FAILURE MAP
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FA-86686 / Procedural level generation constraints / Open access

Decoration scatter with quadrant quota: Odd maps get a third quadrant column · case 01

Quotas are bypassed along the last column of odd-width maps.

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

ROOT CAUSE

Quadrants are computed by dividing by half the size, producing extra quadrants for odd sizes.

THE FAILURE

Quadrants are computed by dividing by half the size, producing extra quadrants for odd sizes.

Unsuccessful approach: Swapping width and height misassigns quadrants on non-square maps.

Case contract

Candidates [x, y] (grid[y][x]) are tried in order. Accept when in bounds on '.', its quadrant (x*2//w, y*2//h) holds fewer than per_quadrant accepted props, and its squared Euclidean distance to every accepted prop is at least radius*radius. Returns accepted [x, y].

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(grid, candidates, radius, per_quadrant):
    h = len(grid)
    w = len(grid[0])
    placed = []
    quota = {}
    for x, y in candidates:
        if not (0 <= y < h and 0 <= x < w) or grid[y][x] != '.':
            continue
        q = (x // (w // 2), y // (h // 2))
        if quota.get(q, 0) >= per_quadrant:
            continue
        if any((x - px) ** 2 + (y - py) ** 2 < radius * radius for px, py in placed):
            continue
        placed.append([x, y])
        quota[q] = quota.get(q, 0) + 1
    return placed
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['~~..#', '.....', '....#'], [[3, 1], [1, 2], [5, 2], [2, 3], [0, 3], [3, 0], [1, 1], [0, 1]], 1, 1],
   [[3, 1], [1, 2], [1, 1]]),
  ('regression quadrant index #2',
   [['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
    [[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
    2,
    1],
   [[1, 6], [0, 0]]),
  ('partial repair boundary #1',
   [['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
   [[2, 0], [2, 1]]),
  ('regression quadrant index #3',
   [['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
   [[1, 4]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
   [[1, 2], [4, 3]]),
  ('control #2', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
   [[1, 4]]),
  ('fault site quadrant index #1',
   [['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
    [[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
    2,
    1],
   [[3, 2], [0, 0]]),
  ('partial repair boundary #1',
   [['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
   [[2, 0], [2, 1]]),
  ('regression quadrant index #2',
   [['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
    [[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
    2,
    1],
   [[1, 6], [0, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]]),
  ('control #2',
   [['..', '~.'],
    [[2, 1], [1, 2], [2, 0], [2, 0], [0, 1], [2, 1], [0, 0], [2, 2], [0, 0], [1, 1], [2, 0]],
    3,
    2],
   [[0, 0]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
    [[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
    1,
    1],
   [[3, 3]]),
  ('fault site quadrant index #1',
   [['...~#~.', '~.~~...', '..~.##.', '......#', '#~.~~.#', '......#', '~#.....'],
    [[0, 1], [0, 7], [2, 6], [2, 6], [6, 0], [7, 3], [6, 3], [0, 1], [7, 1], [3, 6], [6, 3], [1, 3]],
    1,
    1],
   [[2, 6], [6, 0], [1, 3]]),
  ('regression quadrant index #2',
