[ { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.76667, "lon": 144.96667, "name": "Brunswick" }, { "lat": -33.79798, "lon": 151.28826, "name": "Manly" }, { "lat": -33.86436, "lon": 151.0397, "name": "Lidcombe" }, { "lat": -32.83211, "lon": 151.35623, "name": "Cessnock" }, { "lat": 44.63651, "lon": -123.10593, "name": "Albany" } ], "question": "Which location is the geographic outlier among: Brunswick, Manly, Lidcombe, Cessnock, Albany?", "ground_truth": { "answer": "Albany", "outlier_distance_km": 15459.4, "second_furthest_km": 5777.8, "clarity_ratio": 2.68, "median_distance_km": 5774.3, "distances_to_centroid": { "Brunswick": 5249.9, "Manly": 5774.3, "Lidcombe": 5751.6, "Cessnock": 5777.8, "Albany": 15459.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Brunswick: (-37.77°, 144.97°)", " Manly: (-33.80°, 151.29°)", " Lidcombe: (-33.86°, 151.04°)", " Cessnock: (-32.83°, 151.36°)", " Albany: (44.64°, -123.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Albany: 15459.4 km from centroid", " Cessnock: 5777.8 km from centroid", " Manly: 5774.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Albany", "FINAL ANSWER: Albany" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.64083, "lon": -39.55111, "name": "Coaraci" }, { "lat": -6.23122, "lon": -42.68691, "name": "Regeneração" }, { "lat": -3.36841, "lon": -64.72054, "name": "Tefé" }, { "lat": -11.52472, "lon": -61.01278, "name": "Espigão dOeste" }, { "lat": -27.64613, "lon": 152.85965, "name": "Redbank Plains" } ], "question": "Which location is the geographic outlier among: Coaraci, Regeneração, Tefé, Espigão dOeste, Redbank Plains?", "ground_truth": { "answer": "Redbank Plains", "outlier_distance_km": 15206.0, "second_furthest_km": 5991.0, "clarity_ratio": 2.54, "median_distance_km": 5428.4, "distances_to_centroid": { "Coaraci": 3088.2, "Regeneração": 3543.2, "Tefé": 5991.0, "Espigão dOeste": 5428.4, "Redbank Plains": 15206.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Coaraci: (-14.64°, -39.55°)", " Regeneração: (-6.23°, -42.69°)", " Tefé: (-3.37°, -64.72°)", " Espigão dOeste: (-11.52°, -61.01°)", " Redbank Plains: (-27.65°, 152.86°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Redbank Plains: 15206.0 km from centroid", " Tefé: 5991.0 km from centroid", " Espigão dOeste: 5428.4 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": -34.06251, "lon": 151.14961, "name": "Cronulla" }, { "lat": -33.41665, "lon": 149.5806, "name": "Bathurst" }, { "lat": -33.90741, "lon": 151.15546, "name": "Marrickville" }, { "lat": -41.21667, "lon": 174.91667, "name": "Lower Hutt" }, { "lat": 53.4614, "lon": -2.92863, "name": "Fazakerley" } ], "question": "Which location is the geographic outlier among: Cronulla, Bathurst, Marrickville, Lower Hutt, Fazakerley?", "ground_truth": { "answer": "Fazakerley", "outlier_distance_km": 14048.7, "second_furthest_km": 5409.5, "clarity_ratio": 2.6, "median_distance_km": 3179.5, "distances_to_centroid": { "Cronulla": 3179.5, "Bathurst": 3017.7, "Marrickville": 3171.9, "Lower Hutt": 5409.5, "Fazakerley": 14048.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cronulla: (-34.06°, 151.15°)", " Bathurst: (-33.42°, 149.58°)", " Marrickville: (-33.91°, 151.16°)", " Lower Hutt: (-41.22°, 174.92°)", " Fazakerley: (53.46°, -2.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fazakerley: 14048.7 km from centroid", " Lower Hutt: 5409.5 km from centroid", " Cronulla: 3179.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fazakerley", "FINAL ANSWER: Fazakerley" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8149, "lon": 144.95052, "name": "Docklands" }, { "lat": -37.89138, "lon": 144.62368, "name": "Wyndham Vale" }, { "lat": -16.92366, "lon": 145.76613, "name": "Cairns" }, { "lat": -40.91667, "lon": 175.01667, "name": "Paraparaumu" }, { "lat": 9.08296, "lon": -1.81884, "name": "Damongo" } ], "question": "Which location is the geographic outlier among: Docklands, Wyndham Vale, Cairns, Paraparaumu, Damongo?", "ground_truth": { "answer": "Damongo", "outlier_distance_km": 13803.4, "second_furthest_km": 5197.8, "clarity_ratio": 2.66, "median_distance_km": 2646.5, "distances_to_centroid": { "Docklands": 2621.8, "Wyndham Vale": 2600.0, "Cairns": 2646.5, "Paraparaumu": 5197.8, "Damongo": 13803.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Docklands: (-37.81°, 144.95°)", " Wyndham Vale: (-37.89°, 144.62°)", " Cairns: (-16.92°, 145.77°)", " Paraparaumu: (-40.92°, 175.02°)", " Damongo: (9.08°, -1.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Damongo: 13803.4 km from centroid", " Paraparaumu: 5197.8 km from centroid", " Cairns: 2646.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Damongo", "FINAL ANSWER: Damongo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 29.30309, "lon": 108.7702, "name": "Zhuoshui" }, { "lat": 12.54288, "lon": 78.35735, "name": "Bargūr" }, { "lat": 47.23489, "lon": 127.10769, "name": "Suiling" }, { "lat": 33.19133, "lon": 104.42009, "name": "Zhongzhai" }, { "lat": 51.40878, "lon": -0.02526, "name": "Beckenham" } ], "question": "Which location is the geographic outlier among: Zhuoshui, Bargūr, Suiling, Zhongzhai, Beckenham?", "ground_truth": { "answer": "Beckenham", "outlier_distance_km": 6663.2, "second_furthest_km": 3839.3, "clarity_ratio": 1.74, "median_distance_km": 2526.5, "distances_to_centroid": { "Zhuoshui": 2430.1, "Bargūr": 2526.5, "Suiling": 3839.3, "Zhongzhai": 1912.8, "Beckenham": 6663.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zhuoshui: (29.30°, 108.77°)", " Bargūr: (12.54°, 78.36°)", " Suiling: (47.23°, 127.11°)", " Zhongzhai: (33.19°, 104.42°)", " Beckenham: (51.41°, -0.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Beckenham: 6663.2 km from centroid", " Suiling: 3839.3 km from centroid", " Bargūr: 2526.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Beckenham", "FINAL ANSWER: Beckenham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.12014, "lon": 15.28768, "name": "Lubań" }, { "lat": 55.7163, "lon": 60.551, "name": "Kyshtym" }, { "lat": 44.75583, "lon": 44.9925, "name": "Neftekumsk" }, { "lat": 55.82885, "lon": -4.21376, "name": "Rutherglen" }, { "lat": 22.75923, "lon": 113.79452, "name": "Gongheyong" } ], "question": "Which location is the geographic outlier among: Lubań, Kyshtym, Neftekumsk, Rutherglen, Gongheyong?", "ground_truth": { "answer": "Gongheyong", "outlier_distance_km": 6514.3, "second_furthest_km": 3599.5, "clarity_ratio": 1.81, "median_distance_km": 2316.4, "distances_to_centroid": { "Lubań": 2316.4, "Kyshtym": 1473.9, "Neftekumsk": 165.8, "Rutherglen": 3599.5, "Gongheyong": 6514.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lubań: (51.12°, 15.29°)", " Kyshtym: (55.72°, 60.55°)", " Neftekumsk: (44.76°, 44.99°)", " Rutherglen: (55.83°, -4.21°)", " Gongheyong: (22.76°, 113.79°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gongheyong: 6514.3 km from centroid", " Rutherglen: 3599.5 km from centroid", " Lubań: 2316.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gongheyong", "FINAL ANSWER: Gongheyong" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 47.65689, "lon": 9.47554, "name": "Friedrichshafen" }, { "lat": 51.45061, "lon": 0.05225, "name": "Eltham" }, { "lat": 49.95542, "lon": 18.57479, "name": "Jastrzębie Zdrój" }, { "lat": 51.28635, "lon": 7.29388, "name": "Schwelm" }, { "lat": 10.81314, "lon": 76.62869, "name": "Puthuppariyāram" } ], "question": "Which location is the geographic outlier among: Friedrichshafen, Eltham, Jastrzębie Zdrój, Schwelm, Puthuppariyāram?", "ground_truth": { "answer": "Puthuppariyāram", "outlier_distance_km": 6287.5, "second_furthest_km": 1973.3, "clarity_ratio": 3.19, "median_distance_km": 1523.9, "distances_to_centroid": { "Friedrichshafen": 1180.7, "Eltham": 1973.3, "Jastrzębie Zdrój": 907.8, "Schwelm": 1523.9, "Puthuppariyāram": 6287.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Friedrichshafen: (47.66°, 9.48°)", " Eltham: (51.45°, 0.05°)", " Jastrzębie Zdrój: (49.96°, 18.57°)", " Schwelm: (51.29°, 7.29°)", " Puthuppariyāram: (10.81°, 76.63°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Puthuppariyāram: 6287.5 km from centroid", " Eltham: 1973.3 km from centroid", " Schwelm: 1523.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Puthuppariyāram", "FINAL ANSWER: Puthuppariyāram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.92136, "lon": 8.55183, "name": "Verbania" }, { "lat": 40.41409, "lon": -3.66553, "name": "Estrella" }, { "lat": 55.84244, "lon": 38.19362, "name": "Monino" }, { "lat": 51.39894, "lon": 7.18557, "name": "Hattingen" }, { "lat": -28.21901, "lon": 152.03438, "name": "Warwick" } ], "question": "Which location is the geographic outlier among: Verbania, Estrella, Monino, Hattingen, Warwick?", "ground_truth": { "answer": "Warwick", "outlier_distance_km": 13562.9, "second_furthest_km": 3973.2, "clarity_ratio": 3.41, "median_distance_km": 3367.1, "distances_to_centroid": { "Verbania": 3059.8, "Estrella": 3973.2, "Monino": 2538.1, "Hattingen": 3367.1, "Warwick": 13562.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Verbania: (45.92°, 8.55°)", " Estrella: (40.41°, -3.67°)", " Monino: (55.84°, 38.19°)", " Hattingen: (51.40°, 7.19°)", " Warwick: (-28.22°, 152.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Warwick: 13562.9 km from centroid", " Estrella: 3973.2 km from centroid", " Hattingen: 3367.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Warwick", "FINAL ANSWER: Warwick" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 3.43054, "lon": -76.5199, "name": "Cali" }, { "lat": -43.24895, "lon": -65.30505, "name": "Trelew" }, { "lat": -1.8, "lon": -53.48, "name": "Prainha" }, { "lat": -22.15214, "lon": -42.92335, "name": "São José do Vale do Rio Preto" }, { "lat": 37.28766, "lon": -6.0541, "name": "Coria del Río" } ], "question": "Which location is the geographic outlier among: Cali, Trelew, Prainha, São José do Vale do Rio Preto, Coria del Río?", "ground_truth": { "answer": "Coria del Río", "outlier_distance_km": 6483.8, "second_furthest_km": 4518.7, "clarity_ratio": 1.43, "median_distance_km": 3222.2, "distances_to_centroid": { "Cali": 3222.2, "Trelew": 4518.7, "Prainha": 643.7, "São José do Vale do Rio Preto": 1979.9, "Coria del Río": 6483.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cali: (3.43°, -76.52°)", " Trelew: (-43.25°, -65.31°)", " Prainha: (-1.80°, -53.48°)", " São José do Vale do Rio Preto: (-22.15°, -42.92°)", " Coria del Río: (37.29°, -6.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coria del Río: 6483.8 km from centroid", " Trelew: 4518.7 km from centroid", " Cali: 3222.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coria del Río", "FINAL ANSWER: Coria del Río" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.3943, "lon": 136.66898, "name": "Mizuho" }, { "lat": 17.51544, "lon": 78.88563, "name": "Bhongīr" }, { "lat": 11.11723, "lon": 77.37256, "name": "Mannarai" }, { "lat": 34.21024, "lon": 134.33653, "name": "Higashikagawa" }, { "lat": -13.4425, "lon": -42.23889, "name": "Paramirim" } ], "question": "Which location is the geographic outlier among: Mizuho, Bhongīr, Mannarai, Higashikagawa, Paramirim?", "ground_truth": { "answer": "Paramirim", "outlier_distance_km": 13508.6, "second_furthest_km": 6199.4, "clarity_ratio": 2.18, "median_distance_km": 5979.4, "distances_to_centroid": { "Mizuho": 6199.4, "Bhongīr": 209.1, "Mannarai": 650.8, "Higashikagawa": 5979.4, "Paramirim": 13508.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mizuho: (35.39°, 136.67°)", " Bhongīr: (17.52°, 78.89°)", " Mannarai: (11.12°, 77.37°)", " Higashikagawa: (34.21°, 134.34°)", " Paramirim: (-13.44°, -42.24°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Paramirim: 13508.6 km from centroid", " Mizuho: 6199.4 km from centroid", " Higashikagawa: 5979.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Paramirim", "FINAL ANSWER: Paramirim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 6.53891, "lon": 3.3742, "name": "Shomolu" }, { "lat": 12.79881, "lon": 39.64448, "name": "Mehoni" }, { "lat": 6.90412, "lon": -2.56114, "name": "Mim" }, { "lat": -1.29996, "lon": 36.99047, "name": "Githunguri" }, { "lat": -27.54333, "lon": 153.20287, "name": "Capalaba" } ], "question": "Which location is the geographic outlier among: Shomolu, Mehoni, Mim, Githunguri, Capalaba?", "ground_truth": { "answer": "Capalaba", "outlier_distance_km": 11657.5, "second_furthest_km": 5464.1, "clarity_ratio": 2.13, "median_distance_km": 4808.8, "distances_to_centroid": { "Shomolu": 4808.8, "Mehoni": 1644.7, "Mim": 5464.1, "Githunguri": 1019.8, "Capalaba": 11657.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shomolu: (6.54°, 3.37°)", " Mehoni: (12.80°, 39.64°)", " Mim: (6.90°, -2.56°)", " Githunguri: (-1.30°, 36.99°)", " Capalaba: (-27.54°, 153.20°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Capalaba: 11657.5 km from centroid", " Mim: 5464.1 km from centroid", " Shomolu: 4808.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Capalaba", "FINAL ANSWER: Capalaba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.86667, "lon": 145.28333, "name": "Boronia" }, { "lat": -42.87936, "lon": 147.32941, "name": "Hobart" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": -37.8228, "lon": 144.96434, "name": "Southbank" }, { "lat": -7.71361, "lon": -66.97639, "name": "Pauini" } ], "question": "Which location is the geographic outlier among: Boronia, Hobart, Melbourne City Centre, Southbank, Pauini?", "ground_truth": { "answer": "Pauini", "outlier_distance_km": 15387.5, "second_furthest_km": 3990.5, "clarity_ratio": 3.86, "median_distance_km": 3833.2, "distances_to_centroid": { "Boronia": 3833.2, "Hobart": 3990.5, "Melbourne City Centre": 3805.9, "Southbank": 3805.6, "Pauini": 15387.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Boronia: (-37.87°, 145.28°)", " Hobart: (-42.88°, 147.33°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Southbank: (-37.82°, 144.96°)", " Pauini: (-7.71°, -66.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pauini: 15387.5 km from centroid", " Hobart: 3990.5 km from centroid", " Boronia: 3833.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pauini", "FINAL ANSWER: Pauini" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 37.07381, "lon": 14.24038, "name": "Gela" }, { "lat": 51.40878, "lon": -0.02526, "name": "Beckenham" }, { "lat": 48.6328, "lon": 2.44049, "name": "Évry" }, { "lat": 45.11326, "lon": 41.0365, "name": "Novokubansk" }, { "lat": -31.87101, "lon": 26.97862, "name": "Queensdale" } ], "question": "Which location is the geographic outlier among: Gela, Beckenham, Évry, Novokubansk, Queensdale?", "ground_truth": { "answer": "Queensdale", "outlier_distance_km": 6968.7, "second_furthest_km": 2754.6, "clarity_ratio": 2.53, "median_distance_km": 2685.1, "distances_to_centroid": { "Gela": 817.5, "Beckenham": 2754.6, "Évry": 2401.7, "Novokubansk": 2685.1, "Queensdale": 6968.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gela: (37.07°, 14.24°)", " Beckenham: (51.41°, -0.03°)", " Évry: (48.63°, 2.44°)", " Novokubansk: (45.11°, 41.04°)", " Queensdale: (-31.87°, 26.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Queensdale: 6968.7 km from centroid", " Beckenham: 2754.6 km from centroid", " Novokubansk: 2685.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Queensdale", "FINAL ANSWER: Queensdale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.73667, "lon": 139.32361, "name": "Fussa" }, { "lat": -7.9797, "lon": 112.6304, "name": "Malang" }, { "lat": 38.80898, "lon": 77.44861, "name": "Huangdi" }, { "lat": 1.7439, "lon": 103.3207, "name": "Kawasan Penempatan Ulu Benut Lima" }, { "lat": 33.41421, "lon": -111.94348, "name": "Tempe Junction" } ], "question": "Which location is the geographic outlier among: Fussa, Malang, Huangdi, Kawasan Penempatan Ulu Benut Lima, Tempe Junction?", "ground_truth": { "answer": "Tempe Junction", "outlier_distance_km": 14023.0, "second_furthest_km": 7400.4, "clarity_ratio": 1.89, "median_distance_km": 6164.3, "distances_to_centroid": { "Fussa": 7400.4, "Malang": 6164.3, "Huangdi": 2416.1, "Kawasan Penempatan Ulu Benut Lima": 4726.4, "Tempe Junction": 14023.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Fussa: (35.74°, 139.32°)", " Malang: (-7.98°, 112.63°)", " Huangdi: (38.81°, 77.45°)", " Kawasan Penempatan Ulu Benut Lima: (1.74°, 103.32°)", " Tempe Junction: (33.41°, -111.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tempe Junction: 14023.0 km from centroid", " Fussa: 7400.4 km from centroid", " Malang: 6164.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tempe Junction", "FINAL ANSWER: Tempe Junction" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.53221, "lon": 153.22889, "name": "Alexandra Hills" }, { "lat": -37.83333, "lon": 145.05, "name": "Glenferrie" }, { "lat": -37.91667, "lon": 145.11667, "name": "Clayton" }, { "lat": -37.73261, "lon": 144.86504, "name": "Keilor East" }, { "lat": 13.93139, "lon": 121.61722, "name": "Lucena" } ], "question": "Which location is the geographic outlier among: Alexandra Hills, Glenferrie, Clayton, Keilor East, Lucena?", "ground_truth": { "answer": "Lucena", "outlier_distance_km": 4899.8, "second_furthest_km": 1421.1, "clarity_ratio": 3.45, "median_distance_km": 1410.8, "distances_to_centroid": { "Alexandra Hills": 1144.1, "Glenferrie": 1410.8, "Clayton": 1421.1, "Keilor East": 1396.3, "Lucena": 4899.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Alexandra Hills: (-27.53°, 153.23°)", " Glenferrie: (-37.83°, 145.05°)", " Clayton: (-37.92°, 145.12°)", " Keilor East: (-37.73°, 144.87°)", " Lucena: (13.93°, 121.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lucena: 4899.8 km from centroid", " Clayton: 1421.1 km from centroid", " Glenferrie: 1410.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lucena", "FINAL ANSWER: Lucena" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8149, "lon": 144.95052, "name": "Docklands" }, { "lat": -37.6, "lon": 144.95, "name": "Craigieburn" }, { "lat": -37.88461, "lon": 145.29539, "name": "Ferntree Gully" }, { "lat": -32.05251, "lon": 115.88782, "name": "Willetton" }, { "lat": 3.5638, "lon": 101.6581, "name": "Kuala Kubu Baharu" } ], "question": "Which location is the geographic outlier among: Docklands, Craigieburn, Ferntree Gully, Willetton, Kuala Kubu Baharu?", "ground_truth": { "answer": "Kuala Kubu Baharu", "outlier_distance_km": 4705.1, "second_furthest_km": 1730.7, "clarity_ratio": 2.72, "median_distance_km": 1701.2, "distances_to_centroid": { "Docklands": 1701.2, "Craigieburn": 1687.9, "Ferntree Gully": 1730.7, "Willetton": 1466.1, "Kuala Kubu Baharu": 4705.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Docklands: (-37.81°, 144.95°)", " Craigieburn: (-37.60°, 144.95°)", " Ferntree Gully: (-37.88°, 145.30°)", " Willetton: (-32.05°, 115.89°)", " Kuala Kubu Baharu: (3.56°, 101.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kuala Kubu Baharu: 4705.1 km from centroid", " Ferntree Gully: 1730.7 km from centroid", " Docklands: 1701.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kuala Kubu Baharu", "FINAL ANSWER: Kuala Kubu Baharu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.3939, "lon": 114.1464, "name": "Gambiran Satu" }, { "lat": 26.25318, "lon": 108.65785, "name": "Shangchong" }, { "lat": 17.3381, "lon": 77.90441, "name": "Vikārābād" }, { "lat": 21.59556, "lon": 78.52628, "name": "Pāndhurnā" }, { "lat": -36.99282, "lon": 174.87986, "name": "Manukau City" } ], "question": "Which location is the geographic outlier among: Gambiran Satu, Shangchong, Vikārābād, Pāndhurnā, Manukau City?", "ground_truth": { "answer": "Manukau City", "outlier_distance_km": 8019.3, "second_furthest_km": 3997.8, "clarity_ratio": 2.01, "median_distance_km": 3882.7, "distances_to_centroid": { "Gambiran Satu": 1422.3, "Shangchong": 2489.6, "Vikārābād": 3882.7, "Pāndhurnā": 3997.8, "Manukau City": 8019.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gambiran Satu: (-8.39°, 114.15°)", " Shangchong: (26.25°, 108.66°)", " Vikārābād: (17.34°, 77.90°)", " Pāndhurnā: (21.60°, 78.53°)", " Manukau City: (-36.99°, 174.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Manukau City: 8019.3 km from centroid", " Pāndhurnā: 3997.8 km from centroid", " Vikārābād: 3882.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Manukau City", "FINAL ANSWER: Manukau City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 20.91528, "lon": -100.74389, "name": "San Miguel de Allende" }, { "lat": 36.16284, "lon": -85.50164, "name": "Cookeville" }, { "lat": 35.19807, "lon": -111.65127, "name": "Flagstaff" }, { "lat": 38.98067, "lon": -77.10026, "name": "Bethesda" }, { "lat": -32.27682, "lon": 115.72978, "name": "Rockingham" } ], "question": "Which location is the geographic outlier among: San Miguel de Allende, Cookeville, Flagstaff, Bethesda, Rockingham?", "ground_truth": { "answer": "Rockingham", "outlier_distance_km": 18156.8, "second_furthest_km": 6050.0, "clarity_ratio": 3.0, "median_distance_km": 5078.3, "distances_to_centroid": { "San Miguel de Allende": 5078.3, "Cookeville": 3744.4, "Flagstaff": 6050.0, "Bethesda": 3224.9, "Rockingham": 18156.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Miguel de Allende: (20.92°, -100.74°)", " Cookeville: (36.16°, -85.50°)", " Flagstaff: (35.20°, -111.65°)", " Bethesda: (38.98°, -77.10°)", " Rockingham: (-32.28°, 115.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rockingham: 18156.8 km from centroid", " Flagstaff: 6050.0 km from centroid", " San Miguel de Allende: 5078.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rockingham", "FINAL ANSWER: Rockingham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.13333, "lon": 174.85, "name": "Porirua" }, { "lat": -37.87709, "lon": 145.12939, "name": "Mount Waverley" }, { "lat": -37.79086, "lon": 145.09386, "name": "Balwyn North" }, { "lat": -37.78333, "lon": 175.28333, "name": "Hamilton" }, { "lat": 41.74753, "lon": -87.71116, "name": "Ashburn" } ], "question": "Which location is the geographic outlier among: Porirua, Mount Waverley, Balwyn North, Hamilton, Ashburn?", "ground_truth": { "answer": "Ashburn", "outlier_distance_km": 17289.4, "second_furthest_km": 6324.8, "clarity_ratio": 2.73, "median_distance_km": 6268.0, "distances_to_centroid": { "Porirua": 6268.0, "Mount Waverley": 3705.2, "Balwyn North": 3699.4, "Hamilton": 6324.8, "Ashburn": 17289.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Porirua: (-41.13°, 174.85°)", " Mount Waverley: (-37.88°, 145.13°)", " Balwyn North: (-37.79°, 145.09°)", " Hamilton: (-37.78°, 175.28°)", " Ashburn: (41.75°, -87.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ashburn: 17289.4 km from centroid", " Hamilton: 6324.8 km from centroid", " Porirua: 6268.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ashburn", "FINAL ANSWER: Ashburn" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.15892, "lon": -98.40824, "name": "Huejotzingo" }, { "lat": 42.35176, "lon": -71.86341, "name": "Holden" }, { "lat": 38.5245, "lon": -90.35734, "name": "Concord" }, { "lat": 42.06642, "lon": -87.93729, "name": "Mount Prospect" }, { "lat": -40.95972, "lon": 175.6575, "name": "Masterton" } ], "question": "Which location is the geographic outlier among: Huejotzingo, Holden, Concord, Mount Prospect, Masterton?", "ground_truth": { "answer": "Masterton", "outlier_distance_km": 16347.5, "second_furthest_km": 6639.0, "clarity_ratio": 2.46, "median_distance_km": 5679.8, "distances_to_centroid": { "Huejotzingo": 6639.0, "Holden": 4259.7, "Concord": 5679.8, "Mount Prospect": 5521.2, "Masterton": 16347.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Huejotzingo: (19.16°, -98.41°)", " Holden: (42.35°, -71.86°)", " Concord: (38.52°, -90.36°)", " Mount Prospect: (42.07°, -87.94°)", " Masterton: (-40.96°, 175.66°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Masterton: 16347.5 km from centroid", " Huejotzingo: 6639.0 km from centroid", " Concord: 5679.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Masterton", "FINAL ANSWER: Masterton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.68333, "lon": 145.01667, "name": "Thomastown" }, { "lat": -42.87936, "lon": 147.32941, "name": "Hobart" }, { "lat": -32.83211, "lon": 151.35623, "name": "Cessnock" }, { "lat": -33.91938, "lon": 150.92588, "name": "Liverpool" }, { "lat": 11.01667, "lon": 75.86667, "name": "Pariyāpuram" } ], "question": "Which location is the geographic outlier among: Thomastown, Hobart, Cessnock, Liverpool, Pariyāpuram?", "ground_truth": { "answer": "Pariyāpuram", "outlier_distance_km": 7580.1, "second_furthest_km": 2107.6, "clarity_ratio": 3.6, "median_distance_km": 1770.2, "distances_to_centroid": { "Thomastown": 1544.4, "Hobart": 2107.6, "Cessnock": 1770.2, "Liverpool": 1769.7, "Pariyāpuram": 7580.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Thomastown: (-37.68°, 145.02°)", " Hobart: (-42.88°, 147.33°)", " Cessnock: (-32.83°, 151.36°)", " Liverpool: (-33.92°, 150.93°)", " Pariyāpuram: (11.02°, 75.87°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pariyāpuram: 7580.1 km from centroid", " Hobart: 2107.6 km from centroid", " Cessnock: 1770.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pariyāpuram", "FINAL ANSWER: Pariyāpuram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.13325, "lon": 10.02129, "name": "Cremona" }, { "lat": 51.37992, "lon": -0.24445, "name": "Worcester Park" }, { "lat": 52.43367, "lon": 8.61263, "name": "Rahden" }, { "lat": 43.25, "lon": -5.76667, "name": "Mieres" }, { "lat": 30.12303, "lon": 31.13571, "name": "Awsīm" } ], "question": "Which location is the geographic outlier among: Cremona, Worcester Park, Rahden, Mieres, Awsīm?", "ground_truth": { "answer": "Awsīm", "outlier_distance_km": 2527.6, "second_furthest_km": 1170.3, "clarity_ratio": 2.16, "median_distance_km": 1018.7, "distances_to_centroid": { "Cremona": 124.8, "Worcester Park": 1018.7, "Rahden": 886.2, "Mieres": 1170.3, "Awsīm": 2527.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cremona: (45.13°, 10.02°)", " Worcester Park: (51.38°, -0.24°)", " Rahden: (52.43°, 8.61°)", " Mieres: (43.25°, -5.77°)", " Awsīm: (30.12°, 31.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Awsīm: 2527.6 km from centroid", " Mieres: 1170.3 km from centroid", " Worcester Park: 1018.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Awsīm", "FINAL ANSWER: Awsīm" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.035, "lon": 140.85111, "name": "Watari" }, { "lat": 34.61667, "lon": 116.95, "name": "Zhangzhai" }, { "lat": 34.33284, "lon": 132.56967, "name": "Kumano" }, { "lat": 28.24737, "lon": 75.07666, "name": "Bissāu" }, { "lat": 36.20005, "lon": -86.51861, "name": "Mount Juliet" } ], "question": "Which location is the geographic outlier among: Watari, Zhangzhai, Kumano, Bissāu, Mount Juliet?", "ground_truth": { "answer": "Mount Juliet", "outlier_distance_km": 11965.3, "second_furthest_km": 5735.2, "clarity_ratio": 2.09, "median_distance_km": 5143.1, "distances_to_centroid": { "Watari": 5735.2, "Zhangzhai": 3747.7, "Kumano": 5143.1, "Bissāu": 674.9, "Mount Juliet": 11965.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Watari: (38.03°, 140.85°)", " Zhangzhai: (34.62°, 116.95°)", " Kumano: (34.33°, 132.57°)", " Bissāu: (28.25°, 75.08°)", " Mount Juliet: (36.20°, -86.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mount Juliet: 11965.3 km from centroid", " Watari: 5735.2 km from centroid", " Kumano: 5143.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mount Juliet", "FINAL ANSWER: Mount Juliet" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 8.3352, "lon": 77.21361, "name": "Pacode" }, { "lat": 23.72536, "lon": 85.51023, "name": "Kuju" }, { "lat": 9.86667, "lon": 76.5, "name": "Piravam" }, { "lat": 33.78333, "lon": 130.98333, "name": "Kanda" }, { "lat": -33.8178, "lon": 151.00348, "name": "Parramatta" } ], "question": "Which location is the geographic outlier among: Pacode, Kuju, Piravam, Kanda, Parramatta?", "ground_truth": { "answer": "Parramatta", "outlier_distance_km": 6803.6, "second_furthest_km": 3933.8, "clarity_ratio": 1.73, "median_distance_km": 3049.4, "distances_to_centroid": { "Pacode": 2972.9, "Kuju": 2624.1, "Piravam": 3049.4, "Kanda": 3933.8, "Parramatta": 6803.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pacode: (8.34°, 77.21°)", " Kuju: (23.73°, 85.51°)", " Piravam: (9.87°, 76.50°)", " Kanda: (33.78°, 130.98°)", " Parramatta: (-33.82°, 151.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Parramatta: 6803.6 km from centroid", " Kanda: 3933.8 km from centroid", " Piravam: 3049.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Parramatta", "FINAL ANSWER: Parramatta" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -0.0962, "lon": 34.27322, "name": "Bondo" }, { "lat": 25.75089, "lon": 32.6776, "name": "Az Zaynīyah Qiblī" }, { "lat": -29.47795, "lon": 30.23057, "name": "Howick" }, { "lat": -33.93462, "lon": 18.86676, "name": "Stellenbosch" }, { "lat": -19.95194, "lon": -44.34278, "name": "Juatuba" } ], "question": "Which location is the geographic outlier among: Bondo, Az Zaynīyah Qiblī, Howick, Stellenbosch, Juatuba?", "ground_truth": { "answer": "Juatuba", "outlier_distance_km": 6320.5, "second_furthest_km": 4597.4, "clarity_ratio": 1.37, "median_distance_km": 2585.0, "distances_to_centroid": { "Bondo": 2542.5, "Az Zaynīyah Qiblī": 4597.4, "Howick": 2585.0, "Stellenbosch": 2532.0, "Juatuba": 6320.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bondo: (-0.10°, 34.27°)", " Az Zaynīyah Qiblī: (25.75°, 32.68°)", " Howick: (-29.48°, 30.23°)", " Stellenbosch: (-33.93°, 18.87°)", " Juatuba: (-19.95°, -44.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Juatuba: 6320.5 km from centroid", " Az Zaynīyah Qiblī: 4597.4 km from centroid", " Howick: 2585.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Juatuba", "FINAL ANSWER: Juatuba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.74055, "lon": -74.75443, "name": "Palmar de Varela" }, { "lat": 1.25744, "lon": -70.23551, "name": "Mitú" }, { "lat": -10.53944, "lon": -37.41667, "name": "Ribeirópolis" }, { "lat": -15.29333, "lon": -39.07528, "name": "Una" }, { "lat": 44.53889, "lon": 10.81166, "name": "Fiorano" } ], "question": "Which location is the geographic outlier among: Palmar de Varela, Mitú, Ribeirópolis, Una, Fiorano?", "ground_truth": { "answer": "Fiorano", "outlier_distance_km": 6656.5, "second_furthest_km": 3622.1, "clarity_ratio": 1.84, "median_distance_km": 3164.1, "distances_to_centroid": { "Palmar de Varela": 3622.1, "Mitú": 3164.1, "Ribeirópolis": 1926.9, "Una": 2407.1, "Fiorano": 6656.