{"abstract":"Negative coarse PCM loses its sign before refinement.","category":"PCM sample encoding","checks":8,"contract":"Restore PCM from arithmetic-shift coarse samples and optional unsigned low-bit refinements; missing refinement bits are zero and out-of-field residual bits are masked.","contract_signature":"coarse, residuals, missing_bits","evaluation_group":"s3-pcm-pcm-progressive-refinement","failed_approach":"Subtracting low bits uses the wrong residue representation for negative bins.","family":"s3-pcm-pcm-progressive-refinement-signed-coarse-compose","id":"FA-49461","implementations":{"attempt":{"sha256":"301bc02d4e96e5b1b1a83dbbb87cabef32783dc41fb89ccf59ac789c5ba85991","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(coarse, residuals, missing_bits):\n    scale=1<<missing_bits\n    out=[]\n    for index,base in enumerate(coarse):\n        tail=residuals[index] if index<len(residuals) else 0\n        tail &= scale-1\n        out.append(base*scale-tail)\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], [3, 1, 2], 2)), [7, -7, 14])\ncheck('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])\ncheck('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])\ncheck('oracle 4', solve(*([], [], 2)), [])\ncheck('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])\ncheck('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])\ncheck('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])\nif N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])\nif N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])\nif N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])\nif N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])\nif N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])\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":"c384bcc5ecad2f1e1a32d989b4f29a8b2f770be349f571eba432e825bad356fd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(coarse, residuals, missing_bits):\n    scale=1<<missing_bits\n    out=[]\n    for index,base in enumerate(coarse):\n        tail=residuals[index] if index<len(residuals) else 0\n        tail &= scale-1\n        out.append((abs(base)*scale+tail))\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], [3, 1, 2], 2)), [7, -7, 14])\ncheck('oracle 2', solve(*([-1, 0], [7, 4], 2)), [-1, 0])\ncheck('oracle 3', solve(*([2, 3, 4], [1], 3)), [17, 24, 32])\ncheck('oracle 4', solve(*([], [], 2)), [])\ncheck('oracle 5', solve(*([1, -1], [0, 0], 0)), [1, -1])\ncheck('oracle 6', solve(*([0, 0], [3, -1], 2)), [3, 3])\ncheck('oracle 7', solve(*([3, -3], [2, 1], 1)), [6, -5])\nif N == 1: check('variant packet 1', solve(*[[1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12])\nif N == 2: check('variant packet 2', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12])\nif N == 3: check('variant packet 3', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12])\nif N == 4: check('variant packet 4', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])\nif N == 5: check('variant packet 5', solve(*[[1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3, 1, -2, 3], [3, 1, 2], 2]), [7, -7, 14, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12, 4, -8, 12])\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-progressive-refinement-signed-coarse-compose","generated_at":"2026-09-29T14:45:00.230349+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":"Negative coarse PCM loses its sign before refinement.","sha256":"87affc0ebb66b5084e5f48a4dd5974259d82f7825a950235b9dfd95cac064bb9","title":"Pcm progressive refinement: signed coarse compose · 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":39.809,"exit_code":1,"observations":[{"actual":[1,-9,10],"check":"oracle 1","expected":[7,-7,14],"passed":false},{"actual":[-7,0],"check":"oracle 2","expected":[-1,0],"passed":false},{"actual":[15,24,32],"check":"oracle 3","expected":[17,24,32],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[1,-1],"check":"oracle 5","expected":[1,-1],"passed":true},{"actual":[-3,-3],"check":"oracle 6","expected":[3,3],"passed":false},{"actual":[6,-7],"check":"oracle 7","expected":[6,-5],"passed":false},{"actual":[1,-9,10,4,-8,12],"check":"variant packet 1","expected":[7,-7,14,4,-8,12],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [1, -9, 10], \"expected\": [7, -7, 14], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [-7, 0], \"expected\": [-1, 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [15, 24, 32], \"expected\": [17, 24, 32], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [1, -1], \"expected\": [1, -1], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [-3, -3], \"expected\": [3, 3], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [6, -7], \"expected\": [6, -5], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [1, -9, 10, 4, -8, 12], \"expected\": [7, -7, 14, 4, -8, 12], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.716,"exit_code":1,"observations":[{"actual":[7,9,14],"check":"oracle 1","expected":[7,-7,14],"passed":false},{"actual":[7,0],"check":"oracle 2","expected":[-1,0],"passed":false},{"actual":[17,24,32],"check":"oracle 3","expected":[17,24,32],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[1,1],"check":"oracle 5","expected":[1,-1],"passed":false},{"actual":[3,3],"check":"oracle 6","expected":[3,3],"passed":true},{"actual":[6,7],"check":"oracle 7","expected":[6,-5],"passed":false},{"actual":[7,9,14,4,8,12],"check":"variant packet 1","expected":[7,-7,14,4,-8,12],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [7, 9, 14], \"expected\": [7, -7, 14], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [7, 0], \"expected\": [-1, 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [17, 24, 32], \"expected\": [17, 24, 32], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [1, 1], \"expected\": [1, -1], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [3, 3], \"expected\": [3, 3], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [6, 7], \"expected\": [6, -5], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [7, 9, 14, 4, 8, 12], \"expected\": [7, -7, 14, 4, -8, 12], \"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."}}