{"abstract":"Positive codes are biased despite the direct positive mapping.","category":"PCM sample encoding","checks":8,"contract":"Decode bounded ones-complement PCM fields; optionally preserve a per-sample negative-zero sideband while numeric zero stays JSON integer zero.","contract_signature":"codes, width, preserve_negative_zero","evaluation_group":"s3-pcm-ones-complement-pcm","failed_approach":"Subtracting a bias clips low positive samples.","family":"s3-pcm-ones-complement-pcm-positive-magnitude","id":"FA-48926","implementations":{"attempt":{"sha256":"d1a3150b13fb23150fde105e69424c220672af36b41f3c6e1b9aac292939c323","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, preserve_negative_zero):\n    mask=(1<<width)-1\n    sign=1<<(width-1)\n    values=[]\n    negative_zero=[]\n    for raw in codes:\n        code=raw&mask\n        magnitude=(~code)&mask if code&sign else max(0,code-1)\n        value=-magnitude if code&sign else magnitude\n        values.append(value)\n        negative_zero.append(bool(preserve_negative_zero and code==mask))\n    return [values,negative_zero]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 1, 7, 8, 14, 15], 4, True)), [[0, 1, 7, -7, -1, 0], [False, False, False, False, False, True]])\ncheck('oracle 2', solve(*([15, 0, 8], 4, False)), [[0, 0, -7], [False, False, False]])\ncheck('oracle 3', solve(*([31, 16, 17], 4, True)), [[0, 0, 1], [True, False, False]])\ncheck('oracle 4', solve(*([], 4, True)), [[], []])\ncheck('oracle 5', solve(*([0, 3, 4, 6, 7], 3, True)), [[0, 3, -3, -1, 0], [False, False, False, False, True]])\ncheck('oracle 6', solve(*([255, 128, 254, 127], 8, False)), [[0, -127, -1, 127], [False, False, False, False]])\ncheck('oracle 7', solve(*([255], 8, True)), [[0], [True]])\nif N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\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":"88e1adcc5ce9bef4d8290188ad276871ca95138832e4c86d0b9ae6aaa89f66d5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codes, width, preserve_negative_zero):\n    mask=(1<<width)-1\n    sign=1<<(width-1)\n    values=[]\n    negative_zero=[]\n    for raw in codes:\n        code=raw&mask\n        magnitude=(~code)&mask if code&sign else code+1\n        value=-magnitude if code&sign else magnitude\n        values.append(value)\n        negative_zero.append(bool(preserve_negative_zero and code==mask))\n    return [values,negative_zero]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([0, 1, 7, 8, 14, 15], 4, True)), [[0, 1, 7, -7, -1, 0], [False, False, False, False, False, True]])\ncheck('oracle 2', solve(*([15, 0, 8], 4, False)), [[0, 0, -7], [False, False, False]])\ncheck('oracle 3', solve(*([31, 16, 17], 4, True)), [[0, 0, 1], [True, False, False]])\ncheck('oracle 4', solve(*([], 4, True)), [[], []])\ncheck('oracle 5', solve(*([0, 3, 4, 6, 7], 3, True)), [[0, 3, -3, -1, 0], [False, False, False, False, True]])\ncheck('oracle 6', solve(*([255, 128, 254, 127], 8, False)), [[0, -127, -1, 127], [False, False, False, False]])\ncheck('oracle 7', solve(*([255], 8, True)), [[0], [True]])\nif N == 1: check('variant packet 1', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 2: check('variant packet 2', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 3: check('variant packet 3', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 4: check('variant packet 4', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\nif N == 5: check('variant packet 5', solve(*[[0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15, 0, 1, 7, 8, 14, 15], 4, True]), [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True]])\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-ones-complement-pcm-positive-magnitude","generated_at":"2026-09-29T14:44:55.277062+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":"Positive codes are biased despite the direct positive mapping.","sha256":"9bf46f101addb7dfcaacfe63fbbe298944dacc2f2aeb850ae7b01a086b11b10f","title":"Ones complement pcm: positive magnitude · 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":39.123,"exit_code":1,"observations":[{"actual":[[0,0,6,-7,-1,0],[false,false,false,false,false,true]],"check":"oracle 1","expected":[[0,1,7,-7,-1,0],[false,false,false,false,false,true]],"passed":false},{"actual":[[0,0,-7],[false,false,false]],"check":"oracle 2","expected":[[0,0,-7],[false,false,false]],"passed":true},{"actual":[[0,0,0],[true,false,false]],"check":"oracle 3","expected":[[0,0,1],[true,false,false]],"passed":false},{"actual":[[],[]],"check":"oracle 