{"abstract":"Parallel spacing is wrong and southern cones fail outright.","category":"Map projection transforms","checks":8,"contract":"Input [lon, lat, lon0, lat0, lat1, lat2] degrees, sphere R = 6371000, lat1 != -lat2. n = (sin p1 + sin p2)/2; C = cos(p1)**2 + 2*n*sin(p1); rho = R*sqrt(C - 2*n*sin(phi))/n; rho0 likewise at lat0; theta = n*dlon with dlon wrapped to [-180, 180). x = rho*sin(theta), y = rho0 - rho*cos(theta), rounded to 2 decimals.","evaluation_group":"w2-map-projection-transforms-albers-equal-area-conic","failed_approach":"Dividing by |n| makes southern-hemisphere cones project upside down.","family":"w2-map-projection-transforms-albers-equal-area-conic-radius-division-placement","id":"FA-70136","implementations":{"attempt":{"sha256":"b3bdf14c1c6416a23611e65c972a8376701029ef2196f723e3fa430b3a08e0a9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lon, lat, lon0, lat0, lat1, lat2 = x\n    R = 6371000.0\n    p0, p1, p2, phi = [math.radians(v) for v in (lat0, lat1, lat2, lat)]\n    n = (math.sin(p1) + math.sin(p2)) / 2\n    C = math.cos(p1) ** 2 + 2 * n * math.sin(p1)\n    rho = R * math.sqrt(C - 2 * n * math.sin(phi)) / abs(n)\n    rho0 = R * math.sqrt(C - 2 * n * math.sin(p0)) / n\n    dl = math.radians(((lon - lon0 + 180.0) % 360.0) - 180.0)\n    theta = n * dl\n    return [round(rho * math.sin(theta), 2), round(rho0 - rho * math.cos(theta), 2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-74.411, 16.812, -96.0, 23.0, 33.0, 45.0], [2405679.11, -375515.8]), ('control #1', [-7.054, -2.555, 10.0, 52.0, 35.0, 65.0], [-2368752.85, -5460256.95]), ('control #2', [163.654, -41.81, 132.0, 0.0, -18.0, -36.0], [2661851.12, -4920407.16]), ('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #4', [-26.25, -1.472, 0.0, 40.0, 40.0, 40.0], [-3459655.33, -3813601.11]), ('control #5', [24.242, -15.571, 20.0, -45.0, -45.0, -45.0], [499045.1, 3152788.69]), ('control #6', [95.34, 51.232, 100.0, 30.0, 25.0, 47.0], [-331403.06, 2390895.63]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67])], [('control #1', [-7.054, -2.555, 10.0, 52.0, 35.0, 65.0], [-2368752.85, -5460256.95]), ('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #5', [24.242, -15.571, 20.0, -45.0, -45.0, -45.0], [499045.1, 3152788.69]), ('control #6', [95.34, 51.232, 100.0, 30.0, 25.0, 47.0], [-331403.06, 2390895.63]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67]), ('control #8', [-25.931, 8.989, 10.0, 52.0, 35.0, 65.0], [-4374379.83, -3619965.56]), ('control #9', [128.053, -60.735, 132.0, 0.0, -18.0, -36.0], [-277286.95, -6470938.42]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04])], [('control #2', [163.654, -41.81, 132.0, 0.0, -18.0, -36.0], [2661851.12, -4920407.16]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67]), ('control #8', [-25.931, 8.989, 10.0, 52.0, 35.0, 65.0], [-4374379.83, -3619965.56]), ('control #9', [128.053, -60.735, 132.0, 0.0, -18.0, -36.0], [-277286.95, -6470938.42]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #11', [25.244, 44.637, 0.0, 40.0, 40.0, 40.0], [1977746.83, 796959.72]), ('control #12', [-19.298, -12.334, 20.0, -45.0, -45.0, -45.0], [-4597338.48, 2353100.16]), ('control #13', [99.747, 65.471, 100.0, 30.0, 25.0, 47.0], [-14324.17, 3825527.6])], [('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #11', [25.244, 44.637, 0.0, 40.0, 40.0, 40.0], [1977746.83, 796959.72]), ('control #12', [-19.298, -12.334, 