FA-78081 / Subtitle cue timing / Open access

Two-point subtitle synchronisation: zero clamp · case 01

Cues mapped before the start of the video carry negative timestamps.

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

ROOT CAUSE

Mapped times are not clamped at zero.

VERIFIED REPAIR

Clamp both mapped start and end at zero.

Unsuccessful approach: Clamping only the end leaves negative starts on cues that straddle the beginning of the video.

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+Fraction(1,2))
    out=[]
    for s,e in cues:
        ns,ne=m(s),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: zero clamp', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('regression variant: zero clamp', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: zero clamp', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: zero clamp', [[[0, 2]], [[10000, 10500], [11000, 12000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('normal control', [[[1920, 2920]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]])], [('regression: zero clamp', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: zero clamp', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: zero clamp', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: zero clamp', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('normal control', [[[6295, 8795]], [[6000, 5500], [5000, 6000]]], []), ('normal control', [[[1, 1001], [999, 1499], [999, 3499]], [[1000, 1500], [11000, 12500]]], [[401, 1501], [1499, 2049], [1499, 4249]])], [('regression: zero clamp', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: zero clamp', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('partial repair probe: zero clamp', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: zero clamp', [[[1500, 1502], [7286, 7786]], [[10000, 10000], [11000, 12000]]], [[4572, 5572]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[1, 501], [7777, 7778], [251, 253]], [[10000, 10500], [14000, 12000]]], [[6750, 6938], [9666, 9667], [6844, 6845]]), ('normal control', [[[1, 2], [999, 3499]], [[10000, 10000], [12000, 11500]]], [[2501, 2502], [3249, 5124]]), ('normal control', [[[7777, 8777], [7777, 7780], [1500, 2000], [999, 1002]], [[0, 1000], [4000, 4500]]], [[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]])], [('regression: zero clamp', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('regression variant: zero clamp', [[[0, 2]], [[10000, 10500], [11000, 12000]]], []), ('partial repair probe: zero clamp', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('partial repair variant: zero clamp', [[[0, 2500], [0, 3]], [[1000, 1500], [0, -3000]]], [[0, 8250]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[999, 1499], [7777, 10277]], [[10000, 10500], [10003, 9503]]], []), ('normal control', [[[250, 1250]], [[1000, 1000], [5000, 5500]]], [[156, 1281]]), ('normal control', [[[0, 1000], [250, 750]], [[2000, 0], [0, 500]]], [])], [('regression: zero clamp', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('regression variant: zero clamp', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('partial repair probe: zero clamp', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair variant: zero clamp', [[[5033, 5036], [999, 1000]], [[9000, 9000], [5000, 4000]]], [[4041, 4045]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[7777, 10277], [999, 1000], [999, 1999], [1500, 1502]], [[1000, 2000], [1003, 2003]]], [[8777, 11277], [1999, 2000], [1999, 2999], [2500, 2502]]), ('normal control', [[[1, 4]], [[1003, 1003], [1000, 2000]]], []), ('normal control', [[[7777, 8277], [1500, 2000], [7777, 10277], [999, 1499]], [[5000, 5500], [15000, 14500]]], [[7999, 8449], [2350, 2800], [7999, 10249], [1899, 2349]])]]
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: zero clamp	`[[-500, 0]]`	`[]`	Failed
regression variant: zero clamp	`[[4308231, 4975398], [-1666, 1332668], [1998500, 1999834]]`	`[[4308231, 4975398], [0, 1332668], [1998500, 1999834]]`	Failed
partial repair probe: zero clamp	`[[-3125, 625], [-3500, -3495]]`	`[[0, 625]]`	Failed
partial repair variant: zero clamp	`[[-4500, -4497]]`	`[]`	Failed
boundary control	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
boundary control	`[[1, 2]]`	`[[1, 2]]`	Passed
normal control	`[[1500, 1501], [1500, 2000], [4889, 5139]]`	`[[1500, 1501], [1500, 2000], [4889, 5139]]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	Passed

