{"abstract":"Second-order PCM prediction sums history rather than extrapolating slope.","category":"PCM sample encoding","checks":8,"contract":"Decode fixed-order PCM packets with exactly one or two chronological warmup samples, followed by residuals for hold or linear-extrapolation prediction.","evaluation_group":"s3-pcm-pcm-warmup-lpc-packet","failed_approach":"Using only slope omits the current level.","family":"s3-pcm-pcm-warmup-lpc-packet-linear-predictor","id":"FA-50206","implementations":{"attempt":{"sha256":"f2cf725b78181260e01742707de7d50fcd15fb4c0c381bd9960d06dd79eda25b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(packets, order):\n    out=[]\n    for warmup,residuals in packets:\n        if len(warmup)!=order:\n            out.append(None)\n            continue\n        decoded=list(warmup)\n        history=list(reversed(warmup))\n        for residual in residuals:\n            prediction=history[0] if order==1 else history[0]-history[1]\n            sample=prediction+residual\n            decoded.append(sample)\n            history=[sample]+history[:-1]\n        out.append(decoded)\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, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2)), [[1, 3, 5, 8, 10], [4, 2, 1, 0]])\ncheck('oracle 2', solve(*([[[5], [1, 2]]], 1)), [[5, 6, 8]])\ncheck('oracle 3', solve(*([[[1, 2, 3], [0]], [[1], []]], 2)), [None, None])\ncheck('oracle 4', solve(*([], 2)), [])\ncheck('oracle 5', solve(*([[[0, 0], []]], 2)), [[0, 0]])\ncheck('oracle 6', solve(*([[[-2, -1], [1, -1]]], 2)), [[-2, -1, 1, 2]])\ncheck('oracle 7', solve(*([[[3], []], [[0], [1]]], 1)), [[3], [0, 1]])\nif N == 1: check('variant packet 1', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 2: check('variant packet 2', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 3: check('variant packet 3', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 4: check('variant packet 4', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 5: check('variant packet 5', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 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":"a41f9944136de8bddeea8f1b88fcd52044878f3c0e81889c00f5a836eecc94e1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(packets, order):\n    out=[]\n    for warmup,residuals in packets:\n        if len(warmup)!=order:\n            out.append(None)\n            continue\n        decoded=list(warmup)\n        history=list(reversed(warmup))\n        for residual in residuals:\n            prediction=history[0] if order==1 else history[0]+history[1]\n            sample=prediction+residual\n            decoded.append(sample)\n            history=[sample]+history[:-1]\n        out.append(decoded)\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, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2)), [[1, 3, 5, 8, 10], [4, 2, 1, 0]])\ncheck('oracle 2', solve(*([[[5], [1, 2]]], 1)), [[5, 6, 8]])\ncheck('oracle 3', solve(*([[[1, 2, 3], [0]], [[1], []]], 2)), [None, None])\ncheck('oracle 4', solve(*([], 2)), [])\ncheck('oracle 5', solve(*([[[0, 0], []]], 2)), [[0, 0]])\ncheck('oracle 6', solve(*([[[-2, -1], [1, -1]]], 2)), [[-2, -1, 1, 2]])\ncheck('oracle 7', solve(*([[[3], []], [[0], [1]]], 1)), [[3], [0, 1]])\nif N == 1: check('variant packet 1', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 2: check('variant packet 2', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 3: check('variant packet 3', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 4: check('variant packet 4', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 5: check('variant packet 5', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 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":"ca2683d1e20a358476bdd1f49d35198e8d91d09bebc61c5522f93dfb327e5f09","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(packets, order):\n    out=[]\n    for warmup,residuals in packets:\n        if len(warmup)!=order:\n            out.append(None)\n            continue\n        decoded=list(warmup)\n        history=list(reversed(warmup))\n        for residual in residuals:\n            prediction=history[0] if order==1 else 2*history[0]-history[1]\n            sample=prediction+residual\n            decoded.append(sample)\n            history=[sample]+history[:-1]\n        out.append(decoded)\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, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2)), [[1, 3, 5, 8, 10], [4, 2, 1, 0]])\ncheck('oracle 2', solve(*([[[5], [1, 2]]], 1)), [[5, 6, 8]])\ncheck('oracle 3', solve(*([[[1, 2, 3], [0]], [[1], []]], 2)), [None, None])\ncheck('oracle 4', solve(*([], 2)), [])\ncheck('oracle 5', solve(*([[[0, 0], []]], 2)), [[0, 0]])\ncheck('oracle 6', solve(*([[[-2, -1], [1, -1]]], 2)), [[-2, -1, 1, 2]])\ncheck('oracle 7', solve(*([[[3], []], [[0], [1]]], 1)), [[3], [0, 1]])\nif N == 1: check('variant packet 1', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 2: check('variant packet 2', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 