FAILURE MAP
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FA-78041 / Subtitle cue timing / Open access

Overlapping cue row stacking: row free test · case 01

Back-to-back cues climb to a second row instead of reusing the bottom row.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

A row is considered busy at the instant its previous cue ends.

VERIFIED REPAIR

Treat cue ends as exclusive: a row is free when its end is at or before the new start.

Unsuccessful approach: Freeing rows one millisecond early lets overlapping cues share a row.

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]=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 free test', [[[0, 100], [100, 200]]], [0, 0]), ('regression variant: row free test', [[[1000, 1900], [100, 1000], [500, 900], [500, 501], [500, 900], [200, 300]]], [0, 0, 1, 2, 3, 1]), ('partial repair probe: row free test', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair variant: row free test', [[[300, 301], [300, 400]]], [0, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[1000, 1001]]], [0]), ('normal control', [[[1000, 1400]]], [0]), ('normal control', [[[0, 300], [0, 400]]], [0, 1])], [('regression: row free test', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('regression variant: row free test', [[[100, 1000], [500, 600], [200, 500], [200, 500], [0, 200], [100, 101]]], [1, 0, 0, 2, 0, 2]), ('partial repair probe: row free test', [[[200, 201], [300, 500], [200, 201], [1000, 1300], [300, 400], [0, 200]]], [0, 0, 1, 0, 1, 0]), ('partial repair variant: row free test', [[[300, 600], [100, 400], [1000, 1001], [100, 101], [0, 400], [100, 400]]], [2, 1, 0, 2, 0, 3]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[0, 900]]], [0]), ('normal control', [[[100, 500], [200, 300], [1000, 1100]]], [0, 1, 0]), ('normal control', [[[100, 101]]], [0])], [('regression: row free test', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('regression variant: row free test', [[[200, 600], [100, 200], [1000, 1400]]], [0, 0, 0]), ('partial repair probe: row free test', [[[100, 1000], [300, 301], [300, 500], [500, 501]]], [0, 1, 2, 1]), ('partial repair variant: row free test', [[[0, 100], [0, 1], [0, 400], [0, 900], [0, 100]]], [0, 1, 2, 3, 4]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[200, 500], [1000, 1100], [1000, 1200], [0, 900]]], [1, 0, 1, 0]), ('normal control', [[[1000, 1100], [200, 500]]], [0, 0]), ('normal control', [[[1000, 1300], [500, 800], [0, 400], [100, 400]]], [0, 0, 0, 1])], [('regression: row free test', [[[100, 300], [300, 500], [100, 500]]], [0, 0, 1]), ('regression variant: row free test', [[[500, 800], [300, 400], [1000, 1200], [300, 600], [500, 600], [200, 300]]], [0, 0, 0, 1, 2, 0]), ('partial repair probe: row free test', [[[0, 400], [200, 1100], [500, 700], [0, 1], [0, 900], [200, 201]]], [0, 1, 0, 1, 2, 3]), ('partial repair variant: row free test', [[[1000, 1001], [0, 300], [300, 600], [1000, 1001], [0, 1], [0, 900]]], [0, 0, 0, 1, 1, 2]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[300, 1200]]], [0]), ('normal control', [[[0, 900], [500, 1400]]], [0, 1]), ('normal control', [[[500, 600], [0, 1]]], [0, 0])], [('regression: row free test', [[[200, 500], [0, 900], [1000, 1100], [500, 900]]], [1, 0, 0, 1]), ('regression variant: row free test', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair probe: row free test', [[[1000, 1400], [300, 700], [1000, 1001], [0, 400], [300, 1200], [1000, 1100]]], [0, 1, 1, 0, 2, 3]), ('partial repair variant: row free test', [[[0, 200], [300, 700], [1000, 1001], [1000, 1001], [100, 300]]], [0, 0, 0, 1, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[300, 600]]], [0]), ('normal control', [[[0, 100], [0, 900], [300, 700], [0, 200], [200, 400]]], [0, 1, 2, 2, 0]), ('normal control', [[[0, 900], [500, 800], [300, 600]]], [0, 2, 1])]]
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: row free test[0, 1][0, 0]Failed
regression variant: row free test[1, 0, 1, 2, 3, 1][0, 0, 1, 2, 3, 1]Failed
partial repair probe: row free test[0, 2, 0, 0, 3, 1][0, 2, 0, 0, 0, 1]Failed
partial repair variant: row free test[0, 1][0, 1]Passed
boundary control[0][0]Passed
normal control[0][0]Passed
normal control[0][0]Passed
normal control[0, 1][0, 1]Passed