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Palmar de Varela: (10.74°, -74.75°)", " Mitú: (1.26°, -70.24°)", " Ribeirópolis: (-10.54°, -37.42°)", " Una: (-15.29°, -39.08°)", " Fiorano: (44.54°, 10.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fiorano: 6656.5 km from centroid", " Palmar de Varela: 3622.1 km from centroid", " Mitú: 3164.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fiorano", "FINAL ANSWER: Fiorano" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.53333, "lon": 29.06667, "name": "eMbalenhle" }, { "lat": -23.88384, "lon": 29.70557, "name": "Mankweng" }, { "lat": 11.74697, "lon": 11.96083, "name": "Damaturu" }, { "lat": -25.48251, "lon": 29.02763, "name": "Verena" }, { "lat": 6.42942, "lon": 100.28174, "name": "Kampung Hutan Arau" } ], "question": "Which location is the geographic outlier among: eMbalenhle, Mankweng, Damaturu, Verena, Kampung Hutan Arau?", "ground_truth": { "answer": "Kampung Hutan Arau", "outlier_distance_km": 6959.6, "second_furthest_km": 4037.3, "clarity_ratio": 1.72, "median_distance_km": 2022.3, "distances_to_centroid": { "eMbalenhle": 2022.3, "Mankweng": 1751.3, "Damaturu": 4037.3, "Verena": 1932.2, "Kampung Hutan Arau": 6959.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " eMbalenhle: (-26.53°, 29.07°)", " Mankweng: (-23.88°, 29.71°)", " Damaturu: (11.75°, 11.96°)", " Verena: (-25.48°, 29.03°)", " Kampung Hutan Arau: (6.43°, 100.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kampung Hutan Arau: 6959.6 km from centroid", " Damaturu: 4037.3 km from centroid", " eMbalenhle: 2022.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kampung Hutan Arau", "FINAL ANSWER: Kampung Hutan Arau" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 36.12944, "lon": 127.1, "name": "Yŏnmu" }, { "lat": 30.86761, "lon": 108.36969, "name": "Tiancheng" }, { "lat": 25.56078, "lon": 81.49164, "name": "Bharwāri" }, { "lat": 39.49944, "lon": 106.71167, "name": "Wuda" }, { "lat": -22.41139, "lon": -47.56139, "name": "Rio Claro" } ], "question": "Which location is the geographic outlier among: Yŏnmu, Tiancheng, Bharwāri, Wuda, Rio Claro?", "ground_truth": { "answer": "Rio Claro", "outlier_distance_km": 14161.1, "second_furthest_km": 5219.7, "clarity_ratio": 2.71, "median_distance_km": 3559.6, "distances_to_centroid": { "Yŏnmu": 5219.7, "Tiancheng": 3433.3, "Bharwāri": 755.0, "Wuda": 3559.6, "Rio Claro": 14161.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yŏnmu: (36.13°, 127.10°)", " Tiancheng: (30.87°, 108.37°)", " Bharwāri: (25.56°, 81.49°)", " Wuda: (39.50°, 106.71°)", " Rio Claro: (-22.41°, -47.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rio Claro: 14161.1 km from centroid", " Yŏnmu: 5219.7 km from centroid", " Wuda: 3559.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rio Claro", "FINAL ANSWER: Rio Claro" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.86667, "lon": 145.06667, "name": "Glen Iris" }, { "lat": -37.78247, "lon": 145.31682, "name": "Mooroolbark" }, { "lat": -37.94853, "lon": 145.15274, "name": "Springvale" }, { "lat": -33.72197, "lon": 151.04607, "name": "Cherrybrook" }, { "lat": 19.88372, "lon": -103.60073, "name": "Sayula" } ], "question": "Which location is the geographic outlier among: Glen Iris, Mooroolbark, Springvale, Cherrybrook, Sayula?", "ground_truth": { "answer": "Sayula", "outlier_distance_km": 17854.1, "second_furthest_km": 5283.2, "clarity_ratio": 3.38, "median_distance_km": 4753.7, "distances_to_centroid": { "Glen Iris": 4732.1, "Mooroolbark": 4753.7, "Springvale": 4740.1, "Cherrybrook": 5283.2, "Sayula": 17854.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Glen Iris: (-37.87°, 145.07°)", " Mooroolbark: (-37.78°, 145.32°)", " Springvale: (-37.95°, 145.15°)", " Cherrybrook: (-33.72°, 151.05°)", " Sayula: (19.88°, -103.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sayula: 17854.1 km from centroid", " Cherrybrook: 5283.2 km from centroid", " Mooroolbark: 4753.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sayula", "FINAL ANSWER: Sayula" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -5.85833, "lon": -35.35389, "name": "Macaíba" }, { "lat": -3.30708, "lon": -52.53863, "name": "Brasil Novo" }, { "lat": 7.90745, "lon": -72.5049, "name": "Cúcuta" }, { "lat": -25.97972, "lon": -52.56778, "name": "Coronel Vivida" }, { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" } ], "question": "Which location is the geographic outlier among: Macaíba, Brasil Novo, Cúcuta, Coronel Vivida, Hoppers Crossing?", "ground_truth": { "answer": "Hoppers Crossing", "outlier_distance_km": 13921.0, "second_furthest_km": 6903.6, "clarity_ratio": 2.02, "median_distance_km": 4407.3, "distances_to_centroid": { "Macaíba": 2508.2, "Brasil Novo": 4407.3, "Cúcuta": 6903.6, "Coronel Vivida": 4305.8, "Hoppers Crossing": 13921.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Macaíba: (-5.86°, -35.35°)", " Brasil Novo: (-3.31°, -52.54°)", " Cúcuta: (7.91°, -72.50°)", " Coronel Vivida: (-25.98°, -52.57°)", " Hoppers Crossing: (-37.88°, 144.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hoppers Crossing: 13921.0 km from centroid", " Cúcuta: 6903.6 km from centroid", " Brasil Novo: 4407.3 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": -23.84852, "lon": 151.25775, "name": "Gladstone" }, { "lat": -34.78254, "lon": 138.61077, "name": "Parafield Gardens" }, { "lat": -27.96724, "lon": 153.39796, "name": "Southport" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" }, { "lat": -4.95611, "lon": -37.13694, "name": "Areia Branca" } ], "question": "Which location is the geographic outlier among: Gladstone, Parafield Gardens, Southport, New Plymouth, Areia Branca?", "ground_truth": { "answer": "Areia Branca", "outlier_distance_km": 15509.9, "second_furthest_km": 5528.9, "clarity_ratio": 2.81, "median_distance_km": 3690.9, "distances_to_centroid": { "Gladstone": 3547.6, "Parafield Gardens": 2360.7, "Southport": 3690.9, "New Plymouth": 5528.9, "Areia Branca": 15509.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gladstone: (-23.85°, 151.26°)", " Parafield Gardens: (-34.78°, 138.61°)", " Southport: (-27.97°, 153.40°)", " New Plymouth: (-39.07°, 174.08°)", " Areia Branca: (-4.96°, -37.14°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Areia Branca: 15509.9 km from centroid", " New Plymouth: 5528.9 km from centroid", " Southport: 3690.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Areia Branca", "FINAL ANSWER: Areia Branca" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8, "lon": 144.9, "name": "Footscray" }, { "lat": -37.79086, "lon": 145.09386, "name": "Balwyn North" }, { "lat": -37.88333, "lon": 145.21667, "name": "Wantirna South" }, { "lat": -37.0393, "lon": 174.92815, "name": "Takanini" }, { "lat": 51.15, "lon": 7.0, "name": "Ohligs" } ], "question": "Which location is the geographic outlier among: Footscray, Balwyn North, Wantirna South, Takanini, Ohligs?", "ground_truth": { "answer": "Ohligs", "outlier_distance_km": 13546.1, "second_furthest_km": 5312.1, "clarity_ratio": 2.55, "median_distance_km": 2903.0, "distances_to_centroid": { "Footscray": 2875.4, "Balwyn North": 2888.2, "Wantirna South": 2903.0, "Takanini": 5312.1, "Ohligs": 13546.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Footscray: (-37.80°, 144.90°)", " Balwyn North: (-37.79°, 145.09°)", " Wantirna South: (-37.88°, 145.22°)", " Takanini: (-37.04°, 174.93°)", " Ohligs: (51.15°, 7.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ohligs: 13546.1 km from centroid", " Takanini: 5312.1 km from centroid", " Wantirna South: 2903.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ohligs", "FINAL ANSWER: Ohligs" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.60528, "lon": 18.34717, "name": "Reda" }, { "lat": 49.71443, "lon": 7.30776, "name": "Idar-Oberstein" }, { "lat": 51.36973, "lon": 10.87011, "name": "Sondershausen" }, { "lat": 40.49631, "lon": -3.71957, "name": "Mirasierra" }, { "lat": -0.52731, "lon": 34.45714, "name": "Homa Bay" } ], "question": "Which location is the geographic outlier among: Reda, Idar-Oberstein, Sondershausen, Mirasierra, Homa Bay?", "ground_truth": { "answer": "Homa Bay", "outlier_distance_km": 4902.0, "second_furthest_km": 1759.3, "clarity_ratio": 2.79, "median_distance_km": 1472.2, "distances_to_centroid": { "Reda": 1759.3, "Idar-Oberstein": 1272.8, "Sondershausen": 1375.5, "Mirasierra": 1472.2, "Homa Bay": 4902.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Reda: (54.61°, 18.35°)", " Idar-Oberstein: (49.71°, 7.31°)", " Sondershausen: (51.37°, 10.87°)", " Mirasierra: (40.50°, -3.72°)", " Homa Bay: (-0.53°, 34.46°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Homa Bay: 4902.0 km from centroid", " Reda: 1759.3 km from centroid", " Mirasierra: 1472.2 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": -8.80972, "lon": -63.69556, "name": "Candeias do Jamari" }, { "lat": -8.14583, "lon": -36.37111, "name": "Brejo da Madre de Deus" }, { "lat": -30.51436, "lon": -53.48496, "name": "Caçapava do Sul" }, { "lat": -19.22444, "lon": -44.93528, "name": "Pompéu" }, { "lat": -37.86667, "lon": 145.28333, "name": "Boronia" } ], "question": "Which location is the geographic outlier among: Candeias do Jamari, Brejo da Madre de Deus, Caçapava do Sul, Pompéu, Boronia?", "ground_truth": { "answer": "Boronia", "outlier_distance_km": 13011.2, "second_furthest_km": 5831.8, "clarity_ratio": 2.23, "median_distance_km": 4395.6, "distances_to_centroid": { "Candeias do Jamari": 5831.8, "Brejo da Madre de Deus": 3104.7, "Caçapava do Sul": 4395.6, "Pompéu": 3580.1, "Boronia": 13011.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Candeias do Jamari: (-8.81°, -63.70°)", " Brejo da Madre de Deus: (-8.15°, -36.37°)", " Caçapava do Sul: (-30.51°, -53.48°)", " Pompéu: (-19.22°, -44.94°)", " Boronia: (-37.87°, 145.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Boronia: 13011.2 km from centroid", " Candeias do Jamari: 5831.8 km from centroid", " Caçapava do Sul: 4395.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Boronia", "FINAL ANSWER: Boronia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -24.78864, "lon": 31.07938, "name": "Mafemani" }, { "lat": 0.0607, "lon": 34.28806, "name": "Siaya" }, { "lat": 30.18479, "lon": 31.10649, "name": "Manshīyat al Qanāţir" }, { "lat": 5.51737, "lon": 5.75006, "name": "Warri" }, { "lat": -37.69825, "lon": 145.05967, "name": "Bundoora" } ], "question": "Which location is the geographic outlier among: Mafemani, Siaya, Manshīyat al Qanāţir, Warri, Bundoora?", "ground_truth": { "answer": "Bundoora", "outlier_distance_km": 10134.7, "second_furthest_km": 5000.7, "clarity_ratio": 2.03, "median_distance_km": 4407.9, "distances_to_centroid": { "Mafemani": 2918.9, "Siaya": 1788.3, "Manshīyat al Qanāţir": 4407.9, "Warri": 5000.7, "Bundoora": 10134.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mafemani: (-24.79°, 31.08°)", " Siaya: (0.06°, 34.29°)", " Manshīyat al Qanāţir: (30.18°, 31.11°)", " Warri: (5.52°, 5.75°)", " Bundoora: (-37.70°, 145.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bundoora: 10134.7 km from centroid", " Warri: 5000.7 km from centroid", " Manshīyat al Qanāţir: 4407.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bundoora", "FINAL ANSWER: Bundoora" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.03333, "lon": 145.3, "name": "Narre Warren" }, { "lat": -33.95, "lon": 151.11667, "name": "Bexley" }, { "lat": -33.8406, "lon": 151.00748, "name": "Granville" }, { "lat": -37.56622, "lon": 143.84957, "name": "Ballarat" }, { "lat": -8.9475, "lon": -37.42278, "name": "Itaíba" } ], "question": "Which location is the geographic outlier among: Narre Warren, Bexley, Granville, Ballarat, Itaíba?", "ground_truth": { "answer": "Itaíba", "outlier_distance_km": 14471.3, "second_furthest_km": 3791.4, "clarity_ratio": 3.82, "median_distance_km": 3782.6, "distances_to_centroid": { "Narre Warren": 3262.9, "Bexley": 3791.4, "Granville": 3782.6, "Ballarat": 3131.7, "Itaíba": 14471.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Narre Warren: (-38.03°, 145.30°)", " Bexley: (-33.95°, 151.12°)", " Granville: (-33.84°, 151.01°)", " Ballarat: (-37.57°, 143.85°)", " Itaíba: (-8.95°, -37.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Itaíba: 14471.3 km from centroid", " Bexley: 3791.4 km from centroid", " Granville: 3782.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Itaíba", "FINAL ANSWER: Itaíba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.41889, "lon": -48.15222, "name": "Tomé-Açu" }, { "lat": -16.44972, "lon": -39.06472, "name": "Porto Seguro" }, { "lat": -22.50972, "lon": -47.77806, "name": "Charqueada" }, { "lat": -4.02694, "lon": -38.305, "name": "Pindoretama" }, { "lat": -34.06564, "lon": 151.01266, "name": "Engadine" } ], "question": "Which location is the geographic outlier among: Tomé-Açu, Porto Seguro, Charqueada, Pindoretama, Engadine?", "ground_truth": { "answer": "Engadine", "outlier_distance_km": 13882.6, "second_furthest_km": 5010.8, "clarity_ratio": 2.77, "median_distance_km": 4592.5, "distances_to_centroid": { "Tomé-Açu": 5010.8, "Porto Seguro": 3691.9, "Charqueada": 4592.5, "Pindoretama": 3926.4, "Engadine": 13882.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tomé-Açu: (-2.42°, -48.15°)", " Porto Seguro: (-16.45°, -39.06°)", " Charqueada: (-22.51°, -47.78°)", " Pindoretama: (-4.03°, -38.30°)", " Engadine: (-34.07°, 151.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Engadine: 13882.6 km from centroid", " Tomé-Açu: 5010.8 km from centroid", " Charqueada: 4592.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Engadine", "FINAL ANSWER: Engadine" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -1.29389, "lon": -47.92639, "name": "Castanhal" }, { "lat": -22.87278, "lon": -42.34306, "name": "Araruama" }, { "lat": -9.50194, "lon": -36.02278, "name": "Atalaia" }, { "lat": -12.05, "lon": -38.76667, "name": "Irará" }, { "lat": 13.56083, "lon": 38.97389, "name": "Ābīy Ādī" } ], "question": "Which location is the geographic outlier among: Castanhal, Araruama, Atalaia, Irará, Ābīy Ādī?", "ground_truth": { "answer": "Ābīy Ādī", "outlier_distance_km": 7425.3, "second_furthest_km": 2589.8, "clarity_ratio": 2.87, "median_distance_km": 2582.5, "distances_to_centroid": { "Castanhal": 2582.5, "Araruama": 2589.8, "Atalaia": 1237.8, "Irará": 1612.3, "Ābīy Ādī": 7425.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Castanhal: (-1.29°, -47.93°)", " Araruama: (-22.87°, -42.34°)", " Atalaia: (-9.50°, -36.02°)", " Irará: (-12.05°, -38.77°)", " Ābīy Ādī: (13.56°, 38.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ābīy Ādī: 7425.3 km from centroid", " Araruama: 2589.8 km from centroid", " Castanhal: 2582.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ābīy Ādī", "FINAL ANSWER: Ābīy Ādī" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 5.96502, "lon": -75.96541, "name": "Salgar" }, { "lat": -36.61756, "lon": -72.95593, "name": "Tomé" }, { "lat": 5.0668, "lon": -75.50684, "name": "Manizales" }, { "lat": -18.77861, "lon": -46.4075, "name": "Lagoa Formosa" }, { "lat": 54.60638, "lon": 53.71179, "name": "Tuymazy" } ], "question": "Which location is the geographic outlier among: Salgar, Tomé, Manizales, Lagoa Formosa, Tuymazy?", "ground_truth": { "answer": "Tuymazy", "outlier_distance_km": 10280.1, "second_furthest_km": 5273.1, "clarity_ratio": 1.95, "median_distance_km": 3634.7, "distances_to_centroid": { "Salgar": 3634.7, "Tomé": 5273.1, "Manizales": 3575.7, "Lagoa Formosa": 2338.7, "Tuymazy": 10280.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Salgar: (5.97°, -75.97°)", " Tomé: (-36.62°, -72.96°)", " Manizales: (5.07°, -75.51°)", " Lagoa Formosa: (-18.78°, -46.41°)", " Tuymazy: (54.61°, 53.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tuymazy: 10280.1 km from centroid", " Tomé: 5273.1 km from centroid", " Salgar: 3634.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tuymazy", "FINAL ANSWER: Tuymazy" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.91972, "lon": 151.07592, "name": "Lakemba" }, { "lat": -37.81667, "lon": 145.23333, "name": "Ringwood" }, { "lat": -35.13333, "lon": 138.51667, "name": "Morphett Vale" }, { "lat": -35.28346, "lon": 149.12807, "name": "Canberra" }, { "lat": 40.5769, "lon": 16.75655, "name": "Ginosa" } ], "question": "Which location is the geographic outlier among: Lakemba, Ringwood, Morphett Vale, Canberra, Ginosa?", "ground_truth": { "answer": "Ginosa", "outlier_distance_km": 12565.0, "second_furthest_km": 3396.2, "clarity_ratio": 3.7, "median_distance_km": 3282.5, "distances_to_centroid": { "Lakemba": 3396.2, "Ringwood": 3101.9, "Morphett Vale": 2438.5, "Canberra": 3282.5, "Ginosa": 12565.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lakemba: (-33.92°, 151.08°)", " Ringwood: (-37.82°, 145.23°)", " Morphett Vale: (-35.13°, 138.52°)", " Canberra: (-35.28°, 149.13°)", " Ginosa: (40.58°, 16.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ginosa: 12565.0 km from centroid", " Lakemba: 3396.2 km from centroid", " Canberra: 3282.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ginosa", "FINAL ANSWER: Ginosa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.50099, "lon": -46.65744, "name": "Casa Verde" }, { "lat": -23.52278, "lon": -46.18833, "name": "Mogi das Cruzes" }, { "lat": -29.25611, "lon": -51.53361, "name": "Garibaldi" }, { "lat": -34.5651, "lon": -58.69034, "name": "Bella Vista" }, { "lat": 35.76232, "lon": 139.31952, "name": "Hamura" } ], "question": "Which location is the geographic outlier among: Casa Verde, Mogi das Cruzes, Garibaldi, Bella Vista, Hamura?", "ground_truth": { "answer": "Hamura", "outlier_distance_km": 16406.9, "second_furthest_km": 5066.6, "clarity_ratio": 3.24, "median_distance_km": 4272.0, "distances_to_centroid": { "Casa Verde": 3672.3, "Mogi das Cruzes": 3625.4, "Garibaldi": 4272.0, "Bella Vista": 5066.6, "Hamura": 16406.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Casa Verde: (-23.50°, -46.66°)", " Mogi das Cruzes: (-23.52°, -46.19°)", " Garibaldi: (-29.26°, -51.53°)", " Bella Vista: (-34.57°, -58.69°)", " Hamura: (35.76°, 139.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hamura: 16406.9 km from centroid", " Bella Vista: 5066.6 km from centroid", " Garibaldi: 4272.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hamura", "FINAL ANSWER: Hamura" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.55242, "lon": -46.65735, "name": "Consolação" }, { "lat": -25.77889, "lon": -49.32611, "name": "Mandirituba" }, { "lat": -30.00018, "lon": -51.07632, "name": "Alvorada" }, { "lat": -9.00972, "lon": -36.05833, "name": "São José da Laje" }, { "lat": -33.92399, "lon": 151.22749, "name": "Kingsford" } ], "question": "Which location is the geographic outlier among: Consolação, Mandirituba, Alvorada, São José da Laje, Kingsford?", "ground_truth": { "answer": "Kingsford", "outlier_distance_km": 13105.8, "second_furthest_km": 4434.9, "clarity_ratio": 2.96, "median_distance_km": 4307.3, "distances_to_centroid": { "Consolação": 4078.2, "Mandirituba": 4307.3, "Alvorada": 4434.9, "São José da Laje": 3583.5, "Kingsford": 13105.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Consolação: (-23.55°, -46.66°)", " Mandirituba: (-25.78°, -49.33°)", " Alvorada: (-30.00°, -51.08°)", " São José da Laje: (-9.01°, -36.06°)", " Kingsford: (-33.92°, 151.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kingsford: 13105.8 km from centroid", " Alvorada: 4434.9 km from centroid", " Mandirituba: 4307.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kingsford", "FINAL ANSWER: Kingsford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.83634, "lon": 144.65952, "name": "Tarneit" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": -34.92866, "lon": 138.59863, "name": "Adelaide" }, { "lat": -33.71816, "lon": 151.11561, "name": "Wahroonga" }, { "lat": -22.29194, "lon": -51.90639, "name": "Mirante do Paranapanema" } ], "question": "Which location is the geographic outlier among: Tarneit, Cranbourne East, Adelaide, Wahroonga, Mirante do Paranapanema?", "ground_truth": { "answer": "Mirante do Paranapanema", "outlier_distance_km": 13379.8, "second_furthest_km": 4187.1, "clarity_ratio": 3.2, "median_distance_km": 3597.7, "distances_to_centroid": { "Tarneit": 3544.0, "Cranbourne East": 3597.7, "Adelaide": 3031.9, "Wahroonga": 4187.1, "Mirante do Paranapanema": 13379.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tarneit: (-37.84°, 144.66°)", " Cranbourne East: (-38.12°, 145.30°)", " Adelaide: (-34.93°, 138.60°)", " Wahroonga: (-33.72°, 151.12°)", " Mirante do Paranapanema: (-22.29°, -51.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mirante do Paranapanema: 13379.8 km from centroid", " Wahroonga: 4187.1 km from centroid", " Cranbourne East: 3597.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mirante do Paranapanema", "FINAL ANSWER: Mirante do Paranapanema" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -29.20932, "lon": 26.83898, "name": "Thaba Nchu" }, { "lat": -0.90711, "lon": 34.52895, "name": "Awendo" }, { "lat": -23.90449, "lon": 29.46885, "name": "Polokwane" }, { "lat": 5.55221, "lon": -0.33912, "name": "Mandela" }, { "lat": 24.57578, "lon": 77.73123, "name": "Ashoknagar" } ], "question": "Which location is the geographic outlier among: Thaba Nchu, Awendo, Polokwane, Mandela, Ashoknagar?", "ground_truth": { "answer": "Ashoknagar", "outlier_distance_km": 5776.8, "second_furthest_km": 3944.7, "clarity_ratio": 1.46, "median_distance_km": 2809.5, "distances_to_centroid": { "Thaba Nchu": 2809.5, "Awendo": 441.5, "Polokwane": 2173.3, "Mandela": 3944.7, "Ashoknagar": 5776.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Thaba Nchu: (-29.21°, 26.84°)", " Awendo: (-0.91°, 34.53°)", " Polokwane: (-23.90°, 29.47°)", " Mandela: (5.55°, -0.34°)", " Ashoknagar: (24.58°, 77.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ashoknagar: 5776.8 km from centroid", " Mandela: 3944.7 km from centroid", " Thaba Nchu: 2809.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ashoknagar", "FINAL ANSWER: Ashoknagar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.81568, "lon": 2.38487, "name": "Ivry-sur-Seine" }, { "lat": 41.21667, "lon": 1.53333, "name": "El Vendrell" }, { "lat": 51.80924, "lon": 8.42841, "name": "Rietberg" }, { "lat": 42.35055, "lon": 13.39954, "name": "L'Aquila" }, { "lat": 34.09001, "lon": -117.89034, "name": "Covina" } ], "question": "Which location is the geographic outlier among: Ivry-sur-Seine, El Vendrell, Rietberg, L'Aquila, Covina?", "ground_truth": { "answer": "Covina", "outlier_distance_km": 8143.4, "second_furthest_km": 2576.4, "clarity_ratio": 3.16, "median_distance_km": 2187.3, "distances_to_centroid": { "Ivry-sur-Seine": 1694.0, "El Vendrell": 1656.3, "Rietberg": 2187.3, "L'Aquila": 2576.4, "Covina": 8143.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ivry-sur-Seine: (48.82°, 2.38°)", " El Vendrell: (41.22°, 1.53°)", " Rietberg: (51.81°, 8.43°)", " L'Aquila: (42.35°, 13.40°)", " Covina: (34.09°, -117.89°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Covina: 8143.4 km from centroid", " L'Aquila: 2576.4 km from centroid", " Rietberg: 2187.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Covina", "FINAL ANSWER: Covina" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.6, "lon": 37.46667, "name": "Gonder" }, { "lat": -0.4841, "lon": 37.12662, "name": "Karatina" }, { "lat": 9.03333, "lon": 38.4, "name": "Ādīs ‘Alem" }, { "lat": 12.74482, "lon": 4.52514, "name": "Argungu" }, { "lat": 7.97917, "lon": -75.4202, "name": "Montelíbano" } ], "question": "Which location is the geographic outlier among: Gonder, Karatina, Ādīs ‘Alem, Argungu, Montelíbano?", "ground_truth": { "answer": "Montelíbano", "outlier_distance_km": 9206.8, "second_furthest_km": 3330.1, "clarity_ratio": 2.76, "median_distance_km": 3295.2, "distances_to_centroid": { "Gonder": 3208.6, "Karatina": 3330.1, "Ādīs ‘Alem": 3295.2, "Argungu": 646.0, "Montelíbano": 9206.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gonder: (12.60°, 37.47°)", " Karatina: (-0.48°, 37.13°)", " Ādīs ‘Alem: (9.03°, 38.40°)", " Argungu: (12.74°, 4.53°)", " Montelíbano: (7.98°, -75.42°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Montelíbano: 9206.8 km from centroid", " Karatina: 3330.1 km from centroid", " Ādīs ‘Alem: 3295.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Montelíbano", "FINAL ANSWER: Montelíbano" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.08465, "lon": 152.9511, "name": "Caboolture" }, { "lat": -31.95224, "lon": 115.8614, "name": "Perth" }, { "lat": -32.27682, "lon": 115.72978, "name": "Rockingham" }, { "lat": -38.68333, "lon": 176.08333, "name": "Taupo" }, { "lat": 16.62473, "lon": -93.09894, "name": "Suchiapa" } ], "question": "Which location is the geographic outlier among: Caboolture, Perth, Rockingham, Taupo, Suchiapa?", "ground_truth": { "answer": "Suchiapa", "outlier_distance_km": 19050.6, "second_furthest_km": 7838.0, "clarity_ratio": 2.43, "median_distance_km": 5962.2, "distances_to_centroid": { "Caboolture": 5962.2, "Perth": 2431.1, "Rockingham": 2431.8, "Taupo": 7838.0, "Suchiapa": 19050.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Caboolture: (-27.08°, 152.95°)", " Perth: (-31.95°, 115.86°)", " Rockingham: (-32.28°, 115.73°)", " Taupo: (-38.68°, 176.08°)", " Suchiapa: (16.62°, -93.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Suchiapa: 19050.6 km from centroid", " Taupo: 7838.0 km from centroid", " Caboolture: 5962.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Suchiapa", "FINAL ANSWER: Suchiapa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.69303, "lon": -83.41181, "name": "Waterford" }, { "lat": 19.95232, "lon": -102.30781, "name": "Jacona de Plancarte" }, { "lat": 39.08289, "lon": -77.26498, "name": "North Potomac" }, { "lat": 21.17429, "lon": -86.84656, "name": "Cancún" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" } ], "question": "Which location is the geographic outlier among: Waterford, Jacona de Plancarte, North Potomac, Cancún, New Plymouth?", "ground_truth": { "answer": "New Plymouth", "outlier_distance_km": 16251.5, "second_furthest_km": 7049.4, "clarity_ratio": 2.31, "median_distance_km": 5435.5, "distances_to_centroid": { "Waterford": 5380.2, "Jacona de Plancarte": 7049.4, "North Potomac": 4764.1, "Cancún": 5435.5, "New Plymouth": 16251.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Waterford: (42.69°, -83.41°)", " Jacona de Plancarte: (19.95°, -102.31°)", " North Potomac: (39.08°, -77.26°)", " Cancún: (21.17°, -86.85°)", " New Plymouth: (-39.07°, 174.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " New Plymouth: 16251.5 km from centroid", " Jacona de Plancarte: 7049.4 km from centroid", " Cancún: 5435.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: New Plymouth", "FINAL ANSWER: New Plymouth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -22.25222, "lon": -45.70333, "name": "Santa Rita do Sapucaí" }, { "lat": 7.06528, "lon": -73.85472, "name": "Barrancabermeja" }, { "lat": -31.395, "lon": -52.67556, "name": "Canguçu" }, { "lat": -8.51417, "lon": -39.31, "name": "Cabrobó" }, { "lat": 9.46374, "lon": 12.03062, "name": "Numan" } ], "question": "Which location is the geographic outlier among: Santa Rita do Sapucaí, Barrancabermeja, Canguçu, Cabrobó, Numan?", "ground_truth": { "answer": "Numan", "outlier_distance_km": 6109.2, "second_furthest_km": 4170.6, "clarity_ratio": 1.46, "median_distance_km": 2806.1, "distances_to_centroid": { "Santa Rita do Sapucaí": 1585.5, "Barrancabermeja": 4170.6, "Canguçu": 2806.1, "Cabrobó": 94.2, "Numan": 6109.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Rita do Sapucaí: (-22.25°, -45.70°)", " Barrancabermeja: (7.07°, -73.85°)", " Canguçu: (-31.39°, -52.68°)", " Cabrobó: (-8.51°, -39.31°)", " Numan: (9.46°, 12.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Numan: 6109.2 km from centroid", " Barrancabermeja: 4170.6 km from centroid", " Canguçu: 2806.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Numan", "FINAL ANSWER: Numan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.6, "lon": 145.15, "name": "Doreen" }, { "lat": -31.84062, "lon": 115.89549, "name": "Ballajura" }, { "lat": -33.73333, "lon": 151.0, "name": "Castle Hill" }, { "lat": -27.56056, "lon": 151.95386, "name": "Toowoomba" }, { "lat": 28.18779, "lon": -82.73955, "name": "Holiday" } ], "question": "Which location is the geographic outlier among: Doreen, Ballajura, Castle Hill, Toowoomba, Holiday?", "ground_truth": { "answer": "Holiday", "outlier_distance_km": 19155.2, "second_furthest_km": 5665.4, "clarity_ratio": 3.38, "median_distance_km": 5548.5, "distances_to_centroid": { "Doreen": 5053.1, "Ballajura": 2324.0, "Castle Hill": 5548.5, "Toowoomba": 5665.4, "Holiday": 19155.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Doreen: (-37.60°, 145.15°)", " Ballajura: (-31.84°, 115.90°)", " Castle Hill: (-33.73°, 151.00°)", " Toowoomba: (-27.56°, 151.95°)", " Holiday: (28.19°, -82.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Holiday: 19155.2 km from centroid", " Toowoomba: 5665.4 km from centroid", " Castle Hill: 5548.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Holiday", "FINAL ANSWER: Holiday" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -8.39889, "lon": -35.06389, "name": "Ipojuca" }, { "lat": -6.05675, "lon": -77.16651, "name": "Rioja" }, { "lat": -9.89667, "lon": -39.02639, "name": "Canudos" }, { "lat": -34.61082, "lon": -58.481, "name": "Villa Santa Rita" }, { "lat": -33.9049, "lon": 151.01996, "name": "Yagoona" } ], "question": "Which location is the geographic outlier among: Ipojuca, Rioja, Canudos, Villa Santa Rita, Yagoona?", "ground_truth": { "answer": "Yagoona", "outlier_distance_km": 13900.5, "second_furthest_km": 7206.3, "clarity_ratio": 1.93, "median_distance_km": 4926.8, "distances_to_centroid": { "Ipojuca": 2759.3, "Rioja": 7206.3, "Canudos": 3090.0, "Villa Santa Rita": 4926.8, "Yagoona": 13900.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ipojuca: (-8.40°, -35.06°)", " Rioja: (-6.06°, -77.17°)", " Canudos: (-9.90°, -39.03°)", " Villa Santa Rita: (-34.61°, -58.48°)", " Yagoona: (-33.90°, 151.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Yagoona: 13900.5 km from centroid", " Rioja: 7206.3 km from centroid", " Villa Santa Rita: 4926.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Yagoona", "FINAL ANSWER: Yagoona" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.3727, "lon": -99.1564, "name": "Benito Juárez" }, { "lat": 32.93457, "lon": -97.25168, "name": "Keller" }, { "lat": 33.44734, "lon": -84.14686, "name": "McDonough" }, { "lat": 37.22764, "lon": -80.01282, "name": "Cave Spring" }, { "lat": 32.80589, "lon": 130.69181, "name": "Kumamoto" } ], "question": "Which location is the geographic outlier among: Benito Juárez, Keller, McDonough, Cave Spring, Kumamoto?", "ground_truth": { "answer": "Kumamoto", "outlier_distance_km": 12894.0, "second_furthest_km": 5453.9, "clarity_ratio": 2.36, "median_distance_km": 4788.5, "distances_to_centroid": { "Benito Juárez": 5453.9, "Keller": 4788.5, "McDonough": 3576.6, "Cave Spring": 3184.6, "Kumamoto": 12894.