FA-78656 / Broadcast timecode arithmetic / Open access

Programme-relative signed timecode: magnitude for fields · case 01

Negative offsets are printed with garbled fields.

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

ROOT CAUSE

Negative offsets are split into fields without taking the magnitude.

VERIFIED REPAIR

Split the absolute offset into fields.

Unsuccessful approach: Wrapping the negative offset prints the complementary positive time.

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=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: magnitude for fields', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('regression variant: magnitude for fields', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('partial repair probe: magnitude for fields', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('partial repair variant: magnitude for fields', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('normal control', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('normal control', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01')], [('regression: magnitude for fields', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('regression variant: magnitude for fields', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('partial repair probe: magnitude for fields', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('partial repair variant: magnitude for fields', ['00:01:00:00', '01:00:00:00', 25], '-00:59:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('normal control', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('normal control', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('normal control', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00')], [('regression: magnitude for fields', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('regression variant: magnitude for fields', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('partial repair probe: magnitude for fields', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('partial repair variant: magnitude for fields', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('normal control', ['01:00:00:00', '23:59:00:00', 30], '+01:01:00:00'), ('normal control', ['10:29:59:24', '00:00:10:00', 25], '+10:29:49:24')], [('regression: magnitude for fields', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('regression variant: magnitude for fields', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('partial repair probe: magnitude for fields', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('partial repair variant: magnitude for fields', ['12:59:59:24', '00:00:10:00', 30], '-11:00:10:06'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('normal control', ['01:00:30:01', '23:59:00:00', 25], '+01:01:30:01'), ('normal control', ['10:59:30:15', '10:00:00:00', 30], '+00:59:30:15'), ('normal control', ['10:00:30:00', '01:00:00:00', 25], '+09:00:30:00')], [('regression: magnitude for fields', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('regression variant: magnitude for fields', ['00:00:00:00', '01:00:00:00', 30], '-01:00:00:00'), ('partial repair probe: magnitude for fields', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('partial repair variant: magnitude for fields', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['10:29:30:01', '01:00:00:00', 25], '+09:29:30:01'), ('normal control', ['11:59:59:00', '01:00:00:00', 30], '+10:59:59:00'), ('normal control', ['10:01:59:01', '23:59:00:00', 30], '+10:02:59:01')]]
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: magnitude for fields	`--1:59:30:00`	`-00:00:30:00`	Failed
regression variant: magnitude for fields	`--1:00:49:15`	`-00:59:10:15`	Failed
partial repair probe: magnitude for fields	`--11:00:59:24`	`-10:59:00:01`	Failed
partial repair variant: magnitude for fields	`--2:59:59:15`	`-01:00:00:15`	Failed
boundary control	`+00:02:00:00`	`+00:02:00:00`	Passed
boundary control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+02:00:59:29`	`+02:00:59:29`	Passed
normal control	`+00:59:20:00`	`+00:59:20:00`	Passed
normal control	`+00:01:01:01`	`+00:01:01:01`	Passed

SHA-256 / 2b12b19d0b525ad624b1a03863a857e0174c0d181301fb66d4d1416fecdf2827

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=d%day
    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: magnitude for fields', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('regression variant: magnitude for fields', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('partial repair probe: magnitude for fields', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('partial repair variant: magnitude for fields', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('normal control', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('normal control', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01')], [('regression: magnitude for fields', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('regression variant: magnitude for fields', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('partial repair probe: magnitude for fields', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('partial repair variant: magnitude for fields', ['00:01:00:00', '01:00:00:00', 25], '-00:59:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('normal control', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('normal control', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('normal control', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00')], [('regression: magnitude for fields', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('regression variant: magnitude for fields', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('partial repair probe: magnitude for fields', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('partial repair variant: magnitude for fields', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('normal control', ['01:00:00:00', '23:59:00:00', 30], '+01:01:00:00'), ('normal control', ['10:29:59:24', '00:00:10:00', 25], '+10:29:49:24')], [('regression: magnitude for fields', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('regression variant: magnitude for fields', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('partial repair probe: magnitude for fields', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('partial repair variant: magnitude for fields', ['12:59:59:24', '00:00:10:00', 30], '-11:00:10:06'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('normal control', ['01:00:30:01', '23:59:00:00', 25], '+01:01:30:01'), ('normal control', ['10:59:30:15', '10:00:00:00', 30], '+00:59:30:15'), ('normal control', ['10:00:30:00', '01:00:00:00', 25], '+09:00:30:00')], [('regression: magnitude for fields', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('regression variant: magnitude for fields', ['00:00:00:00', '01:00:00:00', 30], '-01:00:00:00'), ('partial repair probe: magnitude for fields', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('partial repair variant: magnitude for fields', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['10:29:30:01', '01:00:00:00', 25], '+09:29:30:01'), ('normal control', ['11:59:59:00', '01:00:00:00', 30], '+10:59:59:00'), ('normal control', ['10:01:59:01', '23:59:00:00', 30], '+10:02:59:01')]]
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: magnitude for fields	`-23:59:30:00`	`-00:00:30:00`	Failed
regression variant: magnitude for fields	`-23:00:49:15`	`-00:59:10:15`	Failed
partial repair probe: magnitude for fields	`-13:00:59:24`	`-10:59:00:01`	Failed
partial repair variant: magnitude for fields	`-22:59:59:15`	`-01:00:00:15`	Failed
boundary control	`+00:02:00:00`	`+00:02:00:00`	Passed
boundary control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+02:00:59:29`	`+02:00:59:29`	Passed
normal control	`+00:59:20:00`	`+00:59:20:00`	Passed
normal control	`+00:01:01:01`	`+00:01:01:01`	Passed

