{"abstract":"PAL sums produce frame fields of 25 to 29.","category":"Broadcast timecode arithmetic","checks":8,"contract":"Add two valid non-drop labels at integer fps field by field with carries (frames into seconds at fps, seconds into minutes at 60, minutes into hours at 60) and wrap hours modulo 24.","evaluation_group":"w2-broadcast-timecode-arithmetic-fieldwise-addition","failed_approach":"Subtracting only above fps leaves an exact fps sum as an invalid frame field.","family":"w2-broadcast-timecode-arithmetic-fieldwise-addition-frame-remainder","id":"FA-78471","implementations":{"attempt":{"sha256":"a0324ee985437f4419c9c41ac37aeb7a4f4e134f29eaa8b7d060b5195e7f609e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(a, b, fps):\n    x=[int(v) for v in a.split(':')]\n    y=[int(v) for v in b.split(':')]\n    f=x[3]+y[3]\n    c=f//fps\n    f=f-fps if f>fps else f\n    s=x[2]+y[2]+c\n    c=s//60\n    s%=60\n    m=x[1]+y[1]+c\n    c=m//60\n    m%=60\n    h=(x[0]+y[0]+c)%24\n    return '%02d:%02d:%02d:%02d'%(h,m,s,f)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: frame remainder', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('regression variant: frame remainder', ['23:30:59:12', '12:59:30:12', 24], '12:30:30:00'), ('partial repair probe: frame remainder', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('partial repair variant: frame remainder', ['01:30:01:24', '23:30:00:01', 25], '01:00:02:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:59:01:00', '01:00:30:12', 25], '01:59:31:12'), ('normal control', ['00:59:30:00', '00:00:59:01', 30], '01:00:29:01'), ('normal control', ['23:00:01:24', '23:00:00:00', 25], '22:00:01:24')], [('regression: frame remainder', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('regression variant: frame remainder', ['23:01:30:24', '01:00:01:12', 25], '00:01:32:11'), ('partial repair probe: frame remainder', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('partial repair variant: frame remainder', ['12:01:00:15', '00:59:30:15', 30], '13:00:31:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:00:59:12', '00:01:01:12', 25], '00:02:00:24'), ('normal control', ['23:01:30:12', '23:00:59:00', 24], '22:02:29:12'), ('normal control', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14')], [('regression: frame remainder', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('regression variant: frame remainder', ['00:00:30:12', '23:30:01:24', 25], '23:30:32:11'), ('partial repair probe: frame remainder', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('partial repair variant: frame remainder', ['01:01:30:24', '01:59:00:01', 25], '03:00:31:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01'), ('normal control', ['12:01:01:15', '12:01:00:00', 30], '00:02:01:15'), ('normal control', ['00:00:01:24', '23:01:59:00', 25], '23:02:00:24')], [('regression: frame remainder', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('regression variant: frame remainder', ['01:30:01:24', '23:30:00:01', 25], '01:00:02:00'), ('partial repair probe: frame remainder', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('partial repair variant: frame remainder', ['12:01:30:29', '01:30:30:01', 30], '13:32:01:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['01:59:01:01', '00:59:01:12', 24], '02:58:02:13'), ('normal control', ['23:30:00:00', '23:01:30:00', 24], '22:31:30:00'), ('normal control', ['00:59:01:00', '12:00:01:23', 24], '12:59:02:23')], [('regression: frame remainder', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('regression variant: frame remainder', ['00:01:30:23', '00:59:30:12', 24], '01:01:01:11'), ('partial repair probe: frame remainder', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: frame remainder', ['12:01:30:01', '01:01:01:29', 30], '13:02:32:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:30:59:00', '12:59:01:15', 30], '13:30:00:15'), ('normal control', ['23:59:59:01', '23:01:01:00', 24], '23:01:00:01'), ('normal control', ['01:59:00:23', '23:01:01:00', 24], '01:00:01:23')]]\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":"fdcb26e94bbb025468e89a03de6a7cc771cdccd170a3dad0d1149af5f05905b4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(a, b, fps):\n    