FA-78481 / Broadcast timecode arithmetic / Open access
Field-wise non-drop timecode addition: minute carry source · case 01
Minute overflow never reaches the hour field.
ROOT CAUSE
The minute carry is computed from the already reduced seconds field.
VERIFIED REPAIR
Derive the hour carry from the minute sum.
Unsuccessful approach: A strict greater-than test misses a minute sum of exactly 60.
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
c=s//60
s%=60
m=x[1]+y[1]+c
c=s//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: minute carry source', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('regression variant: minute carry source', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair probe: minute carry source', ['23:30:00:15', '23:30:01:00', 30], '23:00:01:15'), ('partial repair variant: minute carry source', ['12:01:00:15', '00:59:30:15', 30], '13:00:31:00'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('normal 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', ['23:00:01:24', '23:00:00:00', 25], '22:00:01:24')], [('regression: minute carry source', ['00:59:30:00', '00:00:59:01', 30], '01:00:29:01'), ('regression variant: minute carry source', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair probe: minute carry source', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('partial repair variant: minute carry source', ['01:01:30:24', '01:59:00:01', 25], '03:00:31:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:01:59:24', '23:01:30:00', 25], '23:03:29:24'), ('normal control', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14'), ('normal control', ['12:59:00:29', '00:00:00:15', 30], '12:59:01:14')], [('regression: minute carry source', ['01:30:30:00', '12:59:01:01', 24], '14:29:31:01'), ('regression variant: minute carry source', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('partial repair probe: minute carry source', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: minute carry source', ['01:59:01:12', '12:01:01:01', 25], '14:00:02:13'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('normal control', ['00:00:01:24', '23:01:59:00', 25], '23:02:00:24'), ('normal control', ['00:30:00:15', '23:01:59:15', 30], '23:32:00:00'), ('normal control', ['23:01:30:24', '01:00:01:12', 25], '00:01:32:11')], [('regression: minute carry source', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('regression variant: minute carry source', ['01:30:01:01', '00:30:59:01', 30], '02:01:00:02'), ('partial repair probe: minute carry source', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: minute carry source', ['01:59:00:23', '23:01:01:00', 24], '01:00:01:23'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('normal control', ['01:01:59:23', '01:00:01:00', 24], '02:02:00:23'), ('normal control', ['12:01:00:00', '23:00:00:12', 25], '11:01:00:12'), ('normal control', ['00:00:01:00', '01:01:30:00', 24], '01:01:31:00')], [('regression: minute carry source', ['23:30:00:15', '23:30:01:00', 30], '23:00:01:15'), ('regression variant: minute carry source', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01'), ('partial repair probe: minute carry source', ['23:59:30:00', '23:01:01:12', 24], '23:00:31:12'), ('partial repair variant: minute carry source', ['23:59:01:00', '00:00:59:24', 25], '00:00:00:24'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['12:01:30:29', '01:30:30:01', 30], '13:32:01:00'), ('normal control', ['12:30:30:15', '00:00:30:15', 30], '12:31:01:00'), ('normal control', ['23:01:59:23', '12:00:59:01', 24], '11:02:59:00')]]
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: minute carry source | 23:00:00:00 | 00:00:00:00 | Failed |
| regression variant: minute carry source | 23:30:00:14 | 00:30:00:14 | Failed |
| partial repair probe: minute carry source | 22:00:01:15 | 23:00:01:15 | Failed |
| partial repair variant: minute carry source | 12:00:31:00 | 13:00:31:00 | Failed |
| boundary control | 00:00:01:00 | 00:00:01:00 | Passed |
| boundary control | 00:01:00:00 | 00:01:00:00 | Passed |
| normal control | 00:00:00:00 | 00:00:00:00 | Passed |
| normal control | 01:59:31:12 | 01:59:31:12 | Passed |
