FA-78056 / Subtitle cue timing / Open access
Overlapping cue row stacking: row occupancy update · case 01
Reused rows receive overlapping cues.
ROOT CAUSE
Reusing a row records the cue start as its occupancy end.
VERIFIED REPAIR
Record the cue end as the row occupancy end.
Unsuccessful approach: Recording e-1 frees the row one millisecond before the cue actually ends.
Case contract
Assign overlapping cues to display rows. Cues are processed by (start, input index); a row is free at time t when the last cue placed there ended at or before t (end exclusive). Each cue takes the lowest free row, or opens a new row. Return the row of each cue in input order.
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(cues):
order=sorted(range(len(cues)),key=lambda i:(cues[i][0],i))
row_end=[]
rows=[0]*len(cues)
for i in order:
s,e=cues[i]
for r in range(len(row_end)):
if row_end[r]<=s:
row_end[r]=s
rows[i]=r
break
else:
row_end.append(e)
rows[i]=len(row_end)-1
return rows
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: row occupancy update', [[[500, 700], [200, 400], [300, 400], [500, 900], [300, 500], [1000, 1400]]], [0, 0, 1, 1, 2, 0]), ('regression variant: row occupancy update', [[[500, 800], [300, 400], [1000, 1200], [300, 600], [500, 600], [200, 300]]], [0, 0, 0, 1, 2, 0]), ('partial repair probe: row occupancy update', [[[1000, 1400], [300, 700], [1000, 1001], [0, 400], [300, 1200], [1000, 1100]]], [0, 1, 1, 0, 2, 3]), ('partial repair variant: row occupancy update', [[[500, 501], [300, 301], [1000, 1300], [300, 500], [0, 400], [100, 101]]], [0, 1, 0, 2, 0, 1]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('normal control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('normal control', [[[1000, 1001]]], [0]), ('normal control', [[[100, 1000]]], [0])], [('regression: row occupancy update', [[[1000, 1900], [100, 1000], [500, 900], [500, 501], [500, 900], [200, 300]]], [0, 0, 1, 2, 3, 1]), ('regression variant: row occupancy update', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair probe: row occupancy update', [[[1000, 1001], [0, 300], [300, 600], [1000, 1001], [0, 1], [0, 900]]], [0, 0, 0, 1, 1, 2]), ('partial repair variant: row occupancy update', [[[100, 101], [200, 201], [1000, 1300], [1000, 1100], [0, 200], [200, 201]]], [1, 0, 0, 1, 0, 1]), ('boundary control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('normal control', [[[200, 500], [0, 900], [1000, 1100], [500, 900]]], [1, 0, 0, 1]), ('normal control', [[[200, 300], [500, 900]]], [0, 0]), ('normal control', [[[0, 400], [300, 600]]], [0, 1])], [('regression: row occupancy update', [[[100, 1000], [500, 600], [200, 500], [200, 500], [0, 200], [100, 101]]], [1, 0, 0, 2, 0, 2]), ('regression variant: row occupancy update', [[[200, 201], [300, 500], [200, 201], [1000, 1300], [300, 400], [0, 200]]], [0, 0, 1, 0, 1, 0]), ('partial repair probe: row occupancy update', [[[0, 200], [300, 700], [1000, 1001], [1000, 1001], [100, 300]]], [0, 0, 0, 1, 1]), ('partial repair variant: row occupancy update', [[[500, 501], [500, 1400], [1000, 1400], [1000, 1300], [0, 200]]], [0, 1, 0, 2, 0]), ('boundary control', [[[0, 100]]], [0]), ('boundary control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('normal control', [[[100, 500], [200, 300], [1000, 1100]]], [0, 1, 0]), ('normal control', [[[300, 500], [100, 500]]], [1, 0]), ('normal control', [[[300, 700]]], [0])], [('regression: row occupancy update', [[[0, 300], [500, 1400], [0, 1], [1000, 1001], [1000, 1300]]], [0, 0, 1, 1, 2]), ('regression variant: row occupancy update', [[[200, 500], [1000, 1100], [1000, 1200], [0, 900]]], [1, 0, 1, 0]), ('partial repair probe: row occupancy update', [[[300, 400], [1000, 1001], [1000, 1900]]], [0, 0, 1]), ('partial repair variant: row occupancy update', [[[0, 300], [0, 1], [200, 201], [200, 400], [200, 500]]], [0, 1, 1, 2, 3]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[100, 