{"abstract":"Every NTSC frame is reported as 1601 samples, breaking the five-frame cadence.","category":"Broadcast timecode arithmetic","checks":9,"contract":"At 48000 samples per second and rate N/D, the frame containing sample s is floor(s*N/(48000*D)); frame k starts at sample ceil(k*48000*D/N). Return [frame, offset of s inside its frame, number of samples in that frame].","evaluation_group":"w2-broadcast-timecode-arithmetic-audio-sample-cadence","failed_approach":"A rounded-up constant reports 1602 samples for every frame.","family":"w2-broadcast-timecode-arithmetic-audio-sample-cadence-frame-length","id":"FA-78676","implementations":{"attempt":{"sha256":"1a160c1db2b1041ad73503c7772fde290d697719655d1655e6e18e6bd0dda83d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(sample, rate):\n    num,den={'23.976':(24000,1001),'24':(24,1),'25':(25,1),'29.97':(30000,1001),'30':(30,1)}[rate]\n    frame=sample*num//(48000*den)\n    start=-(-frame*48000*den//num)\n    return [frame,sample-start,-(-48000*den//num)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: frame length', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame length', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: frame length', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair variant: frame length', [6050108, '29.97'], [3777, 864, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1920, '30'], [1, 320, 1600]), ('normal control', [3204, '30'], [2, 4, 1600])], [('regression: frame length', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: frame length', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame length', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair variant: frame length', [8247925, '29.97'], [5149, 1286, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [9138728, '24'], [4569, 728, 2000]), ('normal control', [3203, '25'], [1, 1283, 1920]), ('normal control', [2001, '25'], [1, 81, 1920])], [('regression: frame length', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame length', [1, '29.97'], [0, 1, 1602]), ('partial repair probe: frame length', [8247925, '29.97'], [5149, 1286, 1601]), ('partial repair variant: frame length', [8735595, '29.97'], [5454, 468, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1920, '23.976'], [0, 1920, 2002]), ('normal control', [1, '23.976'], [0, 1, 2002]), ('normal control', [1601, '24'], [0, 1601, 2000])], [('regression: frame length', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame length', [1600, '29.97'], [0, 1600, 1602]), ('partial repair probe: frame length', [8735595, '29.97'], [5454, 468, 1601]), ('partial repair variant: frame length', [7203996, '29.97'], [4497, 1600, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [0, '24'], [0, 0, 2000]), ('normal control', [1920, '24'], [0, 1920, 2000]), ('normal control', [2001, '24'], [1, 1, 2000])], [('regression: frame length', [8008, '29.97'], [5, 0, 1602]), ('regression variant: frame length', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame length', [7203996, '29.97'], [4497, 1600, 1601]), ('partial repair variant: frame length', [3204, '29.97'], [2, 0, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [2839374, '30'], [1774, 974, 1600]), ('normal control', [1601, '23.976'], [0, 1601, 2002]), ('normal control', [1603, '25'], [0, 1603, 1920])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"ce2e96563b9ca0c1b8c4c492f43b7ec54aad0a78fa12f4f2a3eec9e7d4d27ca7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(sample, rate):\n    num,den={'23.976':(24000,1001),'24':(24,1),'25':(25,1),'29.97':(30000,1001),'30':(30,1)}[rate]\n    frame=sample*num//(48000*den)\n    start=-(-frame*48000*den//num)\n    return [frame,sample-start,48000*den//num]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: frame length', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame length', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: frame length', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair variant: frame length', [6050108, '29.97'], [3777, 864, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1920, '30'], [1, 320, 1600]), ('normal control', [3204, '30'], [2, 4, 1600])], [('regression: frame length', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: frame length', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame length', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair variant: frame length', [8247925, '29.97'], [5149, 1286, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [9138728, '24'], [4569, 728, 2000]), ('normal control', [3203, '25'], [1, 1283, 1920]), ('normal control', [2001, '25'], [1, 81, 1920])], [('regression: frame length', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame length', [1, '29.97'], [0, 1, 1602]), ('partial repair probe: frame length', [8247925, '29.97'], [5149, 1286, 1601]), ('partial repair variant: frame length', [8735595, '29.97'], [5454, 468, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1920, '23.976'], [0, 1920, 2002]), ('normal control', [1, '23.976'], [0, 1, 2002]), ('normal control', [1601, '24'], [0, 1601, 2000])], [('regression: frame length', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame length', [1600, '29.97'], [0, 1600, 1602]), ('partial repair probe: frame length', [8735595, '29.97'], [5454, 468, 1601]), ('partial repair variant: frame length', [7203996, '29.97'], [4497, 1600, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [0, '24'], [0, 0, 2000]), ('normal control', [1920, '24'], [0, 1920, 2000]), ('normal control', [2001, '24'], [1, 1, 2000])], [('regression: frame length', [8008, '29.97'], [5, 0, 1602]), ('regression variant: frame length', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame length', [7203996, '29.97'], [4497, 1600, 1601]), ('partial repair variant: frame length', [3204, '29.97'], [2, 0, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [2839374, '30'], [1774, 974, 1600]), ('normal control', [1601, '23.976'], [0, 1601, 2002]), ('normal control', [1603, '25'], [0, 1603, 1920])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"8da93c8614ab6c8e2d0a222e24554e87fded6128bb14c3d504545a593368a494","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(sample, rate):\n    num,den={'23.976':(24000,1001),'24':(24,1),'25':(25,1),'29.97':(30000,1001),'30':(30,1)}[rate]\n    frame=sample*num//(48000*den)\n    start=-(-frame*48000*den//num)\n    return [frame,sample-start,-(-(frame+1)*48000*den//num)-start]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: frame length', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame length', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: frame length', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair variant: frame length', [6050108, '29.97'], [3777, 864, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1920, '30'], [1, 320, 1600]), ('normal control', [3204, '30'], [2, 4, 1600])], [('regression: frame length', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: frame length', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame length', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair variant: frame length', [8247925, '29.97'], [5149, 1286, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [9138728, '24'], [4569, 728, 2000]), ('normal control', [3203, '25'], [1, 1283, 1920]), ('normal control', [2001, '25'], [1, 81, 1920])], [('regression: frame length', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame length', [1, '29.97'], [0, 1, 1602]), ('partial repair probe: frame length', [8247925, '29.97'], [5149, 1286, 1601]), ('partial repair variant: frame length', [8735595, '29.97'], [5454, 468, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1920, '23.976'], [0, 1920, 2002]), ('normal control', [1, '23.976'], [0, 1, 2002]), ('normal control', [1601, '24'], [0, 1601, 2000])], [('regression: frame length', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame length', [1600, '29.97'], [0, 1600, 1602]), ('partial repair probe: frame length', [8735595, '29.97'], [5454, 468, 1601]), ('partial repair variant: frame length', [7203996, '29.97'], [4497, 1600, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [0, '24'], [0, 0, 2000]), ('normal control', [1920, '24'], [0, 1920, 2000]), ('normal control', [2001, '24'], [1, 1, 2000])], [('regression: frame length', [8008, '29.97'], [5, 0, 1602]), ('regression variant: frame length', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame length', [7203996, '29.97'], [4497, 1600, 1601]), ('partial repair variant: frame length', [3204, '29.97'], [2, 0, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [2839374, '30'], [1774, 974, 1600]), ('normal control', [1601, '23.976'], [0, 1601, 2002]), ('normal control', [1603, '25'], [0, 1603, 1920])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"A deterministic bounded teaching model with a stipulated toy contract; it does not claim conformance to SMPTE or any broadcast standard. 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":"w2-broadcast-timecode-arithmetic-audio-sample-cadence-frame-length","generated_at":"2026-09-29T14:49:37.383374+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Timecode arithmetic errors misplace edits, commercial breaks and captions against the broadcast clock.","repair":"Compute the length from consecutive frame start samples.","root_cause":"The frame length is a single truncated constant.","sha256":"17dbf953f7357c9d48ced8ac1150d1ec27c2a0aefb382b05ebb03f2318376180","title":"Audio sample to frame cadence at 48 kHz: frame length · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.725,"exit_code":1,"observations":[{"actual":[1,0,1602],"check":"regression: frame length","expected":[1,0,1602],"passed":true},{"actual":[1,400,1602],"check":"regression variant: frame length","expected":[1,400,1602],"passed":true},{"actual":[1917,122,1602],"check":"partial repair probe: frame length","expected":[1917,122,1601],"passed":false},{"actual":[3777,864,1602],"check":"partial repair variant: frame length","expected":[3777,864,1601],"passed":false},{"actual":[1,0,1920],"check":"boundary control","expected":[1,0,1920],"passed":true},{"actual":[1,0,2002],"check":"boundary control","expected":[1,0,2002],"passed":true},{"actual":[0,1602,2000],"check":"normal