FAILURE MAP
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FA-78671 / Broadcast timecode arithmetic / Open access

Audio sample to frame cadence at 48 kHz: frame start sample · case 01

In-frame offsets are one sample too large at NTSC frame starts.

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

ROOT CAUSE

The frame start sample is floored instead of ceiled.

VERIFIED REPAIR

Frame k starts at the ceiling of k*48000*D/N.

Unsuccessful approach: Multiplying by a truncated samples-per-frame value drifts through the cadence.

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-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: frame start sample', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1600, '25'], [0, 1600, 1920])], [('regression: frame start sample', [3204, '29.97'], [2, 0, 1601]), ('regression variant: frame start sample', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [8008, '25'], [4, 328, 1920]), ('normal control', [0, '25'], [0, 0, 1920]), ('normal control', [1602, '23.976'], [0, 1602, 2002])], [('regression: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('partial repair probe: frame start sample', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('normal control', [1601, '25'], [0, 1601, 1920]), ('normal control', [0, '30'], [0, 0, 1600]), ('normal control', [8009, '24'], [4, 9, 2000])], [('regression: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('partial repair probe: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: frame start sample', [1603, '29.97'], [1, 1, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [3204, '25'], [1, 1284, 1920]), ('normal control', [8009, '23.976'], [4, 1, 2002]), ('normal control', [2002, '24'], [1, 2, 2000])], [('regression: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('regression variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: frame start sample', [3203, '29.97'], [1, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [3203, '24'], [1, 1203, 2000]), ('normal control', [8009, '30'], [5, 9, 1600]), ('normal control', [1603, '24'], [0, 1603, 2000])]]
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: frame start sample[1, 1, 1603][1, 0, 1602]Failed
regression variant: frame start sample[1, 319, 1603][1, 318, 1602]Failed
partial repair probe: frame start sample[1, 318, 1603][1, 317, 1602]Failed
partial repair variant: frame start sample[3663, 1245, 1603][3663, 1244, 1602]Failed
boundary control[0, 1601, 1602][0, 1601, 1602]Passed
boundary control[1, 0, 1920][1, 0, 1920]Passed
normal control[1, 0, 2002][1, 0, 2002]Passed
normal control[0, 1602, 2000][0, 1602, 2000]Passed
normal control[0, 1600, 1920][0, 1600, 1920]Passed

SHA-256 / f8d56ae0d57e666260abb0aa12106e2b724ef8914377ea2ac6f3803b07aed65c

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-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: frame start sample', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1600, '25'], [0, 1600, 1920])], [('regression: frame start sample', [3204, '29.97'], [2, 0, 1601]), ('regression variant: frame start sample', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [8008, '25'], [4, 328, 1920]), ('normal control', [0, '25'], [0, 0, 1920]), ('normal control', [1602, '23.976'], [0, 1602, 2002])], [('regression: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('partial repair probe: frame start sample', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('normal control', [1601, '25'], [0, 1601, 1920]), ('normal control', [0, '30'], [0, 0, 1600]), ('normal control', [8009, '24'], [4, 9, 2000])], [('regression: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('partial repair probe: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: frame start sample', [1603, '29.97'], [1, 1, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [3204, '25'], [1, 1284, 1920]), ('normal control', [8009, '23.976'], [4, 1, 2002]), ('normal control', [2002, '24'], [1, 2, 2000])], [('regression: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('regression variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: frame start sample', [3203, '29.97'], [1, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [3203, '24'], [1, 1203, 2000]), ('normal control', [8009, '30'], [5, 9, 1600]), ('normal control', [1603, '24'], [0, 1603, 2000])]]
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: frame start sample[1, 1, 1603][1, 0, 1602]Failed
regression variant: frame start sample[1, 319, 1603][1, 318, 1602]Failed
partial repair probe: frame start sample[1, 318, 1603][1, 317, 1602]Failed
partial repair variant: frame start sample[3663, 3442, 3800][3663, 1244, 1602]Failed
boundary control[0, 1601, 1602][0, 1601, 1602]Passed
boundary control[1, 0, 1920][1, 0, 1920]Passed
normal control[1, 0, 2002][1, 0, 2002]Passed
normal control[0, 1602, 2000][0, 1602, 2000]Passed
normal control[0, 1600, 1920][0, 1600, 1920]Passed

