }, { "lat": 29.703, "lon": -98.12445, "name": "New Braunfels" }, { "lat": 25.81454, "lon": -80.22394, "name": "Allapattah" }, { "lat": 34.86667, "lon": 137.05, "name": "Nishio" } ], "question": "Which location is the geographic outlier among: Ciudad Río Bravo, Henderson, New Braunfels, Allapattah, Nishio?", "ground_truth": { "answer": "Nishio", "outlier_distance_km": 12704.2, "second_furthest_km": 5135.1, "clarity_ratio": 2.47, "median_distance_km": 5016.8, "distances_to_centroid": { "Ciudad Río Bravo": 5135.1, "Henderson": 3917.4, "New Braunfels": 5016.8, "Allapattah": 3440.4, "Nishio": 12704.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ciudad Río Bravo: (25.99°, -98.09°)", " Henderson: (37.84°, -87.59°)", " New Braunfels: (29.70°, -98.12°)", " Allapattah: (25.81°, -80.22°)", " Nishio: (34.87°, 137.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nishio: 12704.2 km from centroid", " Ciudad Río Bravo: 5135.1 km from centroid", " New Braunfels: 5016.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nishio", "FINAL ANSWER: Nishio" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.61524, "lon": 6.54776, "name": "Minna" }, { "lat": -1.08083, "lon": 35.87111, "name": "Narok" }, { "lat": 7.59383, "lon": 6.21798, "name": "Ogaminana" }, { "lat": 6.45407, "lon": 3.39467, "name": "Lagos" }, { "lat": 24.827, "lon": 87.2125, "name": "Godda" } ], "question": "Which location is the geographic outlier among: Minna, Narok, Ogaminana, Lagos, Godda?", "ground_truth": { "answer": "Godda", "outlier_distance_km": 6483.6, "second_furthest_km": 2713.2, "clarity_ratio": 2.39, "median_distance_km": 2387.4, "distances_to_centroid": { "Minna": 2335.4, "Narok": 1472.6, "Ogaminana": 2387.4, "Lagos": 2713.2, "Godda": 6483.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Minna: (9.62°, 6.55°)", " Narok: (-1.08°, 35.87°)", " Ogaminana: (7.59°, 6.22°)", " Lagos: (6.45°, 3.39°)", " Godda: (24.83°, 87.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Godda: 6483.6 km from centroid", " Lagos: 2713.2 km from centroid", " Ogaminana: 2387.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Godda", "FINAL ANSWER: Godda" ] }, { "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" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 8.71068, "lon": 77.4519, "name": "Ambasamudram" }, { "lat": 12.02999, "lon": 75.28193, "name": "Ezhome" }, { "lat": 25.25034, "lon": 79.06204, "name": "Rānīpur" }, { "lat": 9.65941, "lon": 76.36335, "name": "Srīkandamangalam" }, { "lat": 51.53333, "lon": 0.08333, "name": "Barking" } ], "question": "Which location is the geographic outlier among: Ambasamudram, Ezhome, Rānīpur, Srīkandamangalam, Barking?", "ground_truth": { "answer": "Barking", "outlier_distance_km": 6206.4, "second_furthest_km": 2205.9, "clarity_ratio": 2.81, "median_distance_km": 2046.5, "distances_to_centroid": { "Ambasamudram": 2205.9, "Ezhome": 1787.4, "Rānīpur": 1826.1, "Srīkandamangalam": 2046.5, "Barking": 6206.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ambasamudram: (8.71°, 77.45°)", " Ezhome: (12.03°, 75.28°)", " Rānīpur: (25.25°, 79.06°)", " Srīkandamangalam: (9.66°, 76.36°)", " Barking: (51.53°, 0.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Barking: 6206.4 km from centroid", " Ambasamudram: 2205.9 km from centroid", " Srīkandamangalam: 2046.