FA-78071 / Subtitle cue timing / Open access

Two-point subtitle synchronisation: intercept anchor · case 01

Mapped cues are offset by a constant error unless the first anchor sits at time zero.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The mapping multiplies absolute subtitle time by the slope without subtracting the anchor time.

VERIFIED REPAIR

Map t as b1 + (t - a1) * slope.

Unsuccessful approach: Pairing the second video anchor with the first subtitle anchor shifts every cue by the anchor span.

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(b2-b1,a2-a1)
    def m(t):
        return math.floor(b1+t*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: intercept anchor', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('regression variant: intercept anchor', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]), ('partial repair probe: intercept anchor', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('partial repair variant: intercept anchor', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('normal control', [[[7777, 10277]], [[5000, 6000], [5003, 4503]]], []), ('normal control', [[[250, 251], [8492, 8493]], [[5000, 5500], [9000, 7000]]], []), ('normal control', [[[7777, 7779], [1500, 1503]], [[1000, 1000], [2000, 0]]], [])], [('regression: intercept anchor', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: intercept anchor', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: intercept anchor', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: intercept anchor', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -1000]]], []), ('normal control', [[[250, 252]], [[10000, 10500], [11000, 10501]]], []), ('normal control', [[[7777, 8777], [3213, 3214], [1500, 1501], [250, 750]], [[5000, 6000], [5003, 5003]]], [])], [('regression: intercept anchor', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: intercept anchor', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: intercept anchor', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: intercept anchor', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('normal control', [[[1500, 4000], [6431, 6931], [1, 1001], [862, 1862]], [[2000, 1500], [1000, 2000]]], []), ('normal control', [[[0, 500], [1500, 1502]], [[1000, 1500], [2000, 0]]], []), ('normal control', [[[7777, 7779]], [[5000, 4000], [6000, 4001]]], [])], [('regression: intercept anchor', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: intercept anchor', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair probe: intercept anchor', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair variant: intercept anchor', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('normal control', [[[7777, 7778], [0, 2500]], [[1000, 1000], [2000, 0]]], []), ('normal control', [[[8367, 9367]], [[1000, 1500], [1003, 503]]], []), ('normal control', [[[999, 1001], [1, 501], [1500, 1502], [0, 3]], [[0, 1000], [1000, 500]]], [])], [('regression: intercept anchor', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('regression variant: intercept anchor', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair probe: intercept anchor', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: intercept anchor', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('normal control', [[[250, 253], [1500, 1502], [999, 1499], [999, 1001]], [[1000, 2000], [1003, 1503]]], []), ('normal control', [[[999, 1999], [1, 501], [0, 1]], [[10000, 10000], [10003, 8003]]], []), ('normal control', [[[1500, 1501]], [[1000, 1500], [2000, 1501]]], [])]]
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: intercept anchor	`[[0, 500]]`	`[]`	Failed
regression variant: intercept anchor	`[[12001, 12002], [12001, 12002], [13500, 13501], [12250, 12253]]`	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	Failed
partial repair probe: intercept anchor	`[[1, 2]]`	`[[1, 2]]`	Passed
partial repair variant: intercept anchor	`[[0, 51]]`	`[[0, 51]]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed

SHA-256 / 17682edfdfdbc543c781d3dc8ceb4692c0a3c037485d97d5509a0a74a1aae3c2

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-b1,a2-a1)
    def m(t):
        return math.floor(b2+(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: intercept anchor', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('regression variant: intercept anchor', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]), ('partial repair probe: intercept anchor', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('partial repair variant: intercept anchor', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('normal control', [[[7777, 10277]], [[5000, 6000], [5003, 4503]]], []), ('normal control', [[[250, 251], [8492, 8493]], [[5000, 5500], [9000, 7000]]], []), ('normal control', [[[7777, 7779], [1500, 1503]], [[1000, 1000], [2000, 0]]], [])], [('regression: intercept anchor', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: intercept anchor', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: intercept anchor', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: intercept anchor', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -1000]]], []), ('normal control', [[[250, 252]], [[10000, 10500], [11000, 10501]]], []), ('normal control', [[[7777, 8777], [3213, 3214], [1500, 1501], [250, 750]], [[5000, 6000], [5003, 5003]]], [])], [('regression: intercept anchor', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: intercept anchor', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: intercept anchor', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: intercept anchor', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('normal control', [[[1500, 4000], [6431, 6931], [1, 1001], [862, 1862]], [[2000, 1500], [1000, 2000]]], []), ('normal control', [[[0, 500], [1500, 1502]], [[1000, 1500], [2000, 0]]], []), ('normal control', [[[7777, 7779]], [[5000, 4000], [6000, 4001]]], [])], [('regression: intercept anchor', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: intercept anchor', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair probe: intercept anchor', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair variant: intercept anchor', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('normal control', [[[7777, 7778], [0, 2500]], [[1000, 1000], [2000, 0]]], []), ('normal control', [[[8367, 9367]], [[1000, 1500], [1003, 503]]], []), ('normal control', [[[999, 1001], [1, 501], [1500, 1502], [0, 3]], [[0, 1000], [1000, 500]]], [])], [('regression: intercept anchor', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('regression variant: intercept anchor', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair probe: intercept anchor', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: intercept anchor', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('normal control', [[[250, 253], [1500, 1502], [999, 1499], [999, 1001]], [[1000, 2000], [1003, 1503]]], []), ('normal control', [[[999, 1999], [1, 501], [0, 1]], [[10000, 10000], [10003, 8003]]], []), ('normal control', [[[1500, 1501]], [[1000, 1500], [2000, 1501]]], [])]]
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: intercept anchor	`[[500, 1000]]`	`[]`	Failed
regression variant: intercept anchor	`[[1, 2], [1, 2], [1500, 1501], [250, 253]]`	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	Failed
partial repair probe: intercept anchor	`[[2, 3]]`	`[[1, 2]]`	Failed
partial repair variant: intercept anchor	`[[9501, 10551]]`	`[[0, 51]]`	Failed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed

SHA-256 / 1da20e84b3bf2e071a7204fda667ae3448d4d8449cc3fe3feb6f05b235b47da2

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: intercept anchor', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('regression variant: intercept anchor', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]), ('partial repair probe: intercept anchor', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('partial repair variant: intercept anchor', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('normal control', [[[7777, 10277]], [[5000, 6000], [5003, 4503]]], []), ('normal control', [[[250, 251], [8492, 8493]], [[5000, 5500], [9000, 7000]]], []), ('normal control', [[[7777, 7779], [1500, 1503]], [[1000, 1000], [2000, 0]]], [])], [('regression: intercept anchor', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: intercept anchor', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: intercept anchor', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: intercept anchor', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -1000]]], []), ('normal control', [[[250, 252]], [[10000, 10500], [11000, 10501]]], []), ('normal control', [[[7777, 8777], [3213, 3214], [1500, 1501], [250, 750]], [[5000, 6000], [5003, 5003]]], [])], [('regression: intercept anchor', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: intercept anchor', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: intercept anchor', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: intercept anchor', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('normal control', [[[1500, 4000], [6431, 6931], [1, 1001], [862, 1862]], [[2000, 1500], [1000, 2000]]], []), ('normal control', [[[0, 500], [1500, 1502]], [[1000, 1500], [2000, 0]]], []), ('normal control', [[[7777, 7779]], [[5000, 4000], [6000, 4001]]], [])], [('regression: intercept anchor', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: intercept anchor', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair probe: intercept anchor', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('partial repair variant: intercept anchor', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('normal control', [[[7777, 7778], [0, 2500]], [[1000, 1000], [2000, 0]]], []), ('normal control', [[[8367, 9367]], [[1000, 1500], [1003, 503]]], []), ('normal control', [[[999, 1001], [1, 501], [1500, 1502], [0, 3]], [[0, 1000], [1000, 500]]], [])], [('regression: intercept anchor', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('regression variant: intercept anchor', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair probe: intercept anchor', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: intercept anchor', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('normal control', [[[250, 253], [1500, 1502], [999, 1499], [999, 1001]], [[1000, 2000], [1003, 1503]]], []), ('normal control', [[[999, 1999], [1, 501], [0, 1]], [[10000, 10000], [10003, 8003]]], []), ('normal control', [[[1500, 1501]], [[1000, 1500], [2000, 1501]]], [])]]
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: intercept anchor	`[]`	`[]`	Passed
regression variant: intercept anchor	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	Passed
partial repair probe: intercept anchor	`[[1, 2]]`	`[[1, 2]]`	Passed
partial repair variant: intercept anchor	`[[0, 51]]`	`[[0, 51]]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed

SHA-256 / afc1e1ee700e655f7adaa1c81c470fd797737321cd12de56340df581db48999d

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 2026-09-29T14:49:31.980064+00:00.

Case digest / 33691b86b0edd1b20d58a0b267a8ebf8b99a923a1508ad81ee7dc267ef1eeac8