{"abstract":"Dither is omitted before PCM precision reduction.","category":"PCM sample encoding","checks":8,"contract":"Stipulated subtractive-dither PCM converter with a repeating explicit integer noise sequence, even quantizer step, and both wire codes and reconstructed amplitudes.","evaluation_group":"s3-pcm-pcm-subtractive-dither","failed_approach":"Subtracting noise uses the inverse sequence but decoder still subtracts original noise.","family":"s3-pcm-pcm-subtractive-dither-prequantizer-noise","id":"FA-49621","implementations":{"attempt":{"sha256":"aac15bb02c7d1c88cd7703c583a19a956a959bbd57ae3b4b01bf19e3a421d16d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, noises, step):\n    out=[]\n    for index,sample in enumerate(samples):\n        noise=noises[index%len(noises)]\n        driven=sample-noise\n        code=(driven+step//2)//step\n        restored=code*step-noise\n        out.append([code,restored])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], [0, 1, -1], 4)), [[0, 0], [1, 3], [1, 5], [1, 4]])\ncheck('oracle 2', solve(*([-3, -1, 1, 3], [1, -1], 2)), [[-1, -3], [-1, -1], [1, 1], [1, 3]])\ncheck('oracle 3', solve(*([0, 0, 0], [2, -2, 0], 4)), [[1, 2], [0, 2], [0, 0]])\ncheck('oracle 4', solve(*([], [1], 4)), [])\ncheck('oracle 5', solve(*([8, 9], [0], 4)), [[2, 8], [2, 8]])\ncheck('oracle 6', solve(*([1, 1, 1, 1], [1, 0, -1, 2], 2)), [[1, 1], [1, 2], [0, 1], [2, 2]])\ncheck('oracle 7', solve(*([7, -7, 5], [2, 1, -2], 6)), [[2, 10], [-1, -7], [1, 8]])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4]])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])\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":"070d00f8dbeae010a2f4d396cbf1cc1e5d6d1811133340493aa377346e0b363b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, noises, step):\n    out=[]\n    for index,sample in enumerate(samples):\n        noise=noises[index%len(noises)]\n        driven=sample\n        code=(driven+step//2)//step\n        restored=code*step-noise\n        out.append([code,restored])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], [0, 1, -1], 4)), [[0, 0], [1, 3], [1, 5], [1, 4]])\ncheck('oracle 2', solve(*([-3, -1, 1, 3], [1, -1], 2)), [[-1, -3], [-1, -1], [1, 1], [1, 3]])\ncheck('oracle 3', solve(*([0, 0, 0], [2, -2, 0], 4)), [[1, 2], [0, 2], [0, 0]])\ncheck('oracle 4', solve(*([], [1], 4)), [])\ncheck('oracle 5', solve(*([8, 9], [0], 4)), [[2, 8], [2, 8]])\ncheck('oracle 6', solve(*([1, 1, 1, 1], [1, 0, -1, 2], 2)), [[1, 1], [1, 2], [0, 1], [2, 2]])\ncheck('oracle 7', solve(*([7, -7, 5], [2, 1, -2], 6)), [[2, 10], [-1, -7], [1, 8]])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4]])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])\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":"5564ae7a3d9537d69cbc47015aeeba2a38a760af253d10d894e0bb5507adc3cb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, noises, step):\n    out=[]\n    for index,sample in enumerate(samples):\n        noise=noises[index%len(noises)]\n        driven=sample+noise\n        code=(driven+step//2)//step\n        restored=code*step-noise\n        out.append([code,restored])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], [0, 1, -1], 4)), [[0, 0], [1, 3], [1, 5], [1, 4]])\ncheck('oracle 2', solve(*([-3, -1, 1, 3], [1, -1], 2)), [[-1, -3], [-1, -1], [1, 1], [1, 3]])\ncheck('oracle 3', solve(*([0, 0, 0], [2, -2, 0], 4)), [[1, 2], [0, 2], [0, 0]])\ncheck('oracle 4', solve(*([], [1], 4)), [])\ncheck('oracle 5', solve(*([8, 9], [0], 4)), [[2, 8], [2, 8]])\ncheck('oracle 6', solve(*([1, 1, 1, 1], [1, 0, -1, 2], 2)), [[1, 1], [1, 2], [0, 1], [2, 2]])\ncheck('oracle 7', solve(*([7, -7, 5], [2, 1, -2], 6)), [[2, 10], [-1, -7], [1, 8]])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4]])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], [0, 1, -1], 4]), [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5], [0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3], [1, 5]])\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-subtractive-dither-prequantizer-noise","generated_at":"2026-09-29T14:45:01.639440+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 prequantizer noise.","root_cause":"Dither is omitted before PCM precision reduction.","sha256":"5aadbfd51f6f3cefd9922b01bfeb95c3d2218d25b38221a39fb70fb2f16b6105","title":"Pcm subtractive dither: prequantizer noise · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.155,"exit_code":1,"observations":[{"actual":[[0,0],[0,-1],[1,5],[1,4]],"check":"oracle 1","expected":[[0,0],[1,3],[1,5],[1,4]],"passed":false},{"actual":[[-2,-5],[0,1],[0,-1],[2,5]],"check":"oracle 