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FA-78756 / Broadcast timecode arithmetic / Open access

Decimal seconds to frame label: negative input · case 01

Negative offsets are silently mirrored to positive frames.

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

ROOT CAUSE

Negative seconds are negated instead of rejected.

VERIFIED REPAIR

Return None for negative input.

Unsuccessful approach: Clamping to zero hides the invalid input as frame zero.

Case contract

Convert a decimal seconds string exactly (no binary floating point) at rate [N,D] to the nearest frame, halves rounding up, and a non-drop label using the nominal rate ceil(N/D). Negative input returns None.

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
import math
from fractions import Fraction
N = 1
observations = []
def solve(sec, fps):
    num,den=fps
    x=Fraction(sec)
    if x<0:
        x=-x
    n=x*num/den
    fr=math.floor(n+Fraction(1,2))
    nominal=-(-num//den)
    return [fr,'%02d:%02d:%02d:%02d'%(fr//(3600*nominal)%24,fr//(60*nominal)%60,fr//nominal%60,fr%nominal)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: negative input', ['-1', [25, 1]], None), ('regression variant: negative input', ['-0.5', [30000, 1001]], None), ('partial repair probe: negative input', ['-1', [24, 1]], None), ('partial repair variant: negative input', ['-1', [30000, 1001]], None), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('normal control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('normal control', ['12.345', [24000, 1001]], [296, '00:00:12:08']), ('normal control', ['0.02', [50, 1]], [1, '00:00:00:01'])], [('regression: negative input', ['-1', [24000, 1001]], None), ('regression variant: negative input', ['-1', [50, 1]], None), ('partial repair probe: negative input', ['-0.5', [25, 1]], None), ('partial repair variant: negative input', ['-1', [25, 1]], None), ('boundary control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('normal control', ['0.22', [24, 1]], [5, '00:00:00:05']), ('normal control', ['0', [24000, 1001]], [0, '00:00:00:00']), ('normal control', ['7.3', [24, 1]], [175, '00:00:07:07'])], [('regression: negative input', ['-1', [24, 1]], None), ('regression variant: negative input', ['-0.5', [24000, 1001]], None), ('partial repair probe: negative input', ['-0.5', [50, 1]], None), ('partial repair variant: negative input', ['-1', [24000, 1001]], None), ('boundary control', ['1.001', [30000, 1001]], [30, '00:00:01:00']), ('boundary control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('normal control', ['0.04', [24, 1]], [1, '00:00:00:01']), ('normal control', ['0.18', [24, 1]], [4, '00:00:00:04']), ('normal control', ['0.02', [30000, 1001]], [1, '00:00:00:01'])], [('regression: negative input', ['-0.5', [25, 1]], None), ('regression variant: negative input', ['-0.5', [24, 1]], None), ('partial repair probe: negative input', ['-0.5', [30000, 1001]], None), ('partial repair variant: negative input', ['-1', [24, 1]], None), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('boundary control', ['1.001', [30000, 1001]], [30, '00:00:01:00']), ('normal control', ['0.1', [24000, 1001]], [2, '00:00:00:02']), ('normal control', ['3600', [30000, 1001]], [107892, '00:59:56:12']), ('normal control', ['0.04', [24000, 1001]], [1, '00:00:00:01'])], [('regression: negative input', ['-0.5', [50, 1]], None), ('regression variant: negative input', ['-1', [30000, 1001]], None), ('partial repair probe: negative input', ['-1', [50, 1]], None), ('partial repair variant: negative input', ['-0.5', [25, 1]], None), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('normal control', ['0.14', [30000, 1001]], [4, '00:00:00:04']), ('normal control', ['0.0166', [50, 1]], [1, '00:00:00:01']), ('normal control', ['1.001', [50, 1]], [50, '00:00:01:00'])]]
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 fixtureActualExpectedOutcome
regression: negative input[25, '00:00:01:00']NoneFailed
regression variant: negative input[15, '00:00:00:15']NoneFailed
partial repair probe: negative input[24, '00:00:01:00']NoneFailed
partial repair variant: negative input[30, '00:00:01:00']NoneFailed
boundary control[2, '00:00:00:02'][2, '00:00:00:02']Passed
boundary control[0, '00:00:00:00'][0, '00:00:00:00']Passed
normal control[1, '00:00:00:01'][1, '00:00:00:01']Passed
normal control[296, '00:00:12:08'][296, '00:00:12:08']Passed
normal control[1, '00:00:00:01'][1, '00:00:00:01']Passed