3: check('variant packet 3', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 4: check('variant packet 4', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]])\nif N == 5: check('variant packet 5', solve(*[[[[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]], [[1, 3], [0, 1, -1]], [[4, 2], [1, 0]]], 2]), [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 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-pcm-warmup-lpc-packet-linear-predictor","generated_at":"2026-09-29T14:45:06.913126+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 linear predictor.","root_cause":"Second-order PCM prediction sums history rather than extrapolating slope.","sha256":"f5cc139cf4a848a951e45a3e97e1e301d4ce3b814c98e971167e3ac0764d78b0","title":"Pcm warmup lpc packet: linear predictor · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":37.998,"exit_code":1,"observations":[{"actual":[[1,3,2,0,-3],[4,2,-1,-3]],"check":"oracle 1","expected":[[1,3,5,8,10],[4,2,1,0]],"passed":false},{"actual":[[5,6,8]],"check":"oracle 2","expected":[[5,6,8]],"passed":true},{"actual":[null,null],"check":"oracle 3","expected":[null,null],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[0,0]],"check":"oracle 5","expected":[[0,0]],"passed":true},{"actual":[[-2,-1,2,2]],"check":"oracle 6","expected":[[-2,-1,1,2]],"passed":false},{"actual":[[3],[0,1]],"check":"oracle 7","expected":[[3],[0,1]],"passed":true},{"actual":[[1,3,2,0,-3],[4,2,-1,-3],[1,3,2,0,-3],[4,2,-1,-3]],"check":"variant packet 1","expected":[[1,3,5,8,10],[4,2,1,0],[1,3,5,8,10],[4,2,1,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 3, 2, 0, -3], [4, 2, -1, -3]], \"expected\": [[1, 3, 5, 8, 10], [4, 2, 1, 0]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[5, 6, 8]], \"expected\": [[5, 6, 8]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [null, null], \"expected\": [null, null], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-2, -1, 2, 2]], \"expected\": [[-2, -1, 1, 2]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[3], [0, 1]], \"expected\": [[3], [0, 1]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[1, 3, 2, 0, -3], [4, 2, -1, -3], [1, 3, 2, 0, -3], [4, 2, -1, -3]], \"expected\": [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.26,"exit_code":1,"observations":[{"actual":[[1,3,4,8,11],[4,2,7,9]],"check":"oracle 1","expected":[[1,3,5,8,10],[4,2,1,0]],"passed":false},{"actual":[[5,6,8]],"check":"oracle 2","expected":[[5,6,8]],"passed":true},{"actual":[null,null],"check":"oracle 3","expected":[null,null],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[0,0]],"check":"oracle 5","expected":[[0,0]],"passed":true},{"actual":[[-2,-1,-2,-4]],"check":"oracle 6","expected":[[-2,-1,1,2]],"passed":false},{"actual":[[3],[0,1]],"check":"oracle 7","expected":[[3],[0,1]],"passed":true},{"actual":[[1,3,4,8,11],[4,2,7,9],[1,3,4,8,11],[4,2,7,9]],"check":"variant packet 1","expected":[[1,3,5,8,10],[4,2,1,0],[1,3,5,8,10],[4,2,1,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 3, 4, 8, 11], [4, 2, 7, 9]], \"expected\": [[1, 3, 5, 8, 10], [4, 2, 1, 0]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[5, 6, 8]], \"expected\": [[5, 6, 8]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [null, null], \"expected\": [null, null], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-2, -1, -2, -4]], \"expected\": [[-2, -1, 1, 2]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[3], [0, 1]], \"expected\": [[3], [0, 1]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[1, 3, 4, 8, 11], [4, 2, 7, 9], [1, 3, 4, 8, 11], [4, 2, 7, 9]], \"expected\": [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.264,"exit_code":0,"observations":[{"actual":[[1,3,5,8,10],[4,2,1,0]],"check":"oracle 1","expected":[[1,3,5,8,10],[4,2,1,0]],"passed":true},{"actual":[[5,6,8]],"check":"oracle 2","expected":[[5,6,8]],"passed":true},{"actual":[null,null],"check":"oracle 3","expected":[null,null],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[0,0]],"check":"oracle 5","expected":[[0,0]],"passed":true},{"actual":[[-2,-1,1,2]],"check":"oracle 6","expected":[[-2,-1,1,2]],"passed":true},{"actual":[[3],[0,1]],"check":"oracle 7","expected":[[3],[0,1]],"passed":true},{"actual":[[1,3,5,8,10],[4,2,1,0],[1,3,5,8,10],[4,2,1,0]],"check":"variant packet 1","expected":[[1,3,5,8,10],[4,2,1,0],[1,3,5,8,10],[4,2,1,0]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 3, 5, 8, 10], [4, 2, 1, 0]], \"expected\": [[1, 3, 5, 8, 10], [4, 2, 1, 0]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[5, 6, 8]], \"expected\": [[5, 6, 8]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [null, null], \"expected\": [null, null], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-2, -1, 1, 2]], \"expected\": [[-2, -1, 1, 2]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[3], [0, 1]], \"expected\": [[3], [0, 1]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]], \"expected\": [[1, 3, 5, 8, 10], [4, 2, 1, 0], [1, 3, 5, 8, 10], [4, 2, 1, 0]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}