{"abstract":"Sample cadence for 29.97 video slowly slips against the true 30000/1001 rate.","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].","contract_signature":"sample, rate","evaluation_group":"w2-broadcast-timecode-arithmetic-audio-sample-cadence","failed_approach":"Using integer 30 removes the NTSC cadence entirely.","family":"w2-broadcast-timecode-arithmetic-audio-sample-cadence-ntsc-rate-table","id":"FA-78686","implementations":{"attempt":{"sha256":"c5fe178d436a6600bec782ab1527cceecbc80cbbd2b84596a9e816971597f801","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':(30,1),'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: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: ntsc rate table', [3204, '29.97'], [2, 0, 1601]), ('partial repair variant: ntsc rate table', [1600, '29.97'], [0, 1600, 1602]), ('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: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('regression variant: ntsc rate table', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair probe: ntsc rate table', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: ntsc rate table', [2001, '29.97'], [1, 399, 1602]), ('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: ntsc rate table', [8009, '29.97'], [5, 1, 1602]), ('regression variant: ntsc rate table', [3315925, '29.97'], [2070, 613, 1602]), ('partial repair probe: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('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: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('regression variant: ntsc rate table', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair probe: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: ntsc rate table', [8007, '29.97'], [4, 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: ntsc rate table', [8007, '29.97'], [4, 1600, 1601]), ('regression variant: ntsc rate table', [2419900, '29.97'], [1510, 1484, 1602]), ('partial repair probe: ntsc rate table', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('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":"171be1f81c2ece5a37886488970bc8171fab7adaccf90815575bb80e43f39d93","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':(2997,100),'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: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: ntsc rate table', [3204, '29.97'], [2, 0, 1601]), ('partial repair variant: ntsc rate table', [1600, '29.97'], [0, 1600, 1602]), ('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: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('regression variant: ntsc rate table', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair probe: ntsc rate table', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: ntsc rate table', [2001, '29.97'], [1, 399, 1602]), ('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: ntsc rate table', [8009, '29.97'], [5, 1, 1602]), ('regression variant: ntsc rate table', [3315925, '29.97'], [2070, 613, 1602]), ('partial repair probe: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('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: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('regression variant: ntsc rate table', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair probe: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: ntsc rate table', [8007, '29.97'], [4, 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: ntsc rate table', [8007, '29.97'], [4, 1600, 1601]), ('regression variant: ntsc rate table', [2419900, '29.97'], [1510, 1484, 1602]), ('partial repair probe: ntsc rate table', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('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-ntsc-rate-table","generated_at":"2026-09-29T14:49:37.684302+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.","root_cause":"The rate is taken as exactly 29.97 frames per second.","sha256":"b58116c73401b91b25a84a7ffef7e286408a94c376f81b28ec28650297228dce","title":"Audio sample to frame cadence at 48 kHz: ntsc rate table · 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":42.872,"exit_code":1,"observations":[{"actual":[5987,1301,1600],"check":"regression: ntsc rate table","expected":[5981,1331,1602],"passed":false},{"actual":[2184,232,1600],"check":"regression variant: ntsc rate table","expected":[2181,1542,1602],"passed":false},{"actual":[2,4,1600],"check":"partial repair probe: ntsc rate table","expected":[2,0,1601],"passed":false},{"actual":[1,0,1600],"check":"partial repair variant: ntsc rate table","expected":[0,1600,1602],"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: ntsc rate table\", \"actual\": [5987, 1301, 1600], \"expected\": [5981, 1331, 1602], \"passed\": false}, {\"check\": \"regression variant: ntsc rate table\", \"actual\": [2184, 232, 1600], \"expected\": [2181, 1542, 1602], \"passed\": false}, {\"check\": \"partial repair probe: ntsc rate table\", \"actual\": [2, 4, 1600], \"expected\": [2, 0, 1601], \"passed\": false}, {\"check\": \"partial repair variant: ntsc rate table\", \"actual\": [1, 0, 1600], \"expected\": [0, 1600, 1602], \"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":43.158,"exit_code":1,"observations":[{"actual":[5981,1321,1601],"check":"regression: ntsc rate table","expected":[5981,1331,1602],"passed":false},{"actual":[2181,1538,1601],"check":"regression variant: ntsc rate table","expected":[2181,1542,1602],"passed":false},{"actual":[2,0,1601],"check":"partial repair probe: ntsc rate table","expected":[2,0,1601],"passed":true},{"actual":[0,1600,1602],"check":"partial repair variant: ntsc rate table","expected":[0,1600,1602],"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: ntsc rate table\", \"actual\": [5981, 1321, 1601], \"expected\": [5981, 1331, 1602], \"passed\": false}, {\"check\": \"regression variant: ntsc rate table\", \"actual\": [2181, 1538, 1601], \"expected\": [2181, 1542, 1602], \"passed\": false}, {\"check\": \"partial repair probe: ntsc rate table\", \"actual\": [2, 0, 1601], \"expected\": [2, 0, 1601], \"passed\": true}, {\"check\": \"partial repair variant: ntsc rate table\", \"actual\": [0, 1600, 1602], \"expected\": [0, 1600, 1602], \"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"}},"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."}}