FA-78531 / Broadcast timecode arithmetic / Open access

Film feet and frames conversion: magnitude composition · case 01

Negative footage with frames converts to a count several frames too small.

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

ROOT CAUSE

The frames are added to the signed feet before the sign is applied.

VERIFIED REPAIR

Combine the absolute feet with the frames, then apply the sign.

Unsuccessful approach: Taking the absolute value after combining still subtracts the frames inside the foot.

Case contract

Frames per foot: 35mm4 16, 35mm2 32, 16mm 40. An int frame count converts to "[-]F+ff" (feet, two-digit frames, sign in front for negatives); a string "[-]F+ff" converts to a signed frame count, with ff below frames per foot (else None). "-0+05" means -5.

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, gauge):
    per={'35mm4':16,'35mm2':32,'16mm':40}[gauge]
    if isinstance(value,int):
        sign='-' if value<0 else ''
        v=abs(value)
        return '%s%d+%02d'%(sign,v//per,v%per)
    ft,fr=value.split('+')
    if int(fr)>=per:
        return None
    n=int(ft)*per+int(fr)
    return -n if ft.startswith('-') else n
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: magnitude composition', ['-3+20', '35mm2'], -116), ('regression variant: magnitude composition', ['-1+20', '16mm'], -60), ('partial repair probe: magnitude composition', ['-3+16', '16mm'], -136), ('partial repair variant: magnitude composition', ['-3+01', '35mm4'], -49), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [-1, '35mm4'], '-0+01'), ('normal control', ['0+16', '35mm4'], None), ('normal control', ['2+39', '16mm'], 119)], [('regression: magnitude composition', ['-3+00', '35mm2'], -96), ('regression variant: magnitude composition', ['-1+32', '16mm'], -72), ('partial repair probe: magnitude composition', ['-3+15', '16mm'], -135), ('partial repair variant: magnitude composition', ['-1+31', '35mm2'], -63), ('boundary control', [-1, '35mm4'], '-0+01'), ('boundary control', ['0+16', '35mm4'], None), ('normal control', [-1, '35mm2'], '-0+01'), ('normal control', [1, '16mm'], '0+01'), ('normal control', ['100+16', '16mm'], 4016)], [('regression: magnitude composition', ['-3+01', '35mm2'], -97), ('regression variant: magnitude composition', ['-3+15', '35mm2'], -111), ('partial repair probe: magnitude composition', ['-1+20', '16mm'], -60), ('partial repair variant: magnitude composition', ['-1+20', '35mm2'], -52), ('boundary control', ['-0+05', '35mm4'], -5), ('boundary control', ['2+39', '16mm'], 119), ('normal control', [0, '16mm'], '0+00'), ('normal control', ['100+16', '35mm2'], 3216), ('normal control', [-5, '16mm'], '-0+05')], [('regression: magnitude composition', ['-3+16', '16mm'], -136), ('regression variant: magnitude composition', ['-1+15', '35mm4'], -31), ('partial repair probe: magnitude composition', ['-1+32', '16mm'], -72), ('partial repair variant: magnitude composition', ['-3+31', '16mm'], -151), ('boundary control', ['1+15', '35mm4'], 31), ('boundary control', [16, '35mm4'], '1+00'), ('normal control', [-40, '16mm'], '-1+00'), ('normal control', ['-3+32', '35mm2'], None), ('normal control', ['-0+16', '35mm4'], None)], [('regression: magnitude composition', ['-3+15', '16mm'], -135), ('regression variant: magnitude composition', ['-3+00', '35mm4'], -48), ('partial repair probe: magnitude composition', ['-3+15', '35mm2'], -111), ('partial repair variant: magnitude composition', ['-3+20', '16mm'], -140), ('boundary control', ['0+16', '35mm4'], None), ('boundary control', [-1, '35mm4'], '-0+01'), ('normal control', [39, '16mm'], '0+39'), ('normal control', ['0+00', '35mm2'], 0), ('normal control', [-5, '35mm2'], '-0+05')]]
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: magnitude composition	`76`	`-116`	Failed
regression variant: magnitude composition	`20`	`-60`	Failed
partial repair probe: magnitude composition	`104`	`-136`	Failed
partial repair variant: magnitude composition	`47`	`-49`	Failed
boundary control	`1+00`	`1+00`	Passed
boundary control	`31`	`31`	Passed
normal control	`-0+01`	`-0+01`	Passed
normal control	`None`	`None`	Passed
normal control	`119`	`119`	Passed

