{"abstract":"Film frames after the first cadence group map to video frames far too early.","category":"Broadcast timecode arithmetic","checks":9,"contract":"Film frames follow the A2 B3 C2 D3 field cadence (10 fields per 4 film frames). phase is the cadence position (0=A..3=D) of film frame 0, which starts at video field 0. Negative n returns None. For film frame n return [video frame of its first field, \"upper\" for an even field index else \"lower\", number of fields].","contract_signature":"n, phase","evaluation_group":"w2-broadcast-timecode-arithmetic-pulldown-film-to-video","failed_approach":"Eight fields per group assumes 2:2 pulldown.","family":"w2-broadcast-timecode-arithmetic-pulldown-film-to-video-cadence-group-size","id":"FA-78541","implementations":{"attempt":{"sha256":"368e5f6dc9e52d291805c6e4ba7182567024e034710927618bcd585275dd0fb9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(n, phase):\n    if n<0:\n        return None\n    def sf(a):\n        return 8*(a//4)+[0,2,5,7][a%4]\n    a=n+phase\n    start=sf(a)-sf(phase)\n    count=[2,3,2,3][a%4]\n    return [start//2,'upper' if start%2==0 else 'lower',count]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: cadence group size', [4, 0], [5, 'upper', 2]), ('regression variant: cadence group size', [34, 2], [42, 'lower', 2]), ('partial repair probe: cadence group size', [8, 0], [10, 'upper', 2]), ('partial repair variant: cadence group size', [26, 2], [32, 'lower', 2]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [1, 0], [1, 'upper', 3]), ('normal control', [-3, 2], None), ('normal control', [-4, 2], None)], [('regression: cadence group size', [2, 3], [2, 'lower', 3]), ('regression variant: cadence group size', [9, 3], [11, 'lower', 2]), ('partial repair probe: cadence group size', [9, 1], [11, 'lower', 2]), ('partial repair variant: cadence group size', [36, 1], [45, 'upper', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-2, 3], None), ('normal control', [-6, 1], None), ('normal control', [-3, 0], None)], [('regression: cadence group size', [8, 0], [10, 'upper', 2]), ('regression variant: cadence group size', [10, 1], [12, 'lower', 3]), ('partial repair probe: cadence group size', [35, 1], [44, 'upper', 2]), ('partial repair variant: cadence group size', [38, 3], [47, 'lower', 3]), ('boundary control', [3, 0], [3, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('normal control', [-1, 1], None), ('normal control', [-3, 3], None), ('normal control', [-5, 3], None)], [('regression: cadence group size', [9, 1], [11, 'lower', 2]), ('regression variant: cadence group size', [22, 2], [27, 'lower', 2]), ('partial repair probe: cadence group size', [34, 2], [42, 'lower', 2]), ('partial repair variant: cadence group size', [1, 3], [1, 'lower', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('boundary control', [3, 0], [3, 'lower', 3]), ('normal control', [-1, 0], None), ('normal control', [1, 2], [1, 'upper', 3]), ('normal control', [2, 1], [2, 'lower', 3])], [('regression: cadence group size', [35, 1], [44, 'upper', 2]), ('regression variant: cadence group size', [26, 2], [32, 'lower', 2]), ('partial repair probe: cadence group size', [9, 3], [11, 'lower', 2]), ('partial repair variant: cadence group size', [3, 2], [3, 'lower', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [-1, 2], None), ('normal control', [0, 3], [0, 'upper', 3]), ('normal control', [1, 0], [1, 'upper', 3])]]\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":"d2c80f710cf4b181df5b57f391b0c586cf683fd85c9b582aeaddf5f6786e27ca","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(n, phase):\n    if n<0:\n        return None\n    def sf(a):\n        return 5*(a//4)+[0,2,5,7][a%4]\n    a=n+phase\n    start=sf(a)-sf(phase)\n    count=[2,3,2,3][a%4]\n    return [start//2,'upper' if start%2==0 else 'lower',count]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: cadence group size', [4, 0], [5, 'upper', 2]), ('regression variant: cadence group size', [34, 2], [42, 'lower', 2]), ('partial repair probe: cadence group size', [8, 0], [10, 'upper', 2]), ('partial repair variant: cadence group size', [26, 2], [32, 'lower', 2]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [1, 0], [1, 'upper', 3]), ('normal control', [-3, 2], None), ('normal control', [-4, 2], None)], [('regression: cadence group size', [2, 3], [2, 'lower', 3]), ('regression variant: cadence group size', [9, 3], [11, 'lower', 2]), ('partial repair probe: cadence group size', [9, 1], [11, 'lower', 2]), ('partial repair variant: cadence group size', [36, 1], [45, 'upper', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-2, 3], None), ('normal control', [-6, 1], None), ('normal control', [-3, 0], None)], [('regression: cadence group size', [8, 0], [10, 'upper', 2]), ('regression variant: cadence group size', [10, 1], [12, 'lower', 3]), ('partial repair probe: cadence group size', [35, 1], [44, 'upper', 2]), ('partial repair variant: cadence group size', [38, 3], [47, 'lower', 3]), ('boundary control', [3, 0], [3, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('normal control', [-1, 1], None), ('normal control', [-3, 3], None), ('normal control', [-5, 3], None)], [('regression: cadence group size', [9, 1], [11, 'lower', 2]), ('regression