{"abstract":"Mantissa contribution has the wrong reconstruction weight.","category":"PCM sample encoding","checks":8,"contract":"Decode eight-bit mu-law codewords using complement, three-bit segment, four-bit mantissa and reconstruction bias132; return signed integer PCM amplitudes.","evaluation_group":"s3-pcm-mulaw-expansion","failed_approach":"Halving the mistaken weight again loses a valid low amplitude step.","family":"s3-pcm-mulaw-expansion-mantissa-placement","id":"FA-48971","implementations":{"attempt":{"sha256":"b64164d85016ec1effcee52390d60f3ec67a9cfd36d48cbf0d2bdd9a168bc2c5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes):\n    out=[]\n    for raw in codes:\n        code=(~raw)&255\n        mantissa=code&15\n        exponent=(code>>4)&7\n        amplitude=((mantissa<<2)+132)<<exponent\n        amplitude-=132\n        out.append(-amplitude if code&128 else amplitude)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([255, 127, 0, 128],)), [0, 0, -32124, 32124])\ncheck('oracle 2', solve(*([254, 253, 252],)), [8, 16, 24])\ncheck('oracle 3', solve(*([240, 239, 224],)), [120, 132, 372])\ncheck('oracle 4', solve(*([16, 32, 64],)), [-15996, -7932, -1884])\ncheck('oracle 5', solve(*([],)), [])\ncheck('oracle 6', solve(*([175, 191, 207, 223],)), [4092, 1980, 924, 396])\ncheck('oracle 7', solve(*([1, 2, 126],)), [-31100, -30076, -8])\nif N == 1: check('variant packet 1', solve(*[[255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 2: check('variant packet 2', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 3: check('variant packet 3', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 4: check('variant packet 4', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 5: check('variant packet 5', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\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":"f2409cb691e53d922ddc756cfa200b8bfd240a63493e4bbae08689decdf81fe7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes):\n    out=[]\n    for raw in codes:\n        code=(~raw)&255\n        mantissa=code&15\n        exponent=(code>>4)&7\n        amplitude=((mantissa<<4)+132)<<exponent\n        amplitude-=132\n        out.append(-amplitude if code&128 else amplitude)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([255, 127, 0, 128],)), [0, 0, -32124, 32124])\ncheck('oracle 2', solve(*([254, 253, 252],)), [8, 16, 24])\ncheck('oracle 3', solve(*([240, 239, 224],)), [120, 132, 372])\ncheck('oracle 4', solve(*([16, 32, 64],)), [-15996, -7932, -1884])\ncheck('oracle 5', solve(*([],)), [])\ncheck('oracle 6', solve(*([175, 191, 207, 223],)), [4092, 1980, 924, 396])\ncheck('oracle 7', solve(*([1, 2, 126],)), [-31100, -30076, -8])\nif N == 1: check('variant packet 1', solve(*[[255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 2: check('variant packet 2', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 3: check('variant packet 3', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 4: check('variant packet 4', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 5: check('variant packet 5', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\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":"9ccd6e94810f4fe44df29ea64443af5f55b5ebc2fd0cf11e11073f4702c4b1cb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes):\n    out=[]\n    for raw in codes:\n        code=(~raw)&255\n        mantissa=code&15\n        exponent=(code>>4)&7\n        amplitude=((mantissa<<3)+132)<<exponent\n        amplitude-=132\n        out.append(-amplitude if code&128 else amplitude)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([255, 127, 0, 128],)), [0, 0, -32124, 32124])\ncheck('oracle 2', solve(*([254, 253, 252],)), [8, 16, 24])\ncheck('oracle 3', solve(*([240, 239, 224],)), [120, 132, 372])\ncheck('oracle 4', solve(*([16, 32, 64],)), [-15996, -7932, -1884])\ncheck('oracle 5', solve(*([],)), [])\ncheck('oracle 6', solve(*([175, 191, 207, 223],)), [4092, 1980, 924, 396])\ncheck('oracle 7', solve(*([1, 2, 126],)), [-31100, -30076, -8])\nif N == 1: check('variant packet 1', solve(*[[255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 2: check('variant packet 2', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 3: check('variant packet 3', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 4: check('variant packet 4', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\nif N == 5: check('variant packet 5', solve(*[[255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128, 255, 127, 0, 128]]), [0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124, 0, 0, -32124, 32124])\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-mulaw-expansion-mantissa-placement","generated_at":"2026-09-29T14:44:55.612047+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.","repair":"Use the stated conversion contract at mantissa placement.","root_cause":"Mantissa contribution has the wrong reconstruction