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Barking", "FINAL ANSWER: Barking" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.09861, "lon": -48.92583, "name": "Avaré" }, { "lat": -22.85472, "lon": -46.31833, "name": "Extrema" }, { "lat": 3.93135, "lon": -76.48481, "name": "Darien" }, { "lat": -21.54, "lon": -43.01056, "name": "São João Nepomuceno" }, { "lat": 44.63394, "lon": 39.13582, "name": "Goryachiy Klyuch" } ], "question": "Which location is the geographic outlier among: Avaré, Extrema, Darien, São João Nepomuceno, Goryachiy Klyuch?", "ground_truth": { "answer": "Goryachiy Klyuch", "outlier_distance_km": 9072.3, "second_furthest_km": 4675.4, "clarity_ratio": 1.94, "median_distance_km": 2610.6, "distances_to_centroid": { "Avaré": 2610.6, "Extrema": 2438.8, "Darien": 4675.4, "São João Nepomuceno": 2150.2, "Goryachiy Klyuch": 9072.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Avaré: (-23.10°, -48.93°)", " Extrema: (-22.85°, -46.32°)", " Darien: (3.93°, -76.48°)", " São João Nepomuceno: (-21.54°, -43.01°)", " Goryachiy Klyuch: (44.63°, 39.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Goryachiy Klyuch: 9072.3 km from centroid", " Darien: 4675.4 km from centroid", " Avaré: 2610.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Goryachiy Klyuch", "FINAL ANSWER: Goryachiy Klyuch" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.35867, "lon": -99.20329, "name": "Álvaro Obregón" }, { "lat": 19.28431, "lon": -98.43885, "name": "San Martin Texmelucan de Labastida" }, { "lat": 43.6135, "lon": -116.20345, "name": "Boise" }, { "lat": 37.82159, "lon": -121.99996, "name": "Danville" }, { "lat": -25.40892, "lon": 28.287, "name": "Hammanskraal" } ], "question": "Which location is the geographic outlier among: Álvaro Obregón, San Martin Texmelucan de Labastida, Boise, Danville, Hammanskraal?", "ground_truth": { "answer": "Hammanskraal", "outlier_distance_km": 12829.7, "second_furthest_km": 4436.0, "clarity_ratio": 2.89, "median_distance_km": 4236.8, "distances_to_centroid": { "Álvaro Obregón": 1858.2, "San Martin Texmelucan de Labastida": 1778.2, "Boise": 4236.8, "Danville": 4436.0, "Hammanskraal": 12829.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Álvaro Obregón: (19.36°, -99.20°)", " San Martin Texmelucan de Labastida: (19.28°, -98.44°)", " Boise: (43.61°, -116.20°)", " Danville: (37.82°, -122.00°)", " Hammanskraal: (-25.41°, 28.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hammanskraal: 12829.7 km from centroid", " Danville: 4436.0 km from centroid", " Boise: 4236.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hammanskraal", "FINAL ANSWER: Hammanskraal" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.03609, "lon": 13.91815, "name": "Dikwa" }, { "lat": 5.69951, "lon": -0.03484, "name": "Ashaiman" }, { "lat": 5.84802, "lon": -0.17449, "name": "Aburi" }, { "lat": 1.25881, "lon": 35.09569, "name": "Makutano" }, { "lat": -43.89834, "lon": 171.73011, "name": "Ashburton" } ], "question": "Which location is the geographic outlier among: Dikwa, Ashaiman, Aburi, Makutano, Ashburton?", "ground_truth": { "answer": "Ashburton", "outlier_distance_km": 12579.5, "second_furthest_km": 5033.1, "clarity_ratio": 2.5, "median_distance_km": 5014.7, "distances_to_centroid": { "Dikwa": 3773.7, "Ashaiman": 5014.7, "Aburi": 5033.1, "Makutano": 1149.2, "Ashburton": 12579.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dikwa: (12.04°, 13.92°)", " Ashaiman: (5.70°, -0.03°)", " Aburi: (5.85°, -0.17°)", " Makutano: (1.26°, 35.10°)", " Ashburton: (-43.90°, 171.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ashburton: 12579.5 km from centroid", " Aburi: 5033.1 km from centroid", " Ashaiman: 5014.