| normal control | 22:00:01:24 | 22:00:01:24 | Passed |
SHA-256 / 6e9bed4d0061940496aa9ad749e0859f1c7c6a9647dd697ee2fb4add24b5add8
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]+c
c=s//60
s%=60
m=x[1]+y[1]+c
c=int(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: minute carry source', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('regression variant: minute carry source', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair probe: minute carry source', ['23:30:00:15', '23:30:01:00', 30], '23:00:01:15'), ('partial repair variant: minute carry source', ['12:01:00:15', '00:59:30:15', 30], '13:00:31:00'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('normal 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', ['23:00:01:24', '23:00:00:00', 25], '22:00:01:24')], [('regression: minute carry source', ['00:59:30:00', '00:00:59:01', 30], '01:00:29:01'), ('regression variant: minute carry source', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair probe: minute carry source', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('partial repair variant: minute carry source', ['01:01:30:24', '01:59:00:01', 25], '03:00:31:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:01:59:24', '23:01:30:00', 25], '23:03:29:24'), ('normal control', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14'), ('normal control', ['12:59:00:29', '00:00:00:15', 30], '12:59:01:14')], [('regression: minute carry source', ['01:30:30:00', '12:59:01:01', 24], '14:29:31:01'), ('regression variant: minute carry source', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('partial repair probe: minute carry source', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: minute carry source', ['01:59:01:12', '12:01:01:01', 25], '14:00:02:13'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('normal control', ['00:00:01:24', '23:01:59:00', 25], '23:02:00:24'), ('normal control', ['00:30:00:15', '23:01:59:15', 30], '23:32:00:00'), ('normal control', ['23:01:30:24', '01:00:01:12', 25], '00:01:32:11')], [('regression: minute carry source', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('regression variant: minute carry source', ['01:30:01:01', '00:30:59:01', 30], '02:01:00:02'), ('partial repair probe: minute carry source', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: minute carry source', ['01:59:00:23', '23:01:01:00', 24], '01:00:01:23'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('normal control', ['01:01:59:23', '01:00:01:00', 24], '02:02:00:23'), ('normal control', ['12:01:00:00', '23:00:00:12', 25], '11:01:00:12'), ('normal control', ['00:00:01:00', '01:01:30:00', 24], '01:01:31:00')], [('regression: minute carry source', ['23:30:00:15', '23:30:01:00', 30], '23:00:01:15'), ('regression variant: minute carry source', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01'), ('partial repair probe: minute carry source', ['23:59:30:00', '23:01:01:12', 24], '23:00:31:12'), ('partial repair variant: minute carry source', ['23:59:01:00', '00:00:59:24', 25], '00:00:00:24'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['12:01:30:29', '01:30:30:01', 30], '13:32:01:00'), ('normal control', ['12:30:30:15', '00:00:30:15', 30], '12:31:01:00'), ('normal control', ['23:01:59:23', '12:00:59:01', 24], '11:02:59:00')]]
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: minute carry source | 23:00:00:00 | 00:00:00:00 | Failed |
| regression variant: minute carry source | 00:30:00:14 | 00:30:00:14 | Passed |
| partial repair probe: minute carry source | 22:00:01:15 | 23:00:01:15 | Failed |
| partial repair variant: minute carry source | 12:00:31:00 | 13:00:31:00 | Failed |
| boundary control | 00:00:01:00 | 00:00:01:00 | Passed |
| boundary control | 00:01:00:00 | 00:01:00:00 | Passed |
| normal control | 00:00:00:00 | 00:00:00:00 | Passed |
| normal control | 01:59:31:12 | 01:59:31:12 | Passed |
| normal control | 22:00:01:24 | 22:00:01:24 | Passed |
SHA-256 / c5ce9c5d20e342244339ede89800c3f735f2865e23ea88e4a025fd89c924ecf0