x=[int(v) for v in a.split(':')]\n    y=[int(v) for v in b.split(':')]\n    f=x[3]+y[3]\n    c=f//fps\n    f%=30\n    s=x[2]+y[2]+c\n    c=s//60\n    s%=60\n    m=x[1]+y[1]+c\n    c=m//60\n    m%=60\n    h=(x[0]+y[0]+c)%24\n    return '%02d:%02d:%02d:%02d'%(h,m,s,f)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: frame remainder', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('regression variant: frame remainder', ['23:30:59:12', '12:59:30:12', 24], '12:30:30:00'), ('partial repair probe: frame remainder', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('partial repair variant: frame remainder', ['01:30:01:24', '23:30:00:01', 25], '01:00:02:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:59:01:00', '01:00:30:12', 25], '01:59:31:12'), ('normal control', ['00:59:30:00', '00:00:59:01', 30], '01:00:29:01'), ('normal control', ['23:00:01:24', '23:00:00:00', 25], '22:00:01:24')], [('regression: frame remainder', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('regression variant: frame remainder', ['23:01:30:24', '01:00:01:12', 25], '00:01:32:11'), ('partial repair probe: frame remainder', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('partial repair variant: frame remainder', ['12:01:00:15', '00:59:30:15', 30], '13:00:31:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:00:59:12', '00:01:01:12', 25], '00:02:00:24'), ('normal control', ['23:01:30:12', '23:00:59:00', 24], '22:02:29:12'), ('normal control', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14')], [('regression: frame remainder', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('regression variant: frame remainder', ['00:00:30:12', '23:30:01:24', 25], '23:30:32:11'), ('partial repair probe: frame remainder', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('partial repair variant: frame remainder', ['01:01:30:24', '01:59:00:01', 25], '03:00:31:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01'), ('normal control', ['12:01:01:15', '12:01:00:00', 30], '00:02:01:15'), ('normal control', ['00:00:01:24', '23:01:59:00', 25], '23:02:00:24')], [('regression: frame remainder', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('regression variant: frame remainder', ['01:30:01:24', '23:30:00:01', 25], '01:00:02:00'), ('partial repair probe: frame remainder', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('partial repair variant: frame remainder', ['12:01:30:29', '01:30:30:01', 30], '13:32:01:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['01:59:01:01', '00:59:01:12', 24], '02:58:02:13'), ('normal control', ['23:30:00:00', '23:01:30:00', 24], '22:31:30:00'), ('normal control', ['00:59:01:00', '12:00:01:23', 24], '12:59:02:23')], [('regression: frame remainder', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('regression variant: frame remainder', ['00:01:30:23', '00:59:30:12', 24], '01:01:01:11'), ('partial repair probe: frame remainder', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: frame remainder', ['12:01:30:01', '01:01:01:29', 30], '13:02:32:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:30:59:00', '12:59:01:15', 30], '13:30:00:15'), ('normal control', ['23:59:59:01', '23:01:01:00', 24], '23:01:00:01'), ('normal control', ['01:59:00:23', '23:01:01:00', 24], '01:00:01:23')]]\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":"4a1942671e71eaea5d38902f743489f1093461d25a68296c57e93216a56f189d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(a, b, fps):\n    x=[int(v) for v in a.split(':')]\n    y=[int(v) for v in b.split(':')]\n    f=x[3]+y[3]\n    c=f//fps\n    f%=fps\n    s=x[2]+y[2]+c\n    c=s//60\n    s%=60\n    m=x[1]+y[1]+c\n    c=m//60\n    m%=60\n    h=(x[0]+y[0]+c)%24\n    return '%02d:%02d:%02d:%02d'%(h,m,s,f)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: frame remainder', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('regression variant: frame remainder', ['23:30:59:12', '12:59:30:12', 24], '12:30:30:00'), ('partial repair probe: frame remainder', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('partial repair variant: frame remainder', ['01:30:01:24', '23:30:00:01', 25], '01:00:02:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:59:01:00', '01:00:30:12', 