{"abstract":"Bound constrained termination rejects a valid boundary optimum.","category":"Optimization solver contracts","checks":7,"contract":"Given feasible scalar x and lo<=hi, return whether the unit-step projected gradient mapping is exactly zero.","evaluation_group":"model-93dbdef170968593","failed_approach":"Suppressing all gradients at a bound also suppresses feasible descent directions.","family":"z-optimization-projected-stationarity","id":"FA-11996","implementations":{"attempt":{"sha256":"e4d10e8e3566afe6ec83f98b9332114c7f370a2d374991657aaf8bc30025f2f4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x, g, lo, hi):\n    return g == 0 or x == lo or x == hi\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('lower optimum', solve(0, N, 0, 10), True)\ncheck('lower needs inward step', solve(0, -N, 0, 10), False)\ncheck('upper optimum', solve(10, -N, 0, 10), True)\ncheck('upper needs inward step', solve(10, N, 0, 10), False)\ncheck('interior stationary', solve(5, 0, 0, 10), True)\ncheck('interior moving', solve(5, 1, 0, 10), False)\ncheck('singleton feasible set', solve(3, -N, 3, 3), True)\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":"2599beb5cea48608f318dc5037a3fe6ca2422ce88d6ee7dccd15ff88ec8b4177","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x, g, lo, hi):\n    return g == 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('lower optimum', solve(0, N, 0, 10), True)\ncheck('lower needs inward step', solve(0, -N, 0, 10), False)\ncheck('upper optimum', solve(10, -N, 0, 10), True)\ncheck('upper needs inward step', solve(10, N, 0, 10), False)\ncheck('interior stationary', solve(5, 0, 0, 10), True)\ncheck('interior moving', solve(5, 1, 0, 10), False)\ncheck('singleton feasible set', solve(3, -N, 3, 3), True)\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":"9ae44aa3301d221b843c344e35a1fdff0bbf957a80f092115181b81ff31a27df","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x, g, lo, hi):\n    return x == min(hi, max(lo, x-g))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('lower optimum', solve(0, N, 0, 10), True)\ncheck('lower needs inward step', solve(0, -N, 0, 10), False)\ncheck('upper optimum', solve(10, -N, 0, 10), True)\ncheck('upper needs inward step', solve(10, N, 0, 10), False)\ncheck('interior stationary', solve(5, 0, 0, 10), True)\ncheck('interior moving', solve(5, 1, 0, 10), False)\ncheck('singleton feasible set', solve(3, -N, 3, 3), True)\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-projected-stationarity","generated_at":"2026-09-29T14:38:52.942676+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.","repair":"Check the projected gradient mapping x-clip(x-g,lo,hi).","root_cause":"Termination checks raw gradient magnitude.","sha256":"a40cd6f3c2569e25a78f60af6b4a58a32e0bae9504d3386f560c14473fc43144","title":"Bound constrained termination rejects a valid boundary optimum · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.586,"exit_code":1,"observations":[{"actual":true,"check":"lower optimum","expected":true,"passed":true},{"actual":true,"check":"lower needs inward step","expected":false,"passed":false},{"actual":true,"check":"upper optimum","expected":true,"passed":true},{"actual":true,"check":"upper needs inward step","expected":false,"passed":false},{"actual":true,"check":"interior stationary","expected":true,"passed":true},{"actual":false,"check":"interior moving","expected":false,"passed":true},{"actual":true,"check":"singleton feasible set","expected":true,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"lower optimum\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"lower needs inward step\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"upper optimum\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"upper needs inward step\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"interior stationary\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"interior moving\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"singleton feasible set\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.785,"exit_code":1,"observations":[{"actual":false,"check":"lower optimum","expected":true,"passed":false},{"actual":false,"check":"lower needs inward step","expected":false,"passed":true},{"actual":false,"check":"upper optimum","expected":true,"passed":false},{"actual":false,"check":"upper needs inward step","expected":false,"passed":true},{"actual":true,"check":"interior stationary","expected":true,"passed":true},{"actual":false,"check":"interior moving","expected":false,"passed":true},{"actual":false,"check":"singleton feasible set","expected":true,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"lower optimum\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"lower needs inward step\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"upper optimum\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"upper needs inward step\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"interior stationary\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"interior moving\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"singleton feasible set\", \"actual\": false, \"expected\": true, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.951,"exit_code":0,"observations":[{"actual":true,"check":"lower optimum","expected":true,"passed":true},{"actual":false,"check":"lower needs inward step","expected":false,"passed":true},{"actual":true,"check":"upper optimum","expected":true,"passed":true},{"actual":false,"check":"upper needs inward step","expected":false,"passed":true},{"actual":true,"check":"interior stationary","expected":true,"passed":true},{"actual":false,"check":"interior moving","expected":false,"passed":true},{"actual":true,"check":"singleton feasible set","expected":true,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"lower optimum\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"lower needs inward step\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"upper optimum\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"upper needs inward step\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"interior stationary\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"interior moving\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"singleton feasible set\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}