{"abstract":"The extracted field is sign-corrected using container modulus.","category":"PCM sample encoding","checks":8,"contract":"Extract a signed valid-bit field left justified in an unsigned container; ignore bits above the container and separately return low unused pad bits. valid<container.","evaluation_group":"s3-pcm-validbit-left-container","failed_approach":"Negating the unsigned code does not decode its complement representation.","family":"s3-pcm-validbit-left-container-signed-modulus","id":"FA-48906","implementations":{"attempt":{"sha256":"050564a6671b7fa6b1837bf92b57467663747255eae81b6a3722dd74d7c299fd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(words, valid, container):\n    shift=container-valid\n    mask=(1<<valid)-1\n    values=[]\n    for word in words:\n        code=(word>>shift)&mask\n        sign=1<<(valid-1)\n        values.append(-code if code&sign else code)\n    unused=[word&((1<<shift)-1) for word in words]\n    return [values,unused]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([3840, 1792, 256], 4, 12)), [[-1, 7, 1], [0, 0, 0]])\ncheck('oracle 2', solve(*([128, 112, 0], 4, 8)), [[-8, 7, 0], [0, 0, 0]])\ncheck('oracle 3', solve(*([384, 496], 4, 8)), [[-8, -1], [0, 0]])\ncheck('oracle 4', solve(*([129, 114], 4, 8)), [[-8, 7], [1, 2]])\ncheck('oracle 5', solve(*([], 3, 8)), [[], []])\ncheck('oracle 6', solve(*([224, 32], 3, 8)), [[-1, 1], [0, 0]])\ncheck('oracle 7', solve(*([4092, 4], 10, 12)), [[-1, 1], [0, 0]])\nif N == 1: check('variant packet 1', solve(*[[3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]])\nif N == 2: check('variant packet 2', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 3: check('variant packet 3', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 4: check('variant packet 4', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 5: check('variant packet 5', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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":"0d30444b892907d3b52ad8d057051e7ccf01942681238000bb44bdfe41eae265","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(words, valid, container):\n    shift=container-valid\n    mask=(1<<valid)-1\n    values=[]\n    for word in words:\n        code=(word>>shift)&mask\n        sign=1<<(valid-1)\n        values.append(code-(1<<container) if code&sign else code)\n    unused=[word&((1<<shift)-1) for word in words]\n    return [values,unused]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([3840, 1792, 256], 4, 12)), [[-1, 7, 1], [0, 0, 0]])\ncheck('oracle 2', solve(*([128, 112, 0], 4, 8)), [[-8, 7, 0], [0, 0, 0]])\ncheck('oracle 3', solve(*([384, 496], 4, 8)), [[-8, -1], [0, 0]])\ncheck('oracle 4', solve(*([129, 114], 4, 8)), [[-8, 7], [1, 2]])\ncheck('oracle 5', solve(*([], 3, 8)), [[], []])\ncheck('oracle 6', solve(*([224, 32], 3, 8)), [[-1, 1], [0, 0]])\ncheck('oracle 7', solve(*([4092, 4], 10, 12)), [[-1, 1], [0, 0]])\nif N == 1: check('variant packet 1', solve(*[[3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]])\nif N == 2: check('variant packet 2', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 3: check('variant packet 3', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 4: check('variant packet 4', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 5: check('variant packet 5', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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"},"fixed":{"sha256":"ca7293e7026af013c2db0a94ce1e628036256a4a01402c3fc8b3e0204e17275f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(words, valid, container):\n    shift=container-valid\n    mask=(1<<valid)-1\n    values=[]\n    for word in words:\n        code=(word>>shift)&mask\n        sign=1<<(valid-1)\n        values.append(code-(1<<valid) if code&sign else code)\n    unused=[word&((1<<shift)-1) for word in words]\n    return [values,unused]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([3840, 1792, 256], 4, 12)), [[-1, 7, 1], [0, 0, 0]])\ncheck('oracle 2', solve(*([128, 112, 0], 4, 8)), [[-8, 7, 0], [0, 0, 0]])\ncheck('oracle 3', solve(*([384, 496], 4, 8)), [[-8, -1], [0, 0]])\ncheck('oracle 4', solve(*([129, 114], 4, 8)), [[-8, 7], [1, 2]])\ncheck('oracle 5', solve(*([], 3, 8)), [[], []])\ncheck('oracle 6', solve(*([224, 32], 3, 8)), [[-1, 1], [0, 0]])\ncheck('oracle 7', solve(*([4092, 4], 10, 12)), [[-1, 1], [0, 0]])\nif N == 1: check('variant packet 1', solve(*[[3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]])\nif N == 2: check('variant packet 2', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 3: check('variant packet 3', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 4: check('variant packet 4', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])\nif N == 5: check('variant packet 5', solve(*[[3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256, 3840, 1792, 256], 4, 12]), [[-1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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":"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-validbit-left-container-signed-modulus","generated_at":"2026-09-29T14:44:55.057995+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 signed modulus.","root_cause":"The