{"abstract":"Horizontal scale is correct only when the origin latitude equals the standard parallel.","category":"Map projection transforms","checks":8,"contract":"Input [mode, a, b, lon0, lat0, lat1] on a sphere R = 6371007. mode \"fwd\": a=lon, b=lat; dlon = lon-lon0 wrapped into [-180, 180); x = R*rad(dlon)*cos(rad(lat1)), y = R*rad(lat-lat0). mode \"inv\": a=x, b=y; lon = lon0 + deg(x/(R*cos(rad(lat1)))) wrapped into [-180, 180), lat = lat0 + deg(y/R). Forward results round to 2 decimals, inverse results to 6.","evaluation_group":"w2-map-projection-transforms-equirectangular-standard-parallel","failed_approach":"The standard parallel is used but passed to cos in degrees.","family":"w2-map-projection-transforms-equirectangular-standard-parallel-true-scale-parallel","id":"FA-70041","implementations":{"attempt":{"sha256":"df51db6c635e8a7cc1a96159e1922e1ee339a7095df7b1f809701cecb4f2e9bf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    mode, a, b, lon0, lat0, lat1 = x\n    R = 6371007.0\n    k = math.cos(lat1)\n    if mode == 'fwd':\n        dlon = ((a - lon0 + 180.0) % 360.0) - 180.0\n        return [round(R * math.radians(dlon) * k, 2), round(R * math.radians(b - lat0), 2)]\n    lon = lon0 + math.degrees(a / (R * k))\n    lon = ((lon + 180.0) % 360.0) - 180.0\n    lat = lat0 + math.degrees(b / R)\n    return [round(lon, 6), round(lat, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', ['fwd', 29.215, -48.839, -100.0, 20.0, 0.0], [14368068.23, -7654555.97]), ('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('control #16', ['inv', 5573045.0, 6790547.5, 10.0, -10.0, 45.0], [80.879737, 51.068794]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])]]\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":"36360302907dcb5279b91f529638e798a01805845dfc76ce936e7a43764bfc15","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    mode, a, b, lon0, lat0, lat1 = x\n    R = 6371007.0\n    k = math.cos(math.radians(lat0))\n    if mode == 'fwd':\n        dlon = ((a - lon0 + 180.0) % 360.0) - 180.0\n        return [round(R * math.radians(dlon) * k, 2), round(R * math.radians(b - lat0), 2)]\n    lon = lon0 + math.degrees(a / (R * k))\n    lon = ((lon + 180.0) % 360.0) - 180.0\n    lat = lat0 + math.degrees(b / R)\n    return [round(lon, 6), round(lat, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', ['fwd', 29.215, -48.839, -100.0, 20.0, 0.0], [14368068.23, -7654555.97]), ('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('control #16', ['inv', 5573045.0, 6790547.5, 10.0, -10.0, 45.0], [80.879737, 51.068794]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])]]\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"},"fixed":{"sha256":"9441753c701e69501d9ddf77c1c4f712e0fabe023e626acad8e1e877998fd1ed","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    mode, a, b, lon0, lat0, lat1 = x\n    R = 6371007.0\n    k = math.cos(math.radians(lat1))\n    if mode == 'fwd':\n        dlon = ((a - lon0 + 180.0) % 360.0) - 180.0\n        return [round(R * math.radians(dlon) * k, 2), round(R * math.radians(b - lat0), 2)]\n    lon = lon0 + math.degrees(a / (R * k))\n    lon = ((lon + 180.0) % 360.0) - 180.0\n    lat = lat0 + math.degrees(b / R)\n    return [round(lon, 6), round(lat, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', ['fwd', 29.215, -48.839, -100.0, 20.0, 0.0], [14368068.23, -7654555.97]), ('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412])], [('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('control #16', ['inv', 5573045.0, 6790547.5, 10.0, -10.0, 45.0], [80.879737, 51.068794]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #19', ['inv', 1510017.4, 7976956.2, 150.0, 0.0, 0.0], [163.579898, 71.738412]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])]]\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-equirectangular-standard-parallel-true-scale-parallel","generated_at":"2026-09-29T14:48:17.040368+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Plate carree style grids with a true-scale parallel are common for regional rasters and simple web previews.","repair":"At the true-scale parallel step restore `k = math.cos(math.radians(lat1))`, leaving the rest of the model unchanged.","root_cause":"The horizontal scale uses the latitude of origin instead of the standard parallel.","sha256":"1ae1934cdcfe23ed794d63f1e83523de70145c421fc6e978a4fc3e1bb4956937","title":"Equirectangular projection with standard parallel: true-scale parallel · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.599,"exit_code":1,"observations":[{"actual":[14368068.23,-7654555.97],"check":"control #0","expected":[14368068.23,-7654555.97],"passed":true},{"actual":[5324449.57,-7302846.03],"check":"control #1","expected":[4309310.45,-7302846.03],"passed":false},{"actual":[-4715581.15,-5117196.15],"check":"control #2","expected":[-6347382.14,-5117196.15],"passed":false},{"actual":[-1135433.5,-7314632.7],"check":"control #3","expected":[-918956.11,-7314632.7],"passed":false},{"actual":[-805114.76,-6870630.87],"check":"control #4","expected":[-4520215.78,-6870630.87],"passed":false},{"actual":[49.495875,-71.089824],"check":"control #13","expected":[49.495875,-71.089824],"passed":true},{"actual":[-4.440502,56.056053],"check":"control #17","expected":[-4.440502,56.056053],"passed":true},{"actual":[163.579898,71.738412],"check":"control #19","expected":[163.579898,71.738412],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [14368068.23, -7654555.97], \"expected\": [14368068.23, -7654555.97], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [5324449.57, -7302846.03], \"expected\": [4309310.45, -7302846.03], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [-4715581.15, -5117196.15], \"expected\": [-6347382.14, -5117196.15], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [-1135433.5, -7314632.7], \"expected\": [-918956.11, -7314632.7], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [-805114.76, -6870630.87], \"expected\": [-4520215.78, -6870630.87], \"passed\": false}, {\"check\": \"control #13\", \"actual\": [49.495875, -71.089824], \"expected\": [49.495875, -71.089824], \"passed\": true}, {\"check\": 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