FA-78446 / Broadcast timecode arithmetic / Open access

Drop-frame label increment: second carry · case 01

Labels with a seconds field of 60 appear.

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

ROOT CAUSE

Seconds carry only after exceeding 60.

VERIFIED REPAIR

Carry into the minute when seconds reach 60.

Unsuccessful approach: Carrying at 59 drops the last second of every minute.

Case contract

Given a valid drop-frame label at rate "29.97" (nominal 30, drop 2) or "59.94" (nominal 60, drop 4), return the next label: frames carry into seconds at the nominal rate, seconds into minutes, minutes into hours (wrapping at 24); on entering a new minute not divisible by 10 the first drop labels are skipped.

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
import re
N = 1
observations = []
def solve(tc, rate):
    n=30 if rate=='29.97' else 60
    drop=2 if n==30 else 4
    h,m,s,f=map(int,re.split('[:;]',tc))
    f+=1
    if f==n:
        f=0
        s+=1
        if s>60:
            s=0
            m+=1
            if m==60:
                m=0
                h=(h+1)%24
            if m%10!=0:
                f=drop
    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: second carry', ['00:00:59;29', '29.97'], '00:01:00;02'), ('regression variant: second carry', ['09:10:59;29', '29.97'], '09:11:00;02'), ('partial repair probe: second carry', ['00:00:59;59', '59.94'], '00:01:00;04'), ('partial repair variant: second carry', ['01:10:58;29', '29.97'], '01:10:59;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['01:01:01;02', '29.97'], '01:01:01;03'), ('normal control', ['09:19:58;05', '59.94'], '09:19:58;06'), ('normal control', ['09:19:59;58', '59.94'], '09:19:59;59')], [('regression: second carry', ['00:09:59;29', '29.97'], '00:10:00;00'), ('regression variant: second carry', ['09:00:59;29', '29.97'], '09:01:00;02'), ('partial repair probe: second carry', ['23:59:59;29', '29.97'], '00:00:00;00'), ('partial repair variant: second carry', ['23:09:59;29', '29.97'], '23:10:00;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['01:00:59;02', '29.97'], '01:00:59;03'), ('normal control', ['09:01:01;00', '29.97'], '09:01:01;01'), ('normal control', ['01:29:58;58', '59.94'], '01:29:58;59')], [('regression: second carry', ['00:00:59;59', '59.94'], '00:01:00;04'), ('regression variant: second carry', ['23:59:59;59', '59.94'], '00:00:00;00'), ('partial repair probe: second carry', ['09:01:59;29', '29.97'], '09:02:00;02'), ('partial repair variant: second carry', ['00:59:59;59', '59.94'], '01:00:00;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['23:00:00;00', '59.94'], '23:00:00;01'), ('normal control', ['23:59:59;03', '59.94'], '23:59:59;04'), ('normal control', ['23:01:58;03', '29.97'], '23:01:58;04')], [('regression: second carry', ['23:59:59;29', '29.97'], '00:00:00;00'), ('regression variant: second carry', ['23:09:59;59', '59.94'], '23:10:00;00'), ('partial repair probe: second carry', ['09:10:59;29', '29.97'], '09:11:00;02'), ('partial repair variant: second carry', ['01:00:59;29', '29.97'], '01:01:00;02'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['00:09:01;00', '59.94'], '00:09:01;01'), ('normal control', ['23:19:59;05', '59.94'], '23:19:59;06'), ('normal control', ['09:59:59;30', '59.94'], '09:59:59;31')], [('regression: second carry', ['09:01:59;29', '29.97'], '09:02:00;02'), ('regression variant: second carry', ['23:09:59;29', '29.97'], '23:10:00;00'), ('partial repair probe: second carry', ['09:00:59;29', '29.97'], '09:01:00;02'), ('partial repair variant: second carry', ['01:01:59;59', '59.94'], '01:02:00;04'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['00:10:01;59', '59.94'], '00:10:02;00'), ('normal control', ['23:00:59;58', '59.94'], '23:00:59;59'), ('normal control', ['00:29:58;00', '29.97'], '00:29:58;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: second carry	`00:00:60;00`	`00:01:00;02`	Failed
regression variant: second carry	`09:10:60;00`	`09:11:00;02`	Failed
partial repair probe: second carry	`00:00:60;00`	`00:01:00;04`	Failed
partial repair variant: second carry	`01:10:59;00`	`01:10:59;00`	Passed
boundary control	`00:01:00;03`	`00:01:00;03`	Passed
normal control	`01:01:01;03`	`01:01:01;03`	Passed
normal control	`09:19:58;06`	`09:19:58;06`	Passed
normal control	`09:19:59;59`	`09:19:59;59`	Passed

