FA-78076 / Subtitle cue timing / Open access

Two-point subtitle synchronisation: mapped rounding · case 01

Mapped times with half-millisecond or larger fractions are one millisecond early.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Mapped times are floored instead of rounded half up.

VERIFIED REPAIR

Round the exact mapped time half up.

Unsuccessful approach: Banker rounding sends exact halves with an even floor downwards.

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-a1)*k)
    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: mapped rounding', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('regression variant: mapped rounding', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair probe: mapped rounding', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: mapped rounding', [[[7777, 8777], [7777, 7780], [1500, 2000], [999, 1002]], [[0, 1000], [4000, 4500]]], [[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 10277]], [[5000, 6000], [5003, 4503]]], []), ('normal control', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('normal control', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]])], [('regression: mapped rounding', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: mapped rounding', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair probe: mapped rounding', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair variant: mapped rounding', [[[7777, 7780]], [[2000, 2500], [1000, 0]]], [[16943, 16950]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('normal control', [[[0, 2500], [250, 750], [0, 3]], [[10000, 10500], [20000, 20500]]], [[500, 3000], [750, 1250], [500, 503]]), ('normal control', [[[0, 2500], [0, 3]], [[1000, 1500], [0, -3000]]], [[0, 8250]])], [('regression: mapped rounding', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: mapped rounding', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('partial repair probe: mapped rounding', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair variant: mapped rounding', [[[7777, 7779], [9295, 11795], [7777, 7780]], [[0, 0], [1000, 1500]]], [[11666, 11669], [13943, 17693], [11666, 11670]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[5033, 5036], [999, 1000]], [[9000, 9000], [5000, 4000]]], [[4041, 4045]]), ('normal control', [[[1, 2], [1500, 4000]], [[15000, 15000], [5000, 5000]]], [[1, 2], [1500, 4000]]), ('normal control', [[[250, 251], [1500, 2500], [0, 2], [0, 2]], [[10000, 10500], [14000, 15500]]], [[0, 1125]])], [('regression: mapped rounding', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('regression variant: mapped rounding', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('partial repair probe: mapped rounding', [[[16012, 18512], [0, 2], [999, 1002], [1, 4]], [[10000, 10000], [11000, 10500]]], [[13006, 14256], [5000, 5001], [5500, 5501], [5001, 5002]]), ('partial repair variant: mapped rounding', [[[999, 1999], [0, 3], [7777, 7779]], [[0, 0], [2000, 3000]]], [[1499, 2999], [0, 5], [11666, 11669]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1500, 1501], [999, 1001], [7777, 7780], [250, 252]], [[11000, 10500], [10000, 7000]]], []), ('normal control', [[[1500, 1503], [999, 3499]], [[1000, 0], [3000, 3500]]], [[875, 880], [0, 4373]]), ('normal control', [[[999, 1499], [7777, 10277]], [[10000, 10500], [10003, 9503]]], [])], [('regression: mapped rounding', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('regression variant: mapped rounding', [[[16012, 18512], [0, 2], [999, 1002], [1, 4]], [[10000, 10000], [11000, 10500]]], [[13006, 14256], [5000, 5001], [5500, 5501], [5001, 5002]]), ('partial repair probe: mapped rounding', [[[1, 2501], [5729, 5732], [250, 252]], [[7000, 8500], [5000, 6000]]], [[0, 2876], [6911, 6915], [63, 65]]), ('partial repair variant: mapped rounding', [[[11711, 11713], [1500, 1503]], [[0, -3000], [1000, 2500]]], [[61411, 61422], [5250, 5267]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[250, 1250]], [[1000, 1000], [5000, 5500]]], [[156, 1281]]), ('normal control', [[[13786, 13787], [7777, 8277], [1, 2501], [250, 251]], [[10000, 11000], [10003, 9503]]], []), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -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: mapped rounding	`[[0, 1]]`	`[[1, 2]]`	Failed
regression variant: mapped rounding	`[[3695, 4320], [3694, 3695], [1812, 1813], [2125, 2250]]`	`[[3696, 4321], [3694, 3695], [2125, 2250]]`	Failed
partial repair probe: mapped rounding	`[[3388, 3389], [250, 500]]`	`[[0, 1], [3389, 3390], [250, 500]]`	Failed
partial repair variant: mapped rounding	`[[7804, 8679], [7804, 7807], [2312, 2750], [1874, 1876]]`	`[[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]`	Failed
boundary control	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
boundary control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[0, 625]]`	`[[0, 625]]`	Passed
normal control	`[[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]`	`[[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]`	Passed

