{"abstract":"Per-tap rounding changes the integer LPC prediction.","category":"PCM sample encoding","checks":8,"contract":"Reconstruct bounded integer PCM LPC residuals using newest-first history, floor-divided complete dot products and reconstructed-sample history feedback.","contract_signature":"residuals, history, coefficients, divisor","evaluation_group":"s3-pcm-pcm-lpc-residual-reconstruction","failed_approach":"Truncation toward zero differs from the declared floor for negative predictions.","family":"s3-pcm-pcm-lpc-residual-reconstruction-sum-before-division","id":"FA-50146","implementations":{"attempt":{"sha256":"00cc992912e1faf4f1c6c55561bbd30677b50bb787d035adde3f689e559b36a1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(residuals, history, coefficients, divisor):\n    state=list(history)\n    out=[]\n    for residual in residuals:\n        prediction=int(sum(c*x for c,x in zip(coefficients,state))/divisor)\n        sample=prediction+residual\n        out.append(sample)\n        state=[sample]+state[:-1]\n    return [out,state]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, -1], [3, 1], [2, -1], 1)), [[6, 11, 15], [15, 11]])\ncheck('oracle 2', solve(*([0, 1, -2], [-3, 2], [1, 1], 3)), [[-1, -1, -3], [-3, -1]])\ncheck('oracle 3', solve(*([], [2, 1], [2, -1], 1)), [[], [2, 1]])\ncheck('oracle 4', solve(*([2, 0, 1], [0, 0, 0], [3, -2, 1], 2)), [[2, 3, 3], [3, 3, 2]])\ncheck('oracle 5', solve(*([-1, 3], [5], [1], 2)), [[1, 3], [3]])\ncheck('oracle 6', solve(*([1, 1], [1, 2, 3], [1, 2, 3], 4)), [[4, 4], [4, 4, 1]])\ncheck('oracle 7', solve(*([0, -1], [4, -2], [3, 1], 3)), [[3, 3], [3, 3]])\nif N == 1: check('variant packet 1', solve(*[[1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33], [33, 27]])\nif N == 2: check('variant packet 2', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57], [57, 49]])\nif N == 3: check('variant packet 3', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87], [87, 77]])\nif N == 4: check('variant packet 4', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123], [123, 111]])\nif N == 5: check('variant packet 5', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123, 136, 151, 165], [165, 151]])\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":"e402789626a928e9ccc149af5c9909fcfe99576ec78ea7650eb98e57c388b161","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(residuals, history, coefficients, divisor):\n    state=list(history)\n    out=[]\n    for residual in residuals:\n        prediction=sum(c*x//divisor for c,x in zip(coefficients,state))\n        sample=prediction+residual\n        out.append(sample)\n        state=[sample]+state[:-1]\n    return [out,state]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, -1], [3, 1], [2, -1], 1)), [[6, 11, 15], [15, 11]])\ncheck('oracle 2', solve(*([0, 1, -2], [-3, 2], [1, 1], 3)), [[-1, -1, -3], [-3, -1]])\ncheck('oracle 3', solve(*([], [2, 1], [2, -1], 1)), [[], [2, 1]])\ncheck('oracle 4', solve(*([2, 0, 1], [0, 0, 0], [3, -2, 1], 2)), [[2, 3, 3], [3, 3, 2]])\ncheck('oracle 5', solve(*([-1, 3], [5], [1], 2)), [[1, 3], [3]])\ncheck('oracle 6', solve(*([1, 1], [1, 2, 3], [1, 2, 3], 4)), [[4, 4], [4, 4, 1]])\ncheck('oracle 7', solve(*([0, -1], [4, -2], [3, 1], 3)), [[3, 3], [3, 3]])\nif N == 1: check('variant packet 1', solve(*[[1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33], [33, 27]])\nif N == 2: check('variant packet 2', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57], [57, 49]])\nif N == 3: check('variant packet 3', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87], [87, 77]])\nif N == 4: check('variant packet 4', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123], [123, 111]])\nif N == 5: check('variant packet 5', solve(*[[1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1, 1, 2, -1], [3, 1], [2, -1], 1]), [[6, 11, 15, 20, 27, 33, 40, 49, 57, 