diff --git "a/data/track_applied/splits/task9_spatial_patterns_test.json" "b/data/track_applied/splits/task9_spatial_patterns_test.json" new file mode 100644--- /dev/null +++ "b/data/track_applied/splits/task9_spatial_patterns_test.json" @@ -0,0 +1,63242 @@ +[ + { + "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" + ] + } +] \ No newline at end of file