SHA-256 / 8366c7519f50c8028ef772662e7763facdeb81262e336ebe5652dcb3a786e358

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 round(b1+(t-a1)*k)
    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: mapped rounding', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('regression variant: mapped rounding', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair probe: mapped rounding', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: mapped rounding', [[[7777, 8777], [7777, 7780], [1500, 2000], [999, 1002]], [[0, 1000], [4000, 4500]]], [[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 10277]], [[5000, 6000], [5003, 4503]]], []), ('normal control', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('normal control', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]])], [('regression: mapped rounding', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: mapped rounding', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair probe: mapped rounding', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair variant: mapped rounding', [[[7777, 7780]], [[2000, 2500], [1000, 0]]], [[16943, 16950]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('normal control', [[[0, 2500], [250, 750], [0, 3]], [[10000, 10500], [20000, 20500]]], [[500, 3000], [750, 1250], [500, 503]]), ('normal control', [[[0, 2500], [0, 3]], [[1000, 1500], [0, -3000]]], [[0, 8250]])], [('regression: mapped rounding', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: mapped rounding', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('partial repair probe: mapped rounding', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair variant: mapped rounding', [[[7777, 7779], [9295, 11795], [7777, 7780]], [[0, 0], [1000, 1500]]], [[11666, 11669], [13943, 17693], [11666, 11670]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[5033, 5036], [999, 1000]], [[9000, 9000], [5000, 4000]]], [[4041, 4045]]), ('normal control', [[[1, 2], [1500, 4000]], [[15000, 15000], [5000, 5000]]], [[1, 2], [1500, 4000]]), ('normal control', [[[250, 251], [1500, 2500], [0, 2], [0, 2]], [[10000, 10500], [14000, 15500]]], [[0, 1125]])], [('regression: mapped rounding', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('regression variant: mapped rounding', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('partial repair probe: mapped rounding', [[[16012, 18512], [0, 2], [999, 1002], [1, 4]], [[10000, 10000], [11000, 10500]]], [[13006, 14256], [5000, 5001], [5500, 5501], [5001, 5002]]), ('partial repair variant: mapped rounding', [[[999, 1999], [0, 3], [7777, 7779]], [[0, 0], [2000, 3000]]], [[1499, 2999], [0, 5], [11666, 11669]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1500, 1501], [999, 1001], [7777, 7780], [250, 252]], [[11000, 10500], [10000, 7000]]], []), ('normal control', [[[1500, 1503], [999, 3499]], [[1000, 0], [3000, 3500]]], [[875, 880], [0, 4373]]), ('normal control', [[[999, 1499], [7777, 10277]], [[10000, 10500], [10003, 9503]]], [])], [('regression: mapped rounding', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('regression variant: mapped rounding', [[[16012, 18512], [0, 2], [999, 1002], [1, 4]], [[10000, 10000], [11000, 10500]]], [[13006, 14256], [5000, 5001], [5500, 5501], [5001, 5002]]), ('partial repair probe: mapped rounding', [[[1, 2501], [5729, 5732], [250, 252]], [[7000, 8500], [5000, 6000]]], [[0, 2876], [6911, 6915], [63, 65]]), ('partial repair variant: mapped rounding', [[[11711, 11713], [1500, 1503]], [[0, -3000], [1000, 2500]]], [[61411, 61422], [5250, 5267]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[250, 1250]], [[1000, 1000], [5000, 5500]]], [[156, 1281]]), ('normal control', [[[13786, 13787], [7777, 8277], [1, 2501], [250, 251]], [[10000, 11000], [10003, 9503]]], []), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -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: mapped rounding	`[[0, 2]]`	`[[1, 2]]`	Failed
regression variant: mapped rounding	`[[3696, 4320], [3694, 3695], [1812, 1813], [2125, 2250]]`	`[[3696, 4321], [3694, 3695], [2125, 2250]]`	Failed
partial repair probe: mapped rounding	`[[3388, 3390], [250, 500]]`	`[[0, 1], [3389, 3390], [250, 500]]`	Failed
partial repair variant: mapped rounding	`[[7805, 8680], [7805, 7808], [2312, 2750], [1874, 1877]]`	`[[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]`	Failed
boundary control	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
boundary control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[0, 625]]`	`[[0, 625]]`	Passed
normal control	`[[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]`	`[[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]`	Passed