SHA-256 / 084bdf1bd7ade533a86fdf5d87ce2b9d0950b2e7f3e0fc968eec451fe2fc8766

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: frame start sample', [1602, '29.97'], [1, 0, 1602]), ('regression variant: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair probe: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('partial repair variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [1602, '24'], [0, 1602, 2000]), ('normal control', [1600, '25'], [0, 1600, 1920])], [('regression: frame start sample', [3204, '29.97'], [2, 0, 1601]), ('regression variant: frame start sample', [2001, '29.97'], [1, 399, 1602]), ('partial repair probe: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('partial repair variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [8008, '25'], [4, 328, 1920]), ('normal control', [0, '25'], [0, 0, 1920]), ('normal control', [1602, '23.976'], [0, 1602, 2002])], [('regression: frame start sample', [1919, '29.97'], [1, 317, 1602]), ('regression variant: frame start sample', [5867905, '29.97'], [3663, 1244, 1602]), ('partial repair probe: frame start sample', [8008, '29.97'], [5, 0, 1602]), ('partial repair variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('normal control', [1601, '25'], [0, 1601, 1920]), ('normal control', [0, '30'], [0, 0, 1600]), ('normal control', [8009, '24'], [4, 9, 2000])], [('regression: frame start sample', [9580501, '29.97'], [5981, 1331, 1602]), ('regression variant: frame start sample', [8007, '29.97'], [4, 1600, 1601]), ('partial repair probe: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('partial repair variant: frame start sample', [1603, '29.97'], [1, 1, 1602]), ('boundary control', [1601, '29.97'], [0, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('normal control', [3204, '25'], [1, 1284, 1920]), ('normal control', [8009, '23.976'], [4, 1, 2002]), ('normal control', [2002, '24'], [1, 2, 2000])], [('regression: frame start sample', [2002, '29.97'], [1, 400, 1602]), ('regression variant: frame start sample', [3494632, '29.97'], [2181, 1542, 1602]), ('partial repair probe: frame start sample', [1920, '29.97'], [1, 318, 1602]), ('partial repair variant: frame start sample', [3203, '29.97'], [1, 1601, 1602]), ('boundary control', [1920, '25'], [1, 0, 1920]), ('boundary control', [2002, '23.976'], [1, 0, 2002]), ('normal control', [3203, '24'], [1, 1203, 2000]), ('normal control', [8009, '30'], [5, 9, 1600]), ('normal control', [1603, '24'], [0, 1603, 2000])]]
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: frame start sample[1, 0, 1602][1, 0, 1602]Passed
regression variant: frame start sample[1, 318, 1602][1, 318, 1602]Passed
partial repair probe: frame start sample[1, 317, 1602][1, 317, 1602]Passed
partial repair variant: frame start sample[3663, 1244, 1602][3663, 1244, 1602]Passed
boundary control[0, 1601, 1602][0, 1601, 1602]Passed
boundary control[1, 0, 1920][1, 0, 1920]Passed
normal control[1, 0, 2002][1, 0, 2002]Passed
normal control[0, 1602, 2000][0, 1602, 2000]Passed
normal control[0, 1600, 1920][0, 1600, 1920]Passed

SHA-256 / 04f832a15f859c553d11ba6365ab7b9e6095571a7a0324379425cb88faf76942

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 2026-09-29T14:49:37.379093+00:00.

Case digest / e23cad17dcc9b921474ef5562a8a87175c597ef8f13fcc0cf8c37cbdd96edf38