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FA-78591 / Broadcast timecode arithmetic / Open access

Non-drop label to wall clock at pulled-down rates: pulldown denominator · case 01

An hour of 29.97 labels maps to exactly one hour of wall clock, 3.6 seconds short.

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

ROOT CAUSE

The 1000/1001 pull-down factor is never applied.

VERIFIED REPAIR

Use 1001 for the fractional rates.

Unsuccessful approach: Treating integer 30 as pulled down slows genuine 30 fps material.

Case contract

Rates "23.976", "29.97", "59.94" run at nominal*1000/1001 frames per second while labels count nominal frames per second (non-drop). mode "to_ms": label to elapsed milliseconds, rounded half up. mode "to_tc": milliseconds to the nearest frame (half up), formatted as a non-drop label wrapping at 24 hours.

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(value, rate, mode):
    nominal={'23.976':24,'29.97':30,'59.94':60,'24':24,'25':25,'30':30}[rate]
    den=1000
    num=nominal*1000
    if mode=='to_ms':
        h,m,s,f=map(int,value.split(':'))
        n=((h*60+m)*60+s)*nominal+f
        return (2*n*1000*den+num)//(2*num)
    n=(2*value*num+1000*den)//(2000*den)
    return '%02d:%02d:%02d:%02d'%(n//(3600*nominal)%24,n//(60*nominal)%60,n//nominal%60,n%nominal)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: pulldown denominator', ['01:00:00:00', '29.97', 'to_ms'], 3603600), ('regression variant: pulldown denominator', ['23:59:59:15', '59.94', 'to_ms'], 86485649), ('partial repair probe: pulldown denominator', ['10:00:01:06', '30', 'to_ms'], 36001200), ('partial repair variant: pulldown denominator', ['01:59:01:15', '30', 'to_ms'], 7141500), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [1, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1020, '24', 'to_tc'], '00:00:01:00'), ('normal control', [86399999, '25', 'to_tc'], '00:00:00:00')], [('regression: pulldown denominator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('regression variant: pulldown denominator', [150, '29.97', 'to_tc'], '00:00:00:04'), ('partial repair probe: pulldown denominator', [3600000, '30', 'to_tc'], '01:00:00:00'), ('partial repair variant: pulldown denominator', ['01:01:00:36', '30', 'to_ms'], 3661200), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('normal control', ['10:59:00:00', '24', 'to_ms'], 39540000), ('normal control', [1, '59.94', 'to_tc'], '00:00:00:00'), ('normal control', [1001, '59.94', 'to_tc'], '00:00:01:00')], [('regression: pulldown denominator', [3603600, '23.976', 'to_tc'], '01:00:00:00'), ('regression variant: pulldown denominator', ['01:01:01:15', '23.976', 'to_ms'], 3665287), ('partial repair probe: pulldown denominator', ['10:59:59:36', '30', 'to_ms'], 39600200), ('partial repair variant: pulldown denominator', ['01:59:59:29', '30', 'to_ms'], 7199967), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [100, '23.976', 'to_tc'], '00:00:00:02'), ('normal control', [60, '25', 'to_tc'], '00:00:00:02'), ('normal control', ['10:00:00:36', '24', 'to_ms'], 36001500)], [('regression: pulldown denominator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('regression variant: pulldown denominator', [3603600, '29.97', 'to_tc'], '01:00:00:00'), ('partial repair probe: pulldown denominator', ['10:00:01:15', '30', 'to_ms'], 36001500), ('partial repair variant: pulldown denominator', [32276345, '30', 'to_tc'], '08:57:56:10'), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('normal control', ['10:59:00:45', '25', 'to_ms'], 39541800), ('normal control', [0, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1, '23.976', 'to_tc'], '00:00:00:00')], [('regression: pulldown denominator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('regression variant: pulldown denominator', ['23:00:59:00', '29.97', 'to_ms'], 82941859), ('partial repair probe: pulldown denominator', ['00:59:01:06', '30', 'to_ms'], 3541200), ('partial repair variant: pulldown denominator', [3603600, '30', 'to_tc'], '01:00:03:18'), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [60, '29.97', 'to_tc'], '00:00:00:02'), ('normal control', [20, '29.97', 'to_tc'], '00:00:00:01'), ('normal control', [20, '25', 'to_tc'], '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 fixtureActualExpectedOutcome
regression: pulldown denominator36000003603600Failed
regression variant: pulldown denominator8639925086485649Failed
partial repair probe: pulldown denominator3600120036001200Passed
partial repair variant: pulldown denominator71415007141500Passed
boundary control4242Passed
boundary control4040Passed
normal control00:00:00:0000:00:00:00Passed
normal control00:00:01:0000:00:01:00Passed
normal control00:00:00:0000:00:00:00Passed