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ashburton", "FINAL ANSWER: Ashburton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -10.65167, "lon": -68.50444, "name": "Xapuri" }, { "lat": -22.6083, "lon": -43.70948, "name": "Paracambi" }, { "lat": -20.77556, "lon": -41.67944, "name": "Guaçuí" }, { "lat": -22.54861, "lon": -47.91389, "name": "São Pedro" }, { "lat": 41.10172, "lon": -80.76452, "name": "Austintown" } ], "question": "Which location is the geographic outlier among: Xapuri, Paracambi, Guaçuí, São Pedro, Austintown?", "ground_truth": { "answer": "Austintown", "outlier_distance_km": 5903.2, "second_furthest_km": 2204.9, "clarity_ratio": 2.68, "median_distance_km": 2203.3, "distances_to_centroid": { "Xapuri": 1375.0, "Paracambi": 2203.3, "Guaçuí": 2204.9, "São Pedro": 1949.5, "Austintown": 5903.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Xapuri: (-10.65°, -68.50°)", " Paracambi: (-22.61°, -43.71°)", " Guaçuí: (-20.78°, -41.68°)", " São Pedro: (-22.55°, -47.91°)", " Austintown: (41.10°, -80.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Austintown: 5903.2 km from centroid", " Guaçuí: 2204.9 km from centroid", " Paracambi: 2203.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Austintown", "FINAL ANSWER: Austintown" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.61857, "lon": -95.53772, "name": "Missouri City" }, { "lat": 29.71801, "lon": -95.43383, "name": "West University Place" }, { "lat": 43.64506, "lon": -79.46787, "name": "High Park-Swansea" }, { "lat": 30.26715, "lon": -97.74306, "name": "Austin" }, { "lat": -37.56622, "lon": 143.84957, "name": "Ballarat" } ], "question": "Which location is the geographic outlier among: Missouri City, West University Place, High Park-Swansea, Austin, Ballarat?", "ground_truth": { "answer": "Ballarat", "outlier_distance_km": 17798.1, "second_furthest_km": 5434.8, "clarity_ratio": 3.27, "median_distance_km": 5221.5, "distances_to_centroid": { "Missouri City": 5221.5, "West University Place": 5211.7, "High Park-Swansea": 4215.4, "Austin": 5434.8, "Ballarat": 17798.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Missouri City: (29.62°, -95.54°)", " West University Place: (29.72°, -95.43°)", " High Park-Swansea: (43.65°, -79.47°)", " Austin: (30.27°, -97.74°)", " Ballarat: (-37.57°, 143.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ballarat: 17798.1 km from centroid", " Austin: 5434.8 km from centroid", " Missouri City: 5221.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ballarat", "FINAL ANSWER: Ballarat" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.66778, "lon": -46.46139, "name": "Mauá" }, { "lat": -23.48874, "lon": -46.57762, "name": "Vila Medeiros" }, { "lat": -18.75639, "lon": -44.43083, "name": "Curvelo" }, { "lat": -26.37028, "lon": -50.14444, "name": "Papanduva" }, { "lat": 50.44548, "lon": 18.86147, "name": "Tarnowskie Góry" } ], "question": "Which location is the geographic outlier among: Mauá, Vila Medeiros, Curvelo, Papanduva, Tarnowskie Góry?", "ground_truth": { "answer": "Tarnowskie Góry", "outlier_distance_km": 8263.4, "second_furthest_km": 2645.7, "clarity_ratio": 3.12, "median_distance_km": 2173.9, "distances_to_centroid": { "Mauá": 2173.9, "Vila Medeiros": 2166.6, "Curvelo": 1631.8, "Papanduva": 2645.7, "Tarnowskie Góry": 8263.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mauá: (-23.67°, -46.46°)", " Vila Medeiros: (-23.49°, -46.58°)", " Curvelo: (-18.76°, -44.43°)", " Papanduva: (-26.37°, -50.14°)", " Tarnowskie Góry: (50.45°, 18.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tarnowskie Góry: 8263.4 km from centroid", " Papanduva: 2645.7 km from centroid", " Mauá: 2173.