20.0, -45.0, -45.0, -45.0], [-4597338.48, 2353100.16]), ('control #13', [99.747, 65.471, 100.0, 30.0, 25.0, 47.0], [-14324.17, 3825527.6]), ('control #14', [-128.991, 27.029, -96.0, 23.0, 33.0, 45.0], [-3243071.92, 1029568.66]), ('control #15', [-24.721, 3.031, 10.0, 52.0, 35.0, 65.0], [-4481724.64, -4195384.79]), ('control #16', [154.974, -67.172, 132.0, 0.0, -18.0, -36.0], [1514049.99, -7114831.09])], [('control #4', [-26.25, -1.472, 0.0, 40.0, 40.0, 40.0], [-3459655.33, -3813601.11]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #14', [-128.991, 27.029, -96.0, 23.0, 33.0, 45.0], [-3243071.92, 1029568.66]), ('control #15', [-24.721, 3.031, 10.0, 52.0, 35.0, 65.0], [-4481724.64, -4195384.79]), ('control #16', [154.974, -67.172, 132.0, 0.0, -18.0, -36.0], [1514049.99, -7114831.09]), ('control #17', [-37.667, -43.269, -60.0, -32.0, -5.0, -42.0], [1818158.31, -1416145.5]), ('control #18', [9.83, 73.683, 0.0, 40.0, 40.0, 40.0], [462004.5, 3420297.91]), ('control #19', [-7.283, -57.541, 20.0, -45.0, -45.0, -45.0], [-1648585.12, -1661270.39])]]\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":"2a41b37fde2f424892469d114ba1f1c0573a4c39daad452093d62712ffc12d86","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lon, lat, lon0, lat0, lat1, lat2 = x\n    R = 6371000.0\n    p0, p1, p2, phi = [math.radians(v) for v in (lat0, lat1, lat2, lat)]\n    n = (math.sin(p1) + math.sin(p2)) / 2\n    C = math.cos(p1) ** 2 + 2 * n * math.sin(p1)\n    rho = R * math.sqrt(C - 2 * n * math.sin(phi)) * n\n    rho0 = R * math.sqrt(C - 2 * n * math.sin(p0)) / n\n    dl = math.radians(((lon - lon0 + 180.0) % 360.0) - 180.0)\n    theta = n * dl\n    return [round(rho * math.sin(theta), 2), round(rho0 - rho * math.cos(theta), 2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-74.411, 16.812, -96.0, 23.0, 33.0, 45.0], [2405679.11, -375515.8]), ('control #1', [-7.054, -2.555, 10.0, 52.0, 35.0, 65.0], [-2368752.85, -5460256.95]), ('control #2', [163.654, -41.81, 132.0, 0.0, -18.0, -36.0], [2661851.12, -4920407.16]), ('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #4', [-26.25, -1.472, 0.0, 40.0, 40.0, 40.0], [-3459655.33, -3813601.11]), ('control #5', [24.242, -15.571, 20.0, -45.0, -45.0, -45.0], [499045.1, 3152788.69]), ('control #6', [95.34, 51.232, 100.0, 30.0, 25.0, 47.0], [-331403.06, 2390895.63]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67])], [('control #1', [-7.054, -2.555, 10.0, 52.0, 35.0, 65.0], [-2368752.85, -5460256.95]), ('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #5', [24.242, -15.571, 20.0, -45.0, -45.0, -45.0], [499045.1, 3152788.69]), ('control #6', [95.34, 51.232, 100.0, 30.0, 25.0, 47.0], [-331403.06, 2390895.63]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67]), ('control #8', [-25.931, 8.989, 10.0, 52.0, 35.0, 65.0], [-4374379.83, -3619965.56]), ('control #9', [128.053, -60.735, 132.0, 0.0, -18.0, -36.0], [-277286.95, -6470938.42]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04])], [('control #2', [163.654, -41.81, 132.0, 0.0, -18.0, -36.0], [2661851.12, -4920407.16]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67]), ('control #8', [-25.931, 8.989, 10.0, 52.0, 35.0, 65.0], [-4374379.83, -3619965.56]), ('control #9', [128.053, -60.735, 132.0, 0.0, -18.0, -36.0], [-277286.95, -6470938.42]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #11', [25.244, 44.637, 0.0, 40.0, 40.0, 40.0], [1977746.83, 796959.72]), ('control #12', [-19.298, -12.334, 20.0, -45.0, -45.0, -45.0], [-4597338.48, 2353100.16]), ('control #13', [99.747, 65.471, 100.0, 30.0, 25.0, 47.0], [-14324.17, 3825527.6])], [('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #11', [25.244, 44.637, 0.0, 40.0, 40.0, 40.0], [1977746.83, 796959.72]), ('control #12', [-19.298, -12.334, 20.0, -45.0, -45.0, -45.0], [-4597338.48, 2353100.16]), ('control #13', [99.747, 65.471, 100.0, 30.0, 25.0, 47.0], [-14324.17, 3825527.6]), ('control #14', [-128.991, 27.029, -96.0, 23.0, 33.0, 45.0], [-3243071.92, 1029568.66]), ('control #15', [-24.721, 3.031, 10.0, 52.0, 35.0, 65.0], [-4481724.64, -4195384.79]), ('control #16', [154.974, -67.172, 132.0, 0.0, -18.0, -36.0], [1514049.99, -7114831.09])], [('control #4', [-26.25, -1.472, 0.0, 40.0, 40.0, 40.0], [-3459655.33, -3813601.11]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #14', [-128.991, 27.029, -96.0, 23.0, 33.0, 45.0], [-3243071.92, 1029568.66]), ('control #15', [-24.721, 3.031, 10.0, 52.0, 35.0, 65.0], [-4481724.64, -4195384.79]), ('control #16', [154.974, -67.172, 132.0, 0.0, -18.0, -36.0], [1514049.99, -7114831.09]), ('control #17', [-37.667, -43.269, -60.0, -32.0, -5.0, -42.0], [1818158.31, -1416145.5]), ('control #18', [9.83, 73.683, 0.0, 40.0, 40.0, 40.0], [462004.5, 3420297.91]), ('control #19', [-7.283, -57.541, 20.0, -45.0, -45.0, -45.0], [-1648585.12, -1661270.39])]]\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":"bc6819c013e0d44873f34f107fb15c11c6055641ac4abcf911a2c57280420dbe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lon, lat, lon0, lat0, lat1, lat2 = x\n    R = 6371000.0\n    p0, p1, p2, phi = [math.radians(v) for v in (lat0, lat1, lat2, lat)]\n    n = (math.sin(p1) + math.sin(p2)) / 2\n    C = math.cos(p1) ** 2 + 2 * n * math.sin(p1)\n    rho = R * math.sqrt(C - 2 * n * math.sin(phi)) / n\n    rho0 = R * math.sqrt(C - 2 * n * math.sin(p0)) / n\n    dl = math.radians(((lon - lon0 + 180.0) % 360.0) - 180.0)\n    theta = n * dl\n    return [round(rho * math.sin(theta), 2), round(rho0 - rho * math.cos(theta), 2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-74.411, 16.812, -96.0, 23.0, 33.0, 45.0], [2405679.11, -375515.8]), ('control #1', [-7.054, -2.555, 10.0, 52.0, 35.0, 65.0], [-2368752.85, -5460256.95]), ('control #2', [163.654, -41.81, 132.0, 0.0, -18.0, -36.0], [2661851.12, -4920407.16]), ('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #4', [-26.25, -1.472, 0.0, 40.0, 40.0, 40.0], [-3459655.33, -3813601.11]), ('control #5', [24.242, -15.571, 20.0, -45.0, -45.0, -45.0], [499045.1, 3152788.69]), ('control #6', [95.34, 51.232, 100.0, 30.0, 25.0, 47.0], [-331403.06, 2390895.63]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67])], [('control #1', [-7.054, -2.555, 10.0, 52.0, 35.0, 65.0], [-2368752.85, -5460256.95]), ('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #5', [24.242, -15.571, 20.0, -45.0, -45.0, -45.0], [499045.1, 3152788.69]), ('control #6', [95.34, 51.232, 100.0, 30.0, 25.0, 47.0], [-331403.06, 2390895.63]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67]), ('control #8', [-25.931, 8.989, 10.0, 52.0, 35.0, 65.0], [-4374379.83, -3619965.56]), ('control #9', [128.053, -60.735, 132.0, 0.0, -18.0, -36.0], [-277286.95, -6470938.42]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04])], [('control #2', [163.654, -41.81, 132.0, 0.0, -18.0, -36.0], [2661851.12, -4920407.16]), ('control #7', [-119.961, 31.565, -96.0, 