SHA-256 / 022b641696737b4c693381207a41dcaf00a157c40d06875c232c1e4469cb8c94

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(b1+(t-a1)*k+Fraction(1,2))
    out=[]
    for s,e in cues:
        ns,ne=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: zero clamp', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('regression variant: zero clamp', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: zero clamp', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: zero clamp', [[[0, 2]], [[10000, 10500], [11000, 12000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('normal control', [[[1920, 2920]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]])], [('regression: zero clamp', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: zero clamp', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: zero clamp', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: zero clamp', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('normal control', [[[6295, 8795]], [[6000, 5500], [5000, 6000]]], []), ('normal control', [[[1, 1001], [999, 1499], [999, 3499]], [[1000, 1500], [11000, 12500]]], [[401, 1501], [1499, 2049], [1499, 4249]])], [('regression: zero clamp', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: zero clamp', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('partial repair probe: zero clamp', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: zero clamp', [[[1500, 1502], [7286, 7786]], [[10000, 10000], [11000, 12000]]], [[4572, 5572]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[1, 501], [7777, 7778], [251, 253]], [[10000, 10500], [14000, 12000]]], [[6750, 6938], [9666, 9667], [6844, 6845]]), ('normal control', [[[1, 2], [999, 3499]], [[10000, 10000], [12000, 11500]]], [[2501, 2502], [3249, 5124]]), ('normal control', [[[7777, 8777], [7777, 7780], [1500, 2000], [999, 1002]], [[0, 1000], [4000, 4500]]], [[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]])], [('regression: zero clamp', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('regression variant: zero clamp', [[[0, 2]], [[10000, 10500], [11000, 12000]]], []), ('partial repair probe: zero clamp', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('partial repair variant: zero clamp', [[[0, 2500], [0, 3]], [[1000, 1500], [0, -3000]]], [[0, 8250]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[999, 1499], [7777, 10277]], [[10000, 10500], [10003, 9503]]], []), ('normal control', [[[250, 1250]], [[1000, 1000], [5000, 5500]]], [[156, 1281]]), ('normal control', [[[0, 1000], [250, 750]], [[2000, 0], [0, 500]]], [])], [('regression: zero clamp', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('regression variant: zero clamp', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('partial repair probe: zero clamp', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair variant: zero clamp', [[[5033, 5036], [999, 1000]], [[9000, 9000], [5000, 4000]]], [[4041, 4045]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[7777, 10277], [999, 1000], [999, 1999], [1500, 1502]], [[1000, 2000], [1003, 2003]]], [[8777, 11277], [1999, 2000], [1999, 2999], [2500, 2502]]), ('normal control', [[[1, 4]], [[1003, 1003], [1000, 2000]]], []), ('normal control', [[[7777, 8277], [1500, 2000], [7777, 10277], [999, 1499]], [[5000, 5500], [15000, 14500]]], [[7999, 8449], [2350, 2800], [7999, 10249], [1899, 2349]])]]
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: zero clamp	`[[-500, 0]]`	`[]`	Failed
regression variant: zero clamp	`[[4308231, 4975398], [-1666, 1332668], [1998500, 1999834]]`	`[[4308231, 4975398], [0, 1332668], [1998500, 1999834]]`	Failed
partial repair probe: zero clamp	`[[-3125, 625], [-3500, 0]]`	`[[0, 625]]`	Failed
partial repair variant: zero clamp	`[[-4500, 0]]`	`[]`	Failed
boundary control	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
boundary control	`[[1, 2]]`	`[[1, 2]]`	Passed
normal control	`[[1500, 1501], [1500, 2000], [4889, 5139]]`	`[[1500, 1501], [1500, 2000], [4889, 5139]]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	Passed