   [['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
   [[1, 4]]),
  ('partial repair boundary #1',
   [['.~#', '##.', '~#.', '.##', '...', '.#.'],
    [[3, 5], [1, 0], [0, 4], [1, 2], [3, 6], [2, 4], [2, 0], [1, 0], [0, 3], [2, 4], [3, 3], [0, 4]],
    2,
    1],
   [[0, 4], [2, 4]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1', [['....', '..#.'], [[0, 1], [3, 0], [1, 0]], 3, 2], [[0, 1], [3, 0]]),
  ('control #2',
   [['..', '.#', '..', '~~', '..', '..', '..'],
    [[1, 6], [1, 1], [0, 7], [0, 0], [2, 1], [2, 5], [2, 0], [0, 4], [1, 1], [0, 0], [0, 3], [2, 6]],
    3,
    3],
   [[1, 6], [0, 0]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('regression quadrant index #2',
   [['...~.#..', '~#.###~.', '.#.#..~#', '...#.#~.', '~.~.~..#', '.#...#.#', '#..~#...'],
    [[4, 2], [6, 0], [7, 3], [5, 4], [7, 6], [5, 6], [7, 4], [0, 2], [4, 0], [5, 2], [1, 2]],
    2,
    2],
   [[4, 2], [6, 0], [5, 4], [7, 6], [0, 2]]),
  ('regression quadrant index #3',
   [['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
    [[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
    1,
    1],
   [[3, 3]]),
  ('partial repair boundary #1',
   [['..~...', '......', '#.#.~.', '......'],
    [[3, 1], [5, 1], [0, 2], [6, 0], [5, 2], [0, 0], [0, 3], [4, 1], [4, 3], [4, 4]],
    2,
    1],
   [[3, 1], [5, 2], [0, 0], [0, 3]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['...~#.~~', '~~~~#.~.', '~.#....#', '#~..~...'], [[0, 4], [1, 1], [5, 2], [3, 2], [1, 1]], 2, 2],
   [[5, 2], [3, 2]]),
  ('control #2',
   [['...', '.#.'], [[3, 1], [0, 2], [1, 2], [2, 2], [3, 0], [3, 1], [3, 0], [1, 0]], 1, 2],
   [[1, 0]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('fault site quadrant index #1',
   [['.~~~', '....', '..#~'], [[0, 2], [2, 1], [0, 0], [2, 3], [2, 2], [0, 3], [2, 2], [1, 1], [2, 2]], 1, 1],
   [[0, 2], [2, 1], [0, 0]]),
  ('fault site quadrant index #2',
   [['......~', '.~##.#.', '.~..~.~', '.......', '.......', '#.~.#..', '.~.....', '#.#....'],
    [[0, 0], [4, 4], [4, 8], [2, 5], [3, 0], [1, 7], [0, 8], [6, 2], [1, 6], [4, 8], [5, 2]],
    3,
    1],
   [[0, 0], [4, 4], [1, 7]]),
  ('partial repair boundary #1',
   [['..~...', '......', '#.#.~.', '......'],
    [[3, 1], [5, 1], [0, 2], [6, 0], [5, 2], [0, 0], [0, 3], [4, 1], [4, 3], [4, 4]],
    2,
    1],
   [[3, 1], [5, 2], [0, 0], [0, 3]]),
  ('regression quadrant index #1',
   [['...~.#..', '~#.###~.', '.#.#..~#', '...#.#~.', '~.~.~..#', '.#...#.#', '#..~#...'],
    [[4, 2], [6, 0], [7, 3], [5, 4], [7, 6], [5, 6], [7, 4], [0, 2], [4, 0], [5, 2], [1, 2]],
    2,
    2],
   [[4, 2], [6, 0], [5, 4], [7, 6], [0, 2]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1', [['....', '.~#.'], [[1, 2], [2, 0], [4, 1], [3, 1]], 1, 2], [[2, 0], [3, 1]]),
  ('control #2', [['##.', '...', '...', '.#~'], [[0, 1], [0, 0], [2, 3]], 3, 1], [[0, 1]])]]
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
quadrant full #1[[0, 0], [3, 0]][[0, 0], [3, 0]]Passed
regression quadrant index #1[[3, 1], [1, 2], [3, 0], [1, 1]][[3, 1], [1, 2], [1, 1]]Failed
regression quadrant index #2[[1, 6], [0, 0], [1, 3]][[1, 6], [0, 0]]Failed
partial repair boundary #1[[2, 0], [2, 1]][[2, 0], [2, 1]]Passed
regression quadrant index #3[[1, 4], [1, 6]][[1, 4]]Failed
diagonal within radius #1[[0, 0]][[0, 0]]Passed
control #1[[1, 2], [4, 3]][[1, 2], [4, 3]]Passed
control #2[[1, 1]][[1, 1]]Passed

