FA-78521 / Broadcast timecode arithmetic / Open access

Film feet and frames conversion: frame field bound · case 01

A frame field equal to the frames per foot is accepted.

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

ROOT CAUSE

The bound allows ff equal to the frames per foot.

VERIFIED REPAIR

Reject frame fields at or above frames per foot.

Unsuccessful approach: Using the 35mm 4-perf value of 16 rejects valid 2-perf and 16mm frame fields.

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=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: frame field bound', ['0+16', '35mm4'], None), ('regression variant: frame field bound', ['-0+32', '35mm2'], None), ('partial repair probe: frame field bound', ['100+16', '16mm'], 4016), ('partial repair variant: frame field bound', ['-3+16', '16mm'], -136), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [-1, '35mm4'], '-0+01'), ('normal control', ['0+01', '35mm4'], 1), ('normal control', [-1, '35mm2'], '-0+01')], [('regression: frame field bound', ['-0+40', '16mm'], None), ('regression variant: frame field bound', ['0+32', '35mm2'], None), ('partial repair probe: frame field bound', ['100+16', '35mm2'], 3216), ('partial repair variant: frame field bound', ['-1+20', '16mm'], -60), ('boundary control', [-1, '35mm4'], '-0+01'), ('boundary control', [16, '35mm4'], '1+00'), ('normal control', [1, '16mm'], '0+01'), ('normal control', [0, '16mm'], '0+00'), ('normal control', [-43, '16mm'], '-1+03')], [('regression: frame field bound', ['-3+32', '35mm2'], None), ('regression variant: frame field bound', ['12+16', '35mm4'], None), ('partial repair probe: frame field bound', ['-3+20', '35mm2'], -116), ('partial repair variant: frame field bound', ['-0+31', '16mm'], -31), ('boundary control', ['-0+05', '35mm4'], -5), ('boundary control', [-1, '35mm4'], '-0+01'), ('normal control', ['-3+31', '35mm4'], None), ('normal control', [-32, '35mm2'], '-1+00'), ('normal control', [39, '16mm'], '0+39')], [('regression: frame field bound', ['-0+16', '35mm4'], None), ('regression variant: frame field bound', ['12+40', '16mm'], None), ('partial repair probe: frame field bound', ['1+20', '16mm'], 60), ('partial repair variant: frame field bound', ['-1+32', '16mm'], -72), ('boundary control', ['1+15', '35mm4'], 31), ('boundary control', ['-0+05', '35mm4'], -5), ('normal control', ['0+00', '35mm2'], 0), ('normal control', [33, '35mm2'], '1+01'), ('normal control', ['-0+00', '35mm4'], 0)], [('regression: frame field bound', ['-3+16', '35mm4'], None), ('regression variant: frame field bound', ['100+16', '35mm4'], None), ('partial repair probe: frame field bound', ['1+16', '35mm2'], 48), ('partial repair variant: frame field bound', ['100+39', '16mm'], 4039), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [999, '16mm'], '24+39'), ('normal control', ['-3+40', '35mm4'], None), ('normal control', ['100+31', '35mm4'], None)]]
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: frame field bound	`16`	`None`	Failed
regression variant: frame field bound	`-32`	`None`	Failed
partial repair probe: frame field bound	`4016`	`4016`	Passed
partial repair variant: frame field bound	`-136`	`-136`	Passed
boundary control	`1+00`	`1+00`	Passed
boundary control	`31`	`31`	Passed
normal control	`-0+01`	`-0+01`	Passed
normal control	`1`	`1`	Passed
normal control	`-0+01`	`-0+01`	Passed

