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FA-86526 / Procedural level generation constraints / Open access

BSP dungeon partition: Exactly splittable widths stay whole · case 01

Rooms of exactly twice the minimum width are never divided.

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

ROOT CAUSE

The vertical split test is strict.

THE FAILURE

The vertical split test is strict.

Unsuccessful approach: Comparing against min_size creates children narrower than the minimum.

Case contract

Recursively split the rectangle while depth remains. An axis can be split when that side is >= 2*min_size; if neither can, it is a leaf. Split vertically when w > h, or when w == h at even remaining depth; if the chosen axis cannot be split use the other. The first child gets floor(side/2). Returns leaves [x, y, w, h] in left/top-first order.

Why this case matters

Procedural generators silently emit unplayable or unfair levels when a single constraint check uses the wrong boundary, axis, neighborhood or update order; the defect is visible in exact generated geometry.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x, y, w, h, min_size, depth):
    out = []
    def split(x, y, w, h, d):
        can_v = w > 2 * min_size
        can_h = h >= 2 * min_size
        if d == 0 or not (can_v or can_h):
            out.append([x, y, w, h])
            return
        vertical = w > h or (w == h and d % 2 == 0)
        if vertical and not can_v:
            vertical = False
        elif not vertical and not can_h:
            vertical = True
        if vertical:
            half = w // 2
            split(x, y, half, h, d - 1)
            split(x + half, y, w - half, h, d - 1)
        else:
            half = h // 2
            split(x, y, w, half, d - 1)
            split(x, y + half, w, h - half, d - 1)
    split(x, y, w, h, depth)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [2, 1, 16, 5, 4, 2],
   [[2, 1, 4, 5], [6, 1, 4, 5], [10, 1, 4, 5], [14, 1, 4, 5]]),
  ('regression split eligibility #1',
   [5, 4, 23, 8, 3, 4],
   [[5, 4, 5, 4],
    [5, 8, 5, 4],
    [10, 4, 3, 4],
    [13, 4, 3, 4],
    [10, 8, 3, 4],
    [13, 8, 3, 4],
    [16, 4, 3, 4],
    [19, 4, 3, 4],
    [16, 8, 3, 4],
    [19, 8, 3, 4],
    [22, 4, 3, 4],
    [25, 4, 3, 4],
    [22, 8, 3, 4],
    [25, 8, 3, 4]]),
  ('partial repair boundary #1', [1, 4, 9, 1, 3, 4], [[1, 4, 4, 1], [5, 4, 5, 1]]),
  ('partial repair boundary #2',
   [2, 3, 26, 3, 4, 3],
   [[2, 3, 6, 3], [8, 3, 7, 3], [15, 3, 6, 3], [21, 3, 7, 3]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [2, 3, 16, 10, 5, 1], [[2, 3, 8, 10], [10, 3, 8, 10]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('regression split eligibility #1',
   [5, 4, 23, 8, 3, 4],
   [[5, 4, 5, 4],
    [5, 8, 5, 4],
    [10, 4, 3, 4],
    [13, 4, 3, 4],
    [10, 8, 3, 4],
    [13, 8, 3, 4],
    [16, 4, 3, 4],
    [19, 4, 3, 4],
    [16, 8, 3, 4],
    [19, 8, 3, 4],
    [22, 4, 3, 4],
    [25, 4, 3, 4],
    [22, 8, 3, 4],
    [25, 8, 3, 4]]),
  ('regression split eligibility #2', [5, 1, 12, 7, 6, 3], [[5, 1, 6, 7], [11, 1, 6, 7]]),
  ('partial repair boundary #1', [3, 4, 21, 6, 6, 2], [[3, 4, 10, 6], [13, 4, 11, 6]]),
  ('partial repair boundary #2',
   [4, 0, 10, 3, 2, 4],
   [[4, 0, 2, 3], [6, 0, 3, 3], [9, 0, 2, 3], [11, 0, 3, 3]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [2, 3, 16, 10, 5, 1], [[2, 3, 8, 10], [10, 3, 8, 10]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [1, 0, 6, 24, 3, 4],
   [[1, 0, 3, 3],
    [1, 3, 3, 3],
    [4, 0, 3, 3],
    [4, 3, 3, 3],
    [1, 6, 3, 3],
    [1, 9, 3, 3],
    [4, 6, 3, 3],
    [4, 9, 3, 3],