SHA-256 / d0aeff413ac530ac4a6c9a3c108e21f8c68bfc8fae6da79544310143e0ce10ef

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: mapped rounding', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('regression variant: mapped rounding', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair probe: mapped rounding', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: mapped rounding', [[[7777, 8777], [7777, 7780], [1500, 2000], [999, 1002]], [[0, 1000], [4000, 4500]]], [[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[7777, 10277]], [[5000, 6000], [5003, 4503]]], []), ('normal control', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('normal control', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]])], [('regression: mapped rounding', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('regression variant: mapped rounding', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair probe: mapped rounding', [[[7782, 10282], [7777, 7780], [250, 252], [1500, 2000]], [[1000, 2000], [3000, 2500]]], [[3696, 4321], [3694, 3695], [2125, 2250]]), ('partial repair variant: mapped rounding', [[[7777, 7780]], [[2000, 2500], [1000, 0]]], [[16943, 16950]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('normal control', [[[0, 2500], [250, 750], [0, 3]], [[10000, 10500], [20000, 20500]]], [[500, 3000], [750, 1250], [500, 503]]), ('normal control', [[[0, 2500], [0, 3]], [[1000, 1500], [0, -3000]]], [[0, 8250]])], [('regression: mapped rounding', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: mapped rounding', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('partial repair probe: mapped rounding', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('partial repair variant: mapped rounding', [[[7777, 7779], [9295, 11795], [7777, 7780]], [[0, 0], [1000, 1500]]], [[11666, 11669], [13943, 17693], [11666, 11670]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[5033, 5036], [999, 1000]], [[9000, 9000], [5000, 4000]]], [[4041, 4045]]), ('normal control', [[[1, 2], [1500, 4000]], [[15000, 15000], [5000, 5000]]], [[1, 2], [1500, 4000]]), ('normal control', [[[250, 251], [1500, 2500], [0, 2], [0, 2]], [[10000, 10500], [14000, 15500]]], [[0, 1125]])], [('regression: mapped rounding', [[[7777, 8277], [1523, 1524]], [[5000, 6000], [9000, 10500]]], [[9124, 9687], [2088, 2090]]), ('regression variant: mapped rounding', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('partial repair probe: mapped rounding', [[[16012, 18512], [0, 2], [999, 1002], [1, 4]], [[10000, 10000], [11000, 10500]]], [[13006, 14256], [5000, 5001], [5500, 5501], [5001, 5002]]), ('partial repair variant: mapped rounding', [[[999, 1999], [0, 3], [7777, 7779]], [[0, 0], [2000, 3000]]], [[1499, 2999], [0, 5], [11666, 11669]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1500, 1501], [999, 1001], [7777, 7780], [250, 252]], [[11000, 10500], [10000, 7000]]], []), ('normal control', [[[1500, 1503], [999, 3499]], [[1000, 0], [3000, 3500]]], [[875, 880], [0, 4373]]), ('normal control', [[[999, 1499], [7777, 10277]], [[10000, 10500], [10003, 9503]]], [])], [('regression: mapped rounding', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('regression variant: mapped rounding', [[[16012, 18512], [0, 2], [999, 1002], [1, 4]], [[10000, 10000], [11000, 10500]]], [[13006, 14256], [5000, 5001], [5500, 5501], [5001, 5002]]), ('partial repair probe: mapped rounding', [[[1, 2501], [5729, 5732], [250, 252]], [[7000, 8500], [5000, 6000]]], [[0, 2876], [6911, 6915], [63, 65]]), ('partial repair variant: mapped rounding', [[[11711, 11713], [1500, 1503]], [[0, -3000], [1000, 2500]]], [[61411, 61422], [5250, 5267]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('normal control', [[[250, 1250]], [[1000, 1000], [5000, 5500]]], [[156, 1281]]), ('normal control', [[[13786, 13787], [7777, 8277], [1, 2501], [250, 251]], [[10000, 11000], [10003, 9503]]], []), ('normal control', [[[7777, 8777], [7777, 7779]], [[0, 500], [1000, -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: mapped rounding	`[[1, 2]]`	`[[1, 2]]`	Passed
regression variant: mapped rounding	`[[3696, 4321], [3694, 3695], [2125, 2250]]`	`[[3696, 4321], [3694, 3695], [2125, 2250]]`	Passed
partial repair probe: mapped rounding	`[[0, 1], [3389, 3390], [250, 500]]`	`[[0, 1], [3389, 3390], [250, 500]]`	Passed
partial repair variant: mapped rounding	`[[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]`	`[[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]]`	Passed
boundary control	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
boundary control	`[]`	`[]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[0, 625]]`	`[[0, 625]]`	Passed
normal control	`[[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]`	`[[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]`	Passed

SHA-256 / f95e03bd9aa4f5800d31dcf1263ccee5e1e12ead44b62493067ab735e9448ccc

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 2026-09-29T14:49:31.975810+00:00.

Case digest / e4ac31a194ada9c5417f97a926012ca136894c55ca010621e5d8d1665a2ef045