{"abstract":"Dithered amplitude is emitted without division into PCM code bins.","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.","contract_signature":"samples, noises, step","evaluation_group":"s3-pcm-pcm-subtractive-dither","failed_approach":"Doubling the quantization step changes the agreed reconstruction scale.","family":"s3-pcm-pcm-subtractive-dither-quantizer-step","id":"FA-49631","implementations":{"attempt":{"sha256":"8dc146e6b802dc8551080e4942b3ee2b8db81d7ee02da214bbbeaa53ccc81db8","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*2)\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":"54637750f201c824612ee2543ebaea1732f8319ae7827c59f1cefa2a8cdcdc37","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)\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-quantizer-step","generated_at":"2026-09-29T14:45:01.798045+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.","root_cause":"Dithered amplitude is emitted without division into PCM code bins.","sha256":"90615bc88b6e2edf4d939ac8949ce66e68df5c07335f69cd126e53783d961d46","title":"Pcm subtractive dither: quantizer step · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.171,"exit_code":1,"observations":[{"actual":[[0,0],[0,-1],[0,1],[0,0]],"check":"oracle 1","expected":[[0,0],[1,3],[1,5],[1,4]],"passed":false},{"actual":[[-1,-3],[-1,-1],[0,-1],[0,1]],"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":[[1,4],[1,4]],"check":"oracle 5","expected":[[2,8],[2,8]],"passed":false},{"actual":[[0,-1],[0,0],[0,1],[1,0]],"check":"oracle 6","expected":[[1,1],[1,2],[0,1],[2,2]],"passed":false},{"actual":[[1,4],[-1,-7],[0,2]],"check":"oracle 7","expected":[[2,10],[-1,-7],[1,8]],"passed":false},{"actual":[[0,0],[0,-1],[0,1],[0,0],[0,-1],[0,1],[0,0],[0,-1]],"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], [0, 1], [0, 0]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-1, -3], [-1, -1], [0, -1], [0, 1]], \"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\": [[1, 4], [1, 4]], \"expected\": [[2, 8], [2, 8]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, -1], [0, 0], [0, 1], [1, 0]], \"expected\": [[1, 1], [1, 2], [0, 1], [2, 2]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[1, 4], [-1, -7], [0, 2]], \"expected\": [[2, 10], [-1, -7], [1, 8]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0], [0, -1], [0, 1], [0, 0], [0, -1], [0, 1], [0, 0], [0, -1]], \"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":42.824,"exit_code":1,"observations":[{"actual":[[3,12],[5,19],[4,17],[6,24]],"check":"oracle 1","expected":[[0,0],[1,3],[1,5],[1,4]],"passed":false},{"actual":[[-1,-3],[-1,-1],[3,5],[3,7]],"check":"oracle 2","expected":[[-1,-3],[-1,-1],[1,1],[1,3]],"passed":false},{"actual":[[4,14],[0,2],[2,8]],"check":"oracle 3","expected":[[1,2],[0,2],[0,0]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[10,40],[11,44]],"check":"oracle 5","expected":[[2,8],[2,8]],"passed":false},{"actual":[[3,5],[2,4],[1,3],[4,6]],"check":"oracle 6","expected":[[1,1],[1,2],[0,1],[2,2]],"passed":false},{"actual":[[12,70],[-3,-19],[6,38]],"check":"oracle 7","expected":[[2,10],[-1,-7],[1,8]],"passed":false},{"actual":[[3,12],[5,19],[4,17],[6,24],[4,15],[3,13],[5,20],[7,27]],"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\": [[3, 12], [5, 19], [4, 17], [6, 24]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-1, -3], [-1, -1], [3, 5], [3, 7]], \"expected\": [[-1, -3], [-1, -1], [1, 1], [1, 3]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[4, 14], [0, 2], [2, 8]], \"expected\": [[1, 2], [0, 2], [0, 0]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[10, 40], [11, 44]], \"expected\": [[2, 8], [2, 8]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[3, 5], [2, 4], [1, 3], [4, 6]], \"expected\": [[1, 1], [1, 2], [0, 1], [2, 2]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[12, 70], [-3, -19], [6, 38]], \"expected\": [[2, 10], [-1, -7], [1, 8]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[3, 12], [5, 19], [4, 17], [6, 24], [4, 15], [3, 13], [5, 20], [7, 27]], \"expected\": [[0, 0], [1, 3], [1, 5], [1, 4], [1, 3], [0, 1], [1, 4], [1, 3]], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}