SHA-256 / 4c476fc54b6641dafcd56b4352151e968c46f7965b08613f6eb7ca45ae9abda0

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(grid, candidates, radius, per_quadrant):
    h = len(grid)
    w = len(grid[0])
    placed = []
    quota = {}
    for x, y in candidates:
        if not (0 <= y < h and 0 <= x < w) or grid[y][x] != '.':
            continue
        q = (x * 2 // h, y * 2 // w)
        if quota.get(q, 0) >= per_quadrant:
            continue
        if any((x - px) ** 2 + (y - py) ** 2 < radius * radius for px, py in placed):
            continue
        placed.append([x, y])
        quota[q] = quota.get(q, 0) + 1
    return placed
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['~~..#', '.....', '....#'], [[3, 1], [1, 2], [5, 2], [2, 3], [0, 3], [3, 0], [1, 1], [0, 1]], 1, 1],
   [[3, 1], [1, 2], [1, 1]]),
  ('regression quadrant index #2',
   [['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
    [[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
    2,
    1],
   [[1, 6], [0, 0]]),
  ('partial repair boundary #1',
   [['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
   [[2, 0], [2, 1]]),
  ('regression quadrant index #3',
   [['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
   [[1, 4]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
   [[1, 2], [4, 3]]),
  ('control #2', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
   [[1, 4]]),
  ('fault site quadrant index #1',
   [['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
    [[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
    2,
    1],
   [[3, 2], [0, 0]]),
  ('partial repair boundary #1',
   [['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
   [[2, 0], [2, 1]]),
  ('regression quadrant index #2',
   [['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
    [[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
    2,
    1],
   [[1, 6], [0, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]]),
  ('control #2',
   [['..', '~.'],
    [[2, 1], [1, 2], [2, 0], [2, 0], [0, 1], [2, 1], [0, 0], [2, 2], [0, 0], [1, 1], [2, 0]],
    3,
    2],
   [[0, 0]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
    [[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
    1,
    1],
   [[3, 3]]),
  ('fault site quadrant index #1',
   [['...~#~.', '~.~~...', '..~.##.', '......#', '#~.~~.#', '......#', '~#.....'],
    [[0, 1], [0, 7], [2, 6], [2, 6], [6, 0], [7, 3], [6, 3], [0, 1], [7, 1], [3, 6], [6, 3], [1, 3]],
    1,
    1],
   [[2, 6], [6, 0], [1, 3]]),
  ('regression quadrant index #2',
   [['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
   [[1, 4]]),
  ('partial repair boundary #1',
   [['.~#', '##.', '~#.', '.##', '...', '.#.'],
    [[3, 5], [1, 0], [0, 4], [1, 2], [3, 6], [2, 4], [2, 0], [1, 0], [0, 3], [2, 4], [3, 3], [0, 4]],
    2,
    1],
   [[0, 4], [2, 4]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1', [['....', '..#.'], [[0, 1], [3, 0], [1, 0]], 3, 2], [[0, 1], [3, 0]]),
  ('control #2',
   [['..', '.#', '..', '~~', '..', '..', '..'],
    [[1, 6], [1, 1], [0, 7], [0, 0], [2, 1], [2, 5], [2, 0], [0, 4], [1, 1], [0, 0], [0, 3], [2, 6]],
    3,
    3],