23.0, 33.0, 45.0], [-2250314.51, 1235327.67]), ('control #8', [-25.931, 8.989, 10.0, 52.0, 35.0, 65.0], [-4374379.83, -3619965.56]), ('control #9', [128.053, -60.735, 132.0, 0.0, -18.0, -36.0], [-277286.95, -6470938.42]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #11', [25.244, 44.637, 0.0, 40.0, 40.0, 40.0], [1977746.83, 796959.72]), ('control #12', [-19.298, -12.334, 20.0, -45.0, -45.0, -45.0], [-4597338.48, 2353100.16]), ('control #13', [99.747, 65.471, 100.0, 30.0, 25.0, 47.0], [-14324.17, 3825527.6])], [('control #3', [-52.492, -45.412, -60.0, -32.0, -5.0, -42.0], [601606.86, -1530950.07]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #11', [25.244, 44.637, 0.0, 40.0, 40.0, 40.0], [1977746.83, 796959.72]), ('control #12', [-19.298, -12.334, 20.0, -45.0, -45.0, -45.0], [-4597338.48, 2353100.16]), ('control #13', [99.747, 65.471, 100.0, 30.0, 25.0, 47.0], [-14324.17, 3825527.6]), ('control #14', [-128.991, 27.029, -96.0, 23.0, 33.0, 45.0], [-3243071.92, 1029568.66]), ('control #15', [-24.721, 3.031, 10.0, 52.0, 35.0, 65.0], [-4481724.64, -4195384.79]), ('control #16', [154.974, -67.172, 132.0, 0.0, -18.0, -36.0], [1514049.99, -7114831.09])], [('control #4', [-26.25, -1.472, 0.0, 40.0, 40.0, 40.0], [-3459655.33, -3813601.11]), ('control #10', [-40.992, -24.699, -60.0, -32.0, -5.0, -42.0], [1816236.48, 739740.04]), ('control #14', [-128.991, 27.029, -96.0, 23.0, 33.0, 45.0], [-3243071.92, 1029568.66]), ('control #15', [-24.721, 3.031, 10.0, 52.0, 35.0, 65.0], [-4481724.64, -4195384.79]), ('control #16', [154.974, -67.172, 132.0, 0.0, -18.0, -36.0], [1514049.99, -7114831.09]), ('control #17', [-37.667, -43.269, -60.0, -32.0, -5.0, -42.0], [1818158.31, -1416145.5]), ('control #18', [9.83, 73.683, 0.0, 40.0, 40.0, 40.0], [462004.5, 3420297.91]), ('control #19', [-7.283, -57.541, 20.0, -45.0, -45.0, -45.0], [-1648585.12, -1661270.39])]]\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-albers-equal-area-conic-radius-division-placement","generated_at":"2026-09-29T14:48:17.745853+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Continental statistics maps use Albers because it preserves area; a wrong constant silently biases area totals.","repair":"At the radius division placement step restore `rho = R * math.sqrt(C - 2 * n * math.sin(phi)) / n`, leaving the rest of the model unchanged.","root_cause":"The radius multiplies by the cone constant instead of dividing by it.","sha256":"9c17cccf954b5737299c8a1b6df73d83020d8c206a9f6c092c4eeafb67227fe4","title":"Spherical Albers equal-area conic forward: radius division placement · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.206,"exit_code":1,"observations":[{"actual":[2405679.11,-375515.8],"check":"control #0","expected":[2405679.11,-375515.8],"passed":true},{"actual":[-2368752.85,-5460256.95],"check":"control #1","expected":[-2368752.85,-5460256.95],"passed":true},{"actual":[-2661851.12,-25969222.25],"check":"control #2","expected":[2661851.12,-4920407.16],"passed":false},{"actual":[-601606.86,-25793096.84],"check":"control #3","expected":[601606.86,-1530950.07],"passed":false},{"actual":[-3459655.33,-3813601.11],"check":"control #4","expected":[-3459655.33,-3813601.11],"passed":true},{"actual":[-499045.1,-15894788.69],"check":"control #5","expected":[499045.1,3152788.69],"passed":false},{"actual":[-331403.06,2390895.63],"check":"control 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