{"abstract":"The literal anchor is also encoded as a residual, adding a 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.","contract_signature":"frames","evaluation_group":"s3-pcm-pcm-channel-lifting-chain","failed_approach":"Starting at the third channel loses the second channel amplitude.","family":"s3-pcm-pcm-channel-lifting-chain-first-residual-channel","id":"FA-50306","implementations":{"attempt":{"sha256":"353cdc858756a5604a7be3b77395dc57a01b373f4c3635142957ac4269822e16","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[2:]:\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":"0bdb506018d49f8a2ea301bd9f61ab2653c64b6c905522d692650c2a271fa540","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:\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-first-residual-channel","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.","root_cause":"The literal anchor is also encoded as a residual, adding a channel.","sha256":"6f6adbb2846ec0dcf3c388ff06dc7c9e44bb3a006822c276a25743298925e983","title":"Pcm channel lifting chain: first residual channel · 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":38.297,"exit_code":1,"observations":[{"actual":[[3,5],[1,3]],"check":"oracle 1","expected":[[3,2,3],[1,1,2]],"passed":false},{"actual":[[7]],"check":"oracle 2","expected":[[7]],"passed":true},{"actual":[[]],"check":"oracle 3","expected":[[]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-2,1,5]],"check":"oracle 5","expected":[[-2,5,-4,5]],"passed":false},{"actual":[[0,0],[4,0]],"check":"oracle 6","expected":[[0,0,0],[4,0,0]],"passed":false},{"actual":[[1,1,4]],"check":"oracle 7","expected":[[1,2,-1,4]],"passed":false},{"actual":[[3,5],[1,3],[3,5],[1,3]],"check":"variant packet 1","expected":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 5], [1, 3]], \"expected\": [[3, 2, 3], [1, 1, 2]], \"passed\": false}, {\"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, 1, 5]], \"expected\": [[-2, 5, -4, 5]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, 0], [4, 0]], \"expected\": [[0, 0, 0], [4, 0, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[1, 1, 4]], \"expected\": [[1, 2, -1, 4]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[3, 5], [1, 3], [3, 5], [1, 3]], \"expected\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.543,"exit_code":1,"observations":[{"actual":[[3,0,2,3],[1,0,1,2]],"check":"oracle 1","expected":[[3,2,3],[1,1,2]],"passed":false},{"actual":[[7,0]],"check":"oracle 2","expected":[[7]],"passed":false},{"actual":[[]],"check":"oracle 3","expected":[[]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[-2,0,5,-4,5]],"check":"oracle 5","expected":[[-2,5,-4,5]],"passed":false},{"actual":[[0,0,0,0],[4,0,0,0]],"check":"oracle 6","expected":[[0,0,0],[4,0,0]],"passed":false},{"actual":[[1,0,2,-1,4]],"check":"oracle 7","expected":[[1,2,-1,4]],"passed":false},{"actual":[[3,0,2,3],[1,0,1,2],[3,0,2,3],[1,0,1,2]],"check":"variant packet 1","expected":[[3,2,3],[1,1,2],[3,2,3],[1,1,2]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 0, 2, 3], [1, 0, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[7, 0]], \"expected\": [[7]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[]], \"expected\": [[]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-2, 0, 5, -4, 5]], \"expected\": [[-2, 5, -4, 5]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[0, 0, 0, 0], [4, 0, 0, 0]], \"expected\": [[0, 0, 0], [4, 0, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[1, 0, 2, -1, 4]], \"expected\": [[1, 2, -1, 4]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[3, 0, 2, 3], [1, 0, 1, 2], [3, 0, 2, 3], [1, 0, 1, 2]], \"expected\": [[3, 2, 3], [1, 1, 2], [3, 2, 3], [1, 1, 2]], \"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."}}