{"abstract":"A residual parity sideband is derived from midpoint amplitude.","category":"PCM sample encoding","checks":8,"contract":"Encode stereo integer PCM through reversible floor lifting: side=L-R, mid=R+floor(side/2), with an explicit odd-side parity sideband.","evaluation_group":"s3-pcm-pcm-mid-side-lifting","failed_approach":"Left parity alone cannot indicate odd stereo differences.","family":"s3-pcm-pcm-mid-side-lifting-parity-source","id":"FA-49281","implementations":{"attempt":{"sha256":"539871179f2b22152e772372d3b7ff22b1aa518f4d7d7605613358d019bc7089","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(pairs):\n    out=[]\n    for left,right in pairs:\n        side=left-right\n        half=side//2\n        mid=right+half\n        parity=left&1\n        out.append([mid,side,parity])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[5, 2], [2, 5]],)), [[3, 3, 1], [3, -3, 1]])\ncheck('oracle 2', solve(*([[0, 0], [1, 1]],)), [[0, 0, 0], [1, 0, 0]])\ncheck('oracle 3', solve(*([[-3, 2], [4, -1]],)), [[-1, -5, 1], [1, 5, 1]])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([[1, 0], [0, 1]],)), [[0, 1, 1], [0, -1, 1]])\ncheck('oracle 6', solve(*([[7, 7], [-7, -7]],)), [[7, 0, 0], [-7, 0, 0]])\ncheck('oracle 7', solve(*([[3, 1], [-3, -1]],)), [[2, 2, 0], [-2, -2, 0]])\nif N == 1: check('variant packet 1', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 2: check('variant packet 2', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 3: check('variant packet 3', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 4: check('variant packet 4', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 5: check('variant packet 5', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\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":"7ffc323d75a8fe0c87b3a4159faa26f97d6c2acb6bb02443c6bd27d0c818ea58","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(pairs):\n    out=[]\n    for left,right in pairs:\n        side=left-right\n        half=side//2\n        mid=right+half\n        parity=mid&1\n        out.append([mid,side,parity])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[5, 2], [2, 5]],)), [[3, 3, 1], [3, -3, 1]])\ncheck('oracle 2', solve(*([[0, 0], [1, 1]],)), [[0, 0, 0], [1, 0, 0]])\ncheck('oracle 3', solve(*([[-3, 2], [4, -1]],)), [[-1, -5, 1], [1, 5, 1]])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([[1, 0], [0, 1]],)), [[0, 1, 1], [0, -1, 1]])\ncheck('oracle 6', solve(*([[7, 7], [-7, -7]],)), [[7, 0, 0], [-7, 0, 0]])\ncheck('oracle 7', solve(*([[3, 1], [-3, -1]],)), [[2, 2, 0], [-2, -2, 0]])\nif N == 1: check('variant packet 1', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 2: check('variant packet 2', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 3: check('variant packet 3', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 4: check('variant packet 4', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 5: check('variant packet 5', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\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":"79123109381cb1475989bf579dedc52eb22a62f4a4a76e3ca0d1b674ae109999","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(pairs):\n    out=[]\n    for left,right in pairs:\n        side=left-right\n        half=side//2\n        mid=right+half\n        parity=side&1\n        out.append([mid,side,parity])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[5, 2], [2, 5]],)), [[3, 3, 1], [3, -3, 1]])\ncheck('oracle 2', solve(*([[0, 0], [1, 1]],)), [[0, 0, 0], [1, 0, 0]])\ncheck('oracle 3', solve(*([[-3, 2], [4, -1]],)), [[-1, -5, 1], [1, 5, 1]])\ncheck('oracle 4', solve(*([],)), [])\ncheck('oracle 5', solve(*([[1, 0], [0, 1]],)), [[0, 1, 1], [0, -1, 1]])\ncheck('oracle 6', solve(*([[7, 7], [-7, -7]],)), [[7, 0, 0], [-7, 0, 0]])\ncheck('oracle 7', solve(*([[3, 1], [-3, -1]],)), [[2, 2, 0], [-2, -2, 0]])\nif N == 1: check('variant packet 1', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 2: check('variant packet 2', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 3: check('variant packet 3', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 4: check('variant packet 4', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\nif N == 5: check('variant packet 5', solve(*[[[5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5], [5, 2], [2, 5]]]), [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]])\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-mid-side-lifting-parity-source","generated_at":"2026-09-29T14:44:58.591113+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 parity source.","root_cause":"A residual parity sideband is derived from midpoint amplitude.","sha256":"24c6332a953799b94b33ed9084dcaf833c9be919efb1aaf7bc3e36936d69133b","title":"Pcm mid side lifting: parity source · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.637,"exit_code":1,"observations":[{"actual":[[3,3,1],[3,-3,0]],"check":"oracle 1","expected":[[3,3,1],[3,-3,1]],"passed":false},{"actual":[[0,0,0],[1,0,1]],"check":"oracle 2","expected":[[0,0,0],[1,0,0]],"passed":false},{"actual":[[-1,-5,1],[1,5,0]],"check":"oracle 3","expected":[[-1,-5,1],[1,5,1]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[0,1,1],[0,-1,0]],"check":"oracle 5","expected":[[0,1,1],[0,-1,1]],"passed":false},{"actual":[[7,0,1],[-7,0,1]],"check":"oracle 6","expected":[[7,0,0],[-7,0,0]],"passed":false},{"actual":[[2,2,1],[-2,-2,1]],"check":"oracle 7","expected":[[2,2,0],[-2,-2,0]],"passed":false},{"actual":[[3,3,1],[3,-3,0],[3,3,1],[3,-3,0]],"check":"variant packet 1","expected":[[3,3,1],[3,-3,1],[3,3,1],[3,-3,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 3, 1], [3, -3, 0]], \"expected\": [[3, 3, 1], [3, -3, 1]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[0, 0, 0], [1, 0, 1]], \"expected\": [[0, 0, 0], [1, 0, 0]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[-1, -5, 1], [1, 5, 0]], \"expected\": [[-1, -5, 1], [1, 5, 1]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 1, 1], [0, -1, 0]], \"expected\": [[0, 1, 1], [0, -1, 1]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[7, 0, 1], [-7, 0, 1]], \"expected\": [[7, 0, 0], [-7, 0, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[2, 2, 1], [-2, -2, 1]], \"expected\": [[2, 2, 0], [-2, -2, 0]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[3, 3, 1], [3, -3, 0], [3, 3, 1], [3, -3, 0]], \"expected\": [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.431,"exit_code":1,"observations":[{"actual":[[3,3,1],[3,-3,1]],"check":"oracle 1","expected":[[3,3,1],[3,-3,1]],"passed":true},{"actual":[[0,0,0],[1,0,1]],"check":"oracle 2","expected":[[0,0,0],[1,0,0]],"passed":false},{"actual":[[-1,-5,1],[1,5,1]],"check":"oracle 3","expected":[[-1,-5,1],[1,5,1]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[0,1,0],[0,-1,0]],"check":"oracle 5","expected":[[0,1,1],[0,-1,1]],"passed":false},{"actual":[[7,0,1],[-7,0,1]],"check":"oracle 6","expected":[[7,0,0],[-7,0,0]],"passed":false},{"actual":[[2,2,0],[-2,-2,0]],"check":"oracle 7","expected":[[2,2,0],[-2,-2,0]],"passed":true},{"actual":[[3,3,1],[3,-3,1],[3,3,1],[3,-3,1]],"check":"variant packet 1","expected":[[3,3,1],[3,-3,1],[3,3,1],[3,-3,1]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 3, 1], [3, -3, 1]], \"expected\": [[3, 3, 1], [3, -3, 1]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[0, 0, 0], [1, 0, 1]], \"expected\": [[0, 0, 0], [1, 0, 0]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[-1, -5, 1], [1, 5, 1]], \"expected\": [[-1, -5, 1], [1, 5, 1]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 1, 0], [0, -1, 0]], \"expected\": [[0, 1, 1], [0, -1, 1]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[7, 0, 1], [-7, 0, 1]], \"expected\": [[7, 0, 0], [-7, 0, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[2, 2, 0], [-2, -2, 0]], \"expected\": [[2, 2, 0], [-2, -2, 0]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]], \"expected\": [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.74,"exit_code":0,"observations":[{"actual":[[3,3,1],[3,-3,1]],"check":"oracle 1","expected":[[3,3,1],[3,-3,1]],"passed":true},{"actual":[[0,0,0],[1,0,0]],"check":"oracle 2","expected":[[0,0,0],[1,0,0]],"passed":true},{"actual":[[-1,-5,1],[1,5,1]],"check":"oracle 3","expected":[[-1,-5,1],[1,5,1]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[0,1,1],[0,-1,1]],"check":"oracle 5","expected":[[0,1,1],[0,-1,1]],"passed":true},{"actual":[[7,0,0],[-7,0,0]],"check":"oracle 6","expected":[[7,0,0],[-7,0,0]],"passed":true},{"actual":[[2,2,0],[-2,-2,0]],"check":"oracle 7","expected":[[2,2,0],[-2,-2,0]],"passed":true},{"actual":[[3,3,1],[3,-3,1],[3,3,1],[3,-3,1]],"check":"variant packet 1","expected":[[3,3,1],[3,-3,1],[3,3,1],[3,-3,1]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[3, 3, 1], [3, -3, 1]], \"expected\": [[3, 3, 1], [3, -3, 1]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[0, 0, 0], [1, 0, 0]], \"expected\": [[0, 0, 0], [1, 0, 0]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[-1, -5, 1], [1, 5, 1]], \"expected\": [[-1, -5, 1], [1, 5, 1]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[0, 1, 1], [0, -1, 1]], \"expected\": [[0, 1, 1], [0, -1, 1]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[7, 0, 0], [-7, 0, 0]], \"expected\": [[7, 0, 0], [-7, 0, 0]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[2, 2, 0], [-2, -2, 0]], \"expected\": [[2, 2, 0], [-2, -2, 0]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]], \"expected\": [[3, 3, 1], [3, -3, 1], [3, 3, 1], [3, -3, 1]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}