SHA-256 / 9f48b0354e71099a45e5ceca937bd34494228169bc6c82b6b17ae005ad31e933

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: magnitude for fields', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('regression variant: magnitude for fields', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('partial repair probe: magnitude for fields', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('partial repair variant: magnitude for fields', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('normal control', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('normal control', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01')], [('regression: magnitude for fields', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('regression variant: magnitude for fields', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('partial repair probe: magnitude for fields', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('partial repair variant: magnitude for fields', ['00:01:00:00', '01:00:00:00', 25], '-00:59:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('normal control', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('normal control', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('normal control', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00')], [('regression: magnitude for fields', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('regression variant: magnitude for fields', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('partial repair probe: magnitude for fields', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15'), ('partial repair variant: magnitude for fields', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('normal control', ['01:00:00:00', '23:59:00:00', 30], '+01:01:00:00'), ('normal control', ['10:29:59:24', '00:00:10:00', 25], '+10:29:49:24')], [('regression: magnitude for fields', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('regression variant: magnitude for fields', ['01:00:00:01', '10:00:00:00', 25], '-08:59:59:24'), ('partial repair probe: magnitude for fields', ['00:00:00:00', '00:00:10:00', 25], '-00:00:10:00'), ('partial repair variant: magnitude for fields', ['12:59:59:24', '00:00:10:00', 30], '-11:00:10:06'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('normal control', ['01:00:30:01', '23:59:00:00', 25], '+01:01:30:01'), ('normal control', ['10:59:30:15', '10:00:00:00', 30], '+00:59:30:15'), ('normal control', ['10:00:30:00', '01:00:00:00', 25], '+09:00:30:00')], [('regression: magnitude for fields', ['01:00:01:01', '10:00:00:00', 30], '-08:59:58:29'), ('regression variant: magnitude for fields', ['00:00:00:00', '01:00:00:00', 30], '-01:00:00:00'), ('partial repair probe: magnitude for fields', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('partial repair variant: magnitude for fields', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('boundary control', ['00:01:00:00', '23:59:00:00', 25], '+00:02:00:00'), ('boundary control', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('normal control', ['10:29:30:01', '01:00:00:00', 25], '+09:29:30:01'), ('normal control', ['11:59:59:00', '01:00:00:00', 30], '+10:59:59:00'), ('normal control', ['10:01:59:01', '23:59:00:00', 30], '+10:02:59:01')]]
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: magnitude for fields	`-00:00:30:00`	`-00:00:30:00`	Passed
regression variant: magnitude for fields	`-00:59:10:15`	`-00:59:10:15`	Passed
partial repair probe: magnitude for fields	`-10:59:00:01`	`-10:59:00:01`	Passed
partial repair variant: magnitude for fields	`-01:00:00:15`	`-01:00:00:15`	Passed
boundary control	`+00:02:00:00`	`+00:02:00:00`	Passed
boundary control	`+00:00:00:00`	`+00:00:00:00`	Passed
normal control	`+02:00:59:29`	`+02:00:59:29`	Passed
normal control	`+00:59:20:00`	`+00:59:20:00`	Passed
normal control	`+00:01:01:01`	`+00:01:01:01`	Passed

SHA-256 / 7c903c05d455e8263634fb7161d97100f309125c1d89622efe8e3f68256201e0

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 2026-09-29T14:49:37.338049+00:00.

Case digest / 3eb308c21e96bf042cc9200a05ec477250f178df8ec6f209011a1dd56800e7de