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Benito Juárez: (19.37°, -99.16°)", " Keller: (32.93°, -97.25°)", " McDonough: (33.45°, -84.15°)", " Cave Spring: (37.23°, -80.01°)", " Kumamoto: (32.81°, 130.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kumamoto: 12894.0 km from centroid", " Benito Juárez: 5453.9 km from centroid", " Keller: 4788.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kumamoto", "FINAL ANSWER: Kumamoto" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.73333, "lon": 144.93333, "name": "Pascoe Vale" }, { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -37.83961, "lon": 144.94228, "name": "Port Melbourne" }, { "lat": -37.74124, "lon": 144.73631, "name": "Caroline Springs" }, { "lat": 41.69982, "lon": -72.15702, "name": "Windham" } ], "question": "Which location is the geographic outlier among: Pascoe Vale, Epping, Port Melbourne, Caroline Springs, Windham?", "ground_truth": { "answer": "Windham", "outlier_distance_km": 17729.9, "second_furthest_km": 4506.4, "clarity_ratio": 3.93, "median_distance_km": 4502.3, "distances_to_centroid": { "Pascoe Vale": 4499.4, "Epping": 4506.4, "Port Melbourne": 4502.3, "Caroline Springs": 4482.5, "Windham": 17729.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pascoe Vale: (-37.73°, 144.93°)", " Epping: (-37.65°, 145.03°)", " Port Melbourne: (-37.84°, 144.94°)", " Caroline Springs: (-37.74°, 144.74°)", " Windham: (41.70°, -72.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Windham: 17729.9 km from centroid", " Epping: 4506.4 km from centroid", " Port Melbourne: 4502.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Windham", "FINAL ANSWER: Windham" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.342, "lon": 31.58, "name": "Ncotshane" }, { "lat": 31.03408, "lon": 30.46823, "name": "Damanhur" }, { "lat": -25.91849, "lon": 28.19881, "name": "Midstream" }, { "lat": 8.45, "lon": 39.28333, "name": "Wenjī" }, { "lat": 10.88606, "lon": -72.8487, "name": "Fonseca" } ], "question": "Which location is the geographic outlier among: Ncotshane, Damanhur, Midstream, Wenjī, Fonseca?", "ground_truth": { "answer": "Fonseca", "outlier_distance_km": 9384.9, "second_furthest_km": 4054.0, "clarity_ratio": 2.31, "median_distance_km": 3677.2, "distances_to_centroid": { "Ncotshane": 3677.2, "Damanhur": 4054.0, "Midstream": 3347.5, "Wenjī": 3255.5, "Fonseca": 9384.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ncotshane: (-27.34°, 31.58°)", " Damanhur: (31.03°, 30.47°)", " Midstream: (-25.92°, 28.20°)", " Wenjī: (8.45°, 39.28°)", " Fonseca: (10.89°, -72.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fonseca: 9384.9 km from centroid", " Damanhur: 4054.0 km from centroid", " Ncotshane: 3677.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fonseca", "FINAL ANSWER: Fonseca" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.22436, "lon": -79.42476, "name": "Chepén" }, { "lat": -38.95078, "lon": -68.0592, "name": "Neuquén" }, { "lat": -8.28773, "lon": -35.02925, "name": "Cabo de Santo Agostinho" }, { "lat": -18.08639, "lon": -39.55083, "name": "Mucuri" }, { "lat": -41.28374, "lon": 174.74141, "name": "Karori" } ], "question": "Which location is the geographic outlier among: Chepén, Neuquén, Cabo de Santo Agostinho, Mucuri, Karori?", "ground_truth": { "answer": "Karori", "outlier_distance_km": 12879.8, "second_furthest_km": 7646.8, "clarity_ratio": 1.68, "median_distance_km": 5771.7, "distances_to_centroid": { "Chepén": 7646.8, "Neuquén": 5771.7, "Cabo de Santo Agostinho": 3167.8, "Mucuri": 3172.3, "Karori": 12879.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Chepén: (-7.22°, -79.42°)", " Neuquén: (-38.95°, -68.06°)", " Cabo de Santo Agostinho: (-8.29°, -35.03°)", " Mucuri: (-18.09°, -39.55°)", " Karori: (-41.28°, 174.74°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Karori: 12879.8 km from centroid", " Chepén: 7646.8 km from centroid", " Neuquén: 5771.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Karori", "FINAL ANSWER: Karori" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.76884, "lon": -119.24705, "name": "Delano" }, { "lat": 39.4667, "lon": -87.41391, "name": "Terre Haute" }, { "lat": 33.96358, "lon": -117.56418, "name": "Eastvale" }, { "lat": 44.47588, "lon": -73.21207, "name": "Burlington" }, { "lat": 0.46005, "lon": 34.11169, "name": "Busia" } ], "question": "Which location is the geographic outlier among: Delano, Terre Haute, Eastvale, Burlington, Busia?", "ground_truth": { "answer": "Busia", "outlier_distance_km": 11576.2, "second_furthest_km": 4323.7, "clarity_ratio": 2.68, "median_distance_km": 4196.6, "distances_to_centroid": { "Delano": 4323.7, "Terre Haute": 1646.0, "Eastvale": 4196.6, "Burlington": 1518.4, "Busia": 11576.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Delano: (35.77°, -119.25°)", " Terre Haute: (39.47°, -87.41°)", " Eastvale: (33.96°, -117.56°)", " Burlington: (44.48°, -73.21°)", " Busia: (0.46°, 34.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Busia: 11576.2 km from centroid", " Delano: 4323.7 km from centroid", " Eastvale: 4196.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Busia", "FINAL ANSWER: Busia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.7875, "lon": 39.54222, "name": "Maych’ew" }, { "lat": 25.90107, "lon": 32.72392, "name": "Naqādah" }, { "lat": 11.73292, "lon": 41.082, "name": "Dubti" }, { "lat": 14.18722, "lon": 39.56389, "name": "Idaga Hamus" }, { "lat": 48.86667, "lon": 2.71667, "name": "Lagny-sur-Marne" } ], "question": "Which location is the geographic outlier among: Maych’ew, Naqādah, Dubti, Idaga Hamus, Lagny-sur-Marne?", "ground_truth": { "answer": "Lagny-sur-Marne", "outlier_distance_km": 3833.2, "second_furthest_km": 1612.3, "clarity_ratio": 2.38, "median_distance_km": 1416.2, "distances_to_centroid": { "Maych’ew": 1416.2, "Naqādah": 391.5, "Dubti": 1612.3, "Idaga Hamus": 1298.1, "Lagny-sur-Marne": 3833.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maych’ew: (12.79°, 39.54°)", " Naqādah: (25.90°, 32.72°)", " Dubti: (11.73°, 41.08°)", " Idaga Hamus: (14.19°, 39.56°)", " Lagny-sur-Marne: (48.87°, 2.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lagny-sur-Marne: 3833.2 km from centroid", " Dubti: 1612.3 km from centroid", " Maych’ew: 1416.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lagny-sur-Marne", "FINAL ANSWER: Lagny-sur-Marne" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.56002, "lon": 9.71295, "name": "Petersberg" }, { "lat": 53.5, "lon": -1.45, "name": "Hoyland Nether" }, { "lat": 53.44325, "lon": -1.949, "name": "Glossop" }, { "lat": 41.69993, "lon": 2.84565, "name": "Lloret de Mar" }, { "lat": 16.1026, "lon": 80.78074, "name": "Bhattiprolu" } ], "question": "Which location is the geographic outlier among: Petersberg, Hoyland Nether, Glossop, Lloret de Mar, Bhattiprolu?", "ground_truth": { "answer": "Bhattiprolu", "outlier_distance_km": 6595.5, "second_furthest_km": 1863.1, "clarity_ratio": 3.54, "median_distance_km": 1837.9, "distances_to_centroid": { "Petersberg": 1043.6, "Hoyland Nether": 1837.9, "Glossop": 1863.1, "Lloret de Mar": 1251.2, "Bhattiprolu": 6595.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Petersberg: (50.56°, 9.71°)", " Hoyland Nether: (53.50°, -1.45°)", " Glossop: (53.44°, -1.95°)", " Lloret de Mar: (41.70°, 2.85°)", " Bhattiprolu: (16.10°, 80.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bhattiprolu: 6595.5 km from centroid", " Glossop: 1863.1 km from centroid", " Hoyland Nether: 1837.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bhattiprolu", "FINAL ANSWER: Bhattiprolu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.53635, "lon": 1.34428, "name": "Cugnaux" }, { "lat": 41.64662, "lon": 2.74135, "name": "Malgrat de Mar" }, { "lat": 48.9482, "lon": 2.19169, "name": "Sartrouville" }, { "lat": 48.16783, "lon": 8.62719, "name": "Rottweil" }, { "lat": 31.02795, "lon": 30.71493, "name": "Shubrākhīt" } ], "question": "Which location is the geographic outlier among: Cugnaux, Malgrat de Mar, Sartrouville, Rottweil, Shubrākhīt?", "ground_truth": { "answer": "Shubrākhīt", "outlier_distance_km": 2305.6, "second_furthest_km": 880.6, "clarity_ratio": 2.62, "median_distance_km": 638.8, "distances_to_centroid": { "Cugnaux": 638.8, "Malgrat de Mar": 538.0, "Sartrouville": 880.6, "Rottweil": 613.1, "Shubrākhīt": 2305.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cugnaux: (43.54°, 1.34°)", " Malgrat de Mar: (41.65°, 2.74°)", " Sartrouville: (48.95°, 2.19°)", " Rottweil: (48.17°, 8.63°)", " Shubrākhīt: (31.03°, 30.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shubrākhīt: 2305.6 km from centroid", " Sartrouville: 880.6 km from centroid", " Cugnaux: 638.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shubrākhīt", "FINAL ANSWER: Shubrākhīt" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 42.86736, "lon": 130.35689, "name": "Hunchun" }, { "lat": 36.09047, "lon": 140.21047, "name": "Tsuchiura" }, { "lat": 15.88214, "lon": 108.12092, "name": "Đại Lộc" }, { "lat": 23.84306, "lon": 73.71466, "name": "Dūngarpur" }, { "lat": -41.27078, "lon": 173.28404, "name": "Nelson" } ], "question": "Which location is the geographic outlier among: Hunchun, Tsuchiura, Đại Lộc, Dūngarpur, Nelson?", "ground_truth": { "answer": "Nelson", "outlier_distance_km": 8018.1, "second_furthest_km": 5435.9, "clarity_ratio": 1.48, "median_distance_km": 3085.4, "distances_to_centroid": { "Hunchun": 3085.4, "Tsuchiura": 2735.7, "Đại Lộc": 1821.8, "Dūngarpur": 5435.9, "Nelson": 8018.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hunchun: (42.87°, 130.36°)", " Tsuchiura: (36.09°, 140.21°)", " Đại Lộc: (15.88°, 108.12°)", " Dūngarpur: (23.84°, 73.71°)", " Nelson: (-41.27°, 173.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nelson: 8018.1 km from centroid", " Dūngarpur: 5435.9 km from centroid", " Hunchun: 3085.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nelson", "FINAL ANSWER: Nelson" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.08829, "lon": 16.64866, "name": "Kościan" }, { "lat": 42.54664, "lon": -6.59619, "name": "Ponferrada" }, { "lat": 45.38956, "lon": 4.2886, "name": "Firminy" }, { "lat": 53.45801, "lon": -2.20104, "name": "Longsight" }, { "lat": 29.23552, "lon": 77.01273, "name": "Samālkha" } ], "question": "Which location is the geographic outlier among: Kościan, Ponferrada, Firminy, Longsight, Samālkha?", "ground_truth": { "answer": "Samālkha", "outlier_distance_km": 5404.9, "second_furthest_km": 1973.8, "clarity_ratio": 2.74, "median_distance_km": 1756.2, "distances_to_centroid": { "Kościan": 843.4, "Ponferrada": 1973.8, "Firminy": 1068.2, "Longsight": 1756.2, "Samālkha": 5404.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kościan: (52.09°, 16.65°)", " Ponferrada: (42.55°, -6.60°)", " Firminy: (45.39°, 4.29°)", " Longsight: (53.46°, -2.20°)", " Samālkha: (29.24°, 77.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Samālkha: 5404.9 km from centroid", " Ponferrada: 1973.8 km from centroid", " Longsight: 1756.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Samālkha", "FINAL ANSWER: Samālkha" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.77944, "lon": -39.17, "name": "Conceição do Almeida" }, { "lat": -12.31667, "lon": -38.76667, "name": "Conceição do Jacuípe" }, { "lat": -11.80361, "lon": -61.80333, "name": "Rolim de Moura" }, { "lat": -7.09829, "lon": -49.9435, "name": "Xinguara" }, { "lat": 21.55, "lon": 107.96667, "name": "Dongxing" } ], "question": "Which location is the geographic outlier among: Conceição do Almeida, Conceição do Jacuípe, Rolim de Moura, Xinguara, Dongxing?", "ground_truth": { "answer": "Dongxing", "outlier_distance_km": 13728.6, "second_furthest_km": 5063.2, "clarity_ratio": 2.71, "median_distance_km": 3727.5, "distances_to_centroid": { "Conceição do Almeida": 2670.8, "Conceição do Jacuípe": 2613.4, "Rolim de Moura": 5063.2, "Xinguara": 3727.5, "Dongxing": 13728.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Conceição do Almeida: (-12.78°, -39.17°)", " Conceição do Jacuípe: (-12.32°, -38.77°)", " Rolim de Moura: (-11.80°, -61.80°)", " Xinguara: (-7.10°, -49.94°)", " Dongxing: (21.55°, 107.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dongxing: 13728.6 km from centroid", " Rolim de Moura: 5063.2 km from centroid", " Xinguara: 3727.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Dongxing", "FINAL ANSWER: Dongxing" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.09917, "lon": -98.25417, "name": "Sanctorum" }, { "lat": 41.71087, "lon": -87.75811, "name": "Oak Lawn" }, { "lat": 26.25175, "lon": -80.17894, "name": "Coconut Creek" }, { "lat": 35.91402, "lon": -81.53898, "name": "Lenoir" }, { "lat": 52.50575, "lon": 13.50812, "name": "Friedrichsfelde" } ], "question": "Which location is the geographic outlier among: Sanctorum, Oak Lawn, Coconut Creek, Lenoir, Friedrichsfelde?", "ground_truth": { "answer": "Friedrichsfelde", "outlier_distance_km": 6376.0, "second_furthest_km": 3559.1, "clarity_ratio": 1.79, "median_distance_km": 1958.8, "distances_to_centroid": { "Sanctorum": 3559.1, "Oak Lawn": 1958.8, "Coconut Creek": 1607.8, "Lenoir": 1332.0, "Friedrichsfelde": 6376.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sanctorum: (19.10°, -98.25°)", " Oak Lawn: (41.71°, -87.76°)", " Coconut Creek: (26.25°, -80.18°)", " Lenoir: (35.91°, -81.54°)", " Friedrichsfelde: (52.51°, 13.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Friedrichsfelde: 6376.0 km from centroid", " Sanctorum: 3559.1 km from centroid", " Oak Lawn: 1958.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Friedrichsfelde", "FINAL ANSWER: Friedrichsfelde" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.68333, "lon": -54.64278, "name": "Mojuí dos Campos" }, { "lat": -11.52472, "lon": -61.01278, "name": "Espigão dOeste" }, { "lat": -20.25333, "lon": -43.80139, "name": "Itabirito" }, { "lat": -23.87444, "lon": -53.90167, "name": "Altônia" }, { "lat": -26.31401, "lon": 26.82223, "name": "Ventersdorp" } ], "question": "Which location is the geographic outlier among: Mojuí dos Campos, Espigão dOeste, Itabirito, Altônia, Ventersdorp?", "ground_truth": { "answer": "Ventersdorp", "outlier_distance_km": 6647.7, "second_furthest_km": 2622.6, "clarity_ratio": 2.53, "median_distance_km": 2469.1, "distances_to_centroid": { "Mojuí dos Campos": 2469.1, "Espigão dOeste": 2622.6, "Itabirito": 777.7, "Altônia": 1892.0, "Ventersdorp": 6647.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mojuí dos Campos: (-2.68°, -54.64°)", " Espigão dOeste: (-11.52°, -61.01°)", " Itabirito: (-20.25°, -43.80°)", " Altônia: (-23.87°, -53.90°)", " Ventersdorp: (-26.31°, 26.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ventersdorp: 6647.7 km from centroid", " Espigão dOeste: 2622.6 km from centroid", " Mojuí dos Campos: 2469.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ventersdorp", "FINAL ANSWER: Ventersdorp" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.87811, "lon": 145.16476, "name": "Glen Waverley" }, { "lat": -26.66008, "lon": 153.09953, "name": "Maroochydore" }, { "lat": -41.28374, "lon": 174.74141, "name": "Karori" }, { "lat": -37.75, "lon": 145.01667, "name": "Preston" }, { "lat": -33.51889, "lon": -53.36806, "name": "Santa Vitória do Palmar" } ], "question": "Which location is the geographic outlier among: Glen Waverley, Maroochydore, Karori, Preston, Santa Vitória do Palmar?", "ground_truth": { "answer": "Santa Vitória do Palmar", "outlier_distance_km": 12218.2, "second_furthest_km": 5315.6, "clarity_ratio": 2.3, "median_distance_km": 3920.4, "distances_to_centroid": { "Glen Waverley": 2874.4, "Maroochydore": 3920.4, "Karori": 5315.6, "Preston": 2862.6, "Santa Vitória do Palmar": 12218.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Glen Waverley: (-37.88°, 145.16°)", " Maroochydore: (-26.66°, 153.10°)", " Karori: (-41.28°, 174.74°)", " Preston: (-37.75°, 145.02°)", " Santa Vitória do Palmar: (-33.52°, -53.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santa Vitória do Palmar: 12218.2 km from centroid", " Karori: 5315.6 km from centroid", " Maroochydore: 3920.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santa Vitória do Palmar", "FINAL ANSWER: Santa Vitória do Palmar" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -28.07071, "lon": 153.39329, "name": "Robina" }, { "lat": -33.79176, "lon": 151.08057, "name": "Eastwood" }, { "lat": -35.13333, "lon": 138.51667, "name": "Morphett Vale" }, { "lat": -32.27682, "lon": 115.72978, "name": "Rockingham" }, { "lat": 50.39138, "lon": 116.53355, "name": "Borzya" } ], "question": "Which location is the geographic outlier among: Robina, Eastwood, Morphett Vale, Rockingham, Borzya?", "ground_truth": { "answer": "Borzya", "outlier_distance_km": 7577.1, "second_furthest_km": 2677.3, "clarity_ratio": 2.83, "median_distance_km": 2567.7, "distances_to_centroid": { "Robina": 2329.0, "Eastwood": 2567.7, "Morphett Vale": 2179.9, "Rockingham": 2677.3, "Borzya": 7577.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Robina: (-28.07°, 153.39°)", " Eastwood: (-33.79°, 151.08°)", " Morphett Vale: (-35.13°, 138.52°)", " Rockingham: (-32.28°, 115.73°)", " Borzya: (50.39°, 116.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Borzya: 7577.1 km from centroid", " Rockingham: 2677.3 km from centroid", " Eastwood: 2567.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Borzya", "FINAL ANSWER: Borzya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 8.13333, "lon": 39.23333, "name": "Īteya" }, { "lat": -25.43321, "lon": 31.95478, "name": "Komatipoort" }, { "lat": 10.55, "lon": 37.48333, "name": "Dembech’a" }, { "lat": -1.4275, "lon": 36.6865, "name": "Kiserian" }, { "lat": -3.12873, "lon": -58.15501, "name": "Urucurituba" } ], "question": "Which location is the geographic outlier among: Īteya, Komatipoort, Dembech’a, Kiserian, Urucurituba?", "ground_truth": { "answer": "Urucurituba", "outlier_distance_km": 8395.4, "second_furthest_km": 3009.0, "clarity_ratio": 2.79, "median_distance_km": 2678.8, "distances_to_centroid": { "Īteya": 2678.8, "Komatipoort": 3009.0, "Dembech’a": 2636.1, "Kiserian": 2140.9, "Urucurituba": 8395.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Īteya: (8.13°, 39.23°)", " Komatipoort: (-25.43°, 31.95°)", " Dembech’a: (10.55°, 37.48°)", " Kiserian: (-1.43°, 36.69°)", " Urucurituba: (-3.13°, -58.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Urucurituba: 8395.4 km from centroid", " Komatipoort: 3009.0 km from centroid", " Īteya: 2678.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Urucurituba", "FINAL ANSWER: Urucurituba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.14621, "lon": 140.31507, "name": "Katsuura" }, { "lat": 13.68333, "lon": 79.35, "name": "Tirumala" }, { "lat": 16.78854, "lon": 80.84593, "name": "Nūzvīd" }, { "lat": 38.15389, "lon": 140.27361, "name": "Kaminoyama" }, { "lat": -25.43998, "lon": -54.40161, "name": "Santa Terezinha de Itaipu" } ], "question": "Which location is the geographic outlier among: Katsuura, Tirumala, Nūzvīd, Kaminoyama, Santa Terezinha de Itaipu?", "ground_truth": { "answer": "Santa Terezinha de Itaipu", "outlier_distance_km": 14895.7, "second_furthest_km": 6593.5, "clarity_ratio": 2.26, "median_distance_km": 6580.0, "distances_to_centroid": { "Katsuura": 6580.0, "Tirumala": 313.6, "Nūzvīd": 401.0, "Kaminoyama": 6593.5, "Santa Terezinha de Itaipu": 14895.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Katsuura: (35.15°, 140.32°)", " Tirumala: (13.68°, 79.35°)", " Nūzvīd: (16.79°, 80.85°)", " Kaminoyama: (38.15°, 140.27°)", " Santa Terezinha de Itaipu: (-25.44°, -54.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Santa Terezinha de Itaipu: 14895.7 km from centroid", " Kaminoyama: 6593.5 km from centroid", " Katsuura: 6580.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Santa Terezinha de Itaipu", "FINAL ANSWER: Santa Terezinha de Itaipu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.39841, "lon": 9.99155, "name": "Ulm" }, { "lat": 52.774, "lon": -1.55744, "name": "Swadlincote" }, { "lat": 44.1391, "lon": 12.24315, "name": "Cesena" }, { "lat": 52.85435, "lon": 11.1525, "name": "Salzwedel" }, { "lat": -25.509, "lon": 28.064, "name": "Mabopane" } ], "question": "Which location is the geographic outlier among: Ulm, Swadlincote, Cesena, Salzwedel, Mabopane?", "ground_truth": { "answer": "Mabopane", "outlier_distance_km": 6888.2, "second_furthest_km": 2293.6, "clarity_ratio": 3.0, "median_distance_km": 2038.5, "distances_to_centroid": { "Ulm": 1550.7, "Swadlincote": 2293.6, "Cesena": 1068.6, "Salzwedel": 2038.5, "Mabopane": 6888.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ulm: (48.40°, 9.99°)", " Swadlincote: (52.77°, -1.56°)", " Cesena: (44.14°, 12.24°)", " Salzwedel: (52.85°, 11.15°)", " Mabopane: (-25.51°, 28.06°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mabopane: 6888.2 km from centroid", " Swadlincote: 2293.6 km from centroid", " Salzwedel: 2038.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mabopane", "FINAL ANSWER: Mabopane" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.61917, "lon": -43.22694, "name": "Itabira" }, { "lat": -22.50917, "lon": -48.55778, "name": "Igaraçu do Tietê" }, { "lat": -31.6515, "lon": -68.28216, "name": "Caucete" }, { "lat": 4.9218, "lon": -75.06232, "name": "Líbano" }, { "lat": -2.0561, "lon": 101.3913, "name": "Sungai Penuh" } ], "question": "Which location is the geographic outlier among: Itabira, Igaraçu do Tietê, Caucete, Líbano, Sungai Penuh?", "ground_truth": { "answer": "Sungai Penuh", "outlier_distance_km": 14024.6, "second_furthest_km": 5735.9, "clarity_ratio": 2.45, "median_distance_km": 4639.5, "distances_to_centroid": { "Itabira": 1853.3, "Igaraçu do Tietê": 2477.3, "Caucete": 4639.5, "Líbano": 5735.9, "Sungai Penuh": 14024.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itabira: (-19.62°, -43.23°)", " Igaraçu do Tietê: (-22.51°, -48.56°)", " Caucete: (-31.65°, -68.28°)", " Líbano: (4.92°, -75.06°)", " Sungai Penuh: (-2.06°, 101.39°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sungai Penuh: 14024.6 km from centroid", " Líbano: 5735.9 km from centroid", " Caucete: 4639.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sungai Penuh", "FINAL ANSWER: Sungai Penuh" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.60157, "lon": -98.46152, "name": "Izúcar de Matamoros" }, { "lat": 47.03426, "lon": -122.82319, "name": "Lacey" }, { "lat": 23.1749, "lon": -102.86785, "name": "Fresnillo" }, { "lat": 49.23839, "lon": -122.86676, "name": "Maillardville" }, { "lat": -13.53806, "lon": -39.09861, "name": "Taperoá" } ], "question": "Which location is the geographic outlier among: Izúcar de Matamoros, Lacey, Fresnillo, Maillardville, Taperoá?", "ground_truth": { "answer": "Taperoá", "outlier_distance_km": 7612.8, "second_furthest_km": 3500.5, "clarity_ratio": 2.17, "median_distance_km": 3340.8, "distances_to_centroid": { "Izúcar de Matamoros": 712.2, "Lacey": 3340.8, "Fresnillo": 604.4, "Maillardville": 3500.5, "Taperoá": 7612.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Izúcar de Matamoros: (18.60°, -98.46°)", " Lacey: (47.03°, -122.82°)", " Fresnillo: (23.17°, -102.87°)", " Maillardville: (49.24°, -122.87°)", " Taperoá: (-13.54°, -39.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Taperoá: 7612.8 km from centroid", " Maillardville: 3500.5 km from centroid", " Lacey: 3340.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Taperoá", "FINAL ANSWER: Taperoá" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.34564, "lon": -98.86034, "name": "San Francisco Acuautla" }, { "lat": 41.88142, "lon": -87.88312, "name": "Bellwood" }, { "lat": 41.60232, "lon": -72.98677, "name": "Wolcott" }, { "lat": 33.976, "lon": -118.06909, "name": "West Whittier-Los Nietos" }, { "lat": -26.81358, "lon": 27.81695, "name": "Sasolburg" } ], "question": "Which location is the geographic outlier among: San Francisco Acuautla, Bellwood, Wolcott, West Whittier-Los Nietos, Sasolburg?", "ground_truth": { "answer": "Sasolburg", "outlier_distance_km": 11825.3, "second_furthest_km": 4858.0, "clarity_ratio": 2.43, "median_distance_km": 3012.9, "distances_to_centroid": { "San Francisco Acuautla": 3012.9, "Bellwood": 2769.1, "Wolcott": 2197.7, "West Whittier-Los Nietos": 4858.0, "Sasolburg": 11825.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Francisco Acuautla: (19.35°, -98.86°)", " Bellwood: (41.88°, -87.88°)", " Wolcott: (41.60°, -72.99°)", " West Whittier-Los Nietos: (33.98°, -118.07°)", " Sasolburg: (-26.81°, 27.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sasolburg: 11825.3 km from centroid", " West Whittier-Los Nietos: 4858.0 km from centroid", " San Francisco Acuautla: 3012.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sasolburg", "FINAL ANSWER: Sasolburg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.73475, "lon": 105.38817, "name": "Xigaoshan" }, { "lat": 15.3275, "lon": 120.9192, "name": "Jaen" }, { "lat": 23.53878, "lon": 86.6735, "name": "Raghunathpur" }, { "lat": 28.19874, "lon": 112.97087, "name": "Changsha" }, { "lat": -16.02511, "lon": -48.07121, "name": "Gama" } ], "question": "Which location is the geographic outlier among: Xigaoshan, Jaen, Raghunathpur, Changsha, Gama?", "ground_truth": { "answer": "Gama", "outlier_distance_km": 14027.3, "second_furthest_km": 4836.0, "clarity_ratio": 2.9, "median_distance_km": 4019.0, "distances_to_centroid": { "Xigaoshan": 3508.6, "Jaen": 4836.0, "Raghunathpur": 1368.8, "Changsha": 4019.0, "Gama": 14027.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Xigaoshan: (33.73°, 105.39°)", " Jaen: (15.33°, 120.92°)", " Raghunathpur: (23.54°, 86.67°)", " Changsha: (28.20°, 112.97°)", " Gama: (-16.03°, -48.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gama: 14027.3 km from centroid", " Jaen: 4836.0 km from centroid", " Changsha: 4019.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gama", "FINAL ANSWER: Gama" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 7.26667, "lon": 9.98333, "name": "Takum" }, { "lat": 9.03528, "lon": 38.66083, "name": "Burayu" }, { "lat": -3.63045, "lon": 39.84992, "name": "Kilifi" }, { "lat": 5.96667, "lon": 41.03333, "name": "Ara Ali" }, { "lat": 49.45421, "lon": 11.07752, "name": "Nürnberg" } ], "question": "Which location is the geographic outlier among: Takum, Burayu, Kilifi, Ara Ali, Nürnberg?", "ground_truth": { "answer": "Nürnberg", "outlier_distance_km": 4277.5, "second_furthest_km": 2313.8, "clarity_ratio": 1.85, "median_distance_km": 2104.1, "distances_to_centroid": { "Takum": 2104.1, "Burayu": 1256.7, "Kilifi": 2313.8, "Ara Ali": 1649.9, "Nürnberg": 4277.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Takum: (7.27°, 9.98°)", " Burayu: (9.04°, 38.66°)", " Kilifi: (-3.63°, 39.85°)", " Ara Ali: (5.97°, 41.03°)", " Nürnberg: (49.45°, 11.08°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nürnberg: 4277.5 km from centroid", " Kilifi: 2313.8 km from centroid", " Takum: 2104.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nürnberg", "FINAL ANSWER: Nürnberg" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.99116, "lon": 145.17385, "name": "Keysborough" }, { "lat": -32.23013, "lon": 115.78128, "name": "Kwinana" }, { "lat": -38.13333, "lon": 145.13333, "name": "Frankston East" }, { "lat": -35.28346, "lon": 149.12807, "name": "Canberra" }, { "lat": 55.93924, "lon": 92.37513, "name": "Divnogorsk" } ], "question": "Which location is the geographic outlier among: Keysborough, Kwinana, Frankston East, Canberra, Divnogorsk?", "ground_truth": { "answer": "Divnogorsk", "outlier_distance_km": 8880.2, "second_furthest_km": 2765.1, "clarity_ratio": 3.21, "median_distance_km": 2747.9, "distances_to_centroid": { "Keysborough": 2737.6, "Kwinana": 2137.6, "Frankston East": 2747.9, "Canberra": 2765.1, "Divnogorsk": 8880.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Keysborough: (-37.99°, 145.17°)", " Kwinana: (-32.23°, 115.78°)", " Frankston East: (-38.13°, 145.13°)", " Canberra: (-35.28°, 149.13°)", " Divnogorsk: (55.94°, 92.38°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Divnogorsk: 8880.2 km from centroid", " Canberra: 2765.1 km from centroid", " Frankston East: 2747.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Divnogorsk", "FINAL ANSWER: Divnogorsk" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.26667, "lon": 140.86667, "name": "Sendai" }, { "lat": 44.08436, "lon": 131.11841, "name": "Dongning" }, { "lat": 29.56227, "lon": 103.76386, "name": "Leshan" }, { "lat": 33.71706, "lon": 130.64117, "name": "Miyawaka" }, { "lat": -32.035, "lon": -52.09861, "name": "Rio Grande" } ], "question": "Which location is the geographic outlier among: Sendai, Dongning, Leshan, Miyawaka, Rio Grande?", "ground_truth": { "answer": "Rio Grande", "outlier_distance_km": 16234.0, "second_furthest_km": 5026.1, "clarity_ratio": 3.23, "median_distance_km": 4365.1, "distances_to_centroid": { "Sendai": 5026.1, "Dongning": 4365.1, "Leshan": 1494.6, "Miyawaka": 4057.1, "Rio Grande": 16234.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sendai: (38.27°, 140.87°)", " Dongning: (44.08°, 131.12°)", " Leshan: (29.56°, 103.76°)", " Miyawaka: (33.72°, 130.64°)", " Rio Grande: (-32.03°, -52.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rio Grande: 16234.0 km from centroid", " Sendai: 5026.1 km from centroid", " Dongning: 4365.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rio Grande", "FINAL ANSWER: Rio Grande" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.26639, "lon": 146.80569, "name": "Townsville" }, { "lat": -32.05799, "lon": 115.91814, "name": "Canning Vale" }, { "lat": -33.91972, "lon": 151.07592, "name": "Lakemba" }, { "lat": -38.68333, "lon": 176.08333, "name": "Taupo" }, { "lat": -3.45361, "lon": -44.78, "name": "Arari" } ], "question": "Which location is the geographic outlier among: Townsville, Canning Vale, Lakemba, Taupo, Arari?", "ground_truth": { "answer": "Arari", "outlier_distance_km": 15734.3, "second_furthest_km": 6346.9, "clarity_ratio": 2.48, "median_distance_km": 4139.3, "distances_to_centroid": { "Townsville": 3932.9, "Canning Vale": 993.3, "Lakemba": 4139.3, "Taupo": 6346.9, "Arari": 15734.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Townsville: (-19.27°, 146.81°)", " Canning Vale: (-32.06°, 115.92°)", " Lakemba: (-33.92°, 151.08°)", " Taupo: (-38.68°, 176.08°)", " Arari: (-3.45°, -44.