SHA-256 / 92005760dd39638f0f473482c35f6b0603b5c5d5bff4dd4b9a7fe0174f10ffca

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(value, gauge):
    per={'35mm4':16,'35mm2':32,'16mm':40}[gauge]
    if isinstance(value,int):
        sign='-' if value<0 else ''
        v=abs(value)
        return '%s%d+%02d'%(sign,v//per,v%per)
    ft,fr=value.split('+')
    if int(fr)>=per:
        return None
    n=abs(int(ft)*per+int(fr))
    return -n if ft.startswith('-') else n
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: magnitude composition', ['-3+20', '35mm2'], -116), ('regression variant: magnitude composition', ['-1+20', '16mm'], -60), ('partial repair probe: magnitude composition', ['-3+16', '16mm'], -136), ('partial repair variant: magnitude composition', ['-3+01', '35mm4'], -49), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [-1, '35mm4'], '-0+01'), ('normal control', ['0+16', '35mm4'], None), ('normal control', ['2+39', '16mm'], 119)], [('regression: magnitude composition', ['-3+00', '35mm2'], -96), ('regression variant: magnitude composition', ['-1+32', '16mm'], -72), ('partial repair probe: magnitude composition', ['-3+15', '16mm'], -135), ('partial repair variant: magnitude composition', ['-1+31', '35mm2'], -63), ('boundary control', [-1, '35mm4'], '-0+01'), ('boundary control', ['0+16', '35mm4'], None), ('normal control', [-1, '35mm2'], '-0+01'), ('normal control', [1, '16mm'], '0+01'), ('normal control', ['100+16', '16mm'], 4016)], [('regression: magnitude composition', ['-3+01', '35mm2'], -97), ('regression variant: magnitude composition', ['-3+15', '35mm2'], -111), ('partial repair probe: magnitude composition', ['-1+20', '16mm'], -60), ('partial repair variant: magnitude composition', ['-1+20', '35mm2'], -52), ('boundary control', ['-0+05', '35mm4'], -5), ('boundary control', ['2+39', '16mm'], 119), ('normal control', [0, '16mm'], '0+00'), ('normal control', ['100+16', '35mm2'], 3216), ('normal control', [-5, '16mm'], '-0+05')], [('regression: magnitude composition', ['-3+16', '16mm'], -136), ('regression variant: magnitude composition', ['-1+15', '35mm4'], -31), ('partial repair probe: magnitude composition', ['-1+32', '16mm'], -72), ('partial repair variant: magnitude composition', ['-3+31', '16mm'], -151), ('boundary control', ['1+15', '35mm4'], 31), ('boundary control', [16, '35mm4'], '1+00'), ('normal control', [-40, '16mm'], '-1+00'), ('normal control', ['-3+32', '35mm2'], None), ('normal control', ['-0+16', '35mm4'], None)], [('regression: magnitude composition', ['-3+15', '16mm'], -135), ('regression variant: magnitude composition', ['-3+00', '35mm4'], -48), ('partial repair probe: magnitude composition', ['-3+15', '35mm2'], -111), ('partial repair variant: magnitude composition', ['-3+20', '16mm'], -140), ('boundary control', ['0+16', '35mm4'], None), ('boundary control', [-1, '35mm4'], '-0+01'), ('normal control', [39, '16mm'], '0+39'), ('normal control', ['0+00', '35mm2'], 0), ('normal control', [-5, '35mm2'], '-0+05')]]
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: magnitude composition	`-76`	`-116`	Failed
regression variant: magnitude composition	`-20`	`-60`	Failed
partial repair probe: magnitude composition	`-104`	`-136`	Failed
partial repair variant: magnitude composition	`-47`	`-49`	Failed
boundary control	`1+00`	`1+00`	Passed
boundary control	`31`	`31`	Passed
normal control	`-0+01`	`-0+01`	Passed
normal control	`None`	`None`	Passed
normal control	`119`	`119`	Passed