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tarnowskie Góry", "FINAL ANSWER: Tarnowskie Góry" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.97763, "lon": 60.36582, "name": "Chebarkul’" }, { "lat": 51.13321, "lon": 0.26256, "name": "Royal Tunbridge Wells" }, { "lat": 37.38283, "lon": -5.97317, "name": "Sevilla" }, { "lat": 50.57953, "lon": 13.00627, "name": "Annaberg-Buchholz" }, { "lat": 10.01239, "lon": 76.32633, "name": "Vazhakkala" } ], "question": "Which location is the geographic outlier among: Chebarkul’, Royal Tunbridge Wells, Sevilla, Annaberg-Buchholz, Vazhakkala?", "ground_truth": { "answer": "Vazhakkala", "outlier_distance_km": 5772.4, "second_furthest_km": 3004.8, "clarity_ratio": 1.92, "median_distance_km": 2794.4, "distances_to_centroid": { "Chebarkul’": 2794.4, "Royal Tunbridge Wells": 2463.9, "Sevilla": 3004.8, "Annaberg-Buchholz": 1631.7, "Vazhakkala": 5772.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chebarkul’: (54.98°, 60.37°)", " Royal Tunbridge Wells: (51.13°, 0.26°)", " Sevilla: (37.38°, -5.97°)", " Annaberg-Buchholz: (50.58°, 13.01°)", " Vazhakkala: (10.01°, 76.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vazhakkala: 5772.4 km from centroid", " Sevilla: 3004.8 km from centroid", " Chebarkul’: 2794.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vazhakkala", "FINAL ANSWER: Vazhakkala" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.1074, "lon": 7.64838, "name": "Meinerzhagen" }, { "lat": 49.78498, "lon": 22.76728, "name": "Przemyśl" }, { "lat": 43.67323, "lon": 7.19, "name": "Saint-Laurent-du-Var" }, { "lat": 54.59015, "lon": 55.38201, "name": "Chishmy" }, { "lat": -27.46794, "lon": 153.02809, "name": "Brisbane" } ], "question": "Which location is the geographic outlier among: Meinerzhagen, Przemyśl, Saint-Laurent-du-Var, Chishmy, Brisbane?", "ground_truth": { "answer": "Brisbane", "outlier_distance_km": 12876.5, "second_furthest_km": 3803.9, "clarity_ratio": 3.39, "median_distance_km": 3732.3, "distances_to_centroid": { "Meinerzhagen": 3803.9, "Przemyśl": 2752.3, "Saint-Laurent-du-Var": 3732.3, "Chishmy": 2302.6, "Brisbane": 12876.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Meinerzhagen: (51.11°, 7.65°)", " Przemyśl: (49.78°, 22.77°)", " Saint-Laurent-du-Var: (43.67°, 7.19°)", " Chishmy: (54.59°, 55.38°)", " Brisbane: (-27.47°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brisbane: 12876.5 km from centroid", " Meinerzhagen: 3803.9 km from centroid", " Saint-Laurent-du-Var: 3732.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Brisbane", "FINAL ANSWER: Brisbane" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.22336, "lon": 4.37971, "name": "Jega" }, { "lat": 30.08843, "lon": 31.28351, "name": "Ḩadā’iq al Qubbah" }, { "lat": 6.80355, "lon": -2.5172, "name": "Goaso" }, { "lat": 26.65817, "lon": 31.67137, "name": "Sāqultah" }, { "lat": -33.55384, "lon": -71.60761, "name": "Cartagena" } ], "question": "Which location is the geographic outlier among: Jega, Ḩadā’iq al Qubbah, Goaso, Sāqultah, Cartagena?", "ground_truth": { "answer": "Cartagena", "outlier_distance_km": 8741.6, "second_furthest_km": 4159.7, "clarity_ratio": 2.1, "median_distance_km": 4024.5, "distances_to_centroid": { "Jega": 755.3, "Ḩadā’iq al Qubbah": 4159.7, "Goaso": 222.7, "Sāqultah": 4024.5, "Cartagena": 8741.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jega: (12.22°, 4.38°)", " Ḩadā’iq al Qubbah: (30.09°, 31.28°)", " Goaso: (6.80°, -2.52°)", " Sāqultah: (26.66°, 31.67°)", " Cartagena: (-33.55°, -71.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cartagena: 8741.6 km from centroid", " Ḩadā’iq al Qubbah: 4159.7 km from centroid", " Sāqultah: 4024.