200], [500, 501]]], [0, 0]), ('normal control', [[[0, 900], [200, 1100]]], [0, 1]), ('normal control', [[[300, 1200], [0, 200]]], [0, 0])], [('regression: row occupancy update', [[[300, 1200], [1000, 1100], [300, 301], [100, 101]]], [0, 1, 1, 0]), ('regression variant: row occupancy update', [[[1000, 1900], [100, 200], [500, 501], [200, 1100], [300, 301]]], [1, 0, 1, 0, 1]), ('partial repair probe: row occupancy update', [[[200, 300], [500, 600], [1000, 1001], [1000, 1300], [100, 1000], [0, 300]]], [2, 0, 0, 1, 1, 0]), ('partial repair variant: row occupancy update', [[[1000, 1300], [0, 900], [200, 300], [300, 301], [300, 1200]]], [0, 0, 1, 1, 2]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('normal control', [[[0, 900], [500, 1400]]], [0, 1]), ('normal control', [[[300, 301], [0, 900], [0, 900], [0, 400], [0, 300]]], [3, 0, 1, 2, 3]), ('normal control', [[[300, 600]]], [0])]]
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: row occupancy update | [0, 0, 1, 0, 2, 0] | [0, 0, 1, 1, 2, 0] | Failed |
| regression variant: row occupancy update | [0, 0, 0, 0, 0, 0] | [0, 0, 0, 1, 2, 0] | Failed |
| partial repair probe: row occupancy update | [0, 1, 0, 0, 2, 0] | [0, 1, 1, 0, 2, 3] | Failed |
| partial repair variant: row occupancy update | [0, 1, 0, 1, 0, 1] | [0, 1, 0, 2, 0, 1] | Failed |
| boundary control | [0, 0] | [0, 0] | Passed |
| boundary control | [0, 1, 1] | [0, 1, 1] | Passed |
| normal control | [0, 1, 1] | [0, 1, 1] | Passed |
| normal control | [0] | [0] | Passed |
| normal control | [0] | [0] | Passed |
SHA-256 / 09692c319481f670da0cc3052c05423bd55849137397b622be75c0767cf80c1b
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(cues):
order=sorted(range(len(cues)),key=lambda i:(cues[i][0],i))
row_end=[]
rows=[0]*len(cues)
for i in order:
s,e=cues[i]
for r in range(len(row_end)):
if row_end[r]<=s:
row_end[r]=e-1
rows[i]=r
break
else:
row_end.append(e)
rows[i]=len(row_end)-1
return rows
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: row occupancy update', [[[500, 700], [200, 400], [300, 400], [500, 900], [300, 500], [1000, 1400]]], [0, 0, 1, 1, 2, 0]), ('regression variant: row occupancy update', [[[500, 800], [300, 400], [1000, 1200], [300, 600], [500, 600], [200, 300]]], [0, 0, 0, 1, 2, 0]), ('partial repair probe: row occupancy update', [[[1000, 1400], [300, 700], [1000, 1001], [0, 400], [300, 1200], [1000, 1100]]], [0, 1, 1, 0, 2, 3]), ('partial repair variant: row occupancy update', [[[500, 501], [300, 301], [1000, 1300], [300, 500], [0, 400], [100, 101]]], [0, 1, 0, 2, 0, 1]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('normal control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('normal control', [[[1000, 1001]]], [0]), ('normal control', [[[100, 1000]]], [0])], [('regression: row occupancy update', [[[1000, 1900], [100, 1000], [500, 900], [500, 501], [500, 900], [200, 300]]], [0, 0, 1, 2, 3, 1]), ('regression variant: row occupancy update', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair probe: row occupancy update', [[[1000, 1001], [0, 300], [300, 600], [1000, 1001], [0, 1], [0, 900]]], [0, 0, 0, 1, 1, 2]), ('partial repair variant: row occupancy update', [[[100, 101], [200, 201], [1000, 1300], [1000, 1100], [0, 200], [200, 201]]], [1, 0, 0, 1, 0, 1]), ('boundary control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('normal control', [[[200, 500], [0, 900], [1000, 1100], [500, 900]]], [1, 0, 0, 1]), ('normal control', [[[200, 300], [500, 900]]], [0, 0]), ('normal control', [[[0, 400], [300, 600]]], [0, 1])], [('regression: row occupancy update', [[[100, 1000], [500, 600], [200, 500], [200, 500], [0, 200], [100, 101]]], [1, 0, 0, 2, 0, 2]), ('regression variant: row occupancy update', [[[200, 201], [300, 500], [200, 201], [1000, 1300], [300, 400], [0, 200]]], [0, 0, 1, 0, 1, 0]), ('partial repair probe: row occupancy