{"abstract":"An empty channel frame invents a silence channel.","category":"PCM sample encoding","checks":8,"contract":"Losslessly represent each PCM frame as a first-channel anchor followed by differences from immediately preceding original channels; preserve empty and mono frames.","evaluation_group":"s3-pcm-pcm-channel-lifting-chain","failed_approach":"An empty valid frame is conflated with a failed decode.","family":"s3-pcm-pcm-channel-lifting-chain-empty-channel-frame","id":"FA-50311","implementations":{"attempt":{"sha256":"496a7482eceb24bcd394f2d24f40a6c47b3034ee2220e9bb1fa75a7674b5cfda","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(frames):\n    out=[]\n    for frame in frames:\n        if not frame:\n            out.append(None)\n            continue\n        transformed=[frame[0]]\n        previous=frame[0]\n        for sample in frame[1:]:\n            transformed.append(sample-previous)\n            previous=sample\n        out.append(transformed)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[3, 5, 8], [1, 2, 4]],)), [[3, 2, 3], [1, 1, 2]])\ncheck('oracle 2', solve(*([[7]],)), [[7]])\ncheck('oracle 3', solve(*([[]],)), [[]])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([[-2, 3, -1, 4]],)), [[-2, 5, -4, 5]])\ncheck('oracle 6', solve(*([[0, 0, 0], [4, 4, 4]],)), [[0, 0, 0], [4, 0, 0]])\ncheck('oracle 7', solve(*([[1, 3, 2, 6]],)), [[1, 2, -1, 4]])\nif N == 1: check('variant packet 1', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 2: check('variant packet 2', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 3: check('variant packet 3', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 4: check('variant packet 4', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 5: check('variant packet 5', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 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":"bc1a80eeba4b465358c07bb02f76e7375e1c618257cd18c986b8940868a1ec32","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(frames):\n    out=[]\n    for frame in frames:\n        if not frame:\n            out.append([0])\n            continue\n        transformed=[frame[0]]\n        previous=frame[0]\n        for sample in frame[1:]:\n            transformed.append(sample-previous)\n            previous=sample\n        out.append(transformed)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[3, 5, 8], [1, 2, 4]],)), [[3, 2, 3], [1, 1, 2]])\ncheck('oracle 2', solve(*([[7]],)), [[7]])\ncheck('oracle 3', solve(*([[]],)), [[]])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([[-2, 3, -1, 4]],)), [[-2, 5, -4, 5]])\ncheck('oracle 6', solve(*([[0, 0, 0], [4, 4, 4]],)), [[0, 0, 0], [4, 0, 0]])\ncheck('oracle 7', solve(*([[1, 3, 2, 6]],)), [[1, 2, -1, 4]])\nif N == 1: check('variant packet 1', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 2: check('variant packet 2', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 3: check('variant packet 3', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 4: check('variant packet 4', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 5: check('variant packet 5', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 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":"26fd14af573ca2a19bba5ac989e4bf14157d913c7eb51f640848db2afe1de033","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(frames):\n    out=[]\n    for frame in frames:\n        if not frame:\n            out.append([])\n            continue\n        transformed=[frame[0]]\n        previous=frame[0]\n        for sample in frame[1:]:\n            transformed.append(sample-previous)\n            previous=sample\n        out.append(transformed)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[3, 5, 8], [1, 2, 4]],)), [[3, 2, 3], [1, 1, 2]])\ncheck('oracle 2', solve(*([[7]],)), [[7]])\ncheck('oracle 3', solve(*([[]],)), [[]])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([[-2, 3, -1, 4]],)), [[-2, 5, -4, 5]])\ncheck('oracle 6', solve(*([[0, 0, 0], [4, 4, 4]],)), [[0, 0, 0], [4, 0, 0]])\ncheck('oracle 7', solve(*([[1, 3, 2, 6]],)), [[1, 2, -1, 4]])\nif N == 1: check('variant packet 1', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 2: check('variant packet 2', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 3: check('variant packet 3', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 4: check('variant