FA-78276 / Subtitle cue timing / Open access
Recommended cue duration on frame grid: frame ceiling · case 01
Recommended durations fall short of the computed minimum by part of a frame.
ROOT CAUSE
The duration is floored to whole frames.
VERIFIED REPAIR
Round up to whole frames.
Unsuccessful approach: Adding one half and rounding uses half-to-even, so exact odd frame counts gain an extra frame.
Case contract
rules [base,per_char,min,max]. Count characters other than spaces and line breaks; duration = base + count*per_char, clamped to [min,max]; then rounded up to whole frames at fps [N,D]. Return [frames, ceil(frames*1000*D/N)].
Why this case matters
Subtitle timing defects shift, hide or overlap captions that viewers depend on for comprehension and accessibility.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(text, fps, rules):
base,per,lo,hi=rules
n=len(text.replace(' ','').replace('\n',''))
d=base+n*per
d=max(lo,min(hi,d))
num,den=fps
fr=(d*num)//(1000*den)
return [fr,-((-fr*1000*den)//num)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: frame ceiling', ['Two\nlines here', [30000, 1001], [0, 70, 800, 7000]], [26, 868]), ('regression variant: frame ceiling', ['Two\nlines here', [30000, 1001], [300, 50, 1200, 1500]], [36, 1202]), ('partial repair probe: frame ceiling', ['Hello world', [30, 1], [700, 100, 1000, 2000]], [51, 1700]), ('partial repair variant: frame ceiling', ['Hello world', [30, 1], [500, 60, 1000, 6000]], [33, 1100]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['Two\nlines here', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['Hello world', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['ok', [30, 1], [700, 100, 1000, 2000]], [30, 1000])], [('regression: frame ceiling', ['ok', [24, 1], [0, 70, 800, 7000]], [20, 834]), ('regression variant: frame ceiling', ['Two\nlines here', [24000, 1001], [700, 100, 1000, 2000]], [46, 1919]), ('partial repair probe: frame ceiling', ['Two\nlines here', [30, 1], [700, 100, 1000, 2000]], [57, 1900]), ('partial repair variant: frame ceiling', ['A much longer subtitle line to read', [30, 1], [300, 50, 1200, 1500]], [45, 1500]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['Hello world', [30, 1], [0, 70, 800, 7000]], [24, 800]), ('normal control', [' ', [24, 1], [700, 100, 1000, 2000]], [24, 1000]), ('normal control', ['ok', [24, 1], [500, 60, 1000, 6000]], [24, 1000])], [('regression: frame ceiling', ['A much longer subtitle line to read', [24000, 1001], [300, 50, 1200, 1500]], [36, 1502]), ('regression variant: frame ceiling', ['Hello world', [30000, 1001], [0, 70, 800, 7000]], [24, 801]), ('partial repair probe: frame ceiling', [' ', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('partial repair variant: frame ceiling', ['ok', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['ok', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['A much longer subtitle line to read', [24, 1], [700, 100, 1000, 2000]], [48, 2000]), ('normal control', ['', [24, 1], [700, 100, 1000, 2000]], [24, 1000])], [('regression: frame ceiling', ['Hi', [24, 1], [0, 70, 800, 7000]], [20, 834]), ('regression variant: frame ceiling', ['ok', [30000, 1001], [300, 50, 1200, 1500]], [36, 1202]), ('partial repair probe: frame ceiling', ['Hi', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('partial repair variant: frame ceiling', ['', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', [' ', [24, 1], [500, 60, 1000, 6000]], [24, 1000]), ('normal control', ['Hi', [25, 1], [0, 70, 800, 7000]], [20, 800]), ('normal control', ['', [24, 1], [500, 60, 1000, 6000]], [24, 1000])], [('regression: frame ceiling', [' ', [24000, 1001], [0, 70, 800, 7000]], [20, 835]), ('regression variant: frame ceiling', ['', [24, 1], [300, 50, 1200, 1500]], [29, 1209]), ('partial repair probe: frame ceiling', ['ok', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('partial repair variant: frame ceiling', ['Hi', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['A much longer subtitle line to read', [24, 1], [300, 50, 1200, 1500]], [36, 1500]), ('normal control', ['', [30, 1], [700, 100, 1000, 2000]], [30, 1000]), ('normal control', ['', [30, 1], [500, 60, 1000, 6000]], [30, 1000])]]
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 ceiling | [25, 835] | [26, 868] | Failed |
| regression variant: frame ceiling | [35, 1168] | [36, 1202] | Failed |
| partial repair probe: frame ceiling | [51, 1700] | [51, 1700] | Passed |
