{"abstract":"Sums whose frames overflow lose a whole second.","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":"Recomputing the carry from the already reduced frame field always yields zero.","family":"w2-broadcast-timecode-arithmetic-fieldwise-addition-seconds-carry-in","id":"FA-78476","implementations":{"attempt":{"sha256":"1ecfd2d7c69192746d89c993b5e9532bff3ff26a28943e37032dd6e2273f7c8b","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]+f//fps\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: seconds carry-in', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('regression variant: seconds carry-in', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair probe: seconds carry-in', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('partial repair variant: seconds carry-in', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('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: seconds carry-in', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('regression variant: seconds carry-in', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair probe: seconds carry-in', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('partial repair variant: seconds carry-in', ['12:59:00:29', '00:00:00:15', 30], '12:59:01:14'), ('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', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('normal control', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01')], [('regression: seconds carry-in', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('regression variant: seconds carry-in', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14'), ('partial repair probe: seconds carry-in', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('partial repair variant: seconds carry-in', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['12:01:01:15', '12:01:00:00', 30], '00:02:01:15'), ('normal control', ['12:30:01:00', '01:30:59:00', 24], '14:01:00:00'), ('normal control', ['00:00:00:12', '23:00:01:01', 25], '23:00:01:13')], [('regression: seconds carry-in', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('regression variant: seconds carry-in', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('partial repair probe: seconds carry-in', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair variant: seconds carry-in', ['00:30:00:15', '23:01:59:15', 30], '23:32:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['23:30:00:00', '23:01:30:00', 24], '22:31:30:00'), ('normal control', ['00:30:59:00', '12:59:01:15', 30], '13:30:00:15'), ('normal control', ['23:01:59:12', '23:01:30:00', 25], '22:03:29:12')], [('regression: seconds carry-in', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('regression variant: seconds carry-in', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('partial repair probe: seconds carry-in', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair variant: seconds carry-in', ['23:30:59:12', '12:59:30:12', 24], '12:30:30:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['01:59:01:12', '12:01:01:01', 25], '14:00:02:13'), ('normal control', ['23:30:01:12', '00:01:59:12', 25], '23:32:00:24'), ('normal control', ['00:00:01:00', '01:01:30:00', 24], '01:01:31:00')]]\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":"ced26ac873e36e0d0aae6601ede31668fefa1ef5e463cc30b5f7a8b941a29f75","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]\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: seconds carry-in', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('regression variant: seconds carry-in', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair probe: seconds carry-in', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('partial repair variant: seconds carry-in', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('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: seconds carry-in', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('regression variant: seconds carry-in', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair probe: seconds carry-in', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('partial repair variant: seconds carry-in', ['12:59:00:29', '00:00:00:15', 30], '12:59:01:14'), ('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', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('normal control', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01')], [('regression: seconds carry-in', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('regression variant: seconds carry-in', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14'), ('partial repair probe: seconds carry-in', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('partial repair variant: seconds carry-in', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['12:01:01:15', '12:01:00:00', 30], '00:02:01:15'), ('normal control', ['12:30:01:00', '01:30:59:00', 24], '14:01:00:00'), ('normal control', ['00:00:00:12', '23:00:01:01', 25], '23:00:01:13')], [('regression: seconds carry-in', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('regression variant: seconds carry-in', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('partial repair probe: seconds carry-in', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair variant: seconds carry-in', ['00:30:00:15', '23:01:59:15', 30], '23:32:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['23:30:00:00', '23:01:30:00', 24], '22:31:30:00'), ('normal control', ['00:30:59:00', '12:59:01:15', 30], '13:30:00:15'), ('normal control', ['23:01:59:12', '23:01:30:00', 25], '22:03:29:12')], [('regression: seconds carry-in', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('regression variant: seconds carry-in', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('partial repair probe: seconds carry-in', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair variant: seconds carry-in', ['23:30:59:12', '12:59:30:12', 24], '12:30:30:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['01:59:01:12', '12:01:01:01', 25], '14:00:02:13'), ('normal control', ['23:30:01:12', '00:01:59:12', 25], '23:32:00:24'), ('normal control', ['00:00:01:00', '01:01:30:00', 24], '01:01:31:00')]]\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":"493314532526e9b6d41d6b55541f675c0844e86d0d071a2e620ba1f697d2bc8c","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: seconds