SHA-256 / b7ce14ef2eb019086f0ed24b027f774a84d27eeafc7ed813b3b474b4002f26e8

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(sec, fps):
    num,den=fps
    x=Fraction(sec)
    if x<0:
        x=0
    n=x*num/den
    fr=math.floor(n+Fraction(1,2))
    nominal=-(-num//den)
    return [fr,'%02d:%02d:%02d:%02d'%(fr//(3600*nominal)%24,fr//(60*nominal)%60,fr//nominal%60,fr%nominal)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: negative input', ['-1', [25, 1]], None), ('regression variant: negative input', ['-0.5', [30000, 1001]], None), ('partial repair probe: negative input', ['-1', [24, 1]], None), ('partial repair variant: negative input', ['-1', [30000, 1001]], None), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('normal control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('normal control', ['12.345', [24000, 1001]], [296, '00:00:12:08']), ('normal control', ['0.02', [50, 1]], [1, '00:00:00:01'])], [('regression: negative input', ['-1', [24000, 1001]], None), ('regression variant: negative input', ['-1', [50, 1]], None), ('partial repair probe: negative input', ['-0.5', [25, 1]], None), ('partial repair variant: negative input', ['-1', [25, 1]], None), ('boundary control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('normal control', ['0.22', [24, 1]], [5, '00:00:00:05']), ('normal control', ['0', [24000, 1001]], [0, '00:00:00:00']), ('normal control', ['7.3', [24, 1]], [175, '00:00:07:07'])], [('regression: negative input', ['-1', [24, 1]], None), ('regression variant: negative input', ['-0.5', [24000, 1001]], None), ('partial repair probe: negative input', ['-0.5', [50, 1]], None), ('partial repair variant: negative input', ['-1', [24000, 1001]], None), ('boundary control', ['1.001', [30000, 1001]], [30, '00:00:01:00']), ('boundary control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('normal control', ['0.04', [24, 1]], [1, '00:00:00:01']), ('normal control', ['0.18', [24, 1]], [4, '00:00:00:04']), ('normal control', ['0.02', [30000, 1001]], [1, '00:00:00:01'])], [('regression: negative input', ['-0.5', [25, 1]], None), ('regression variant: negative input', ['-0.5', [24, 1]], None), ('partial repair probe: negative input', ['-0.5', [30000, 1001]], None), ('partial repair variant: negative input', ['-1', [24, 1]], None), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('boundary control', ['1.001', [30000, 1001]], [30, '00:00:01:00']), ('normal control', ['0.1', [24000, 1001]], [2, '00:00:00:02']), ('normal control', ['3600', [30000, 1001]], [107892, '00:59:56:12']), ('normal control', ['0.04', [24000, 1001]], [1, '00:00:00:01'])], [('regression: negative input', ['-0.5', [50, 1]], None), ('regression variant: negative input', ['-1', [30000, 1001]], None), ('partial repair probe: negative input', ['-1', [50, 1]], None), ('partial repair variant: negative input', ['-0.5', [25, 1]], None), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('normal control', ['0.14', [30000, 1001]], [4, '00:00:00:04']), ('normal control', ['0.0166', [50, 1]], [1, '00:00:00:01']), ('normal control', ['1.001', [50, 1]], [50, '00:00:01:00'])]]
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 fixtureActualExpectedOutcome
regression: negative input[0, '00:00:00:00']NoneFailed
regression variant: negative input[0, '00:00:00:00']NoneFailed
partial repair probe: negative input[0, '00:00:00:00']NoneFailed
partial repair variant: negative input[0, '00:00:00:00']NoneFailed
boundary control[2, '00:00:00:02'][2, '00:00:00:02']Passed
boundary control[0, '00:00:00:00'][0, '00:00:00:00']Passed
normal control[1, '00:00:00:01'][1, '00:00:00:01']Passed
normal control[296, '00:00:12:08'][296, '00:00:12:08']Passed
normal control[1, '00:00:00:01'][1, '00:00:00:01']Passed

