FA-78066 / Subtitle cue timing / Open access

Two-point subtitle synchronisation: slope orientation · case 01

Subtitles drift in the wrong direction the further they are from the first anchor.

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

ROOT CAUSE

The slope is computed as subtitle span over video span, the reciprocal of the mapping.

VERIFIED REPAIR

Use (b2-b1)/(a2-a1) as the slope.

Unsuccessful approach: A slope through the origin from the second anchor ignores the first anchor and mis-scales offset files.

Case contract

anchors [[a1,b1],[a2,b2]] (a1 != a2, b1 != b2) map subtitle time a to video time b linearly through both points. Each time is mapped exactly, rounded half up, clamped at 0; cues whose mapped end is not after the mapped start are dropped.

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
import math
from fractions import Fraction
N = 1
observations = []
def solve(cues, anchors):
    (a1,b1),(a2,b2)=anchors
    k=Fraction(a2-a1,b2-b1)
    def m(t):
        return math.floor(b1+(t-a1)*k+Fraction(1,2))
    out=[]
    for s,e in cues:
        ns,ne=max(0,m(s)),max(0,m(e))
        if ne>ns:
            out.append([ns,ne])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: slope orientation', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('regression variant: slope orientation', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair probe: slope orientation', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: slope orientation', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[1920, 2920]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[0, 1]], [[5000, 6000], [5003, 6503]]], []), ('normal control', [[[0, 500], [1, 1001]], [[1000, 0], [11000, 12000]]], [[0, 1]])], [('regression: slope orientation', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('regression variant: slope orientation', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair probe: slope orientation', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: slope orientation', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -1000]]], []), ('normal control', [[[1, 4]], [[1003, 1003], [1000, 2000]]], []), ('normal control', [[[7777, 7779], [250, 1250], [3735, 3737]], [[10000, 10000], [11000, 11000]]], [[7777, 7779], [250, 1250], [3735, 3737]])], [('regression: slope orientation', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: slope orientation', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('partial repair probe: slope orientation', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair variant: slope orientation', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[250, 750]], [[5000, 5000], [15000, 15000]]], [[250, 750]]), ('normal control', [[[0, 500], [1500, 1502]], [[1000, 1500], [2000, 0]]], []), ('normal control', [[[1500, 1502], [250, 252]], [[5000, 5000], [5003, 5003]]], [[1500, 1502], [250, 252]])], [('regression: slope orientation', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: slope orientation', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: slope orientation', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: slope orientation', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 7778], [0, 2500]], [[1000, 1000], [2000, 0]]], []), ('normal control', [[[999, 1000], [1, 501], [1, 501]], [[1000, 0], [11000, 12000]]], []), ('normal control', [[[1500, 1502]], [[0, 0], [1000, 1000]]], [[1500, 1502]])], [('regression: slope orientation', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: slope orientation', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: slope orientation', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]), ('partial repair variant: slope orientation', [[[0, 2500], [250, 750], [0, 3]], [[10000, 10500], [20000, 20500]]], [[500, 3000], [750, 1250], [500, 503]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[999, 1499], [999, 1002], [5305, 5306], [1, 501]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[0, 3]], [[10000, 9000], [20000, 19500]]], []), ('normal control', [[[999, 1002]], [[1000, 1000], [11000, 11000]]], [[999, 1002]])]]
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: slope orientation	`[[500, 1000]]`	`[[2000, 4000]]`	Failed
regression variant: slope orientation	`[[8468, 8913], [2909, 2910]]`	`[[9124, 9687], [2088, 2090]]`	Failed
partial repair probe: slope orientation	`[[833, 2500], [667, 669]]`	`[[0, 625]]`	Failed
partial repair variant: slope orientation	`[[1504, 1506], [1503, 1504]]`	`[[2248500, 6001000], [0, 1498000]]`	Failed
boundary control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[0, 1]]`	`[[0, 1]]`	Passed