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cartagena", "FINAL ANSWER: Cartagena" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.39318, "lon": 41.51929, "name": "Otradnaya" }, { "lat": 41.3799, "lon": 2.18971, "name": "la Barceloneta" }, { "lat": 43.13763, "lon": 5.98317, "name": "La Valette-du-Var" }, { "lat": 43.41727, "lon": 5.21462, "name": "Marignane" }, { "lat": 32.40732, "lon": 104.52738, "name": "Pingwu County" } ], "question": "Which location is the geographic outlier among: Otradnaya, la Barceloneta, La Valette-du-Var, Marignane, Pingwu County?", "ground_truth": { "answer": "Pingwu County", "outlier_distance_km": 6362.0, "second_furthest_km": 2474.2, "clarity_ratio": 2.57, "median_distance_km": 2205.2, "distances_to_centroid": { "Otradnaya": 875.0, "la Barceloneta": 2474.2, "La Valette-du-Var": 2144.3, "Marignane": 2205.2, "Pingwu County": 6362.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Otradnaya: (44.39°, 41.52°)", " la Barceloneta: (41.38°, 2.19°)", " La Valette-du-Var: (43.14°, 5.98°)", " Marignane: (43.42°, 5.21°)", " Pingwu County: (32.41°, 104.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pingwu County: 6362.0 km from centroid", " la Barceloneta: 2474.2 km from centroid", " Marignane: 2205.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pingwu County", "FINAL ANSWER: Pingwu County" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.61633, "lon": 7.64451, "name": "Bergkamen" }, { "lat": 37.48613, "lon": -5.98091, "name": "La Rinconada" }, { "lat": 48.70522, "lon": 2.39147, "name": "Athis-Mons" }, { "lat": 51.06713, "lon": 19.44477, "name": "Radomsko" }, { "lat": -33.20443, "lon": -70.67474, "name": "Colina" } ], "question": "Which location is the geographic outlier among: Bergkamen, La Rinconada, Athis-Mons, Radomsko, Colina?", "ground_truth": { "answer": "Colina", "outlier_distance_km": 9615.8, "second_furthest_km": 3243.3, "clarity_ratio": 2.96, "median_distance_km": 2671.9, "distances_to_centroid": { "Bergkamen": 2671.9, "La Rinconada": 774.1, "Athis-Mons": 2192.8, "Radomsko": 3243.3, "Colina": 9615.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bergkamen: (51.62°, 7.64°)", " La Rinconada: (37.49°, -5.98°)", " Athis-Mons: (48.71°, 2.39°)", " Radomsko: (51.07°, 19.44°)", " Colina: (-33.20°, -70.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Colina: 9615.8 km from centroid", " Radomsko: 3243.3 km from centroid", " Bergkamen: 2671.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Colina", "FINAL ANSWER: Colina" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 21.63333, "lon": 108.95, "name": "Xichang" }, { "lat": 11.83223, "lon": 75.48252, "name": "Peralassery" }, { "lat": 17.04325, "lon": 99.08128, "name": "Ban Tak" }, { "lat": 29.07888, "lon": 106.262, "name": "Lishi" }, { "lat": -37.6, "lon": 145.15, "name": "Doreen" } ], "question": "Which location is the geographic outlier among: Xichang, Peralassery, Ban Tak, Lishi, Doreen?", "ground_truth": { "answer": "Doreen", "outlier_distance_km": 6470.1, "second_furthest_km": 3467.6, "clarity_ratio": 1.87, "median_distance_km": 2300.9, "distances_to_centroid": { "Xichang": 1486.7, "Peralassery": 3467.6, "Ban Tak": 1287.4, "Lishi": 2300.9, "Doreen": 6470.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Xichang: (21.63°, 108.95°)", " Peralassery: (11.83°, 75.48°)", " Ban Tak: (17.04°, 99.08°)", " Lishi: (29.08°, 106.26°)", " Doreen: (-37.60°, 145.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Doreen: 6470.1 km from centroid", " Peralassery: 3467.6 km from centroid", " Lishi: 2300.