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arari: 15734.3 km from centroid", " Taupo: 6346.9 km from centroid", " Lakemba: 4139.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arari", "FINAL ANSWER: Arari" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.29306, "lon": -98.84167, "name": "San Jerónimo Cuatro Vientos" }, { "lat": 36.10803, "lon": -115.245, "name": "Spring Valley" }, { "lat": 41.34559, "lon": -88.84258, "name": "Ottawa" }, { "lat": 41.7942, "lon": -87.59394, "name": "Hyde Park" }, { "lat": -37.66667, "lon": 145.06667, "name": "Mill Park" } ], "question": "Which location is the geographic outlier among: San Jerónimo Cuatro Vientos, Spring Valley, Ottawa, Hyde Park, Mill Park?", "ground_truth": { "answer": "Mill Park", "outlier_distance_km": 17637.9, "second_furthest_km": 6599.1, "clarity_ratio": 2.67, "median_distance_km": 5188.0, "distances_to_centroid": { "San Jerónimo Cuatro Vientos": 5188.0, "Spring Valley": 6599.1, "Ottawa": 4412.4, "Hyde Park": 4333.0, "Mill Park": 17637.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " San Jerónimo Cuatro Vientos: (19.29°, -98.84°)", " Spring Valley: (36.11°, -115.25°)", " Ottawa: (41.35°, -88.84°)", " Hyde Park: (41.79°, -87.59°)", " Mill Park: (-37.67°, 145.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mill Park: 17637.9 km from centroid", " Spring Valley: 6599.1 km from centroid", " San Jerónimo Cuatro Vientos: 5188.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mill Park", "FINAL ANSWER: Mill Park" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.69825, "lon": 145.05967, "name": "Bundoora" }, { "lat": -31.9652, "lon": 141.4512, "name": "Broken Hill" }, { "lat": -27.56056, "lon": 151.95386, "name": "Toowoomba" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" }, { "lat": 41.38022, "lon": 2.17319, "name": "Ciutat Vella" } ], "question": "Which location is the geographic outlier among: Bundoora, Broken Hill, Toowoomba, Cheltenham, Ciutat Vella?", "ground_truth": { "answer": "Ciutat Vella", "outlier_distance_km": 13435.6, "second_furthest_km": 3677.7, "clarity_ratio": 3.65, "median_distance_km": 3442.8, "distances_to_centroid": { "Bundoora": 3428.5, "Broken Hill": 2839.4, "Toowoomba": 3677.7, "Cheltenham": 3442.8, "Ciutat Vella": 13435.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bundoora: (-37.70°, 145.06°)", " Broken Hill: (-31.97°, 141.45°)", " Toowoomba: (-27.56°, 151.95°)", " Cheltenham: (-37.97°, 145.05°)", " Ciutat Vella: (41.38°, 2.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ciutat Vella: 13435.6 km from centroid", " Toowoomba: 3677.7 km from centroid", " Cheltenham: 3442.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ciutat Vella", "FINAL ANSWER: Ciutat Vella" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" }, { "lat": -37.69863, "lon": 144.78631, "name": "Taylors Lakes" }, { "lat": -27.56056, "lon": 151.95386, "name": "Toowoomba" }, { "lat": -37.86667, "lon": 145.28333, "name": "Boronia" }, { "lat": -24.24423, "lon": -49.70932, "name": "Jaguariaíva" } ], "question": "Which location is the geographic outlier among: Cheltenham, Taylors Lakes, Toowoomba, Boronia, Jaguariaíva?", "ground_truth": { "answer": "Jaguariaíva", "outlier_distance_km": 13199.1, "second_furthest_km": 4281.9, "clarity_ratio": 3.08, "median_distance_km": 3441.8, "distances_to_centroid": { "Cheltenham": 3420.7, "Taylors Lakes": 3399.1, "Toowoomba": 4281.9, "Boronia": 3441.8, "Jaguariaíva": 13199.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Cheltenham: (-37.97°, 145.05°)", " Taylors Lakes: (-37.70°, 144.79°)", " Toowoomba: (-27.56°, 151.95°)", " Boronia: (-37.87°, 145.28°)", " Jaguariaíva: (-24.24°, -49.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Jaguariaíva: 13199.1 km from centroid", " Toowoomba: 4281.9 km from centroid", " Boronia: 3441.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Jaguariaíva", "FINAL ANSWER: Jaguariaíva" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.46538, "lon": -73.2531, "name": "Valledupar" }, { "lat": -23.43861, "lon": -47.06139, "name": "Araçariguama" }, { "lat": -15.80976, "lon": -47.97202, "name": "Guará" }, { "lat": -30.18111, "lon": -50.20556, "name": "Cidreira" }, { "lat": 28.73548, "lon": 77.03522, "name": "Karāla" } ], "question": "Which location is the geographic outlier among: Valledupar, Araçariguama, Guará, Cidreira, Karāla?", "ground_truth": { "answer": "Karāla", "outlier_distance_km": 11823.0, "second_furthest_km": 5305.8, "clarity_ratio": 2.23, "median_distance_km": 3529.0, "distances_to_centroid": { "Valledupar": 5305.8, "Araçariguama": 2788.2, "Guará": 2404.5, "Cidreira": 3529.0, "Karāla": 11823.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Valledupar: (10.47°, -73.25°)", " Araçariguama: (-23.44°, -47.06°)", " Guará: (-15.81°, -47.97°)", " Cidreira: (-30.18°, -50.21°)", " Karāla: (28.74°, 77.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Karāla: 11823.0 km from centroid", " Valledupar: 5305.8 km from centroid", " Cidreira: 3529.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Karāla", "FINAL ANSWER: Karāla" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" }, { "lat": -37.92845, "lon": 145.17708, "name": "Mulgrave" }, { "lat": -37.8329, "lon": 145.0367, "name": "Hawthorn South" }, { "lat": -38.11342, "lon": 145.28326, "name": "Cranbourne" }, { "lat": 51.93333, "lon": 7.35, "name": "Nottuln" } ], "question": "Which location is the geographic outlier among: Coogee, Mulgrave, Hawthorn South, Cranbourne, Nottuln?", "ground_truth": { "answer": "Nottuln", "outlier_distance_km": 13137.2, "second_furthest_km": 3597.3, "clarity_ratio": 3.65, "median_distance_km": 3310.7, "distances_to_centroid": { "Coogee": 3597.3, "Mulgrave": 3292.0, "Hawthorn South": 3275.9, "Cranbourne": 3310.7, "Nottuln": 13137.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Coogee: (-33.92°, 151.26°)", " Mulgrave: (-37.93°, 145.18°)", " Hawthorn South: (-37.83°, 145.04°)", " Cranbourne: (-38.11°, 145.28°)", " Nottuln: (51.93°, 7.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nottuln: 13137.2 km from centroid", " Coogee: 3597.3 km from centroid", " Cranbourne: 3310.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nottuln", "FINAL ANSWER: Nottuln" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.86472, "lon": 174.64768, "name": "Te Atatu South" }, { "lat": -41.13827, "lon": 175.0502, "name": "Upper Hutt" }, { "lat": -34.06564, "lon": 151.01266, "name": "Engadine" }, { "lat": -37.82289, "lon": 147.61041, "name": "Bairnsdale" }, { "lat": -21.90389, "lon": -47.61944, "name": "Descalvado" } ], "question": "Which location is the geographic outlier among: Te Atatu South, Upper Hutt, Engadine, Bairnsdale, Descalvado?", "ground_truth": { "answer": "Descalvado", "outlier_distance_km": 13626.4, "second_furthest_km": 4867.7, "clarity_ratio": 2.8, "median_distance_km": 4806.2, "distances_to_centroid": { "Te Atatu South": 4867.7, "Upper Hutt": 4806.2, "Engadine": 2827.9, "Bairnsdale": 2489.0, "Descalvado": 13626.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Te Atatu South: (-36.86°, 174.65°)", " Upper Hutt: (-41.14°, 175.05°)", " Engadine: (-34.07°, 151.01°)", " Bairnsdale: (-37.82°, 147.61°)", " Descalvado: (-21.90°, -47.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Descalvado: 13626.4 km from centroid", " Te Atatu South: 4867.7 km from centroid", " Upper Hutt: 4806.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Descalvado", "FINAL ANSWER: Descalvado" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -24.72459, "lon": 31.19939, "name": "Thulamahashi" }, { "lat": 7.01667, "lon": 39.98333, "name": "Goba" }, { "lat": 3.93726, "lon": 41.85688, "name": "Mandera" }, { "lat": 9.40079, "lon": -0.8393, "name": "Tamale" }, { "lat": 19.34361, "lon": -98.97472, "name": "Emiliano Zapata" } ], "question": "Which location is the geographic outlier among: Thulamahashi, Goba, Mandera, Tamale, Emiliano Zapata?", "ground_truth": { "answer": "Emiliano Zapata", "outlier_distance_km": 11112.0, "second_furthest_km": 4359.3, "clarity_ratio": 2.55, "median_distance_km": 4353.1, "distances_to_centroid": { "Thulamahashi": 4359.3, "Goba": 4158.6, "Mandera": 4353.1, "Tamale": 809.7, "Emiliano Zapata": 11112.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Thulamahashi: (-24.72°, 31.20°)", " Goba: (7.02°, 39.98°)", " Mandera: (3.94°, 41.86°)", " Tamale: (9.40°, -0.84°)", " Emiliano Zapata: (19.34°, -98.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Emiliano Zapata: 11112.0 km from centroid", " Thulamahashi: 4359.3 km from centroid", " Mandera: 4353.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Emiliano Zapata", "FINAL ANSWER: Emiliano Zapata" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.5842, "lon": 45.7338, "name": "Znamensk" }, { "lat": 44.8546, "lon": 38.3031, "name": "Akhtyrskiy" }, { "lat": 50.53439, "lon": 36.68462, "name": "Razumnoye" }, { "lat": 48.75568, "lon": 2.32241, "name": "Fresnes" }, { "lat": 20.14085, "lon": -101.18251, "name": "Uriangato" } ], "question": "Which location is the geographic outlier among: Znamensk, Akhtyrskiy, Razumnoye, Fresnes, Uriangato?", "ground_truth": { "answer": "Uriangato", "outlier_distance_km": 9704.5, "second_furthest_km": 3246.0, "clarity_ratio": 2.99, "median_distance_km": 2718.9, "distances_to_centroid": { "Znamensk": 3246.0, "Akhtyrskiy": 2718.9, "Razumnoye": 2599.9, "Fresnes": 705.5, "Uriangato": 9704.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Znamensk: (48.58°, 45.73°)", " Akhtyrskiy: (44.85°, 38.30°)", " Razumnoye: (50.53°, 36.68°)", " Fresnes: (48.76°, 2.32°)", " Uriangato: (20.14°, -101.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Uriangato: 9704.5 km from centroid", " Znamensk: 3246.0 km from centroid", " Akhtyrskiy: 2718.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Uriangato", "FINAL ANSWER: Uriangato" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.48417, "lon": -51.99056, "name": "Palmas" }, { "lat": -6.60667, "lon": -39.06222, "name": "Cedro" }, { "lat": -13.54232, "lon": -43.57968, "name": "Serra do Ramalho" }, { "lat": -27.77333, "lon": -54.24, "name": "Três de Maio" }, { "lat": 2.3829, "lon": 102.3311, "name": "Kampung Machap Baru" } ], "question": "Which location is the geographic outlier among: Palmas, Cedro, Serra do Ramalho, Três de Maio, Kampung Machap Baru?", "ground_truth": { "answer": "Kampung Machap Baru", "outlier_distance_km": 13262.2, "second_furthest_km": 4089.6, "clarity_ratio": 3.24, "median_distance_km": 3839.6, "distances_to_centroid": { "Palmas": 3839.6, "Cedro": 2529.2, "Serra do Ramalho": 2834.9, "Três de Maio": 4089.6, "Kampung Machap Baru": 13262.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Palmas: (-26.48°, -51.99°)", " Cedro: (-6.61°, -39.06°)", " Serra do Ramalho: (-13.54°, -43.58°)", " Três de Maio: (-27.77°, -54.24°)", " Kampung Machap Baru: (2.38°, 102.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kampung Machap Baru: 13262.2 km from centroid", " Três de Maio: 4089.6 km from centroid", " Palmas: 3839.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kampung Machap Baru", "FINAL ANSWER: Kampung Machap Baru" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.8045, "lon": 135.76681, "name": "Kyōtanabe" }, { "lat": 22.89396, "lon": 88.41521, "name": "Naihāti" }, { "lat": 14.00774, "lon": 77.60846, "name": "Somandepalle" }, { "lat": 10.1664, "lon": 76.20179, "name": "Vadakakarai" }, { "lat": -37.90232, "lon": 145.01734, "name": "Brighton East" } ], "question": "Which location is the geographic outlier among: Kyōtanabe, Naihāti, Somandepalle, Vadakakarai, Brighton East?", "ground_truth": { "answer": "Brighton East", "outlier_distance_km": 6673.3, "second_furthest_km": 4291.2, "clarity_ratio": 1.56, "median_distance_km": 3117.6, "distances_to_centroid": { "Kyōtanabe": 4291.2, "Naihāti": 2331.5, "Somandepalle": 2996.7, "Vadakakarai": 3117.6, "Brighton East": 6673.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kyōtanabe: (34.80°, 135.77°)", " Naihāti: (22.89°, 88.42°)", " Somandepalle: (14.01°, 77.61°)", " Vadakakarai: (10.17°, 76.20°)", " Brighton East: (-37.90°, 145.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Brighton East: 6673.3 km from centroid", " Kyōtanabe: 4291.2 km from centroid", " Vadakakarai: 3117.6 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": 45.33341, "lon": -79.21632, "name": "Huntsville" }, { "lat": 40.72149, "lon": -73.7693, "name": "Terrace Heights" }, { "lat": 45.27413, "lon": -93.59135, "name": "Otsego" }, { "lat": 19.26757, "lon": -99.53214, "name": "San Mateo Atenco" }, { "lat": -23.56729, "lon": -46.69232, "name": "Pinheiros" } ], "question": "Which location is the geographic outlier among: Huntsville, Terrace Heights, Otsego, San Mateo Atenco, Pinheiros?", "ground_truth": { "answer": "Pinheiros", "outlier_distance_km": 6436.6, "second_furthest_km": 2586.3, "clarity_ratio": 2.49, "median_distance_km": 2259.2, "distances_to_centroid": { "Huntsville": 2216.6, "Terrace Heights": 1759.8, "Otsego": 2586.3, "San Mateo Atenco": 2259.2, "Pinheiros": 6436.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Huntsville: (45.33°, -79.22°)", " Terrace Heights: (40.72°, -73.77°)", " Otsego: (45.27°, -93.59°)", " San Mateo Atenco: (19.27°, -99.53°)", " Pinheiros: (-23.57°, -46.69°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pinheiros: 6436.6 km from centroid", " Otsego: 2586.3 km from centroid", " San Mateo Atenco: 2259.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Pinheiros", "FINAL ANSWER: Pinheiros" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 56.10921, "lon": 94.58698, "name": "Zelenogorsk" }, { "lat": 51.20219, "lon": 7.36027, "name": "Radevormwald" }, { "lat": 48.81568, "lon": 2.38487, "name": "Ivry-sur-Seine" }, { "lat": 50.48333, "lon": 2.55, "name": "Bruay-la-Buissière" }, { "lat": -36.8, "lon": 174.75, "name": "North Shore" } ], "question": "Which location is the geographic outlier among: Zelenogorsk, Radevormwald, Ivry-sur-Seine, Bruay-la-Buissière, North Shore?", "ground_truth": { "answer": "North Shore", "outlier_distance_km": 14521.9, "second_furthest_km": 4682.0, "clarity_ratio": 3.1, "median_distance_km": 4673.2, "distances_to_centroid": { "Zelenogorsk": 3805.2, "Radevormwald": 4342.5, "Ivry-sur-Seine": 4682.0, "Bruay-la-Buissière": 4673.2, "North Shore": 14521.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zelenogorsk: (56.11°, 94.59°)", " Radevormwald: (51.20°, 7.36°)", " Ivry-sur-Seine: (48.82°, 2.38°)", " Bruay-la-Buissière: (50.48°, 2.55°)", " North Shore: (-36.80°, 174.75°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " North Shore: 14521.9 km from centroid", " Ivry-sur-Seine: 4682.0 km from centroid", " Bruay-la-Buissière: 4673.2 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": 51.46026, "lon": 22.60952, "name": "Lubartów" }, { "lat": 47.8082, "lon": 7.63035, "name": "Müllheim" }, { "lat": 49.95542, "lon": 18.57479, "name": "Jastrzębie Zdrój" }, { "lat": 51.88056, "lon": 45.00609, "name": "Atkarsk" }, { "lat": 28.45433, "lon": 104.71498, "name": "Xunchang" } ], "question": "Which location is the geographic outlier among: Lubartów, Müllheim, Jastrzębie Zdrój, Atkarsk, Xunchang?", "ground_truth": { "answer": "Xunchang", "outlier_distance_km": 5902.5, "second_furthest_km": 2430.4, "clarity_ratio": 2.43, "median_distance_km": 1631.1, "distances_to_centroid": { "Lubartów": 1394.0, "Müllheim": 2430.4, "Jastrzębie Zdrój": 1631.1, "Atkarsk": 768.0, "Xunchang": 5902.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lubartów: (51.46°, 22.61°)", " Müllheim: (47.81°, 7.63°)", " Jastrzębie Zdrój: (49.96°, 18.57°)", " Atkarsk: (51.88°, 45.01°)", " Xunchang: (28.45°, 104.71°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Xunchang: 5902.5 km from centroid", " Müllheim: 2430.4 km from centroid", " Jastrzębie Zdrój: 1631.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Xunchang", "FINAL ANSWER: Xunchang" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.66917, "lon": -42.07611, "name": "Itaocara" }, { "lat": -3.74611, "lon": -39.78333, "name": "Irauçuba" }, { "lat": -22.84333, "lon": -47.60611, "name": "Rio das Pedras" }, { "lat": -9.56333, "lon": -35.82444, "name": "Satuba" }, { "lat": 9.8, "lon": 38.4, "name": "Gebre Guracha" } ], "question": "Which location is the geographic outlier among: Itaocara, Irauçuba, Rio das Pedras, Satuba, Gebre Guracha?", "ground_truth": { "answer": "Gebre Guracha", "outlier_distance_km": 7379.5, "second_furthest_km": 2786.1, "clarity_ratio": 2.65, "median_distance_km": 2231.7, "distances_to_centroid": { "Itaocara": 2231.7, "Irauçuba": 1718.4, "Rio das Pedras": 2786.1, "Satuba": 1145.3, "Gebre Guracha": 7379.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itaocara: (-21.67°, -42.08°)", " Irauçuba: (-3.75°, -39.78°)", " Rio das Pedras: (-22.84°, -47.61°)", " Satuba: (-9.56°, -35.82°)", " Gebre Guracha: (9.80°, 38.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gebre Guracha: 7379.5 km from centroid", " Rio das Pedras: 2786.1 km from centroid", " Itaocara: 2231.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gebre Guracha", "FINAL ANSWER: Gebre Guracha" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.9682, "lon": 174.84019, "name": "Papatoetoe" }, { "lat": -37.78828, "lon": 145.12373, "name": "Doncaster" }, { "lat": -38.26667, "lon": 145.01667, "name": "Mount Martha" }, { "lat": -32.5269, "lon": 115.7217, "name": "Mandurah" }, { "lat": -13.03667, "lon": -46.77167, "name": "Campos Belos" } ], "question": "Which location is the geographic outlier among: Papatoetoe, Doncaster, Mount Martha, Mandurah, Campos Belos?", "ground_truth": { "answer": "Campos Belos", "outlier_distance_km": 14296.1, "second_furthest_km": 6142.2, "clarity_ratio": 2.33, "median_distance_km": 3541.5, "distances_to_centroid": { "Papatoetoe": 6142.2, "Doncaster": 3541.5, "Mount Martha": 3531.9, "Mandurah": 846.0, "Campos Belos": 14296.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Papatoetoe: (-36.97°, 174.84°)", " Doncaster: (-37.79°, 145.12°)", " Mount Martha: (-38.27°, 145.02°)", " Mandurah: (-32.53°, 115.72°)", " Campos Belos: (-13.04°, -46.77°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Campos Belos: 14296.1 km from centroid", " Papatoetoe: 6142.2 km from centroid", " Doncaster: 3541.5 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": -26.66008, "lon": 153.09953, "name": "Maroochydore" }, { "lat": -33.72976, "lon": 151.15977, "name": "Saint Ives" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": -37.57742, "lon": 144.72607, "name": "Sunbury" }, { "lat": 40.4842, "lon": -88.99369, "name": "Bloomington" } ], "question": "Which location is the geographic outlier among: Maroochydore, Saint Ives, Melbourne City Centre, Sunbury, Bloomington?", "ground_truth": { "answer": "Bloomington", "outlier_distance_km": 17449.5, "second_furthest_km": 5370.0, "clarity_ratio": 3.25, "median_distance_km": 5201.4, "distances_to_centroid": { "Maroochydore": 5370.0, "Saint Ives": 5201.4, "Melbourne City Centre": 4723.1, "Sunbury": 4696.3, "Bloomington": 17449.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maroochydore: (-26.66°, 153.10°)", " Saint Ives: (-33.73°, 151.16°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Sunbury: (-37.58°, 144.73°)", " Bloomington: (40.48°, -88.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bloomington: 17449.5 km from centroid", " Maroochydore: 5370.0 km from centroid", " Saint Ives: 5201.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bloomington", "FINAL ANSWER: Bloomington" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.78269, "lon": 151.04888, "name": "Carlingford" }, { "lat": -36.9682, "lon": 174.84019, "name": "Papatoetoe" }, { "lat": -33.2792, "lon": 115.71504, "name": "Australind" }, { "lat": -37.89138, "lon": 144.62368, "name": "Wyndham Vale" }, { "lat": 49.31406, "lon": -123.0725, "name": "Lower Lonsdale" } ], "question": "Which location is the geographic outlier among: Carlingford, Papatoetoe, Australind, Wyndham Vale, Lower Lonsdale?", "ground_truth": { "answer": "Lower Lonsdale", "outlier_distance_km": 15342.0, "second_furthest_km": 8108.2, "clarity_ratio": 1.89, "median_distance_km": 5992.0, "distances_to_centroid": { "Carlingford": 5992.0, "Papatoetoe": 8108.2, "Australind": 2821.3, "Wyndham Vale": 5450.1, "Lower Lonsdale": 15342.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Carlingford: (-33.78°, 151.05°)", " Papatoetoe: (-36.97°, 174.84°)", " Australind: (-33.28°, 115.72°)", " Wyndham Vale: (-37.89°, 144.62°)", " Lower Lonsdale: (49.31°, -123.07°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lower Lonsdale: 15342.0 km from centroid", " Papatoetoe: 8108.2 km from centroid", " Carlingford: 5992.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lower Lonsdale", "FINAL ANSWER: Lower Lonsdale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8149, "lon": 144.95052, "name": "Docklands" }, { "lat": -38.26667, "lon": 145.01667, "name": "Mount Martha" }, { "lat": -38.03333, "lon": 145.25, "name": "Hampton Park" }, { "lat": -31.09048, "lon": 150.92905, "name": "Tamworth" }, { "lat": 43.78609, "lon": -79.33502, "name": "Pleasant View" } ], "question": "Which location is the geographic outlier among: Docklands, Mount Martha, Hampton Park, Tamworth, Pleasant View?", "ground_truth": { "answer": "Pleasant View", "outlier_distance_km": 17401.0, "second_furthest_km": 5067.7, "clarity_ratio": 3.43, "median_distance_km": 4642.5, "distances_to_centroid": { "Docklands": 4611.6, "Mount Martha": 4628.2, "Hampton Park": 4642.5, "Tamworth": 5067.7, "Pleasant View": 17401.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Docklands: (-37.81°, 144.95°)", " Mount Martha: (-38.27°, 145.02°)", " Hampton Park: (-38.03°, 145.25°)", " Tamworth: (-31.09°, 150.93°)", " Pleasant View: (43.79°, -79.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Pleasant View: 17401.0 km from centroid", " Tamworth: 5067.7 km from centroid", " Hampton Park: 4642.5 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": -32.24295, "lon": 148.60484, "name": "Dubbo" }, { "lat": -19.26639, "lon": 146.80569, "name": "Townsville" }, { "lat": -36.86472, "lon": 174.64768, "name": "Te Atatu South" }, { "lat": -38.05916, "lon": 145.40947, "name": "Officer" }, { "lat": 19.31556, "lon": -98.88284, "name": "Ixtapaluca" } ], "question": "Which location is the geographic outlier among: Dubbo, Townsville, Te Atatu South, Officer, Ixtapaluca?", "ground_truth": { "answer": "Ixtapaluca", "outlier_distance_km": 17691.1, "second_furthest_km": 6979.9, "clarity_ratio": 2.53, "median_distance_km": 4616.0, "distances_to_centroid": { "Dubbo": 4616.0, "Townsville": 4526.2, "Te Atatu South": 6979.9, "Officer": 4417.6, "Ixtapaluca": 17691.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dubbo: (-32.24°, 148.60°)", " Townsville: (-19.27°, 146.81°)", " Te Atatu South: (-36.86°, 174.65°)", " Officer: (-38.06°, 145.41°)", " Ixtapaluca: (19.32°, -98.88°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ixtapaluca: 17691.1 km from centroid", " Te Atatu South: 6979.9 km from centroid", " Dubbo: 4616.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ixtapaluca", "FINAL ANSWER: Ixtapaluca" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.88264, "lon": 144.7003, "name": "Hoppers Crossing" }, { "lat": -38.15912, "lon": 145.93118, "name": "Warragul" }, { "lat": -37.98333, "lon": 145.2, "name": "Dandenong" }, { "lat": -32.83211, "lon": 151.35623, "name": "Cessnock" }, { "lat": -21.83222, "lon": -46.89361, "name": "Vargem Grande do Sul" } ], "question": "Which location is the geographic outlier among: Hoppers Crossing, Warragul, Dandenong, Cessnock, Vargem Grande do Sul?", "ground_truth": { "answer": "Vargem Grande do Sul", "outlier_distance_km": 13290.6, "second_furthest_km": 3995.9, "clarity_ratio": 3.33, "median_distance_km": 3420.5, "distances_to_centroid": { "Hoppers Crossing": 3314.7, "Warragul": 3420.5, "Dandenong": 3357.8, "Cessnock": 3995.9, "Vargem Grande do Sul": 13290.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Hoppers Crossing: (-37.88°, 144.70°)", " Warragul: (-38.16°, 145.93°)", " Dandenong: (-37.98°, 145.20°)", " Cessnock: (-32.83°, 151.36°)", " Vargem Grande do Sul: (-21.83°, -46.89°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vargem Grande do Sul: 13290.6 km from centroid", " Cessnock: 3995.9 km from centroid", " Warragul: 3420.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vargem Grande do Sul", "FINAL ANSWER: Vargem Grande do Sul" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.9382, "lon": 174.84019, "name": "Otahuhu" }, { "lat": -36.88333, "lon": 174.7, "name": "Avondale" }, { "lat": -34.06564, "lon": 151.01266, "name": "Engadine" }, { "lat": -33.95, "lon": 151.23333, "name": "Maroubra" }, { "lat": 19.3467, "lon": -99.16174, "name": "Coyoacán" } ], "question": "Which location is the geographic outlier among: Otahuhu, Avondale, Engadine, Maroubra, Coyoacán?", "ground_truth": { "answer": "Coyoacán", "outlier_distance_km": 16906.0, "second_furthest_km": 6186.6, "clarity_ratio": 2.73, "median_distance_km": 6174.9, "distances_to_centroid": { "Otahuhu": 6186.6, "Avondale": 6174.9, "Engadine": 4040.1, "Maroubra": 4059.4, "Coyoacán": 16906.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Otahuhu: (-36.94°, 174.84°)", " Avondale: (-36.88°, 174.70°)", " Engadine: (-34.07°, 151.01°)", " Maroubra: (-33.95°, 151.23°)", " Coyoacán: (19.35°, -99.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coyoacán: 16906.0 km from centroid", " Otahuhu: 6186.6 km from centroid", " Avondale: 6174.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coyoacán", "FINAL ANSWER: Coyoacán" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.02333, "lon": 106.42963, "name": "Shuangfeng" }, { "lat": 18.71364, "lon": 76.06718, "name": "Kaij" }, { "lat": 3.6253, "lon": 98.864, "name": "Percut" }, { "lat": 5.02917, "lon": 119.77306, "name": "Bongao" }, { "lat": -6.89028, "lon": -38.55528, "name": "Cajazeiras" } ], "question": "Which location is the geographic outlier among: Shuangfeng, Kaij, Percut, Bongao, Cajazeiras?", "ground_truth": { "answer": "Cajazeiras", "outlier_distance_km": 12438.9, "second_furthest_km": 5234.9, "clarity_ratio": 2.38, "median_distance_km": 4151.1, "distances_to_centroid": { "Shuangfeng": 4151.1, "Kaij": 1031.2, "Percut": 2994.6, "Bongao": 5234.9, "Cajazeiras": 12438.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Shuangfeng: (30.02°, 106.43°)", " Kaij: (18.71°, 76.07°)", " Percut: (3.63°, 98.86°)", " Bongao: (5.03°, 119.77°)", " Cajazeiras: (-6.89°, -38.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Cajazeiras: 12438.9 km from centroid", " Bongao: 5234.9 km from centroid", " Shuangfeng: 4151.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Cajazeiras", "FINAL ANSWER: Cajazeiras" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.27194, "lon": -101.98602, "name": "Loreto" }, { "lat": 47.40177, "lon": -122.32429, "name": "Des Moines" }, { "lat": 33.86726, "lon": -112.14682, "name": "Anthem" }, { "lat": 39.52963, "lon": -119.8138, "name": "Reno" }, { "lat": -7.50528, "lon": -35.31833, "name": "Timbaúba" } ], "question": "Which location is the geographic outlier among: Loreto, Des Moines, Anthem, Reno, Timbaúba?", "ground_truth": { "answer": "Timbaúba", "outlier_distance_km": 7789.8, "second_furthest_km": 3073.9, "clarity_ratio": 2.53, "median_distance_km": 2417.7, "distances_to_centroid": { "Loreto": 653.4, "Des Moines": 3073.9, "Anthem": 1521.0, "Reno": 2417.7, "Timbaúba": 7789.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Loreto: (22.27°, -101.99°)", " Des Moines: (47.40°, -122.32°)", " Anthem: (33.87°, -112.15°)", " Reno: (39.53°, -119.81°)", " Timbaúba: (-7.51°, -35.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Timbaúba: 7789.8 km from centroid", " Des Moines: 3073.9 km from centroid", " Reno: 2417.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Timbaúba", "FINAL ANSWER: Timbaúba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.61357, "lon": 79.37442, "name": "Peddapalli" }, { "lat": 29.409, "lon": 106.14228, "name": "Dingjia" }, { "lat": 38.13387, "lon": 85.52992, "name": "Qiemo" }, { "lat": 34.72083, "lon": 104.88583, "name": "Wushan" }, { "lat": 53.4614, "lon": -2.92863, "name": "Fazakerley" } ], "question": "Which location is the geographic outlier among: Peddapalli, Dingjia, Qiemo, Wushan, Fazakerley?", "ground_truth": { "answer": "Fazakerley", "outlier_distance_km": 6183.7, "second_furthest_km": 3018.2, "clarity_ratio": 2.05, "median_distance_km": 2754.8, "distances_to_centroid": { "Peddapalli": 1867.8, "Dingjia": 3018.2, "Qiemo": 1041.4, "Wushan": 2754.8, "Fazakerley": 6183.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Peddapalli: (18.61°, 79.37°)", " Dingjia: (29.41°, 106.14°)", " Qiemo: (38.13°, 85.53°)", " Wushan: (34.72°, 104.89°)", " Fazakerley: (53.46°, -2.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fazakerley: 6183.7 km from centroid", " Dingjia: 3018.2 km from centroid", " Wushan: 2754.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fazakerley", "FINAL ANSWER: Fazakerley" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.73308, "lon": 151.5574, "name": "Maitland" }, { "lat": -37.89359, "lon": 145.05534, "name": "Carnegie" }, { "lat": -32.5269, "lon": 115.7217, "name": "Mandurah" }, { "lat": -38.13333, "lon": 145.13333, "name": "Frankston East" }, { "lat": 30.8248, "lon": 30.81805, "name": "Kafr az Zayyāt" } ], "question": "Which location is the geographic outlier among: Maitland, Carnegie, Mandurah, Frankston East, Kafr az Zayyāt?", "ground_truth": { "answer": "Kafr az Zayyāt", "outlier_distance_km": 10959.4, "second_furthest_km": 3531.0, "clarity_ratio": 3.1, "median_distance_km": 3168.5, "distances_to_centroid": { "Maitland": 3531.0, "Carnegie": 3150.6, "Mandurah": 1175.8, "Frankston East": 3168.5, "Kafr az Zayyāt": 10959.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Maitland: (-32.73°, 151.56°)", " Carnegie: (-37.89°, 145.06°)", " Mandurah: (-32.53°, 115.72°)", " Frankston East: (-38.13°, 145.13°)", " Kafr az Zayyāt: (30.82°, 30.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kafr az Zayyāt: 10959.4 km from centroid", " Maitland: 3531.0 km from centroid", " Frankston East: 3168.