{"abstract":"Every latitude away from the equator comes back halved.","category":"Map projection transforms","checks":8,"contract":"Input [x, y] metres (sphere radius 6378137). Eastings outside the world extent E = 20037508.342789244 are wrapped into [-E, E) first. Return [lon, lat] in degrees rounded to 7 decimals.","contract_signature":"x","evaluation_group":"w2-map-projection-transforms-web-mercator-inverse","failed_approach":"The factor of two was restored on the arctangent but not on the pi/4 offset, so the equator itself moves.","family":"w2-map-projection-transforms-web-mercator-inverse-gudermannian-scaling","id":"FA-69866","implementations":{"attempt":{"sha256":"18b6ae1182c2868535859e0615e80d8a00ffd89d4e78cf8655e12bc713959169","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    px, py = x\n    R = 6378137.0\n    E = 20037508.342789244\n    px = ((px + E) % (2 * E)) - E\n    lon = math.degrees(px / R)\n    lat = math.degrees(2 * math.atan(math.exp(py / R)) - math.pi / 4)\n    return [round(lon, 7), round(lat, 7)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression #0', [25000000.0, 1000000.0], [-135.421179, 8.9465739]), ('regression #1', [-30000000.0, -2000000.0], [90.5054148, -17.6789142]), ('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #3', [0.0, 0.0], [0.0, 0.0]), ('control #4', [1113194.9, 1118889.97], [9.9999999, 10.0]), ('control #5', [-8237642.3, 4970241.3], [-73.9999998, 40.7139556]), ('control #6', [15000000.0, -6000000.0], [134.7472926, -47.3537047]), ('boundary #7', [0.0, 20037508.342789244], [0.0, 85.0511288])], [('regression #1', [-30000000.0, -2000000.0], [90.5054148, -17.6789142]), ('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #5', [-8237642.3, 4970241.3], [-73.9999998, 40.7139556]), ('control #6', [15000000.0, -6000000.0], [134.7472926, -47.3537047]), ('boundary #7', [0.0, 20037508.342789244], [0.0, 85.0511288]), ('boundary #8', [0.0, -20037508.342789244], [0.0, -85.0511288]), ('control #9', [500000.0, -500000.0], [4.4915764, -4.486983]), ('control #10', [-19000000.0, 12000000.0], [-170.679904, 72.6726763])], [('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #4', [1113194.9, 1118889.97], [9.9999999, 10.0]), ('boundary #8', [0.0, -20037508.342789244], [0.0, -85.0511288]), ('control #9', [500000.0, -500000.0], [4.4915764, -4.486983]), ('control #10', [-19000000.0, 12000000.0], [-170.679904, 72.6726763]), ('control #11', [3000000.0, 9000000.0], [26.9494585, 62.5882773]), ('regression #12', [45000000.0, 3000000.0], [44.2418779, 26.0074202]), ('control #13', [-1234567.0, 7654321.0], [-11.0903041, 56.4787668])], [('control #3', [0.0, 0.0], [0.0, 0.0]), ('control #5', [-8237642.3, 4970241.3], [-73.9999998, 40.7139556]), ('control #11', [3000000.0, 9000000.0], [26.9494585, 62.5882773]), ('regression #12', [45000000.0, 3000000.0], [44.2418779, 26.0074202]), ('control #13', [-1234567.0, 7654321.0], [-11.0903041, 56.4787668]), ('regression #14', [-21000000.0, 500000.0], [171.3537903, 4.486983]), ('regression #15', [-25000000.0, -4000000.0], [135.421179, -33.7852301]), ('regression #16', [-40075016.0, 0.0], [6.2e-06, 0.0])], [('regression #0', [25000000.0, 1000000.0], [-135.421179, 8.9465739]), ('regression #1', [-30000000.0, -2000000.0], [90.5054148, -17.6789142]), ('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #4', [1113194.9, 1118889.97], [9.9999999, 10.0]), ('control #6', [15000000.0, -6000000.0], [134.7472926, -47.3537047]), ('regression #14', [-21000000.0, 500000.0], [171.3537903, 4.486983]), ('regression #15', [-25000000.0, -4000000.0], [135.421179, -33.7852301]), ('regression #16', [-40075016.0, 0.0], [6.2e-06, 