{"abstract":"An exact pulse threshold is delayed by one sample.","category":"PCM sample encoding","checks":8,"contract":"Convert bounded nonnegative PCM levels no greater than denominator into a deterministic one-bit pulse-density stream, preserving fractional accumulator state.","contract_signature":"samples, denominator, accumulator","evaluation_group":"s3-pcm-pcm-onebit-pulse-density","failed_approach":"Thresholding only the current level ignores density accumulation.","family":"s3-pcm-pcm-onebit-pulse-density-threshold-inclusive","id":"FA-49696","implementations":{"attempt":{"sha256":"084ff08c9f2118a9df4590a02132c3af210fc22aebb75f6fed6c79739e146e38","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, denominator, accumulator):\n    bits=[]\n    for sample in samples:\n        accumulator+=sample\n        pulse=sample>=denominator\n        if pulse:\n            accumulator-=denominator\n        bits.append(int(pulse))\n    return [bits,accumulator]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])\ncheck('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])\ncheck('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])\ncheck('oracle 4', solve(*([], 5, 2)), [[], 2])\ncheck('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])\ncheck('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])\ncheck('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\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":"235bb0211424cb2459c5953e3030cee8eda7e8850e48836d52588fe52184a44b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, denominator, accumulator):\n    bits=[]\n    for sample in samples:\n        accumulator+=sample\n        pulse=accumulator>denominator\n        if pulse:\n            accumulator-=denominator\n        bits.append(int(pulse))\n    return [bits,accumulator]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 2, 3, 4], 5, 0)), [[0, 0, 1, 1], 0])\ncheck('oracle 2', solve(*([5, 0, 5], 5, 0)), [[1, 0, 1], 0])\ncheck('oracle 3', solve(*([2, 2, 2, 2], 3, 1)), [[1, 0, 1, 1], 0])\ncheck('oracle 4', solve(*([], 5, 2)), [[], 2])\ncheck('oracle 5', solve(*([0, 0], 4, 3)), [[0, 0], 3])\ncheck('oracle 6', solve(*([3, 3, 3], 4, 2)), [[1, 1, 0], 3])\ncheck('oracle 7', solve(*([1, 1, 1], 2, 0)), [[0, 1, 0], 1])\nif N == 1: check('variant packet 1', solve(*[[1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 2: check('variant packet 2', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 3: check('variant packet 3', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 4: check('variant packet 4', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\nif N == 5: check('variant packet 5', solve(*[[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4], 5, 0]), [[0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1], 0])\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-onebit-pulse-density-threshold-inclusive","generated_at":"2026-09-29T14:45:02.435115+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":"An exact pulse threshold is delayed by one sample.","sha256":"5880308397e0a7f09556d8158242e2264ad5a1ffdfd79671a4c83888da812504","title":"Pcm onebit pulse density: threshold inclusive · 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":39.308,"exit_code":1,"observations":[{"actual":[[0,0,0,0],10],"check":"oracle 1","expected":[[0,0,1,1],0],"passed":false},{"actual":[[1,0,1],0],"check":"oracle 2","expected":[[1,0,1],0],"passed":true},{"actual":[[0,0,0,0],9],"check":"oracle 3","expected":[[1,0,1,1],0],"passed":false},{"actual":[[],2],"check":"oracle 4","expected":[[],2],"passed":true},{"actual":[[0,0],3],"check":"oracle 5","expected":[[0,0],3],"passed":true},{"actual":[[0,0,0],11],"check":"oracle 6","expected":[[1,1,0],3],"passed":false},{"actual":[[0,0,0],3],"check":"oracle 7","expected":[[0,1,0],1],"passed":false},{"actual":[[0,0,0,0,0,0,0,0],20],"check":"variant packet 1","expected":[[0,0,1,1,0,0,1,1],0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0, 0, 0], 10], \"expected\": [[0, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[1, 0, 1], 0], \"expected\": [[1, 0, 1], 0], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[0, 0, 0, 0], 9], \"expected\": [[1, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], 2], \"expected\": [[], 2], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 0], 3], \"expected\": [[0, 0], 3], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0, 0, 0], 11], \"expected\": [[1, 1, 0], 3], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[0, 0, 0], 3], \"expected\": [[0, 1, 0], 1], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0, 0, 0, 0, 0, 0, 0], 20], \"expected\": [[0, 0, 1, 1, 0, 0, 1, 1], 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":36.448,"exit_code":1,"observations":[{"actual":[[0,0,1,0],5],"check":"oracle 1","expected":[[0,0,1,1],0],"passed":false},{"actual":[[0,0,1],5],"check":"oracle 2","expected":[[1,0,1],0],"passed":false},{"actual":[[0,1,1,0],3],"check":"oracle 3","expected":[[1,0,1,1],0],"passed":false},{"actual":[[],2],"check":"oracle 4","expected":[[],2],"passed":true},{"actual":[[0,0],3],"check":"oracle 5","expected":[[0,0],3],"passed":true},{"actual":[[1,0,1],3],"check":"oracle 6","expected":[[1,1,0],3],"passed":false},{"actual":[[0,0,1],1],"check":"oracle 7","expected":[[0,1,0],1],"passed":false},{"actual":[[0,0,1,0,1,0,1,0],5],"check":"variant packet 1","expected":[[0,0,1,1,0,0,1,1],0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[0, 0, 1, 0], 5], \"expected\": [[0, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[0, 0, 1], 5], \"expected\": [[1, 0, 1], 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[0, 1, 1, 0], 3], \"expected\": [[1, 0, 1, 1], 0], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[], 2], \"expected\": [[], 2], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 0], 3], \"expected\": [[0, 0], 3], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[1, 0, 1], 3], \"expected\": [[1, 1, 0], 3], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[0, 0, 1], 1], \"expected\": [[0, 1, 0], 1], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[0, 0, 1, 0, 1, 0, 1, 0], 5], \"expected\": [[0, 0, 1, 1, 0, 0, 1, 1], 0], \"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."}}