{"abstract":"Every zoom level reports half the correct resolution.","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":"Clamping the exponent at 1 is correct except at zoom 0, which is reported at zoom 1 resolution.","family":"w2-map-projection-transforms-ground-resolution-scale-zoom-exponent","id":"FA-69976","implementations":{"attempt":{"sha256":"c585587757ff04d7f544aebb69e7ebfbc241c98e3691b930a5bf6be3a6a5584f","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(math.radians(lat)) / (tile * 2 ** max(z, 1))\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]), ('control #7', [76.6, 19, 512, 300], [0.034598, 409])], [('control #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('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]), ('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 #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('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]), ('control #13', [-69.8, 6, 256, 300], [844.594183, 9975522])], [('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('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]), ('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 #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('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":"b9d4431f3beca4dc8c94729a32e1b169a422645d1e264cd14c0889cea2d92c3d","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(math.radians(lat)) / (tile * 2 ** (z + 1))\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]), ('control #7', [76.6, 19, 512, 300], [0.034598, 409])], [('control #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('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]), ('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 #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #2', [-22.5, 12, 512, 72], [17.654651, 50045]), ('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]), ('control #13', [-69.8, 6, 256, 300], [844.594183, 9975522])], [('control #3', [75.86, 10, 256, 300], [37.345917, 441094]), ('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]), ('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 #1', [-33.07, 0, 512, 72], [65591.886576, 185929757]), ('control #4', [30.21, 20, 256, 72], [0.129015, 366]), ('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-zoom-exponent","generated_at":"2026-09-29T14:48:16.407849+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 zoom factor uses 2**(z+1), as though zoom levels started at 1.","sha256":"62211daad20d5b064bda19fe424079c02de5966ecf9a239e74954da301c83378","title":"Web mercator ground resolution and scale denominator: zoom exponent · 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":40.161,"exit_code":1,"observations":[{"actual":[1.194188,3385],"check":"control #0","expected":[1.194188,3385],"passed":true},{"actual":[32795.943288,92964879],"check":"control #1","expected":[65591.886576,185929757],"passed":false},{"actual":[17.654651,50045],"check":"control #2","expected":[17.654651,50045],"passed":true},{"actual":[37.345917,441094],"check":"control #3","expected":[37.345917,441094],"passed":true},{"actual":[0.129015,366],"check":"control #4","expected":[0.129015,366],"passed":true},{"actual":[2403.383393,28386418],"check":"control #5","expected":[2403.383393,28386418],"passed":true},{"actual":[147.321225,417603],"check":"control #6","expected":[147.321225,417603],"passed":true},{"actual":[0.034598,409],"check":"control #7","expected":[0.034598,409],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [1.194188, 3385], \"expected\": [1.194188, 3385], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [32795.943288, 92964879], \"expected\": [65591.886576, 185929757], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [17.654651, 50045], \"expected\": [17.654651, 50045], \"passed\": true}, {\"check\": \"control #3\", \"actual\": [37.345917, 441094], \"expected\": [37.345917, 441094], \"passed\": true}, {\"check\": \"control #4\", \"actual\": [0.129015, 366], \"expected\": [0.129015, 366], \"passed\": true}, {\"check\": \"control #5\", \"actual\": [2403.383393, 28386418], \"expected\": [2403.383393, 28386418], \"passed\": true}, {\"check\": \"control #6\", \"actual\": [147.321225, 417603], \"expected\": [147.321225, 417603], \"passed\": true}, {\"check\": \"control #7\", \"actual\": [0.034598, 409], \"expected\": [0.034598, 409], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.732,"exit_code":1,"observations":[{"actual":[0.597094,1693],"check":"control #0","expected":[1.194188,3385],"passed":false},{"actual":[32795.943288,92964879],"check":"control #1","expected":[65591.886576,185929757],"passed":false},{"actual":[8.827326,25022],"check":"control #2","expected":[17.654651,50045],"passed":false},{"actual":[18.672958,220547],"check":"control #3","expected":[37.345917,441094],"passed":false},{"actual":[0.064508,183],"check":"control #4","expected":[0.129015,366],"passed":false},{"actual":[1201.691697,14193209],"check":"control #5","expected":[2403.383393,28386418],"passed":false},{"actual":[73.660612,208802],"check":"control #6","expected":[147.321225,417603],"passed":false},{"actual":[0.017299,204],"check":"control #7","expected":[0.034598,409],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [0.597094, 1693], \"expected\": [1.194188, 3385], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [32795.943288, 92964879], \"expected\": [65591.886576, 185929757], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [8.827326, 25022], \"expected\": [17.654651, 50045], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [18.672958, 220547], \"expected\": [37.345917, 441094], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [0.064508, 183], \"expected\": [0.129015, 366], \"passed\": false}, {\"check\": \"control #5\", \"actual\": [1201.691697, 14193209], \"expected\": [2403.383393, 28386418], \"passed\": false}, {\"check\": \"control #6\", \"actual\": [73.660612, 208802], \"expected\": [147.321225, 417603], \"passed\": false}, {\"check\": \"control #7\", \"actual\": [0.017299, 204], \"expected\": [0.034598, 409], \"passed\": false}], \"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."}}