SHA-256 / 9e19f4d31515a2c2dab9ae59cf34054fa263aa2822ec2d47d3b38b2b13253254

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(value, rate, mode):
    nominal={'23.976':24,'29.97':30,'59.94':60,'24':24,'25':25,'30':30}[rate]
    den=1001 if rate not in ('24','25') else 1000
    num=nominal*1000
    if mode=='to_ms':
        h,m,s,f=map(int,value.split(':'))
        n=((h*60+m)*60+s)*nominal+f
        return (2*n*1000*den+num)//(2*num)
    n=(2*value*num+1000*den)//(2000*den)
    return '%02d:%02d:%02d:%02d'%(n//(3600*nominal)%24,n//(60*nominal)%60,n//nominal%60,n%nominal)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: pulldown denominator', ['01:00:00:00', '29.97', 'to_ms'], 3603600), ('regression variant: pulldown denominator', ['23:59:59:15', '59.94', 'to_ms'], 86485649), ('partial repair probe: pulldown denominator', ['10:00:01:06', '30', 'to_ms'], 36001200), ('partial repair variant: pulldown denominator', ['01:59:01:15', '30', 'to_ms'], 7141500), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [1, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1020, '24', 'to_tc'], '00:00:01:00'), ('normal control', [86399999, '25', 'to_tc'], '00:00:00:00')], [('regression: pulldown denominator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('regression variant: pulldown denominator', [150, '29.97', 'to_tc'], '00:00:00:04'), ('partial repair probe: pulldown denominator', [3600000, '30', 'to_tc'], '01:00:00:00'), ('partial repair variant: pulldown denominator', ['01:01:00:36', '30', 'to_ms'], 3661200), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('normal control', ['10:59:00:00', '24', 'to_ms'], 39540000), ('normal control', [1, '59.94', 'to_tc'], '00:00:00:00'), ('normal control', [1001, '59.94', 'to_tc'], '00:00:01:00')], [('regression: pulldown denominator', [3603600, '23.976', 'to_tc'], '01:00:00:00'), ('regression variant: pulldown denominator', ['01:01:01:15', '23.976', 'to_ms'], 3665287), ('partial repair probe: pulldown denominator', ['10:59:59:36', '30', 'to_ms'], 39600200), ('partial repair variant: pulldown denominator', ['01:59:59:29', '30', 'to_ms'], 7199967), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [100, '23.976', 'to_tc'], '00:00:00:02'), ('normal control', [60, '25', 'to_tc'], '00:00:00:02'), ('normal control', ['10:00:00:36', '24', 'to_ms'], 36001500)], [('regression: pulldown denominator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('regression variant: pulldown denominator', [3603600, '29.97', 'to_tc'], '01:00:00:00'), ('partial repair probe: pulldown denominator', ['10:00:01:15', '30', 'to_ms'], 36001500), ('partial repair variant: pulldown denominator', [32276345, '30', 'to_tc'], '08:57:56:10'), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('normal control', ['10:59:00:45', '25', 'to_ms'], 39541800), ('normal control', [0, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1, '23.976', 'to_tc'], '00:00:00:00')], [('regression: pulldown denominator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('regression variant: pulldown denominator', ['23:00:59:00', '29.97', 'to_ms'], 82941859), ('partial repair probe: pulldown denominator', ['00:59:01:06', '30', 'to_ms'], 3541200), ('partial repair variant: pulldown denominator', [3603600, '30', 'to_tc'], '01:00:03:18'), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [60, '29.97', 'to_tc'], '00:00:00:02'), ('normal control', [20, '29.97', 'to_tc'], '00:00:00:01'), ('normal control', [20, '25', 'to_tc'], '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 fixtureActualExpectedOutcome
regression: pulldown denominator36036003603600Passed
regression variant: pulldown denominator8648564986485649Passed
partial repair probe: pulldown denominator3603720136001200Failed
partial repair variant: pulldown denominator71486427141500Failed
boundary control4242Passed
boundary control4040Passed
normal control00:00:00:0000:00:00:00Passed
normal control00:00:01:0000:00:01:00Passed
normal control00:00:00:0000:00:00:00Passed

