{"abstract":"Negative available amplitude is inferred from positive headroom.","category":"PCM sample encoding","checks":8,"contract":"Recenter bounded unsigned PCM around an explicitly calibrated zero code and report asymmetric representable headroom; clamp invalid code inputs before recentering.","contract_signature":"codes, width, zero_code","evaluation_group":"s3-pcm-excess-code-recenter","failed_approach":"Assuming a symmetric midpoint ignores zero calibration.","family":"s3-pcm-excess-code-recenter-negative-headroom","id":"FA-49026","implementations":{"attempt":{"sha256":"ab0cad2fe89454a1dee83ddc3d80624d1241811fafd38b43f80f2702b905eb0b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, zero_code):\n    limit=(1<<width)-1\n    out=[]\n    for code in codes:\n        bounded=max(0,min(limit,code))\n        delta=bounded-zero_code\n        low=-(1<<(width-1))\n        high=limit-zero_code\n        out.append([delta,low,high])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 3, 7, 8], 3, 3)), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\ncheck('oracle 2', solve(*([-1, 0, 10], 3, 2)), [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]])\ncheck('oracle 3', solve(*([1, 2, 3], 2, 1)), [[0, -1, 2], [1, -1, 2], [2, -1, 2]])\ncheck('oracle 4', solve(*([], 4, 5)), [])\ncheck('oracle 5', solve(*([0, 15, 16], 4, 6)), [[-6, -6, 9], [9, -6, 9], [9, -6, 9]])\ncheck('oracle 6', solve(*([0, 1], 1, 0)), [[0, 0, 1], [1, 0, 1]])\ncheck('oracle 7', solve(*([2, 4, 7], 3, 5)), [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]])\nif N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\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":"086dfb83e61541056b6ae7ecfd2962ee68dd225f18214d78cae8e539afc0eef1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, zero_code):\n    limit=(1<<width)-1\n    out=[]\n    for code in codes:\n        bounded=max(0,min(limit,code))\n        delta=bounded-zero_code\n        low=zero_code-limit\n        high=limit-zero_code\n        out.append([delta,low,high])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 3, 7, 8], 3, 3)), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\ncheck('oracle 2', solve(*([-1, 0, 10], 3, 2)), [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]])\ncheck('oracle 3', solve(*([1, 2, 3], 2, 1)), [[0, -1, 2], [1, -1, 2], [2, -1, 2]])\ncheck('oracle 4', solve(*([], 4, 5)), [])\ncheck('oracle 5', solve(*([0, 15, 16], 4, 6)), [[-6, -6, 9], [9, -6, 9], [9, -6, 9]])\ncheck('oracle 6', solve(*([0, 1], 1, 0)), [[0, 0, 1], [1, 0, 1]])\ncheck('oracle 7', solve(*([2, 4, 7], 3, 5)), [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]])\nif N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\nif N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8, 0, 3, 7, 8], 3, 3]), [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]])\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 finite model; no claim of hardware timing or full file-format conformance. 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":"s3-pcm-excess-code-recenter-negative-headroom","generated_at":"2026-09-29T14:44:56.249862+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Offline PCM interchange uses these exact bounded packet and sample representation decisions.","root_cause":"Negative available amplitude is inferred from positive headroom.","sha256":"61301a16c0dcfdbed187ed3823f2d8fab5b664842b5309296e7f9ae9699edb36","title":"Excess code recenter: negative headroom · 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":41.553,"exit_code":1,"observations":[{"actual":[[-3,-4,4],[0,-4,4],[4,-4,4],[4,-4,4]],"check":"oracle 