{"abstract":"Projection divides by vector magnitude in the wrong norm.","category":"Planar geometry","checks":4,"contract":"Integer coordinates and lengths, with exact arithmetic except for indicated division results. Lengths are nonnegative. Rectangles are (xmin,ymin,xmax,ymax) with ordered bounds; coordinate vectors have matching dimensions. p and v are same-length integer vectors and v is nonzero. Return reduced Fraction strings for the orthogonal projection onto span(v). Exact operational definition: [str(Fraction(sum(a*b for a,b in zip(p,v))*x,sum(x*x for x in v))) for x in v]","contract_signature":"p, v","evaluation_group":"model-81434059407389c7","failed_approach":"The projection coefficient is returned without multiplying by the direction.","family":"xn-point-projection-onto-vector","id":"FA-5866","implementations":{"attempt":{"sha256":"1e9a7fc06244a34ca4ae3c8ddbde5dd04da1069ef205889d637615c0b3de3b08","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(p, v):\n    return [str(Fraction(sum(a*b for a,b in zip(p,v)),sum(x*x for x in v))) for x in v]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((2, 3), (1, 0))', solve(*((2, 3), (1, 0))), ['2', '0'])\ncheck('fixture 2: ((2, 3), (1, 1))', solve(*((2, 3), (1, 1))), ['5/2', '5/2'])\ncheck('fixture 3: ((1, 0), (2, 0))', solve(*((1, 0), (2, 0))), ['1', '0'])\ncheck('fixture 4: ((0, 0), (1, 2))', solve(*((0, 0), (1, 2))), ['0', '0'])\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":"4c0dd9734f1dc423769112946e6934bcf787a9d4fb5179569e3ad9a7fca4339b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(p, v):\n    return [str(Fraction(sum(a*b for a,b in zip(p,v))*x,sum(abs(x) for x in v))) for x in v]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((2, 3), (1, 0))', solve(*((2, 3), (1, 0))), ['2', '0'])\ncheck('fixture 2: ((2, 3), (1, 1))', solve(*((2, 3), (1, 1))), ['5/2', '5/2'])\ncheck('fixture 3: ((1, 0), (2, 0))', solve(*((1, 0), (2, 0))), ['1', '0'])\ncheck('fixture 4: ((0, 0), (1, 2))', solve(*((0, 0), (1, 2))), ['0', '0'])\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":" 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":"xn-point-projection-onto-vector","generated_at":"2026-09-29T14:37:54.511490+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Planar geometry results depend on the stated convention.","root_cause":"Projection divides by vector magnitude in the wrong norm.","sha256":"ce100e34b1f2ffca6ceaf97f320e65ccb2034afecb4646157fc2ead531668555","title":"Point projection onto vector · 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":51.347,"exit_code":1,"observations":[{"actual":["2","2"],"check":"fixture 1: ((2, 3), (1, 0))","expected":["2","0"],"passed":false},{"actual":["5/2","5/2"],"check":"fixture 2: ((2, 3), (1, 1))","expected":["5/2","5/2"],"passed":true},{"actual":["1/2","1/2"],"check":"fixture 3: ((1, 0), (2, 0))","expected":["1","0"],"passed":false},{"actual":["0","0"],"check":"fixture 4: ((0, 0), (1, 2))","expected":["0","0"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((2, 3), (1, 0))\", \"actual\": [\"2\", \"2\"], \"expected\": [\"2\", \"0\"], \"passed\": false}, {\"check\": \"fixture 2: ((2, 3), (1, 1))\", \"actual\": [\"5/2\", \"5/2\"], \"expected\": [\"5/2\", \"5/2\"], \"passed\": true}, {\"check\": \"fixture 3: ((1, 0), (2, 0))\", \"actual\": [\"1/2\", \"1/2\"], \"expected\": [\"1\", \"0\"], \"passed\": false}, {\"check\": \"fixture 4: ((0, 0), (1, 2))\", \"actual\": [\"0\", \"0\"], \"expected\": [\"0\", \"0\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":59.405,"exit_code":1,"observations":[{"actual":["2","0"],"check":"fixture 1: ((2, 3), (1, 0))","expected":["2","0"],"passed":true},{"actual":["5/2","5/2"],"check":"fixture 2: ((2, 3), (1, 1))","expected":["5/2","5/2"],"passed":true},{"actual":["2","0"],"check":"fixture 3: ((1, 0), (2, 0))","expected":["1","0"],"passed":false},{"actual":["0","0"],"check":"fixture 4: ((0, 0), (1, 2))","expected":["0","0"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((2, 3), (1, 0))\", \"actual\": [\"2\", \"0\"], \"expected\": [\"2\", \"0\"], \"passed\": true}, {\"check\": \"fixture 2: ((2, 3), (1, 1))\", \"actual\": [\"5/2\", \"5/2\"], \"expected\": [\"5/2\", \"5/2\"], \"passed\": true}, {\"check\": \"fixture 3: ((1, 0), (2, 0))\", \"actual\": [\"2\", \"0\"], \"expected\": [\"1\", \"0\"], \"passed\": false}, {\"check\": \"fixture 4: ((0, 0), (1, 2))\", \"actual\": [\"0\", \"0\"], \"expected\": [\"0\", \"0\"], \"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."}}