{"abstract":"Resolution oscillates and even turns negative across latitudes.","category":"Map projection transforms","checks":8,"contract":"Input [lat, z, tile_size, dpi]. Ground resolution in metres per pixel is 2*pi*6378137*cos(lat)/(tile_size*2**z) with the equatorial circumference computed exactly. The map scale denominator is resolution*dpi/0.0254. Return [resolution rounded to 6 decimals, scale denominator rounded to the nearest integer] computed from the unrounded resolution.","contract_signature":"x","evaluation_group":"w2-map-projection-transforms-ground-resolution-scale","failed_approach":"Dividing by 360 halves the angle, so resolution is overestimated away from the equator.","family":"w2-map-projection-transforms-ground-resolution-scale-latitude-cosine-unit","id":"FA-69966","implementations":{"attempt":{"sha256":"b4029e036dbf915da8a300590efccda93388a1cad3c0d631385a5a98836a4959","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lat, z, tile, dpi = x\n    circumference = 2 * math.pi * 6378137.0\n    res = circumference * abs(math.cos(lat * math.pi / 360.0)) / (tile * 2 ** z)\n    scale = res * dpi / 0.0254\n    return [round(res, 6), round(scale)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-0.88, 17, 256, 72], [1.194188, 3385]), ('control #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('control #5', [-75.78, 4, 256, 300], [2403.383393, 28386418]), ('control #6', [-15.49, 9, 512, 72], [147.321225, 417603]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('control #5', [-75.78, 4, 256, 300], [2403.383393, 28386418]), ('control #6', [-15.49, 9, 512, 72], [147.321225, 417603]), ('control #7', [76.6, 19, 512, 300], [0.034598, 409]), ('control #8', [20.0, 19, 512, 72], [0.140288, 398]), ('control #9', [-14.77, 4, 256, 96], [9460.648974, 35756784]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('control #8', [20.0, 19, 512, 72], [0.140288, 398]), ('control #9', [-14.77, 4, 256, 96], [9460.648974, 35756784]), ('control #10', [6.58, 15, 256, 300], [4.745845, 56053]), ('control #11', [-18.37, 9, 256, 72], [290.167542, 822522]), ('control #12', [-51.53, 14, 512, 300], [2.97199, 35102]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('control #11', [-18.37, 9, 256, 72], [290.167542, 822522]), ('control #12', [-51.53, 14, 512, 300], [2.97199, 35102]), ('control #13', [-69.8, 6, 256, 300], [844.594183, 9975522]), ('control #14', [-23.41, 10, 256, 72], [140.290274, 397673]), ('control #15', [-37.12, 12, 256, 96], [30.474424, 115179]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('control #5', [-75.78, 4, 256, 300], [2403.383393, 28386418]), ('control #14', [-23.41, 10, 256, 72], [140.290274, 397673]), ('control #15', [-37.12, 12, 256, 96], [30.474424, 115179]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711]), ('boundary #17', [60.0, 1, 512, 96], [19567.879241, 73957339]), ('regression #18', [45.0, 10, 512, 90.7], [54.049141, 193002]), ('boundary #19', [-60.0, 3, 256, 300], [9783.939621, 115558342])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"6640c38b32ab3f91132375229c98b84fc8eae65b16df305661ecafa6bc6e6e0e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lat, z, tile, dpi = x\n    circumference = 2 * math.pi * 6378137.0\n    res = circumference * math.cos(lat) / (tile * 2 ** z)\n    scale = res * dpi / 0.0254\n    return [round(res, 6), round(scale)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-0.88, 17, 256, 72], [1.194188, 3385]), ('control #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('control #5', [-75.78, 4, 256, 300], [2403.383393, 28386418]), ('control #6', [-15.49, 9, 512, 72], [147.321225, 417603]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('control #5', [-75.78, 4, 256, 300], [2403.383393, 28386418]), ('control #6', [-15.49, 9, 512, 72], [147.321225, 417603]), ('control #7', [76.6, 19, 512, 300], [0.034598, 409]), ('control #8', [20.0, 19, 512, 72], [0.140288, 398]), ('control #9', [-14.77, 4, 256, 96], [9460.648974, 35756784]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('control #8', [20.0, 19, 512, 72], [0.140288, 398]), ('control #9', [-14.77, 4, 256, 96], [9460.648974, 35756784]), ('control #10', [6.58, 15, 256, 300], [4.745845, 56053]), ('control #11', [-18.37, 9, 256, 72], [290.167542, 822522]), ('control #12', [-51.53, 14, 512, 300], [2.97199, 35102]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('control #11', [-18.37, 9, 256, 72], [290.167542, 822522]), ('control #12', [-51.53, 14, 512, 300], [2.97199, 35102]), ('control #13', [-69.8, 6, 256, 300], [844.594183, 9975522]), ('control #14', [-23.41, 10, 256, 72], [140.290274, 397673]), ('control #15', [-37.12, 12, 256, 96], [30.474424, 115179]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711])], [('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('control #5', [-75.78, 4, 256, 300], [2403.383393, 28386418]), ('control #14', [-23.41, 10, 256, 72], [140.290274, 397673]), ('control #15', [-37.12, 12, 256, 96], [30.474424, 115179]), ('boundary #16', [0.0, 0, 256, 96], [156543.033928, 591658711]), ('boundary #17', [60.0, 1, 512, 96], [19567.879241, 73957339]), ('regression #18', [45.0, 10, 512, 90.7], [54.049141, 193002]), ('boundary #19', [-60.0, 3, 256, 300], [9783.939621, 115558342])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Stipulated deterministic toy contract on a bounded input domain; results are rounded as stated and no conformance with any published standard or library is claimed. