FAILURE MAP
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FA-78681 / Broadcast timecode arithmetic / Open access

Audio sample to frame cadence at 48 kHz: in-frame offset · case 01

Offsets inside NTSC frames drift across the cadence.

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

ROOT CAUSE

The offset is a modulo by a truncated samples-per-frame value.

VERIFIED REPAIR

Subtract the exact frame start sample.

Unsuccessful approach: Subtracting a floored frame start disagrees with the ceiled start convention.

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':(30000,1001),'30':(30,1)}[rate]
    frame=sample*num//(48000*den)
    start=-(-frame*48000*den//num)
    return [frame,sample%(48000*den//num),-(-(frame+1)*48000*den//num)-start]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: in-frame offset', [1602, '29.97'], [1, 0, 1602]), ('regression variant: in-frame offset', [8008, '29.97'], [5, 0, 1602]), ('partial repair probe: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: in-frame offset', [3494632, '29.97'], [2181, 1542, 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: in-frame offset', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: in-frame offset', [1603, '29.97'], [1, 1, 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: in-frame offset', [3204, '29.97'], [2, 0, 1601]), ('regression variant: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: in-frame offset', [3203, '29.97'], [1, 1601, 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: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('regression variant: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: in-frame offset', [3070390, '29.97'], [1917, 122, 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: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: in-frame offset', [8009, '29.97'], [5, 1, 1602]), ('partial repair probe: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair variant: in-frame offset', [298951, '29.97'], [186, 1053, 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: in-frame offset[1, 1, 1602][1, 0, 1602]Failed
regression variant: in-frame offset[5, 3, 1602][5, 0, 1602]Failed
partial repair probe: in-frame offset[1, 318, 1602][1, 317, 1602]Failed
partial repair variant: in-frame offset[2181, 1250, 1602][2181, 1542, 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 / 59fbcea97020a02be16e6c3b9642f55b2521bf82381caa1a80ed8443e600871a

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':(30000,1001),'30':(30,1)}[rate]
    frame=sample*num//(48000*den)
    start=-(-frame*48000*den//num)
    return [frame,sample-frame*48000*den//num,-(-(frame+1)*48000*den//num)-start]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: in-frame offset', [1602, '29.97'], [1, 0, 1602]), ('regression variant: in-frame offset', [8008, '29.97'], [5, 0, 1602]), ('partial repair probe: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: in-frame offset', [3494632, '29.97'], [2181, 1542, 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: in-frame offset', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: in-frame offset', [1603, '29.97'], [1, 1, 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: in-frame offset', [3204, '29.97'], [2, 0, 1601]), ('regression variant: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: in-frame offset', [3203, '29.97'], [1, 1601, 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: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('regression variant: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: in-frame offset', [3070390, '29.97'], [1917, 122, 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: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: in-frame offset', [8009, '29.97'], [5, 1, 1602]), ('partial repair probe: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair variant: in-frame offset', [298951, '29.97'], [186, 1053, 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: in-frame offset[1, 1, 1602][1, 0, 1602]Failed
regression variant: in-frame offset[5, 0, 1602][5, 0, 1602]Passed
partial repair probe: in-frame offset[1, 318, 1602][1, 317, 1602]Failed
partial repair variant: in-frame offset[2181, 1543, 1602][2181, 1542, 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 / 310f02ce9de9efbcc8db08ec2a86d99172fc27816aaa88e4178f0b911037aee1

3 / The verified repair

Exit 0
"""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':(30000,1001),'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: in-frame offset', [1602, '29.97'], [1, 0, 1602]), ('regression variant: in-frame offset', [8008, '29.97'], [5, 0, 1602]), ('partial repair probe: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: in-frame offset', [3494632, '29.97'], [2181, 1542, 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: in-frame offset', [1601, '29.97'], [0, 1601, 1602]), ('regression variant: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair probe: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: in-frame offset', [1603, '29.97'], [1, 1, 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: in-frame offset', [3204, '29.97'], [2, 0, 1601]), ('regression variant: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: in-frame offset', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: in-frame offset', [3203, '29.97'], [1, 1601, 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: in-frame offset', [1919, '29.97'], [1, 317, 1602]), ('regression variant: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: in-frame offset', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: in-frame offset', [3070390, '29.97'], [1917, 122, 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: in-frame offset', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: in-frame offset', [8009, '29.97'], [5, 1, 1602]), ('partial repair probe: in-frame offset', [2001, '29.97'], [1, 399, 1602]), ('partial repair variant: in-frame offset', [298951, '29.97'], [186, 1053, 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: in-frame offset[1, 0, 1602][1, 0, 1602]Passed
regression variant: in-frame offset[5, 0, 1602][5, 0, 1602]Passed
partial repair probe: in-frame offset[1, 317, 1602][1, 317, 1602]Passed
partial repair variant: in-frame offset[2181, 1542, 1602][2181, 1542, 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 / 1f406489063307864cbfdd2b761559b34205c7a7cea1fa78317294d660f50359

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 2026-09-29T14:49:37.422269+00:00.

Case digest / fc826780b2e741f5de36afdc587f7e3fd222fa806bb4a384308c76db011e4269