{"abstract":"LPC residual sign is inverted.","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":"Returning only residuals discards the predicted signal.","family":"s3-pcm-pcm-lpc-residual-reconstruction-residual-addition","id":"FA-50151","implementations":{"attempt":{"sha256":"9d4d0fba6042d379117828cf74e012ee67ddc065ff8da053e5bbc9b1a20609a4","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 for c,x in zip(coefficients,state))//divisor\n        sample=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":"69feb603406e1a60acb8e5c2deeaace3fe8d98fa6e7e8839bd3fdf7c8c284504","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 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"}},"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-residual-addition","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":"LPC residual sign is inverted.","sha256":"f7232777a69302e338cd24cb9d8aca28923c3c52fa7ef43e1e47e7453a66c681","title":"Pcm lpc residual reconstruction: residual addition · 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":39.035,"exit_code":1,"observations":[{"actual":[[1,2,-1],[-1,2]],"check":"oracle 1","expected":[[6,11,15],[15,11]],"passed":false},{"actual":[[0,1,-2],[-2,1]],"check":"oracle 2","expected":[[-1,-1,-3],[-3,-1]],"passed":false},{"actual":[[],[2,1]],"check":"oracle 3","expected":[[],[2,1]],"passed":true},{"actual":[[2,0,1],[1,0,2]],"check":"oracle 4","expected":[[2,3,3],[3,3,2]],"passed":false},{"actual":[[-1,3],[3]],"check":"oracle 5","expected":[[1,3],[3]],"passed":false},{"actual":[[1,1],[1,1,1]],"check":"oracle 6","expected":[[4,4],[4,4,1]],"passed":false},{"actual":[[0,-1],[-1,0]],"check":"oracle 7","expected":[[3,3],[3,3]],"passed":false},{"actual":[[1,2,-1,1,2,-1],[-1,2]],"check":"variant packet 1","expected":[[6,11,15,20,27,33],[33,27]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 2, -1], [-1, 2]], \"expected\": [[6, 11, 15], [15, 11]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[0, 1, -2], [-2, 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, 0, 1], [1, 0, 2]], \"expected\": [[2, 3, 3], [3, 3, 2]], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [[-1, 3], [3]], \"expected\": [[1, 3], [3]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[1, 1], [1, 1, 1]], \"expected\": [[4, 4], [4, 4, 1]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[0, -1], [-1, 0]], \"expected\": [[3, 3], [3, 3]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[1, 2, -1, 1, 2, -1], [-1, 2]], \"expected\": [[6, 11, 15, 20, 27, 33], [33, 27]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.66,"exit_code":1,"observations":[{"actual":[[4,3,3],[3,3]],"check":"oracle 1","expected":[[6,11,15],[15,11]],"passed":false},{"actual":[[-1,-3,0],[0,-3]],"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,-4],[-4,-3,-2]],"check":"oracle 4","expected":[[2,3,3],[3,3,2]],"passed":false},{"actual":[[3,-2],[-2]],"check":"oracle 5","expected":[[1,3],[3]],"passed":false},{"actual":[[2,1],[1,2,1]],"check":"oracle 6","expected":[[4,4],[4,4,1]],"passed":false},{"actual":[[3,5],[5,3]],"check":"oracle 7","expected":[[3,3],[3,3]],"passed":false},{"actual":[[4,3,3,2,-1,-3],[-3,-1]],"check":"variant packet 1","expected":[[6,11,15,20,27,33],[33,27]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[4, 3, 3], [3, 3]], \"expected\": [[6, 11, 15], [15, 11]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-1, -3, 0], [0, -3]], \"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, -4], [-4, -3, -2]], \"expected\": [[2, 3, 3], [3, 3, 2]], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [[3, -2], [-2]], \"expected\": [[1, 3], [3]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[2, 1], [1, 2, 1]], \"expected\": [[4, 4], [4, 4, 1]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[3, 5], [5, 3]], \"expected\": [[3, 3], [3, 3]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[4, 3, 3, 2, -1, -3], [-3, -1]], \"expected\": [[6, 11, 15, 20, 27, 33], [33, 27]], \"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."}}