FAILURE MAP
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FA-86696 / Procedural level generation constraints / Open access

Decoration scatter with quadrant quota: Quadrant counter never exceeds one · case 01

Quotas above one are ignored.

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

ROOT CAUSE

The quadrant counter is reset to one on each placement.

VERIFIED REPAIR

Restore `quota[q] = quota.get(q, 0) + 1` at the quota increment step.

Unsuccessful approach: Storing the global count mixes quadrants.

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 * 2 // w, y * 2 // h)
        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] = 1
    return placed
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['......~.', '#..~.#.#', '~#..~..#', '..~...~#', '~.......', '....#~..'],
    [[0, 2], [7, 4], [6, 2], [5, 1], [4, 1], [5, 0], [6, 5], [7, 1], [2, 5], [4, 5], [2, 6]],
    1,
    3],
   [[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]]),
  ('partial repair boundary #2',
   [['.~~...'], [[2, 0], [0, 0], [4, 0], [4, 0], [3, 1], [6, 1], [5, 0], [3, 1]], 1, 2],
   [[0, 0], [4, 0], [5, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('control #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 quota increment #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]]),
  ('regression quota increment #2',
   [['~#...##', '...##..', '~..~~..', '#.#.~..', '..#...#', '~#.~~~.'],
    [[0, 0], [1, 3], [3, 0], [7, 1], [6, 3], [5, 2], [2, 0], [2, 6], [1, 1], [7, 1], [1, 2], [7, 4]],
    1,
    2],
   [[1, 3], [3, 0], [6, 3], [5, 2], [2, 0]]),
  ('partial repair boundary #1',
   [['#..~.##', '..~.#..', '#.~#..~'],
    [[3, 1], [7, 1], [4, 1], [0, 3], [6, 0], [5, 2], [5, 3], [6, 3], [1, 0], [6, 1], [2, 0], [6, 1]],
    1,
    3],
   [[3, 1], [5, 2], [1, 0], [6, 1], [2, 0]]),
  ('partial repair boundary #2',
   [['~..#.#', '~.#~..', '......', '.~.#.#', '..~...', '....#.', '..~~.#'],
    [[1, 5], [0, 0], [0, 4], [1, 3], [1, 0], [5, 1], [2, 6], [3, 0], [1, 1], [5, 1]],
    1,
    3],
   [[1, 5], [0, 4], [1, 0], [5, 1], [1, 1]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('control #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]]),
  ('control #2',
   [['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
   [[1, 2], [4, 3]])],
 [('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['.~....', '...~..'], [[0, 0], [5, 1], [6, 0], [4, 1], [0, 1], [3, 2], [1, 0]], 1, 2],
   [[0, 0], [5, 1], [4, 1], [0, 1]]),
  ('partial repair boundary #2',
   [['#.~', '.~#', '.~.', '...', '#..', '..~'],
    [[3, 5], [2, 2], [2, 6], [0, 2], [3, 1], [1, 2], [2, 2], [1, 0], [2, 1]],
    2,
    2],
   [[2, 2], [0, 2], [1, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 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]])],
 [('regression quota increment #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]]),
  ('regression quota increment #2',
   [['~#...##', '...##..', '~..~~..', '#.#.~..', '..#...#', '~#.~~~.'],
    [[0, 0], [1, 3], [3, 0], [7, 1], [6, 3], [5, 2], [2, 0], [2, 6], [1, 1], [7, 1], [1, 2], [7, 4]],
    1,
    2],
   [[1, 3], [3, 0], [6, 3], [5, 2], [2, 0]]),
  ('partial repair boundary #1',
   [['......#', '~~..#~.', '.~.~~..', '#......', '..~..~#'],
    [[5, 3], [1, 2], [0, 3], [4, 0], [1, 4], [4, 3], [0, 3], [3, 4], [1, 3], [7, 5]],
    1,
    3],
   [[5, 3], [4, 0], [1, 4], [4, 3], [3, 4], [1, 3]]),
  ('partial repair boundary #2',
   [['~.#...', '......', '.~#~~#', '..~..~', '~#~#~#', '.~~...', '......'],
    [[4, 0], [3, 1], [1, 1], [1, 3], [3, 1], [5, 2], [3, 4]],
    1,
    2],
   [[4, 0], [3, 1], [1, 1], [1, 3]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['..', '~.'],
    [[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]]),
  ('control #2', [['.'], [[0, 0], [0, 0], [1, 0], [1, 1]], 1, 2], [[0, 0]])],
 [('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['.#..#..', '.#.~...', '.###..~', '~#..#.#', '.......', '...##~.'],
    [[2, 4], [6, 3], [0, 2], [6, 0], [2, 1], [4, 3], [4, 4], [0, 0], [4, 3], [0, 3]],
    1,
    3],
   [[2, 4], [0, 2], [6, 0], [2, 1], [4, 4], [0, 0]]),
  ('partial repair boundary #2',
   [['~~.....', '..#...~', '....#..', '.~.....', '#...~~~', '....~..'],
    [[1, 1], [3, 5], [5, 5], [5, 4], [4, 4], [1, 0], [0, 0], [1, 4], [3, 1], [4, 1], [6, 0], [3, 4]],
    2,
    2],
   [[1, 1], [3, 5], [5, 5], [1, 4], [3, 1], [6, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 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]])]]
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
fault site quota increment #1[[1, 1], [0, 1], [0, 0], [4, 2]][[1, 1], [0, 1], [4, 2]]Failed
fault site quota increment #2[[2, 1], [3, 1], [1, 1], [5, 0]][[2, 1], [3, 1], [5, 0]]Failed
partial repair boundary #1[[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]][[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]]Passed
partial repair boundary #2[[0, 0], [4, 0], [5, 0]][[0, 0], [4, 0], [5, 0]]Passed
exact radius spacing #1[[0, 0], [2, 0]][[0, 0], [2, 0]]Passed
diagonal within radius #1[[0, 0]][[0, 0]]Passed
quadrant full #1[[0, 0], [3, 0]][[0, 0], [3, 0]]Passed
control #1[[3, 1], [1, 2], [1, 1]][[3, 1], [1, 2], [1, 1]]Passed

