FA-78606 / Broadcast timecode arithmetic / Open access

Non-drop label to wall clock at pulled-down rates: rate numerator · case 01

Wall-clock conversions run fast by 0.2 percent at pulled-down rates.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The 1001 factor is applied to the numerator as well as the denominator.

THE FAILURE

The 1001 factor is applied to the numerator as well as the denominator.

Unsuccessful approach: Dropping the scale of 1000 breaks the ratio against the millisecond denominator.

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=1001 if '.' in rate else 1000
    num=nominal*1001
    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: rate numerator', ['01:00:00:00', '29.97', 'to_ms'], 3603600), ('regression variant: rate numerator', ['10:00:01:24', '25', 'to_ms'], 36001960), ('partial repair probe: rate numerator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('partial repair variant: rate numerator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('normal control', [1, '24', 'to_tc'], '00:00:00:00'), ('normal control', [0, '24', 'to_tc'], '00:00:00:00'), ('normal control', ['00:00:00:00', '29.97', 'to_ms'], 0)], [('regression: rate numerator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('regression variant: rate numerator', [86399999, '25', 'to_tc'], '00:00:00:00'), ('partial repair probe: rate numerator', ['00:00:00:01', '25', 'to_ms'], 40), ('partial repair variant: rate numerator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('normal control', [0, '59.94', 'to_tc'], '00:00:00:00'), ('normal control', [1, '25', 'to_tc'], '00:00:00:00'), ('normal control', [1, '30', 'to_tc'], '00:00:00:00')], [('regression: rate numerator', [3603600, '23.976', 'to_tc'], '01:00:00:00'), ('regression variant: rate numerator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('partial repair probe: rate numerator', [1020, '24', 'to_tc'], '00:00:01:00'), ('partial repair variant: rate numerator', [250, '59.94', 'to_tc'], '00:00:00:15'), ('normal control', [0, '29.97', 'to_tc'], '00:00:00:00'), ('normal control', [20, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1, '24', 'to_tc'], '00:00:00:00')], [('regression: rate numerator', [1020, '24', 'to_tc'], '00:00:01:00'), ('regression variant: rate numerator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('partial repair probe: rate numerator', ['23:01:00:12', '30', 'to_ms'], 82860400), ('partial repair variant: rate numerator', ['10:59:00:00', '24', 'to_ms'], 39540000), ('normal control', [0, '23.976', 'to_tc'], '00:00:00:00'), ('normal control', ['00:00:00:00', '29.97', 'to_ms'], 0), ('normal control', [0, '59.94', 'to_tc'], '00:00:00:00')], [('regression: rate numerator', ['23:01:00:12', '30', 'to_ms'], 82860400), ('regression variant: rate numerator', ['10:59:00:00', '24', 'to_ms'], 39540000), ('partial repair probe: rate numerator', ['10:00:01:24', '25', 'to_ms'], 36001960), ('partial repair variant: rate numerator', ['01:01:01:36', '30', 'to_ms'], 3662200), ('normal control', [0, '30', 'to_tc'], '00:00:00:00'), ('normal control', [1, '30', 'to_tc'], '00:00:00:00'), ('normal control', [0, '29.97', 'to_tc'], '00:00:00:00')]]
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 fixture	Actual	Expected	Outcome
regression: rate numerator	`3600000`	`3603600`	Failed
regression variant: rate numerator	`35965994`	`36001960`	Failed
partial repair probe: rate numerator	`01:00:00:00`	`00:59:56:12`	Failed
partial repair variant: rate numerator	`39541875`	`39581417`	Failed
normal control	`00:00:00:00`	`00:00:00:00`	Passed
normal control	`00:00:00:00`	`00:00:00:00`	Passed
normal control	`0`	`0`	Passed

SHA-256 / afb5473b00362fbc010a4fc7d3ed594b6e09c3a008eb55cfa2ee59aad2c569f8

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 '.' in rate else 1000
    num=nominal
    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: rate numerator', ['01:00:00:00', '29.97', 'to_ms'], 3603600), ('regression variant: rate numerator', ['10:00:01:24', '25', 'to_ms'], 36001960), ('partial repair probe: rate numerator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('partial repair variant: rate numerator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('normal control', [1, '24', 'to_tc'], '00:00:00:00'), ('normal control', [0, '24', 'to_tc'], '00:00:00:00'), ('normal control', ['00:00:00:00', '29.97', 'to_ms'], 0)], [('regression: rate numerator', [3600000, '29.97', 'to_tc'], '00:59:56:12'), ('regression variant: rate numerator', [86399999, '25', 'to_tc'], '00:00:00:00'), ('partial repair probe: rate numerator', ['00:00:00:01', '25', 'to_ms'], 40), ('partial repair variant: rate numerator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('normal control', [0, '59.94', 'to_tc'], '00:00:00:00'), ('normal control', [1, '25', 'to_tc'], '00:00:00:00'), ('normal control', [1, '30', 'to_tc'], '00:00:00:00')], [('regression: rate numerator', [3603600, '23.976', 'to_tc'], '01:00:00:00'), ('regression variant: rate numerator', ['10:59:00:45', '23.976', 'to_ms'], 39581417), ('partial repair probe: rate numerator', [1020, '24', 'to_tc'], '00:00:01:00'), ('partial repair variant: rate numerator', [250, '59.94', 'to_tc'], '00:00:00:15'), ('normal control', [0, '29.97', 'to_tc'], '00:00:00:00'), ('normal control', [20, '24', 'to_tc'], '00:00:00:00'), ('normal control', [1, '24', 'to_tc'], '00:00:00:00')], [('regression: rate numerator', [1020, '24', 'to_tc'], '00:00:01:00'), ('regression variant: rate numerator', [86399999, '23.976', 'to_tc'], '23:58:33:16'), ('partial repair probe: rate numerator', ['23:01:00:12', '30', 'to_ms'], 82860400), ('partial repair variant: rate numerator', ['10:59:00:00', '24', 'to_ms'], 39540000), ('normal control', [0, '23.976', 'to_tc'], '00:00:00:00'), ('normal control', ['00:00:00:00', '29.97', 'to_ms'], 0), ('normal control', [0, '59.94', 'to_tc'], '00:00:00:00')], [('regression: rate numerator', ['23:01:00:12', '30', 'to_ms'], 82860400), ('regression variant: rate numerator', ['10:59:00:00', '24', 'to_ms'], 39540000), ('partial repair probe: rate numerator', ['10:00:01:24', '25', 'to_ms'], 36001960), ('partial repair variant: rate numerator', ['01:01:01:36', '30', 'to_ms'], 3662200), ('normal control', [0, '30', 'to_tc'], '00:00:00:00'), ('normal control', [1, '30', 'to_tc'], '00:00:00:00'), ('normal control', [0, '29.97', 'to_tc'], '00:00:00:00')]]
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 fixture	Actual	Expected	Outcome
regression: rate numerator	`3603600000`	`3603600`	Failed
regression variant: rate numerator	`36001960000`	`36001960`	Failed
partial repair probe: rate numerator	`00:00:03:18`	`00:59:56:12`	Failed
partial repair variant: rate numerator	`39581416875`	`39581417`	Failed
normal control	`00:00:00:00`	`00:00:00:00`	Passed
normal control	`00:00:00:00`	`00:00:00:00`	Passed
normal control	`0`	`0`	Passed

SHA-256 / e07153020de46f58523ace7c66779c34ac97b470580edb5260b35b48fd6ad988

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:49:36.685794+00:00.

Case digest / 71340301c7c44a959719f54a98cb48546c58a7348716695e26a351e07c15b9b4