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Doreen", "FINAL ANSWER: Doreen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.01667, "lon": 39.63333, "name": "Robīt" }, { "lat": -28.16678, "lon": 30.23371, "name": "Dundee" }, { "lat": 4.64231, "lon": 7.92438, "name": "Eket" }, { "lat": -25.47776, "lon": 31.14559, "name": "Tekwane" }, { "lat": -37.91928, "lon": 145.05301, "name": "Bentleigh East" } ], "question": "Which location is the geographic outlier among: Robīt, Dundee, Eket, Tekwane, Bentleigh East?", "ground_truth": { "answer": "Bentleigh East", "outlier_distance_km": 9354.5, "second_furthest_km": 5202.6, "clarity_ratio": 1.8, "median_distance_km": 3244.0, "distances_to_centroid": { "Robīt": 3244.0, "Dundee": 2575.9, "Eket": 5202.6, "Tekwane": 2354.8, "Bentleigh East": 9354.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Robīt: (12.02°, 39.63°)", " Dundee: (-28.17°, 30.23°)", " Eket: (4.64°, 7.92°)", " Tekwane: (-25.48°, 31.15°)", " Bentleigh East: (-37.92°, 145.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bentleigh East: 9354.5 km from centroid", " Eket: 5202.6 km from centroid", " Robīt: 3244.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bentleigh East", "FINAL ANSWER: Bentleigh East" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.97371, "lon": 32.52627, "name": "Suez" }, { "lat": 9.62376, "lon": -0.82705, "name": "Savelugu" }, { "lat": -0.56333, "lon": 34.93583, "name": "Nyamira" }, { "lat": 5.65396, "lon": 0.0264, "name": "Tema New Town" }, { "lat": 28.62778, "lon": -81.36312, "name": "Maitland" } ], "question": "Which location is the geographic outlier among: Suez, Savelugu, Nyamira, Tema New Town, Maitland?", "ground_truth": { "answer": "Maitland", "outlier_distance_km": 8121.7, "second_furthest_km": 4496.5, "clarity_ratio": 1.81, "median_distance_km": 4003.1, "distances_to_centroid": { "Suez": 4003.1, "Savelugu": 605.6, "Nyamira": 4496.5, "Tema New Town": 1053.0, "Maitland": 8121.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Suez: (29.97°, 32.53°)", " Savelugu: (9.62°, -0.83°)", " Nyamira: (-0.56°, 34.94°)", " Tema New Town: (5.65°, 0.03°)", " Maitland: (28.63°, -81.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Maitland: 8121.7 km from centroid", " Nyamira: 4496.5 km from centroid", " Suez: 4003.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Maitland", "FINAL ANSWER: Maitland" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.48839, "lon": -4.99123, "name": "San Pedro Alcántara" }, { "lat": 52.71083, "lon": 5.74861, "name": "Emmeloord" }, { "lat": 56.01141, "lon": -3.72183, "name": "Grangemouth" }, { "lat": 48.79702, "lon": 2.54046, "name": "Chennevières-sur-Marne" }, { "lat": 5.96669, "lon": 8.70632, "name": "Ikom" } ], "question": "Which location is the geographic outlier among: San Pedro Alcántara, Emmeloord, Grangemouth, Chennevières-sur-Marne, Ikom?", "ground_truth": { "answer": "Ikom", "outlier_distance_km": 3848.9, "second_furthest_km": 1824.0, "clarity_ratio": 2.11, "median_distance_km": 1447.8, "distances_to_centroid": { "San Pedro Alcántara": 699.0, "Emmeloord": 1447.8, "Grangemouth": 1824.0, "Chennevières-sur-Marne": 981.3, "Ikom": 3848.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Pedro Alcántara: (36.49°, -4.99°)", " Emmeloord: (52.71°, 5.75°)", " Grangemouth: (56.01°, -3.72°)", " Chennevières-sur-Marne: (48.80°, 2.54°)", " Ikom: (5.97°, 8.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ikom: 3848.9 km from centroid", " Grangemouth: 1824.0 km from centroid", " Emmeloord: 1447.