    [1, 12, 3, 3],
    [1, 15, 3, 3],
    [4, 12, 3, 3],
    [4, 15, 3, 3],
    [1, 18, 3, 3],
    [1, 21, 3, 3],
    [4, 18, 3, 3],
    [4, 21, 3, 3]]),
  ('regression split eligibility #1',
   [3, 2, 19, 20, 5, 4],
   [[3, 2, 9, 5],
    [3, 7, 9, 5],
    [12, 2, 5, 5],
    [12, 7, 5, 5],
    [17, 2, 5, 5],
    [17, 7, 5, 5],
    [3, 12, 9, 5],
    [3, 17, 9, 5],
    [12, 12, 5, 5],
    [12, 17, 5, 5],
    [17, 12, 5, 5],
    [17, 17, 5, 5]]),
  ('partial repair boundary #1',
   [2, 3, 15, 3, 3, 3],
   [[2, 3, 3, 3], [5, 3, 4, 3], [9, 3, 4, 3], [13, 3, 4, 3]]),
  ('partial repair boundary #2',
   [3, 5, 26, 4, 5, 4],
   [[3, 5, 6, 4], [9, 5, 7, 4], [16, 5, 6, 4], [22, 5, 7, 4]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [2, 3, 16, 10, 5, 1], [[2, 3, 8, 10], [10, 3, 8, 10]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [2, 1, 12, 14, 6, 2],
   [[2, 1, 6, 7], [8, 1, 6, 7], [2, 8, 6, 7], [8, 8, 6, 7]]),
  ('regression split eligibility #1',
   [2, 1, 6, 21, 3, 4],
   [[2, 1, 3, 5],
    [5, 1, 3, 5],
    [2, 6, 3, 5],
    [5, 6, 3, 5],
    [2, 11, 3, 5],
    [5, 11, 3, 5],
    [2, 16, 3, 3],
    [2, 19, 3, 3],
    [5, 16, 3, 3],
    [5, 19, 3, 3]]),
  ('partial repair boundary #1',
   [5, 5, 9, 8, 3, 4],
   [[5, 5, 4, 4], [5, 9, 4, 4], [9, 5, 5, 4], [9, 9, 5, 4]]),
  ('partial repair boundary #2',
   [1, 1, 29, 13, 5, 4],
   [[1, 1, 7, 6],
    [1, 7, 7, 7],
    [8, 1, 7, 6],
    [8, 7, 7, 7],
    [15, 1, 7, 6],
    [15, 7, 7, 7],
    [22, 1, 8, 6],
    [22, 7, 8, 7]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [3, 0, 14, 28, 4, 1], [[3, 0, 14, 14], [3, 14, 14, 14]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [2, 5, 8, 28, 4, 3],
   [[2, 5, 4, 7],
    [6, 5, 4, 7],
    [2, 12, 4, 7],
    [6, 12, 4, 7],
    [2, 19, 4, 7],
    [6, 19, 4, 7],
    [2, 26, 4, 7],
    [6, 26, 4, 7]]),
  ('fault site split eligibility #2',
   [5, 4, 8, 15, 2, 4],
   [[5, 4, 2, 3],
    [7, 4, 2, 3],
    [5, 7, 4, 2],
    [5, 9, 4, 2],
    [9, 4, 2, 3],
    [11, 4, 2, 3],
    [9, 7, 4, 2],
    [9, 9, 4, 2],
    [5, 11, 4, 2],
    [5, 13, 4, 2],
    [9, 11, 4, 2],
    [9, 13, 4, 2],
    [5, 15, 4, 2],
    [5, 17, 4, 2],
    [9, 15, 4, 2],
    [9, 17, 4, 2]]),
  ('partial repair boundary #1', [4, 3, 17, 5, 5, 4], [[4, 3, 8, 5], [12, 3, 9, 5]]),
  ('partial repair boundary #2', [2, 4, 6, 4, 4, 3], [[2, 4, 6, 4]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [5, 1, 1, 10, 4, 2], [[5, 1, 1, 5], [5, 6, 1, 5]])]]
for label, args, expected in cases[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
exactly splittable #1[[0, 0, 8, 3]][[0, 0, 4, 3], [4, 0, 4, 3]]Failed
fault site split eligibility #1[[2, 1, 8, 5], [10, 1, 8, 5]][[2, 1, 4, 5], [6, 1, 4, 5], [10, 1, 4, 5], [14, 1, 4, 5]]Failed
regression split eligibility #1[[5, 4, 5, 4], [5, 8, 5, 4], [10, 4, 6, 4], [10, 8, 6, 4], [16, 4, 6, 4], [16, 8, 6, 4], [22, 4, 6, 4], [22, 8, 6, 4]][[5, 4, 5, 4], [5, 8, 5, 4], [10, 4, 3, 4], [13, 4, 3, 4], [10, 8, 3, 4], [13, 8, 3, 4], [16, 4, 3, 4], [19, 4, 3, 4], [16, 8, 3, 4], [19, 8, 3, 4], [22, 4, 3, 4], [25, 4, 3, 4], [22, 8, 3, 4], [25, 8, 3, 4]]Failed
partial repair boundary #1[[1, 4, 4, 1], [5, 4, 5, 1]][[1, 4, 4, 1], [5, 4, 5, 1]]Passed
partial repair boundary #2[[2, 3, 6, 3], [8, 3, 7, 3], [15, 3, 6, 3], [21, 3, 7, 3]][[2, 3, 6, 3], [8, 3, 7, 3], [15, 3, 6, 3], [21, 3, 7, 3]]Passed
square at even depth #1[[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]][[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]Passed
odd width #1[[1, 1, 4, 4], [5, 1, 5, 4]][[1, 1, 4, 4], [5, 1, 5, 4]]Passed
control #1[[2, 3, 8, 10], [10, 3, 8, 10]][[2, 3, 8, 10], [10, 3, 8, 10]]Passed

