{"abstract":"Mu-law mantissa extraction leaves three discarded precision bits.","category":"PCM sample encoding","checks":8,"contract":"Bounded mu-law-style selection model: clamp magnitude32635, add bias132, select segment and mantissa then complement the full eight-bit code.","evaluation_group":"s3-pcm-pcm-mulaw-code-selection","failed_approach":"Discarding four bits halves mantissa resolution.","family":"s3-pcm-pcm-mulaw-code-selection-mantissa-shift","id":"FA-49851","implementations":{"attempt":{"sha256":"6e62ec0cc6a6f51323dc6446a3cf184cbfdc00683e0e02bd9d2d634e3d9f1606","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples):\n    out=[]\n    for sample in samples:\n        negative=sample<0\n        amplitude=min(32635,abs(sample))+132\n        exponent=0\n        while exponent<7 and amplitude>=(256<<exponent):\n            exponent+=1\n        mantissa=(amplitude>>(exponent+4))&15\n        code=(128 if negative else 0)|(exponent<<4)|mantissa\n        out.append((~code)&255)\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, 1, -1, 100, -100],)), [255, 255, 127, 242, 114])\ncheck('oracle 2', solve(*([124, 125, -124],)), [239, 239, 111])\ncheck('oracle 3', solve(*([32635, 40000, -40000],)), [128, 128, 0])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([1000, 4000, 16000],)), [206, 175, 144])\ncheck('oracle 6', solve(*([380, 892, 1916],)), [223, 207, 191])\ncheck('oracle 7', solve(*([-1000, -4000, -16000],)), [78, 47, 16])\nif N == 1: check('variant packet 1', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 2: check('variant packet 2', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 3: check('variant packet 3', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 4: check('variant packet 4', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 5: check('variant packet 5', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\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":"44b5e6f0e0f73ee2a23ff408479297bcc07da1c4d7a01c3515fe54194dd6ee30","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples):\n    out=[]\n    for sample in samples:\n        negative=sample<0\n        amplitude=min(32635,abs(sample))+132\n        exponent=0\n        while exponent<7 and amplitude>=(256<<exponent):\n            exponent+=1\n        mantissa=(amplitude>>exponent)&15\n        code=(128 if negative else 0)|(exponent<<4)|mantissa\n        out.append((~code)&255)\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, 1, -1, 100, -100],)), [255, 255, 127, 242, 114])\ncheck('oracle 2', solve(*([124, 125, -124],)), [239, 239, 111])\ncheck('oracle 3', solve(*([32635, 40000, -40000],)), [128, 128, 0])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([1000, 4000, 16000],)), [206, 175, 144])\ncheck('oracle 6', solve(*([380, 892, 1916],)), [223, 207, 191])\ncheck('oracle 7', solve(*([-1000, -4000, -16000],)), [78, 47, 16])\nif N == 1: check('variant packet 1', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 2: check('variant packet 2', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 3: check('variant packet 3', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 4: check('variant packet 4', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 5: check('variant packet 5', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\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":"9a61544a71b8062ad93686f3ed544e53c854273e6558ea0c346d7822c4809892","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples):\n    out=[]\n    for sample in samples:\n        negative=sample<0\n        amplitude=min(32635,abs(sample))+132\n        exponent=0\n        while exponent<7 and amplitude>=(256<<exponent):\n            exponent+=1\n        mantissa=(amplitude>>(exponent+3))&15\n        code=(128 if negative else 0)|(exponent<<4)|mantissa\n        out.append((~code)&255)\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, 1, -1, 100, -100],)), [255, 255, 127, 242, 114])\ncheck('oracle 2', solve(*([124, 125, -124],)), [239, 239, 111])\ncheck('oracle 3', solve(*([32635, 40000, -40000],)), [128, 128, 0])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([1000, 4000, 16000],)), [206, 175, 144])\ncheck('oracle 6', solve(*([380, 892, 1916],)), [223, 207, 191])\ncheck('oracle 7', solve(*([-1000, -4000, -16000],)), [78, 47, 16])\nif N == 1: check('variant packet 1', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 2: check('variant packet 2', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 3: check('variant packet 3', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 4: check('variant packet 4', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\nif N == 5: check('variant packet 5', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])\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-pcm-mulaw-code-selection-mantissa-shift","generated_at":"2026-09-29T14:45:03.755586+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 