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kafr az Zayyāt", "FINAL ANSWER: Kafr az Zayyāt" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.52754, "lon": 11.54835, "name": "Eisleben Lutherstadt" }, { "lat": 53.41667, "lon": -1.2, "name": "Maltby" }, { "lat": 38.01328, "lon": -3.3705, "name": "Úbeda" }, { "lat": 43.31195, "lon": 45.68895, "name": "Grozny" }, { "lat": -11.79667, "lon": -49.52889, "name": "Formoso do Araguaia" } ], "question": "Which location is the geographic outlier among: Eisleben Lutherstadt, Maltby, Úbeda, Grozny, Formoso do Araguaia?", "ground_truth": { "answer": "Formoso do Araguaia", "outlier_distance_km": 7403.5, "second_furthest_km": 3949.0, "clarity_ratio": 1.87, "median_distance_km": 2064.5, "distances_to_centroid": { "Eisleben Lutherstadt": 2045.2, "Maltby": 2064.5, "Úbeda": 498.0, "Grozny": 3949.0, "Formoso do Araguaia": 7403.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Eisleben Lutherstadt: (51.53°, 11.55°)", " Maltby: (53.42°, -1.20°)", " Úbeda: (38.01°, -3.37°)", " Grozny: (43.31°, 45.69°)", " Formoso do Araguaia: (-11.80°, -49.53°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Formoso do Araguaia: 7403.5 km from centroid", " Grozny: 3949.0 km from centroid", " Maltby: 2064.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Formoso do Araguaia", "FINAL ANSWER: Formoso do Araguaia" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.88333, "lon": 174.7, "name": "Avondale" }, { "lat": -37.58333, "lon": 145.03333, "name": "Wollert" }, { "lat": -37.76667, "lon": 144.96667, "name": "Brunswick" }, { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" }, { "lat": -29.71671, "lon": -52.50321, "name": "Vera Cruz" } ], "question": "Which location is the geographic outlier among: Avondale, Wollert, Brunswick, Coogee, Vera Cruz?", "ground_truth": { "answer": "Vera Cruz", "outlier_distance_km": 12634.7, "second_furthest_km": 5477.7, "clarity_ratio": 2.31, "median_distance_km": 3512.5, "distances_to_centroid": { "Avondale": 5477.7, "Wollert": 2893.6, "Brunswick": 2886.1, "Coogee": 3512.5, "Vera Cruz": 12634.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Avondale: (-36.88°, 174.70°)", " Wollert: (-37.58°, 145.03°)", " Brunswick: (-37.77°, 144.97°)", " Coogee: (-33.92°, 151.26°)", " Vera Cruz: (-29.72°, -52.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vera Cruz: 12634.7 km from centroid", " Avondale: 5477.7 km from centroid", " Coogee: 3512.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vera Cruz", "FINAL ANSWER: Vera Cruz" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.77148, "lon": 127.07996, "name": "Boseong" }, { "lat": 31.21288, "lon": 108.34026, "name": "Dade" }, { "lat": 25.33061, "lon": 76.50973, "name": "Māngrol" }, { "lat": 20.81717, "lon": 105.33759, "name": "Hòa Bình" }, { "lat": -20.53389, "lon": -49.31417, "name": "Nova Granada" } ], "question": "Which location is the geographic outlier among: Boseong, Dade, Māngrol, Hòa Bình, Nova Granada?", "ground_truth": { "answer": "Nova Granada", "outlier_distance_km": 14053.3, "second_furthest_km": 5556.2, "clarity_ratio": 2.53, "median_distance_km": 3769.8, "distances_to_centroid": { "Boseong": 5556.2, "Dade": 3769.8, "Māngrol": 835.7, "Hòa Bình": 3332.5, "Nova Granada": 14053.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Boseong: (34.77°, 127.08°)", " Dade: (31.21°, 108.34°)", " Māngrol: (25.33°, 76.51°)", " Hòa Bình: (20.82°, 105.34°)", " Nova Granada: (-20.53°, -49.31°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nova Granada: 14053.3 km from centroid", " Boseong: 5556.2 km from centroid", " Dade: 3769.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nova Granada", "FINAL ANSWER: Nova Granada" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.86472, "lon": 174.64768, "name": "Te Atatu South" }, { "lat": -31.91099, "lon": 152.45387, "name": "Taree" }, { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -37.86667, "lon": 145.06667, "name": "Glen Iris" }, { "lat": -17.13806, "lon": -49.98806, "name": "Indiara" } ], "question": "Which location is the geographic outlier among: Te Atatu South, Taree, Epping, Glen Iris, Indiara?", "ground_truth": { "answer": "Indiara", "outlier_distance_km": 14243.0, "second_furthest_km": 5531.0, "clarity_ratio": 2.58, "median_distance_km": 3654.3, "distances_to_centroid": { "Te Atatu South": 5531.0, "Taree": 3654.3, "Epping": 2925.2, "Glen Iris": 2929.1, "Indiara": 14243.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Te Atatu South: (-36.86°, 174.65°)", " Taree: (-31.91°, 152.45°)", " Epping: (-37.65°, 145.03°)", " Glen Iris: (-37.87°, 145.07°)", " Indiara: (-17.14°, -49.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Indiara: 14243.0 km from centroid", " Te Atatu South: 5531.0 km from centroid", " Taree: 3654.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Indiara", "FINAL ANSWER: Indiara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.09639, "lon": -35.23278, "name": "Sapé" }, { "lat": -22.99835, "lon": -43.36545, "name": "Barra da Tijuca" }, { "lat": -30.00018, "lon": -51.07632, "name": "Alvorada" }, { "lat": -8.96389, "lon": -37.62833, "name": "Manari" }, { "lat": 30.71877, "lon": 31.56299, "name": "Al Ibrāhīmīyah" } ], "question": "Which location is the geographic outlier among: Sapé, Barra da Tijuca, Alvorada, Manari, Al Ibrāhīmīyah?", "ground_truth": { "answer": "Al Ibrāhīmīyah", "outlier_distance_km": 7563.2, "second_furthest_km": 3519.8, "clarity_ratio": 2.15, "median_distance_km": 2430.4, "distances_to_centroid": { "Sapé": 893.8, "Barra da Tijuca": 2430.4, "Alvorada": 3519.8, "Manari": 1162.0, "Al Ibrāhīmīyah": 7563.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sapé: (-7.10°, -35.23°)", " Barra da Tijuca: (-23.00°, -43.37°)", " Alvorada: (-30.00°, -51.08°)", " Manari: (-8.96°, -37.63°)", " Al Ibrāhīmīyah: (30.72°, 31.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Al Ibrāhīmīyah: 7563.2 km from centroid", " Alvorada: 3519.8 km from centroid", " Barra da Tijuca: 2430.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Al Ibrāhīmīyah", "FINAL ANSWER: Al Ibrāhīmīyah" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 30.85711, "lon": 32.31183, "name": "Al Qanţarah" }, { "lat": 11.28333, "lon": 36.21667, "name": "Mambuk" }, { "lat": -25.68991, "lon": 30.03504, "name": "Belfast" }, { "lat": 8.72851, "lon": 5.75561, "name": "Patigi" }, { "lat": -5.0925, "lon": -80.1625, "name": "Chulucanas" } ], "question": "Which location is the geographic outlier among: Al Qanţarah, Mambuk, Belfast, Patigi, Chulucanas?", "ground_truth": { "answer": "Chulucanas", "outlier_distance_km": 9494.2, "second_furthest_km": 4277.1, "clarity_ratio": 2.22, "median_distance_km": 4145.7, "distances_to_centroid": { "Al Qanţarah": 4145.7, "Mambuk": 3548.8, "Belfast": 4277.1, "Patigi": 533.7, "Chulucanas": 9494.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Al Qanţarah: (30.86°, 32.31°)", " Mambuk: (11.28°, 36.22°)", " Belfast: (-25.69°, 30.04°)", " Patigi: (8.73°, 5.76°)", " Chulucanas: (-5.09°, -80.16°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chulucanas: 9494.2 km from centroid", " Belfast: 4277.1 km from centroid", " Al Qanţarah: 4145.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chulucanas", "FINAL ANSWER: Chulucanas" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -41.31946, "lon": -72.98538, "name": "Puerto Varas" }, { "lat": -23.64889, "lon": -46.85222, "name": "Embu das Artes" }, { "lat": -20.76361, "lon": -41.53306, "name": "Alegre" }, { "lat": -22.74389, "lon": -43.7075, "name": "Seropédica" }, { "lat": 41.31755, "lon": -81.34539, "name": "Aurora" } ], "question": "Which location is the geographic outlier among: Puerto Varas, Embu das Artes, Alegre, Seropédica, Aurora?", "ground_truth": { "answer": "Aurora", "outlier_distance_km": 6570.6, "second_furthest_km": 3453.9, "clarity_ratio": 1.9, "median_distance_km": 1860.3, "distances_to_centroid": { "Puerto Varas": 3453.9, "Embu das Artes": 1579.8, "Alegre": 1860.3, "Seropédica": 1767.7, "Aurora": 6570.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Puerto Varas: (-41.32°, -72.99°)", " Embu das Artes: (-23.65°, -46.85°)", " Alegre: (-20.76°, -41.53°)", " Seropédica: (-22.74°, -43.71°)", " Aurora: (41.32°, -81.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Aurora: 6570.6 km from centroid", " Puerto Varas: 3453.9 km from centroid", " Alegre: 1860.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Aurora", "FINAL ANSWER: Aurora" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.93964, "lon": 9.25995, "name": "Marbach am Neckar" }, { "lat": 42.82562, "lon": -1.61671, "name": "Burlata" }, { "lat": 44.74471, "lon": -0.68194, "name": "Cestas" }, { "lat": 51.41505, "lon": -0.0927, "name": "Upper Norwood" }, { "lat": -34.28853, "lon": 146.05093, "name": "Griffith" } ], "question": "Which location is the geographic outlier among: Marbach am Neckar, Burlata, Cestas, Upper Norwood, Griffith?", "ground_truth": { "answer": "Griffith", "outlier_distance_km": 14053.6, "second_furthest_km": 3405.6, "clarity_ratio": 4.13, "median_distance_km": 3142.3, "distances_to_centroid": { "Marbach am Neckar": 2704.4, "Burlata": 3142.3, "Cestas": 3132.3, "Upper Norwood": 3405.6, "Griffith": 14053.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Marbach am Neckar: (48.94°, 9.26°)", " Burlata: (42.83°, -1.62°)", " Cestas: (44.74°, -0.68°)", " Upper Norwood: (51.42°, -0.09°)", " Griffith: (-34.29°, 146.05°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Griffith: 14053.6 km from centroid", " Upper Norwood: 3405.6 km from centroid", " Burlata: 3142.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Griffith", "FINAL ANSWER: Griffith" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.11667, "lon": 37.78333, "name": "Ādīs Zemen" }, { "lat": 30.90711, "lon": 32.02341, "name": "Munsha‘at Abū ‘Umar" }, { "lat": 25.29336, "lon": 32.55402, "name": "Esna" }, { "lat": 12.37299, "lon": 14.2069, "name": "Gamboru" }, { "lat": 34.81667, "lon": 137.4, "name": "Toyokawa" } ], "question": "Which location is the geographic outlier among: Ādīs Zemen, Munsha‘at Abū ‘Umar, Esna, Gamboru, Toyokawa?", "ground_truth": { "answer": "Toyokawa", "outlier_distance_km": 8274.2, "second_furthest_km": 4041.1, "clarity_ratio": 2.05, "median_distance_km": 2048.3, "distances_to_centroid": { "Ādīs Zemen": 1839.8, "Munsha‘at Abū ‘Umar": 2048.3, "Esna": 1864.4, "Gamboru": 4041.1, "Toyokawa": 8274.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ādīs Zemen: (12.12°, 37.78°)", " Munsha‘at Abū ‘Umar: (30.91°, 32.02°)", " Esna: (25.29°, 32.55°)", " Gamboru: (12.37°, 14.21°)", " Toyokawa: (34.82°, 137.40°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Toyokawa: 8274.2 km from centroid", " Gamboru: 4041.1 km from centroid", " Munsha‘at Abū ‘Umar: 2048.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Toyokawa", "FINAL ANSWER: Toyokawa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.3125, "lon": -39.32333, "name": "Ubaitaba" }, { "lat": -23.63083, "lon": -46.59817, "name": "Sacomã" }, { "lat": -5.14556, "lon": -38.09806, "name": "Limoeiro do Norte" }, { "lat": -2.18611, "lon": -56.71306, "name": "Nhamundá" }, { "lat": 52.66917, "lon": 4.70417, "name": "Bergen" } ], "question": "Which location is the geographic outlier among: Ubaitaba, Sacomã, Limoeiro do Norte, Nhamundá, Bergen?", "ground_truth": { "answer": "Bergen", "outlier_distance_km": 6777.7, "second_furthest_km": 3051.8, "clarity_ratio": 2.22, "median_distance_km": 2425.5, "distances_to_centroid": { "Ubaitaba": 1813.5, "Sacomã": 3051.8, "Limoeiro do Norte": 803.6, "Nhamundá": 2425.5, "Bergen": 6777.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ubaitaba: (-14.31°, -39.32°)", " Sacomã: (-23.63°, -46.60°)", " Limoeiro do Norte: (-5.15°, -38.10°)", " Nhamundá: (-2.19°, -56.71°)", " Bergen: (52.67°, 4.70°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bergen: 6777.7 km from centroid", " Sacomã: 3051.8 km from centroid", " Nhamundá: 2425.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bergen", "FINAL ANSWER: Bergen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.12705, "lon": 83.89148, "name": "Bilthra" }, { "lat": 23.67595, "lon": 91.28325, "name": "Bisālgarh" }, { "lat": 30.12796, "lon": 77.28371, "name": "Yamuna Nagar" }, { "lat": 37.31739, "lon": 79.70532, "name": "Puqiakeqi" }, { "lat": -37.81992, "lon": 145.0358, "name": "Hawthorn" } ], "question": "Which location is the geographic outlier among: Bilthra, Bisālgarh, Yamuna Nagar, Puqiakeqi, Hawthorn?", "ground_truth": { "answer": "Hawthorn", "outlier_distance_km": 7901.2, "second_furthest_km": 2841.3, "clarity_ratio": 2.78, "median_distance_km": 2435.0, "distances_to_centroid": { "Bilthra": 1651.6, "Bisālgarh": 969.1, "Yamuna Nagar": 2435.0, "Puqiakeqi": 2841.3, "Hawthorn": 7901.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bilthra: (26.13°, 83.89°)", " Bisālgarh: (23.68°, 91.28°)", " Yamuna Nagar: (30.13°, 77.28°)", " Puqiakeqi: (37.32°, 79.71°)", " Hawthorn: (-37.82°, 145.04°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hawthorn: 7901.2 km from centroid", " Puqiakeqi: 2841.3 km from centroid", " Yamuna Nagar: 2435.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hawthorn", "FINAL ANSWER: Hawthorn" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.05048, "lon": -76.97335, "name": "Santa Anita - Los Ficus" }, { "lat": -29.44806, "lon": -50.58361, "name": "São Francisco de Paula" }, { "lat": -17.345, "lon": -44.94194, "name": "Pirapora" }, { "lat": -10.34472, "lon": -39.83556, "name": "Andorinha" }, { "lat": 49.12426, "lon": 8.59804, "name": "Bruchsal" } ], "question": "Which location is the geographic outlier among: Santa Anita - Los Ficus, São Francisco de Paula, Pirapora, Andorinha, Bruchsal?", "ground_truth": { "answer": "Bruchsal", "outlier_distance_km": 7576.4, "second_furthest_km": 4082.8, "clarity_ratio": 1.86, "median_distance_km": 3012.1, "distances_to_centroid": { "Santa Anita - Los Ficus": 4082.8, "São Francisco de Paula": 3012.1, "Pirapora": 1551.4, "Andorinha": 711.2, "Bruchsal": 7576.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santa Anita - Los Ficus: (-12.05°, -76.97°)", " São Francisco de Paula: (-29.45°, -50.58°)", " Pirapora: (-17.34°, -44.94°)", " Andorinha: (-10.34°, -39.84°)", " Bruchsal: (49.12°, 8.60°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bruchsal: 7576.4 km from centroid", " Santa Anita - Los Ficus: 4082.8 km from centroid", " São Francisco de Paula: 3012.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bruchsal", "FINAL ANSWER: Bruchsal" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.50246, "lon": -98.75358, "name": "Axochiapan" }, { "lat": 34.77453, "lon": -96.67834, "name": "Ada" }, { "lat": 38.784, "lon": -77.46971, "name": "Manassas Park" }, { "lat": 19.13325, "lon": -97.64167, "name": "San Salvador El Seco" }, { "lat": 43.38285, "lon": -3.22043, "name": "Castro-Urdiales" } ], "question": "Which location is the geographic outlier among: Axochiapan, Ada, Manassas Park, San Salvador El Seco, Castro-Urdiales?", "ground_truth": { "answer": "Castro-Urdiales", "outlier_distance_km": 6294.2, "second_furthest_km": 2780.3, "clarity_ratio": 2.26, "median_distance_km": 2644.1, "distances_to_centroid": { "Axochiapan": 2780.3, "Ada": 2088.3, "Manassas Park": 909.3, "San Salvador El Seco": 2644.1, "Castro-Urdiales": 6294.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Axochiapan: (18.50°, -98.75°)", " Ada: (34.77°, -96.68°)", " Manassas Park: (38.78°, -77.47°)", " San Salvador El Seco: (19.13°, -97.64°)", " Castro-Urdiales: (43.38°, -3.22°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Castro-Urdiales: 6294.2 km from centroid", " Axochiapan: 2780.3 km from centroid", " San Salvador El Seco: 2644.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Castro-Urdiales", "FINAL ANSWER: Castro-Urdiales" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -28.21298, "lon": 153.53634, "name": "Banora Point" }, { "lat": -37.81667, "lon": 144.75, "name": "Truganina" }, { "lat": -36.9682, "lon": 174.84019, "name": "Papatoetoe" }, { "lat": -36.9382, "lon": 174.84019, "name": "Otahuhu" }, { "lat": 11.19152, "lon": 40.01675, "name": "Batī" } ], "question": "Which location is the geographic outlier among: Banora Point, Truganina, Papatoetoe, Otahuhu, Batī?", "ground_truth": { "answer": "Batī", "outlier_distance_km": 11296.1, "second_furthest_km": 3722.2, "clarity_ratio": 3.03, "median_distance_km": 3721.6, "distances_to_centroid": { "Banora Point": 1601.8, "Truganina": 1501.3, "Papatoetoe": 3722.2, "Otahuhu": 3721.6, "Batī": 11296.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Banora Point: (-28.21°, 153.54°)", " Truganina: (-37.82°, 144.75°)", " Papatoetoe: (-36.97°, 174.84°)", " Otahuhu: (-36.94°, 174.84°)", " Batī: (11.19°, 40.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Batī: 11296.1 km from centroid", " Papatoetoe: 3722.2 km from centroid", " Otahuhu: 3721.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Batī", "FINAL ANSWER: Batī" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 9.31387, "lon": 42.11815, "name": "Harar" }, { "lat": 30.72508, "lon": 31.67148, "name": "Abū Kabīr" }, { "lat": 10.31032, "lon": 9.84388, "name": "Bauchi" }, { "lat": 31.61166, "lon": 25.92539, "name": "Sīdī Barānī" }, { "lat": 13.08449, "lon": 79.67053, "name": "Arakkonam" } ], "question": "Which location is the geographic outlier among: Harar, Abū Kabīr, Bauchi, Sīdī Barānī, Arakkonam?", "ground_truth": { "answer": "Arakkonam", "outlier_distance_km": 4507.4, "second_furthest_km": 3158.6, "clarity_ratio": 1.43, "median_distance_km": 1840.9, "distances_to_centroid": { "Harar": 1172.1, "Abū Kabīr": 1443.2, "Bauchi": 3158.6, "Sīdī Barānī": 1840.9, "Arakkonam": 4507.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Harar: (9.31°, 42.12°)", " Abū Kabīr: (30.73°, 31.67°)", " Bauchi: (10.31°, 9.84°)", " Sīdī Barānī: (31.61°, 25.93°)", " Arakkonam: (13.08°, 79.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Arakkonam: 4507.4 km from centroid", " Bauchi: 3158.6 km from centroid", " Sīdī Barānī: 1840.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Arakkonam", "FINAL ANSWER: Arakkonam" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": -37.2, "lon": 174.95, "name": "Pukekohe East" }, { "lat": -39.06667, "lon": 174.08333, "name": "New Plymouth" }, { "lat": -38.02388, "lon": 144.40617, "name": "Lara" }, { "lat": 51.33678, "lon": -0.11201, "name": "Purley" } ], "question": "Which location is the geographic outlier among: Yarraville, Pukekohe East, New Plymouth, Lara, Purley?", "ground_truth": { "answer": "Purley", "outlier_distance_km": 14334.6, "second_furthest_km": 4928.9, "clarity_ratio": 2.91, "median_distance_km": 4891.7, "distances_to_centroid": { "Yarraville": 2574.1, "Pukekohe East": 4928.9, "New Plymouth": 4891.7, "Lara": 2560.2, "Purley": 14334.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yarraville: (-37.82°, 144.90°)", " Pukekohe East: (-37.20°, 174.95°)", " New Plymouth: (-39.07°, 174.08°)", " Lara: (-38.02°, 144.41°)", " Purley: (51.34°, -0.11°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Purley: 14334.6 km from centroid", " Pukekohe East: 4928.9 km from centroid", " New Plymouth: 4891.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Purley", "FINAL ANSWER: Purley" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -36.93754, "lon": 174.65584, "name": "Titirangi" }, { "lat": -41.43876, "lon": 147.13467, "name": "Launceston" }, { "lat": -27.63917, "lon": 153.10944, "name": "Logan City" }, { "lat": -37.81501, "lon": 144.96657, "name": "Melbourne City Centre" }, { "lat": 35.64595, "lon": 139.7155, "name": "Ebisu" } ], "question": "Which location is the geographic outlier among: Titirangi, Launceston, Logan City, Melbourne City Centre, Ebisu?", "ground_truth": { "answer": "Ebisu", "outlier_distance_km": 6497.9, "second_furthest_km": 2772.4, "clarity_ratio": 2.34, "median_distance_km": 2247.0, "distances_to_centroid": { "Titirangi": 2772.4, "Launceston": 2247.0, "Logan City": 678.2, "Melbourne City Centre": 1918.4, "Ebisu": 6497.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Titirangi: (-36.94°, 174.66°)", " Launceston: (-41.44°, 147.13°)", " Logan City: (-27.64°, 153.11°)", " Melbourne City Centre: (-37.82°, 144.97°)", " Ebisu: (35.65°, 139.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Ebisu: 6497.9 km from centroid", " Titirangi: 2772.4 km from centroid", " Launceston: 2247.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Ebisu", "FINAL ANSWER: Ebisu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" }, { "lat": -33.88834, "lon": 151.12274, "name": "Ashfield" }, { "lat": -25.28762, "lon": 152.76936, "name": "Hervey Bay" }, { "lat": -37.98333, "lon": 145.2, "name": "Dandenong" }, { "lat": 41.82399, "lon": -71.41283, "name": "Providence" } ], "question": "Which location is the geographic outlier among: Saint Albans, Ashfield, Hervey Bay, Dandenong, Providence?", "ground_truth": { "answer": "Providence", "outlier_distance_km": 17405.3, "second_furthest_km": 5007.8, "clarity_ratio": 3.48, "median_distance_km": 4902.7, "distances_to_centroid": { "Saint Albans": 4439.1, "Ashfield": 4902.7, "Hervey Bay": 5007.8, "Dandenong": 4480.9, "Providence": 17405.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint Albans: (-37.73°, 144.80°)", " Ashfield: (-33.89°, 151.12°)", " Hervey Bay: (-25.29°, 152.77°)", " Dandenong: (-37.98°, 145.20°)", " Providence: (41.82°, -71.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Providence: 17405.3 km from centroid", " Hervey Bay: 5007.8 km from centroid", " Ashfield: 4902.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Providence", "FINAL ANSWER: Providence" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.65, "lon": 145.03333, "name": "Epping" }, { "lat": -27.44187, "lon": 152.93861, "name": "The Gap" }, { "lat": -38.07758, "lon": 145.29871, "name": "Cranbourne North" }, { "lat": -26.68443, "lon": 153.05705, "name": "Buderim" }, { "lat": 19.45229, "lon": -96.96148, "name": "Coatepec" } ], "question": "Which location is the geographic outlier among: Epping, The Gap, Cranbourne North, Buderim, Coatepec?", "ground_truth": { "answer": "Coatepec", "outlier_distance_km": 18241.5, "second_furthest_km": 5373.0, "clarity_ratio": 3.4, "median_distance_km": 5352.1, "distances_to_centroid": { "Epping": 4633.7, "The Gap": 5352.1, "Cranbourne North": 4664.1, "Buderim": 5373.0, "Coatepec": 18241.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Epping: (-37.65°, 145.03°)", " The Gap: (-27.44°, 152.94°)", " Cranbourne North: (-38.08°, 145.30°)", " Buderim: (-26.68°, 153.06°)", " Coatepec: (19.45°, -96.96°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coatepec: 18241.5 km from centroid", " Buderim: 5373.0 km from centroid", " The Gap: 5352.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coatepec", "FINAL ANSWER: Coatepec" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.03857, "lon": 151.10005, "name": "Miranda" }, { "lat": -37.75, "lon": 144.96667, "name": "Coburg" }, { "lat": -38.07018, "lon": 145.47411, "name": "Pakenham" }, { "lat": -37.83634, "lon": 144.65952, "name": "Tarneit" }, { "lat": 35.80167, "lon": 128.50083, "name": "Hwawŏn" } ], "question": "Which location is the geographic outlier among: Miranda, Coburg, Pakenham, Tarneit, Hwawŏn?", "ground_truth": { "answer": "Hwawŏn", "outlier_distance_km": 6645.5, "second_furthest_km": 1761.5, "clarity_ratio": 3.77, "median_distance_km": 1726.7, "distances_to_centroid": { "Miranda": 1521.8, "Coburg": 1720.2, "Pakenham": 1761.5, "Tarneit": 1726.7, "Hwawŏn": 6645.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Miranda: (-34.04°, 151.10°)", " Coburg: (-37.75°, 144.97°)", " Pakenham: (-38.07°, 145.47°)", " Tarneit: (-37.84°, 144.66°)", " Hwawŏn: (35.80°, 128.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hwawŏn: 6645.5 km from centroid", " Pakenham: 1761.5 km from centroid", " Tarneit: 1726.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hwawŏn", "FINAL ANSWER: Hwawŏn" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.79798, "lon": 151.28826, "name": "Manly" }, { "lat": -33.79068, "lon": 150.6693, "name": "Glenmore Park" }, { "lat": -21.15345, "lon": 149.16554, "name": "Mackay" }, { "lat": -28.21298, "lon": 153.53634, "name": "Banora Point" }, { "lat": -22.07889, "lon": -54.78944, "name": "Itaporã" } ], "question": "Which location is the geographic outlier among: Manly, Glenmore Park, Mackay, Banora Point, Itaporã?", "ground_truth": { "answer": "Itaporã", "outlier_distance_km": 14231.7, "second_furthest_km": 4253.0, "clarity_ratio": 3.35, "median_distance_km": 4017.4, "distances_to_centroid": { "Manly": 3975.1, "Glenmore Park": 3917.9, "Mackay": 4017.4, "Banora Point": 4253.0, "Itaporã": 14231.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Manly: (-33.80°, 151.29°)", " Glenmore Park: (-33.79°, 150.67°)", " Mackay: (-21.15°, 149.17°)", " Banora Point: (-28.21°, 153.54°)", " Itaporã: (-22.08°, -54.79°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Itaporã: 14231.7 km from centroid", " Banora Point: 4253.0 km from centroid", " Mackay: 4017.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Itaporã", "FINAL ANSWER: Itaporã" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.89611, "lon": -51.37944, "name": "Andradina" }, { "lat": -37.15276, "lon": -58.48838, "name": "Ayacucho" }, { "lat": -5.89056, "lon": -38.62194, "name": "Jaguaribe" }, { "lat": -23.51, "lon": -46.41566, "name": "Vila Curuca" }, { "lat": 42.69764, "lon": 2.89541, "name": "Perpignan" } ], "question": "Which location is the geographic outlier among: Andradina, Ayacucho, Jaguaribe, Vila Curuca, Perpignan?", "ground_truth": { "answer": "Perpignan", "outlier_distance_km": 7105.4, "second_furthest_km": 3730.7, "clarity_ratio": 1.9, "median_distance_km": 1923.4, "distances_to_centroid": { "Andradina": 1923.4, "Ayacucho": 3730.7, "Jaguaribe": 341.1, "Vila Curuca": 1829.7, "Perpignan": 7105.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Andradina: (-20.90°, -51.38°)", " Ayacucho: (-37.15°, -58.49°)", " Jaguaribe: (-5.89°, -38.62°)", " Vila Curuca: (-23.51°, -46.42°)", " Perpignan: (42.70°, 2.90°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Perpignan: 7105.4 km from centroid", " Ayacucho: 3730.7 km from centroid", " Andradina: 1923.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Perpignan", "FINAL ANSWER: Perpignan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.7511, "lon": 151.28886, "name": "Dee Why" }, { "lat": -37.73333, "lon": 144.93333, "name": "Pascoe Vale" }, { "lat": -37.71667, "lon": 145.0, "name": "Reservoir" }, { "lat": -33.79176, "lon": 151.08057, "name": "Eastwood" }, { "lat": 42.37537, "lon": -72.51925, "name": "Amherst Center" } ], "question": "Which location is the geographic outlier among: Dee Why, Pascoe Vale, Reservoir, Eastwood, Amherst Center?", "ground_truth": { "answer": "Amherst Center", "outlier_distance_km": 17518.8, "second_furthest_km": 4884.1, "clarity_ratio": 3.59, "median_distance_km": 4865.4, "distances_to_centroid": { "Dee Why": 4884.1, "Pascoe Vale": 4396.6, "Reservoir": 4401.8, "Eastwood": 4865.4, "Amherst Center": 17518.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dee Why: (-33.75°, 151.29°)", " Pascoe Vale: (-37.73°, 144.93°)", " Reservoir: (-37.72°, 145.00°)", " Eastwood: (-33.79°, 151.08°)", " Amherst Center: (42.38°, -72.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Amherst Center: 17518.8 km from centroid", " Dee Why: 4884.1 km from centroid", " Eastwood: 4865.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Amherst Center", "FINAL ANSWER: Amherst Center" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 46.8458, "lon": -1.87942, "name": "Challans" }, { "lat": 55.7, "lon": 37.46667, "name": "Amin’yevo" }, { "lat": 40.44682, "lon": -3.70347, "name": "Cuatro Caminos" }, { "lat": 45.52569, "lon": 4.87484, "name": "Vienne" }, { "lat": -38.1, "lon": 145.13333, "name": "Seaford" } ], "question": "Which location is the geographic outlier among: Challans, Amin’yevo, Cuatro Caminos, Vienne, Seaford?", "ground_truth": { "answer": "Seaford", "outlier_distance_km": 13553.1, "second_furthest_km": 3780.8, "clarity_ratio": 3.58, "median_distance_km": 3765.0, "distances_to_centroid": { "Challans": 3765.0, "Amin’yevo": 2849.7, "Cuatro Caminos": 3780.8, "Vienne": 3225.6, "Seaford": 13553.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Challans: (46.85°, -1.88°)", " Amin’yevo: (55.70°, 37.47°)", " Cuatro Caminos: (40.45°, -3.70°)", " Vienne: (45.53°, 4.87°)", " Seaford: (-38.10°, 145.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Seaford: 13553.1 km from centroid", " Cuatro Caminos: 3780.8 km from centroid", " Challans: 3765.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Seaford", "FINAL ANSWER: Seaford" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -35.4232, "lon": -71.64974, "name": "Talca" }, { "lat": -13.07541, "lon": -76.31719, "name": "Nuevo Imperial" }, { "lat": -7.54528, "lon": -35.7075, "name": "Aroeiras" }, { "lat": -23.52508, "lon": -46.63889, "name": "Bom Retiro" }, { "lat": 21.6, "lon": 109.71667, "name": "Shankou" } ], "question": "Which location is the geographic outlier among: Talca, Nuevo Imperial, Aroeiras, Bom Retiro, Shankou?", "ground_truth": { "answer": "Shankou", "outlier_distance_km": 14990.6, "second_furthest_km": 5662.7, "clarity_ratio": 2.65, "median_distance_km": 5453.5, "distances_to_centroid": { "Talca": 5453.5, "Nuevo Imperial": 5662.7, "Aroeiras": 1347.7, "Bom Retiro": 2725.1, "Shankou": 14990.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Talca: (-35.42°, -71.65°)", " Nuevo Imperial: (-13.08°, -76.32°)", " Aroeiras: (-7.55°, -35.71°)", " Bom Retiro: (-23.53°, -46.64°)", " Shankou: (21.60°, 109.72°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shankou: 14990.6 km from centroid", " Nuevo Imperial: 5662.7 km from centroid", " Talca: 5453.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shankou", "FINAL ANSWER: Shankou" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.96649, "lon": 145.2081, "name": "Dandenong North" }, { "lat": -33.9205, "lon": 151.25522, "name": "Coogee" }, { "lat": -37.70988, "lon": 144.75483, "name": "Taylors Hill" }, { "lat": -27.96724, "lon": 153.39796, "name": "Southport" }, { "lat": 7.15139, "lon": 37.17184, "name": "Tarch’a Sodo" } ], "question": "Which location is the geographic outlier among: Dandenong North, Coogee, Taylors Hill, Southport, Tarch’a Sodo?", "ground_truth": { "answer": "Tarch’a Sodo", "outlier_distance_km": 10275.7, "second_furthest_km": 2681.2, "clarity_ratio": 3.83, "median_distance_km": 2543.0, "distances_to_centroid": { "Dandenong North": 2207.2, "Coogee": 2543.0, "Taylors Hill": 2158.3, "Southport": 2681.2, "Tarch’a Sodo": 10275.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dandenong North: (-37.97°, 145.21°)", " Coogee: (-33.92°, 151.26°)", " Taylors Hill: (-37.71°, 144.75°)", " Southport: (-27.97°, 153.40°)", " Tarch’a Sodo: (7.15°, 37.