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FA-78651 / Broadcast timecode arithmetic / Open access

Programme-relative signed timecode: zero sign · case 01

The programme start itself is labelled -00:00:00:00.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Zero is treated as negative.

VERIFIED REPAIR

Use "+" for zero and positive offsets.

Unsuccessful approach: Omitting the plus sign breaks the fixed signed format.

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)%60,a//fps%60,a%fps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: zero sign', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('normal control', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('normal control', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15')], [('regression: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['23:59:00:00', '23:59:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: zero sign', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('normal control', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('normal control', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00')], [('regression: zero sign', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['10:00:00:00', '10:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('normal control', ['23:01:59:12', '10:00:00:00', 25], '-10:58:00:13'), ('normal control', ['00:01:00:00', '01:00:00:00', 30], '-00:59:00:00')], [('regression: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: zero sign', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:59:01:00', '10:00:00:00', 25], '-09:00:59:00'), ('normal control', ['13:00:00:00', '23:59:00:00', 30], '-10:59:00:00'), ('normal control', ['00:01:00:01', '10:00:00:00', 25], '-09:58:59:24')], [('regression: zero sign', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('partial repair variant: zero sign', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['23:59:50:00', '01:00:00:00', 30], '-01:00:10:00'), ('normal control', ['23:01:01:12', '00:00:10:00', 25], '-00:59:08:13'), ('normal control', ['23:29:30:15', '00:00:10:00', 30], '-00:30:39:15')]]
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 fixtureActualExpectedOutcome
regression: zero sign-00:00:00:00+00:00:00:00Failed
regression variant: zero sign-00:00:00:00+00:00:00:00Failed
partial repair probe: zero sign+02:00:59:29+02:00:59:29Passed
partial repair variant: zero sign+11:59:59:24+11:59:59:24Passed
boundary control-00:00:30:00-00:00:30:00Passed
boundary control-00:00:20:00-00:00:20:00Passed
normal control-12:00:00:00-12:00:00:00Passed
normal control-10:59:00:01-10:59:00:01Passed
normal control-00:59:10:15-00:59:10:15Passed

SHA-256 / 8c70cff6b8bc685428494d472c5b84bd99454c233ce906c6556f84ec825c3945

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//(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: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: zero sign', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('normal control', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('normal control', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15')], [('regression: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['23:59:00:00', '23:59:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: zero sign', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('normal control', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('normal control', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00')], [('regression: zero sign', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['10:00:00:00', '10:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('normal control', ['23:01:59:12', '10:00:00:00', 25], '-10:58:00:13'), ('normal control', ['00:01:00:00', '01:00:00:00', 30], '-00:59:00:00')], [('regression: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: zero sign', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:59:01:00', '10:00:00:00', 25], '-09:00:59:00'), ('normal control', ['13:00:00:00', '23:59:00:00', 30], '-10:59:00:00'), ('normal control', ['00:01:00:01', '10:00:00:00', 25], '-09:58:59:24')], [('regression: zero sign', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('partial repair variant: zero sign', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['23:59:50:00', '01:00:00:00', 30], '-01:00:10:00'), ('normal control', ['23:01:01:12', '00:00:10:00', 25], '-00:59:08:13'), ('normal control', ['23:29:30:15', '00:00:10:00', 30], '-00:30:39:15')]]
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 fixtureActualExpectedOutcome
regression: zero sign00:00:00:00+00:00:00:00Failed
regression variant: zero sign00:00:00:00+00:00:00:00Failed
partial repair probe: zero sign02:00:59:29+02:00:59:29Failed
partial repair variant: zero sign11:59:59:24+11:59:59:24Failed
boundary control-00:00:30:00-00:00:30:00Passed
boundary control-00:00:20:00-00:00:20:00Passed
normal control-12:00:00:00-12:00:00:00Passed
normal control-10:59:00:01-10:59:00:01Passed
normal control-00:59:10:15-00:59:10:15Passed

SHA-256 / 5834e4d3e68c873b1fdd891cea27634b647b51106a07fca27e58241b079c1329

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: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: zero sign', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('normal control', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('normal control', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15')], [('regression: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['23:59:00:00', '23:59:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: zero sign', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('normal control', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('normal control', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00')], [('regression: zero sign', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['10:00:00:00', '10:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('normal control', ['23:01:59:12', '10:00:00:00', 25], '-10:58:00:13'), ('normal control', ['00:01:00:00', '01:00:00:00', 30], '-00:59:00:00')], [('regression: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: zero sign', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:59:01:00', '10:00:00:00', 25], '-09:00:59:00'), ('normal control', ['13:00:00:00', '23:59:00:00', 30], '-10:59:00:00'), ('normal control', ['00:01:00:01', '10:00:00:00', 25], '-09:58:59:24')], [('regression: zero sign', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('partial repair variant: zero sign', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['23:59:50:00', '01:00:00:00', 30], '-01:00:10:00'), ('normal control', ['23:01:01:12', '00:00:10:00', 25], '-00:59:08:13'), ('normal control', ['23:29:30:15', '00:00:10:00', 30], '-00:30:39:15')]]
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 fixtureActualExpectedOutcome
regression: zero sign+00:00:00:00+00:00:00:00Passed
regression variant: zero sign+00:00:00:00+00:00:00:00Passed
partial repair probe: zero sign+02:00:59:29+02:00:59:29Passed
partial repair variant: zero sign+11:59:59:24+11:59:59:24Passed
boundary control-00:00:30:00-00:00:30:00Passed
boundary control-00:00:20:00-00:00:20:00Passed
normal control-12:00:00:00-12:00:00:00Passed
normal control-10:59:00:01-10:59:00:01Passed
normal control-00:59:10:15-00:59:10:15Passed

SHA-256 / 9fe1520a791c85c6be68c94f236ec49485050a99b89b90e49f8309d9f059bb83

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 2026-09-29T14:49:37.333165+00:00.

Case digest / b52497885cd447faf77b3182013f1d24a1f8a32d16eda10c35bfac2b8f5d1510