{"abstract":"A hardware line-inversion map is applied as a bit-set mask.","category":"PCM sample encoding","checks":8,"contract":"Undo a per-line XOR inversion map within a signed PCM field before interpreting sign and detecting canonical zero.","evaluation_group":"s3-pcm-xor-coded-pcm","failed_approach":"AND filtering destroys every non-inverted signal line.","family":"s3-pcm-xor-coded-pcm-mask-operation","id":"FA-49041","implementations":{"attempt":{"sha256":"3bd2e14577e7525415702be2a5a7640a404a6ac69485e98aaca57625ac244e07","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, xor_mask):\n    field=(1<<width)-1\n    out=[]\n    for raw in codes:\n        code=(raw&xor_mask)&field\n        sign=1<<(width-1)\n        value=code-(1<<width) if code&sign else code\n        out.append([value, code==0])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])\ncheck('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])\ncheck('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])\ncheck('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])\ncheck('oracle 5', solve(*([], 3, 7)), [])\ncheck('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])\ncheck('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])\nif N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\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":"2142d41c37290a7382fd652a52d8946f015b22060f72c2b9578d2791e549dd72","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, xor_mask):\n    field=(1<<width)-1\n    out=[]\n    for raw in codes:\n        code=(raw|xor_mask)&field\n        sign=1<<(width-1)\n        value=code-(1<<width) if code&sign else code\n        out.append([value, code==0])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])\ncheck('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])\ncheck('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])\ncheck('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])\ncheck('oracle 5', solve(*([], 3, 7)), [])\ncheck('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])\ncheck('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])\nif N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\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":"677436fbf1c31a2198a83bd1495490a6162935ebca710bd28a5712c0b7f3cf3d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, xor_mask):\n    field=(1<<width)-1\n    out=[]\n    for raw in codes:\n        code=(raw^xor_mask)&field\n        sign=1<<(width-1)\n        value=code-(1<<width) if code&sign else code\n        out.append([value, code==0])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 3, 7, 8, 15], 4, 5)), [[5, False], [6, False], [2, False], [-3, False], [-6, False]])\ncheck('oracle 2', solve(*([8, 0, 15], 4, 8)), [[0, True], [-8, False], [7, False]])\ncheck('oracle 3', solve(*([16, 31, 0], 4, 32)), [[0, True], [-1, False], [0, True]])\ncheck('oracle 4', solve(*([0, 255], 8, 85)), [[85, False], [-86, False]])\ncheck('oracle 5', solve(*([], 3, 7)), [])\ncheck('oracle 6', solve(*([0, 1], 1, 1)), [[-1, False], [0, True]])\ncheck('oracle 7', solve(*([3, 4, 7], 3, 2)), [[1, False], [-2, False], [-3, False]])\nif N == 1: check('variant packet 1', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 2: check('variant packet 2', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 3: check('variant packet 3', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 4: check('variant packet 4', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\nif N == 5: check('variant packet 5', solve(*[[0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15, 0, 3, 7, 8, 15], 4, 5]), [[5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False], [5, False], [6, False], [2, False], [-3, False], [-6, False]])\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-xor-coded-pcm-mask-operation","generated_at":"2026-09-29T14:44:56.253192+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 mask operation.","root_cause":"A hardware line-inversion map is applied as a bit-set mask.","sha256":"a554036bf7ee2bcfb730af2059a323cf4e964253303202019b78155c574fa981","title":"Xor coded pcm: mask operation · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.422,"exit_code":1,"observations":[{"actual":[[0,true],[1,false],[5,false],[0,true],[5,false]],"check":"oracle 1","expected":[[5,false],[6,false],[2,false],[-3,false],[-6,false]],"passed":false},{"actual":[[-8,false],[0,true],[-8,false]],"check":"oracle 2","expected":[[0,true],[-8,false],[7,false]],"passed":false},{"actual":[[0,true],[0,true],[0,true]],"check":"oracle 3","expected":[[0,true],[-1,false],[0,true]],"passed":false},{"actual":[[0,true],[85,false]],"check":"oracle 4","expected":[[85,false],[-86,false]],"passed":false},{"actual":[],"check":"oracle 5","expected":[],"passed":true},{"actual":[[0,true],[-1,false]],"check":"oracle 6","expected":[[-1,false],[0,true]],"passed":false},{"actual":[[2,false],[0,true],[2,false]],"check":"oracle 7","expected":[[1,false],[-2,false],[-3,false]],"passed":false},{"actual":[[0,true],[1,false],[5,false],[0,true],[5,false],[0,true],[1,false],[5,false],[0,true],[5,false]],"check":"variant packet 