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tarch’a Sodo: 10275.7 km from centroid", " Southport: 2681.2 km from centroid", " Coogee: 2543.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tarch’a Sodo", "FINAL ANSWER: Tarch’a Sodo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 49.76741, "lon": -94.48985, "name": "Kenora" }, { "lat": 42.18169, "lon": -87.80034, "name": "Highland Park" }, { "lat": 49.01667, "lon": -123.08333, "name": "Tsawwassen" }, { "lat": 33.56504, "lon": -117.72712, "name": "Aliso Viejo" }, { "lat": 12.91808, "lon": 79.27756, "name": "Vishāram" } ], "question": "Which location is the geographic outlier among: Kenora, Highland Park, Tsawwassen, Aliso Viejo, Vishāram?", "ground_truth": { "answer": "Vishāram", "outlier_distance_km": 13492.3, "second_furthest_km": 4478.1, "clarity_ratio": 3.01, "median_distance_km": 4402.6, "distances_to_centroid": { "Kenora": 2460.7, "Highland Park": 1702.8, "Tsawwassen": 4478.1, "Aliso Viejo": 4402.6, "Vishāram": 13492.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kenora: (49.77°, -94.49°)", " Highland Park: (42.18°, -87.80°)", " Tsawwassen: (49.02°, -123.08°)", " Aliso Viejo: (33.57°, -117.73°)", " Vishāram: (12.92°, 79.28°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vishāram: 13492.3 km from centroid", " Tsawwassen: 4478.1 km from centroid", " Aliso Viejo: 4402.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vishāram", "FINAL ANSWER: Vishāram" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -34.92866, "lon": 138.59863, "name": "Adelaide" }, { "lat": -37.68333, "lon": 145.01667, "name": "Thomastown" }, { "lat": -34.92873, "lon": 138.60334, "name": "Adelaide city centre" }, { "lat": -37.81667, "lon": 144.9, "name": "Yarraville" }, { "lat": 31.31146, "lon": 31.14766, "name": "Al Ḩāmūl" } ], "question": "Which location is the geographic outlier among: Adelaide, Thomastown, Adelaide city centre, Yarraville, Al Ḩāmūl?", "ground_truth": { "answer": "Al Ḩāmūl", "outlier_distance_km": 11166.6, "second_furthest_km": 2928.9, "clarity_ratio": 3.81, "median_distance_km": 2926.6, "distances_to_centroid": { "Adelaide": 2277.7, "Thomastown": 2928.9, "Adelaide city centre": 2278.1, "Yarraville": 2926.6, "Al Ḩāmūl": 11166.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Adelaide: (-34.93°, 138.60°)", " Thomastown: (-37.68°, 145.02°)", " Adelaide city centre: (-34.93°, 138.60°)", " Yarraville: (-37.82°, 144.90°)", " Al Ḩāmūl: (31.31°, 31.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Al Ḩāmūl: 11166.6 km from centroid", " Thomastown: 2928.9 km from centroid", " Yarraville: 2926.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Al Ḩāmūl", "FINAL ANSWER: Al Ḩāmūl" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.39462, "lon": -76.0715, "name": "Zarzal" }, { "lat": -9.335, "lon": -50.35, "name": "Santana do Araguaia" }, { "lat": -34.57365, "lon": -58.44924, "name": "Colegiales" }, { "lat": -16.08333, "lon": -69.66667, "name": "Ilave" }, { "lat": -38.05916, "lon": 145.40947, "name": "Officer" } ], "question": "Which location is the geographic outlier among: Zarzal, Santana do Araguaia, Colegiales, Ilave, Officer?", "ground_truth": { "answer": "Officer", "outlier_distance_km": 13560.9, "second_furthest_km": 6470.3, "clarity_ratio": 2.1, "median_distance_km": 5069.9, "distances_to_centroid": { "Zarzal": 6470.3, "Santana do Araguaia": 3243.9, "Colegiales": 4013.3, "Ilave": 5069.9, "Officer": 13560.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Zarzal: (4.39°, -76.07°)", " Santana do Araguaia: (-9.34°, -50.35°)", " Colegiales: (-34.57°, -58.45°)", " Ilave: (-16.08°, -69.67°)", " Officer: (-38.06°, 145.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Officer: 13560.9 km from centroid", " Zarzal: 6470.3 km from centroid", " Ilave: 5069.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Officer", "FINAL ANSWER: Officer" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -2.04639, "lon": -47.55056, "name": "Mãe do Rio" }, { "lat": -10.28139, "lon": -37.01861, "name": "Aquidabã" }, { "lat": -35.6593, "lon": -63.75787, "name": "General Pico" }, { "lat": -10.5075, "lon": -39.01583, "name": "Euclides da Cunha" }, { "lat": 7.8275, "lon": 123.4782, "name": "Muricay" } ], "question": "Which location is the geographic outlier among: Mãe do Rio, Aquidabã, General Pico, Euclides da Cunha, Muricay?", "ground_truth": { "answer": "Muricay", "outlier_distance_km": 15206.6, "second_furthest_km": 5859.3, "clarity_ratio": 2.6, "median_distance_km": 3945.1, "distances_to_centroid": { "Mãe do Rio": 3945.1, "Aquidabã": 2652.7, "General Pico": 5859.3, "Euclides da Cunha": 2870.3, "Muricay": 15206.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mãe do Rio: (-2.05°, -47.55°)", " Aquidabã: (-10.28°, -37.02°)", " General Pico: (-35.66°, -63.76°)", " Euclides da Cunha: (-10.51°, -39.02°)", " Muricay: (7.83°, 123.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Muricay: 15206.6 km from centroid", " General Pico: 5859.3 km from centroid", " Mãe do Rio: 3945.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Muricay", "FINAL ANSWER: Muricay" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 4.96531, "lon": -73.91301, "name": "Tocancipá" }, { "lat": -23.66778, "lon": -46.46139, "name": "Mauá" }, { "lat": -19.7625, "lon": -44.31389, "name": "Esmeraldas" }, { "lat": -34.5627, "lon": -58.45829, "name": "Belgrano" }, { "lat": 35.70749, "lon": 139.7788, "name": "Taito" } ], "question": "Which location is the geographic outlier among: Tocancipá, Mauá, Esmeraldas, Belgrano, Taito?", "ground_truth": { "answer": "Taito", "outlier_distance_km": 16065.3, "second_furthest_km": 6499.0, "clarity_ratio": 2.47, "median_distance_km": 5221.4, "distances_to_centroid": { "Tocancipá": 6499.0, "Mauá": 3650.5, "Esmeraldas": 3277.6, "Belgrano": 5221.4, "Taito": 16065.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Tocancipá: (4.97°, -73.91°)", " Mauá: (-23.67°, -46.46°)", " Esmeraldas: (-19.76°, -44.31°)", " Belgrano: (-34.56°, -58.46°)", " Taito: (35.71°, 139.78°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Taito: 16065.3 km from centroid", " Tocancipá: 6499.0 km from centroid", " Belgrano: 5221.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Taito", "FINAL ANSWER: Taito" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 1.6561, "lon": 103.6032, "name": "Kulai" }, { "lat": 30.39759, "lon": 107.3895, "name": "Xinmin" }, { "lat": 23.54109, "lon": 74.4425, "name": "Bānswāra" }, { "lat": 17.89241, "lon": 75.02138, "name": "Aklūj" }, { "lat": -37.74981, "lon": 144.9109, "name": "Essendon" } ], "question": "Which location is the geographic outlier among: Kulai, Xinmin, Bānswāra, Aklūj, Essendon?", "ground_truth": { "answer": "Essendon", "outlier_distance_km": 6747.0, "second_furthest_km": 3376.2, "clarity_ratio": 2.0, "median_distance_km": 3064.5, "distances_to_centroid": { "Kulai": 671.9, "Xinmin": 2667.9, "Bānswāra": 3376.2, "Aklūj": 3064.5, "Essendon": 6747.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kulai: (1.66°, 103.60°)", " Xinmin: (30.40°, 107.39°)", " Bānswāra: (23.54°, 74.44°)", " Aklūj: (17.89°, 75.02°)", " Essendon: (-37.75°, 144.91°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Essendon: 6747.0 km from centroid", " Bānswāra: 3376.2 km from centroid", " Aklūj: 3064.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Essendon", "FINAL ANSWER: Essendon" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.8226, "lon": -73.81958, "name": "Throgs Neck" }, { "lat": 42.26391, "lon": -88.84427, "name": "Belvidere" }, { "lat": 35.41968, "lon": -119.01955, "name": "Oildale" }, { "lat": 32.29785, "lon": -110.9187, "name": "Catalina Foothills" }, { "lat": 28.92406, "lon": 30.98544, "name": "Bibā" } ], "question": "Which location is the geographic outlier among: Throgs Neck, Belvidere, Oildale, Catalina Foothills, Bibā?", "ground_truth": { "answer": "Bibā", "outlier_distance_km": 9236.1, "second_furthest_km": 4176.5, "clarity_ratio": 2.21, "median_distance_km": 3552.8, "distances_to_centroid": { "Throgs Neck": 557.7, "Belvidere": 1585.6, "Oildale": 4176.5, "Catalina Foothills": 3552.8, "Bibā": 9236.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Throgs Neck: (40.82°, -73.82°)", " Belvidere: (42.26°, -88.84°)", " Oildale: (35.42°, -119.02°)", " Catalina Foothills: (32.30°, -110.92°)", " Bibā: (28.92°, 30.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bibā: 9236.1 km from centroid", " Oildale: 4176.5 km from centroid", " Catalina Foothills: 3552.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bibā", "FINAL ANSWER: Bibā" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 18.26321, "lon": 75.46316, "name": "Paranda" }, { "lat": 22.59373, "lon": 75.29774, "name": "Dhār" }, { "lat": 14.905, "lon": 76.38527, "name": "Kūdligi" }, { "lat": 18.85779, "lon": 79.7956, "name": "Chinnūr" }, { "lat": 47.09621, "lon": -122.35873, "name": "Frederickson" } ], "question": "Which location is the geographic outlier among: Paranda, Dhār, Kūdligi, Chinnūr, Frederickson?", "ground_truth": { "answer": "Frederickson", "outlier_distance_km": 11803.5, "second_furthest_km": 4457.8, "clarity_ratio": 2.65, "median_distance_km": 4249.3, "distances_to_centroid": { "Paranda": 4037.2, "Dhār": 3907.3, "Kūdligi": 4249.3, "Chinnūr": 4457.8, "Frederickson": 11803.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paranda: (18.26°, 75.46°)", " Dhār: (22.59°, 75.30°)", " Kūdligi: (14.90°, 76.39°)", " Chinnūr: (18.86°, 79.80°)", " Frederickson: (47.10°, -122.36°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Frederickson: 11803.5 km from centroid", " Chinnūr: 4457.8 km from centroid", " Kūdligi: 4249.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Frederickson", "FINAL ANSWER: Frederickson" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.2, "lon": 8.63333, "name": "Kirchlengern" }, { "lat": 43.68374, "lon": 43.53507, "name": "Baksan" }, { "lat": 58.19077, "lon": 40.17081, "name": "Danilov" }, { "lat": 38.03922, "lon": -4.05077, "name": "Andújar" }, { "lat": 40.06928, "lon": -75.16629, "name": "West Oak Lane" } ], "question": "Which location is the geographic outlier among: Kirchlengern, Baksan, Danilov, Andújar, West Oak Lane?", "ground_truth": { "answer": "West Oak Lane", "outlier_distance_km": 6081.4, "second_furthest_km": 3191.8, "clarity_ratio": 1.91, "median_distance_km": 2817.6, "distances_to_centroid": { "Kirchlengern": 774.3, "Baksan": 3191.8, "Danilov": 2817.6, "Andújar": 1082.5, "West Oak Lane": 6081.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kirchlengern: (52.20°, 8.63°)", " Baksan: (43.68°, 43.54°)", " Danilov: (58.19°, 40.17°)", " Andújar: (38.04°, -4.05°)", " West Oak Lane: (40.07°, -75.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " West Oak Lane: 6081.4 km from centroid", " Baksan: 3191.8 km from centroid", " Danilov: 2817.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: West Oak Lane", "FINAL ANSWER: West Oak Lane" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.49325, "lon": 153.05826, "name": "Coorparoo" }, { "lat": -41.26667, "lon": 174.95, "name": "Wainuiomata" }, { "lat": -36.9482, "lon": 174.87019, "name": "Otara" }, { "lat": -38.03333, "lon": 145.25, "name": "Hampton Park" }, { "lat": 43.44775, "lon": 3.75524, "name": "Frontignan" } ], "question": "Which location is the geographic outlier among: Coorparoo, Wainuiomata, Otara, Hampton Park, Frontignan?", "ground_truth": { "answer": "Frontignan", "outlier_distance_km": 14454.4, "second_furthest_km": 4801.7, "clarity_ratio": 3.01, "median_distance_km": 4684.3, "distances_to_centroid": { "Coorparoo": 2446.8, "Wainuiomata": 4801.7, "Otara": 4684.3, "Hampton Park": 2459.5, "Frontignan": 14454.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Coorparoo: (-27.49°, 153.06°)", " Wainuiomata: (-41.27°, 174.95°)", " Otara: (-36.95°, 174.87°)", " Hampton Park: (-38.03°, 145.25°)", " Frontignan: (43.45°, 3.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Frontignan: 14454.4 km from centroid", " Wainuiomata: 4801.7 km from centroid", " Otara: 4684.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Frontignan", "FINAL ANSWER: Frontignan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 15.76983, "lon": 76.75581, "name": "Sindhnūr" }, { "lat": 36.01839, "lon": 139.66034, "name": "Shiraoka" }, { "lat": 30.32443, "lon": 78.03392, "name": "Dehra Dūn" }, { "lat": 35.46028, "lon": 110.42917, "name": "Hancheng" }, { "lat": 31.72294, "lon": -116.57196, "name": "Rodolfo Sánchez Taboada" } ], "question": "Which location is the geographic outlier among: Sindhnūr, Shiraoka, Dehra Dūn, Hancheng, Rodolfo Sánchez Taboada?", "ground_truth": { "answer": "Rodolfo Sánchez Taboada", "outlier_distance_km": 13140.5, "second_furthest_km": 7452.3, "clarity_ratio": 1.76, "median_distance_km": 4921.0, "distances_to_centroid": { "Sindhnūr": 2499.9, "Shiraoka": 7452.3, "Dehra Dūn": 1958.1, "Hancheng": 4921.0, "Rodolfo Sánchez Taboada": 13140.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sindhnūr: (15.77°, 76.76°)", " Shiraoka: (36.02°, 139.66°)", " Dehra Dūn: (30.32°, 78.03°)", " Hancheng: (35.46°, 110.43°)", " Rodolfo Sánchez Taboada: (31.72°, -116.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rodolfo Sánchez Taboada: 13140.5 km from centroid", " Shiraoka: 7452.3 km from centroid", " Hancheng: 4921.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rodolfo Sánchez Taboada", "FINAL ANSWER: Rodolfo Sánchez Taboada" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -30.50123, "lon": 151.66553, "name": "Armidale" }, { "lat": -37.8, "lon": 144.96667, "name": "Carlton" }, { "lat": -27.96724, "lon": 153.39796, "name": "Southport" }, { "lat": -38.11531, "lon": 145.29814, "name": "Cranbourne East" }, { "lat": 41.77976, "lon": -87.64588, "name": "Englewood" } ], "question": "Which location is the geographic outlier among: Armidale, Carlton, Southport, Cranbourne East, Englewood?", "ground_truth": { "answer": "Englewood", "outlier_distance_km": 17286.3, "second_furthest_km": 5362.8, "clarity_ratio": 3.22, "median_distance_km": 5200.2, "distances_to_centroid": { "Armidale": 5200.2, "Carlton": 4711.5, "Southport": 5362.8, "Cranbourne East": 4748.5, "Englewood": 17286.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Armidale: (-30.50°, 151.67°)", " Carlton: (-37.80°, 144.97°)", " Southport: (-27.97°, 153.40°)", " Cranbourne East: (-38.12°, 145.30°)", " Englewood: (41.78°, -87.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Englewood: 17286.3 km from centroid", " Southport: 5362.8 km from centroid", " Armidale: 5200.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Englewood", "FINAL ANSWER: Englewood" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -32.23013, "lon": 115.78128, "name": "Kwinana" }, { "lat": -37.8676, "lon": 144.98099, "name": "Saint Kilda" }, { "lat": -33.2792, "lon": 115.71504, "name": "Australind" }, { "lat": -36.88158, "lon": 174.76204, "name": "Mount Eden" }, { "lat": -3.22028, "lon": -45.00361, "name": "Viana" } ], "question": "Which location is the geographic outlier among: Kwinana, Saint Kilda, Australind, Mount Eden, Viana?", "ground_truth": { "answer": "Viana", "outlier_distance_km": 14958.6, "second_furthest_km": 6764.9, "clarity_ratio": 2.21, "median_distance_km": 4151.6, "distances_to_centroid": { "Kwinana": 1446.0, "Saint Kilda": 4151.6, "Australind": 1468.7, "Mount Eden": 6764.9, "Viana": 14958.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kwinana: (-32.23°, 115.78°)", " Saint Kilda: (-37.87°, 144.98°)", " Australind: (-33.28°, 115.72°)", " Mount Eden: (-36.88°, 174.76°)", " Viana: (-3.22°, -45.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Viana: 14958.6 km from centroid", " Mount Eden: 6764.9 km from centroid", " Saint Kilda: 4151.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Viana", "FINAL ANSWER: Viana" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 44.86136, "lon": -92.62381, "name": "River Falls" }, { "lat": 37.08339, "lon": -88.60005, "name": "Paducah" }, { "lat": 19.25465, "lon": -99.10356, "name": "Xochimilco" }, { "lat": 43.90012, "lon": -78.84957, "name": "Oshawa" }, { "lat": 11.49984, "lon": 76.48152, "name": "Kollivāyal" } ], "question": "Which location is the geographic outlier among: River Falls, Paducah, Xochimilco, Oshawa, Kollivāyal?", "ground_truth": { "answer": "Kollivāyal", "outlier_distance_km": 13106.8, "second_furthest_km": 4454.1, "clarity_ratio": 2.94, "median_distance_km": 3461.1, "distances_to_centroid": { "River Falls": 3461.1, "Paducah": 3002.3, "Xochimilco": 4454.1, "Oshawa": 2399.5, "Kollivāyal": 13106.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " River Falls: (44.86°, -92.62°)", " Paducah: (37.08°, -88.60°)", " Xochimilco: (19.25°, -99.10°)", " Oshawa: (43.90°, -78.85°)", " Kollivāyal: (11.50°, 76.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kollivāyal: 13106.8 km from centroid", " Xochimilco: 4454.1 km from centroid", " River Falls: 3461.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kollivāyal", "FINAL ANSWER: Kollivāyal" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -13.07127, "lon": -55.91479, "name": "Lucas do Rio Verde" }, { "lat": -5.0925, "lon": -80.1625, "name": "Chulucanas" }, { "lat": -3.22083, "lon": -64.80417, "name": "Alvarães" }, { "lat": -23.10417, "lon": -55.22583, "name": "Amambai" }, { "lat": 38.70144, "lon": -90.14872, "name": "Granite City" } ], "question": "Which location is the geographic outlier among: Lucas do Rio Verde, Chulucanas, Alvarães, Amambai, Granite City?", "ground_truth": { "answer": "Granite City", "outlier_distance_km": 4920.4, "second_furthest_km": 2871.8, "clarity_ratio": 1.71, "median_distance_km": 1977.9, "distances_to_centroid": { "Lucas do Rio Verde": 1977.9, "Chulucanas": 1287.8, "Alvarães": 544.8, "Amambai": 2871.8, "Granite City": 4920.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Lucas do Rio Verde: (-13.07°, -55.91°)", " Chulucanas: (-5.09°, -80.16°)", " Alvarães: (-3.22°, -64.80°)", " Amambai: (-23.10°, -55.23°)", " Granite City: (38.70°, -90.15°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Granite City: 4920.4 km from centroid", " Amambai: 2871.8 km from centroid", " Lucas do Rio Verde: 1977.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Granite City", "FINAL ANSWER: Granite City" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.51314, "lon": 9.14343, "name": "Quarto Oggiaro" }, { "lat": 46.06251, "lon": 6.57497, "name": "Cluses" }, { "lat": 51.31889, "lon": -2.20861, "name": "Trowbridge" }, { "lat": 43.34122, "lon": 3.21402, "name": "Béziers" }, { "lat": 6.78611, "lon": 125.21333, "name": "Bansalan" } ], "question": "Which location is the geographic outlier among: Quarto Oggiaro, Cluses, Trowbridge, Béziers, Bansalan?", "ground_truth": { "answer": "Bansalan", "outlier_distance_km": 10125.4, "second_furthest_km": 2762.1, "clarity_ratio": 3.67, "median_distance_km": 2169.0, "distances_to_centroid": { "Quarto Oggiaro": 1758.7, "Cluses": 1967.0, "Trowbridge": 2762.1, "Béziers": 2169.0, "Bansalan": 10125.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Quarto Oggiaro: (45.51°, 9.14°)", " Cluses: (46.06°, 6.57°)", " Trowbridge: (51.32°, -2.21°)", " Béziers: (43.34°, 3.21°)", " Bansalan: (6.79°, 125.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bansalan: 10125.4 km from centroid", " Trowbridge: 2762.1 km from centroid", " Béziers: 2169.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bansalan", "FINAL ANSWER: Bansalan" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -9.805, "lon": -37.68444, "name": "Poço Redondo" }, { "lat": -8.41889, "lon": -37.05389, "name": "Arcoverde" }, { "lat": -33.67571, "lon": -65.45783, "name": "Villa Mercedes" }, { "lat": -33.14091, "lon": -59.31257, "name": "Gualeguay" }, { "lat": 31.81667, "lon": 130.3, "name": "Sendai" } ], "question": "Which location is the geographic outlier among: Poço Redondo, Arcoverde, Villa Mercedes, Gualeguay, Sendai?", "ground_truth": { "answer": "Sendai", "outlier_distance_km": 15649.0, "second_furthest_km": 5825.7, "clarity_ratio": 2.69, "median_distance_km": 5260.2, "distances_to_centroid": { "Poço Redondo": 2610.1, "Arcoverde": 2556.8, "Villa Mercedes": 5825.7, "Gualeguay": 5260.2, "Sendai": 15649.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Poço Redondo: (-9.80°, -37.68°)", " Arcoverde: (-8.42°, -37.05°)", " Villa Mercedes: (-33.68°, -65.46°)", " Gualeguay: (-33.14°, -59.31°)", " Sendai: (31.82°, 130.30°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sendai: 15649.0 km from centroid", " Villa Mercedes: 5825.7 km from centroid", " Gualeguay: 5260.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sendai", "FINAL ANSWER: Sendai" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -26.39022, "lon": -70.04556, "name": "Diego de Almagro" }, { "lat": -2.90472, "lon": -41.77667, "name": "Parnaíba" }, { "lat": -23.87389, "lon": -49.80278, "name": "Wenceslau Braz" }, { "lat": -23.2325, "lon": -51.66556, "name": "Astorga" }, { "lat": 51.18459, "lon": 6.81249, "name": "Wersten" } ], "question": "Which location is the geographic outlier among: Diego de Almagro, Parnaíba, Wenceslau Braz, Astorga, Wersten?", "ground_truth": { "answer": "Wersten", "outlier_distance_km": 7740.2, "second_furthest_km": 3866.8, "clarity_ratio": 2.0, "median_distance_km": 2308.3, "distances_to_centroid": { "Diego de Almagro": 3866.8, "Parnaíba": 243.7, "Wenceslau Braz": 2283.4, "Astorga": 2308.3, "Wersten": 7740.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Diego de Almagro: (-26.39°, -70.05°)", " Parnaíba: (-2.90°, -41.78°)", " Wenceslau Braz: (-23.87°, -49.80°)", " Astorga: (-23.23°, -51.67°)", " Wersten: (51.18°, 6.81°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Wersten: 7740.2 km from centroid", " Diego de Almagro: 3866.8 km from centroid", " Astorga: 2308.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Wersten", "FINAL ANSWER: Wersten" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 26.20437, "lon": 127.75267, "name": "Yonabaru" }, { "lat": 37.5986, "lon": 127.1394, "name": "Guri-si" }, { "lat": 11.02427, "lon": 77.12565, "name": "Sulur" }, { "lat": 9.65556, "lon": 123.85219, "name": "Tagbilaran City" }, { "lat": 37.26383, "lon": -122.02301, "name": "Saratoga" } ], "question": "Which location is the geographic outlier among: Yonabaru, Guri-si, Sulur, Tagbilaran City, Saratoga?", "ground_truth": { "answer": "Saratoga", "outlier_distance_km": 13102.5, "second_furthest_km": 6242.0, "clarity_ratio": 2.1, "median_distance_km": 6076.9, "distances_to_centroid": { "Yonabaru": 6076.9, "Guri-si": 5840.4, "Sulur": 1841.6, "Tagbilaran City": 6242.0, "Saratoga": 13102.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Yonabaru: (26.20°, 127.75°)", " Guri-si: (37.60°, 127.14°)", " Sulur: (11.02°, 77.13°)", " Tagbilaran City: (9.66°, 123.85°)", " Saratoga: (37.26°, -122.02°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Saratoga: 13102.5 km from centroid", " Tagbilaran City: 6242.0 km from centroid", " Yonabaru: 6076.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Saratoga", "FINAL ANSWER: Saratoga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.0021, "lon": 0.20251, "name": "Le Mans" }, { "lat": 51.5824, "lon": -0.09956, "name": "Harringay" }, { "lat": 37.64442, "lon": 14.86685, "name": "Biancavilla" }, { "lat": 45.67574, "lon": 9.23723, "name": "Carate Brianza" }, { "lat": 27.06193, "lon": -101.54891, "name": "San Buenaventura" } ], "question": "Which location is the geographic outlier among: Le Mans, Harringay, Biancavilla, Carate Brianza, San Buenaventura?", "ground_truth": { "answer": "San Buenaventura", "outlier_distance_km": 7732.0, "second_furthest_km": 2621.3, "clarity_ratio": 2.95, "median_distance_km": 2015.0, "distances_to_centroid": { "Le Mans": 1398.0, "Harringay": 1577.2, "Biancavilla": 2621.3, "Carate Brianza": 2015.0, "San Buenaventura": 7732.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Le Mans: (48.00°, 0.20°)", " Harringay: (51.58°, -0.10°)", " Biancavilla: (37.64°, 14.87°)", " Carate Brianza: (45.68°, 9.24°)", " San Buenaventura: (27.06°, -101.55°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " San Buenaventura: 7732.0 km from centroid", " Biancavilla: 2621.3 km from centroid", " Carate Brianza: 2015.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: San Buenaventura", "FINAL ANSWER: San Buenaventura" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.11667, "lon": 8.83333, "name": "Mühlheim am Main" }, { "lat": 49.74657, "lon": 8.11513, "name": "Alzey" }, { "lat": 53.91887, "lon": 10.69691, "name": "Bad Schwartau" }, { "lat": 55.83116, "lon": -3.22608, "name": "Penicuik" }, { "lat": 30.31269, "lon": 31.32018, "name": "Shibīn al Qanāţir" } ], "question": "Which location is the geographic outlier among: Mühlheim am Main, Alzey, Bad Schwartau, Penicuik, Shibīn al Qanāţir?", "ground_truth": { "answer": "Shibīn al Qanāţir", "outlier_distance_km": 2608.2, "second_furthest_km": 1312.0, "clarity_ratio": 1.99, "median_distance_km": 660.5, "distances_to_centroid": { "Mühlheim am Main": 290.9, "Alzey": 295.9, "Bad Schwartau": 660.5, "Penicuik": 1312.0, "Shibīn al Qanāţir": 2608.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Mühlheim am Main: (50.12°, 8.83°)", " Alzey: (49.75°, 8.12°)", " Bad Schwartau: (53.92°, 10.70°)", " Penicuik: (55.83°, -3.23°)", " Shibīn al Qanāţir: (30.31°, 31.32°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shibīn al Qanāţir: 2608.2 km from centroid", " Penicuik: 1312.0 km from centroid", " Bad Schwartau: 660.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shibīn al Qanāţir", "FINAL ANSWER: Shibīn al Qanāţir" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 33.6103, "lon": -117.72533, "name": "Laguna Woods" }, { "lat": 17.17291, "lon": -92.33392, "name": "Yajalón" }, { "lat": 21.35087, "lon": -97.68656, "name": "Naranjos" }, { "lat": 33.04623, "lon": -96.99417, "name": "Lewisville" }, { "lat": -37.71667, "lon": 145.0, "name": "Reservoir" } ], "question": "Which location is the geographic outlier among: Laguna Woods, Yajalón, Naranjos, Lewisville, Reservoir?", "ground_truth": { "answer": "Reservoir", "outlier_distance_km": 16842.4, "second_furthest_km": 6952.1, "clarity_ratio": 2.42, "median_distance_km": 5039.5, "distances_to_centroid": { "Laguna Woods": 6952.1, "Yajalón": 4342.7, "Naranjos": 4913.6, "Lewisville": 5039.5, "Reservoir": 16842.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Laguna Woods: (33.61°, -117.73°)", " Yajalón: (17.17°, -92.33°)", " Naranjos: (21.35°, -97.69°)", " Lewisville: (33.05°, -96.99°)", " Reservoir: (-37.72°, 145.00°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Reservoir: 16842.4 km from centroid", " Laguna Woods: 6952.1 km from centroid", " Lewisville: 5039.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Reservoir", "FINAL ANSWER: Reservoir" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 50.35357, "lon": 7.57883, "name": "Koblenz" }, { "lat": 51.34948, "lon": -0.2494, "name": "Ewell" }, { "lat": 52.00667, "lon": 4.35556, "name": "Delft" }, { "lat": 48.89198, "lon": 2.20675, "name": "Nanterre" }, { "lat": -27.66757, "lon": 152.92488, "name": "Springfield Lakes" } ], "question": "Which location is the geographic outlier among: Koblenz, Ewell, Delft, Nanterre, Springfield Lakes?", "ground_truth": { "answer": "Springfield Lakes", "outlier_distance_km": 14302.5, "second_furthest_km": 3233.6, "clarity_ratio": 4.42, "median_distance_km": 2975.0, "distances_to_centroid": { "Koblenz": 2689.6, "Ewell": 3233.6, "Delft": 2975.0, "Nanterre": 2974.2, "Springfield Lakes": 14302.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Koblenz: (50.35°, 7.58°)", " Ewell: (51.35°, -0.25°)", " Delft: (52.01°, 4.36°)", " Nanterre: (48.89°, 2.21°)", " Springfield Lakes: (-27.67°, 152.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Springfield Lakes: 14302.5 km from centroid", " Ewell: 3233.6 km from centroid", " Delft: 2975.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Springfield Lakes", "FINAL ANSWER: Springfield Lakes" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.43167, "lon": -54.05111, "name": "Paranatinga" }, { "lat": -25.32472, "lon": -49.31, "name": "Almirante Tamandaré" }, { "lat": -9.74583, "lon": -41.88528, "name": "Sento Sé" }, { "lat": -20.53861, "lon": -47.40083, "name": "Franca" }, { "lat": 40.79677, "lon": -74.48154, "name": "Morristown" } ], "question": "Which location is the geographic outlier among: Paranatinga, Almirante Tamandaré, Sento Sé, Franca, Morristown?", "ground_truth": { "answer": "Morristown", "outlier_distance_km": 5614.1, "second_furthest_km": 2209.5, "clarity_ratio": 2.54, "median_distance_km": 1758.1, "distances_to_centroid": { "Paranatinga": 956.8, "Almirante Tamandaré": 2209.5, "Sento Sé": 1342.9, "Franca": 1758.1, "Morristown": 5614.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paranatinga: (-14.43°, -54.05°)", " Almirante Tamandaré: (-25.32°, -49.31°)", " Sento Sé: (-9.75°, -41.89°)", " Franca: (-20.54°, -47.40°)", " Morristown: (40.80°, -74.48°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Morristown: 5614.1 km from centroid", " Almirante Tamandaré: 2209.5 km from centroid", " Franca: 1758.1 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Morristown", "FINAL ANSWER: Morristown" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.78609, "lon": -79.33502, "name": "Pleasant View" }, { "lat": 30.31188, "lon": -95.45605, "name": "Conroe" }, { "lat": 45.42067, "lon": -122.67065, "name": "Lake Oswego" }, { "lat": 35.26266, "lon": -77.58164, "name": "Kinston" }, { "lat": -37.8, "lon": 144.96667, "name": "Carlton" } ], "question": "Which location is the geographic outlier among: Pleasant View, Conroe, Lake Oswego, Kinston, Carlton?", "ground_truth": { "answer": "Carlton", "outlier_distance_km": 18102.7, "second_furthest_km": 7164.9, "clarity_ratio": 2.53, "median_distance_km": 4926.8, "distances_to_centroid": { "Pleasant View": 3787.6, "Conroe": 4926.8, "Lake Oswego": 7164.9, "Kinston": 3313.8, "Carlton": 18102.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pleasant View: (43.79°, -79.34°)", " Conroe: (30.31°, -95.46°)", " Lake Oswego: (45.42°, -122.67°)", " Kinston: (35.26°, -77.58°)", " Carlton: (-37.80°, 144.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Carlton: 18102.7 km from centroid", " Lake Oswego: 7164.9 km from centroid", " Conroe: 4926.