control","expected":[0,1602,2000],"passed":true},{"actual":[1,320,1600],"check":"normal control","expected":[1,320,1600],"passed":true},{"actual":[2,4,1600],"check":"normal control","expected":[2,4,1600],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame length\", \"actual\": [1, 0, 1602], \"expected\": [1, 0, 1602], \"passed\": true}, {\"check\": \"regression variant: frame length\", \"actual\": [1, 400, 1602], \"expected\": [1, 400, 1602], \"passed\": true}, {\"check\": \"partial repair probe: frame length\", \"actual\": [1917, 122, 1602], \"expected\": [1917, 122, 1601], \"passed\": false}, {\"check\": \"partial repair variant: frame length\", \"actual\": [3777, 864, 1602], \"expected\": [3777, 864, 1601], \"passed\": false}, {\"check\": \"boundary control\", \"actual\": [1, 0, 1920], \"expected\": [1, 0, 1920], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 2002], \"expected\": [1, 0, 2002], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [0, 1602, 2000], \"expected\": [0, 1602, 2000], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [1, 320, 1600], \"expected\": [1, 320, 1600], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [2, 4, 1600], \"expected\": [2, 4, 1600], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.251,"exit_code":1,"observations":[{"actual":[1,0,1601],"check":"regression: frame length","expected":[1,0,1602],"passed":false},{"actual":[1,400,1601],"check":"regression variant: frame length","expected":[1,400,1602],"passed":false},{"actual":[1917,122,1601],"check":"partial repair probe: frame length","expected":[1917,122,1601],"passed":true},{"actual":[3777,864,1601],"check":"partial repair variant: frame length","expected":[3777,864,1601],"passed":true},{"actual":[1,0,1920],"check":"boundary control","expected":[1,0,1920],"passed":true},{"actual":[1,0,2002],"check":"boundary control","expected":[1,0,2002],"passed":true},{"actual":[0,1602,2000],"check":"normal control","expected":[0,1602,2000],"passed":true},{"actual":[1,320,1600],"check":"normal control","expected":[1,320,1600],"passed":true},{"actual":[2,4,1600],"check":"normal control","expected":[2,4,1600],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame length\", \"actual\": [1, 0, 1601], \"expected\": [1, 0, 1602], \"passed\": false}, {\"check\": \"regression variant: frame length\", \"actual\": [1, 400, 1601], \"expected\": [1, 400, 1602], \"passed\": false}, {\"check\": \"partial repair probe: frame length\", \"actual\": [1917, 122, 1601], \"expected\": [1917, 122, 1601], \"passed\": true}, {\"check\": \"partial repair variant: frame length\", \"actual\": [3777, 864, 1601], \"expected\": [3777, 864, 1601], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 1920], \"expected\": [1, 0, 1920], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 2002], \"expected\": [1, 0, 2002], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [0, 1602, 2000], \"expected\": [0, 1602, 2000], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [1, 320, 1600], \"expected\": [1, 320, 1600], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [2, 4, 1600], \"expected\": [2, 4, 1600], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.367,"exit_code":0,"observations":[{"actual":[1,0,1602],"check":"regression: frame length","expected":[1,0,1602],"passed":true},{"actual":[1,400,1602],"check":"regression variant: frame length","expected":[1,400,1602],"passed":true},{"actual":[1917,122,1601],"check":"partial repair probe: frame length","expected":[1917,122,1601],"passed":true},{"actual":[3777,864,1601],"check":"partial repair variant: frame length","expected":[3777,864,1601],"passed":true},{"actual":[1,0,1920],"check":"boundary control","expected":[1,0,1920],"passed":true},{"actual":[1,0,2002],"check":"boundary control","expected":[1,0,2002],"passed":true},{"actual":[0,1602,2000],"check":"normal control","expected":[0,1602,2000],"passed":true},{"actual":[1,320,1600],"check":"normal control","expected":[1,320,1600],"passed":true},{"actual":[2,4,1600],"check":"normal control","expected":[2,4,1600],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame length\", \"actual\": [1, 0, 1602], \"expected\": [1, 0, 1602], \"passed\": true}, {\"check\": \"regression variant: frame length\", \"actual\": [1, 400, 1602], \"expected\": [1, 400, 1602], \"passed\": true}, {\"check\": \"partial repair probe: frame length\", \"actual\": [1917, 122, 1601], \"expected\": [1917, 122, 1601], \"passed\": true}, {\"check\": \"partial repair variant: frame length\", \"actual\": [3777, 864, 1601], \"expected\": [3777, 864, 1601], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 1920], \"expected\": [1, 0, 1920], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 2002], \"expected\": [1, 0, 2002], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [0, 1602, 2000], \"expected\": [0, 1602, 2000], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [1, 320, 1600], \"expected\": [1, 320, 1600], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [2, 4, 1600], \"expected\": [2, 4, 1600], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}