{"abstract":"The ambiguous half-cycle packet is accepted as a forward gap.","category":"PCM sample encoding","checks":8,"contract":"Bounded PCM packet sequence adapter with one null marker per lost packet (not per lost sample); reject old or half-cycle-ambiguous packets and retain modular cursor.","evaluation_group":"s3-pcm-pcm-frame-sequence","failed_approach":"Accepting all nonzero distances replays old packets after huge gaps.","family":"s3-pcm-pcm-frame-sequence-gap-threshold","id":"FA-49171","implementations":{"attempt":{"sha256":"1fc22e649fc3fccfc4fca0494b607e712c7bbdecd16195bb74da6fd325881ebe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(packets, start, modulus):\n    expected=start\n    out=[]\n    for sequence,samples in packets:\n        delta=(sequence-expected)%modulus\n        if delta==0:\n            out.extend(samples)\n            expected=(expected+1)%modulus\n        elif delta<modulus:\n            out.extend([None]*delta)\n            out.extend(samples)\n            expected=(sequence+1)%modulus\n    return [out,expected]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[7, [4]], [0, [5]], [1, [6]]], 7, 8)), [[4, 5, 6], 2])\ncheck('oracle 2', solve(*([[0, [1]], [2, [3]], [3, [4]]], 0, 8)), [[1, None, 3, 4], 4])\ncheck('oracle 3', solve(*([[4, [9]], [0, [2]]], 0, 8)), [[2], 1])\ncheck('oracle 4', solve(*([[7, [9]], [0, [1]]], 0, 8)), [[1], 1])\ncheck('oracle 5', solve(*([], 3, 8)), [[], 3])\ncheck('oracle 6', solve(*([[6, [1]], [1, [2]]], 6, 8)), [[1, None, None, 2], 2])\ncheck('oracle 7', solve(*([[0, [1, 2]], [0, [3]], [1, [4]]], 0, 8)), [[1, 2, 4], 2])\nif N == 1: check('variant packet 1', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 2: check('variant packet 2', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 3: check('variant packet 3', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 4: check('variant packet 4', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 5: check('variant packet 5', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\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":"19068f924cbd0c773fb52dabfabfbb0961ec09289fd9103261ecccd2524aa94d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(packets, start, modulus):\n    expected=start\n    out=[]\n    for sequence,samples in packets:\n        delta=(sequence-expected)%modulus\n        if delta==0:\n            out.extend(samples)\n            expected=(expected+1)%modulus\n        elif delta<=modulus//2:\n            out.extend([None]*delta)\n            out.extend(samples)\n            expected=(sequence+1)%modulus\n    return [out,expected]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[7, [4]], [0, [5]], [1, [6]]], 7, 8)), [[4, 5, 6], 2])\ncheck('oracle 2', solve(*([[0, [1]], [2, [3]], [3, [4]]], 0, 8)), [[1, None, 3, 4], 4])\ncheck('oracle 3', solve(*([[4, [9]], [0, [2]]], 0, 8)), [[2], 1])\ncheck('oracle 4', solve(*([[7, [9]], [0, [1]]], 0, 8)), [[1], 1])\ncheck('oracle 5', solve(*([], 3, 8)), [[], 3])\ncheck('oracle 6', solve(*([[6, [1]], [1, [2]]], 6, 8)), [[1, None, None, 2], 2])\ncheck('oracle 7', solve(*([[0, [1, 2]], [0, [3]], [1, [4]]], 0, 8)), [[1, 2, 4], 2])\nif N == 1: check('variant packet 1', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 2: check('variant packet 2', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 3: check('variant packet 3', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 4: check('variant packet 4', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 5: check('variant packet 5', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\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":"77f56d5c81666a70a87e514b0dbd130c5bbb4cd6d07d3d0c13f6f21f55c36222","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(packets, start, modulus):\n    expected=start\n    out=[]\n    for sequence,samples in packets:\n        delta=(sequence-expected)%modulus\n        if delta==0:\n            out.extend(samples)\n            expected=(expected+1)%modulus\n        elif delta<modulus//2:\n            out.extend([None]*delta)\n            out.extend(samples)\n            expected=(sequence+1)%modulus\n    return [out,expected]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[7, [4]], [0, [5]], [1, [6]]], 7, 8)), [[4, 5, 6], 2])\ncheck('oracle 2', solve(*([[0, [1]], [2, [3]], [3, [4]]], 0, 8)), [[1, None, 3, 4], 4])\ncheck('oracle 3', solve(*([[4, [9]], [0, [2]]], 0, 8)), [[2], 1])\ncheck('oracle 4', solve(*([[7, [9]], [0, [1]]], 0, 8)), [[1], 1])\ncheck('oracle 5', solve(*([], 3, 8)), [[], 3])\ncheck('oracle 6', solve(*([[6, [1]], [1, [2]]], 6, 8)), [[1, None, None, 2], 2])\ncheck('oracle 7', solve(*([[0, [1, 2]], [0, [3]], [1, [4]]], 0, 8)), [[1, 2, 4], 2])\nif N == 1: check('variant packet 1', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 2: check('variant packet 2', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 3: check('variant packet 3', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 4: check('variant packet 4', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\nif N == 5: check('variant packet 5', solve(*[[[7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]], [7, [4]], [0, [5]], [1, [6]]], 7, 8]), [[4, 5, 6], 