2","expected":[[-1,-3],[-1,-1],[1,1],[1,3]],"passed":false},{"actual":[[0,-2],[1,6],[0,0]],"check":"oracle 3","expected":[[1,2],[0,2],[0,0]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[2,8],[2,8]],"check":"oracle 5","expected":[[2,8],[2,8]],"passed":true},{"actual":[[0,-1],[1,2],[1,3],[0,-2]],"check":"oracle 6","expected":[[1,1],[1,2],[0,1],[2,2]],"passed":false},{"actual":[[1,4],[-1,-7],[1,8]],"check":"oracle 7","expected":[[2,10],[-1,-7],[1,8]],"passed":false},{"actual":[[0,0],[0,-1],[1,5],[1,4],[0,-1],[1,5],[1,4],[1,3]],"check":"variant packet 1","expected":[[0,0],[1,3],[1,5],[1,4],[1,3],[0,1],[1,4],[1,3]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0], [0, -1], [1, 5], [1, 4]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-2, -5], [0, 1], [0, -1], [2, 5]], \"expected\": [[-1, -3], [-1, -1], [1, 1], [1, 3]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, -2], [1, 6], [0, 0]], \"expected\": [[1, 2], [0, 2], [0, 0]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[2, 8], [2, 8]], \"expected\": [[2, 8], [2, 8]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0, -1], [1, 2], [1, 3], [0, -2]], \"expected\": [[1, 1], [1, 2], [0, 1], [2, 2]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[1, 4], [-1, -7], [1, 8]], \"expected\": [[2, 10], [-1, -7], [1, 8]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0], [0, -1], [1, 5], [1, 4], [0, -1], [1, 5], [1, 4], [1, 3]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.708,"exit_code":1,"observations":[{"actual":[[0,0],[1,3],[1,5],[1,4]],"check":"oracle 1","expected":[[0,0],[1,3],[1,5],[1,4]],"passed":true},{"actual":[[-1,-3],[0,1],[1,1],[2,5]],"check":"oracle 2","expected":[[-1,-3],[-1,-1],[1,1],[1,3]],"passed":false},{"actual":[[0,-2],[0,2],[0,0]],"check":"oracle 3","expected":[[1,2],[0,2],[0,0]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[2,8],[2,8]],"check":"oracle 5","expected":[[2,8],[2,8]],"passed":true},{"actual":[[1,1],[1,2],[1,3],[1,0]],"check":"oracle 6","expected":[[1,1],[1,2],[0,1],[2,2]],"passed":false},{"actual":[[1,4],[-1,-7],[1,8]],"check":"oracle 7","expected":[[2,10],[-1,-7],[1,8]],"passed":false},{"actual":[[0,0],[1,3],[1,5],[1,4],[0,-1],[1,5],[1,4],[1,3]],"check":"variant packet 1","expected":[[0,0],[1,3],[1,5],[1,4],[1,3],[0,1],[1,4],[1,3]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[-1, -3], [0, 1], [1, 1], [2, 5]], \"expected\": [[-1, -3], [-1, -1], [1, 1], [1, 3]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, -2], [0, 2], [0, 0]], \"expected\": [[1, 2], [0, 2], [0, 0]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[2, 8], [2, 8]], \"expected\": [[2, 8], [2, 8]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[1, 1], [1, 2], [1, 3], [1, 0]], \"expected\": [[1, 1], [1, 2], [0, 1], [2, 2]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[1, 4], [-1, -7], [1, 8]], \"expected\": [[2, 10], [-1, -7], [1, 8]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0], [1, 3], [1, 5], [1, 4], [0, -1], [1, 5], [1, 4], [1, 3]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.61,"exit_code":0,"observations":[{"actual":[[0,0],[1,3],[1,5],[1,4]],"check":"oracle 1","expected":[[0,0],[1,3],[1,5],[1,4]],"passed":true},{"actual":[[-1,-3],[-1,-1],[1,1],[1,3]],"check":"oracle 2","expected":[[-1,-3],[-1,-1],[1,1],[1,3]],"passed":true},{"actual":[[1,2],[0,2],[0,0]],"check":"oracle 3","expected":[[1,2],[0,2],[0,0]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[2,8],[2,8]],"check":"oracle 5","expected":[[2,8],[2,8]],"passed":true},{"actual":[[1,1],[1,2],[0,1],[2,2]],"check":"oracle 6","expected":[[1,1],[1,2],[0,1],[2,2]],"passed":true},{"actual":[[2,10],[-1,-7],[1,8]],"check":"oracle 7","expected":[[2,10],[-1,-7],[1,8]],"passed":true},{"actual":[[0,0],[1,3],[1,5],[1,4],[1,3],[0,1],[1,4],[1,3]],"check":"variant packet 1","expected":[[0,0],[1,3],[1,5],[1,4],[1,3],[0,1],[1,4],[1,3]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[-1, -3], [-1, -1], [1, 1], [1, 3]], \"expected\": [[-1, -3], [-1, -1], [1, 1], [1, 3]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[1, 2], [0, 2], [0, 0]], \"expected\": [[1, 2], [0, 2], [0, 0]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[2, 8], [2, 8]], \"expected\": [[2, 8], [2, 8]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[1, 1], [1, 2], [0, 1], [2, 2]], \"expected\": [[1, 1], [1, 2], [0, 1], [2, 2]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[2, 10], [-1, -7], [1, 8]], \"expected\": [[2, 10], [-1, -7], [1, 8]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}