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Carlton", "FINAL ANSWER: Carlton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -12.54667, "lon": -38.71194, "name": "Santo Amaro" }, { "lat": 7.83389, "lon": -72.47417, "name": "Villa del Rosario" }, { "lat": -27.69934, "lon": -48.53219, "name": "Ribeirão da Ilha" }, { "lat": -23.62623, "lon": -46.72828, "name": "Vila Andrade" }, { "lat": 2.2152, "lon": 102.2851, "name": "Kampung Bukit Baharu" } ], "question": "Which location is the geographic outlier among: Santo Amaro, Villa del Rosario, Ribeirão da Ilha, Vila Andrade, Kampung Bukit Baharu?", "ground_truth": { "answer": "Kampung Bukit Baharu", "outlier_distance_km": 13668.8, "second_furthest_km": 6077.3, "clarity_ratio": 2.25, "median_distance_km": 3449.7, "distances_to_centroid": { "Santo Amaro": 1956.8, "Villa del Rosario": 6077.3, "Ribeirão da Ilha": 3449.7, "Vila Andrade": 3091.9, "Kampung Bukit Baharu": 13668.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Santo Amaro: (-12.55°, -38.71°)", " Villa del Rosario: (7.83°, -72.47°)", " Ribeirão da Ilha: (-27.70°, -48.53°)", " Vila Andrade: (-23.63°, -46.73°)", " Kampung Bukit Baharu: (2.22°, 102.29°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kampung Bukit Baharu: 13668.8 km from centroid", " Villa del Rosario: 6077.3 km from centroid", " Ribeirão da Ilha: 3449.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kampung Bukit Baharu", "FINAL ANSWER: Kampung Bukit Baharu" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.73333, "lon": 144.8, "name": "Saint Albans" }, { "lat": -33.7457, "lon": 151.04764, "name": "West Pennant Hills" }, { "lat": -37.75405, "lon": 145.14864, "name": "Templestowe" }, { "lat": -37.82289, "lon": 147.61041, "name": "Bairnsdale" }, { "lat": 53.8426, "lon": -1.63754, "name": "Horsforth" } ], "question": "Which location is the geographic outlier among: Saint Albans, West Pennant Hills, Templestowe, Bairnsdale, Horsforth?", "ground_truth": { "answer": "Horsforth", "outlier_distance_km": 13561.9, "second_furthest_km": 3730.5, "clarity_ratio": 3.64, "median_distance_km": 3620.9, "distances_to_centroid": { "Saint Albans": 3400.6, "West Pennant Hills": 3730.5, "Templestowe": 3428.1, "Bairnsdale": 3620.9, "Horsforth": 13561.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saint Albans: (-37.73°, 144.80°)", " West Pennant Hills: (-33.75°, 151.05°)", " Templestowe: (-37.75°, 145.15°)", " Bairnsdale: (-37.82°, 147.61°)", " Horsforth: (53.84°, -1.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Horsforth: 13561.9 km from centroid", " West Pennant Hills: 3730.5 km from centroid", " Bairnsdale: 3620.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Horsforth", "FINAL ANSWER: Horsforth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.12056, "lon": 17.03761, "name": "Rejon placu Świętego Macieja" }, { "lat": 48.8162, "lon": 2.31393, "name": "Montrouge" }, { "lat": 52.51108, "lon": 4.67165, "name": "Heemskerk" }, { "lat": 36.82145, "lon": 14.95132, "name": "Rosolini" }, { "lat": -25.44141, "lon": 27.51114, "name": "Hartbeestfontein-A" } ], "question": "Which location is the geographic outlier among: Rejon placu Świętego Macieja, Montrouge, Heemskerk, Rosolini, Hartbeestfontein-A?", "ground_truth": { "answer": "Hartbeestfontein-A", "outlier_distance_km": 6645.1, "second_furthest_km": 2302.3, "clarity_ratio": 2.89, "median_distance_km": 2063.6, "distances_to_centroid": { "Rejon placu Świętego Macieja": 2063.6, "Montrouge": 2005.2, "Heemskerk": 2302.3, "Rosolini": 475.6, "Hartbeestfontein-A": 6645.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rejon placu Świętego Macieja: (51.12°, 17.04°)", " Montrouge: (48.82°, 2.31°)", " Heemskerk: (52.51°, 4.67°)", " Rosolini: (36.82°, 14.95°)", " Hartbeestfontein-A: (-25.44°, 27.51°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hartbeestfontein-A: 6645.1 km from centroid", " Heemskerk: 2302.3 km from centroid", " Rejon placu Świętego Macieja: 2063.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hartbeestfontein-A", "FINAL ANSWER: Hartbeestfontein-A" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -27.61025, "lon": 153.05388, "name": "Sunnybank Hills" }, { "lat": -25.54073, "lon": 152.70493, "name": "Maryborough" }, { "lat": -33.86667, "lon": 150.95, "name": "Fairfield" }, { "lat": -41.51603, "lon": 173.9528, "name": "Blenheim" }, { "lat": 45.78693, "lon": 4.9251, "name": "Vaulx-en-Velin" } ], "question": "Which location is the geographic outlier among: Sunnybank Hills, Maryborough, Fairfield, Blenheim, Vaulx-en-Velin?", "ground_truth": { "answer": "Vaulx-en-Velin", "outlier_distance_km": 13796.5, "second_furthest_km": 5245.2, "clarity_ratio": 2.63, "median_distance_km": 3060.8, "distances_to_centroid": { "Sunnybank Hills": 2933.3, "Maryborough": 2831.0, "Fairfield": 3060.8, "Blenheim": 5245.2, "Vaulx-en-Velin": 13796.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sunnybank Hills: (-27.61°, 153.05°)", " Maryborough: (-25.54°, 152.70°)", " Fairfield: (-33.87°, 150.95°)", " Blenheim: (-41.52°, 173.95°)", " Vaulx-en-Velin: (45.79°, 4.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Vaulx-en-Velin: 13796.5 km from centroid", " Blenheim: 5245.2 km from centroid", " Fairfield: 3060.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Vaulx-en-Velin", "FINAL ANSWER: Vaulx-en-Velin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.38333, "lon": 136.26667, "name": "Nagahama" }, { "lat": 34.86472, "lon": 117.55417, "name": "Zaozhuang" }, { "lat": 18.57506, "lon": 76.02186, "name": "Kallam" }, { "lat": 15.35116, "lon": 121.00393, "name": "Peñaranda" }, { "lat": 12.63056, "lon": 39.03472, "name": "Sek’ot’a" } ], "question": "Which location is the geographic outlier among: Nagahama, Zaozhuang, Kallam, Peñaranda, Sek’ot’a?", "ground_truth": { "answer": "Sek’ot’a", "outlier_distance_km": 6306.0, "second_furthest_km": 3915.0, "clarity_ratio": 1.61, "median_distance_km": 2570.5, "distances_to_centroid": { "Nagahama": 3915.0, "Zaozhuang": 2285.1, "Kallam": 2338.2, "Peñaranda": 2570.5, "Sek’ot’a": 6306.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nagahama: (35.38°, 136.27°)", " Zaozhuang: (34.86°, 117.55°)", " Kallam: (18.58°, 76.02°)", " Peñaranda: (15.35°, 121.00°)", " Sek’ot’a: (12.63°, 39.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sek’ot’a: 6306.0 km from centroid", " Nagahama: 3915.0 km from centroid", " Peñaranda: 2570.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sek’ot’a", "FINAL ANSWER: Sek’ot’a" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -9.89667, "lon": -39.02639, "name": "Canudos" }, { "lat": -7.86806, "lon": -37.97472, "name": "Flores" }, { "lat": -5.57667, "lon": -36.90861, "name": "Açu" }, { "lat": -37.15276, "lon": -58.48838, "name": "Ayacucho" }, { "lat": 34.84184, "lon": 116.55722, "name": "Shunhe" } ], "question": "Which location is the geographic outlier among: Canudos, Flores, Açu, Ayacucho, Shunhe?", "ground_truth": { "answer": "Shunhe", "outlier_distance_km": 13727.4, "second_furthest_km": 5970.1, "clarity_ratio": 2.3, "median_distance_km": 3115.0, "distances_to_centroid": { "Canudos": 3115.0, "Flores": 2976.6, "Açu": 2849.9, "Ayacucho": 5970.1, "Shunhe": 13727.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Canudos: (-9.90°, -39.03°)", " Flores: (-7.87°, -37.97°)", " Açu: (-5.58°, -36.91°)", " Ayacucho: (-37.15°, -58.49°)", " Shunhe: (34.84°, 116.56°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Shunhe: 13727.4 km from centroid", " Ayacucho: 5970.1 km from centroid", " Canudos: 3115.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Shunhe", "FINAL ANSWER: Shunhe" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -14.67806, "lon": -39.375, "name": "Itajuípe" }, { "lat": -16.735, "lon": -43.86167, "name": "Montes Claros" }, { "lat": -19.96722, "lon": -43.80417, "name": "Raposos" }, { "lat": -26.76389, "lon": -48.67167, "name": "Balneário Piçarras" }, { "lat": -38.13874, "lon": 176.24516, "name": "Rotorua" } ], "question": "Which location is the geographic outlier among: Itajuípe, Montes Claros, Raposos, Balneário Piçarras, Rotorua?", "ground_truth": { "answer": "Rotorua", "outlier_distance_km": 13176.3, "second_furthest_km": 4901.4, "clarity_ratio": 2.69, "median_distance_km": 4634.0, "distances_to_centroid": { "Itajuípe": 4245.9, "Montes Claros": 4634.0, "Raposos": 4537.4, "Balneário Piçarras": 4901.4, "Rotorua": 13176.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itajuípe: (-14.68°, -39.38°)", " Montes Claros: (-16.73°, -43.86°)", " Raposos: (-19.97°, -43.80°)", " Balneário Piçarras: (-26.76°, -48.67°)", " Rotorua: (-38.14°, 176.25°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rotorua: 13176.3 km from centroid", " Balneário Piçarras: 4901.4 km from centroid", " Montes Claros: 4634.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rotorua", "FINAL ANSWER: Rotorua" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 11.19152, "lon": 40.01675, "name": "Batī" }, { "lat": -26.53333, "lon": 29.06667, "name": "eMbalenhle" }, { "lat": 12.01667, "lon": 39.63333, "name": "Robīt" }, { "lat": -26.1466, "lon": 28.68322, "name": "Delmas" }, { "lat": 41.82649, "lon": -72.73009, "name": "Bloomfield" } ], "question": "Which location is the geographic outlier among: Batī, eMbalenhle, Robīt, Delmas, Bloomfield?", "ground_truth": { "answer": "Bloomfield", "outlier_distance_km": 9465.1, "second_furthest_km": 3661.1, "clarity_ratio": 2.59, "median_distance_km": 3604.6, "distances_to_centroid": { "Batī": 3140.1, "eMbalenhle": 3661.1, "Robīt": 3126.8, "Delmas": 3604.6, "Bloomfield": 9465.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Batī: (11.19°, 40.02°)", " eMbalenhle: (-26.53°, 29.07°)", " Robīt: (12.02°, 39.63°)", " Delmas: (-26.15°, 28.68°)", " Bloomfield: (41.83°, -72.73°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bloomfield: 9465.1 km from centroid", " eMbalenhle: 3661.1 km from centroid", " Delmas: 3604.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bloomfield", "FINAL ANSWER: Bloomfield" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.66663, "lon": -92.97464, "name": "Austin" }, { "lat": 43.73766, "lon": -79.34972, "name": "Banbury-Don Mills" }, { "lat": 35.40888, "lon": -80.58158, "name": "Concord" }, { "lat": 43.68417, "lon": -79.29936, "name": "East End-Danforth" }, { "lat": -41.51603, "lon": 173.9528, "name": "Blenheim" } ], "question": "Which location is the geographic outlier among: Austin, Banbury-Don Mills, Concord, East End-Danforth, Blenheim?", "ground_truth": { "answer": "Blenheim", "outlier_distance_km": 17028.0, "second_furthest_km": 5857.0, "clarity_ratio": 2.91, "median_distance_km": 4792.8, "distances_to_centroid": { "Austin": 5857.0, "Banbury-Don Mills": 4767.3, "Concord": 4792.8, "East End-Danforth": 4762.3, "Blenheim": 17028.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Austin: (43.67°, -92.97°)", " Banbury-Don Mills: (43.74°, -79.35°)", " Concord: (35.41°, -80.58°)", " East End-Danforth: (43.68°, -79.30°)", " Blenheim: (-41.52°, 173.95°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Blenheim: 17028.0 km from centroid", " Austin: 5857.0 km from centroid", " Concord: 4792.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Blenheim", "FINAL ANSWER: Blenheim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.13874, "lon": 176.24516, "name": "Rotorua" }, { "lat": -33.92893, "lon": 151.05111, "name": "Punchbowl" }, { "lat": -41.28374, "lon": 174.74141, "name": "Karori" }, { "lat": -33.73333, "lon": 150.88333, "name": "Quakers Hill" }, { "lat": 30.83481, "lon": 109.50499, "name": "Fengping" } ], "question": "Which location is the geographic outlier among: Rotorua, Punchbowl, Karori, Quakers Hill, Fengping?", "ground_truth": { "answer": "Fengping", "outlier_distance_km": 7559.7, "second_furthest_km": 2881.7, "clarity_ratio": 2.62, "median_distance_km": 2796.9, "distances_to_centroid": { "Rotorua": 2796.9, "Punchbowl": 1195.6, "Karori": 2881.7, "Quakers Hill": 1176.1, "Fengping": 7559.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Rotorua: (-38.14°, 176.25°)", " Punchbowl: (-33.93°, 151.05°)", " Karori: (-41.28°, 174.74°)", " Quakers Hill: (-33.73°, 150.88°)", " Fengping: (30.83°, 109.50°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Fengping: 7559.7 km from centroid", " Karori: 2881.7 km from centroid", " Rotorua: 2796.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Fengping", "FINAL ANSWER: Fengping" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 43.45777, "lon": -88.83733, "name": "Beaver Dam" }, { "lat": 25.94065, "lon": -80.2456, "name": "Carol City" }, { "lat": 40.04122, "lon": -75.12379, "name": "Olney" }, { "lat": 17.54528, "lon": -98.57599, "name": "Tlapa de Comonfort" }, { "lat": -34.03857, "lon": 151.10005, "name": "Miranda" } ], "question": "Which location is the geographic outlier among: Beaver Dam, Carol City, Olney, Tlapa de Comonfort, Miranda?", "ground_truth": { "answer": "Miranda", "outlier_distance_km": 18059.1, "second_furthest_km": 6337.7, "clarity_ratio": 2.85, "median_distance_km": 5441.6, "distances_to_centroid": { "Beaver Dam": 5441.6, "Carol City": 4370.8, "Olney": 4243.9, "Tlapa de Comonfort": 6337.7, "Miranda": 18059.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Beaver Dam: (43.46°, -88.84°)", " Carol City: (25.94°, -80.25°)", " Olney: (40.04°, -75.12°)", " Tlapa de Comonfort: (17.55°, -98.58°)", " Miranda: (-34.04°, 151.10°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Miranda: 18059.1 km from centroid", " Tlapa de Comonfort: 6337.7 km from centroid", " Beaver Dam: 5441.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Miranda", "FINAL ANSWER: Miranda" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 35.0907, "lon": -80.68618, "name": "Stallings" }, { "lat": 47.51659, "lon": -52.78135, "name": "Mount Pearl" }, { "lat": 33.88168, "lon": -118.11701, "name": "Bellflower" }, { "lat": 19.10059, "lon": -98.8788, "name": "Juchitepec" }, { "lat": -27.3171, "lon": 153.03097, "name": "Bracken Ridge" } ], "question": "Which location is the geographic outlier among: Stallings, Mount Pearl, Bellflower, Juchitepec, Bracken Ridge?", "ground_truth": { "answer": "Bracken Ridge", "outlier_distance_km": 18601.7, "second_furthest_km": 7676.2, "clarity_ratio": 2.42, "median_distance_km": 6159.6, "distances_to_centroid": { "Stallings": 4263.2, "Mount Pearl": 3112.4, "Bellflower": 7676.2, "Juchitepec": 6159.6, "Bracken Ridge": 18601.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Stallings: (35.09°, -80.69°)", " Mount Pearl: (47.52°, -52.78°)", " Bellflower: (33.88°, -118.12°)", " Juchitepec: (19.10°, -98.88°)", " Bracken Ridge: (-27.32°, 153.03°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bracken Ridge: 18601.7 km from centroid", " Bellflower: 7676.2 km from centroid", " Juchitepec: 6159.6 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": 5.65825, "lon": -0.25223, "name": "Taifa" }, { "lat": 31.21114, "lon": 31.05119, "name": "Sīdī Ghāzī" }, { "lat": 31.29443, "lon": 30.52248, "name": "Muţūbas" }, { "lat": 27.25738, "lon": 33.81291, "name": "Hurghada" }, { "lat": 41.95503, "lon": -87.94007, "name": "Bensenville" } ], "question": "Which location is the geographic outlier among: Taifa, Sīdī Ghāzī, Muţūbas, Hurghada, Bensenville?", "ground_truth": { "answer": "Bensenville", "outlier_distance_km": 7961.9, "second_furthest_km": 3187.8, "clarity_ratio": 2.5, "median_distance_km": 2891.5, "distances_to_centroid": { "Taifa": 2432.5, "Sīdī Ghāzī": 2891.5, "Muţūbas": 2841.4, "Hurghada": 3187.8, "Bensenville": 7961.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Taifa: (5.66°, -0.25°)", " Sīdī Ghāzī: (31.21°, 31.05°)", " Muţūbas: (31.29°, 30.52°)", " Hurghada: (27.26°, 33.81°)", " Bensenville: (41.96°, -87.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bensenville: 7961.9 km from centroid", " Hurghada: 3187.8 km from centroid", " Sīdī Ghāzī: 2891.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bensenville", "FINAL ANSWER: Bensenville" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 48.70311, "lon": 45.19611, "name": "Leninsk" }, { "lat": 52.83492, "lon": 13.81951, "name": "Eberswalde" }, { "lat": 51.47274, "lon": 58.45155, "name": "Gay" }, { "lat": 56.11095, "lon": 47.47755, "name": "Novocheboksarsk" }, { "lat": -0.45275, "lon": 39.64601, "name": "Garissa" } ], "question": "Which location is the geographic outlier among: Leninsk, Eberswalde, Gay, Novocheboksarsk, Garissa?", "ground_truth": { "answer": "Garissa", "outlier_distance_km": 4692.7, "second_furthest_km": 2366.5, "clarity_ratio": 1.98, "median_distance_km": 1714.8, "distances_to_centroid": { "Leninsk": 843.9, "Eberswalde": 2366.5, "Gay": 1714.8, "Novocheboksarsk": 1667.1, "Garissa": 4692.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Leninsk: (48.70°, 45.20°)", " Eberswalde: (52.83°, 13.82°)", " Gay: (51.47°, 58.45°)", " Novocheboksarsk: (56.11°, 47.48°)", " Garissa: (-0.45°, 39.65°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Garissa: 4692.7 km from centroid", " Eberswalde: 2366.5 km from centroid", " Gay: 1714.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Garissa", "FINAL ANSWER: Garissa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -19.80083, "lon": -41.71306, "name": "Ipanema" }, { "lat": -8.35806, "lon": -42.24667, "name": "São João do Piauí" }, { "lat": -37.15276, "lon": -58.48838, "name": "Ayacucho" }, { "lat": 2.77717, "lon": -75.25642, "name": "Rivera" }, { "lat": -37.62581, "lon": 144.92555, "name": "Roxburgh Park" } ], "question": "Which location is the geographic outlier among: Ipanema, São João do Piauí, Ayacucho, Rivera, Roxburgh Park?", "ground_truth": { "answer": "Roxburgh Park", "outlier_distance_km": 13253.8, "second_furthest_km": 7086.3, "clarity_ratio": 1.87, "median_distance_km": 4641.6, "distances_to_centroid": { "Ipanema": 2836.1, "São João do Piauí": 3247.8, "Ayacucho": 4641.6, "Rivera": 7086.3, "Roxburgh Park": 13253.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ipanema: (-19.80°, -41.71°)", " São João do Piauí: (-8.36°, -42.25°)", " Ayacucho: (-37.15°, -58.49°)", " Rivera: (2.78°, -75.26°)", " Roxburgh Park: (-37.63°, 144.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Roxburgh Park: 13253.8 km from centroid", " Rivera: 7086.3 km from centroid", " Ayacucho: 4641.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Roxburgh Park", "FINAL ANSWER: Roxburgh Park" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -3.43944, "lon": -39.14833, "name": "Paraipaba" }, { "lat": -14.06944, "lon": -42.475, "name": "Caetité" }, { "lat": 6.15515, "lon": -75.37371, "name": "Rionegro" }, { "lat": -3.47222, "lon": -51.19778, "name": "Anapu" }, { "lat": 36.63333, "lon": 139.98333, "name": "Hōshakuji" } ], "question": "Which location is the geographic outlier among: Paraipaba, Caetité, Rionegro, Anapu, Hōshakuji?", "ground_truth": { "answer": "Hōshakuji", "outlier_distance_km": 14697.9, "second_furthest_km": 6834.8, "clarity_ratio": 2.15, "median_distance_km": 4262.5, "distances_to_centroid": { "Paraipaba": 2963.6, "Caetité": 3783.3, "Rionegro": 6834.8, "Anapu": 4262.5, "Hōshakuji": 14697.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Paraipaba: (-3.44°, -39.15°)", " Caetité: (-14.07°, -42.48°)", " Rionegro: (6.16°, -75.37°)", " Anapu: (-3.47°, -51.20°)", " Hōshakuji: (36.63°, 139.98°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Hōshakuji: 14697.9 km from centroid", " Rionegro: 6834.8 km from centroid", " Anapu: 4262.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Hōshakuji", "FINAL ANSWER: Hōshakuji" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 54.09989, "lon": 35.34254, "name": "Sukhinichi" }, { "lat": 40.59144, "lon": -4.14738, "name": "San Lorenzo de El Escorial" }, { "lat": 60.74985, "lon": 72.85824, "name": "Pyt-Yakh" }, { "lat": 41.37732, "lon": 2.08809, "name": "Esplugues de Llobregat" }, { "lat": 38.49602, "lon": -121.40884, "name": "Florin" } ], "question": "Which location is the geographic outlier among: Sukhinichi, San Lorenzo de El Escorial, Pyt-Yakh, Esplugues de Llobregat, Florin?", "ground_truth": { "answer": "Florin", "outlier_distance_km": 8708.5, "second_furthest_km": 4888.6, "clarity_ratio": 1.78, "median_distance_km": 2783.2, "distances_to_centroid": { "Sukhinichi": 2783.2, "San Lorenzo de El Escorial": 724.9, "Pyt-Yakh": 4888.6, "Esplugues de Llobregat": 753.0, "Florin": 8708.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Sukhinichi: (54.10°, 35.34°)", " San Lorenzo de El Escorial: (40.59°, -4.15°)", " Pyt-Yakh: (60.75°, 72.86°)", " Esplugues de Llobregat: (41.38°, 2.09°)", " Florin: (38.50°, -121.41°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Florin: 8708.5 km from centroid", " Pyt-Yakh: 4888.6 km from centroid", " Sukhinichi: 2783.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Florin", "FINAL ANSWER: Florin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.22961, "lon": 8.91612, "name": "Porta Westfalica" }, { "lat": 41.40392, "lon": 2.20413, "name": "el Poblenou" }, { "lat": 52.13129, "lon": 11.63189, "name": "Magdeburg" }, { "lat": 53.86437, "lon": -1.68743, "name": "Yeadon" }, { "lat": 41.10172, "lon": -80.76452, "name": "Austintown" } ], "question": "Which location is the geographic outlier among: Porta Westfalica, el Poblenou, Magdeburg, Yeadon, Austintown?", "ground_truth": { "answer": "Austintown", "outlier_distance_km": 5318.9, "second_furthest_km": 1728.9, "clarity_ratio": 3.08, "median_distance_km": 1546.5, "distances_to_centroid": { "Porta Westfalica": 1546.5, "el Poblenou": 1341.5, "Magdeburg": 1728.9, "Yeadon": 956.9, "Austintown": 5318.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Porta Westfalica: (52.23°, 8.92°)", " el Poblenou: (41.40°, 2.20°)", " Magdeburg: (52.13°, 11.63°)", " Yeadon: (53.86°, -1.69°)", " Austintown: (41.10°, -80.76°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Austintown: 5318.9 km from centroid", " Magdeburg: 1728.9 km from centroid", " Porta Westfalica: 1546.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Austintown", "FINAL ANSWER: Austintown" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.8, "lon": 144.96667, "name": "Carlton" }, { "lat": -37.8676, "lon": 144.98099, "name": "Saint Kilda" }, { "lat": -33.92399, "lon": 151.22749, "name": "Kingsford" }, { "lat": -25.28762, "lon": 152.76936, "name": "Hervey Bay" }, { "lat": 43.42896, "lon": 39.92391, "name": "Adler" } ], "question": "Which location is the geographic outlier among: Carlton, Saint Kilda, Kingsford, Hervey Bay, Adler?", "ground_truth": { "answer": "Adler", "outlier_distance_km": 11146.7, "second_furthest_km": 2983.7, "clarity_ratio": 3.74, "median_distance_km": 2804.6, "distances_to_centroid": { "Carlton": 2798.3, "Saint Kilda": 2804.6, "Kingsford": 2983.7, "Hervey Bay": 2789.1, "Adler": 11146.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Carlton: (-37.80°, 144.97°)", " Saint Kilda: (-37.87°, 144.98°)", " Kingsford: (-33.92°, 151.23°)", " Hervey Bay: (-25.29°, 152.77°)", " Adler: (43.43°, 39.92°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Adler: 11146.7 km from centroid", " Kingsford: 2983.7 km from centroid", " Saint Kilda: 2804.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Adler", "FINAL ANSWER: Adler" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.01167, "lon": 17.9442, "name": "Saldanha" }, { "lat": -1.85238, "lon": 36.77683, "name": "Kajiado" }, { "lat": 7.85, "lon": 36.65, "name": "Āgaro" }, { "lat": 12.11451, "lon": 12.8262, "name": "Magumeri" }, { "lat": -37.96649, "lon": 145.2081, "name": "Dandenong North" } ], "question": "Which location is the geographic outlier among: Saldanha, Kajiado, Āgaro, Magumeri, Dandenong North?", "ground_truth": { "answer": "Dandenong North", "outlier_distance_km": 9746.7, "second_furthest_km": 4807.7, "clarity_ratio": 2.03, "median_distance_km": 4104.9, "distances_to_centroid": { "Saldanha": 4104.9, "Kajiado": 1741.9, "Āgaro": 2518.2, "Magumeri": 4807.7, "Dandenong North": 9746.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Saldanha: (-33.01°, 17.94°)", " Kajiado: (-1.85°, 36.78°)", " Āgaro: (7.85°, 36.65°)", " Magumeri: (12.11°, 12.83°)", " Dandenong North: (-37.97°, 145.21°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Dandenong North: 9746.7 km from centroid", " Magumeri: 4807.7 km from centroid", " Saldanha: 4104.9 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": -26.23806, "lon": -51.07833, "name": "Porto União" }, { "lat": 4.43139, "lon": -61.14639, "name": "Pacaraima" }, { "lat": -7.94083, "lon": -34.87306, "name": "Paulista" }, { "lat": -14.63126, "lon": -69.44638, "name": "La Rinconada" }, { "lat": 1.72837, "lon": 128.00948, "name": "Tobelo" } ], "question": "Which location is the geographic outlier among: Porto União, Pacaraima, Paulista, La Rinconada, Tobelo?", "ground_truth": { "answer": "Tobelo", "outlier_distance_km": 16146.3, "second_furthest_km": 5665.4, "clarity_ratio": 2.85, "median_distance_km": 5027.6, "distances_to_centroid": { "Porto União": 4031.7, "Pacaraima": 5027.6, "Paulista": 1890.1, "La Rinconada": 5665.4, "Tobelo": 16146.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Porto União: (-26.24°, -51.08°)", " Pacaraima: (4.43°, -61.15°)", " Paulista: (-7.94°, -34.87°)", " La Rinconada: (-14.63°, -69.45°)", " Tobelo: (1.73°, 128.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tobelo: 16146.3 km from centroid", " La Rinconada: 5665.4 km from centroid", " Pacaraima: 5027.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tobelo", "FINAL ANSWER: Tobelo" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 45.80463, "lon": 13.53292, "name": "Monfalcone" }, { "lat": 53.86893, "lon": 10.68729, "name": "Lübeck" }, { "lat": 51.66931, "lon": -4.04163, "name": "Gorseinon" }, { "lat": 62.26537, "lon": 74.47906, "name": "Kogalym" }, { "lat": -8.44869, "lon": 115.60621, "name": "Amlapura city" } ], "question": "Which location is the geographic outlier among: Monfalcone, Lübeck, Gorseinon, Kogalym, Amlapura city?", "ground_truth": { "answer": "Amlapura city", "outlier_distance_km": 9274.5, "second_furthest_km": 3660.8, "clarity_ratio": 2.53, "median_distance_km": 3188.2, "distances_to_centroid": { "Monfalcone": 2350.3, "Lübeck": 2723.6, "Gorseinon": 3660.8, "Kogalym": 3188.2, "Amlapura city": 9274.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Monfalcone: (45.80°, 13.53°)", " Lübeck: (53.87°, 10.69°)", " Gorseinon: (51.67°, -4.04°)", " Kogalym: (62.27°, 74.48°)", " Amlapura city: (-8.45°, 115.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Amlapura city: 9274.5 km from centroid", " Gorseinon: 3660.8 km from centroid", " Kogalym: 3188.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Amlapura city", "FINAL ANSWER: Amlapura city" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.92399, "lon": 151.22749, "name": "Kingsford" }, { "lat": -37.60075, "lon": 145.09555, "name": "Mernda" }, { "lat": -38.02388, "lon": 144.40617, "name": "Lara" }, { "lat": -37.70988, "lon": 144.75483, "name": "Taylors Hill" }, { "lat": -27.24179, "lon": 27.57422, "name": "Koppies" } ], "question": "Which location is the geographic outlier among: Kingsford, Mernda, Lara, Taylors Hill, Koppies?", "ground_truth": { "answer": "Koppies", "outlier_distance_km": 8738.5, "second_furthest_km": 2618.4, "clarity_ratio": 3.34, "median_distance_km": 2033.4, "distances_to_centroid": { "Kingsford": 2618.4, "Mernda": 2033.4, "Lara": 1975.0, "Taylors Hill": 2003.9, "Koppies": 8738.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kingsford: (-33.92°, 151.23°)", " Mernda: (-37.60°, 145.10°)", " Lara: (-38.02°, 144.41°)", " Taylors Hill: (-37.71°, 144.75°)", " Koppies: (-27.24°, 27.57°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Koppies: 8738.5 km from centroid", " Kingsford: 2618.4 km from centroid", " Mernda: 2033.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Koppies", "FINAL ANSWER: Koppies" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -10.32, "lon": -36.57944, "name": "Neópolis" }, { "lat": -23.44077, "lon": -46.73774, "name": "Jaraguá" }, { "lat": -27.21787, "lon": -61.18738, "name": "Charata" }, { "lat": -6.96333, "lon": -35.69167, "name": "Areia" }, { "lat": 14.40076, "lon": 37.93399, "name": "Sheraro" } ], "question": "Which location is the geographic outlier among: Neópolis, Jaraguá, Charata, Areia, Sheraro?", "ground_truth": { "answer": "Sheraro", "outlier_distance_km": 7831.1, "second_furthest_km": 3882.4, "clarity_ratio": 2.02, "median_distance_km": 2399.9, "distances_to_centroid": { "Neópolis": 889.5, "Jaraguá": 2399.9, "Charata": 3882.4, "Areia": 897.7, "Sheraro": 7831.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Neópolis: (-10.32°, -36.58°)", " Jaraguá: (-23.44°, -46.74°)", " Charata: (-27.22°, -61.19°)", " Areia: (-6.96°, -35.69°)", " Sheraro: (14.40°, 37.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Sheraro: 7831.1 km from centroid", " Charata: 3882.4 km from centroid", " Jaraguá: 2399.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Sheraro", "FINAL ANSWER: Sheraro" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.00166, "lon": 13.6488, "name": "Freital" }, { "lat": 48.98994, "lon": 2.1699, "name": "Herblay-sur-Seine" }, { "lat": 50.95753, "lon": 6.93611, "name": "Neuehrenfeld" }, { "lat": 55.58183, "lon": 38.91994, "name": "Kurovskoye" }, { "lat": 28.91154, "lon": 79.52009, "name": "Kichha" } ], "question": "Which location is the geographic outlier among: Freital, Herblay-sur-Seine, Neuehrenfeld, Kurovskoye, Kichha?", "ground_truth": { "answer": "Kichha", "outlier_distance_km": 4822.9, "second_furthest_km": 1940.0, "clarity_ratio": 2.49, "median_distance_km": 1605.5, "distances_to_centroid": { "Freital": 1146.5, "Herblay-sur-Seine": 1940.0, "Neuehrenfeld": 1605.5, "Kurovskoye": 1198.2, "Kichha": 4822.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Freital: (51.00°, 13.65°)", " Herblay-sur-Seine: (48.99°, 2.17°)", " Neuehrenfeld: (50.96°, 6.94°)", " Kurovskoye: (55.58°, 38.92°)", " Kichha: (28.91°, 79.52°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kichha: 4822.9 km from centroid", " Herblay-sur-Seine: 1940.0 km from centroid", " Neuehrenfeld: 1605.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kichha", "FINAL ANSWER: Kichha" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -38.16604, "lon": 145.13643, "name": "Frankston South" }, { "lat": -37.66667, "lon": 145.01667, "name": "Lalor" }, { "lat": -33.9681, "lon": 151.13564, "name": "Kogarah" }, { "lat": -28.00274, "lon": 153.42999, "name": "Surfers Paradise" }, { "lat": 56.03715, "lon": 93.12684, "name": "Berëzovka" } ], "question": "Which location is the geographic outlier among: Frankston South, Lalor, Kogarah, Surfers Paradise, Berëzovka?", "ground_truth": { "answer": "Berëzovka", "outlier_distance_km": 9053.5, "second_furthest_km": 2535.7, "clarity_ratio": 3.57, "median_distance_km": 2479.8, "distances_to_centroid": { "Frankston South": 2535.7, "Lalor": 2479.8, "Kogarah": 2382.1, "Surfers Paradise": 2080.6, "Berëzovka": 9053.