{"abstract":"Two supplied uniform draws are added rather than differenced for centered dither.","category":"PCM sample encoding","checks":8,"contract":"Construct a bounded deterministic highpass triangular PCM dither sequence from paired supplied draws; return raw-noise delay for packet continuation.","evaluation_group":"s3-pcm-pcm-triangular-dither","failed_approach":"Reusing the same draw cancels all dither.","family":"s3-pcm-pcm-triangular-dither-independent-difference","id":"FA-49641","implementations":{"attempt":{"sha256":"fee78a3126f6d04ea71b66b33e5189cd1ece1cccce1d5a74d55d2dc15a0c65ea","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(pairs, amplitude, previous):\n    out=[]\n    for a,b in pairs:\n        difference=a-a\n        noise=difference*amplitude\n        shaped=noise-previous\n        previous=noise\n        out.append(shaped)\n    return [out,previous]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[1, 3], [4, 0], [2, 2]], 2, 1)), [[-5, 12, -8], 0])\ncheck('oracle 2', solve(*([[0, 0], [1, 0]], 1, -2)), [[2, 1], 1])\ncheck('oracle 3', solve(*([], 3, 4)), [[], 4])\ncheck('oracle 4', solve(*([[4, 1], [1, 4]], 3, 0)), [[9, -18], -9])\ncheck('oracle 5', solve(*([[1, 2], [2, 1], [0, 0]], 0, 3)), [[-3, 0, 0], 0])\ncheck('oracle 6', solve(*([[3, 3]], 2, 0)), [[0], 0])\ncheck('oracle 7', solve(*([[0, 2], [2, 0], [1, 1]], 4, -4)), [[-4, 16, -8], 0])\nif N == 1: check('variant packet 1', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8], 0])\nif N == 2: check('variant packet 2', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 3: check('variant packet 3', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 4: check('variant packet 4', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 5: check('variant packet 5', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 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":"828f944a1f4b9ed76b871dc884b9be2b6998a3fb877e9a2b74ab9212669eaad4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(pairs, amplitude, previous):\n    out=[]\n    for a,b in pairs:\n        difference=a+b\n        noise=difference*amplitude\n        shaped=noise-previous\n        previous=noise\n        out.append(shaped)\n    return [out,previous]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[1, 3], [4, 0], [2, 2]], 2, 1)), [[-5, 12, -8], 0])\ncheck('oracle 2', solve(*([[0, 0], [1, 0]], 1, -2)), [[2, 1], 1])\ncheck('oracle 3', solve(*([], 3, 4)), [[], 4])\ncheck('oracle 4', solve(*([[4, 1], [1, 4]], 3, 0)), [[9, -18], -9])\ncheck('oracle 5', solve(*([[1, 2], [2, 1], [0, 0]], 0, 3)), [[-3, 0, 0], 0])\ncheck('oracle 6', solve(*([[3, 3]], 2, 0)), [[0], 0])\ncheck('oracle 7', solve(*([[0, 2], [2, 0], [1, 1]], 4, -4)), [[-4, 16, -8], 0])\nif N == 1: check('variant packet 1', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8], 0])\nif N == 2: check('variant packet 2', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 3: check('variant packet 3', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 4: check('variant packet 4', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 5: check('variant packet 5', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 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"},"fixed":{"sha256":"16582d6aa6e87885df33a4775af5112e3d2053ba8627eca5cc05527757520dbf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(pairs, amplitude, previous):\n    out=[]\n    for a,b in pairs:\n        difference=a-b\n        noise=difference*amplitude\n        shaped=noise-previous\n        previous=noise\n        out.append(shaped)\n    return [out,previous]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([[1, 3], [4, 0], [2, 2]], 2, 1)), [[-5, 12, -8], 0])\ncheck('oracle 2', solve(*([[0, 0], [1, 0]], 1, -2)), [[2, 1], 1])\ncheck('oracle 3', solve(*([], 3, 4)), [[], 4])\ncheck('oracle 4', solve(*([[4, 1], [1, 4]], 3, 0)), [[9, -18], -9])\ncheck('oracle 5', solve(*([[1, 2], [2, 1], [0, 0]], 0, 3)), [[-3, 0, 0], 0])\ncheck('oracle 6', solve(*([[3, 3]], 2, 0)), [[0], 0])\ncheck('oracle 7', solve(*([[0, 2], [2, 0], [1, 1]], 4, -4)), [[-4, 16, -8], 0])\nif N == 1: check('variant packet 1', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8], 0])\nif N == 2: check('variant packet 2', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 3: check('variant packet 3', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 4: check('variant packet 4', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 0])\nif N == 5: check('variant packet 5', solve(*[[[1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2], [1, 3], [4, 0], [2, 2]], 2, 1]), [[-5, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8, -4, 12, -8], 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-triangular-dither-independent-difference","generated_at":"2026-09-29T14:45:01.806947+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 