| partial repair variant: frame ceiling | [33, 1100] | [33, 1100] | Passed |
| boundary control | [50, 2000] | [50, 2000] | Passed |
| normal control | [30, 1200] | [30, 1200] | Passed |
| normal control | [30, 1200] | [30, 1200] | Passed |
| normal control | [30, 1000] | [30, 1000] | Passed |
SHA-256 / eb0b299c948c4857b95a72a056c31331b4b91fc11ef45faee9a5a0c23cb758e3
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(text, fps, rules):
base,per,lo,hi=rules
n=len(text.replace(' ','').replace('\n',''))
d=base+n*per
d=max(lo,min(hi,d))
num,den=fps
fr=round(d*num/(1000*den)+0.5)
return [fr,-((-fr*1000*den)//num)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: frame ceiling', ['Two\nlines here', [30000, 1001], [0, 70, 800, 7000]], [26, 868]), ('regression variant: frame ceiling', ['Two\nlines here', [30000, 1001], [300, 50, 1200, 1500]], [36, 1202]), ('partial repair probe: frame ceiling', ['Hello world', [30, 1], [700, 100, 1000, 2000]], [51, 1700]), ('partial repair variant: frame ceiling', ['Hello world', [30, 1], [500, 60, 1000, 6000]], [33, 1100]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['Two\nlines here', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['Hello world', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['ok', [30, 1], [700, 100, 1000, 2000]], [30, 1000])], [('regression: frame ceiling', ['ok', [24, 1], [0, 70, 800, 7000]], [20, 834]), ('regression variant: frame ceiling', ['Two\nlines here', [24000, 1001], [700, 100, 1000, 2000]], [46, 1919]), ('partial repair probe: frame ceiling', ['Two\nlines here', [30, 1], [700, 100, 1000, 2000]], [57, 1900]), ('partial repair variant: frame ceiling', ['A much longer subtitle line to read', [30, 1], [300, 50, 1200, 1500]], [45, 1500]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['Hello world', [30, 1], [0, 70, 800, 7000]], [24, 800]), ('normal control', [' ', [24, 1], [700, 100, 1000, 2000]], [24, 1000]), ('normal control', ['ok', [24, 1], [500, 60, 1000, 6000]], [24, 1000])], [('regression: frame ceiling', ['A much longer subtitle line to read', [24000, 1001], [300, 50, 1200, 1500]], [36, 1502]), ('regression variant: frame ceiling', ['Hello world', [30000, 1001], [0, 70, 800, 7000]], [24, 801]), ('partial repair probe: frame ceiling', [' ', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('partial repair variant: frame ceiling', ['ok', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['ok', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['A much longer subtitle line to read', [24, 1], [700, 100, 1000, 2000]], [48, 2000]), ('normal control', ['', [24, 1], [700, 100, 1000, 2000]], [24, 1000])], [('regression: frame ceiling', ['Hi', [24, 1], [0, 70, 800, 7000]], [20, 834]), ('regression variant: frame ceiling', ['ok', [30000, 1001], [300, 50, 1200, 1500]], [36, 1202]), ('partial repair probe: frame ceiling', ['Hi', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('partial repair variant: frame ceiling', ['', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', [' ', [24, 1], [500, 60, 1000, 6000]], [24, 1000]), ('normal control', ['Hi', [25, 1], [0, 70, 800, 7000]], [20, 800]), ('normal control', ['', [24, 1], [500, 60, 1000, 6000]], [24, 1000])], [('regression: frame ceiling', [' ', [24000, 1001], [0, 70, 800, 7000]], [20, 835]), ('regression variant: frame ceiling', ['', [24, 1], [300, 50, 1200, 1500]], [29, 1209]), ('partial repair probe: frame ceiling', ['ok', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('partial repair variant: frame ceiling', ['Hi', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['A much longer subtitle line to read', [24, 1], [300, 50, 1200, 1500]], [36, 1500]), ('normal control', ['', [30, 1], [700, 100, 1000, 2000]], [30, 1000]), ('normal control', ['', [30, 1], [500, 60, 1000, 6000]], [30, 1000])]]
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 ceiling | [26, 868] | [26, 868] | Passed |
| regression variant: frame ceiling | [36, 1202] | [36, 1202] | Passed |
| partial repair probe: frame ceiling | [52, 1734] | [51, 1700] | Failed |
| partial repair variant: frame ceiling | [34, 1134] | [33, 1100] | Failed |
| boundary control | [50, 2000] | [50, 2000] | Passed |
| normal control | [30, 1200] | [30, 1200] | Passed |
| normal control | [30, 1200] | [30, 1200] | Passed |
| normal control | [30, 1000] | [30, 1000] | Passed |
SHA-256 / dee4a727342e2698e95981d23e21359353f41b306c7f1d36987a44f10aef8df4
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(text, fps, rules):