SHA-256 / d0b4883ce1e7e0bd83e439400c60a1e1e6400770d069d2aa7dfc97137c97a160

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]-1<=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 free test', [[[0, 100], [100, 200]]], [0, 0]), ('regression variant: row free test', [[[1000, 1900], [100, 1000], [500, 900], [500, 501], [500, 900], [200, 300]]], [0, 0, 1, 2, 3, 1]), ('partial repair probe: row free test', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair variant: row free test', [[[300, 301], [300, 400]]], [0, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[1000, 1001]]], [0]), ('normal control', [[[1000, 1400]]], [0]), ('normal control', [[[0, 300], [0, 400]]], [0, 1])], [('regression: row free test', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('regression variant: row free test', [[[100, 1000], [500, 600], [200, 500], [200, 500], [0, 200], [100, 101]]], [1, 0, 0, 2, 0, 2]), ('partial repair probe: row free test', [[[200, 201], [300, 500], [200, 201], [1000, 1300], [300, 400], [0, 200]]], [0, 0, 1, 0, 1, 0]), ('partial repair variant: row free test', [[[300, 600], [100, 400], [1000, 1001], [100, 101], [0, 400], [100, 400]]], [2, 1, 0, 2, 0, 3]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[0, 900]]], [0]), ('normal control', [[[100, 500], [200, 300], [1000, 1100]]], [0, 1, 0]), ('normal control', [[[100, 101]]], [0])], [('regression: row free test', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('regression variant: row free test', [[[200, 600], [100, 200], [1000, 1400]]], [0, 0, 0]), ('partial repair probe: row free test', [[[100, 1000], [300, 301], [300, 500], [500, 501]]], [0, 1, 2, 1]), ('partial repair variant: row free test', [[[0, 100], [0, 1], [0, 400], [0, 900], [0, 100]]], [0, 1, 2, 3, 4]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[200, 500], [1000, 1100], [1000, 1200], [0, 900]]], [1, 0, 1, 0]), ('normal control', [[[1000, 1100], [200, 500]]], [0, 0]), ('normal control', [[[1000, 1300], [500, 800], [0, 400], [100, 400]]], [0, 0, 0, 1])], [('regression: row free test', [[[100, 300], [300, 500], [100, 500]]], [0, 0, 1]), ('regression variant: row free test', [[[500, 800], [300, 400], [1000, 1200], [300, 600], [500, 600], [200, 300]]], [0, 0, 0, 1, 2, 0]), ('partial repair probe: row free test', [[[0, 400], [200, 1100], [500, 700], [0, 1], [0, 900], [200, 201]]], [0, 1, 0, 1, 2, 3]), ('partial repair variant: row free test', [[[1000, 1001], [0, 300], [300, 600], [1000, 1001], [0, 1], [0, 900]]], [0, 0, 0, 1, 1, 2]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[300, 1200]]], [0]), ('normal control', [[[0, 900], [500, 1400]]], [0, 1]), ('normal control', [[[500, 600], [0, 1]]], [0, 0])], [('regression: row free test', [[[200, 500], [0, 900], [1000, 1100], [500, 900]]], [1, 0, 0, 1]), ('regression variant: row free test', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair probe: row free test', [[[1000, 1400], [300, 700], [1000, 1001], [0, 400], [300, 1200], [1000, 1100]]], [0, 1, 1, 0, 2, 3]), ('partial repair variant: row free test', [[[0, 200], [300, 700], [1000, 1001], [1000, 1001], [100, 300]]], [0, 0, 0, 1, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[300, 600]]], [0]), ('normal control', [[[0, 100], [0, 900], [300, 700], [0, 200], [200, 400]]], [0, 1, 2, 2, 0]), ('normal control', [[[0, 900], [500, 800], [300, 600]]], [0, 2, 1])]]
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: row free test[0, 0][0, 0]Passed
regression variant: row free test[0, 0, 1, 2, 2, 1][0, 0, 1, 2, 3, 1]Failed
partial repair probe: row free test[0, 2, 0, 1, 1, 0][0, 2, 0, 0, 0, 1]Failed
partial repair variant: row free test[0, 0][0, 1]Failed
boundary control[0][0]Passed
normal control[0][0]Passed
normal control[0][0]Passed
normal control[0, 1][0, 1]Passed