SHA-256 / 5f88214b42d6d5cf6df9086e6c4a681ee2e5c03633e5c106b4aa524765fabf3e

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(sec, fps):
    num,den=fps
    x=Fraction(sec)
    if x<0:
        return None
    n=x*num/den
    fr=math.floor(n+Fraction(1,2))
    nominal=-(-num//den)
    return [fr,'%02d:%02d:%02d:%02d'%(fr//(3600*nominal)%24,fr//(60*nominal)%60,fr//nominal%60,fr%nominal)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: negative input', ['-1', [25, 1]], None), ('regression variant: negative input', ['-0.5', [30000, 1001]], None), ('partial repair probe: negative input', ['-1', [24, 1]], None), ('partial repair variant: negative input', ['-1', [30000, 1001]], None), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('normal control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('normal control', ['12.345', [24000, 1001]], [296, '00:00:12:08']), ('normal control', ['0.02', [50, 1]], [1, '00:00:00:01'])], [('regression: negative input', ['-1', [24000, 1001]], None), ('regression variant: negative input', ['-1', [50, 1]], None), ('partial repair probe: negative input', ['-0.5', [25, 1]], None), ('partial repair variant: negative input', ['-1', [25, 1]], None), ('boundary control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('normal control', ['0.22', [24, 1]], [5, '00:00:00:05']), ('normal control', ['0', [24000, 1001]], [0, '00:00:00:00']), ('normal control', ['7.3', [24, 1]], [175, '00:00:07:07'])], [('regression: negative input', ['-1', [24, 1]], None), ('regression variant: negative input', ['-0.5', [24000, 1001]], None), ('partial repair probe: negative input', ['-0.5', [50, 1]], None), ('partial repair variant: negative input', ['-1', [24000, 1001]], None), ('boundary control', ['1.001', [30000, 1001]], [30, '00:00:01:00']), ('boundary control', ['0.02', [25, 1]], [1, '00:00:00:01']), ('normal control', ['0.04', [24, 1]], [1, '00:00:00:01']), ('normal control', ['0.18', [24, 1]], [4, '00:00:00:04']), ('normal control', ['0.02', [30000, 1001]], [1, '00:00:00:01'])], [('regression: negative input', ['-0.5', [25, 1]], None), ('regression variant: negative input', ['-0.5', [24, 1]], None), ('partial repair probe: negative input', ['-0.5', [30000, 1001]], None), ('partial repair variant: negative input', ['-1', [24, 1]], None), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('boundary control', ['1.001', [30000, 1001]], [30, '00:00:01:00']), ('normal control', ['0.1', [24000, 1001]], [2, '00:00:00:02']), ('normal control', ['3600', [30000, 1001]], [107892, '00:59:56:12']), ('normal control', ['0.04', [24000, 1001]], [1, '00:00:00:01'])], [('regression: negative input', ['-0.5', [50, 1]], None), ('regression variant: negative input', ['-1', [30000, 1001]], None), ('partial repair probe: negative input', ['-1', [50, 1]], None), ('partial repair variant: negative input', ['-0.5', [25, 1]], None), ('boundary control', ['0.06', [25, 1]], [2, '00:00:00:02']), ('boundary control', ['0', [24, 1]], [0, '00:00:00:00']), ('normal control', ['0.14', [30000, 1001]], [4, '00:00:00:04']), ('normal control', ['0.0166', [50, 1]], [1, '00:00:00:01']), ('normal control', ['1.001', [50, 1]], [50, '00:00:01:00'])]]
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 fixtureActualExpectedOutcome
regression: negative inputNoneNonePassed
regression variant: negative inputNoneNonePassed
partial repair probe: negative inputNoneNonePassed
partial repair variant: negative inputNoneNonePassed
boundary control[2, '00:00:00:02'][2, '00:00:00:02']Passed
boundary control[0, '00:00:00:00'][0, '00:00:00:00']Passed
normal control[1, '00:00:00:01'][1, '00:00:00:01']Passed
normal control[296, '00:00:12:08'][296, '00:00:12:08']Passed
normal control[1, '00:00:00:01'][1, '00:00:00:01']Passed

SHA-256 / 6f906ac1aded622f667cf8719819bbfd2d15a4dbdade4b47aeac0a6a790836f3

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 2026-09-29T14:49:38.309956+00:00.

Case digest / 2e5b1f4a7c9c88b349c16a8bd1b7281cd5bf1dcbf6acb5295416d32fe3951c57