SHA-256 / 470e2c14afa03940f56d0ddb11e33f758455d2a6e9fd5bbc4404f2dec81e9e68

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x, y, w, h, min_size, depth):
    out = []
    def split(x, y, w, h, d):
        can_v = w >= min_size
        can_h = h >= 2 * min_size
        if d == 0 or not (can_v or can_h):
            out.append([x, y, w, h])
            return
        vertical = w > h or (w == h and d % 2 == 0)
        if vertical and not can_v:
            vertical = False
        elif not vertical and not can_h:
            vertical = True
        if vertical:
            half = w // 2
            split(x, y, half, h, d - 1)
            split(x + half, y, w - half, h, d - 1)
        else:
            half = h // 2
            split(x, y, w, half, d - 1)
            split(x, y + half, w, h - half, d - 1)
    split(x, y, w, h, depth)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [2, 1, 16, 5, 4, 2],
   [[2, 1, 4, 5], [6, 1, 4, 5], [10, 1, 4, 5], [14, 1, 4, 5]]),
  ('regression split eligibility #1',
   [5, 4, 23, 8, 3, 4],
   [[5, 4, 5, 4],
    [5, 8, 5, 4],
    [10, 4, 3, 4],
    [13, 4, 3, 4],
    [10, 8, 3, 4],
    [13, 8, 3, 4],
    [16, 4, 3, 4],
    [19, 4, 3, 4],
    [16, 8, 3, 4],
    [19, 8, 3, 4],
    [22, 4, 3, 4],
    [25, 4, 3, 4],
    [22, 8, 3, 4],
    [25, 8, 3, 4]]),
  ('partial repair boundary #1', [1, 4, 9, 1, 3, 4], [[1, 4, 4, 1], [5, 4, 5, 1]]),
  ('partial repair boundary #2',
   [2, 3, 26, 3, 4, 3],
   [[2, 3, 6, 3], [8, 3, 7, 3], [15, 3, 6, 3], [21, 3, 7, 3]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [2, 3, 16, 10, 5, 1], [[2, 3, 8, 10], [10, 3, 8, 10]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('regression split eligibility #1',
   [5, 4, 23, 8, 3, 4],
   [[5, 4, 5, 4],
    [5, 8, 5, 4],
    [10, 4, 3, 4],
    [13, 4, 3, 4],
    [10, 8, 3, 4],
    [13, 8, 3, 4],
    [16, 4, 3, 4],
    [19, 4, 3, 4],
    [16, 8, 3, 4],
    [19, 8, 3, 4],
    [22, 4, 3, 4],
    [25, 4, 3, 4],
    [22, 8, 3, 4],
    [25, 8, 3, 4]]),
  ('regression split eligibility #2', [5, 1, 12, 7, 6, 3], [[5, 1, 6, 7], [11, 1, 6, 7]]),
  ('partial repair boundary #1', [3, 4, 21, 6, 6, 2], [[3, 4, 10, 6], [13, 4, 11, 6]]),
  ('partial repair boundary #2',
   [4, 0, 10, 3, 2, 4],