weight.","sha256":"00aa79f637bb6d43d082272dc4bf1c1d846b63d9ddc9b4f3fa09b3cecc503c38","title":"Mulaw expansion: mantissa placement · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.083,"exit_code":1,"observations":[{"actual":[0,0,-24444,24444],"check":"oracle 1","expected":[0,0,-32124,32124],"passed":false},{"actual":[4,8,12],"check":"oracle 2","expected":[8,16,24],"passed":false},{"actual":[60,132,252],"check":"oracle 3","expected":[120,132,372],"passed":false},{"actual":[-12156,-6012,-1404],"check":"oracle 4","expected":[-15996,-7932,-1884],"passed":false},{"actual":[],"check":"oracle 5","expected":[],"passed":true},{"actual":[4092,1980,924,396],"check":"oracle 6","expected":[4092,1980,924,396],"passed":true},{"actual":[-23932,-23420,-4],"check":"oracle 7","expected":[-31100,-30076,-8],"passed":false},{"actual":[0,0,-24444,24444,0,0,-24444,24444],"check":"variant packet 1","expected":[0,0,-32124,32124,0,0,-32124,32124],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [0, 0, -24444, 24444], \"expected\": [0, 0, -32124, 32124], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [4, 8, 12], \"expected\": [8, 16, 24], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [60, 132, 252], \"expected\": [120, 132, 372], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [-12156, -6012, -1404], \"expected\": [-15996, -7932, -1884], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [4092, 1980, 924, 396], \"expected\": [4092, 1980, 924, 396], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [-23932, -23420, -4], \"expected\": [-31100, -30076, -8], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [0, 0, -24444, 24444, 0, 0, -24444, 24444], \"expected\": [0, 0, -32124, 32124, 0, 0, -32124, 32124], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.335,"exit_code":1,"observations":[{"actual":[0,0,-47484,47484],"check":"oracle 1","expected":[0,0,-32124,32124],"passed":false},{"actual":[16,32,48],"check":"oracle 2","expected":[8,16,24],"passed":false},{"actual":[240,132,612],"check":"oracle 3","expected":[120,132,372],"passed":false},{"actual":[-23676,-11772,-2844],"check":"oracle 4","expected":[-15996,-7932,-1884],"passed":false},{"actual":[],"check":"oracle 5","expected":[],"passed":true},{"actual":[4092,1980,924,396],"check":"oracle 6","expected":[4092,1980,924,396],"passed":true},{"actual":[-45436,-43388,-16],"check":"oracle 7","expected":[-31100,-30076,-8],"passed":false},{"actual":[0,0,-47484,47484,0,0,-47484,47484],"check":"variant packet 1","expected":[0,0,-32124,32124,0,0,-32124,32124],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [0, 0, -47484, 47484], \"expected\": [0, 0, -32124, 32124], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [16, 32, 48], \"expected\": [8, 16, 24], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [240, 132, 612], \"expected\": [120, 132, 372], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [-23676, -11772, -2844], \"expected\": [-15996, -7932, -1884], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [4092, 1980, 924, 396], \"expected\": [4092, 1980, 924, 396], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [-45436, -43388, -16], \"expected\": [-31100, -30076, -8], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [0, 0, -47484, 47484, 0, 0, -47484, 47484], \"expected\": [0, 0, -32124, 32124, 0, 0, -32124, 32124], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.68,"exit_code":0,"observations":[{"actual":[0,0,-32124,32124],"check":"oracle 1","expected":[0,0,-32124,32124],"passed":true},{"actual":[8,16,24],"check":"oracle 2","expected":[8,16,24],"passed":true},{"actual":[120,132,372],"check":"oracle 3","expected":[120,132,372],"passed":true},{"actual":[-15996,-7932,-1884],"check":"oracle 4","expected":[-15996,-7932,-1884],"passed":true},{"actual":[],"check":"oracle 5","expected":[],"passed":true},{"actual":[4092,1980,924,396],"check":"oracle 6","expected":[4092,1980,924,396],"passed":true},{"actual":[-31100,-30076,-8],"check":"oracle 7","expected":[-31100,-30076,-8],"passed":true},{"actual":[0,0,-32124,32124,0,0,-32124,32124],"check":"variant packet 1","expected":[0,0,-32124,32124,0,0,-32124,32124],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [0, 0, -32124, 32124], \"expected\": [0, 0, -32124, 32124], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [8, 16, 24], \"expected\": [8, 16, 24], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [120, 132, 372], \"expected\": [120, 132, 372], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [-15996, -7932, -1884], \"expected\": [-15996, -7932, -1884], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [4092, 1980, 924, 396], \"expected\": [4092, 1980, 924, 396], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [-31100, -30076, -8], \"expected\": [-31100, -30076, -8], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [0, 0, -32124, 32124, 0, 0, -32124, 32124], \"expected\": [0, 0, -32124, 32124, 0, 0, -32124, 32124], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}