FA-78661 / Broadcast timecode arithmetic / Open access

Programme-relative signed timecode: minute field · case 01

Offsets beyond an hour show minute fields above 59.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Total minutes are printed without reducing modulo 60.

VERIFIED REPAIR

Reduce the minute field modulo 60.

Unsuccessful approach: Dividing the in-hour remainder by 60 forgets to divide by fps.

Case contract

Express label tc relative to programme start as "+HH:MM:SS:FF" or "-HH:MM:SS:FF" along the shorter way round the 24-hour clock (an offset of exactly 12 hours is negative). Zero is "+".

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(tc, start, fps):
    def fr(t):
        h,m,s,f=map(int,t.split(':'))
        return ((h*60+m)*60+s)*fps+f
    day=86400*fps
    d=(fr(tc)-fr(start))%day
    if d>=day//2:
        d-=day
    sign='-' if d<0 else '+'
    a=abs(d)
    return '%s%02d:%02d:%02d:%02d'%(sign,a//(3600*fps),a//(60*fps),a//fps%60,a%fps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: minute field', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('regression variant: minute field', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('partial repair probe: minute field', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('partial repair variant: minute field', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00')], [('regression: minute field', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('regression variant: minute field', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('partial repair probe: minute field', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: minute field', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29'), ('normal control', ['01:00:00:01', '01:00:00:00', 30], '+00:00:00:01'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00')], [('regression: minute field', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('regression variant: minute field', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('partial repair probe: minute field', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: minute field', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29')], [('regression: minute field', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('regression variant: minute field', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('partial repair probe: minute field', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: minute field', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:01', '01:00:00:00', 25], '+00:00:00:01'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('normal control', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00')], [('regression: minute field', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('regression variant: minute field', ['00:00:00:00', '01:00:00:00', 30], '-01:00:00:00'), ('partial repair probe: minute field', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: minute field', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29'), ('normal control', ['01:00:00:01', '01:00:00:00', 25], '+00:00:00:01')]]
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 field	`+02:120:59:29`	`+02:00:59:29`	Failed
regression variant: minute field	`-08:539:59:24`	`-08:59:59:24`	Failed
partial repair probe: minute field	`-00:00:20:00`	`-00:00:20:00`	Passed
partial repair variant: minute field	`-00:59:10:15`	`-00:59:10:15`	Passed
boundary control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed

SHA-256 / 66f376b2ec0598f5d0b8ac498d6c5545eeb0928898da6be892b9c564575a5ba4

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(tc, start, fps):
    def fr(t):
        h,m,s,f=map(int,t.split(':'))
        return ((h*60+m)*60+s)*fps+f
    day=86400*fps
    d=(fr(tc)-fr(start))%day
    if d>=day//2:
        d-=day
    sign='-' if d<0 else '+'
    a=abs(d)
    return '%s%02d:%02d:%02d:%02d'%(sign,a//(3600*fps),a%(3600*fps)//60,a//fps%60,a%fps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: minute field', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('regression variant: minute field', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('partial repair probe: minute field', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('partial repair variant: minute field', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00')], [('regression: minute field', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('regression variant: minute field', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('partial repair probe: minute field', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: minute field', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29'), ('normal control', ['01:00:00:01', '01:00:00:00', 30], '+00:00:00:01'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00')], [('regression: minute field', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('regression variant: minute field', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('partial repair probe: minute field', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: minute field', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29')], [('regression: minute field', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('regression variant: minute field', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('partial repair probe: minute field', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: minute field', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:01', '01:00:00:00', 25], '+00:00:00:01'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('normal control', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00')], [('regression: minute field', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('regression variant: minute field', ['00:00:00:00', '01:00:00:00', 30], '-01:00:00:00'), ('partial repair probe: minute field', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: minute field', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29'), ('normal control', ['01:00:00:01', '01:00:00:00', 25], '+00:00:00:01')]]
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 field	`+02:29:59:29`	`+02:00:59:29`	Failed
regression variant: minute field	`-08:1499:59:24`	`-08:59:59:24`	Failed
partial repair probe: minute field	`-00:08:20:00`	`-00:00:20:00`	Failed
partial repair variant: minute field	`-00:1775:10:15`	`-00:59:10:15`	Failed
boundary control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed

SHA-256 / 7ccee4be5ea845b6ff3ec4b3666b6cb4f8a78c60c700552eb95466e643294796

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(tc, start, fps):
    def fr(t):
        h,m,s,f=map(int,t.split(':'))
        return ((h*60+m)*60+s)*fps+f
    day=86400*fps
    d=(fr(tc)-fr(start))%day
    if d>=day//2:
        d-=day
    sign='-' if d<0 else '+'
    a=abs(d)
    return '%s%02d:%02d:%02d:%02d'%(sign,a//(3600*fps),a//(60*fps)%60,a//fps%60,a%fps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: minute field', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('regression variant: minute field', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('partial repair probe: minute field', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('partial repair variant: minute field', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00')], [('regression: minute field', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('regression variant: minute field', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('partial repair probe: minute field', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: minute field', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29'), ('normal control', ['01:00:00:01', '01:00:00:00', 30], '+00:00:00:01'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00')], [('regression: minute field', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('regression variant: minute field', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('partial repair probe: minute field', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: minute field', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('normal control', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29')], [('regression: minute field', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('regression variant: minute field', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('partial repair probe: minute field', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: minute field', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:00:00:01', '01:00:00:00', 25], '+00:00:00:01'), ('normal control', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('normal control', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00')], [('regression: minute field', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('regression variant: minute field', ['00:00:00:00', '01:00:00:00', 30], '-01:00:00:00'), ('partial repair probe: minute field', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: minute field', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('normal control', ['01:00:00:29', '01:00:00:00', 30], '+00:00:00:29'), ('normal control', ['01:00:00:01', '01:00:00:00', 25], '+00:00:00:01')]]
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 field	`+02:00:59:29`	`+02:00:59:29`	Passed
regression variant: minute field	`-08:59:59:24`	`-08:59:59:24`	Passed
partial repair probe: minute field	`-00:00:20:00`	`-00:00:20:00`	Passed
partial repair variant: minute field	`-00:59:10:15`	`-00:59:10:15`	Passed
boundary control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+00:00:00:00`	`+00:00:00:00`	Passed

SHA-256 / b8dd8620948d5766da0069b7a282e20656f37ddae35dbe165a282c7300dcd440

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 2026-09-29T14:49:37.333076+00:00.

Case digest / 3bdb2ca9b4976c3b42563b88aa7bbf8709b1db6758604d232fc0650659cca866