SHA-256 / ad5bb594e3641512f33e2b2404500edf5a216f6723465ab6d9217ba5b55e8559

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import re
N = 1
observations = []
def solve(tc, rate):
    n=30 if rate=='29.97' else 60
    drop=2 if n==30 else 4
    h,m,s,f=map(int,re.split('[:;]',tc))
    f+=1
    if f==n:
        f=0
        s+=1
        if s==59:
            s=0
            m+=1
            if m==60:
                m=0
                h=(h+1)%24
            if m%10!=0:
                f=drop
    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: second carry', ['00:00:59;29', '29.97'], '00:01:00;02'), ('regression variant: second carry', ['09:10:59;29', '29.97'], '09:11:00;02'), ('partial repair probe: second carry', ['00:00:59;59', '59.94'], '00:01:00;04'), ('partial repair variant: second carry', ['01:10:58;29', '29.97'], '01:10:59;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['01:01:01;02', '29.97'], '01:01:01;03'), ('normal control', ['09:19:58;05', '59.94'], '09:19:58;06'), ('normal control', ['09:19:59;58', '59.94'], '09:19:59;59')], [('regression: second carry', ['00:09:59;29', '29.97'], '00:10:00;00'), ('regression variant: second carry', ['09:00:59;29', '29.97'], '09:01:00;02'), ('partial repair probe: second carry', ['23:59:59;29', '29.97'], '00:00:00;00'), ('partial repair variant: second carry', ['23:09:59;29', '29.97'], '23:10:00;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['01:00:59;02', '29.97'], '01:00:59;03'), ('normal control', ['09:01:01;00', '29.97'], '09:01:01;01'), ('normal control', ['01:29:58;58', '59.94'], '01:29:58;59')], [('regression: second carry', ['00:00:59;59', '59.94'], '00:01:00;04'), ('regression variant: second carry', ['23:59:59;59', '59.94'], '00:00:00;00'), ('partial repair probe: second carry', ['09:01:59;29', '29.97'], '09:02:00;02'), ('partial repair variant: second carry', ['00:59:59;59', '59.94'], '01:00:00;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['23:00:00;00', '59.94'], '23:00:00;01'), ('normal control', ['23:59:59;03', '59.94'], '23:59:59;04'), ('normal control', ['23:01:58;03', '29.97'], '23:01:58;04')], [('regression: second carry', ['23:59:59;29', '29.97'], '00:00:00;00'), ('regression variant: second carry', ['23:09:59;59', '59.94'], '23:10:00;00'), ('partial repair probe: second carry', ['09:10:59;29', '29.97'], '09:11:00;02'), ('partial repair variant: second carry', ['01:00:59;29', '29.97'], '01:01:00;02'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['00:09:01;00', '59.94'], '00:09:01;01'), ('normal control', ['23:19:59;05', '59.94'], '23:19:59;06'), ('normal control', ['09:59:59;30', '59.94'], '09:59:59;31')], [('regression: second carry', ['09:01:59;29', '29.97'], '09:02:00;02'), ('regression variant: second carry', ['23:09:59;29', '29.97'], '23:10:00;00'), ('partial repair probe: second carry', ['09:00:59;29', '29.97'], '09:01:00;02'), ('partial repair variant: second carry', ['01:01:59;59', '59.94'], '01:02:00;04'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['00:10:01;59', '59.94'], '00:10:02;00'), ('normal control', ['23:00:59;58', '59.94'], '23:00:59;59'), ('normal control', ['00:29:58;00', '29.97'], '00:29:58;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: second carry	`00:00:60;00`	`00:01:00;02`	Failed
regression variant: second carry	`09:10:60;00`	`09:11:00;02`	Failed
partial repair probe: second carry	`00:00:60;00`	`00:01:00;04`	Failed
partial repair variant: second carry	`01:11:00;02`	`01:10:59;00`	Failed
boundary control	`00:01:00;03`	`00:01:00;03`	Passed
normal control	`01:01:01;03`	`01:01:01;03`	Passed
normal control	`09:19:58;06`	`09:19:58;06`	Passed
normal control	`09:19:59;59`	`09:19:59;59`	Passed