25], '01:59:31:12'), ('normal control', ['00:59:30:00', '00:00:59:01', 30], '01:00:29:01'), ('normal control', ['23:00:01:24', '23:00:00:00', 25], '22:00:01:24')], [('regression: frame remainder', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('regression variant: frame remainder', ['23:01:30:24', '01:00:01:12', 25], '00:01:32:11'), ('partial repair probe: frame remainder', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('partial repair variant: frame remainder', ['12:01:00:15', '00:59:30:15', 30], '13:00:31:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:00:59:12', '00:01:01:12', 25], '00:02:00:24'), ('normal control', ['23:01:30:12', '23:00:59:00', 24], '22:02:29:12'), ('normal control', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14')], [('regression: frame remainder', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('regression variant: frame remainder', ['00:00:30:12', '23:30:01:24', 25], '23:30:32:11'), ('partial repair probe: frame remainder', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('partial repair variant: frame remainder', ['01:01:30:24', '01:59:00:01', 25], '03:00:31:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01'), ('normal control', ['12:01:01:15', '12:01:00:00', 30], '00:02:01:15'), ('normal control', ['00:00:01:24', '23:01:59:00', 25], '23:02:00:24')], [('regression: frame remainder', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('regression variant: frame remainder', ['01:30:01:24', '23:30:00:01', 25], '01:00:02:00'), ('partial repair probe: frame remainder', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('partial repair variant: frame remainder', ['12:01:30:29', '01:30:30:01', 30], '13:32:01:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['01:59:01:01', '00:59:01:12', 24], '02:58:02:13'), ('normal control', ['23:30:00:00', '23:01:30:00', 24], '22:31:30:00'), ('normal control', ['00:59:01:00', '12:00:01:23', 24], '12:59:02:23')], [('regression: frame remainder', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('regression variant: frame remainder', ['00:01:30:23', '00:59:30:12', 24], '01:01:01:11'), ('partial repair probe: frame remainder', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: frame remainder', ['12:01:30:01', '01:01:01:29', 30], '13:02:32:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:30:59:00', '12:59:01:15', 30], '13:30:00:15'), ('normal control', ['23:59:59:01', '23:01:01:00', 24], '23:01:00:01'), ('normal control', ['01:59:00:23', '23:01:01:00', 24], '01:00:01:23')]]\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-fieldwise-addition-frame-remainder","generated_at":"2026-09-29T14:49:35.406617+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":"Reduce the frame field modulo fps.","root_cause":"The frame remainder uses 30 regardless of the rate.","sha256":"dd3a5c196f8ff4c411ca228b85744a570228a9a46add8e02d3a919429a6b8eb1","title":"Field-wise non-drop timecode addition: frame remainder · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.254,"exit_code":1,"observations":[{"actual":"00:00:01:25","check":"regression: frame remainder","expected":"00:00:01:00","passed":false},{"actual":"12:30:30:24","check":"regression variant: frame remainder","expected":"12:30:30:00","passed":false},{"actual":"00:00:00:30","check":"partial repair probe: frame remainder","expected":"00:00:00:00","passed":false},{"actual":"01:00:02:25","check":"partial repair variant: frame remainder","expected":"01:00:02:00","passed":false},{"actual":"00:00:00:00","check":"boundary control","expected":"00:00:00:00","passed":true},{"actual":"01:59:31:12","check":"normal control","expected":"01:59:31:12","passed":true},{"actual":"01:00:29:01","check":"normal control","expected":"01:00:29:01","passed":true},{"actual":"22:00:01:24","check":"normal control","expected":"22:00:01:24","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame remainder\", \"actual\": \"00:00:01:25\", \"expected\": \"00:00:01:00\", \"passed\": false}, {\"check\": \"regression variant: frame remainder\", \"actual\": \"12:30:30:24\", \"expected\": \"12:30:30:00\", \"passed\": false}, {\"check\": \"partial repair probe: frame