{"abstract":"A selected magnitude bit does not reduce the remaining residual.","category":"PCM sample encoding","checks":8,"contract":"Bounded fixed-step adaptive-nibble PCM encoder: greedy magnitude bits, a half-bin base, and predictor feedback from reconstructed rather than original amplitudes.","evaluation_group":"s3-pcm-pcm-adaptive-nibble-selection","failed_approach":"Subtracting bit code rather than amplitude weight changes later decisions.","family":"s3-pcm-pcm-adaptive-nibble-selection-magnitude-remainder","id":"FA-49756","implementations":{"attempt":{"sha256":"c57d03e6bdee434f2599d2884e25ea3144391112186fc6ed91cd96dc68e82b46","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, predictor, step):\n    out=[]\n    for sample in samples:\n        difference=sample-predictor\n        sign=8 if difference<0 else 0\n        magnitude=abs(difference)\n        code=0\n        restored=step//8\n        for bit,part in [(4,step),(2,step//2),(1,step//4)]:\n            if magnitude>=part:\n                code|=bit\n                magnitude-=bit\n                restored+=part\n        predictor+=-restored if sign else restored\n        out.append(sign|code)\n    return [out,predictor]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([2, 6, -4, 10], 0, 8)), [[1, 1, 13, 7], 10])\ncheck('oracle 2', solve(*([10, 10, 10], 3, 12)), [[2, 0, 8], 10])\ncheck('oracle 3', solve(*([-5, -10, 0], 0, 8)), [[10, 10, 5], 1])\ncheck('oracle 4', solve(*([], 4, 8)), [[], 4])\ncheck('oracle 5', solve(*([0, 1, 2, 3], 0, 16)), [[0, 8, 0, 0], 4])\ncheck('oracle 6', solve(*([8, 16, 24], 0, 8)), [[4, 3, 4], 25])\ncheck('oracle 7', solve(*([6, -6, 6], 1, 4)), [[5, 15, 7], 6])\nif N == 1: check('variant packet 1', solve(*[[2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7], 10])\nif N == 2: check('variant packet 2', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 3: check('variant packet 3', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 4: check('variant packet 4', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 5: check('variant packet 5', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\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":"54e08c44a04800591c67c86823e92f7eb10904e7634d8f640eac0d91f2b7f04e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, predictor, step):\n    out=[]\n    for sample in samples:\n        difference=sample-predictor\n        sign=8 if difference<0 else 0\n        magnitude=abs(difference)\n        code=0\n        restored=step//8\n        for bit,part in [(4,step),(2,step//2),(1,step//4)]:\n            if magnitude>=part:\n                code|=bit\n                magnitude=magnitude\n                restored+=part\n        predictor+=-restored if sign else restored\n        out.append(sign|code)\n    return [out,predictor]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([2, 6, -4, 10], 0, 8)), [[1, 1, 13, 7], 10])\ncheck('oracle 2', solve(*([10, 10, 10], 3, 12)), [[2, 0, 8], 10])\ncheck('oracle 3', solve(*([-5, -10, 0], 0, 8)), [[10, 10, 5], 1])\ncheck('oracle 4', solve(*([], 4, 8)), [[], 4])\ncheck('oracle 5', solve(*([0, 1, 2, 3], 0, 16)), [[0, 8, 0, 0], 4])\ncheck('oracle 6', solve(*([8, 16, 24], 0, 8)), [[4, 3, 4], 25])\ncheck('oracle 7', solve(*([6, -6, 6], 1, 4)), [[5, 15, 7], 6])\nif N == 1: check('variant packet 1', solve(*[[2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7], 10])\nif N == 2: check('variant packet 2', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 3: check('variant packet 3', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 4: check('variant packet 4', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 5: check('variant packet 5', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\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":"534d9e881616e3a48d8bf1858d3373a1afd0e6587667e3ba78af3402ed89fa60","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, predictor, step):\n    out=[]\n    for sample in samples:\n        difference=sample-predictor\n        sign=8 if difference<0 else 0\n        magnitude=abs(difference)\n        code=0\n        restored=step//8\n        for bit,part in [(4,step),(2,step//2),(1,step//4)]:\n            if magnitude>=part:\n                code|=bit\n                magnitude-=part\n                restored+=part\n        predictor+=-restored if sign else restored\n        out.append(sign|code)\n    return [out,predictor]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([2, 6, -4, 10], 0, 8)), [[1, 1, 13, 7], 10])\ncheck('oracle 2', solve(*([10, 10, 10], 3, 12)), [[2, 0, 8], 10])\ncheck('oracle 3', solve(*([-5, -10, 0], 0, 8)), [[10, 10, 5], 1])\ncheck('oracle 4', solve(*([], 4, 8)), [[], 4])\ncheck('oracle 5', solve(*([0, 1, 2, 3], 0, 16)), [[0, 8, 0, 0], 4])\ncheck('oracle 6', solve(*([8, 16, 24], 0, 8)), [[4, 3, 4], 25])\ncheck('oracle 7', solve(*([6, -6, 6], 1, 4)), [[5, 15, 7], 6])\nif N == 1: check('variant packet 1', solve(*[[2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7], 10])\nif N == 2: check('variant packet 2', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 3: check('variant packet 3', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 4: check('variant packet 4', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\nif N == 5: check('variant packet 5', solve(*[[2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10, 