0.0])]]\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":"2559a336d0ac4fbcfb13a30c16c3dc06c679203b15cfe1050091a6102ca65343","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    px, py = x\n    R = 6378137.0\n    E = 20037508.342789244\n    px = ((px + E) % (2 * E)) - E\n    lon = math.degrees(px / R)\n    lat = math.degrees(math.atan(math.exp(py / R)) - math.pi / 4)\n    return [round(lon, 7), round(lat, 7)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression #0', [25000000.0, 1000000.0], [-135.421179, 8.9465739]), ('regression #1', [-30000000.0, -2000000.0], [90.5054148, -17.6789142]), ('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #3', [0.0, 0.0], [0.0, 0.0]), ('control #4', [1113194.9, 1118889.97], [9.9999999, 10.0]), ('control #5', [-8237642.3, 4970241.3], [-73.9999998, 40.7139556]), ('control #6', [15000000.0, -6000000.0], [134.7472926, -47.3537047]), ('boundary #7', [0.0, 20037508.342789244], [0.0, 85.0511288])], [('regression #1', [-30000000.0, -2000000.0], [90.5054148, -17.6789142]), ('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #5', [-8237642.3, 4970241.3], [-73.9999998, 40.7139556]), ('control #6', [15000000.0, -6000000.0], [134.7472926, -47.3537047]), ('boundary #7', [0.0, 20037508.342789244], [0.0, 85.0511288]), ('boundary #8', [0.0, -20037508.342789244], [0.0, -85.0511288]), ('control #9', [500000.0, -500000.0], [4.4915764, -4.486983]), ('control #10', [-19000000.0, 12000000.0], [-170.679904, 72.6726763])], [('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #4', [1113194.9, 1118889.97], [9.9999999, 10.0]), ('boundary #8', [0.0, -20037508.342789244], [0.0, -85.0511288]), ('control #9', [500000.0, -500000.0], [4.4915764, -4.486983]), ('control #10', [-19000000.0, 12000000.0], [-170.679904, 72.6726763]), ('control #11', [3000000.0, 9000000.0], [26.9494585, 62.5882773]), ('regression #12', [45000000.0, 3000000.0], [44.2418779, 26.0074202]), ('control #13', [-1234567.0, 7654321.0], [-11.0903041, 56.4787668])], [('control #3', [0.0, 0.0], [0.0, 0.0]), ('control #5', [-8237642.3, 4970241.3], [-73.9999998, 40.7139556]), ('control #11', [3000000.0, 9000000.0], [26.9494585, 62.5882773]), ('regression #12', [45000000.0, 3000000.0], [44.2418779, 26.0074202]), ('control #13', [-1234567.0, 7654321.0], [-11.0903041, 56.4787668]), ('regression #14', [-21000000.0, 500000.0], [171.3537903, 4.486983]), ('regression #15', [-25000000.0, -4000000.0], [135.421179, -33.7852301]), ('regression #16', [-40075016.0, 0.0], [6.2e-06, 0.0])], [('regression #0', [25000000.0, 1000000.0], [-135.421179, 8.9465739]), ('regression #1', [-30000000.0, -2000000.0], [90.5054148, -17.6789142]), ('boundary #2', [20037508.342789244, 0.0], [-180.0, 0.0]), ('control #4', [1113194.9, 1118889.97], [9.9999999, 10.0]), ('control #6', [15000000.0, -6000000.0], [134.7472926, -47.3537047]), ('regression #14', [-21000000.0, 500000.0], [171.3537903, 4.486983]), ('regression #15', [-25000000.0, -4000000.0], [135.421179, -33.7852301]), ('regression #16', [-40075016.0, 0.0], [6.2e-06, 0.0])]]\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-web-mercator-inverse-gudermannian-scaling","generated_at":"2026-09-29T14:48:15.572353+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Converting clicked map positions or tile corners back to geographic coordinates uses this inverse; faults misplace every reverse-geocoded point.","root_cause":"The inverse Gudermannian omits the factor of two, returning atan(e^(y/R)) - pi/4 which is half the latitude.","sha256":"5aefd74ae281283fa5a8cf1c1c3f1ba1e06ac925c2be5f8ad11e2f9e419d61ec","title":"Spherical web mercator inverse projection: gudermannian scaling · 