FA-78476 / Broadcast timecode arithmetic / Open access
Field-wise non-drop timecode addition: seconds carry-in · case 01
Sums whose frames overflow lose a whole second.
ROOT CAUSE
The frame carry is not added into the seconds.
VERIFIED REPAIR
Add the frame carry into the seconds sum.
Unsuccessful approach: Recomputing the carry from the already reduced frame field always yields zero.
Case 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.
Why this case matters
Timecode arithmetic errors misplace edits, commercial breaks and captions against the broadcast clock.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(a, b, fps):
x=[int(v) for v in a.split(':')]
y=[int(v) for v in b.split(':')]
f=x[3]+y[3]
c=f//fps
f%=fps
s=x[2]+y[2]
c=s//60
s%=60
m=x[1]+y[1]+c
c=m//60
m%=60
h=(x[0]+y[0]+c)%24
return '%02d:%02d:%02d:%02d'%(h,m,s,f)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('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')]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: seconds carry-in | 00:00:00:00 | 00:00:01:00 | Failed |
| regression variant: seconds carry-in | 00:29:59:14 | 00:30:00:14 | Failed |
| partial repair probe: seconds carry-in | 23:59:59:00 | 00:00:00:00 | Failed |
| partial repair variant: seconds carry-in | 01:58:31:00 | 01:58:32:00 | Failed |
| boundary control | 00:00:00:00 | 00:00:00:00 | Passed |
| normal control | 01:59:31:12 | 01:59:31:12 | Passed |
| normal control | 01:00:29:01 | 01:00:29:01 | Passed |
| normal control | 22:00:01:24 | 22:00:01:24 | Passed |
SHA-256 / ced26ac873e36e0d0aae6601ede31668fefa1ef5e463cc30b5f7a8b941a29f75
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(a, b, fps):
x=[int(v) for v in a.split(':')]
y=[int(v) for v in b.split(':')]
f=x[3]+y[3]
c=f//fps
f%=fps
s=x[2]+y[2]+f//fps
c=s//60
s%=60
m=x[1]+y[1]+c
c=m//60
m%=60
h=(x[0]+y[0]+c)%24
return '%02d:%02d:%02d:%02d'%(h,m,s,f)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('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')]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: seconds carry-in | 00:00:00:00 | 00:00:01:00 | Failed |
| regression variant: seconds carry-in | 00:29:59:14 | 00:30:00:14 | Failed |
| partial repair probe: seconds carry-in | 23:59:59:00 | 00:00:00:00 | Failed |
| partial repair variant: seconds carry-in | 01:58:31:00 | 01:58:32:00 | Failed |
| boundary control | 00:00:00:00 | 00:00:00:00 | Passed |
| normal control | 01:59:31:12 | 01:59:31:12 | Passed |
| normal control | 01:00:29:01 | 01:00:29:01 | Passed |
| normal control | 22:00:01:24 | 22:00:01:24 | Passed |
SHA-256 / 1ecfd2d7c69192746d89c993b5e9532bff3ff26a28943e37032dd6e2273f7c8b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(a, b, fps):
x=[int(v) for v in a.split(':')]
y=[int(v) for v in b.split(':')]
f=x[3]+y[3]
c=f//fps
f%=fps
s=x[2]+y[2]+c
c=s//60
s%=60
m=x[1]+y[1]+c
c=m//60
m%=60
h=(x[0]+y[0]+c)%24
return '%02d:%02d:%02d:%02d'%(h,m,s,f)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('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')]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: seconds carry-in | 00:00:01:00 | 00:00:01:00 | Passed |
| regression variant: seconds carry-in | 00:30:00:14 | 00:30:00:14 | Passed |
| partial repair probe: seconds carry-in | 00:00:00:00 | 00:00:00:00 | Passed |
| partial repair variant: seconds carry-in | 01:58:32:00 | 01:58:32:00 | Passed |
| boundary control | 00:00:00:00 | 00:00:00:00 | Passed |
| normal control | 01:59:31:12 | 01:59:31:12 | Passed |
| normal control | 01:00:29:01 | 01:00:29:01 | Passed |
| normal control | 22:00:01:24 | 22:00:01:24 | Passed |
SHA-256 / 493314532526e9b6d41d6b55541f675c0844e86d0d071a2e620ba1f697d2bc8c
Verification & scope
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.
Observations recorded using Python 3.12.14 at 2026-09-29T14:49:35.664919+00:00.
Case digest / d21e6208f6380144dbc80f5b0c12f784f3a0e9fadce4698f4c756589659e2074