   [[4, 0, 2, 3], [6, 0, 3, 3], [9, 0, 2, 3], [11, 0, 3, 3]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [2, 3, 16, 10, 5, 1], [[2, 3, 8, 10], [10, 3, 8, 10]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [1, 0, 6, 24, 3, 4],
   [[1, 0, 3, 3],
    [1, 3, 3, 3],
    [4, 0, 3, 3],
    [4, 3, 3, 3],
    [1, 6, 3, 3],
    [1, 9, 3, 3],
    [4, 6, 3, 3],
    [4, 9, 3, 3],
    [1, 12, 3, 3],
    [1, 15, 3, 3],
    [4, 12, 3, 3],
    [4, 15, 3, 3],
    [1, 18, 3, 3],
    [1, 21, 3, 3],
    [4, 18, 3, 3],
    [4, 21, 3, 3]]),
  ('regression split eligibility #1',
   [3, 2, 19, 20, 5, 4],
   [[3, 2, 9, 5],
    [3, 7, 9, 5],
    [12, 2, 5, 5],
    [12, 7, 5, 5],
    [17, 2, 5, 5],
    [17, 7, 5, 5],
    [3, 12, 9, 5],
    [3, 17, 9, 5],
    [12, 12, 5, 5],
    [12, 17, 5, 5],
    [17, 12, 5, 5],
    [17, 17, 5, 5]]),
  ('partial repair boundary #1',
   [2, 3, 15, 3, 3, 3],
   [[2, 3, 3, 3], [5, 3, 4, 3], [9, 3, 4, 3], [13, 3, 4, 3]]),
  ('partial repair boundary #2',
   [3, 5, 26, 4, 5, 4],
   [[3, 5, 6, 4], [9, 5, 7, 4], [16, 5, 6, 4], [22, 5, 7, 4]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [2, 3, 16, 10, 5, 1], [[2, 3, 8, 10], [10, 3, 8, 10]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [2, 1, 12, 14, 6, 2],
   [[2, 1, 6, 7], [8, 1, 6, 7], [2, 8, 6, 7], [8, 8, 6, 7]]),
  ('regression split eligibility #1',
   [2, 1, 6, 21, 3, 4],
   [[2, 1, 3, 5],
    [5, 1, 3, 5],
    [2, 6, 3, 5],
    [5, 6, 3, 5],
    [2, 11, 3, 5],
    [5, 11, 3, 5],
    [2, 16, 3, 3],
    [2, 19, 3, 3],
    [5, 16, 3, 3],
    [5, 19, 3, 3]]),
  ('partial repair boundary #1',
   [5, 5, 9, 8, 3, 4],
   [[5, 5, 4, 4], [5, 9, 4, 4], [9, 5, 5, 4], [9, 9, 5, 4]]),
  ('partial repair boundary #2',
   [1, 1, 29, 13, 5, 4],
   [[1, 1, 7, 6],
    [1, 7, 7, 7],
    [8, 1, 7, 6],
    [8, 7, 7, 7],
    [15, 1, 7, 6],
    [15, 7, 7, 7],
    [22, 1, 8, 6],
    [22, 7, 8, 7]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [3, 0, 14, 28, 4, 1], [[3, 0, 14, 14], [3, 14, 14, 14]])],
 [('exactly splittable #1', [0, 0, 8, 3, 4, 1], [[0, 0, 4, 3], [4, 0, 4, 3]]),
  ('fault site split eligibility #1',
   [2, 5, 8, 28, 4, 3],
   [[2, 5, 4, 7],
    [6, 5, 4, 7],
    [2, 12, 4, 7],
    [6, 12, 4, 7],
    [2, 19, 4, 7],
    [6, 19, 4, 7],
    [2, 26, 4, 7],
    [6, 26, 4, 7]]),
  ('fault site split eligibility #2',
   [5, 4, 8, 15, 2, 4],
   [[5, 4, 2, 3],
    [7, 4, 2, 3],
    [5, 7, 4, 2],
    [5, 9, 4, 2],
    [9, 4, 2, 3],
    [11, 4, 2, 3],