shift.","root_cause":"Mu-law mantissa extraction leaves three discarded precision bits.","sha256":"01df75109baeb8d81d8949b71bb4d501b1266e5d3897e65625b55e0e7486c177","title":"Pcm mulaw code selection: mantissa shift · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.804,"exit_code":1,"observations":[{"actual":[247,247,119,241,113],"check":"oracle 1","expected":[255,255,127,242,114],"passed":false},{"actual":[231,231,103],"check":"oracle 2","expected":[239,239,111],"passed":false},{"actual":[128,128,0],"check":"oracle 3","expected":[128,128,0],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[199,167,144],"check":"oracle 5","expected":[206,175,144],"passed":false},{"actual":[215,199,183],"check":"oracle 6","expected":[223,207,191],"passed":false},{"actual":[71,39,16],"check":"oracle 7","expected":[78,47,16],"passed":false},{"actual":[247,247,119,241,113,247,247,119,241,113],"check":"variant packet 1","expected":[255,255,127,242,114,255,255,127,242,114],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [247, 247, 119, 241, 113], \"expected\": [255, 255, 127, 242, 114], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [231, 231, 103], \"expected\": [239, 239, 111], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [128, 128, 0], \"expected\": [128, 128, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [199, 167, 144], \"expected\": [206, 175, 144], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [215, 199, 183], \"expected\": [223, 207, 191], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [71, 39, 16], \"expected\": [78, 47, 16], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [247, 247, 119, 241, 113, 247, 247, 119, 241, 113], \"expected\": [255, 255, 127, 242, 114, 255, 255, 127, 242, 114], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.951,"exit_code":1,"observations":[{"actual":[251,250,122,247,119],"check":"oracle 1","expected":[255,255,127,242,114],"passed":false},{"actual":[239,239,111],"check":"oracle 2","expected":[239,239,111],"passed":true},{"actual":[128,128,0],"check":"oracle 3","expected":[128,128,0],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[194,174,147],"check":"oracle 5","expected":[206,175,144],"passed":false},{"actual":[223,207,191],"check":"oracle 6","expected":[223,207,191],"passed":true},{"actual":[66,46,19],"check":"oracle 7","expected":[78,47,16],"passed":false},{"actual":[251,250,122,247,119,251,250,122,247,119],"check":"variant packet 1","expected":[255,255,127,242,114,255,255,127,242,114],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [251, 250, 122, 247, 119], \"expected\": [255, 255, 127, 242, 114], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [239, 239, 111], \"expected\": [239, 239, 111], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [128, 128, 0], \"expected\": [128, 128, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [194, 174, 147], \"expected\": [206, 175, 144], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [223, 207, 191], \"expected\": [223, 207, 191], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [66, 46, 19], \"expected\": [78, 47, 16], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [251, 250, 122, 247, 119, 251, 250, 122, 247, 119], \"expected\": [255, 255, 127, 242, 114, 255, 255, 127, 242, 114], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.991,"exit_code":0,"observations":[{"actual":[255,255,127,242,114],"check":"oracle 1","expected":[255,255,127,242,114],"passed":true},{"actual":[239,239,111],"check":"oracle 2","expected":[239,239,111],"passed":true},{"actual":[128,128,0],"check":"oracle 3","expected":[128,128,0],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[206,175,144],"check":"oracle 5","expected":[206,175,144],"passed":true},{"actual":[223,207,191],"check":"oracle 6","expected":[223,207,191],"passed":true},{"actual":[78,47,16],"check":"oracle 7","expected":[78,47,16],"passed":true},{"actual":[255,255,127,242,114,255,255,127,242,114],"check":"variant packet 1","expected":[255,255,127,242,114,255,255,127,242,114],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [255, 255, 127, 242, 114], \"expected\": [255, 255, 127, 242, 114], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [239, 239, 111], \"expected\": [239, 239, 111], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [128, 128, 0], \"expected\": [128, 128, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [206, 175, 144], \"expected\": [206, 175, 144], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [223, 207, 191], \"expected\": [223, 207, 191], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [78, 47, 16], \"expected\": [78, 47, 16], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [255, 255, 127, 242, 114, 255, 255, 127, 242, 114], \"expected\": [255, 255, 127, 242, 114, 255, 255, 127, 242, 114], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}