update', [[[0, 200], [300, 700], [1000, 1001], [1000, 1001], [100, 300]]], [0, 0, 0, 1, 1]), ('partial repair variant: row occupancy update', [[[500, 501], [500, 1400], [1000, 1400], [1000, 1300], [0, 200]]], [0, 1, 0, 2, 0]), ('boundary control', [[[0, 100]]], [0]), ('boundary control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('normal control', [[[100, 500], [200, 300], [1000, 1100]]], [0, 1, 0]), ('normal control', [[[300, 500], [100, 500]]], [1, 0]), ('normal control', [[[300, 700]]], [0])], [('regression: row occupancy update', [[[0, 300], [500, 1400], [0, 1], [1000, 1001], [1000, 1300]]], [0, 0, 1, 1, 2]), ('regression variant: row occupancy update', [[[200, 500], [1000, 1100], [1000, 1200], [0, 900]]], [1, 0, 1, 0]), ('partial repair probe: row occupancy update', [[[300, 400], [1000, 1001], [1000, 1900]]], [0, 0, 1]), ('partial repair variant: row occupancy update', [[[0, 300], [0, 1], [200, 201], [200, 400], [200, 500]]], [0, 1, 1, 2, 3]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[100, 200], [500, 501]]], [0, 0]), ('normal control', [[[0, 900], [200, 1100]]], [0, 1]), ('normal control', [[[300, 1200], [0, 200]]], [0, 0])], [('regression: row occupancy update', [[[300, 1200], [1000, 1100], [300, 301], [100, 101]]], [0, 1, 1, 0]), ('regression variant: row occupancy update', [[[1000, 1900], [100, 200], [500, 501], [200, 1100], [300, 301]]], [1, 0, 1, 0, 1]), ('partial repair probe: row occupancy update', [[[200, 300], [500, 600], [1000, 1001], [1000, 1300], [100, 1000], [0, 300]]], [2, 0, 0, 1, 1, 0]), ('partial repair variant: row occupancy update', [[[1000, 1300], [0, 900], [200, 300], [300, 301], [300, 1200]]], [0, 0, 1, 1, 2]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('normal control', [[[0, 900], [500, 1400]]], [0, 1]), ('normal control', [[[300, 301], [0, 900], [0, 900], [0, 400], [0, 300]]], [3, 0, 1, 2, 3]), ('normal control', [[[300, 600]]], [0])]]
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: row occupancy update | [0, 0, 1, 1, 2, 0] | [0, 0, 1, 1, 2, 0] | Passed |
| regression variant: row occupancy update | [0, 0, 0, 1, 2, 0] | [0, 0, 0, 1, 2, 0] | Passed |
| partial repair probe: row occupancy update | [0, 1, 1, 0, 2, 1] | [0, 1, 1, 0, 2, 3] | Failed |
| partial repair variant: row occupancy update | [0, 1, 0, 1, 0, 1] | [0, 1, 0, 2, 0, 1] | Failed |
| boundary control | [0, 0] | [0, 0] | Passed |
| boundary control | [0, 1, 1] | [0, 1, 1] | Passed |
| normal control | [0, 1, 1] | [0, 1, 1] | Passed |
| normal control | [0] | [0] | Passed |
| normal control | [0] | [0] | Passed |
SHA-256 / 6c46f1aae21ede5cbd782f5f7f1b395734886ae8103c76e08de6d514093da70c
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(cues):
order=sorted(range(len(cues)),key=lambda i:(cues[i][0],i))
row_end=[]
rows=[0]*len(cues)
for i in order:
s,e=cues[i]
for r in range(len(row_end)):
if row_end[r]<=s:
row_end[r]=e
rows[i]=r
break
else:
row_end.append(e)
rows[i]=len(row_end)-1
return rows
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: row occupancy update', [[[500, 700], [200, 400], [300, 400], [500, 900], [300, 500], [1000, 1400]]], [0, 0, 1, 1, 2, 0]), ('regression variant: row occupancy update', [[[500, 800], [300, 400], [1000, 1200], [300, 600], [500, 600], [200, 300]]], [0, 0, 0, 1, 2, 0]), ('partial repair probe: row occupancy update', [[[1000, 1400], [300, 700], [1000, 1001], [0, 400], [300, 1200], [1000, 1100]]], [0, 1, 1, 0, 2, 3]), ('partial repair variant: row occupancy update', [[[500, 501], [300, 301], [1000, 1300], [300, 500], [0, 400], [100, 101]]], [0, 1, 0, 2, 0, 1]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('normal control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('normal control', [[[1000, 1001]]], [0]), ('normal control', [[[100, 1000]]], [0])], [('regression: row occupancy update', [[[1000, 1900], [100, 1000], [500, 900], [500, 501], [500, 900], [200, 