66, 77, 87, 98, 111, 123, 136, 151, 165], [165, 151]])\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-lpc-residual-reconstruction-sum-before-division","generated_at":"2026-09-29T14:45:06.619573+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":"Per-tap rounding changes the integer LPC prediction.","sha256":"784ab7351907c6b828fba32b657a26a19ebd57d27ad6656fd110e1504cc1ea4d","title":"Pcm lpc residual reconstruction: sum before division · 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":39.878,"exit_code":1,"observations":[{"actual":[[6,11,15],[15,11]],"check":"oracle 1","expected":[[6,11,15],[15,11]],"passed":true},{"actual":[[0,0,-2],[-2,0]],"check":"oracle 2","expected":[[-1,-1,-3],[-3,-1]],"passed":false},{"actual":[[],[2,1]],"check":"oracle 3","expected":[[],[2,1]],"passed":true},{"actual":[[2,3,3],[3,3,2]],"check":"oracle 4","expected":[[2,3,3],[3,3,2]],"passed":true},{"actual":[[1,3],[3]],"check":"oracle 5","expected":[[1,3],[3]],"passed":true},{"actual":[[4,4],[4,4,1]],"check":"oracle 6","expected":[[4,4],[4,4,1]],"passed":true},{"actual":[[3,3],[3,3]],"check":"oracle 7","expected":[[3,3],[3,3]],"passed":true},{"actual":[[6,11,15,20,27,33],[33,27]],"check":"variant packet 1","expected":[[6,11,15,20,27,33],[33,27]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[6, 11, 15], [15, 11]], \"expected\": [[6, 11, 15], [15, 11]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[0, 0, -2], [-2, 0]], \"expected\": [[-1, -1, -3], [-3, -1]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[], [2, 1]], \"expected\": [[], [2, 1]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[2, 3, 3], [3, 3, 2]], \"expected\": [[2, 3, 3], [3, 3, 2]], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[1, 3], [3]], \"expected\": [[1, 3], [3]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[4, 4], [4, 4, 1]], \"expected\": [[4, 4], [4, 4, 1]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[3, 3], [3, 3]], \"expected\": [[3, 3], [3, 3]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[6, 11, 15, 20, 27, 33], [33, 27]], \"expected\": [[6, 11, 15, 20, 27, 33], [33, 27]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":37.449,"exit_code":1,"observations":[{"actual":[[6,11,15],[15,11]],"check":"oracle 1","expected":[[6,11,15],[15,11]],"passed":true},{"actual":[[-1,-1,-4],[-4,-1]],"check":"oracle 2","expected":[[-1,-1,-3],[-3,-1]],"passed":false},{"actual":[[],[2,1]],"check":"oracle 3","expected":[[],[2,1]],"passed":true},{"actual":[[2,3,3],[3,3,2]],"check":"oracle 4","expected":[[2,3,3],[3,3,2]],"passed":true},{"actual":[[1,3],[3]],"check":"oracle 5","expected":[[1,3],[3]],"passed":true},{"actual":[[4,3],[3,4,1]],"check":"oracle 6","expected":[[4,4],[4,4,1]],"passed":false},{"actual":[[3,3],[3,3]],"check":"oracle 7","expected":[[3,3],[3,3]],"passed":true},{"actual":[[6,11,15,20,27,33],[33,27]],"check":"variant packet 1","expected":[[6,11,15,20,27,33],[33,27]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[6, 11, 15], [15, 11]], \"expected\": [[6, 11, 15], [15, 11]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[-1, -1, -4], [-4, -1]], \"expected\": [[-1, -1, -3], [-3, -1]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[], [2, 1]], \"expected\": [[], [2, 1]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[2, 3, 3], [3, 3, 2]], \"expected\": [[2, 3, 3], [3, 3, 2]], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[1, 3], [3]], \"expected\": [[1, 3], [3]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[4, 3], [3, 4, 1]], \"expected\": [[4, 4], [4, 4, 1]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[3, 3], [3, 3]], \"expected\": [[3, 3], [3, 3]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[6, 11, 15, 20, 27, 33], [33, 27]], \"expected\": [[6, 11, 15, 20, 27, 33], [33, 27]], \"passed\": true}], \"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."}}