   [[1, 6], [0, 0]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('regression quadrant index #1',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('regression quadrant index #2',
   [['...~.#..', '~#.###~.', '.#.#..~#', '...#.#~.', '~.~.~..#', '.#...#.#', '#..~#...'],
    [[4, 2], [6, 0], [7, 3], [5, 4], [7, 6], [5, 6], [7, 4], [0, 2], [4, 0], [5, 2], [1, 2]],
    2,
    2],
   [[4, 2], [6, 0], [5, 4], [7, 6], [0, 2]]),
  ('regression quadrant index #3',
   [['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
    [[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
    1,
    1],
   [[3, 3]]),
  ('partial repair boundary #1',
   [['..~...', '......', '#.#.~.', '......'],
    [[3, 1], [5, 1], [0, 2], [6, 0], [5, 2], [0, 0], [0, 3], [4, 1], [4, 3], [4, 4]],
    2,
    1],
   [[3, 1], [5, 2], [0, 0], [0, 3]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['...~#.~~', '~~~~#.~.', '~.#....#', '#~..~...'], [[0, 4], [1, 1], [5, 2], [3, 2], [1, 1]], 2, 2],
   [[5, 2], [3, 2]]),
  ('control #2',
   [['...', '.#.'], [[3, 1], [0, 2], [1, 2], [2, 2], [3, 0], [3, 1], [3, 0], [1, 0]], 1, 2],
   [[1, 0]])],
 [('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('fault site quadrant index #1',
   [['.~~~', '....', '..#~'], [[0, 2], [2, 1], [0, 0], [2, 3], [2, 2], [0, 3], [2, 2], [1, 1], [2, 2]], 1, 1],
   [[0, 2], [2, 1], [0, 0]]),
  ('fault site quadrant index #2',
   [['......~', '.~##.#.', '.~..~.~', '.......', '.......', '#.~.#..', '.~.....', '#.#....'],
    [[0, 0], [4, 4], [4, 8], [2, 5], [3, 0], [1, 7], [0, 8], [6, 2], [1, 6], [4, 8], [5, 2]],
    3,
    1],
   [[0, 0], [4, 4], [1, 7]]),
  ('partial repair boundary #1',
   [['..~...', '......', '#.#.~.', '......'],
    [[3, 1], [5, 1], [0, 2], [6, 0], [5, 2], [0, 0], [0, 3], [4, 1], [4, 3], [4, 4]],
    2,
    1],
   [[3, 1], [5, 2], [0, 0], [0, 3]]),
  ('regression quadrant index #1',
   [['...~.#..', '~#.###~.', '.#.#..~#', '...#.#~.', '~.~.~..#', '.#...#.#', '#..~#...'],
    [[4, 2], [6, 0], [7, 3], [5, 4], [7, 6], [5, 6], [7, 4], [0, 2], [4, 0], [5, 2], [1, 2]],
    2,
    2],
   [[4, 2], [6, 0], [5, 4], [7, 6], [0, 2]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1', [['....', '.~#.'], [[1, 2], [2, 0], [4, 1], [3, 1]], 1, 2], [[2, 0], [3, 1]]),
  ('control #2', [['##.', '...', '...', '.#~'], [[0, 1], [0, 0], [2, 3]], 3, 1], [[0, 1]])]]
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
quadrant full #1[[0, 0], [1, 0], [3, 0]][[0, 0], [3, 0]]Failed
regression quadrant index #1[[3, 1], [1, 2]][[3, 1], [1, 2], [1, 1]]Failed
regression quadrant index #2[[1, 6], [0, 0], [1, 3]][[1, 6], [0, 0]]Failed
partial repair boundary #1[[2, 0], [0, 1]][[2, 0], [2, 1]]Failed
regression quadrant index #3[[1, 4], [1, 6]][[1, 4]]Failed
diagonal within radius #1[[0, 0]][[0, 0]]Passed
control #1[[1, 2], [4, 3]][[1, 2], [4, 3]]Passed
control #2[[1, 1]][[1, 1]]Passed

SHA-256 / c61e5ca34af2467e7ba364dedecc894020dd4241814052582a82d912f16f226b

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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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 2026-09-29T14:50:51.899008+00:00.

Case digest / 4b919cc2b3d79c4be48c10b7d46ad8fac65c32f2a9b6b8710b38016ad00666fc