FAILURE MAP
← Case archive

FA-78686 / Broadcast timecode arithmetic / Open access

Audio sample to frame cadence at 48 kHz: ntsc rate table · case 01

Sample cadence for 29.97 video slowly slips against the true 30000/1001 rate.

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

ROOT CAUSE

The rate is taken as exactly 29.97 frames per second.

THE FAILURE

The rate is taken as exactly 29.97 frames per second.

Unsuccessful approach: Using integer 30 removes the NTSC cadence entirely.

Case contract

At 48000 samples per second and rate N/D, the frame containing sample s is floor(s*N/(48000*D)); frame k starts at sample ceil(k*48000*D/N). Return [frame, offset of s inside its frame, number of samples in that frame].

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(sample, rate):
    num,den={'23.976':(24000,1001),'24':(24,1),'25':(25,1),'29.97':(2997,100),'30':(30,1)}[rate]
    frame=sample*num//(48000*den)
    start=-(-frame*48000*den//num)
    return [frame,sample-start,-(-(frame+1)*48000*den//num)-start]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: ntsc rate table', [3204, '29.97'], [2, 0, 1601]), ('partial repair variant: ntsc rate table', [1600, '29.97'], [0, 1600, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1920, '30'], [1, 320, 1600]), ('normal control', [3204, '30'], [2, 4, 1600])], [('regression: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('regression variant: ntsc rate table', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair probe: ntsc rate table', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: ntsc rate table', [2001, '29.97'], [1, 399, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [9138728, '24'], [4569, 728, 2000]), ('normal control', [3203, '25'], [1, 1283, 1920]), ('normal control', [2001, '25'], [1, 81, 1920])], [('regression: ntsc rate table', [8009, '29.97'], [5, 1, 1602]), ('regression variant: ntsc rate table', [3315925, '29.97'], [2070, 613, 1602]), ('partial repair probe: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1920, '23.976'], [0, 1920, 2002]), ('normal control', [1, '23.976'], [0, 1, 2002]), ('normal control', [1601, '24'], [0, 1601, 2000])], [('regression: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('regression variant: ntsc rate table', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair probe: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: ntsc rate table', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [0, '24'], [0, 0, 2000]), ('normal control', [1920, '24'], [0, 1920, 2000]), ('normal control', [2001, '24'], [1, 1, 2000])], [('regression: ntsc rate table', [8007, '29.97'], [4, 1600, 1601]), ('regression variant: ntsc rate table', [2419900, '29.97'], [1510, 1484, 1602]), ('partial repair probe: ntsc rate table', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [2839374, '30'], [1774, 974, 1600]), ('normal control', [1601, '23.976'], [0, 1601, 2002]), ('normal control', [1603, '25'], [0, 1603, 1920])]]
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: ntsc rate table[5981, 1321, 1601][5981, 1331, 1602]Failed
regression variant: ntsc rate table[2181, 1538, 1601][2181, 1542, 1602]Failed
partial repair probe: ntsc rate table[2, 0, 1601][2, 0, 1601]Passed
partial repair variant: ntsc rate table[0, 1600, 1602][0, 1600, 1602]Passed
boundary control[1, 0, 1920][1, 0, 1920]Passed
boundary control[1, 0, 2002][1, 0, 2002]Passed
normal control[0, 1602, 2000][0, 1602, 2000]Passed
normal control[1, 320, 1600][1, 320, 1600]Passed
normal control[2, 4, 1600][2, 4, 1600]Passed

SHA-256 / 171be1f81c2ece5a37886488970bc8171fab7adaccf90815575bb80e43f39d93

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(sample, rate):
    num,den={'23.976':(24000,1001),'24':(24,1),'25':(25,1),'29.97':(30,1),'30':(30,1)}[rate]
    frame=sample*num//(48000*den)
    start=-(-frame*48000*den//num)
    return [frame,sample-start,-(-(frame+1)*48000*den//num)-start]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: ntsc rate table', [3204, '29.97'], [2, 0, 1601]), ('partial repair variant: ntsc rate table', [1600, '29.97'], [0, 1600, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1920, '30'], [1, 320, 1600]), ('normal control', [3204, '30'], [2, 4, 1600])], [('regression: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('regression variant: ntsc rate table', [3070390, '29.97'], [1917, 122, 1601]), ('partial repair probe: ntsc rate table', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: ntsc rate table', [2001, '29.97'], [1, 399, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [9138728, '24'], [4569, 728, 2000]), ('normal control', [3203, '25'], [1, 1283, 1920]), ('normal control', [2001, '25'], [1, 81, 1920])], [('regression: ntsc rate table', [8009, '29.97'], [5, 1, 1602]), ('regression variant: ntsc rate table', [3315925, '29.97'], [2070, 613, 1602]), ('partial repair probe: ntsc rate table', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1920, '23.976'], [0, 1920, 2002]), ('normal control', [1, '23.976'], [0, 1, 2002]), ('normal control', [1601, '24'], [0, 1601, 2000])], [('regression: ntsc rate table', [5867905, '29.97'], [3663, 1244, 1602]), ('regression variant: ntsc rate table', [6050108, '29.97'], [3777, 864, 1601]), ('partial repair probe: ntsc rate table', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: ntsc rate table', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [0, '24'], [0, 0, 2000]), ('normal control', [1920, '24'], [0, 1920, 2000]), ('normal control', [2001, '24'], [1, 1, 2000])], [('regression: ntsc rate table', [8007, '29.97'], [4, 1600, 1601]), ('regression variant: ntsc rate table', [2419900, '29.97'], [1510, 1484, 1602]), ('partial repair probe: ntsc rate table', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: ntsc rate table', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [2839374, '30'], [1774, 974, 1600]), ('normal control', [1601, '23.976'], [0, 1601, 2002]), ('normal control', [1603, '25'], [0, 1603, 1920])]]
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: ntsc rate table[5987, 1301, 1600][5981, 1331, 1602]Failed
regression variant: ntsc rate table[2184, 232, 1600][2181, 1542, 1602]Failed
partial repair probe: ntsc rate table[2, 4, 1600][2, 0, 1601]Failed
partial repair variant: ntsc rate table[1, 0, 1600][0, 1600, 1602]Failed
boundary control[1, 0, 1920][1, 0, 1920]Passed
boundary control[1, 0, 2002][1, 0, 2002]Passed
normal control[0, 1602, 2000][0, 1602, 2000]Passed
normal control[1, 320, 1600][1, 320, 1600]Passed
normal control[2, 4, 1600][2, 4, 1600]Passed

SHA-256 / c5fe178d436a6600bec782ab1527cceecbc80cbbd2b84596a9e816971597f801

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 9 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.

Sign in to the archive ↗

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 2026-09-29T14:49:37.684302+00:00.

Case digest / b58116c73401b91b25a84a7ffef7e286408a94c376f81b28ec28650297228dce