SHA-256 / 031d5f5b926183c9934caa55cb11ee8cb694d7f4f08693dc7e25f5d3dcd3cf3e

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: zero clamp', [[[0, 1000]], [[1000, 0], [3000, 1000]]], []), ('regression variant: zero clamp', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair probe: zero clamp', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('partial repair variant: zero clamp', [[[0, 2]], [[10000, 10500], [11000, 12000]]], []), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[999, 1002], [999, 1999], [7777, 8277]], [[1000, 1500], [2000, 2000]]], [[1500, 1501], [1500, 2000], [4889, 5139]]), ('normal control', [[[1920, 2920]], [[0, 1000], [2000, 0]]], []), ('normal control', [[[1, 2], [1, 2], [1500, 1501], [250, 253]], [[11000, 12000], [10000, 11000]]], [[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]])], [('regression: zero clamp', [[[250, 2750], [0, 3]], [[5000, 4000], [6000, 5500]]], [[0, 625]]), ('regression variant: zero clamp', [[[1500, 4000], [0, 1000]], [[3, 1503], [0, -3000]]], [[2248500, 6001000], [0, 1498000]]), ('partial repair probe: zero clamp', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('partial repair variant: zero clamp', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[1, 1001], [1500, 1503]], [[1000, 500], [0, 0]]], [[1, 501], [750, 752]]), ('normal control', [[[6295, 8795]], [[6000, 5500], [5000, 6000]]], []), ('normal control', [[[1, 1001], [999, 1499], [999, 3499]], [[1000, 1500], [11000, 12500]]], [[401, 1501], [1499, 2049], [1499, 4249]])], [('regression: zero clamp', [[[999, 1001], [7777, 7779], [1500, 2000], [250, 251]], [[3000, 1000], [1000, 0]]], [[0, 1], [3389, 3390], [250, 500]]), ('regression variant: zero clamp', [[[7777, 7780], [6684, 6687], [0, 500], [999, 3499]], [[0, -1000], [3, 1503]]], [[6487610, 6490113], [5575684, 5578187], [0, 416167], [832499, 2918332]]), ('partial repair probe: zero clamp', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('partial repair variant: zero clamp', [[[1500, 1502], [7286, 7786]], [[10000, 10000], [11000, 12000]]], [[4572, 5572]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[1, 501], [7777, 7778], [251, 253]], [[10000, 10500], [14000, 12000]]], [[6750, 6938], [9666, 9667], [6844, 6845]]), ('normal control', [[[1, 2], [999, 3499]], [[10000, 10000], [12000, 11500]]], [[2501, 2502], [3249, 5124]]), ('normal control', [[[7777, 8777], [7777, 7780], [1500, 2000], [999, 1002]], [[0, 1000], [4000, 4500]]], [[7805, 8680], [7805, 7808], [2313, 2750], [1874, 1877]])], [('regression: zero clamp', [[[999, 1999], [1, 2501], [7777, 8277], [250, 253]], [[0, -1000], [3, 503]]], [[499499, 1000499], [0, 1252001], [3895277, 4145777], [124250, 125753]]), ('regression variant: zero clamp', [[[0, 2]], [[10000, 10500], [11000, 12000]]], []), ('partial repair probe: zero clamp', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('partial repair variant: zero clamp', [[[0, 2500], [0, 3]], [[1000, 1500], [0, -3000]]], [[0, 8250]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('normal control', [[[999, 1499], [7777, 10277]], [[10000, 10500], [10003, 9503]]], []), ('normal control', [[[250, 1250]], [[1000, 1000], [5000, 5500]]], [[156, 1281]]), ('normal control', [[[0, 1000], [250, 750]], [[2000, 0], [0, 500]]], [])], [('regression: zero clamp', [[[1, 1001]], [[0, -1000], [10000, 9500]]], [[0, 51]]), ('regression variant: zero clamp', [[[1, 501], [7777, 7778]], [[1000, 0], [11000, 12500]]], [[8471, 8473]]), ('partial repair probe: zero clamp', [[[3231, 3731], [1, 1001], [1500, 1501]], [[3, 1003], [0, -3000]]], [[4308231, 4975398], [0, 1332668], [1998500, 1999834]]), ('partial repair variant: zero clamp', [[[5033, 5036], [999, 1000]], [[9000, 9000], [5000, 4000]]], [[4041, 4045]]), ('boundary control', [[[1000, 2000]], [[0, 0], [1000, 2000]]], [[2000, 4000]]), ('boundary control', [[[1, 3]], [[0, 0], [2, 1]]], [[1, 2]]), ('normal control', [[[7777, 10277], [999, 1000], [999, 1999], [1500, 1502]], [[1000, 2000], [1003, 2003]]], [[8777, 11277], [1999, 2000], [1999, 2999], [2500, 2502]]), ('normal control', [[[1, 4]], [[1003, 1003], [1000, 2000]]], []), ('normal control', [[[7777, 8277], [1500, 2000], [7777, 10277], [999, 1499]], [[5000, 5500], [15000, 14500]]], [[7999, 8449], [2350, 2800], [7999, 10249], [1899, 2349]])]]
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: zero clamp	`[]`	`[]`	Passed
regression variant: zero clamp	`[[4308231, 4975398], [0, 1332668], [1998500, 1999834]]`	`[[4308231, 4975398], [0, 1332668], [1998500, 1999834]]`	Passed
partial repair probe: zero clamp	`[[0, 625]]`	`[[0, 625]]`	Passed
partial repair variant: zero clamp	`[]`	`[]`	Passed
boundary control	`[[2000, 4000]]`	`[[2000, 4000]]`	Passed
boundary control	`[[1, 2]]`	`[[1, 2]]`	Passed
normal control	`[[1500, 1501], [1500, 2000], [4889, 5139]]`	`[[1500, 1501], [1500, 2000], [4889, 5139]]`	Passed
normal control	`[]`	`[]`	Passed
normal control	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	`[[1001, 1002], [1001, 1002], [2500, 2501], [1250, 1253]]`	Passed

SHA-256 / dbb4eeddcbd12755585b8b891fbf1200fc13a5991419d2f1a2a20f1a11c53a73

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 2026-09-29T14:49:31.979616+00:00.

Case digest / 6bef96a54e821127070c8bc921ea87f93b1e0d5b37739c2ef92e386e9182391f