4","expected":[[],[]],"passed":true},{"actual":[[0,2,-3,-1,0],[false,false,false,false,true]],"check":"oracle 5","expected":[[0,3,-3,-1,0],[false,false,false,false,true]],"passed":false},{"actual":[[0,-127,-1,126],[false,false,false,false]],"check":"oracle 6","expected":[[0,-127,-1,127],[false,false,false,false]],"passed":false},{"actual":[[0],[true]],"check":"oracle 7","expected":[[0],[true]],"passed":true},{"actual":[[0,0,6,-7,-1,0,0,0,6,-7,-1,0],[false,false,false,false,false,true,false,false,false,false,false,true]],"check":"variant packet 1","expected":[[0,1,7,-7,-1,0,0,1,7,-7,-1,0],[false,false,false,false,false,true,false,false,false,false,false,true]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0, 6, -7, -1, 0], [false, false, false, false, false, true]], \"expected\": [[0, 1, 7, -7, -1, 0], [false, false, false, false, false, true]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[0, 0, -7], [false, false, false]], \"expected\": [[0, 0, -7], [false, false, false]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[0, 0, 0], [true, false, false]], \"expected\": [[0, 0, 1], [true, false, false]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], []], \"expected\": [[], []], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 2, -3, -1, 0], [false, false, false, false, true]], \"expected\": [[0, 3, -3, -1, 0], [false, false, false, false, true]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, -127, -1, 126], [false, false, false, false]], \"expected\": [[0, -127, -1, 127], [false, false, false, false]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[0], [true]], \"expected\": [[0], [true]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0, 6, -7, -1, 0, 0, 0, 6, -7, -1, 0], [false, false, false, false, false, true, false, false, false, false, false, true]], \"expected\": [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [false, false, false, false, false, true, false, false, false, false, false, true]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.417,"exit_code":1,"observations":[{"actual":[[1,2,8,-7,-1,0],[false,false,false,false,false,true]],"check":"oracle 1","expected":[[0,1,7,-7,-1,0],[false,false,false,false,false,true]],"passed":false},{"actual":[[0,1,-7],[false,false,false]],"check":"oracle 2","expected":[[0,0,-7],[false,false,false]],"passed":false},{"actual":[[0,1,2],[true,false,false]],"check":"oracle 3","expected":[[0,0,1],[true,false,false]],"passed":false},{"actual":[[],[]],"check":"oracle 4","expected":[[],[]],"passed":true},{"actual":[[1,4,-3,-1,0],[false,false,false,false,true]],"check":"oracle 5","expected":[[0,3,-3,-1,0],[false,false,false,false,true]],"passed":false},{"actual":[[0,-127,-1,128],[false,false,false,false]],"check":"oracle 6","expected":[[0,-127,-1,127],[false,false,false,false]],"passed":false},{"actual":[[0],[true]],"check":"oracle 7","expected":[[0],[true]],"passed":true},{"actual":[[1,2,8,-7,-1,0,1,2,8,-7,-1,0],[false,false,false,false,false,true,false,false,false,false,false,true]],"check":"variant packet 1","expected":[[0,1,7,-7,-1,0,0,1,7,-7,-1,0],[false,false,false,false,false,true,false,false,false,false,false,true]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[1, 2, 8, -7, -1, 0], [false, false, false, false, false, true]], \"expected\": [[0, 1, 7, -7, -1, 0], [false, false, false, false, false, true]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[0, 1, -7], [false, false, false]], \"expected\": [[0, 0, -7], [false, false, false]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, 1, 2], [true, false, false]], \"expected\": [[0, 0, 1], [true, false, false]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], []], \"expected\": [[], []], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[1, 4, -3, -1, 0], [false, false, false, false, true]], \"expected\": [[0, 3, -3, -1, 0], [false, false, false, false, true]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, -127, -1, 128], [false, false, false, false]], \"expected\": [[0, -127, -1, 127], [false, false, false, false]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[0], [true]], \"expected\": [[0], [true]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[1, 2, 8, -7, -1, 0, 1, 2, 8, -7, -1, 0], [false, false, false, false, false, true, false, false, false, false, false, true]], \"expected\": [[0, 1, 7, -7, -1, 0, 0, 1, 7, -7, -1, 0], [false, false, false, false, false, true, false, false, false, false, false, true]], \"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."}}