SHA-256 / 75088f821f4f8717d3758426409fcd13ea34c9ba1f89ce43238c7982773216a1

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(value, rate, mode):
    nominal={'23.976':24,'29.97':30,'59.94':60,'24':24,'25':25,'30':30}[rate]
    den=1001 if '.' in rate else 1000
    num=nominal*1000
    if mode=='to_ms':
        h,m,s,f=map(int,value.split(':'))
        n=((h*60+m)*60+s)*nominal+f
        return (2*n*1000*den+num)//(2*num)
    n=(2*value*num+1000*den)//(2000*den)
    return '%02d:%02d:%02d:%02d'%(n//(3600*nominal)%24,n//(60*nominal)%60,n//nominal%60,n%nominal)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: pulldown denominator', ['01:00:00:00', '29.97', 'to_ms'], 3603600), ('regression variant: pulldown denominator', ['23:59:59:15', '59.94', 'to_ms'], 86485649), ('partial repair probe: pulldown denominator', ['10:00:01:06', '30', 'to_ms'], 36001200), ('partial repair variant: pulldown denominator', ['01:59:01:15', '30', 'to_ms'], 7141500), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [1, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1020, '24', 'to_tc'], '00:00:01:00'), ('normal control', [86399999, '25', 'to_tc'], '00:00:00:00')], [('regression: pulldown denominator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('regression variant: pulldown denominator', [150, '29.97', 'to_tc'], '00:00:00:04'), ('partial repair probe: pulldown denominator', [3600000, '30', 'to_tc'], '01:00:00:00'), ('partial repair variant: pulldown denominator', ['01:01:00:36', '30', 'to_ms'], 3661200), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('normal control', ['10:59:00:00', '24', 'to_ms'], 39540000), ('normal control', [1, '59.94', 'to_tc'], '00:00:00:00'), ('normal control', [1001, '59.94', 'to_tc'], '00:00:01:00')], [('regression: pulldown denominator', [3603600, '23.976', 'to_tc'], '01:00:00:00'), ('regression variant: pulldown denominator', ['01:01:01:15', '23.976', 'to_ms'], 3665287), ('partial repair probe: pulldown denominator', ['10:59:59:36', '30', 'to_ms'], 39600200), ('partial repair variant: pulldown denominator', ['01:59:59:29', '30', 'to_ms'], 7199967), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [100, '23.976', 'to_tc'], '00:00:00:02'), ('normal control', [60, '25', 'to_tc'], '00:00:00:02'), ('normal control', ['10:00:00:36', '24', 'to_ms'], 36001500)], [('regression: pulldown denominator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('regression variant: pulldown denominator', [3603600, '29.97', 'to_tc'], '01:00:00:00'), ('partial repair probe: pulldown denominator', ['10:00:01:15', '30', 'to_ms'], 36001500), ('partial repair variant: pulldown denominator', [32276345, '30', 'to_tc'], '08:57:56:10'), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('normal control', ['10:59:00:45', '25', 'to_ms'], 39541800), ('normal control', [0, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1, '23.976', 'to_tc'], '00:00:00:00')], [('regression: pulldown denominator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('regression variant: pulldown denominator', ['23:00:59:00', '29.97', 'to_ms'], 82941859), ('partial repair probe: pulldown denominator', ['00:59:01:06', '30', 'to_ms'], 3541200), ('partial repair variant: pulldown denominator', [3603600, '30', 'to_tc'], '01:00:03:18'), ('boundary control', ['00:00:00:01', '23.976', 'to_ms'], 42), ('boundary control', ['00:00:00:01', '25', 'to_ms'], 40), ('normal control', [60, '29.97', 'to_tc'], '00:00:00:02'), ('normal control', [20, '29.97', 'to_tc'], '00:00:00:01'), ('normal control', [20, '25', 'to_tc'], '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 fixtureActualExpectedOutcome
regression: pulldown denominator36036003603600Passed
regression variant: pulldown denominator8648564986485649Passed
partial repair probe: pulldown denominator3600120036001200Passed
partial repair variant: pulldown denominator71415007141500Passed
boundary control4242Passed
boundary control4040Passed
normal control00:00:00:0000:00:00:00Passed
normal control00:00:01:0000:00:01:00Passed
normal control00:00:00:0000:00:00:00Passed

SHA-256 / 972191f6b833c4ecdae720a40ed523aed15ca1943c279a366e71ad725b80b7c2

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 2026-09-29T14:49:36.643039+00:00.

Case digest / 71fef35d634f05b4e23f02f5b908e6281610463ce09011c640f8264b9c4a84e6