carry-in', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('regression variant: seconds carry-in', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair probe: seconds carry-in', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('partial repair variant: seconds carry-in', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('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: seconds carry-in', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('regression variant: seconds carry-in', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair probe: seconds carry-in', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('partial repair variant: seconds carry-in', ['12:59:00:29', '00:00:00:15', 30], '12:59:01:14'), ('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', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('normal control', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01')], [('regression: seconds carry-in', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('regression variant: seconds carry-in', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14'), ('partial repair probe: seconds carry-in', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('partial repair variant: seconds carry-in', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['12:01:01:15', '12:01:00:00', 30], '00:02:01:15'), ('normal control', ['12:30:01:00', '01:30:59:00', 24], '14:01:00:00'), ('normal control', ['00:00:00:12', '23:00:01:01', 25], '23:00:01:13')], [('regression: seconds carry-in', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('regression variant: seconds carry-in', ['12:00:30:23', '01:00:30:01', 24], '13:01:01:00'), ('partial repair probe: seconds carry-in', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair variant: seconds carry-in', ['00:30:00:15', '23:01:59:15', 30], '23:32:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['23:30:00:00', '23:01:30:00', 24], '22:31:30:00'), ('normal control', ['00:30:59:00', '12:59:01:15', 30], '13:30:00:15'), ('normal control', ['23:01:59:12', '23:01:30:00', 25], '22:03:29:12')], [('regression: seconds carry-in', ['12:00:00:12', '12:00:01:24', 25], '00:00:02:11'), ('regression variant: seconds carry-in', ['12:59:01:15', '12:59:30:15', 30], '01:58:32:00'), ('partial repair probe: seconds carry-in', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair variant: seconds carry-in', ['23:30:59:12', '12:59:30:12', 24], '12:30:30:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['01:59:01:12', '12:01:01:01', 25], '14:00:02:13'), ('normal control', ['23:30:01:12', '00:01:59:12', 25], '23:32:00:24'), ('normal control', ['00:00:01:00', '01:01:30:00', 24], '01:01:31:00')]]\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-seconds-carry-in","generated_at":"2026-09-29T14:49:35.664919+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":"Add the frame carry into the seconds sum.","root_cause":"The frame carry is not added into the seconds.","sha256":"d21e6208f6380144dbc80f5b0c12f784f3a0e9fadce4698f4c756589659e2074","title":"Field-wise non-drop timecode addition: seconds carry-in · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.633,"exit_code":1,"observations":[{"actual":"00:00:00:00","check":"regression: seconds carry-in","expected":"00:00:01:00","passed":false},{"actual":"00:29:59:14","check":"regression variant: seconds carry-in","expected":"00:30:00:14","passed":false},{"actual":"23:59:59:00","check":"partial repair probe: seconds carry-in","expected":"00:00:00:00","passed":false},{"actual":"01:58:31:00","check":"partial repair variant: seconds carry-in","expected":"01:58:32:00","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: seconds carry-in\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:01:00\", \"passed\": false}, {\"check\": \"regression variant: seconds carry-in\", \"actual\": \"00:29:59:14\", \"expected\": \"00:30:00:14\", \"passed\": false}, {\"check\": \"partial repair probe: seconds carry-in\", \"actual\": \"23:59:59:00\", \"expected\": \"00:00:00:00\", \"passed\": false}, {\"check\": \"partial repair variant: seconds carry-in\", \"actual\": \"01:58:31:00\", \"expected\": \"01:58:32:00\", \"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":40.378,"exit_code":1,"observations":[{"actual":"00:00:00:00","check":"regression: seconds carry-in","expected":"00:00:01:00","passed":false},{"actual":"00:29:59:14","check":"regression variant: seconds carry-in","expected":"00:30:00:14","passed":false},{"actual":"23:59:59:00","check":"partial repair probe: seconds carry-in","expected":"00:00:00:00","passed":false},{"actual":"01:58:31:00","check":"partial repair variant: seconds carry-in","expected":"01:58:32:00","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: seconds carry-in\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:01:00\", \"passed\": false}, {\"check\": \"regression variant: seconds carry-in\", \"actual\": \"00:29:59:14\", \"expected\": \"00:30:00:14\", \"passed\": false}, {\"check\": \"partial repair probe: seconds carry-in\", \"actual\": \"23:59:59:00\", \"expected\": \"00:00:00:00\", \"passed\": false}, {\"check\": \"partial repair variant: seconds carry-in\", \"actual\": \"01:58:31:00\", \"expected\": \"01:58:32:00\", \"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":40.903,"exit_code":0,"observations":[{"actual":"00:00:01:00","check":"regression: seconds carry-in","expected":"00:00:01:00","passed":true},{"actual":"00:30:00:14","check":"regression variant: seconds carry-in","expected":"00:30:00:14","passed":true},{"actual":"00:00:00:00","check":"partial repair probe: seconds carry-in","expected":"00:00:00:00","passed":true},{"actual":"01:58:32:00","check":"partial repair variant: seconds carry-in","expected":"01:58:32:00","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: seconds carry-in\", \"actual\": \"00:00:01:00\", \"expected\": \"00:00:01:00\", \"passed\": true}, {\"check\": \"regression variant: seconds carry-in\", \"actual\": \"00:30:00:14\", \"expected\": \"00:30:00:14\", \"passed\": true}, {\"check\": \"partial repair probe: seconds carry-in\", \"actual\": \"00:00:00:00\", \"expected\": \"00:00:00:00\", \"passed\": true}, {\"check\": \"partial repair variant: seconds carry-in\", \"actual\": \"01:58:32:00\", \"expected\": \"01:58:32:00\", \"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"}