{"abstract":"In-frame offsets are one sample too large at NTSC frame starts.","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":"Multiplying by a truncated samples-per-frame value drifts through the cadence.","family":"w2-broadcast-timecode-arithmetic-audio-sample-cadence-frame-start-sample","id":"FA-78671","implementations":{"attempt":{"sha256":"084bdf1bd7ade533a86fdf5d87ce2b9d0950b2e7f3e0fc968eec451fe2fc8766","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 start sample', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1600, '25'], [0, 1600, 1920])], [('regression: frame start sample', [3204, '29.97'], [2, 0, 1601]), ('regression variant: frame start sample', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [8008, '25'], [4, 328, 1920]), ('normal control', [0, '25'], [0, 0, 1920]), ('normal control', [1602, '23.976'], [0, 1602, 2002])], [('regression: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('partial repair probe: frame start sample', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('normal control', [1601, '25'], [0, 1601, 1920]), ('normal control', [0, '30'], [0, 0, 1600]), ('normal control', [8009, '24'], [4, 9, 2000])], [('regression: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('partial repair probe: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: frame start sample', [1603, '29.97'], [1, 1, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [3204, '25'], [1, 1284, 1920]), ('normal control', [8009, '23.976'], [4, 1, 2002]), ('normal control', [2002, '24'], [1, 2, 2000])], [('regression: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('regression variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: frame start sample', [3203, '29.97'], [1, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [3203, '24'], [1, 1203, 2000]), ('normal control', [8009, '30'], [5, 9, 1600]), ('normal control', [1603, '24'], [0, 1603, 2000])]]\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":"f8d56ae0d57e666260abb0aa12106e2b724ef8914377ea2ac6f3803b07aed65c","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 start sample', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1600, '25'], [0, 1600, 1920])], [('regression: frame start sample', [3204, '29.97'], [2, 0, 1601]), ('regression variant: frame start sample', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [8008, '25'], [4, 328, 1920]), ('normal control', [0, '25'], [0, 0, 1920]), ('normal control', [1602, '23.976'], [0, 1602, 2002])], [('regression: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('partial repair probe: frame start sample', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('normal control', [1601, '25'], [0, 1601, 1920]), ('normal control', [0, '30'], [0, 0, 1600]), ('normal control', [8009, '24'], [4, 9, 2000])], [('regression: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('partial repair probe: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: frame start sample', [1603, '29.97'], [1, 1, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [3204, '25'], [1, 1284, 1920]), ('normal control', [8009, '23.976'], [4, 1, 2002]), ('normal control', [2002, '24'], [1, 2, 2000])], [('regression: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('regression variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: frame start sample', [3203, '29.97'], [1, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [3203, '24'], [1, 1203, 2000]), ('normal control', [8009, '30'], [5, 9, 1600]), ('normal control', [1603, '24'], [0, 1603, 2000])]]\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":"04f832a15f859c553d11ba6365ab7b9e6095571a7a0324379425cb88faf76942","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 start sample', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1600, '25'], [0, 1600, 1920])], [('regression: frame start sample', [3204, '29.97'], [2, 0, 1601]), ('regression variant: frame start sample', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [8008, '25'], [4, 328, 1920]), ('normal control', [0, '25'], [0, 0, 1920]), ('normal control', [1602, '23.976'], [0, 1602, 2002])], [('regression: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('partial repair probe: frame start sample', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('normal control', [1601, '25'], [0, 1601, 1920]), ('normal control', [0, '30'], [0, 0, 1600]), ('normal control', [8009, '24'], [4, 9, 2000])], [('regression: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('partial repair probe: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: frame start sample', [1603, '29.97'], [1, 1, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [3204, '25'], [1, 1284, 1920]), ('normal control', [8009, '23.976'], [4, 1, 2002]), ('normal control', [2002, '24'], [1, 2, 2000])], [('regression: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('regression variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: frame start sample', [3203, '29.97'], [1, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [3203, '24'], [1, 1203, 2000]), ('normal control', [8009, '30'], [5, 9, 1600]), ('normal control', [1603, '24'], [0, 1603, 2000])]]\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-start-sample","generated_at":"2026-09-29T14:49:37.379093+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":"Frame k starts at the ceiling of k*48000*D/N.","root_cause":"The frame start sample is floored instead of ceiled.","sha256":"e23cad17dcc9b921474ef5562a8a87175c597ef8f13fcc0cf8c37cbdd96edf38","title":"Audio sample to frame cadence at 48 kHz: frame start sample · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.718,"exit_code":1,"observations":[{"actual":[1,1,1603],"check":"regression: frame start sample","expected":[1,0,1602],"passed":false},{"actual":[1,319,1603],"check":"regression variant: frame start sample","expected":[1,318,1602],"passed":false},{"actual":[1,318,1603],"check":"partial repair probe: frame start sample","expected":[1,317,1602],"passed":false},{"actual":[3663,3442,3800],"check":"partial repair variant: frame start sample","expected":[3663,1244,1602],"passed":false},{"actual":[0,1601,1602],"check":"boundary control","expected":[0,1601,1602],"passed":true},{"actual":[1,0,1920],"check":"boundary control","expected":[1,0,1920],"passed":true},{"actual":[1,0,2002],"check":"normal control","expected":[1,0,2002],"passed":true},{"actual":[0,1602,2000],"check":"normal control","expected":[0,1602,2000],"passed":true},{"actual":[0,1600,1920],"check":"normal control","expected":[0,1600,1920],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame start sample\", \"actual\": [1, 1, 1603], \"expected\": [1, 0, 1602], \"passed\": false}, {\"check\": \"regression variant: frame start sample\", \"actual\": [1, 319, 1603], \"expected\": [1, 318, 1602], \"passed\": false}, {\"check\": \"partial repair probe: frame start sample\", \"actual\": [1, 318, 1603], \"expected\": [1, 317, 1602], \"passed\": false}, {\"check\": \"partial repair variant: frame start sample\", \"actual\": [3663, 3442, 3800], \"expected\": [3663, 1244, 1602], \"passed\": false}, {\"check\": \"boundary control\", \"actual\": [0, 1601, 1602], \"expected\": [0, 1601, 1602], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 1920], \"expected\": [1, 0, 1920], \"passed\": true}, {\"check\": \"normal 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\": [0, 1600, 1920], \"expected\": [0, 1600, 1920], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.598,"exit_code":1,"observations":[{"actual":[1,1,1603],"check":"regression: frame start sample","expected":[1,0,1602],"passed":false},{"actual":[1,319,1603],"check":"regression variant: frame start sample","expected":[1,318,1602],"passed":false},{"actual":[1,318,1603],"check":"partial repair probe: frame start sample","expected":[1,317,1602],"passed":false},{"actual":[3663,1245,1603],"check":"partial repair variant: frame start sample","expected":[3663,1244,1602],"passed":false},{"actual":[0,1601,1602],"check":"boundary control","expected":[0,1601,1602],"passed":true},{"actual":[1,0,1920],"check":"boundary control","expected":[1,0,1920],"passed":true},{"actual":[1,0,2002],"check":"normal control","expected":[1,0,2002],"passed":true},{"actual":[0,1602,2000],"check":"normal control","expected":[0,1602,2000],"passed":true},{"actual":[0,1600,1920],"check":"normal control","expected":[0,1600,1920],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame start sample\", \"actual\": [1, 1, 1603], \"expected\": [1, 0, 1602], \"passed\": false}, {\"check\": \"regression variant: frame start sample\", \"actual\": [1, 319, 1603], \"expected\": [1, 318, 1602], \"passed\": false}, {\"check\": \"partial repair probe: frame start sample\", \"actual\": [1, 318, 1603], \"expected\": [1, 317, 1602], \"passed\": false}, {\"check\": \"partial repair variant: frame start sample\", \"actual\": [3663, 1245, 1603], \"expected\": [3663, 1244, 1602], \"passed\": false}, {\"check\": \"boundary control\", \"actual\": [0, 1601, 1602], \"expected\": [0, 1601, 1602], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 1920], \"expected\": [1, 0, 1920], \"passed\": true}, {\"check\": \"normal 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\": [0, 1600, 1920], \"expected\": [0, 1600, 1920], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.704,"exit_code":0,"observations":[{"actual":[1,0,1602],"check":"regression: frame start sample","expected":[1,0,1602],"passed":true},{"actual":[1,318,1602],"check":"regression variant: frame start sample","expected":[1,318,1602],"passed":true},{"actual":[1,317,1602],"check":"partial repair probe: frame start sample","expected":[1,317,1602],"passed":true},{"actual":[3663,1244,1602],"check":"partial repair variant: frame start sample","expected":[3663,1244,1602],"passed":true},{"actual":[0,1601,1602],"check":"boundary control","expected":[0,1601,1602],"passed":true},{"actual":[1,0,1920],"check":"boundary control","expected":[1,0,1920],"passed":true},{"actual":[1,0,2002],"check":"normal control","expected":[1,0,2002],"passed":true},{"actual":[0,1602,2000],"check":"normal control","expected":[0,1602,2000],"passed":true},{"actual":[0,1600,1920],"check":"normal control","expected":[0,1600,1920],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame start sample\", \"actual\": [1, 0, 1602], \"expected\": [1, 0, 1602], \"passed\": true}, {\"check\": \"regression variant: frame start sample\", \"actual\": [1, 318, 1602], \"expected\": [1, 318, 1602], \"passed\": true}, {\"check\": \"partial repair probe: frame start sample\", \"actual\": [1, 317, 1602], \"expected\": [1, 317, 1602], \"passed\": true}, {\"check\": \"partial repair variant: frame start sample\", \"actual\": [3663, 1244, 1602], \"expected\": [3663, 1244, 1602], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [0, 1601, 1602], \"expected\": [0, 1601, 1602], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [1, 0, 1920], \"expected\": [1, 0, 1920], \"passed\": true}, {\"check\": \"normal 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\": [0, 1600, 1920], \"expected\": [0, 1600, 1920], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}