{"abstract":"Distances from the central meridian are doubled.","category":"Map projection transforms","checks":8,"contract":"Input [lon, lat, zone, hemisphere] with |lat| <= 80 and lon within 4 degrees of the zone central meridian 6*zone-183. On a sphere R = 6371000 with k0 = 0.9996: B = cos(phi)*sin(dl); x = 0.5*k0*R*ln((1+B)/(1-B)); y = k0*R*atan2(tan(phi), cos(dl)). Easting = 500000 + x. Northing = y plus 10000000 when the requested grid hemisphere is \"S\" (the caller may deliberately project points just north of the equator in a southern grid). Return [easting, northing] rounded to 2 decimals.","contract_signature":"x","evaluation_group":"w2-map-projection-transforms-spherical-utm-forward","failed_approach":"The half factor was restored but the central scale factor k0 was dropped from the easting.","family":"w2-map-projection-transforms-spherical-utm-forward-easting-half-factor","id":"FA-70026","implementations":{"attempt":{"sha256":"29e6e64193a39dba00c011665ccc44859a5e86fb713dd9ea9d78186185b33713","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lon, lat, zone, hemi = x\n    R = 6371000.0\n    k0 = 0.9996\n    lon0 = zone * 6 - 183\n    dl = math.radians(lon - lon0)\n    phi = math.radians(lat)\n    B = math.cos(phi) * math.sin(dl)\n    xm = 0.5 * R * math.log((1 + B) / (1 - B))\n    ym = k0 * R * math.atan2(math.tan(phi), math.cos(dl))\n    easting = 500000.0 + xm\n    northing = ym + (10000000.0 if hemi == 'S' else 0.0)\n    return [round(easting, 2), round(northing, 2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-146.456, 65.451, 6, 'S'], [525121.58, 17275016.5]), ('control #1', [-24.305, 48.206, 26, 'S'], [699628.48, 15361620.03]), ('control #2', [-3.252, -34.222, 30, 'N'], [476839.56, -3803819.3]), ('control #3', [140.223, -1.339, 54, 'S'], [413657.04, 9851155.87]), ('control #4', [-99.681, -57.299, 14, 'S'], [459106.63, 3630985.93]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #1', [-24.305, 48.206, 26, 'S'], [699628.48, 15361620.03]), ('control #2', [-3.252, -34.222, 30, 'N'], [476839.56, -3803819.3]), ('control #5', [131.956, -7.201, 52, 'S'], [826109.36, 9198550.44]), ('control #6', [-63.683, 39.81, 20, 'S'], [441683.41, 14425121.91]), ('control #7', [-31.602, 39.795, 25, 'S'], [619393.11, 14424164.48]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #2', [-3.252, -34.222, 30, 'N'], [476839.56, -3803819.3]), ('control #3', [140.223, -1.339, 54, 'S'], [413657.04, 9851155.87]), ('control #8', [87.283, -45.722, 45, 'N'], [521960.41, -5082059.64]), ('control #9', [74.243, 54.044, 43, 'S'], [450595.96, 16007279.04]), ('control #10', [-96.557, 39.544, 14, 'S'], [709406.66, 14398176.63]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #3', [140.223, -1.339, 54, 'S'], [413657.04, 9851155.87]), ('control #4', [-99.681, -57.299, 14, 'S'], [459106.63, 3630985.93]), ('control #11', [162.356, -15.269, 58, 'N'], [216405.53, -1698880.3]), ('control #12', [-107.58, 5.652, 13, 'N'], [214531.37, 628855.65]), ('control #13', [100.982, 3.293, 47, 'S'], [719980.03, 10366237.05]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #4', [-99.681, -57.299, 14, 'S'], [459106.63, 3630985.93]), ('control #5', [131.956, -7.201, 52, 'S'], [826109.36, 9198550.44]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('regression #15', [-75.5, 0.2, 18, 'S'], [444424.41, 10022230.94]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('regression #17', [30.0, -0.3, 36, 'N'], [166400.77, -33390.89]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19]), ('control #19', [12.3, -35.0, 33, 'S'], [254136.28, 