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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.

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

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 fixtureActualExpectedOutcome
regression: minute carry source23:00:00:0000:00:00:00Failed
regression variant: minute carry source23:30:00:1400:30:00:14Failed
partial repair probe: minute carry source22:00:01:1523:00:01:15Failed
partial repair variant: minute carry source12:00:31:0013:00:31:00Failed
boundary control00:00:01:0000:00:01:00Passed
boundary control00:01:00:0000:01:00:00Passed
normal control00:00:00:0000:00:00:00Passed
normal control01:59:31:1201:59:31:12Passed
normal control22:00:01:2422:00:01:24Passed

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 fixtureActualExpectedOutcome
regression: minute carry source23:00:00:0000:00:00:00Failed
regression variant: minute carry source00:30:00:1400:30:00:14Passed
partial repair probe: minute carry source22:00:01:1523:00:01:15Failed
partial repair variant: minute carry source12:00:31:0013:00:31:00Failed
boundary control00:00:01:0000:00:01:00Passed
boundary control00:01:00:0000:01:00:00Passed
normal control00:00:00:0000:00:00:00Passed
normal control01:59:31:1201:59:31:12Passed
normal control22:00:01:2422:00:01:24Passed

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 fixtureActualExpectedOutcome
regression: minute carry source00:00:00:0000:00:00:00Passed
regression variant: minute carry source00:30:00:1400:30:00:14Passed
partial repair probe: minute carry source23:00:01:1523:00:01:15Passed
partial repair variant: minute carry source13:00:31:0013:00:31:00Passed
boundary control00:00:01:0000:00:01:00Passed
boundary control00:01:00:0000:01:00:00Passed
normal control00:00:00:0000:00:00:00Passed
normal control01:59:31:1201:59:31:12Passed
normal control22:00:01:2422:00:01:24Passed

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