    [9, 7, 4, 2],
    [9, 9, 4, 2],
    [5, 11, 4, 2],
    [5, 13, 4, 2],
    [9, 11, 4, 2],
    [9, 13, 4, 2],
    [5, 15, 4, 2],
    [5, 17, 4, 2],
    [9, 15, 4, 2],
    [9, 17, 4, 2]]),
  ('partial repair boundary #1', [4, 3, 17, 5, 5, 4], [[4, 3, 8, 5], [12, 3, 9, 5]]),
  ('partial repair boundary #2', [2, 4, 6, 4, 4, 3], [[2, 4, 6, 4]]),
  ('square at even depth #1', [0, 0, 10, 10, 2, 2], [[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]),
  ('odd width #1', [1, 1, 9, 4, 2, 1], [[1, 1, 4, 4], [5, 1, 5, 4]]),
  ('control #1', [5, 1, 1, 10, 4, 2], [[5, 1, 1, 5], [5, 6, 1, 5]])]]
for label, args, expected in cases[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
exactly splittable #1[[0, 0, 4, 3], [4, 0, 4, 3]][[0, 0, 4, 3], [4, 0, 4, 3]]Passed
fault site split eligibility #1[[2, 1, 4, 5], [6, 1, 4, 5], [10, 1, 4, 5], [14, 1, 4, 5]][[2, 1, 4, 5], [6, 1, 4, 5], [10, 1, 4, 5], [14, 1, 4, 5]]Passed
regression split eligibility #1[[5, 4, 2, 4], [7, 4, 3, 4], [5, 8, 2, 4], [7, 8, 3, 4], [10, 4, 3, 4], [13, 4, 3, 4], [10, 8, 3, 4], [13, 8, 3, 4], [16, 4, 3, 4], [19, 4, 3, 4], [16, 8, 3, 4], [19, 8, 3, 4], [22, 4, 3, 4], [25, 4, 3, 4], [22, 8, 3, 4], [25, 8, 3, 4]][[5, 4, 5, 4], [5, 8, 5, 4], [10, 4, 3, 4], [13, 4, 3, 4], [10, 8, 3, 4], [13, 8, 3, 4], [16, 4, 3, 4], [19, 4, 3, 4], [16, 8, 3, 4], [19, 8, 3, 4], [22, 4, 3, 4], [25, 4, 3, 4], [22, 8, 3, 4], [25, 8, 3, 4]]Failed
partial repair boundary #1[[1, 4, 2, 1], [3, 4, 2, 1], [5, 4, 2, 1], [7, 4, 1, 1], [8, 4, 2, 1]][[1, 4, 4, 1], [5, 4, 5, 1]]Failed
partial repair boundary #2[[2, 3, 3, 3], [5, 3, 3, 3], [8, 3, 3, 3], [11, 3, 4, 3], [15, 3, 3, 3], [18, 3, 3, 3], [21, 3, 3, 3], [24, 3, 4, 3]][[2, 3, 6, 3], [8, 3, 7, 3], [15, 3, 6, 3], [21, 3, 7, 3]]Failed
square at even depth #1[[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]][[0, 0, 5, 5], [0, 5, 5, 5], [5, 0, 5, 5], [5, 5, 5, 5]]Passed
odd width #1[[1, 1, 4, 4], [5, 1, 5, 4]][[1, 1, 4, 4], [5, 1, 5, 4]]Passed
control #1[[2, 3, 8, 10], [10, 3, 8, 10]][[2, 3, 8, 10], [10, 3, 8, 10]]Passed

SHA-256 / e944c6559919e0601adc51a897fb2895100206c0adb4cb1f21b3acb073180561

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. 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 2026-09-29T14:50:50.263957+00:00.

Case digest / f3dcfbb6ca66bbc4a85b3c3452abf665a9899897e9ee4d1f2310dace67768d9a