{"abstract":"Offsets inside NTSC frames drift across the 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":"Subtracting a floored frame start disagrees with the ceiled start convention.","family":"w2-broadcast-timecode-arithmetic-audio-sample-cadence-in-frame-offset","id":"FA-78681","implementations":{"attempt":{"sha256":"310f02ce9de9efbcc8db08ec2a86d99172fc27816aaa88e4178f0b911037aee1","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-frame*48000*den//num,-(-(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: in-frame offset', [1602, '29.97'], [1, 0, 1602]), ('regression variant: in-frame offset', [8008, '29.97'], [5, 0, 1602]), ('partial repair probe: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: in-frame offset', [3494632, '29.97'], [2181, 1542, 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: in-frame offset', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: in-frame offset', [1603, '29.97'], [1, 1, 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: in-frame offset', [3204, '29.97'], [2, 0, 1601]), ('regression variant: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: in-frame offset', [3203, '29.97'], [1, 1601, 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: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('regression variant: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: in-frame offset', [3070390, '29.97'], [1917, 122, 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: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: in-frame offset', [8009, '29.97'], [5, 1, 1602]), ('partial repair probe: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair variant: in-frame offset', [298951, '29.97'], [186, 1053, 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":"59fbcea97020a02be16e6c3b9642f55b2521bf82381caa1a80ed8443e600871a","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%(48000*den//num),-(-(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: in-frame offset', [1602, '29.97'], [1, 0, 1602]), ('regression variant: in-frame offset', [8008, '29.97'], [5, 0, 1602]), ('partial repair probe: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: in-frame offset', [3494632, '29.97'], [2181, 1542, 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: in-frame offset', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: in-frame offset', [1603, '29.97'], [1, 1, 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: in-frame offset', [3204, '29.97'], [2, 0, 1601]), ('regression variant: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: in-frame offset', [3203, '29.97'], [1, 1601, 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: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('regression variant: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: in-frame offset', [3070390, '29.97'], [1917, 122, 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: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: in-frame offset', [8009, '29.97'], [5, 1, 1602]), ('partial repair probe: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair variant: in-frame offset', [298951, '29.97'], [186, 1053, 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"},"fixed":{"sha256":"1f406489063307864cbfdd2b761559b34205c7a7cea1fa78317294d660f50359","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: in-frame offset', [1602, '29.97'], [1, 0, 1602]), ('regression variant: in-frame offset', [8008, '29.97'], [5, 0, 1602]), ('partial repair probe: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: in-frame offset', [3494632, '29.97'], [2181, 1542, 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: in-frame offset', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: in-frame offset', [1603, '29.97'], [1, 1, 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: in-frame offset', [3204, '29.97'], [2, 0, 1601]), ('regression variant: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: in-frame offset', [3203, '29.97'], [1, 1601, 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: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('regression variant: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: in-frame offset', [3070390, '29.97'], [1917, 122, 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: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: in-frame offset', [8009, '29.97'], [5, 1, 1602]), ('partial repair probe: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair variant: in-frame offset', [298951, '29.97'], [186, 1053, 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-in-frame-offset","generated_at":"2026-09-29T14:49:37.422269+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":"Subtract the exact frame start sample.","root_cause":"The offset is a modulo by a truncated samples-per-frame value.","sha256":"fc826780b2e741f5de36afdc587f7e3fd222fa806bb4a384308c76db011e4269","title":"Audio sample to frame cadence at 48 kHz: in-frame offset · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.041,"exit_code":1,"observations":[{"actual":[1,1,1602],"check":"regression: in-frame offset","expected":[1,0,1602],"passed":false},{"actual":[5,0,1602],"check":"regression variant: in-frame offset","expected":[5,0,1602],"passed":true},{"actual":[1,318,1602],"check":"partial repair probe: in-frame offset","expected":[1,317,1602],"passed":false},{"actual":[2181,1543,1602],"check":"partial repair variant: in-frame offset","expected":[2181,1542,1602],"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: in-frame offset\", \"actual\": [1, 1, 1602], \"expected\": [1, 0, 1602], \"passed\": false}, {\"check\": \"regression variant: in-frame offset\", \"actual\": [5, 0, 1602], \"expected\": [5, 0, 1602], \"passed\": true}, {\"check\": \"partial repair probe: in-frame offset\", \"actual\": [1, 318, 1602], \"expected\": [1, 317, 1602], \"passed\": false}, {\"check\": \"partial repair variant: in-frame offset\", \"actual\": [2181, 1543, 1602], \"expected\": [2181, 1542, 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":38.997,"exit_code":1,"observations":[{"actual":[1,1,1602],"check":"regression: in-frame offset","expected":[1,0,1602],"passed":false},{"actual":[5,3,1602],"check":"regression variant: in-frame offset","expected":[5,0,1602],"passed":false},{"actual":[1,318,1602],"check":"partial repair probe: in-frame offset","expected":[1,317,1602],"passed":false},{"actual":[2181,1250,1602],"check":"partial repair variant: in-frame offset","expected":[2181,1542,1602],"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: in-frame offset\", \"actual\": [1, 1, 1602], \"expected\": [1, 0, 1602], \"passed\": false}, {\"check\": \"regression variant: in-frame offset\", \"actual\": [5, 3, 1602], \"expected\": [5, 0, 1602], \"passed\": false}, {\"check\": \"partial repair probe: in-frame offset\", \"actual\": [1, 318, 1602], \"expected\": [1, 317, 1602], \"passed\": false}, {\"check\": \"partial repair variant: in-frame offset\", \"actual\": [2181, 1250, 1602], \"expected\": [2181, 1542, 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"},"fixed":{"elapsed_ms":40.615,"exit_code":0,"observations":[{"actual":[1,0,1602],"check":"regression: in-frame offset","expected":[1,0,1602],"passed":true},{"actual":[5,0,1602],"check":"regression variant: in-frame offset","expected":[5,0,1602],"passed":true},{"actual":[1,317,1602],"check":"partial repair probe: in-frame offset","expected":[1,317,1602],"passed":true},{"actual":[2181,1542,1602],"check":"partial repair variant: in-frame offset","expected":[2181,1542,1602],"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":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: in-frame offset\", \"actual\": [1, 0, 1602], \"expected\": [1, 0, 1602], \"passed\": true}, {\"check\": \"regression variant: in-frame offset\", \"actual\": [5, 0, 1602], \"expected\": [5, 0, 1602], \"passed\": true}, {\"check\": \"partial repair probe: in-frame offset\", \"actual\": [1, 317, 1602], \"expected\": [1, 317, 1602], \"passed\": true}, {\"check\": \"partial repair variant: in-frame offset\", \"actual\": [2181, 1542, 1602], \"expected\": [2181, 1542, 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\": true}\n"}},"verified":true,"visibility":"public"}