SHA-256 / f4daf0cc8979ae2130c14de197b5740334b1daccfd074e613980faf6b0b1c2a8

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import re
N = 1
observations = []
def solve(tc, rate):
    n=30 if rate=='29.97' else 60
    drop=2 if n==30 else 4
    h,m,s,f=map(int,re.split('[:;]',tc))
    f+=1
    if f==n:
        f=0
        s+=1
        if s==60:
            s=0
            m+=1
            if m==60:
                m=0
                h=(h+1)%24
            if m%10!=0:
                f=drop
    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: second carry', ['00:00:59;29', '29.97'], '00:01:00;02'), ('regression variant: second carry', ['09:10:59;29', '29.97'], '09:11:00;02'), ('partial repair probe: second carry', ['00:00:59;59', '59.94'], '00:01:00;04'), ('partial repair variant: second carry', ['01:10:58;29', '29.97'], '01:10:59;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['01:01:01;02', '29.97'], '01:01:01;03'), ('normal control', ['09:19:58;05', '59.94'], '09:19:58;06'), ('normal control', ['09:19:59;58', '59.94'], '09:19:59;59')], [('regression: second carry', ['00:09:59;29', '29.97'], '00:10:00;00'), ('regression variant: second carry', ['09:00:59;29', '29.97'], '09:01:00;02'), ('partial repair probe: second carry', ['23:59:59;29', '29.97'], '00:00:00;00'), ('partial repair variant: second carry', ['23:09:59;29', '29.97'], '23:10:00;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['01:00:59;02', '29.97'], '01:00:59;03'), ('normal control', ['09:01:01;00', '29.97'], '09:01:01;01'), ('normal control', ['01:29:58;58', '59.94'], '01:29:58;59')], [('regression: second carry', ['00:00:59;59', '59.94'], '00:01:00;04'), ('regression variant: second carry', ['23:59:59;59', '59.94'], '00:00:00;00'), ('partial repair probe: second carry', ['09:01:59;29', '29.97'], '09:02:00;02'), ('partial repair variant: second carry', ['00:59:59;59', '59.94'], '01:00:00;00'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['23:00:00;00', '59.94'], '23:00:00;01'), ('normal control', ['23:59:59;03', '59.94'], '23:59:59;04'), ('normal control', ['23:01:58;03', '29.97'], '23:01:58;04')], [('regression: second carry', ['23:59:59;29', '29.97'], '00:00:00;00'), ('regression variant: second carry', ['23:09:59;59', '59.94'], '23:10:00;00'), ('partial repair probe: second carry', ['09:10:59;29', '29.97'], '09:11:00;02'), ('partial repair variant: second carry', ['01:00:59;29', '29.97'], '01:01:00;02'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['00:09:01;00', '59.94'], '00:09:01;01'), ('normal control', ['23:19:59;05', '59.94'], '23:19:59;06'), ('normal control', ['09:59:59;30', '59.94'], '09:59:59;31')], [('regression: second carry', ['09:01:59;29', '29.97'], '09:02:00;02'), ('regression variant: second carry', ['23:09:59;29', '29.97'], '23:10:00;00'), ('partial repair probe: second carry', ['09:00:59;29', '29.97'], '09:01:00;02'), ('partial repair variant: second carry', ['01:01:59;59', '59.94'], '01:02:00;04'), ('boundary control', ['00:01:00;02', '29.97'], '00:01:00;03'), ('normal control', ['00:10:01;59', '59.94'], '00:10:02;00'), ('normal control', ['23:00:59;58', '59.94'], '23:00:59;59'), ('normal control', ['00:29:58;00', '29.97'], '00:29:58;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: second carry	`00:01:00;02`	`00:01:00;02`	Passed
regression variant: second carry	`09:11:00;02`	`09:11:00;02`	Passed
partial repair probe: second carry	`00:01:00;04`	`00:01:00;04`	Passed
partial repair variant: second carry	`01:10:59;00`	`01:10:59;00`	Passed
boundary control	`00:01:00;03`	`00:01:00;03`	Passed
normal control	`01:01:01;03`	`01:01:01;03`	Passed
normal control	`09:19:58;06`	`09:19:58;06`	Passed
normal control	`09:19:59;59`	`09:19:59;59`	Passed

SHA-256 / 4ab2b4954aac388cc9d9d4d4cfd524253ce07f25e9015e440c7ce71c62e5d5ff

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 2026-09-29T14:49:35.323493+00:00.

Case digest / ec3955fac3b42b3a6cf03896d690ea20e8694532589b0b7df4d010f3a067c631