6106410.11])]]\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":"af3fc611ad5c378b9f650d088537a882cf8cd3cb930e3ff135666c2fdac3eaed","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    lon, lat, zone, hemi = x\n    R = 6371000.0\n    k0 = 0.9996\n    lon0 = zone * 6 - 183\n    dl = math.radians(lon - lon0)\n    phi = math.radians(lat)\n    B = math.cos(phi) * math.sin(dl)\n    xm = k0 * R * math.log((1 + B) / (1 - B))\n    ym = k0 * R * math.atan2(math.tan(phi), math.cos(dl))\n    easting = 500000.0 + xm\n    northing = ym + (10000000.0 if hemi == 'S' else 0.0)\n    return [round(easting, 2), round(northing, 2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [-146.456, 65.451, 6, 'S'], [525121.58, 17275016.5]), ('control #1', [-24.305, 48.206, 26, 'S'], [699628.48, 15361620.03]), ('control #2', [-3.252, -34.222, 30, 'N'], [476839.56, -3803819.3]), ('control #3', [140.223, -1.339, 54, 'S'], [413657.04, 9851155.87]), ('control #4', [-99.681, -57.299, 14, 'S'], [459106.63, 3630985.93]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #1', [-24.305, 48.206, 26, 'S'], [699628.48, 15361620.03]), ('control #2', [-3.252, -34.222, 30, 'N'], [476839.56, -3803819.3]), ('control #5', [131.956, -7.201, 52, 'S'], [826109.36, 9198550.44]), ('control #6', [-63.683, 39.81, 20, 'S'], [441683.41, 14425121.91]), ('control #7', [-31.602, 39.795, 25, 'S'], [619393.11, 14424164.48]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #2', [-3.252, -34.222, 30, 'N'], [476839.56, -3803819.3]), ('control #3', [140.223, -1.339, 54, 'S'], [413657.04, 9851155.87]), ('control #8', [87.283, -45.722, 45, 'N'], [521960.41, -5082059.64]), ('control #9', [74.243, 54.044, 43, 'S'], [450595.96, 16007279.04]), ('control #10', [-96.557, 39.544, 14, 'S'], [709406.66, 14398176.63]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #3', [140.223, -1.339, 54, 'S'], [413657.04, 9851155.87]), ('control #4', [-99.681, -57.299, 14, 'S'], [459106.63, 3630985.93]), ('control #11', [162.356, -15.269, 58, 'N'], [216405.53, -1698880.3]), ('control #12', [-107.58, 5.652, 13, 'N'], [214531.37, 628855.65]), ('control #13', [100.982, 3.293, 47, 'S'], [719980.03, 10366237.05]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19])], [('control #4', [-99.681, -57.299, 14, 'S'], [459106.63, 3630985.93]), ('control #5', [131.956, -7.201, 52, 'S'], [826109.36, 9198550.44]), ('regression #14', [9.0, 0.5, 32, 'S'], [500000.0, 10055575.22]), ('regression #15', [-75.5, 0.2, 18, 'S'], [444424.41, 10022230.94]), ('boundary #16', [15.0, 0.0, 33, 'N'], [500000.0, 0.0]), ('regression #17', [30.0, -0.3, 36, 'N'], [166400.77, -33390.89]), ('boundary #18', [3.0, 45.0, 31, 'N'], [500000.0, 5001770.19]), ('control #19', [12.3, -35.0, 33, 'S'], [254136.28, 6106410.11])]]\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-spherical-utm-forward-easting-half-factor","generated_at":"2026-09-29T14:48:16.825181+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Survey exports and GPS receivers express positions as UTM eastings and northings; a wrong false origin or meridian moves points by hundreds of kilometres.","root_cause":"The inverse hyperbolic tangent is written as ln((1+B)/(1-B)) without the 1/2 factor.","sha256":"e2786817239c7d0ca6eef40c7231c1e21b5369e1bb9964d5a00418938015adf0","title":"Spherical transverse mercator in a UTM grid: easting half factor · 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":41.164,"exit_code":1,"observations":[{"actual":[525131.63,17275016.5],"check":"control #0","expected":[525121.58,17275016.5],"passed":false},{"actual":[699708.36,15361620.03],"check":"control #1","expected":[699628.48,15361620.03],"passed":false},{"actual":[476830.3,-3803819.3],"check":"control #2","expected":[476839.56,-3803819.3],"passed":false},{"actual":[413622.49,9851155.87],"check":"control #3","expected":[413657.04,9851155.87],"passed":false},{"actual":[459090.27,3630985.93],"check":"control #4","expected":[459106.63,3630985.93],"passed":false},{"actual":[500000.0,10055575.22],"check":"regression #14","expected":[500000.0,10055575.22],"passed":true},{"actual":[500000.0,0.0],"check":"boundary #16","expected":[500000.0,0.0],"passed":true},{"actual":[500000.0,5001770.19],"check":"boundary #18","expected":[500000.0,5001770.19],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [525131.63, 17275016.5], \"expected\": [525121.58, 17275016.5], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [699708.36, 15361620.03], \"expected\": [699628.48, 15361620.03], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [476830.3, -3803819.3], \"expected\": [476839.56, -3803819.3], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [413622.49, 9851155.87], \"expected\": [413657.04, 9851155.87], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [459090.27, 3630985.93], \"expected\": [459106.63, 3630985.93], \"passed\": false}, {\"check\": \"regression #14\", \"actual\": [500000.0, 10055575.22], \"expected\": [500000.0, 10055575.22], \"passed\": true}, {\"check\": \"boundary #16\", \"actual\": [500000.0, 0.0], \"expected\": [500000.0, 0.0], \"passed\": true}, {\"check\": \"boundary #18\", \"actual\": [500000.0, 5001770.19], \"expected\": [500000.0, 5001770.19], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.093,"exit_code":1,"observations":[{"actual":[550243.15,17275016.5],"check":"control #0","expected":[525121.58,17275016.5],"passed":false},{"actual":[899256.95,15361620.03],"check":"control #1","expected":[699628.48,15361620.03],"passed":false},{"actual":[453679.13,-3803819.3],"check":"control #2","expected":[476839.56,-3803819.3],"passed":false},{"actual":[327314.08,9851155.87],"check":"control #3","expected":[413657.04,9851155.87],"passed":false},{"actual":[418213.26,3630985.93],"check":"control #4","expected":[459106.63,3630985.93],"passed":false},{"actual":[500000.0,10055575.22],"check":"regression #14","expected":[500000.0,10055575.22],"passed":true},{"actual":[500000.0,0.0],"check":"boundary #16","expected":[500000.0,0.0],"passed":true},{"actual":[500000.0,5001770.19],"check":"boundary #18","expected":[500000.0,5001770.19],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [550243.15, 17275016.5], \"expected\": [525121.58, 17275016.5], \"passed\": false}, {\"check\": \"control #1\", \"actual\": [899256.95, 15361620.03], \"expected\": [699628.48, 15361620.03], \"passed\": false}, {\"check\": \"control #2\", \"actual\": [453679.13, -3803819.3], \"expected\": [476839.56, -3803819.3], \"passed\": false}, {\"check\": \"control #3\", \"actual\": [327314.08, 9851155.87], \"expected\": [413657.04, 9851155.87], \"passed\": false}, {\"check\": \"control #4\", \"actual\": [418213.26, 3630985.93], \"expected\": [459106.63, 3630985.93], \"passed\": false}, {\"check\": \"regression #14\", \"actual\": [500000.0, 10055575.22], \"expected\": [500000.0, 10055575.22], \"passed\": true}, {\"check\": \"boundary #16\", \"actual\": [500000.0, 0.0], \"expected\": [500000.0, 0.0], \"passed\": true}, {\"check\": \"boundary #18\", \"actual\": [500000.0, 5001770.19], \"expected\": [500000.0, 5001770.19], \"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."}}