variant: cadence group size', [22, 2], [27, 'lower', 2]), ('partial repair probe: cadence group size', [34, 2], [42, 'lower', 2]), ('partial repair variant: cadence group size', [1, 3], [1, 'lower', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('boundary control', [3, 0], [3, 'lower', 3]), ('normal control', [-1, 0], None), ('normal control', [1, 2], [1, 'upper', 3]), ('normal control', [2, 1], [2, 'lower', 3])], [('regression: cadence group size', [35, 1], [44, 'upper', 2]), ('regression variant: cadence group size', [26, 2], [32, 'lower', 2]), ('partial repair probe: cadence group size', [9, 3], [11, 'lower', 2]), ('partial repair variant: cadence group size', [3, 2], [3, 'lower', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [-1, 2], None), ('normal control', [0, 3], [0, 'upper', 3]), ('normal control', [1, 0], [1, 'upper', 3])]]\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-pulldown-film-to-video-cadence-group-size","generated_at":"2026-09-29T14:49:36.026243+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":"Each four-frame group advances by five units, mixing video frames with fields.","sha256":"0d8a78caf7ba7efb3b87d8469e0a4d48fdc460720abbeb9f94e9c4007b965505","title":"2:3 pulldown film frame placement: cadence group size · 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":38.927,"exit_code":1,"observations":[{"actual":[4,"upper",2],"check":"regression: cadence group size","expected":[5,"upper",2],"passed":false},{"actual":[33,"lower",2],"check":"regression variant: cadence group size","expected":[42,"lower",2],"passed":false},{"actual":[8,"upper",2],"check":"partial repair probe: cadence group size","expected":[10,"upper",2],"passed":false},{"actual":[25,"lower",2],"check":"partial repair variant: cadence group size","expected":[32,"lower",2],"passed":false},{"actual":[0,"upper",2],"check":"boundary control","expected":[0,"upper",2],"passed":true},{"actual":[0,"upper",3],"check":"boundary control","expected":[0,"upper",3],"passed":true},{"actual":[1,"upper",3],"check":"normal control","expected":[1,"upper",3],"passed":true},{"actual":null,"check":"normal control","expected":null,"passed":true},{"actual":null,"check":"normal control","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: cadence group size\", \"actual\": [4, \"upper\", 2], \"expected\": [5, \"upper\", 2], \"passed\": false}, {\"check\": \"regression variant: cadence group size\", \"actual\": [33, \"lower\", 2], \"expected\": [42, \"lower\", 2], \"passed\": false}, {\"check\": \"partial repair probe: cadence group size\", \"actual\": [8, \"upper\", 2], \"expected\": [10, \"upper\", 2], \"passed\": false}, {\"check\": \"partial repair variant: cadence group size\", \"actual\": [25, \"lower\", 2], \"expected\": [32, \"lower\", 2], \"passed\": false}, {\"check\": \"boundary control\", \"actual\": [0, \"upper\", 2], \"expected\": [0, \"upper\", 2], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [0, \"upper\", 3], \"expected\": [0, \"upper\", 3], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [1, \"upper\", 3], \"expected\": [1, \"upper\", 3], \"passed\": true}, {\"check\": \"normal control\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"normal control\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.175,"exit_code":1,"observations":[{"actual":[2,"lower",2],"check":"regression: cadence group size","expected":[5,"upper",2],"passed":false},{"actual":[20,"upper",2],"check":"regression variant: cadence group size","expected":[42,"lower",2],"passed":false},{"actual":[5,"upper",2],"check":"partial repair probe: cadence group size","expected":[10,"upper",2],"passed":false},{"actual":[15,"upper",2],"check":"partial repair variant: cadence group size","expected":[32,"lower",2],"passed":false},{"actual":[0,"upper",2],"check":"boundary control","expected":[0,"upper",2],"passed":true},{"actual":[0,"upper",3],"check":"boundary control","expected":[0,"upper",3],"passed":true},{"actual":[1,"upper",3],"check":"normal control","expected":[1,"upper",3],"passed":true},{"actual":null,"check":"normal control","expected":null,"passed":true},{"actual":null,"check":"normal control","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: cadence group size\", \"actual\": [2, \"lower\", 2], \"expected\": [5, \"upper\", 2], \"passed\": false}, {\"check\": \"regression variant: cadence group size\", \"actual\": [20, \"upper\", 2], \"expected\": [42, \"lower\", 2], \"passed\": false}, {\"check\": \"partial repair probe: cadence group size\", \"actual\": [5, \"upper\", 2], \"expected\": [10, \"upper\", 2], \"passed\": false}, {\"check\": \"partial repair variant: cadence group size\", \"actual\": [15, \"upper\", 2], \"expected\": [32, \"lower\", 2], \"passed\": false}, {\"check\": \"boundary control\", \"actual\": [0, \"upper\", 2], \"expected\": [0, \"upper\", 2], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [0, \"upper\", 3], \"expected\": [0, \"upper\", 3], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [1, \"upper\", 3], \"expected\": [1, \"upper\", 3], \"passed\": true}, {\"check\": \"normal control\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"normal control\", \"actual\": null, \"expected\": null, \"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."}}