SHA-256 / ea7574f831e8ea2d7b2a73ac394d8785a7293b52fe574c59b610c50f9ded5adc

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(value, gauge):
    per={'35mm4':16,'35mm2':32,'16mm':40}[gauge]
    if isinstance(value,int):
        sign='-' if value<0 else ''
        v=abs(value)
        return '%s%d+%02d'%(sign,v//per,v%per)
    ft,fr=value.split('+')
    if int(fr)>=per:
        return None
    n=abs(int(ft))*per+int(fr)
    return -n if ft.startswith('-') else n
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: magnitude composition', ['-3+20', '35mm2'], -116), ('regression variant: magnitude composition', ['-1+20', '16mm'], -60), ('partial repair probe: magnitude composition', ['-3+16', '16mm'], -136), ('partial repair variant: magnitude composition', ['-3+01', '35mm4'], -49), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [-1, '35mm4'], '-0+01'), ('normal control', ['0+16', '35mm4'], None), ('normal control', ['2+39', '16mm'], 119)], [('regression: magnitude composition', ['-3+00', '35mm2'], -96), ('regression variant: magnitude composition', ['-1+32', '16mm'], -72), ('partial repair probe: magnitude composition', ['-3+15', '16mm'], -135), ('partial repair variant: magnitude composition', ['-1+31', '35mm2'], -63), ('boundary control', [-1, '35mm4'], '-0+01'), ('boundary control', ['0+16', '35mm4'], None), ('normal control', [-1, '35mm2'], '-0+01'), ('normal control', [1, '16mm'], '0+01'), ('normal control', ['100+16', '16mm'], 4016)], [('regression: magnitude composition', ['-3+01', '35mm2'], -97), ('regression variant: magnitude composition', ['-3+15', '35mm2'], -111), ('partial repair probe: magnitude composition', ['-1+20', '16mm'], -60), ('partial repair variant: magnitude composition', ['-1+20', '35mm2'], -52), ('boundary control', ['-0+05', '35mm4'], -5), ('boundary control', ['2+39', '16mm'], 119), ('normal control', [0, '16mm'], '0+00'), ('normal control', ['100+16', '35mm2'], 3216), ('normal control', [-5, '16mm'], '-0+05')], [('regression: magnitude composition', ['-3+16', '16mm'], -136), ('regression variant: magnitude composition', ['-1+15', '35mm4'], -31), ('partial repair probe: magnitude composition', ['-1+32', '16mm'], -72), ('partial repair variant: magnitude composition', ['-3+31', '16mm'], -151), ('boundary control', ['1+15', '35mm4'], 31), ('boundary control', [16, '35mm4'], '1+00'), ('normal control', [-40, '16mm'], '-1+00'), ('normal control', ['-3+32', '35mm2'], None), ('normal control', ['-0+16', '35mm4'], None)], [('regression: magnitude composition', ['-3+15', '16mm'], -135), ('regression variant: magnitude composition', ['-3+00', '35mm4'], -48), ('partial repair probe: magnitude composition', ['-3+15', '35mm2'], -111), ('partial repair variant: magnitude composition', ['-3+20', '16mm'], -140), ('boundary control', ['0+16', '35mm4'], None), ('boundary control', [-1, '35mm4'], '-0+01'), ('normal control', [39, '16mm'], '0+39'), ('normal control', ['0+00', '35mm2'], 0), ('normal control', [-5, '35mm2'], '-0+05')]]
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: magnitude composition	`-116`	`-116`	Passed
regression variant: magnitude composition	`-60`	`-60`	Passed
partial repair probe: magnitude composition	`-136`	`-136`	Passed
partial repair variant: magnitude composition	`-49`	`-49`	Passed
boundary control	`1+00`	`1+00`	Passed
boundary control	`31`	`31`	Passed
normal control	`-0+01`	`-0+01`	Passed
normal control	`None`	`None`	Passed
normal control	`119`	`119`	Passed

SHA-256 / 7e4480cce81027ea9445329977cbde79e101b96619e7337f12c9e0cbf1d701d7

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 2026-09-29T14:49:35.983696+00:00.

Case digest / c151fbcf8041422779ff204b3877d8d91c6fd96410a600dad0cc7ecec521f598