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-map-projection-transforms-ground-resolution-scale-latitude-cosine-unit","generated_at":"2026-09-29T14:48:16.363809+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Scale bars, level-of-detail choice and print exports depend on these values.","root_cause":"The cosine is evaluated on degrees instead of radians.","sha256":"92cd18f6e8d02e2bb2a40c1ac856fea0cc55c77078029984200d0165f5ce7f9e","title":"Web mercator ground resolution and scale denominator: latitude cosine unit · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":38.225,"exit_code":1,"observations":[{"actual":[1.194293,3385],"check":"control #0","expected":[1.194188,3385],"passed":false},{"actual":[75034.681417,212696735],"check":"control #1","expected":[65591.886576,185929757],"passed":false},{"actual":[18.742078,53127],"check":"control #2","expected":[17.654651,50045],"passed":false},{"actual":[120.581298,1424189],"check":"control #3","expected":[37.345917,441094],"passed":false},{"actual":[0.144133,409],"check":"control #4","expected":[0.129015,366],"passed":false},{"actual":[7721.399889,91197636],"check":"control #5","expected":[2403.383393,28386418],"passed":false},{"actual":[151.479488,429391],"check":"control #6","expected":[147.321225,417603],"passed":false},{"actual":[156543.033928,591658711],"check":"boundary #16","expected":[156543.033928,591658711],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [1.194293, 3385], \"expected\": [1.194188, 3385], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [75034.681417, 212696735], \"expected\": [65591.886576, 185929757], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [18.742078, 53127], \"expected\": [17.654651, 50045], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [120.581298, 1424189], \"expected\": [37.345917, 441094], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [0.144133, 409], \"expected\": [0.129015, 366], \"passed\": false}, {\"check\": \"control #5\", \"actual\": [7721.399889, 91197636], \"expected\": [2403.383393, 28386418], \"passed\": false}, {\"check\": \"control #6\", \"actual\": [151.479488, 429391], \"expected\": [147.321225, 417603], \"passed\": false}, {\"check\": \"boundary #16\", \"actual\": [156543.033928, 591658711], \"expected\": [156543.033928, 591658711], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.703,"exit_code":1,"observations":[{"actual":[0.760968,2157],"check":"control #0","expected":[1.194188,3385],"passed":false},{"actual":[-6510.696404,-18455517],"check":"control #1","expected":[65591.886576,185929757],"passed":false},{"actual":[-16.688203,-47305],"check":"control #2","expected":[17.654651,50045],"passed":false},{"actual":[136.862409,1616485],"check":"control #3","expected":[37.345917,441094],"passed":false},{"actual":[0.053271,151],"check":"control #4","expected":[0.129015,366],"passed":false},{"actual":[9079.538035,107238638],"check":"control #5","expected":[2403.383393,28386418],"passed":false},{"actual":[-149.257041,-423091],"check":"control #6","expected":[147.321225,417603],"passed":false},{"actual":[156543.033928,591658711],"check":"boundary #16","expected":[156543.033928,591658711],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [0.760968, 2157], \"expected\": [1.194188, 3385], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [-6510.696404, -18455517], \"expected\": [65591.886576, 185929757], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [-16.688203, -47305], \"expected\": [17.654651, 50045], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [136.862409, 1616485], \"expected\": [37.345917, 441094], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [0.053271, 151], \"expected\": [0.129015, 366], \"passed\": false}, {\"check\": \"control #5\", \"actual\": [9079.538035, 107238638], \"expected\": [2403.383393, 28386418], \"passed\": false}, {\"check\": \"control #6\", \"actual\": [-149.257041, -423091], \"expected\": [147.321225, 417603], \"passed\": false}, {\"check\": \"boundary #16\", \"actual\": [156543.033928, 591658711], \"expected\": [156543.033928, 591658711], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}