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ikom", "FINAL ANSWER: Ikom" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.28881, "lon": -99.51163, "name": "Lerma de Villada" }, { "lat": 41.64753, "lon": -88.08951, "name": "Romeoville" }, { "lat": 34.39916, "lon": -118.91815, "name": "Fillmore" }, { "lat": 40.71427, "lon": -73.83097, "name": "Kew Gardens" }, { "lat": -34.65072, "lon": -59.43143, "name": "Mercedes" } ], "question": "Which location is the geographic outlier among: Lerma de Villada, Romeoville, Fillmore, Kew Gardens, Mercedes?", "ground_truth": { "answer": "Mercedes", "outlier_distance_km": 6811.3, "second_furthest_km": 3418.0, "clarity_ratio": 1.99, "median_distance_km": 2636.7, "distances_to_centroid": { "Lerma de Villada": 1213.8, "Romeoville": 2376.0, "Fillmore": 3418.0, "Kew Gardens": 2636.7, "Mercedes": 6811.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lerma de Villada: (19.29°, -99.51°)", " Romeoville: (41.65°, -88.09°)", " Fillmore: (34.40°, -118.92°)", " Kew Gardens: (40.71°, -73.83°)", " Mercedes: (-34.65°, -59.43°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mercedes: 6811.3 km from centroid", " Fillmore: 3418.0 km from centroid", " Kew Gardens: 2636.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mercedes", "FINAL ANSWER: Mercedes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.63116, "lon": 105.83065, "name": "Shima" }, { "lat": 28.1368, "lon": 106.822, "name": "Loushanguan" }, { "lat": 10.80603, "lon": 78.75031, "name": "Ellakkudi" }, { "lat": 30.79953, "lon": 76.02355, "name": "Dorāha" }, { "lat": 18.90815, "lon": -98.43613, "name": "Atlixco" } ], "question": "Which location is the geographic outlier among: Shima, Loushanguan, Ellakkudi, Dorāha, Atlixco?", "ground_truth": { "answer": "Atlixco", "outlier_distance_km": 14405.2, "second_furthest_km": 5286.4, "clarity_ratio": 2.72, "median_distance_km": 5171.9, "distances_to_centroid": { "Shima": 5171.9, "Loushanguan": 5286.4, "Ellakkudi": 3002.7, "Dorāha": 2331.5, "Atlixco": 14405.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shima: (29.63°, 105.83°)", " Loushanguan: (28.14°, 106.82°)", " Ellakkudi: (10.81°, 78.75°)", " Dorāha: (30.80°, 76.02°)", " Atlixco: (18.91°, -98.44°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Atlixco: 14405.2 km from centroid", " Loushanguan: 5286.4 km from centroid", " Shima: 5171.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Atlixco", "FINAL ANSWER: Atlixco" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -25.6575, "lon": -49.30806, "name": "Fazenda Rio Grande" }, { "lat": -12.71194, "lon": -39.69806, "name": "Itatim" }, { "lat": -29.68861, "lon": -51.46111, "name": "Montenegro" }, { "lat": -31.43722, "lon": -68.52556, "name": "Albardón" }, { "lat": 14.98333, "lon": 102.65, "name": "Ban Huai Thalaeng" } ], "question": "Which location is the geographic outlier among: Fazenda Rio Grande, Itatim, Montenegro, Albardón, Ban Huai Thalaeng?", "ground_truth": { "answer": "Ban Huai Thalaeng", "outlier_distance_km": 14035.3, "second_furthest_km": 5016.3, "clarity_ratio": 2.8, "median_distance_km": 3381.2, "distances_to_centroid": { "Fazenda Rio Grande": 3056.4, "Itatim": 2034.2, "Montenegro": 3381.2, "Albardón": 5016.3, "Ban Huai Thalaeng": 14035.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fazenda Rio Grande: (-25.66°, -49.31°)", " Itatim: (-12.71°, -39.70°)", " Montenegro: (-29.69°, -51.46°)", " Albardón: (-31.44°, -68.53°)", " Ban Huai Thalaeng: (14.98°, 102.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ban Huai Thalaeng: 14035.3 km from centroid", " Albardón: 5016.3 km from centroid", " Montenegro: 3381.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ban Huai Thalaeng", "FINAL ANSWER: Ban Huai Thalaeng" ] } ]