{"abstract":"Quasi Newton update admits nonpositive curvature.","category":"Optimization solver contracts","checks":9,"contract":"Return whether a finite Python integer/float vector pair may enter an undamped BFGS update under the strict curvature condition s dot y>0, evaluated exactly for the represented inputs; equal vector lengths are assumed.","contract_signature":"s, y","evaluation_group":"model-6a4ea2d15da18497","failed_approach":"Taking an absolute value before testing positivity admits negative curvature.","family":"z-optimization-bfgs-curvature","id":"FA-12001","implementations":{"attempt":{"sha256":"f860649c73083b7a2c1a1a7211da5c12b6abd8db33e054043359c6b2d3bb16f6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(s, y):\n    return abs(sum(a*b for a,b in zip(s,y))) > 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('negative pair', solve([N], [-1]), False)\ncheck('positive pair', solve([N], [1]), True)\ncheck('zero step', solve([0], [N]), False)\ncheck('orthogonal', solve([1,0], [0,N]), False)\ncheck('cancellation', solve([1,1], [N,-N]), False)\ncheck('mixed positive', solve([1,2], [-N,N]), True)\ncheck('mixed negative', solve([2,1], [-N,N]), False)\ncheck('overflow cancellation retains positive curvature', solve([1e308,1e308,N],[2.0,-2.0,1.0]), True)\ncheck('overflow cancellation retains negative curvature', solve([1e308,1e308,N],[2.0,-2.0,-1.0]), False)\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":"68b9ef59f95af0d13fb703a46249f6f9eaf3c1b1a653edb4141e924ce8cda49c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(s, y):\n    return sum(a*b for a,b in zip(s,y)) != 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('negative pair', solve([N], [-1]), False)\ncheck('positive pair', solve([N], [1]), True)\ncheck('zero step', solve([0], [N]), False)\ncheck('orthogonal', solve([1,0], [0,N]), False)\ncheck('cancellation', solve([1,1], [N,-N]), False)\ncheck('mixed positive', solve([1,2], [-N,N]), True)\ncheck('mixed negative', solve([2,1], [-N,N]), False)\ncheck('overflow cancellation retains positive curvature', solve([1e308,1e308,N],[2.0,-2.0,1.0]), True)\ncheck('overflow cancellation retains negative curvature', solve([1e308,1e308,N],[2.0,-2.0,-1.0]), False)\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":"Controlled finite inputs and explicit one-step contracts; this is not a production solver or a numerical stability benchmark. 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":"z-optimization-bfgs-curvature","generated_at":"2026-09-29T14:38:52.960065+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"This deterministic solver-step model isolates an algorithmic invariant used by iterative optimization implementations.","root_cause":"The secant pair is used whenever its dot product is nonzero.","sha256":"4f70745545a62324e68a6b40c105fd1c2f4e16d610ae70b445cf5a7b17ff01ba","title":"Quasi Newton update admits nonpositive curvature · 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":41.217,"exit_code":1,"observations":[{"actual":true,"check":"negative pair","expected":false,"passed":false},{"actual":true,"check":"positive pair","expected":true,"passed":true},{"actual":false,"check":"zero step","expected":false,"passed":true},{"actual":false,"check":"orthogonal","expected":false,"passed":true},{"actual":false,"check":"cancellation","expected":false,"passed":true},{"actual":true,"check":"mixed positive","expected":true,"passed":true},{"actual":true,"check":"mixed negative","expected":false,"passed":false},{"actual":false,"check":"overflow cancellation retains positive curvature","expected":true,"passed":false},{"actual":false,"check":"overflow cancellation retains negative curvature","expected":false,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"negative pair\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"positive pair\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"zero step\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"orthogonal\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"cancellation\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"mixed positive\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"mixed negative\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"overflow cancellation retains positive curvature\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"overflow cancellation retains negative curvature\", \"actual\": false, \"expected\": false, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.506,"exit_code":1,"observations":[{"actual":true,"check":"negative pair","expected":false,"passed":false},{"actual":true,"check":"positive pair","expected":true,"passed":true},{"actual":false,"check":"zero step","expected":false,"passed":true},{"actual":false,"check":"orthogonal","expected":false,"passed":true},{"actual":false,"check":"cancellation","expected":false,"passed":true},{"actual":true,"check":"mixed positive","expected":true,"passed":true},{"actual":true,"check":"mixed negative","expected":false,"passed":false},{"actual":true,"check":"overflow cancellation retains positive curvature","expected":true,"passed":true},{"actual":true,"check":"overflow cancellation retains negative curvature","expected":false,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"negative pair\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"positive pair\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"zero step\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"orthogonal\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"cancellation\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"mixed positive\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"mixed negative\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"overflow cancellation retains positive curvature\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"overflow cancellation retains negative curvature\", \"actual\": true, \"expected\": false, \"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."}}