2, 6, -4, 10], 0, 8]), [[1, 1, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7, 12, 2, 13, 7], 10])\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-adaptive-nibble-selection-magnitude-remainder","generated_at":"2026-09-29T14:45:02.874735+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 magnitude remainder.","root_cause":"A selected magnitude bit does not reduce the remaining residual.","sha256":"3f80dc3869657a12fd4b07058ba0f54cd77193084cfbc5d105d916e447f037ee","title":"Pcm adaptive nibble selection: magnitude remainder · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.319,"exit_code":1,"observations":[{"actual":[[1,1,15,7],6],"check":"oracle 1","expected":[[1,1,13,7],10],"passed":false},{"actual":[[3,9,0],10],"check":"oracle 2","expected":[[2,0,8],10],"passed":false},{"actual":[[11,9,7],5],"check":"oracle 3","expected":[[10,10,5],1],"passed":false},{"actual":[[],4],"check":"oracle 4","expected":[[],4],"passed":true},{"actual":[[0,8,0,0],4],"check":"oracle 5","expected":[[0,8,0,0],4],"passed":true},{"actual":[[7,0,7],31],"check":"oracle 6","expected":[[4,3,4],25],"passed":false},{"actual":[[5,15,7],6],"check":"oracle 7","expected":[[5,15,7],6],"passed":true},{"actual":[[1,1,15,7,11,3,15,7],6],"check":"variant packet 1","expected":[[1,1,13,7,12,2,13,7],10],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 1, 15, 7], 6], \"expected\": [[1, 1, 13, 7], 10], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[3, 9, 0], 10], \"expected\": [[2, 0, 8], 10], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[11, 9, 7], 5], \"expected\": [[10, 10, 5], 1], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], 4], \"expected\": [[], 4], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 8, 0, 0], 4], \"expected\": [[0, 8, 0, 0], 4], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[7, 0, 7], 31], \"expected\": [[4, 3, 4], 25], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[5, 15, 7], 6], \"expected\": [[5, 15, 7], 6], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[1, 1, 15, 7, 11, 3, 15, 7], 6], \"expected\": [[1, 1, 13, 7, 12, 2, 13, 7], 10], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.361,"exit_code":1,"observations":[{"actual":[[1,1,15,7],6],"check":"oracle 1","expected":[[1,1,13,7],10],"passed":false},{"actual":[[3,9,0],10],"check":"oracle 2","expected":[[2,0,8],10],"passed":false},{"actual":[[11,9,7],5],"check":"oracle 3","expected":[[10,10,5],1],"passed":false},{"actual":[[],4],"check":"oracle 4","expected":[[],4],"passed":true},{"actual":[[0,8,0,0],4],"check":"oracle 5","expected":[[0,8,0,0],4],"passed":true},{"actual":[[7,0,7],31],"check":"oracle 6","expected":[[4,3,4],25],"passed":false},{"actual":[[7,15,7],8],"check":"oracle 7","expected":[[5,15,7],6],"passed":false},{"actual":[[1,1,15,7,11,3,15,7],6],"check":"variant packet 1","expected":[[1,1,13,7,12,2,13,7],10],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 1, 15, 7], 6], \"expected\": [[1, 1, 13, 7], 10], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[3, 9, 0], 10], \"expected\": [[2, 0, 8], 10], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[11, 9, 7], 5], \"expected\": [[10, 10, 5], 1], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], 4], \"expected\": [[], 4], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 8, 0, 0], 4], \"expected\": [[0, 8, 0, 0], 4], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[7, 0, 7], 31], \"expected\": [[4, 3, 4], 25], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[7, 15, 7], 8], \"expected\": [[5, 15, 7], 6], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[1, 1, 15, 7, 11, 3, 15, 7], 6], \"expected\": [[1, 1, 13, 7, 12, 2, 13, 7], 10], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.848,"exit_code":0,"observations":[{"actual":[[1,1,13,7],10],"check":"oracle 1","expected":[[1,1,13,7],10],"passed":true},{"actual":[[2,0,8],10],"check":"oracle 2","expected":[[2,0,8],10],"passed":true},{"actual":[[10,10,5],1],"check":"oracle 3","expected":[[10,10,5],1],"passed":true},{"actual":[[],4],"check":"oracle 4","expected":[[],4],"passed":true},{"actual":[[0,8,0,0],4],"check":"oracle 5","expected":[[0,8,0,0],4],"passed":true},{"actual":[[4,3,4],25],"check":"oracle 6","expected":[[4,3,4],25],"passed":true},{"actual":[[5,15,7],6],"check":"oracle 7","expected":[[5,15,7],6],"passed":true},{"actual":[[1,1,13,7,12,2,13,7],10],"check":"variant packet 1","expected":[[1,1,13,7,12,2,13,7],10],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 1, 13, 7], 10], \"expected\": [[1, 1, 13, 7], 10], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[2, 0, 8], 10], \"expected\": [[2, 0, 8], 10], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[10, 10, 5], 1], \"expected\": [[10, 10, 5], 1], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[], 4], \"expected\": [[], 4], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 8, 0, 0], 4], \"expected\": [[0, 8, 0, 0], 4], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[4, 3, 4], 25], \"expected\": [[4, 3, 4], 25], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[5, 15, 7], 6], \"expected\": [[5, 15, 7], 6], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[1, 1, 13, 7, 12, 2, 13, 7], 10], \"expected\": [[1, 1, 13, 7, 12, 2, 13, 7], 10], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}