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":40.271,"exit_code":1,"observations":[{"actual":[-135.421179,53.9465739],"check":"regression #0","expected":[-135.421179,8.9465739],"passed":false},{"actual":[90.5054148,27.3210858],"check":"regression #1","expected":[90.5054148,-17.6789142],"passed":false},{"actual":[-180.0,45.0],"check":"boundary #2","expected":[-180.0,0.0],"passed":false},{"actual":[0.0,45.0],"check":"control #3","expected":[0.0,0.0],"passed":false},{"actual":[9.9999999,55.0],"check":"control #4","expected":[9.9999999,10.0],"passed":false},{"actual":[-73.9999998,85.7139556],"check":"control #5","expected":[-73.9999998,40.7139556],"passed":false},{"actual":[134.7472926,-2.3537047],"check":"control #6","expected":[134.7472926,-47.3537047],"passed":false},{"actual":[0.0,130.0511288],"check":"boundary #7","expected":[0.0,85.0511288],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression #0\", \"actual\": [-135.421179, 53.9465739], \"expected\": [-135.421179, 8.9465739], \"passed\": false}, {\"check\": \"regression #1\", \"actual\": [90.5054148, 27.3210858], \"expected\": [90.5054148, -17.6789142], \"passed\": false}, {\"check\": \"boundary #2\", \"actual\": [-180.0, 45.0], \"expected\": [-180.0, 0.0], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [0.0, 45.0], \"expected\": [0.0, 0.0], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [9.9999999, 55.0], \"expected\": [9.9999999, 10.0], \"passed\": false}, {\"check\": \"control #5\", \"actual\": [-73.9999998, 85.7139556], \"expected\": [-73.9999998, 40.7139556], \"passed\": false}, {\"check\": \"control #6\", \"actual\": [134.7472926, -2.3537047], \"expected\": [134.7472926, -47.3537047], \"passed\": false}, {\"check\": \"boundary #7\", \"actual\": [0.0, 130.0511288], \"expected\": [0.0, 85.0511288], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.803,"exit_code":1,"observations":[{"actual":[-135.421179,4.4732869],"check":"regression #0","expected":[-135.421179,8.9465739],"passed":false},{"actual":[90.5054148,-8.8394571],"check":"regression #1","expected":[90.5054148,-17.6789142],"passed":false},{"actual":[-180.0,0.0],"check":"boundary #2","expected":[-180.0,0.0],"passed":true},{"actual":[0.0,0.0],"check":"control #3","expected":[0.0,0.0],"passed":true},{"actual":[9.9999999,5.0],"check":"control #4","expected":[9.9999999,10.0],"passed":false},{"actual":[-73.9999998,20.3569778],"check":"control #5","expected":[-73.9999998,40.7139556],"passed":false},{"actual":[134.7472926,-23.6768524],"check":"control #6","expected":[134.7472926,-47.3537047],"passed":false},{"actual":[0.0,42.5255644],"check":"boundary #7","expected":[0.0,85.0511288],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression #0\", \"actual\": [-135.421179, 4.4732869], \"expected\": [-135.421179, 8.9465739], \"passed\": false}, {\"check\": \"regression #1\", \"actual\": [90.5054148, -8.8394571], \"expected\": [90.5054148, -17.6789142], \"passed\": false}, {\"check\": \"boundary #2\", \"actual\": [-180.0, 0.0], \"expected\": [-180.0, 0.0], \"passed\": true}, {\"check\": \"control #3\", \"actual\": [0.0, 0.0], \"expected\": [0.0, 0.0], \"passed\": true}, {\"check\": \"control #4\", \"actual\": [9.9999999, 5.0], \"expected\": [9.9999999, 10.0], \"passed\": false}, {\"check\": \"control #5\", \"actual\": [-73.9999998, 20.3569778], \"expected\": [-73.9999998, 40.7139556], \"passed\": false}, {\"check\": \"control #6\", \"actual\": [134.7472926, -23.6768524], \"expected\": [134.7472926, -47.3537047], \"passed\": false}, {\"check\": \"boundary #7\", \"actual\": [0.0, 42.5255644], \"expected\": [0.0, 85.0511288], \"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."}}