independent difference.","root_cause":"Two supplied uniform draws are added rather than differenced for centered dither.","sha256":"9912bba7ac2071dd2e810d5ad5862b3639dc79e4fd2e60345aac194421784a9d","title":"Pcm triangular dither: independent difference · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.832,"exit_code":1,"observations":[{"actual":[[-1,0,0],0],"check":"oracle 1","expected":[[-5,12,-8],0],"passed":false},{"actual":[[2,0],0],"check":"oracle 2","expected":[[2,1],1],"passed":false},{"actual":[[],4],"check":"oracle 3","expected":[[],4],"passed":true},{"actual":[[0,0],0],"check":"oracle 4","expected":[[9,-18],-9],"passed":false},{"actual":[[-3,0,0],0],"check":"oracle 5","expected":[[-3,0,0],0],"passed":true},{"actual":[[0],0],"check":"oracle 6","expected":[[0],0],"passed":true},{"actual":[[4,0,0],0],"check":"oracle 7","expected":[[-4,16,-8],0],"passed":false},{"actual":[[-1,0,0,0,0,0],0],"check":"variant packet 1","expected":[[-5,12,-8,-4,12,-8],0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-1, 0, 0], 0], \"expected\": [[-5, 12, -8], 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[2, 0], 0], \"expected\": [[2, 1], 1], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[], 4], \"expected\": [[], 4], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[0, 0], 0], \"expected\": [[9, -18], -9], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [[-3, 0, 0], 0], \"expected\": [[-3, 0, 0], 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0], 0], \"expected\": [[0], 0], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[4, 0, 0], 0], \"expected\": [[-4, 16, -8], 0], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[-1, 0, 0, 0, 0, 0], 0], \"expected\": [[-5, 12, -8, -4, 12, -8], 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.989,"exit_code":1,"observations":[{"actual":[[7,0,0],8],"check":"oracle 1","expected":[[-5,12,-8],0],"passed":false},{"actual":[[2,1],1],"check":"oracle 2","expected":[[2,1],1],"passed":true},{"actual":[[],4],"check":"oracle 3","expected":[[],4],"passed":true},{"actual":[[15,0],15],"check":"oracle 4","expected":[[9,-18],-9],"passed":false},{"actual":[[-3,0,0],0],"check":"oracle 5","expected":[[-3,0,0],0],"passed":true},{"actual":[[12],12],"check":"oracle 6","expected":[[0],0],"passed":false},{"actual":[[12,0,0],8],"check":"oracle 7","expected":[[-4,16,-8],0],"passed":false},{"actual":[[7,0,0,0,0,0],8],"check":"variant packet 1","expected":[[-5,12,-8,-4,12,-8],0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[7, 0, 0], 8], \"expected\": [[-5, 12, -8], 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[2, 1], 1], \"expected\": [[2, 1], 1], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[], 4], \"expected\": [[], 4], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[15, 0], 15], \"expected\": [[9, -18], -9], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": [[-3, 0, 0], 0], \"expected\": [[-3, 0, 0], 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[12], 12], \"expected\": [[0], 0], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[12, 0, 0], 8], \"expected\": [[-4, 16, -8], 0], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[7, 0, 0, 0, 0, 0], 8], \"expected\": [[-5, 12, -8, -4, 12, -8], 0], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.098,"exit_code":0,"observations":[{"actual":[[-5,12,-8],0],"check":"oracle 1","expected":[[-5,12,-8],0],"passed":true},{"actual":[[2,1],1],"check":"oracle 2","expected":[[2,1],1],"passed":true},{"actual":[[],4],"check":"oracle 3","expected":[[],4],"passed":true},{"actual":[[9,-18],-9],"check":"oracle 4","expected":[[9,-18],-9],"passed":true},{"actual":[[-3,0,0],0],"check":"oracle 5","expected":[[-3,0,0],0],"passed":true},{"actual":[[0],0],"check":"oracle 6","expected":[[0],0],"passed":true},{"actual":[[-4,16,-8],0],"check":"oracle 7","expected":[[-4,16,-8],0],"passed":true},{"actual":[[-5,12,-8,-4,12,-8],0],"check":"variant packet 1","expected":[[-5,12,-8,-4,12,-8],0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[-5, 12, -8], 0], \"expected\": [[-5, 12, -8], 0], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [[2, 1], 1], \"expected\": [[2, 1], 1], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[], 4], \"expected\": [[], 4], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [[9, -18], -9], \"expected\": [[9, -18], -9], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[-3, 0, 0], 0], \"expected\": [[-3, 0, 0], 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[0], 0], \"expected\": [[0], 0], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[-4, 16, -8], 0], \"expected\": [[-4, 16, -8], 0], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[-5, 12, -8, -4, 12, -8], 0], \"expected\": [[-5, 12, -8, -4, 12, -8], 0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}