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Frankston South: (-38.17°, 145.14°)", " Lalor: (-37.67°, 145.02°)", " Kogarah: (-33.97°, 151.14°)", " Surfers Paradise: (-28.00°, 153.43°)", " Berëzovka: (56.04°, 93.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Berëzovka: 9053.5 km from centroid", " Frankston South: 2535.7 km from centroid", " Lalor: 2479.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Berëzovka", "FINAL ANSWER: Berëzovka" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -7.40056, "lon": -79.57139, "name": "Pacasmayo" }, { "lat": 5.06692, "lon": -74.59499, "name": "Guaduas" }, { "lat": -24.4875, "lon": -47.84361, "name": "Registro" }, { "lat": 3.23114, "lon": -76.41668, "name": "Puerto Tejada" }, { "lat": -28.41789, "lon": 32.18483, "name": "Mtubatuba" } ], "question": "Which location is the geographic outlier among: Pacasmayo, Guaduas, Registro, Puerto Tejada, Mtubatuba?", "ground_truth": { "answer": "Mtubatuba", "outlier_distance_km": 8628.4, "second_furthest_km": 3368.1, "clarity_ratio": 2.56, "median_distance_km": 3346.5, "distances_to_centroid": { "Pacasmayo": 3346.5, "Guaduas": 3291.8, "Registro": 1573.3, "Puerto Tejada": 3368.1, "Mtubatuba": 8628.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Pacasmayo: (-7.40°, -79.57°)", " Guaduas: (5.07°, -74.59°)", " Registro: (-24.49°, -47.84°)", " Puerto Tejada: (3.23°, -76.42°)", " Mtubatuba: (-28.42°, 32.18°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Mtubatuba: 8628.4 km from centroid", " Puerto Tejada: 3368.1 km from centroid", " Pacasmayo: 3346.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Mtubatuba", "FINAL ANSWER: Mtubatuba" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 19.02681, "lon": 74.71487, "name": "Ārangaon" }, { "lat": 14.9127, "lon": 120.56659, "name": "Santa Cruz" }, { "lat": 34.06153, "lon": 108.62905, "name": "Yuxia" }, { "lat": 34.38889, "lon": 118.05, "name": "Chenlou" }, { "lat": 19.60833, "lon": -99.16944, "name": "Buenavista" } ], "question": "Which location is the geographic outlier among: Ārangaon, Santa Cruz, Yuxia, Chenlou, Buenavista?", "ground_truth": { "answer": "Buenavista", "outlier_distance_km": 14814.0, "second_furthest_km": 5921.3, "clarity_ratio": 2.5, "median_distance_km": 5239.8, "distances_to_centroid": { "Ārangaon": 1206.7, "Santa Cruz": 5921.3, "Yuxia": 4374.1, "Chenlou": 5239.8, "Buenavista": 14814.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ārangaon: (19.03°, 74.71°)", " Santa Cruz: (14.91°, 120.57°)", " Yuxia: (34.06°, 108.63°)", " Chenlou: (34.39°, 118.05°)", " Buenavista: (19.61°, -99.17°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Buenavista: 14814.0 km from centroid", " Santa Cruz: 5921.3 km from centroid", " Chenlou: 5239.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Buenavista", "FINAL ANSWER: Buenavista" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.96572, "lon": 10.56111, "name": "Uelzen" }, { "lat": 45.55301, "lon": 9.29907, "name": "Brugherio" }, { "lat": 52.14, "lon": 5.58472, "name": "Barneveld" }, { "lat": 45.44207, "lon": 9.09445, "name": "Cesano Boscone" }, { "lat": 20.52353, "lon": -100.8157, "name": "Celaya" } ], "question": "Which location is the geographic outlier among: Uelzen, Brugherio, Barneveld, Cesano Boscone, Celaya?", "ground_truth": { "answer": "Celaya", "outlier_distance_km": 8268.7, "second_furthest_km": 2052.2, "clarity_ratio": 4.03, "median_distance_km": 1801.6, "distances_to_centroid": { "Uelzen": 2052.2, "Brugherio": 1801.6, "Barneveld": 1708.3, "Cesano Boscone": 1785.7, "Celaya": 8268.7 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Uelzen: (52.97°, 10.56°)", " Brugherio: (45.55°, 9.30°)", " Barneveld: (52.14°, 5.58°)", " Cesano Boscone: (45.44°, 9.09°)", " Celaya: (20.52°, -100.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Celaya: 8268.7 km from centroid", " Uelzen: 2052.2 km from centroid", " Brugherio: 1801.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Celaya", "FINAL ANSWER: Celaya" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 52.89, "lon": 4.74028, "name": "Julianadorp" }, { "lat": 51.965, "lon": 6.28889, "name": "Doetinchem" }, { "lat": 49.58333, "lon": 3.0, "name": "Noyon" }, { "lat": 42.95488, "lon": 12.70268, "name": "Foligno" }, { "lat": 9.56561, "lon": 36.63569, "name": "Gutin" } ], "question": "Which location is the geographic outlier among: Julianadorp, Doetinchem, Noyon, Foligno, Gutin?", "ground_truth": { "answer": "Gutin", "outlier_distance_km": 4247.3, "second_furthest_km": 1410.3, "clarity_ratio": 3.01, "median_distance_km": 1271.4, "distances_to_centroid": { "Julianadorp": 1410.3, "Doetinchem": 1271.4, "Noyon": 1180.5, "Foligno": 173.8, "Gutin": 4247.3 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Julianadorp: (52.89°, 4.74°)", " Doetinchem: (51.97°, 6.29°)", " Noyon: (49.58°, 3.00°)", " Foligno: (42.95°, 12.70°)", " Gutin: (9.57°, 36.64°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Gutin: 4247.3 km from centroid", " Julianadorp: 1410.3 km from centroid", " Doetinchem: 1271.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Gutin", "FINAL ANSWER: Gutin" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 51.33568, "lon": 1.41797, "name": "Ramsgate" }, { "lat": 41.89184, "lon": 48.41247, "name": "Belidzhi" }, { "lat": 43.66141, "lon": 10.63067, "name": "Pontedera" }, { "lat": 50.72374, "lon": 2.53729, "name": "Hazebrouck" }, { "lat": 8.56102, "lon": 77.97214, "name": "Nazareth" } ], "question": "Which location is the geographic outlier among: Ramsgate, Belidzhi, Pontedera, Hazebrouck, Nazareth?", "ground_truth": { "answer": "Nazareth", "outlier_distance_km": 5996.9, "second_furthest_km": 2468.2, "clarity_ratio": 2.43, "median_distance_km": 2369.8, "distances_to_centroid": { "Ramsgate": 2468.2, "Belidzhi": 1729.1, "Pontedera": 1540.8, "Hazebrouck": 2369.8, "Nazareth": 5996.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Ramsgate: (51.34°, 1.42°)", " Belidzhi: (41.89°, 48.41°)", " Pontedera: (43.66°, 10.63°)", " Hazebrouck: (50.72°, 2.54°)", " Nazareth: (8.56°, 77.97°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Nazareth: 5996.9 km from centroid", " Ramsgate: 2468.2 km from centroid", " Hazebrouck: 2369.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Nazareth", "FINAL ANSWER: Nazareth" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -21.66917, "lon": -42.07611, "name": "Itaocara" }, { "lat": -22.50917, "lon": -48.55778, "name": "Igaraçu do Tietê" }, { "lat": -3.79833, "lon": -40.26056, "name": "Forquilha" }, { "lat": -15.84003, "lon": -70.02198, "name": "Puno" }, { "lat": 13.69157, "lon": 99.92982, "name": "Bang Phae" } ], "question": "Which location is the geographic outlier among: Itaocara, Igaraçu do Tietê, Forquilha, Puno, Bang Phae?", "ground_truth": { "answer": "Bang Phae", "outlier_distance_km": 13502.1, "second_furthest_km": 5426.5, "clarity_ratio": 2.49, "median_distance_km": 3321.2, "distances_to_centroid": { "Itaocara": 2669.3, "Igaraçu do Tietê": 3321.2, "Forquilha": 2319.2, "Puno": 5426.5, "Bang Phae": 13502.1 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Itaocara: (-21.67°, -42.08°)", " Igaraçu do Tietê: (-22.51°, -48.56°)", " Forquilha: (-3.80°, -40.26°)", " Puno: (-15.84°, -70.02°)", " Bang Phae: (13.69°, 99.93°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bang Phae: 13502.1 km from centroid", " Puno: 5426.5 km from centroid", " Igaraçu do Tietê: 3321.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bang Phae", "FINAL ANSWER: Bang Phae" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.55, "lon": 37.48333, "name": "Dembech’a" }, { "lat": 10.16756, "lon": 12.73684, "name": "Gombi" }, { "lat": 9.92849, "lon": 8.89212, "name": "Jos" }, { "lat": 29.85, "lon": 31.26667, "name": "Al Badrashayn" }, { "lat": -27.25204, "lon": 152.99226, "name": "Kallangur" } ], "question": "Which location is the geographic outlier among: Dembech’a, Gombi, Jos, Al Badrashayn, Kallangur?", "ground_truth": { "answer": "Kallangur", "outlier_distance_km": 11758.5, "second_furthest_km": 4390.0, "clarity_ratio": 2.68, "median_distance_km": 3970.3, "distances_to_centroid": { "Dembech’a": 1304.3, "Gombi": 3970.3, "Jos": 4390.0, "Al Badrashayn": 3157.6, "Kallangur": 11758.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Dembech’a: (10.55°, 37.48°)", " Gombi: (10.17°, 12.74°)", " Jos: (9.93°, 8.89°)", " Al Badrashayn: (29.85°, 31.27°)", " Kallangur: (-27.25°, 152.99°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Kallangur: 11758.5 km from centroid", " Jos: 4390.0 km from centroid", " Gombi: 3970.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Kallangur", "FINAL ANSWER: Kallangur" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 10.01636, "lon": 76.34168, "name": "Kakkanad" }, { "lat": 14.31812, "lon": 120.76609, "name": "Naic" }, { "lat": 28.9629, "lon": 106.92844, "name": "Wansheng" }, { "lat": 10.1624, "lon": 123.7076, "name": "San Fernando" }, { "lat": -3.54281, "lon": -45.60852, "name": "Bom Jardim" } ], "question": "Which location is the geographic outlier among: Kakkanad, Naic, Wansheng, San Fernando, Bom Jardim?", "ground_truth": { "answer": "Bom Jardim", "outlier_distance_km": 13571.8, "second_furthest_km": 5157.4, "clarity_ratio": 2.63, "median_distance_km": 4801.0, "distances_to_centroid": { "Kakkanad": 218.9, "Naic": 4801.0, "Wansheng": 3677.6, "San Fernando": 5157.4, "Bom Jardim": 13571.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kakkanad: (10.02°, 76.34°)", " Naic: (14.32°, 120.77°)", " Wansheng: (28.96°, 106.93°)", " San Fernando: (10.16°, 123.71°)", " Bom Jardim: (-3.54°, -45.61°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Bom Jardim: 13571.8 km from centroid", " San Fernando: 5157.4 km from centroid", " Naic: 4801.0 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Bom Jardim", "FINAL ANSWER: Bom Jardim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.70365, "lon": -89.40731, "name": "Washington" }, { "lat": 38.77261, "lon": -77.22109, "name": "West Springfield" }, { "lat": 38.88584, "lon": -94.53301, "name": "Grandview" }, { "lat": 22.74678, "lon": -102.5188, "name": "Guadalupe" }, { "lat": -4.23116, "lon": -69.93858, "name": "Tabatinga" } ], "question": "Which location is the geographic outlier among: Washington, West Springfield, Grandview, Guadalupe, Tabatinga?", "ground_truth": { "answer": "Tabatinga", "outlier_distance_km": 3949.4, "second_furthest_km": 1670.6, "clarity_ratio": 2.36, "median_distance_km": 1543.9, "distances_to_centroid": { "Washington": 1502.3, "West Springfield": 1543.9, "Grandview": 1470.6, "Guadalupe": 1670.6, "Tabatinga": 3949.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Washington: (40.70°, -89.41°)", " West Springfield: (38.77°, -77.22°)", " Grandview: (38.89°, -94.53°)", " Guadalupe: (22.75°, -102.52°)", " Tabatinga: (-4.23°, -69.94°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Tabatinga: 3949.4 km from centroid", " Guadalupe: 1670.6 km from centroid", " West Springfield: 1543.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Tabatinga", "FINAL ANSWER: Tabatinga" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 59.70056, "lon": 30.78472, "name": "Nikol’skoye" }, { "lat": 51.37, "lon": 6.16806, "name": "Venlo" }, { "lat": 28.92313, "lon": -13.66579, "name": "Puerto del Carmen" }, { "lat": 28.31122, "lon": -16.41276, "name": "Güimar" }, { "lat": 33.59259, "lon": -84.67294, "name": "South Fulton" } ], "question": "Which location is the geographic outlier among: Nikol’skoye, Venlo, Puerto del Carmen, Güimar, South Fulton?", "ground_truth": { "answer": "South Fulton", "outlier_distance_km": 6029.0, "second_furthest_km": 3830.2, "clarity_ratio": 1.57, "median_distance_km": 2066.2, "distances_to_centroid": { "Nikol’skoye": 3830.2, "Venlo": 2066.2, "Puerto del Carmen": 1285.5, "Güimar": 1344.2, "South Fulton": 6029.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Nikol’skoye: (59.70°, 30.78°)", " Venlo: (51.37°, 6.17°)", " Puerto del Carmen: (28.92°, -13.67°)", " Güimar: (28.31°, -16.41°)", " South Fulton: (33.59°, -84.67°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " South Fulton: 6029.0 km from centroid", " Nikol’skoye: 3830.2 km from centroid", " Venlo: 2066.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: South Fulton", "FINAL ANSWER: South Fulton" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.82289, "lon": 147.61041, "name": "Bairnsdale" }, { "lat": -37.58333, "lon": 145.03333, "name": "Wollert" }, { "lat": -38.09968, "lon": 145.17248, "name": "Carrum Downs" }, { "lat": -43.58333, "lon": 172.38333, "name": "Rolleston" }, { "lat": 27.06309, "lon": 31.34425, "name": "As Sāḩil" } ], "question": "Which location is the geographic outlier among: Bairnsdale, Wollert, Carrum Downs, Rolleston, As Sāḩil?", "ground_truth": { "answer": "As Sāḩil", "outlier_distance_km": 11925.6, "second_furthest_km": 4408.5, "clarity_ratio": 2.71, "median_distance_km": 2238.6, "distances_to_centroid": { "Bairnsdale": 2238.6, "Wollert": 2032.9, "Carrum Downs": 2075.8, "Rolleston": 4408.5, "As Sāḩil": 11925.6 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bairnsdale: (-37.82°, 147.61°)", " Wollert: (-37.58°, 145.03°)", " Carrum Downs: (-38.10°, 145.17°)", " Rolleston: (-43.58°, 172.38°)", " As Sāḩil: (27.06°, 31.34°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " As Sāḩil: 11925.6 km from centroid", " Rolleston: 4408.5 km from centroid", " Bairnsdale: 2238.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: As Sāḩil", "FINAL ANSWER: As Sāḩil" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.85677, "lon": -74.12848, "name": "Passaic" }, { "lat": 20.06417, "lon": -98.71722, "name": "La Providencia Siglo XXI" }, { "lat": 38.98872, "lon": -76.98136, "name": "Langley Park" }, { "lat": 40.8351, "lon": -73.13122, "name": "Lake Ronkonkoma" }, { "lat": -28.21298, "lon": 153.53634, "name": "Banora Point" } ], "question": "Which location is the geographic outlier among: Passaic, La Providencia Siglo XXI, Langley Park, Lake Ronkonkoma, Banora Point?", "ground_truth": { "answer": "Banora Point", "outlier_distance_km": 19036.5, "second_furthest_km": 6669.1, "clarity_ratio": 2.85, "median_distance_km": 4456.5, "distances_to_centroid": { "Passaic": 4269.2, "La Providencia Siglo XXI": 6669.1, "Langley Park": 4456.5, "Lake Ronkonkoma": 4188.1, "Banora Point": 19036.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Passaic: (40.86°, -74.13°)", " La Providencia Siglo XXI: (20.06°, -98.72°)", " Langley Park: (38.99°, -76.98°)", " Lake Ronkonkoma: (40.84°, -73.13°)", " Banora Point: (-28.21°, 153.54°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Banora Point: 19036.5 km from centroid", " La Providencia Siglo XXI: 6669.1 km from centroid", " Langley Park: 4456.5 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": -33.88333, "lon": 151.1, "name": "Burwood" }, { "lat": -32.05251, "lon": 115.88782, "name": "Willetton" }, { "lat": -43.53333, "lon": 172.63333, "name": "Christchurch" }, { "lat": -33.32711, "lon": 115.64137, "name": "Bunbury" }, { "lat": 33.93807, "lon": -118.35258, "name": "Lennox" } ], "question": "Which location is the geographic outlier among: Burwood, Willetton, Christchurch, Bunbury, Lennox?", "ground_truth": { "answer": "Lennox", "outlier_distance_km": 17158.0, "second_furthest_km": 7991.3, "clarity_ratio": 2.15, "median_distance_km": 6311.4, "distances_to_centroid": { "Burwood": 6311.4, "Willetton": 3036.9, "Christchurch": 7991.3, "Bunbury": 3054.6, "Lennox": 17158.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Burwood: (-33.88°, 151.10°)", " Willetton: (-32.05°, 115.89°)", " Christchurch: (-43.53°, 172.63°)", " Bunbury: (-33.33°, 115.64°)", " Lennox: (33.94°, -118.35°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Lennox: 17158.0 km from centroid", " Christchurch: 7991.3 km from centroid", " Burwood: 6311.4 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Lennox", "FINAL ANSWER: Lennox" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -33.76667, "lon": 150.91667, "name": "Blacktown" }, { "lat": -40.95972, "lon": 175.6575, "name": "Masterton" }, { "lat": -32.06003, "lon": 115.955, "name": "Thornlie" }, { "lat": -33.9209, "lon": 151.12506, "name": "Earlwood" }, { "lat": 50.07139, "lon": 8.85123, "name": "Obertshausen" } ], "question": "Which location is the geographic outlier among: Blacktown, Masterton, Thornlie, Earlwood, Obertshausen?", "ground_truth": { "answer": "Obertshausen", "outlier_distance_km": 13078.9, "second_furthest_km": 5795.6, "clarity_ratio": 2.26, "median_distance_km": 3507.3, "distances_to_centroid": { "Blacktown": 3483.0, "Masterton": 5795.6, "Thornlie": 1614.9, "Earlwood": 3507.3, "Obertshausen": 13078.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Blacktown: (-33.77°, 150.92°)", " Masterton: (-40.96°, 175.66°)", " Thornlie: (-32.06°, 115.95°)", " Earlwood: (-33.92°, 151.13°)", " Obertshausen: (50.07°, 8.85°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Obertshausen: 13078.9 km from centroid", " Masterton: 5795.6 km from centroid", " Earlwood: 3507.3 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Obertshausen", "FINAL ANSWER: Obertshausen" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 53.05962, "lon": 60.64125, "name": "Kartaly" }, { "lat": 50.78351, "lon": -1.09071, "name": "Southsea" }, { "lat": 43.24622, "lon": 5.39788, "name": "Mazargues" }, { "lat": 50.41342, "lon": 36.92537, "name": "Shebekino" }, { "lat": 8.96727, "lon": 76.54188, "name": "Chavara" } ], "question": "Which location is the geographic outlier among: Kartaly, Southsea, Mazargues, Shebekino, Chavara?", "ground_truth": { "answer": "Chavara", "outlier_distance_km": 5379.8, "second_furthest_km": 2991.3, "clarity_ratio": 1.8, "median_distance_km": 2487.7, "distances_to_centroid": { "Kartaly": 2276.7, "Southsea": 2991.3, "Mazargues": 2487.7, "Shebekino": 1018.5, "Chavara": 5379.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kartaly: (53.06°, 60.64°)", " Southsea: (50.78°, -1.09°)", " Mazargues: (43.25°, 5.40°)", " Shebekino: (50.41°, 36.93°)", " Chavara: (8.97°, 76.54°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Chavara: 5379.8 km from centroid", " Southsea: 2991.3 km from centroid", " Mazargues: 2487.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Chavara", "FINAL ANSWER: Chavara" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 38.81144, "lon": -89.95316, "name": "Edwardsville" }, { "lat": 42.13919, "lon": -87.92896, "name": "Wheeling" }, { "lat": 38.25424, "lon": -85.75941, "name": "Louisville" }, { "lat": 40.57455, "lon": -74.30209, "name": "Colonia" }, { "lat": -8.87556, "lon": -36.36667, "name": "São João" } ], "question": "Which location is the geographic outlier among: Edwardsville, Wheeling, Louisville, Colonia, São João?", "ground_truth": { "answer": "São João", "outlier_distance_km": 5980.0, "second_furthest_km": 1768.9, "clarity_ratio": 3.38, "median_distance_km": 1679.7, "distances_to_centroid": { "Edwardsville": 1679.7, "Wheeling": 1768.9, "Louisville": 1343.5, "Colonia": 1156.8, "São João": 5980.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Edwardsville: (38.81°, -89.95°)", " Wheeling: (42.14°, -87.93°)", " Louisville: (38.25°, -85.76°)", " Colonia: (40.57°, -74.30°)", " São João: (-8.88°, -36.37°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " São João: 5980.0 km from centroid", " Wheeling: 1768.9 km from centroid", " Edwardsville: 1679.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: São João", "FINAL ANSWER: São João" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 34.69926, "lon": -86.74833, "name": "Madison" }, { "lat": 31.87149, "lon": -116.60071, "name": "Ensenada" }, { "lat": 37.52021, "lon": -122.2758, "name": "Belmont" }, { "lat": 39.28844, "lon": -77.20387, "name": "Damascus" }, { "lat": -20.42833, "lon": -47.82417, "name": "Guará" } ], "question": "Which location is the geographic outlier among: Madison, Ensenada, Belmont, Damascus, Guará?", "ground_truth": { "answer": "Guará", "outlier_distance_km": 6781.9, "second_furthest_km": 3360.5, "clarity_ratio": 2.02, "median_distance_km": 2708.5, "distances_to_centroid": { "Madison": 1170.4, "Ensenada": 2708.5, "Belmont": 3360.5, "Damascus": 2034.6, "Guará": 6781.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Madison: (34.70°, -86.75°)", " Ensenada: (31.87°, -116.60°)", " Belmont: (37.52°, -122.28°)", " Damascus: (39.29°, -77.20°)", " Guará: (-20.43°, -47.82°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Guará: 6781.9 km from centroid", " Belmont: 3360.5 km from centroid", " Ensenada: 2708.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Guará", "FINAL ANSWER: Guará" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 40.87822, "lon": 14.14352, "name": "Quarto" }, { "lat": 41.38125, "lon": 2.11744, "name": "la Maternitat i Sant Ramon" }, { "lat": 48.79947, "lon": 9.79809, "name": "Schwäbisch Gmünd" }, { "lat": 50.94159, "lon": -2.63211, "name": "Yeovil" }, { "lat": -4.25667, "lon": -43.01278, "name": "Coelho Neto" } ], "question": "Which location is the geographic outlier among: Quarto, la Maternitat i Sant Ramon, Schwäbisch Gmünd, Yeovil, Coelho Neto?", "ground_truth": { "answer": "Coelho Neto", "outlier_distance_km": 6014.2, "second_furthest_km": 1850.9, "clarity_ratio": 3.25, "median_distance_km": 1714.7, "distances_to_centroid": { "Quarto": 1681.6, "la Maternitat i Sant Ramon": 834.2, "Schwäbisch Gmünd": 1850.9, "Yeovil": 1714.7, "Coelho Neto": 6014.2 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Quarto: (40.88°, 14.14°)", " la Maternitat i Sant Ramon: (41.38°, 2.12°)", " Schwäbisch Gmünd: (48.80°, 9.80°)", " Yeovil: (50.94°, -2.63°)", " Coelho Neto: (-4.26°, -43.01°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Coelho Neto: 6014.2 km from centroid", " Schwäbisch Gmünd: 1850.9 km from centroid", " Yeovil: 1714.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Coelho Neto", "FINAL ANSWER: Coelho Neto" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -37.74981, "lon": 144.9109, "name": "Essendon" }, { "lat": -37.96944, "lon": 145.04806, "name": "Cheltenham" }, { "lat": -37.83382, "lon": 144.93834, "name": "City of Port Phillip" }, { "lat": -33.76667, "lon": 150.91667, "name": "Blacktown" }, { "lat": 7.84855, "lon": 4.32981, "name": "Inisa" } ], "question": "Which location is the geographic outlier among: Essendon, Cheltenham, City of Port Phillip, Blacktown, Inisa?", "ground_truth": { "answer": "Inisa", "outlier_distance_km": 12739.5, "second_furthest_km": 3193.2, "clarity_ratio": 3.99, "median_distance_km": 2746.2, "distances_to_centroid": { "Essendon": 2727.9, "Cheltenham": 2746.2, "City of Port Phillip": 2732.7, "Blacktown": 3193.2, "Inisa": 12739.5 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Essendon: (-37.75°, 144.91°)", " Cheltenham: (-37.97°, 145.05°)", " City of Port Phillip: (-37.83°, 144.94°)", " Blacktown: (-33.77°, 150.92°)", " Inisa: (7.85°, 4.33°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Inisa: 12739.5 km from centroid", " Blacktown: 3193.2 km from centroid", " Cheltenham: 2746.2 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Inisa", "FINAL ANSWER: Inisa" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 31.35573, "lon": 31.68484, "name": "Kafr Sa‘d" }, { "lat": -32.33083, "lon": 28.14981, "name": "Butterworth" }, { "lat": 8.83784, "lon": 3.75628, "name": "Igboho" }, { "lat": 27.3126, "lon": 30.96987, "name": "Manfalūţ" }, { "lat": -33.95, "lon": 151.13333, "name": "Rockdale" } ], "question": "Which location is the geographic outlier among: Kafr Sa‘d, Butterworth, Igboho, Manfalūţ, Rockdale?", "ground_truth": { "answer": "Rockdale", "outlier_distance_km": 11126.8, "second_furthest_km": 5114.8, "clarity_ratio": 2.18, "median_distance_km": 4239.8, "distances_to_centroid": { "Kafr Sa‘d": 3917.3, "Butterworth": 4239.8, "Igboho": 5114.8, "Manfalūţ": 3580.7, "Rockdale": 11126.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Kafr Sa‘d: (31.36°, 31.68°)", " Butterworth: (-32.33°, 28.15°)", " Igboho: (8.84°, 3.76°)", " Manfalūţ: (27.31°, 30.97°)", " Rockdale: (-33.95°, 151.13°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Rockdale: 11126.8 km from centroid", " Igboho: 5114.8 km from centroid", " Butterworth: 4239.8 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Rockdale", "FINAL ANSWER: Rockdale" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -23.4837, "lon": -46.41309, "name": "Jardim Helena" }, { "lat": -23.02639, "lon": -45.55528, "name": "Taubaté" }, { "lat": -10.90889, "lon": -37.03861, "name": "Barra dos Coqueiros" }, { "lat": -7.85583, "lon": -35.58833, "name": "João Alfredo" }, { "lat": 40.75566, "lon": -73.58763, "name": "Westbury" } ], "question": "Which location is the geographic outlier among: Jardim Helena, Taubaté, Barra dos Coqueiros, João Alfredo, Westbury?", "ground_truth": { "answer": "Westbury", "outlier_distance_km": 5724.0, "second_furthest_km": 2070.1, "clarity_ratio": 2.77, "median_distance_km": 2027.5, "distances_to_centroid": { "Jardim Helena": 2070.1, "Taubaté": 2027.5, "Barra dos Coqueiros": 1344.2, "João Alfredo": 1371.1, "Westbury": 5724.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Jardim Helena: (-23.48°, -46.41°)", " Taubaté: (-23.03°, -45.56°)", " Barra dos Coqueiros: (-10.91°, -37.04°)", " João Alfredo: (-7.86°, -35.59°)", " Westbury: (40.76°, -73.59°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Westbury: 5724.0 km from centroid", " Jardim Helena: 2070.1 km from centroid", " Taubaté: 2027.5 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Westbury", "FINAL ANSWER: Westbury" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 22.61523, "lon": 84.50208, "name": "Simdega" }, { "lat": 8.69264, "lon": 76.79332, "name": "Kīlattingal" }, { "lat": 13.78126, "lon": 100.64506, "name": "Khlong Chan" }, { "lat": 36.25449, "lon": 140.37962, "name": "Omitama" }, { "lat": 50.45008, "lon": -104.6178, "name": "Regina" } ], "question": "Which location is the geographic outlier among: Simdega, Kīlattingal, Khlong Chan, Omitama, Regina?", "ground_truth": { "answer": "Regina", "outlier_distance_km": 11332.9, "second_furthest_km": 7540.7, "clarity_ratio": 1.5, "median_distance_km": 4492.7, "distances_to_centroid": { "Simdega": 2555.9, "Kīlattingal": 2677.4, "Khlong Chan": 4492.7, "Omitama": 7540.7, "Regina": 11332.9 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Simdega: (22.62°, 84.50°)", " Kīlattingal: (8.69°, 76.79°)", " Khlong Chan: (13.78°, 100.65°)", " Omitama: (36.25°, 140.38°)", " Regina: (50.45°, -104.62°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Regina: 11332.9 km from centroid", " Omitama: 7540.7 km from centroid", " Khlong Chan: 4492.7 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Regina", "FINAL ANSWER: Regina" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 12.00423, "lon": 107.69074, "name": "Gia Nghĩa" }, { "lat": 2.6579, "lon": 101.5629, "name": "Tanjung Sepat" }, { "lat": 34.73333, "lon": 135.56667, "name": "Moriguchi" }, { "lat": 30.79834, "lon": 108.37089, "name": "Jiuchi" }, { "lat": -2.90222, "lon": -40.84111, "name": "Camocim" } ], "question": "Which location is the geographic outlier among: Gia Nghĩa, Tanjung Sepat, Moriguchi, Jiuchi, Camocim?", "ground_truth": { "answer": "Camocim", "outlier_distance_km": 13658.0, "second_furthest_km": 5686.0, "clarity_ratio": 2.4, "median_distance_km": 3136.9, "distances_to_centroid": { "Gia Nghĩa": 2749.5, "Tanjung Sepat": 2530.0, "Moriguchi": 5686.0, "Jiuchi": 3136.9, "Camocim": 13658.0 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Gia Nghĩa: (12.00°, 107.69°)", " Tanjung Sepat: (2.66°, 101.56°)", " Moriguchi: (34.73°, 135.57°)", " Jiuchi: (30.80°, 108.37°)", " Camocim: (-2.90°, -40.84°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Camocim: 13658.0 km from centroid", " Moriguchi: 5686.0 km from centroid", " Jiuchi: 3136.9 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Camocim", "FINAL ANSWER: Camocim" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": -20.94944, "lon": -48.47917, "name": "Bebedouro" }, { "lat": -7.56056, "lon": -35.0025, "name": "Goiana" }, { "lat": -34.09584, "lon": -59.02423, "name": "Zárate" }, { "lat": 8.27515, "lon": -76.37641, "name": "San Pedro de Urabá" }, { "lat": 28.50254, "lon": 77.23117, "name": "Deoli" } ], "question": "Which location is the geographic outlier among: Bebedouro, Goiana, Zárate, San Pedro de Urabá, Deoli?", "ground_truth": { "answer": "Deoli", "outlier_distance_km": 11800.8, "second_furthest_km": 5533.6, "clarity_ratio": 2.13, "median_distance_km": 4510.6, "distances_to_centroid": { "Bebedouro": 2793.9, "Goiana": 783.9, "Zárate": 4510.6, "San Pedro de Urabá": 5533.6, "Deoli": 11800.8 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Bebedouro: (-20.95°, -48.48°)", " Goiana: (-7.56°, -35.00°)", " Zárate: (-34.10°, -59.02°)", " San Pedro de Urabá: (8.28°, -76.38°)", " Deoli: (28.50°, 77.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Deoli: 11800.8 km from centroid", " San Pedro de Urabá: 5533.6 km from centroid", " Zárate: 4510.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Deoli", "FINAL ANSWER: Deoli" ] }, { "task": "spatial_patterns", "subtask": "outlier_detection", "points": [ { "lat": 55.45978, "lon": 38.44358, "name": "Beloozyorskiy" }, { "lat": 51.96236, "lon": 7.62571, "name": "Münster" }, { "lat": 40.43533, "lon": -3.6251, "name": "Simancas" }, { "lat": 48.99712, "lon": 2.28249, "name": "Eaubonne" }, { "lat": 15.31771, "lon": 78.22669, "name": "Banganapalle" } ], "question": "Which location is the geographic outlier among: Beloozyorskiy, Münster, Simancas, Eaubonne, Banganapalle?", "ground_truth": { "answer": "Banganapalle", "outlier_distance_km": 5905.4, "second_furthest_km": 2351.8, "clarity_ratio": 2.51, "median_distance_km": 1870.6, "distances_to_centroid": { "Beloozyorskiy": 1759.7, "Münster": 1655.8, "Simancas": 2351.8, "Eaubonne": 1870.6, "Banganapalle": 5905.4 } }, "reasoning_steps": [ "Step 1: Identify all points (5 locations)", " Beloozyorskiy: (55.46°, 38.44°)", " Münster: (51.96°, 7.63°)", " Simancas: (40.44°, -3.63°)", " Eaubonne: (49.00°, 2.28°)", " Banganapalle: (15.32°, 78.23°)", "Step 2: Calculate centroid of all points", "Step 3: Calculate distance from each point to centroid", " Banganapalle: 5905.4 km from centroid", " Simancas: 2351.8 km from centroid", " Eaubonne: 1870.6 km from centroid", "Step 4: Identify geographic outlier (furthest from centroid)", " Outlier: Banganapalle", "FINAL ANSWER: Banganapalle" ] } ]