300]]], [0, 0, 1, 2, 3, 1]), ('regression variant: row occupancy update', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair probe: row occupancy update', [[[1000, 1001], [0, 300], [300, 600], [1000, 1001], [0, 1], [0, 900]]], [0, 0, 0, 1, 1, 2]), ('partial repair variant: row occupancy update', [[[100, 101], [200, 201], [1000, 1300], [1000, 1100], [0, 200], [200, 201]]], [1, 0, 0, 1, 0, 1]), ('boundary control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('normal control', [[[200, 500], [0, 900], [1000, 1100], [500, 900]]], [1, 0, 0, 1]), ('normal control', [[[200, 300], [500, 900]]], [0, 0]), ('normal control', [[[0, 400], [300, 600]]], [0, 1])], [('regression: row occupancy update', [[[100, 1000], [500, 600], [200, 500], [200, 500], [0, 200], [100, 101]]], [1, 0, 0, 2, 0, 2]), ('regression variant: row occupancy update', [[[200, 201], [300, 500], [200, 201], [1000, 1300], [300, 400], [0, 200]]], [0, 0, 1, 0, 1, 0]), ('partial repair probe: row occupancy update', [[[0, 200], [300, 700], [1000, 1001], [1000, 1001], [100, 300]]], [0, 0, 0, 1, 1]), ('partial repair variant: row occupancy update', [[[500, 501], [500, 1400], [1000, 1400], [1000, 1300], [0, 200]]], [0, 1, 0, 2, 0]), ('boundary control', [[[0, 100]]], [0]), ('boundary control', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('normal control', [[[100, 500], [200, 300], [1000, 1100]]], [0, 1, 0]), ('normal control', [[[300, 500], [100, 500]]], [1, 0]), ('normal control', [[[300, 700]]], [0])], [('regression: row occupancy update', [[[0, 300], [500, 1400], [0, 1], [1000, 1001], [1000, 1300]]], [0, 0, 1, 1, 2]), ('regression variant: row occupancy update', [[[200, 500], [1000, 1100], [1000, 1200], [0, 900]]], [1, 0, 1, 0]), ('partial repair probe: row occupancy update', [[[300, 400], [1000, 1001], [1000, 1900]]], [0, 0, 1]), ('partial repair variant: row occupancy update', [[[0, 300], [0, 1], [200, 201], [200, 400], [200, 500]]], [0, 1, 1, 2, 3]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[100, 200], [500, 501]]], [0, 0]), ('normal control', [[[0, 900], [200, 1100]]], [0, 1]), ('normal control', [[[300, 1200], [0, 200]]], [0, 0])], [('regression: row occupancy update', [[[300, 1200], [1000, 1100], [300, 301], [100, 101]]], [0, 1, 1, 0]), ('regression variant: row occupancy update', [[[1000, 1900], [100, 200], [500, 501], [200, 1100], [300, 301]]], [1, 0, 1, 0, 1]), ('partial repair probe: row occupancy update', [[[200, 300], [500, 600], [1000, 1001], [1000, 1300], [100, 1000], [0, 300]]], [2, 0, 0, 1, 1, 0]), ('partial repair variant: row occupancy update', [[[1000, 1300], [0, 900], [200, 300], [300, 301], [300, 1200]]], [0, 0, 1, 1, 2]), ('boundary control', [[[0, 100], [100, 200]]], [0, 0]), ('boundary control', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('normal control', [[[0, 900], [500, 1400]]], [0, 1]), ('normal control', [[[300, 301], [0, 900], [0, 900], [0, 400], [0, 300]]], [3, 0, 1, 2, 3]), ('normal control', [[[300, 600]]], [0])]]
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: row occupancy update | [0, 0, 1, 1, 2, 0] | [0, 0, 1, 1, 2, 0] | Passed |
| regression variant: row occupancy update | [0, 0, 0, 1, 2, 0] | [0, 0, 0, 1, 2, 0] | Passed |
| partial repair probe: row occupancy update | [0, 1, 1, 0, 2, 3] | [0, 1, 1, 0, 2, 3] | Passed |
| partial repair variant: row occupancy update | [0, 1, 0, 2, 0, 1] | [0, 1, 0, 2, 0, 1] | Passed |
| boundary control | [0, 0] | [0, 0] | Passed |
| boundary control | [0, 1, 1] | [0, 1, 1] | Passed |
| normal control | [0, 1, 1] | [0, 1, 1] | Passed |
| normal control | [0] | [0] | Passed |
| normal control | [0] | [0] | Passed |
SHA-256 / 6fbad1d082a1752150438dd293bdb47cc12a866e8f1b41ccceca490061219956
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 2026-09-29T14:49:31.749248+00:00.
Case digest / 00f98dda02877c08a7ecf766e9d5885293c68b54838e2b9b04ef2dd79c54a957