base,per,lo,hi=rules
n=len(text.replace(' ','').replace('\n',''))
d=base+n*per
d=max(lo,min(hi,d))
num,den=fps
fr=-((-d*num)//(1000*den))
return [fr,-((-fr*1000*den)//num)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: frame ceiling', ['Two\nlines here', [30000, 1001], [0, 70, 800, 7000]], [26, 868]), ('regression variant: frame ceiling', ['Two\nlines here', [30000, 1001], [300, 50, 1200, 1500]], [36, 1202]), ('partial repair probe: frame ceiling', ['Hello world', [30, 1], [700, 100, 1000, 2000]], [51, 1700]), ('partial repair variant: frame ceiling', ['Hello world', [30, 1], [500, 60, 1000, 6000]], [33, 1100]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['Two\nlines here', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['Hello world', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['ok', [30, 1], [700, 100, 1000, 2000]], [30, 1000])], [('regression: frame ceiling', ['ok', [24, 1], [0, 70, 800, 7000]], [20, 834]), ('regression variant: frame ceiling', ['Two\nlines here', [24000, 1001], [700, 100, 1000, 2000]], [46, 1919]), ('partial repair probe: frame ceiling', ['Two\nlines here', [30, 1], [700, 100, 1000, 2000]], [57, 1900]), ('partial repair variant: frame ceiling', ['A much longer subtitle line to read', [30, 1], [300, 50, 1200, 1500]], [45, 1500]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['Hello world', [30, 1], [0, 70, 800, 7000]], [24, 800]), ('normal control', [' ', [24, 1], [700, 100, 1000, 2000]], [24, 1000]), ('normal control', ['ok', [24, 1], [500, 60, 1000, 6000]], [24, 1000])], [('regression: frame ceiling', ['A much longer subtitle line to read', [24000, 1001], [300, 50, 1200, 1500]], [36, 1502]), ('regression variant: frame ceiling', ['Hello world', [30000, 1001], [0, 70, 800, 7000]], [24, 801]), ('partial repair probe: frame ceiling', [' ', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('partial repair variant: frame ceiling', ['ok', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['ok', [25, 1], [300, 50, 1200, 1500]], [30, 1200]), ('normal control', ['A much longer subtitle line to read', [24, 1], [700, 100, 1000, 2000]], [48, 2000]), ('normal control', ['', [24, 1], [700, 100, 1000, 2000]], [24, 1000])], [('regression: frame ceiling', ['Hi', [24, 1], [0, 70, 800, 7000]], [20, 834]), ('regression variant: frame ceiling', ['ok', [30000, 1001], [300, 50, 1200, 1500]], [36, 1202]), ('partial repair probe: frame ceiling', ['Hi', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('partial repair variant: frame ceiling', ['', [25, 1], [700, 100, 1000, 2000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', [' ', [24, 1], [500, 60, 1000, 6000]], [24, 1000]), ('normal control', ['Hi', [25, 1], [0, 70, 800, 7000]], [20, 800]), ('normal control', ['', [24, 1], [500, 60, 1000, 6000]], [24, 1000])], [('regression: frame ceiling', [' ', [24000, 1001], [0, 70, 800, 7000]], [20, 835]), ('regression variant: frame ceiling', ['', [24, 1], [300, 50, 1200, 1500]], [29, 1209]), ('partial repair probe: frame ceiling', ['ok', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('partial repair variant: frame ceiling', ['Hi', [25, 1], [500, 60, 1000, 6000]], [25, 1000]), ('boundary control', ['A much longer subtitle line to read', [25, 1], [500, 60, 1000, 2000]], [50, 2000]), ('normal control', ['A much longer subtitle line to read', [24, 1], [300, 50, 1200, 1500]], [36, 1500]), ('normal control', ['', [30, 1], [700, 100, 1000, 2000]], [30, 1000]), ('normal control', ['', [30, 1], [500, 60, 1000, 6000]], [30, 1000])]]
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 ceiling | [26, 868] | [26, 868] | Passed |
| regression variant: frame ceiling | [36, 1202] | [36, 1202] | Passed |
| partial repair probe: frame ceiling | [51, 1700] | [51, 1700] | Passed |
| partial repair variant: frame ceiling | [33, 1100] | [33, 1100] | Passed |
| boundary control | [50, 2000] | [50, 2000] | Passed |
| normal control | [30, 1200] | [30, 1200] | Passed |
| normal control | [30, 1200] | [30, 1200] | Passed |
| normal control | [30, 1000] | [30, 1000] | Passed |
SHA-256 / 0d81b67c8c187e804f5691928864539b4d448e22a5c1b3fcf965bc759513d606
Verification & scope
A deterministic bounded teaching model with a stipulated toy contract; it does not claim conformance to any subtitle 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 2026-09-29T14:49:33.982477+00:00.
Case digest / 3d1a5d80a7dae0c84853feb50a8e1a74d514641391edec66c47515dbd2655058