remainder\", \"actual\": \"00:00:00:30\", \"expected\": \"00:00:00:00\", \"passed\": false}, {\"check\": \"partial repair variant: frame remainder\", \"actual\": \"01:00:02:25\", \"expected\": \"01:00:02:00\", \"passed\": false}, {\"check\": \"boundary control\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:00:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"01:59:31:12\", \"expected\": \"01:59:31:12\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"01:00:29:01\", \"expected\": \"01:00:29:01\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"22:00:01:24\", \"expected\": \"22:00:01:24\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":37.541,"exit_code":1,"observations":[{"actual":"00:00:01:25","check":"regression: frame remainder","expected":"00:00:01:00","passed":false},{"actual":"12:30:30:24","check":"regression variant: frame remainder","expected":"12:30:30:00","passed":false},{"actual":"00:00:00:00","check":"partial repair probe: frame remainder","expected":"00:00:00:00","passed":true},{"actual":"01:00:02:25","check":"partial repair variant: frame remainder","expected":"01:00:02:00","passed":false},{"actual":"00:00:00:00","check":"boundary control","expected":"00:00:00:00","passed":true},{"actual":"01:59:31:12","check":"normal control","expected":"01:59:31:12","passed":true},{"actual":"01:00:29:01","check":"normal control","expected":"01:00:29:01","passed":true},{"actual":"22:00:01:24","check":"normal control","expected":"22:00:01:24","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame remainder\", \"actual\": \"00:00:01:25\", \"expected\": \"00:00:01:00\", \"passed\": false}, {\"check\": \"regression variant: frame remainder\", \"actual\": \"12:30:30:24\", \"expected\": \"12:30:30:00\", \"passed\": false}, {\"check\": \"partial repair probe: frame remainder\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:00:00\", \"passed\": true}, {\"check\": \"partial repair variant: frame remainder\", \"actual\": \"01:00:02:25\", \"expected\": \"01:00:02:00\", \"passed\": false}, {\"check\": \"boundary control\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:00:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"01:59:31:12\", \"expected\": \"01:59:31:12\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"01:00:29:01\", \"expected\": \"01:00:29:01\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"22:00:01:24\", \"expected\": \"22:00:01:24\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.565,"exit_code":0,"observations":[{"actual":"00:00:01:00","check":"regression: frame remainder","expected":"00:00:01:00","passed":true},{"actual":"12:30:30:00","check":"regression variant: frame remainder","expected":"12:30:30:00","passed":true},{"actual":"00:00:00:00","check":"partial repair probe: frame remainder","expected":"00:00:00:00","passed":true},{"actual":"01:00:02:00","check":"partial repair variant: frame remainder","expected":"01:00:02:00","passed":true},{"actual":"00:00:00:00","check":"boundary control","expected":"00:00:00:00","passed":true},{"actual":"01:59:31:12","check":"normal control","expected":"01:59:31:12","passed":true},{"actual":"01:00:29:01","check":"normal control","expected":"01:00:29:01","passed":true},{"actual":"22:00:01:24","check":"normal control","expected":"22:00:01:24","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: frame remainder\", \"actual\": \"00:00:01:00\", \"expected\": \"00:00:01:00\", \"passed\": true}, {\"check\": \"regression variant: frame remainder\", \"actual\": \"12:30:30:00\", \"expected\": \"12:30:30:00\", \"passed\": true}, {\"check\": \"partial repair probe: frame remainder\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:00:00\", \"passed\": true}, {\"check\": \"partial repair variant: frame remainder\", \"actual\": \"01:00:02:00\", \"expected\": \"01:00:02:00\", \"passed\": true}, {\"check\": \"boundary control\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:00:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"01:59:31:12\", \"expected\": \"01:59:31:12\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"01:00:29:01\", \"expected\": \"01:00:29:01\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"22:00:01:24\", \"expected\": \"22:00:01:24\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}