1","expected":[[5,false],[6,false],[2,false],[-3,false],[-6,false],[5,false],[6,false],[2,false],[-3,false],[-6,false]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, true], [1, false], [5, false], [0, true], [5, false]], \"expected\": [[5, false], [6, false], [2, false], [-3, false], [-6, false]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-8, false], [0, true], [-8, false]], \"expected\": [[0, true], [-8, false], [7, false]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, true], [0, true], [0, true]], \"expected\": [[0, true], [-1, false], [0, true]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[0, true], [85, false]], \"expected\": [[85, false], [-86, false]], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0, true], [-1, false]], \"expected\": [[-1, false], [0, true]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[2, false], [0, true], [2, false]], \"expected\": [[1, false], [-2, false], [-3, false]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, true], [1, false], [5, false], [0, true], [5, false], [0, true], [1, false], [5, false], [0, true], [5, false]], \"expected\": [[5, false], [6, false], [2, false], [-3, false], [-6, false], [5, false], [6, false], [2, false], [-3, false], [-6, false]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.984,"exit_code":1,"observations":[{"actual":[[5,false],[7,false],[7,false],[-3,false],[-1,false]],"check":"oracle 1","expected":[[5,false],[6,false],[2,false],[-3,false],[-6,false]],"passed":false},{"actual":[[-8,false],[-8,false],[-1,false]],"check":"oracle 2","expected":[[0,true],[-8,false],[7,false]],"passed":false},{"actual":[[0,true],[-1,false],[0,true]],"check":"oracle 3","expected":[[0,true],[-1,false],[0,true]],"passed":true},{"actual":[[85,false],[-1,false]],"check":"oracle 4","expected":[[85,false],[-86,false]],"passed":false},{"actual":[],"check":"oracle 5","expected":[],"passed":true},{"actual":[[-1,false],[-1,false]],"check":"oracle 6","expected":[[-1,false],[0,true]],"passed":false},{"actual":[[3,false],[-2,false],[-1,false]],"check":"oracle 7","expected":[[1,false],[-2,false],[-3,false]],"passed":false},{"actual":[[5,false],[7,false],[7,false],[-3,false],[-1,false],[5,false],[7,false],[7,false],[-3,false],[-1,false]],"check":"variant packet 1","expected":[[5,false],[6,false],[2,false],[-3,false],[-6,false],[5,false],[6,false],[2,false],[-3,false],[-6,false]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[5, false], [7, false], [7, false], [-3, false], [-1, false]], \"expected\": [[5, false], [6, false], [2, false], [-3, false], [-6, false]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[-8, false], [-8, false], [-1, false]], \"expected\": [[0, true], [-8, false], [7, false]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, true], [-1, false], [0, true]], \"expected\": [[0, true], [-1, false], [0, true]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[85, false], [-1, false]], \"expected\": [[85, false], [-86, false]], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-1, false], [-1, false]], \"expected\": [[-1, false], [0, true]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[3, false], [-2, false], [-1, false]], \"expected\": [[1, false], [-2, false], [-3, false]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[5, false], [7, false], [7, false], [-3, false], [-1, false], [5, false], [7, false], [7, false], [-3, false], [-1, false]], \"expected\": [[5, false], [6, false], [2, false], [-3, false], [-6, false], [5, false], [6, false], [2, false], [-3, false], [-6, false]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.349,"exit_code":0,"observations":[{"actual":[[5,false],[6,false],[2,false],[-3,false],[-6,false]],"check":"oracle 1","expected":[[5,false],[6,false],[2,false],[-3,false],[-6,false]],"passed":true},{"actual":[[0,true],[-8,false],[7,false]],"check":"oracle 2","expected":[[0,true],[-8,false],[7,false]],"passed":true},{"actual":[[0,true],[-1,false],[0,true]],"check":"oracle 3","expected":[[0,true],[-1,false],[0,true]],"passed":true},{"actual":[[85,false],[-86,false]],"check":"oracle 4","expected":[[85,false],[-86,false]],"passed":true},{"actual":[],"check":"oracle 5","expected":[],"passed":true},{"actual":[[-1,false],[0,true]],"check":"oracle 6","expected":[[-1,false],[0,true]],"passed":true},{"actual":[[1,false],[-2,false],[-3,false]],"check":"oracle 7","expected":[[1,false],[-2,false],[-3,false]],"passed":true},{"actual":[[5,false],[6,false],[2,false],[-3,false],[-6,false],[5,false],[6,false],[2,false],[-3,false],[-6,false]],"check":"variant packet 1","expected":[[5,false],[6,false],[2,false],[-3,false],[-6,false],[5,false],[6,false],[2,false],[-3,false],[-6,false]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[5, false], [6, false], [2, false], [-3, false], [-6, false]], \"expected\": [[5, false], [6, false], [2, false], [-3, false], [-6, false]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[0, true], [-8, false], [7, false]], \"expected\": [[0, true], [-8, false], [7, false]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[0, true], [-1, false], [0, true]], \"expected\": [[0, true], [-1, false], [0, true]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[85, false], [-86, false]], \"expected\": [[85, false], [-86, false]], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[-1, false], [0, true]], \"expected\": [[-1, false], [0, true]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, false], [-2, false], [-3, false]], \"expected\": [[1, false], [-2, false], [-3, false]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[5, false], [6, false], [2, false], [-3, false], [-6, false], [5, false], [6, false], [2, false], [-3, false], [-6, false]], \"expected\": [[5, false], [6, false], [2, false], [-3, false], [-6, false], [5, false], [6, false], [2, false], [-3, false], [-6, false]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}