packet 4', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]])\nif N == 5: check('variant packet 5', solve(*[[[3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4], [3, 5, 8], [1, 2, 4]]]), [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 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-channel-lifting-chain-empty-channel-frame","generated_at":"2026-09-29T14:45:07.952167+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 empty channel frame.","root_cause":"An empty channel frame invents a silence channel.","sha256":"c09f82a3615d3091bee6f94cf1fa1528a2c31ee2d97cda55f10184213ecc4b26","title":"Pcm channel lifting chain: empty channel frame · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.41,"exit_code":1,"observations":[{"actual":[[3,2,3],[1,1,2]],"check":"oracle 1","expected":[[3,2,3],[1,1,2]],"passed":true},{"actual":[[7]],"check":"oracle 2","expected":[[7]],"passed":true},{"actual":[null],"check":"oracle 3","expected":[[]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-2,5,-4,5]],"check":"oracle 5","expected":[[-2,5,-4,5]],"passed":true},{"actual":[[0,0,0],[4,0,0]],"check":"oracle 6","expected":[[0,0,0],[4,0,0]],"passed":true},{"actual":[[1,2,-1,4]],"check":"oracle 7","expected":[[1,2,-1,4]],"passed":true},{"actual":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"check":"variant packet 1","expected":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 2, 3], [1, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[7]], \"expected\": [[7]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [null], \"expected\": [[]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-2, 5, -4, 5]], \"expected\": [[-2, 5, -4, 5]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0, 0, 0], [4, 0, 0]], \"expected\": [[0, 0, 0], [4, 0, 0]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, 2, -1, 4]], \"expected\": [[1, 2, -1, 4]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.326,"exit_code":1,"observations":[{"actual":[[3,2,3],[1,1,2]],"check":"oracle 1","expected":[[3,2,3],[1,1,2]],"passed":true},{"actual":[[7]],"check":"oracle 2","expected":[[7]],"passed":true},{"actual":[[0]],"check":"oracle 3","expected":[[]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-2,5,-4,5]],"check":"oracle 5","expected":[[-2,5,-4,5]],"passed":true},{"actual":[[0,0,0],[4,0,0]],"check":"oracle 6","expected":[[0,0,0],[4,0,0]],"passed":true},{"actual":[[1,2,-1,4]],"check":"oracle 7","expected":[[1,2,-1,4]],"passed":true},{"actual":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"check":"variant packet 1","expected":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 2, 3], [1, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[7]], \"expected\": [[7]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[0]], \"expected\": [[]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-2, 5, -4, 5]], \"expected\": [[-2, 5, -4, 5]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0, 0, 0], [4, 0, 0]], \"expected\": [[0, 0, 0], [4, 0, 0]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, 2, -1, 4]], \"expected\": [[1, 2, -1, 4]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.149,"exit_code":0,"observations":[{"actual":[[3,2,3],[1,1,2]],"check":"oracle 1","expected":[[3,2,3],[1,1,2]],"passed":true},{"actual":[[7]],"check":"oracle 2","expected":[[7]],"passed":true},{"actual":[[]],"check":"oracle 3","expected":[[]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-2,5,-4,5]],"check":"oracle 5","expected":[[-2,5,-4,5]],"passed":true},{"actual":[[0,0,0],[4,0,0]],"check":"oracle 6","expected":[[0,0,0],[4,0,0]],"passed":true},{"actual":[[1,2,-1,4]],"check":"oracle 7","expected":[[1,2,-1,4]],"passed":true},{"actual":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"check":"variant packet 1","expected":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 2, 3], [1, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[7]], \"expected\": [[7]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[]], \"expected\": [[]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-2, 5, -4, 5]], \"expected\": [[-2, 5, -4, 5]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0, 0, 0], [4, 0, 0]], \"expected\": [[0, 0, 0], [4, 0, 0]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[1, 2, -1, 4]], \"expected\": [[1, 2, -1, 4]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}