SHA-256 / 7f86d322a58554c74e147d5e0781db541db1890ef8757075410bc997d8fcba26

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(cues, anchors):
    (a1,b1),(a2,b2)=anchors
    k=Fraction(b2,a2) if a2 else Fraction(1)
    def m(t):
        return math.floor(b1+(t-a1)*k+Fraction(1,2))
    out=[]
    for s,e in cues:
        ns,ne=max(0,m(s)),max(0,m(e))
        if ne>ns:
            out.append([ns,ne])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: slope orientation', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('regression variant: slope orientation', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair probe: slope orientation', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: slope orientation', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[1920, 2920]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[0, 1]], [[5000, 6000], [5003, 6503]]], []), ('normal control', [[[0, 500], [1, 1001]], [[1000, 0], [11000, 12000]]], [[0, 1]])], [('regression: slope orientation', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('regression variant: slope orientation', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair probe: slope orientation', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: slope orientation', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -1000]]], []), ('normal control', [[[1, 4]], [[1003, 1003], [1000, 2000]]], []), ('normal control', [[[7777, 7779], [250, 1250], [3735, 3737]], [[10000, 10000], [11000, 11000]]], [[7777, 7779], [250, 1250], [3735, 3737]])], [('regression: slope orientation', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: slope orientation', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('partial repair probe: slope orientation', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair variant: slope orientation', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[250, 750]], [[5000, 5000], [15000, 15000]]], [[250, 750]]), ('normal control', [[[0, 500], [1500, 1502]], [[1000, 1500], [2000, 0]]], []), ('normal control', [[[1500, 1502], [250, 252]], [[5000, 5000], [5003, 5003]]], [[1500, 1502], [250, 252]])], [('regression: slope orientation', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: slope orientation', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: slope orientation', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: slope orientation', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 7778], [0, 2500]], [[1000, 1000], [2000, 0]]], []), ('normal control', [[[999, 1000], [1, 501], [1, 501]], [[1000, 0], [11000, 12000]]], []), ('normal control', [[[1500, 1502]], [[0, 0], [1000, 1000]]], [[1500, 1502]])], [('regression: slope orientation', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: slope orientation', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: slope orientation', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]), ('partial repair variant: slope orientation', [[[0, 2500], [250, 750], [0, 3]], [[10000, 10500], [20000, 20500]]], [[500, 3000], [750, 1250], [500, 503]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[999, 1499], [999, 1002], [5305, 5306], [1, 501]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[0, 3]], [[10000, 9000], [20000, 19500]]], []), ('normal control', [[[999, 1002]], [[1000, 1000], [11000, 11000]]], [[999, 1002]])]]
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: slope orientation	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
regression variant: slope orientation	`[[9240, 9823], [1944, 1945]]`	`[[9124, 9687], [2088, 2090]]`	Failed
partial repair probe: slope orientation	`[[0, 1938]]`	`[[0, 625]]`	Failed
partial repair variant: slope orientation	`[[3000, 5500], [1500, 2500]]`	`[[2248500, 6001000], [0, 1498000]]`	Failed
boundary control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[0, 1]]`	`[[0, 1]]`	Passed

SHA-256 / 34481161d769b02dd45737d2cdeb0596b01b6d260d5593a5023d2b42391490d4

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(cues, anchors):
    (a1,b1),(a2,b2)=anchors
    k=Fraction(b2-b1,a2-a1)
    def m(t):
        return math.floor(b1+(t-a1)*k+Fraction(1,2))
    out=[]
    for s,e in cues:
        ns,ne=max(0,m(s)),max(0,m(e))
        if ne>ns:
            out.append([ns,ne])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: slope orientation', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('regression variant: slope orientation', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair probe: slope orientation', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: slope orientation', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[1920, 2920]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[0, 1]], [[5000, 6000], [5003, 6503]]], []), ('normal control', [[[0, 500], [1, 1001]], [[1000, 0], [11000, 12000]]], [[0, 1]])], [('regression: slope orientation', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('regression variant: slope orientation', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair probe: slope orientation', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: slope orientation', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -1000]]], []), ('normal control', [[[1, 4]], [[1003, 1003], [1000, 2000]]], []), ('normal control', [[[7777, 7779], [250, 1250], [3735, 3737]], [[10000, 10000], [11000, 11000]]], [[7777, 7779], [250, 1250], [3735, 3737]])], [('regression: slope orientation', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: slope orientation', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('partial repair probe: slope orientation', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair variant: slope orientation', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[250, 750]], [[5000, 5000], [15000, 15000]]], [[250, 750]]), ('normal control', [[[0, 500], [1500, 1502]], [[1000, 1500], [2000, 0]]], []), ('normal control', [[[1500, 1502], [250, 252]], [[5000, 5000], [5003, 5003]]], [[1500, 1502], [250, 252]])], [('regression: slope orientation', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: slope orientation', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: slope orientation', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: slope orientation', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 7778], [0, 2500]], [[1000, 1000], [2000, 0]]], []), ('normal control', [[[999, 1000], [1, 501], [1, 501]], [[1000, 0], [11000, 12000]]], []), ('normal control', [[[1500, 1502]], [[0, 0], [1000, 1000]]], [[1500, 1502]])], [('regression: slope orientation', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: slope orientation', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: slope orientation', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]), ('partial repair variant: slope orientation', [[[0, 2500], [250, 750], [0, 3]], [[10000, 10500], [20000, 20500]]], [[500, 3000], [750, 1250], [500, 503]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[999, 1499], [999, 1002], [5305, 5306], [1, 501]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[0, 3]], [[10000, 9000], [20000, 19500]]], []), ('normal control', [[[999, 1002]], [[1000, 1000], [11000, 11000]]], [[999, 1002]])]]
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: slope orientation	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
regression variant: slope orientation	`[[9124, 9687], [2088, 2090]]`	`[[9124, 9687], [2088, 2090]]`	Passed
partial repair probe: slope orientation	`[[0, 625]]`	`[[0, 625]]`	Passed
partial repair variant: slope orientation	`[[2248500, 6001000], [0, 1498000]]`	`[[2248500, 6001000], [0, 1498000]]`	Passed
boundary control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[0, 1]]`	`[[0, 1]]`	Passed

SHA-256 / 1b0db27c5ea3b7b6aae2a4e79a55dfb2271047712a6244f56e18023a629de7fe

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 2026-09-29T14:49:31.934097+00:00.

Case digest / de494a7c79daa2805eff12a0243fd4c42dedef4d7c1f2ed94eed3a5119f89fd8