SHA-256 / e3e9e20cdaa06a1cd88ccc0190e3bb58c5d7e3355585267aa41a774e9aecf9a0

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)>=16:
        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: frame field bound', ['0+16', '35mm4'], None), ('regression variant: frame field bound', ['-0+32', '35mm2'], None), ('partial repair probe: frame field bound', ['100+16', '16mm'], 4016), ('partial repair variant: frame field bound', ['-3+16', '16mm'], -136), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [-1, '35mm4'], '-0+01'), ('normal control', ['0+01', '35mm4'], 1), ('normal control', [-1, '35mm2'], '-0+01')], [('regression: frame field bound', ['-0+40', '16mm'], None), ('regression variant: frame field bound', ['0+32', '35mm2'], None), ('partial repair probe: frame field bound', ['100+16', '35mm2'], 3216), ('partial repair variant: frame field bound', ['-1+20', '16mm'], -60), ('boundary control', [-1, '35mm4'], '-0+01'), ('boundary control', [16, '35mm4'], '1+00'), ('normal control', [1, '16mm'], '0+01'), ('normal control', [0, '16mm'], '0+00'), ('normal control', [-43, '16mm'], '-1+03')], [('regression: frame field bound', ['-3+32', '35mm2'], None), ('regression variant: frame field bound', ['12+16', '35mm4'], None), ('partial repair probe: frame field bound', ['-3+20', '35mm2'], -116), ('partial repair variant: frame field bound', ['-0+31', '16mm'], -31), ('boundary control', ['-0+05', '35mm4'], -5), ('boundary control', [-1, '35mm4'], '-0+01'), ('normal control', ['-3+31', '35mm4'], None), ('normal control', [-32, '35mm2'], '-1+00'), ('normal control', [39, '16mm'], '0+39')], [('regression: frame field bound', ['-0+16', '35mm4'], None), ('regression variant: frame field bound', ['12+40', '16mm'], None), ('partial repair probe: frame field bound', ['1+20', '16mm'], 60), ('partial repair variant: frame field bound', ['-1+32', '16mm'], -72), ('boundary control', ['1+15', '35mm4'], 31), ('boundary control', ['-0+05', '35mm4'], -5), ('normal control', ['0+00', '35mm2'], 0), ('normal control', [33, '35mm2'], '1+01'), ('normal control', ['-0+00', '35mm4'], 0)], [('regression: frame field bound', ['-3+16', '35mm4'], None), ('regression variant: frame field bound', ['100+16', '35mm4'], None), ('partial repair probe: frame field bound', ['1+16', '35mm2'], 48), ('partial repair variant: frame field bound', ['100+39', '16mm'], 4039), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [999, '16mm'], '24+39'), ('normal control', ['-3+40', '35mm4'], None), ('normal control', ['100+31', '35mm4'], None)]]
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: frame field bound	`None`	`None`	Passed
regression variant: frame field bound	`None`	`None`	Passed
partial repair probe: frame field bound	`None`	`4016`	Failed
partial repair variant: frame field bound	`None`	`-136`	Failed
boundary control	`1+00`	`1+00`	Passed
boundary control	`31`	`31`	Passed
normal control	`-0+01`	`-0+01`	Passed
normal control	`1`	`1`	Passed
normal control	`-0+01`	`-0+01`	Passed

SHA-256 / 080c06aec34bd665810b964ce095296573e3010043b42da15ae56441146514e5

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: frame field bound', ['0+16', '35mm4'], None), ('regression variant: frame field bound', ['-0+32', '35mm2'], None), ('partial repair probe: frame field bound', ['100+16', '16mm'], 4016), ('partial repair variant: frame field bound', ['-3+16', '16mm'], -136), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [-1, '35mm4'], '-0+01'), ('normal control', ['0+01', '35mm4'], 1), ('normal control', [-1, '35mm2'], '-0+01')], [('regression: frame field bound', ['-0+40', '16mm'], None), ('regression variant: frame field bound', ['0+32', '35mm2'], None), ('partial repair probe: frame field bound', ['100+16', '35mm2'], 3216), ('partial repair variant: frame field bound', ['-1+20', '16mm'], -60), ('boundary control', [-1, '35mm4'], '-0+01'), ('boundary control', [16, '35mm4'], '1+00'), ('normal control', [1, '16mm'], '0+01'), ('normal control', [0, '16mm'], '0+00'), ('normal control', [-43, '16mm'], '-1+03')], [('regression: frame field bound', ['-3+32', '35mm2'], None), ('regression variant: frame field bound', ['12+16', '35mm4'], None), ('partial repair probe: frame field bound', ['-3+20', '35mm2'], -116), ('partial repair variant: frame field bound', ['-0+31', '16mm'], -31), ('boundary control', ['-0+05', '35mm4'], -5), ('boundary control', [-1, '35mm4'], '-0+01'), ('normal control', ['-3+31', '35mm4'], None), ('normal control', [-32, '35mm2'], '-1+00'), ('normal control', [39, '16mm'], '0+39')], [('regression: frame field bound', ['-0+16', '35mm4'], None), ('regression variant: frame field bound', ['12+40', '16mm'], None), ('partial repair probe: frame field bound', ['1+20', '16mm'], 60), ('partial repair variant: frame field bound', ['-1+32', '16mm'], -72), ('boundary control', ['1+15', '35mm4'], 31), ('boundary control', ['-0+05', '35mm4'], -5), ('normal control', ['0+00', '35mm2'], 0), ('normal control', [33, '35mm2'], '1+01'), ('normal control', ['-0+00', '35mm4'], 0)], [('regression: frame field bound', ['-3+16', '35mm4'], None), ('regression variant: frame field bound', ['100+16', '35mm4'], None), ('partial repair probe: frame field bound', ['1+16', '35mm2'], 48), ('partial repair variant: frame field bound', ['100+39', '16mm'], 4039), ('boundary control', [16, '35mm4'], '1+00'), ('boundary control', ['1+15', '35mm4'], 31), ('normal control', [999, '16mm'], '24+39'), ('normal control', ['-3+40', '35mm4'], None), ('normal control', ['100+31', '35mm4'], None)]]
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: frame field bound	`None`	`None`	Passed
regression variant: frame field bound	`None`	`None`	Passed
partial repair probe: frame field bound	`4016`	`4016`	Passed
partial repair variant: frame field bound	`-136`	`-136`	Passed
boundary control	`1+00`	`1+00`	Passed
boundary control	`31`	`31`	Passed
normal control	`-0+01`	`-0+01`	Passed
normal control	`1`	`1`	Passed
normal control	`-0+01`	`-0+01`	Passed

SHA-256 / 776ad82a693fae7d6f8b5a0c311b516bd9a07fb81a6d8b05f784b225f410151c

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 2026-09-29T14:49:35.957255+00:00.

Case digest / 88e152484e5eaae2d0535048e31168325a43c2dc410b48adf71714e71856fa0f