1","expected":[[-3,-3,4],[0,-3,4],[4,-3,4],[4,-3,4]],"passed":false},{"actual":[[-2,-4,5],[-2,-4,5],[5,-4,5]],"check":"oracle 2","expected":[[-2,-2,5],[-2,-2,5],[5,-2,5]],"passed":false},{"actual":[[0,-2,2],[1,-2,2],[2,-2,2]],"check":"oracle 3","expected":[[0,-1,2],[1,-1,2],[2,-1,2]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-6,-8,9],[9,-8,9],[9,-8,9]],"check":"oracle 5","expected":[[-6,-6,9],[9,-6,9],[9,-6,9]],"passed":false},{"actual":[[0,-1,1],[1,-1,1]],"check":"oracle 6","expected":[[0,0,1],[1,0,1]],"passed":false},{"actual":[[-3,-4,2],[-1,-4,2],[2,-4,2]],"check":"oracle 7","expected":[[-3,-5,2],[-1,-5,2],[2,-5,2]],"passed":false},{"actual":[[-3,-4,4],[0,-4,4],[4,-4,4],[4,-4,4],[-3,-4,4],[0,-4,4],[4,-4,4],[4,-4,4]],"check":"variant packet 1","expected":[[-3,-3,4],[0,-3,4],[4,-3,4],[4,-3,4],[-3,-3,4],[0,-3,4],[4,-3,4],[4,-3,4]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]], \"expected\": [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-2, -4, 5], [-2, -4, 5], [5, -4, 5]], \"expected\": [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, -2, 2], [1, -2, 2], [2, -2, 2]], \"expected\": [[0, -1, 2], [1, -1, 2], [2, -1, 2]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-6, -8, 9], [9, -8, 9], [9, -8, 9]], \"expected\": [[-6, -6, 9], [9, -6, 9], [9, -6, 9]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, -1, 1], [1, -1, 1]], \"expected\": [[0, 0, 1], [1, 0, 1]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[-3, -4, 2], [-1, -4, 2], [2, -4, 2]], \"expected\": [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4], [-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]], \"expected\": [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.568,"exit_code":1,"observations":[{"actual":[[-3,-4,4],[0,-4,4],[4,-4,4],[4,-4,4]],"check":"oracle 1","expected":[[-3,-3,4],[0,-3,4],[4,-3,4],[4,-3,4]],"passed":false},{"actual":[[-2,-5,5],[-2,-5,5],[5,-5,5]],"check":"oracle 2","expected":[[-2,-2,5],[-2,-2,5],[5,-2,5]],"passed":false},{"actual":[[0,-2,2],[1,-2,2],[2,-2,2]],"check":"oracle 3","expected":[[0,-1,2],[1,-1,2],[2,-1,2]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-6,-9,9],[9,-9,9],[9,-9,9]],"check":"oracle 5","expected":[[-6,-6,9],[9,-6,9],[9,-6,9]],"passed":false},{"actual":[[0,-1,1],[1,-1,1]],"check":"oracle 6","expected":[[0,0,1],[1,0,1]],"passed":false},{"actual":[[-3,-2,2],[-1,-2,2],[2,-2,2]],"check":"oracle 7","expected":[[-3,-5,2],[-1,-5,2],[2,-5,2]],"passed":false},{"actual":[[-3,-4,4],[0,-4,4],[4,-4,4],[4,-4,4],[-3,-4,4],[0,-4,4],[4,-4,4],[4,-4,4]],"check":"variant packet 1","expected":[[-3,-3,4],[0,-3,4],[4,-3,4],[4,-3,4],[-3,-3,4],[0,-3,4],[4,-3,4],[4,-3,4]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]], \"expected\": [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-2, -5, 5], [-2, -5, 5], [5, -5, 5]], \"expected\": [[-2, -2, 5], [-2, -2, 5], [5, -2, 5]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, -2, 2], [1, -2, 2], [2, -2, 2]], \"expected\": [[0, -1, 2], [1, -1, 2], [2, -1, 2]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-6, -9, 9], [9, -9, 9], [9, -9, 9]], \"expected\": [[-6, -6, 9], [9, -6, 9], [9, -6, 9]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, -1, 1], [1, -1, 1]], \"expected\": [[0, 0, 1], [1, 0, 1]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[-3, -2, 2], [-1, -2, 2], [2, -2, 2]], \"expected\": [[-3, -5, 2], [-1, -5, 2], [2, -5, 2]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4], [-3, -4, 4], [0, -4, 4], [4, -4, 4], [4, -4, 4]], \"expected\": [[-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4], [-3, -3, 4], [0, -3, 4], [4, -3, 4], [4, -3, 4]], \"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."}}