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: minute carry source', ['23:59:59:29', '00:00:00:01', 30], '00:00:00:00'), ('regression variant: minute carry source', ['00:59:59:15', '23:30:00:29', 30], '00:30:00:14'), ('partial repair probe: minute carry source', ['23:30:00:15', '23:30:01:00', 30], '23:00:01:15'), ('partial repair variant: minute carry source', ['12:01:00:15', '00:59:30:15', 30], '13:00:31:00'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('normal 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', ['23:00:01:24', '23:00:00:00', 25], '22:00:01:24')], [('regression: minute carry source', ['00:59:30:00', '00:00:59:01', 30], '01:00:29:01'), ('regression variant: minute carry source', ['12:00:59:12', '00:59:59:24', 25], '13:00:59:11'), ('partial repair probe: minute carry source', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('partial repair variant: minute carry source', ['01:01:30:24', '01:59:00:01', 25], '03:00:31:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['00:01:59:24', '23:01:30:00', 25], '23:03:29:24'), ('normal control', ['01:00:00:29', '00:30:00:15', 30], '01:30:01:14'), ('normal control', ['12:59:00:29', '00:00:00:15', 30], '12:59:01:14')], [('regression: minute carry source', ['01:30:30:00', '12:59:01:01', 24], '14:29:31:01'), ('regression variant: minute carry source', ['01:59:30:24', '12:01:00:00', 25], '14:00:30:24'), ('partial repair probe: minute carry source', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: minute carry source', ['01:59:01:12', '12:01:01:01', 25], '14:00:02:13'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('normal control', ['00:00:01:24', '23:01:59:00', 25], '23:02:00:24'), ('normal control', ['00:30:00:15', '23:01:59:15', 30], '23:32:00:00'), ('normal control', ['23:01:30:24', '01:00:01:12', 25], '00:01:32:11')], [('regression: minute carry source', ['01:30:30:15', '01:59:30:15', 30], '03:30:01:00'), ('regression variant: minute carry source', ['01:30:01:01', '00:30:59:01', 30], '02:01:00:02'), ('partial repair probe: minute carry source', ['01:01:00:15', '01:59:00:15', 30], '03:00:01:00'), ('partial repair variant: minute carry source', ['01:59:00:23', '23:01:01:00', 24], '01:00:01:23'), ('boundary control', ['00:00:00:12', '00:00:00:13', 25], '00:00:01:00'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('normal control', ['01:01:59:23', '01:00:01:00', 24], '02:02:00:23'), ('normal control', ['12:01:00:00', '23:00:00:12', 25], '11:01:00:12'), ('normal control', ['00:00:01:00', '01:01:30:00', 24], '01:01:31:00')], [('regression: minute carry source', ['23:30:00:15', '23:30:01:00', 30], '23:00:01:15'), ('regression variant: minute carry source', ['00:59:59:01', '23:01:59:00', 25], '00:01:58:01'), ('partial repair probe: minute carry source', ['23:59:30:00', '23:01:01:12', 24], '23:00:31:12'), ('partial repair variant: minute carry source', ['23:59:01:00', '00:00:59:24', 25], '00:00:00:24'), ('boundary control', ['00:00:59:24', '00:00:00:01', 25], '00:01:00:00'), ('boundary control', ['00:00:00:00', '00:00:00:00', 24], '00:00:00:00'), ('normal control', ['12:01:30:29', '01:30:30:01', 30], '13:32:01:00'), ('normal control', ['12:30:30:15', '00:00:30:15', 30], '12:31:01:00'), ('normal control', ['23:01:59:23', '12:00:59:01', 24], '11:02:59:00')]]
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: minute carry source | 00:00:00:00 | 00:00:00:00 | Passed |
| regression variant: minute carry source | 00:30:00:14 | 00:30:00:14 | Passed |
| partial repair probe: minute carry source | 23:00:01:15 | 23:00:01:15 | Passed |
| partial repair variant: minute carry source | 13:00:31:00 | 13:00:31:00 | Passed |
| boundary control | 00:00:01:00 | 00:00:01:00 | Passed |
| boundary control | 00:01:00:00 | 00:01:00:00 | Passed |
| normal control | 00:00:00:00 | 00:00:00:00 | Passed |
| normal control | 01:59:31:12 | 01:59:31:12 | Passed |
| normal control | 22:00:01:24 | 22:00:01:24 | Passed |
SHA-256 / cdb1d6ad8d6eb40e4de4f0e7c88f4afbd46d053ddba91ed5597f7efedb91c6d1
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 2026-09-29T14:49:35.707677+00:00.
Case digest / c9fcdefa62f8b02ece975eba351b612790b7fd247c231edbff00f73324067e1f