2])\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-frame-sequence-gap-threshold","generated_at":"2026-09-29T14:44:57.544018+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 gap threshold.","root_cause":"The ambiguous half-cycle packet is accepted as a forward gap.","sha256":"bed64c91c3ef84b0ff15d48eff6ad964913fa9a7e8b20571569626ff70b94be6","title":"Pcm frame sequence: gap threshold · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.861,"exit_code":1,"observations":[{"actual":[[4,5,6],2],"check":"oracle 1","expected":[[4,5,6],2],"passed":true},{"actual":[[1,null,3,4],4],"check":"oracle 2","expected":[[1,null,3,4],4],"passed":true},{"actual":[[null,null,null,null,9,null,null,null,2],1],"check":"oracle 3","expected":[[2],1],"passed":false},{"actual":[[null,null,null,null,null,null,null,9,1],1],"check":"oracle 4","expected":[[1],1],"passed":false},{"actual":[[],3],"check":"oracle 5","expected":[[],3],"passed":true},{"actual":[[1,null,null,2],2],"check":"oracle 6","expected":[[1,null,null,2],2],"passed":true},{"actual":[[1,2,null,null,null,null,null,null,null,3,4],2],"check":"oracle 7","expected":[[1,2,4],2],"passed":false},{"actual":[[4,5,6,null,null,null,null,null,4,5,6],2],"check":"variant packet 1","expected":[[4,5,6],2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[4, 5, 6], 2], \"expected\": [[4, 5, 6], 2], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[1, null, 3, 4], 4], \"expected\": [[1, null, 3, 4], 4], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[null, null, null, null, 9, null, null, null, 2], 1], \"expected\": [[2], 1], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[null, null, null, null, null, null, null, 9, 1], 1], \"expected\": [[1], 1], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [[], 3], \"expected\": [[], 3], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[1, null, null, 2], 2], \"expected\": [[1, null, null, 2], 2], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, 2, null, null, null, null, null, null, null, 3, 4], 2], \"expected\": [[1, 2, 4], 2], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[4, 5, 6, null, null, null, null, null, 4, 5, 6], 2], \"expected\": [[4, 5, 6], 2], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.504,"exit_code":1,"observations":[{"actual":[[4,5,6],2],"check":"oracle 1","expected":[[4,5,6],2],"passed":true},{"actual":[[1,null,3,4],4],"check":"oracle 2","expected":[[1,null,3,4],4],"passed":true},{"actual":[[null,null,null,null,9,null,null,null,2],1],"check":"oracle 3","expected":[[2],1],"passed":false},{"actual":[[1],1],"check":"oracle 4","expected":[[1],1],"passed":true},{"actual":[[],3],"check":"oracle 5","expected":[[],3],"passed":true},{"actual":[[1,null,null,2],2],"check":"oracle 6","expected":[[1,null,null,2],2],"passed":true},{"actual":[[1,2,4],2],"check":"oracle 7","expected":[[1,2,4],2],"passed":true},{"actual":[[4,5,6],2],"check":"variant packet 1","expected":[[4,5,6],2],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[4, 5, 6], 2], \"expected\": [[4, 5, 6], 2], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[1, null, 3, 4], 4], \"expected\": [[1, null, 3, 4], 4], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[null, null, null, null, 9, null, null, null, 2], 1], \"expected\": [[2], 1], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [[1], 1], \"expected\": [[1], 1], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[], 3], \"expected\": [[], 3], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[1, null, null, 2], 2], \"expected\": [[1, null, null, 2], 2], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, 2, 4], 2], \"expected\": [[1, 2, 4], 2], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[4, 5, 6], 2], \"expected\": [[4, 5, 6], 2], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.944,"exit_code":0,"observations":[{"actual":[[4,5,6],2],"check":"oracle 1","expected":[[4,5,6],2],"passed":true},{"actual":[[1,null,3,4],4],"check":"oracle 2","expected":[[1,null,3,4],4],"passed":true},{"actual":[[2],1],"check":"oracle 3","expected":[[2],1],"passed":true},{"actual":[[1],1],"check":"oracle 4","expected":[[1],1],"passed":true},{"actual":[[],3],"check":"oracle 5","expected":[[],3],"passed":true},{"actual":[[1,null,null,2],2],"check":"oracle 6","expected":[[1,null,null,2],2],"passed":true},{"actual":[[1,2,4],2],"check":"oracle 7","expected":[[1,2,4],2],"passed":true},{"actual":[[4,5,6],2],"check":"variant packet 1","expected":[[4,5,6],2],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[4, 5, 6], 2], \"expected\": [[4, 5, 6], 2], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[1, null, 3, 4], 4], \"expected\": [[1, null, 3, 4], 4], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[2], 1], \"expected\": [[2], 1], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[1], 1], \"expected\": [[1], 1], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[], 3], \"expected\": [[], 3], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[1, null, null, 2], 2], \"expected\": [[1, null, null, 2], 2], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, 2, 4], 2], \"expected\": [[1, 2, 4], 2], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[4, 5, 6], 2], \"expected\": [[4, 5, 6], 2], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}