SHA-256 / 76505a770c297cea106099e641c203bfc15bd6be2d36785e3cecc51823af979b

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 free test', [[[0, 100], [100, 200]]], [0, 0]), ('regression variant: row free test', [[[1000, 1900], [100, 1000], [500, 900], [500, 501], [500, 900], [200, 300]]], [0, 0, 1, 2, 3, 1]), ('partial repair probe: row free test', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair variant: row free test', [[[300, 301], [300, 400]]], [0, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[1000, 1001]]], [0]), ('normal control', [[[1000, 1400]]], [0]), ('normal control', [[[0, 300], [0, 400]]], [0, 1])], [('regression: row free test', [[[0, 300], [100, 200], [200, 400]]], [0, 1, 1]), ('regression variant: row free test', [[[100, 1000], [500, 600], [200, 500], [200, 500], [0, 200], [100, 101]]], [1, 0, 0, 2, 0, 2]), ('partial repair probe: row free test', [[[200, 201], [300, 500], [200, 201], [1000, 1300], [300, 400], [0, 200]]], [0, 0, 1, 0, 1, 0]), ('partial repair variant: row free test', [[[300, 600], [100, 400], [1000, 1001], [100, 101], [0, 400], [100, 400]]], [2, 1, 0, 2, 0, 3]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[0, 900]]], [0]), ('normal control', [[[100, 500], [200, 300], [1000, 1100]]], [0, 1, 0]), ('normal control', [[[100, 101]]], [0])], [('regression: row free test', [[[0, 500], [0, 100], [100, 200]]], [0, 1, 1]), ('regression variant: row free test', [[[200, 600], [100, 200], [1000, 1400]]], [0, 0, 0]), ('partial repair probe: row free test', [[[100, 1000], [300, 301], [300, 500], [500, 501]]], [0, 1, 2, 1]), ('partial repair variant: row free test', [[[0, 100], [0, 1], [0, 400], [0, 900], [0, 100]]], [0, 1, 2, 3, 4]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[200, 500], [1000, 1100], [1000, 1200], [0, 900]]], [1, 0, 1, 0]), ('normal control', [[[1000, 1100], [200, 500]]], [0, 0]), ('normal control', [[[1000, 1300], [500, 800], [0, 400], [100, 400]]], [0, 0, 0, 1])], [('regression: row free test', [[[100, 300], [300, 500], [100, 500]]], [0, 0, 1]), ('regression variant: row free test', [[[500, 800], [300, 400], [1000, 1200], [300, 600], [500, 600], [200, 300]]], [0, 0, 0, 1, 2, 0]), ('partial repair probe: row free test', [[[0, 400], [200, 1100], [500, 700], [0, 1], [0, 900], [200, 201]]], [0, 1, 0, 1, 2, 3]), ('partial repair variant: row free test', [[[1000, 1001], [0, 300], [300, 600], [1000, 1001], [0, 1], [0, 900]]], [0, 0, 0, 1, 1, 2]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[300, 1200]]], [0]), ('normal control', [[[0, 900], [500, 1400]]], [0, 1]), ('normal control', [[[500, 600], [0, 1]]], [0, 0])], [('regression: row free test', [[[200, 500], [0, 900], [1000, 1100], [500, 900]]], [1, 0, 0, 1]), ('regression variant: row free test', [[[1000, 1900], [200, 500], [0, 1], [100, 500], [500, 700], [0, 900]]], [0, 2, 0, 0, 0, 1]), ('partial repair probe: row free test', [[[1000, 1400], [300, 700], [1000, 1001], [0, 400], [300, 1200], [1000, 1100]]], [0, 1, 1, 0, 2, 3]), ('partial repair variant: row free test', [[[0, 200], [300, 700], [1000, 1001], [1000, 1001], [100, 300]]], [0, 0, 0, 1, 1]), ('boundary control', [[[0, 100]]], [0]), ('normal control', [[[300, 600]]], [0]), ('normal control', [[[0, 100], [0, 900], [300, 700], [0, 200], [200, 400]]], [0, 1, 2, 2, 0]), ('normal control', [[[0, 900], [500, 800], [300, 600]]], [0, 2, 1])]]
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: row free test[0, 0][0, 0]Passed
regression variant: row free test[0, 0, 1, 2, 3, 1][0, 0, 1, 2, 3, 1]Passed
partial repair probe: row free test[0, 2, 0, 0, 0, 1][0, 2, 0, 0, 0, 1]Passed
partial repair variant: row free test[0, 1][0, 1]Passed
boundary control[0][0]Passed
normal control[0][0]Passed
normal control[0][0]Passed
normal control[0, 1][0, 1]Passed

SHA-256 / 883076dce79526c67a553c2ff342501620fa8e7730029f6990caecae0ed7e826

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 2026-09-29T14:49:31.428320+00:00.

Case digest / 044af7337c1f9f4ff918a33472c0325d4511637efea23ed93014c2e9b63aedfb