extracted field is sign-corrected using container modulus.","sha256":"a265cb9ecb492f10c23e858674ef418efe68249e1ab0bdc273c2b7dc5d13dbb8","title":"Validbit left container: signed modulus · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.116,"exit_code":1,"observations":[{"actual":[[-15,7,1],[0,0,0]],"check":"oracle 1","expected":[[-1,7,1],[0,0,0]],"passed":false},{"actual":[[-8,7,0],[0,0,0]],"check":"oracle 2","expected":[[-8,7,0],[0,0,0]],"passed":true},{"actual":[[-8,-15],[0,0]],"check":"oracle 3","expected":[[-8,-1],[0,0]],"passed":false},{"actual":[[-8,7],[1,2]],"check":"oracle 4","expected":[[-8,7],[1,2]],"passed":true},{"actual":[[],[]],"check":"oracle 5","expected":[[],[]],"passed":true},{"actual":[[-7,1],[0,0]],"check":"oracle 6","expected":[[-1,1],[0,0]],"passed":false},{"actual":[[-1023,1],[0,0]],"check":"oracle 7","expected":[[-1,1],[0,0]],"passed":false},{"actual":[[-15,7,1,-15,7,1],[0,0,0,0,0,0]],"check":"variant packet 1","expected":[[-1,7,1,-1,7,1],[0,0,0,0,0,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-15, 7, 1], [0, 0, 0]], \"expected\": [[-1, 7, 1], [0, 0, 0]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-8, 7, 0], [0, 0, 0]], \"expected\": [[-8, 7, 0], [0, 0, 0]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[-8, -15], [0, 0]], \"expected\": [[-8, -1], [0, 0]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[-8, 7], [1, 2]], \"expected\": [[-8, 7], [1, 2]], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[], []], \"expected\": [[], []], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-7, 1], [0, 0]], \"expected\": [[-1, 1], [0, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[-1023, 1], [0, 0]], \"expected\": [[-1, 1], [0, 0]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[-15, 7, 1, -15, 7, 1], [0, 0, 0, 0, 0, 0]], \"expected\": [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.43,"exit_code":1,"observations":[{"actual":[[-4081,7,1],[0,0,0]],"check":"oracle 1","expected":[[-1,7,1],[0,0,0]],"passed":false},{"actual":[[-248,7,0],[0,0,0]],"check":"oracle 2","expected":[[-8,7,0],[0,0,0]],"passed":false},{"actual":[[-248,-241],[0,0]],"check":"oracle 3","expected":[[-8,-1],[0,0]],"passed":false},{"actual":[[-248,7],[1,2]],"check":"oracle 4","expected":[[-8,7],[1,2]],"passed":false},{"actual":[[],[]],"check":"oracle 5","expected":[[],[]],"passed":true},{"actual":[[-249,1],[0,0]],"check":"oracle 6","expected":[[-1,1],[0,0]],"passed":false},{"actual":[[-3073,1],[0,0]],"check":"oracle 7","expected":[[-1,1],[0,0]],"passed":false},{"actual":[[-4081,7,1,-4081,7,1],[0,0,0,0,0,0]],"check":"variant packet 1","expected":[[-1,7,1,-1,7,1],[0,0,0,0,0,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-4081, 7, 1], [0, 0, 0]], \"expected\": [[-1, 7, 1], [0, 0, 0]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-248, 7, 0], [0, 0, 0]], \"expected\": [[-8, 7, 0], [0, 0, 0]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[-248, -241], [0, 0]], \"expected\": [[-8, -1], [0, 0]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[-248, 7], [1, 2]], \"expected\": [[-8, 7], [1, 2]], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [[], []], \"expected\": [[], []], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-249, 1], [0, 0]], \"expected\": [[-1, 1], [0, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[-3073, 1], [0, 0]], \"expected\": [[-1, 1], [0, 0]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[-4081, 7, 1, -4081, 7, 1], [0, 0, 0, 0, 0, 0]], \"expected\": [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.632,"exit_code":0,"observations":[{"actual":[[-1,7,1],[0,0,0]],"check":"oracle 1","expected":[[-1,7,1],[0,0,0]],"passed":true},{"actual":[[-8,7,0],[0,0,0]],"check":"oracle 2","expected":[[-8,7,0],[0,0,0]],"passed":true},{"actual":[[-8,-1],[0,0]],"check":"oracle 3","expected":[[-8,-1],[0,0]],"passed":true},{"actual":[[-8,7],[1,2]],"check":"oracle 4","expected":[[-8,7],[1,2]],"passed":true},{"actual":[[],[]],"check":"oracle 5","expected":[[],[]],"passed":true},{"actual":[[-1,1],[0,0]],"check":"oracle 6","expected":[[-1,1],[0,0]],"passed":true},{"actual":[[-1,1],[0,0]],"check":"oracle 7","expected":[[-1,1],[0,0]],"passed":true},{"actual":[[-1,7,1,-1,7,1],[0,0,0,0,0,0]],"check":"variant packet 1","expected":[[-1,7,1,-1,7,1],[0,0,0,0,0,0]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-1, 7, 1], [0, 0, 0]], \"expected\": [[-1, 7, 1], [0, 0, 0]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[-8, 7, 0], [0, 0, 0]], \"expected\": [[-8, 7, 0], [0, 0, 0]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[-8, -1], [0, 0]], \"expected\": [[-8, -1], [0, 0]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[-8, 7], [1, 2]], \"expected\": [[-8, 7], [1, 2]], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[], []], \"expected\": [[], []], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-1, 1], [0, 0]], \"expected\": [[-1, 1], [0, 0]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[-1, 1], [0, 0]], \"expected\": [[-1, 1], [0, 0]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]], \"expected\": [[-1, 7, 1, -1, 7, 1], [0, 0, 0, 0, 0, 0]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}