SHA-256 / 3feec1047667f53ef915654e171d605f89d133d7fe25446b6578731bb6d05160

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 // w, y * 2 // h)
        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] = len(placed)
    return placed
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['......~.', '#..~.#.#', '~#..~..#', '..~...~#', '~.......', '....#~..'],
    [[0, 2], [7, 4], [6, 2], [5, 1], [4, 1], [5, 0], [6, 5], [7, 1], [2, 5], [4, 5], [2, 6]],
    1,
    3],
   [[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]]),
  ('partial repair boundary #2',
   [['.~~...'], [[2, 0], [0, 0], [4, 0], [4, 0], [3, 1], [6, 1], [5, 0], [3, 1]], 1, 2],
   [[0, 0], [4, 0], [5, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('control #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 quota increment #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]]),
  ('regression quota increment #2',
   [['~#...##', '...##..', '~..~~..', '#.#.~..', '..#...#', '~#.~~~.'],
    [[0, 0], [1, 3], [3, 0], [7, 1], [6, 3], [5, 2], [2, 0], [2, 6], [1, 1], [7, 1], [1, 2], [7, 4]],
    1,
    2],
   [[1, 3], [3, 0], [6, 3], [5, 2], [2, 0]]),
  ('partial repair boundary #1',
   [['#..~.##', '..~.#..', '#.~#..~'],
    [[3, 1], [7, 1], [4, 1], [0, 3], [6, 0], [5, 2], [5, 3], [6, 3], [1, 0], [6, 1], [2, 0], [6, 1]],
    1,
    3],
   [[3, 1], [5, 2], [1, 0], [6, 1], [2, 0]]),
  ('partial repair boundary #2',
   [['~..#.#', '~.#~..', '......', '.~.#.#', '..~...', '....#.', '..~~.#'],
    [[1, 5], [0, 0], [0, 4], [1, 3], [1, 0], [5, 1], [2, 6], [3, 0], [1, 1], [5, 1]],
    1,
    3],
   [[1, 5], [0, 4], [1, 0], [5, 1], [1, 1]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('control #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]]),
  ('control #2',
   [['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
   [[1, 2], [4, 3]])],
 [('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['.~....', '...~..'], [[0, 0], [5, 1], [6, 0], [4, 1], [0, 1], [3, 2], [1, 0]], 1, 2],
   [[0, 0], [5, 1], [4, 1], [0, 1]]),
  ('partial repair boundary #2',
   [['#.~', '.~#', '.~.', '...', '#..', '..~'],
    [[3, 5], [2, 2], [2, 6], [0, 2], [3, 1], [1, 2], [2, 2], [1, 0], [2, 1]],
    2,
    2],
   [[2, 2], [0, 2], [1, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 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]])],
 [('regression quota increment #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]]),
  ('regression quota increment #2',
   [['~#...##', '...##..', '~..~~..', '#.#.~..', '..#...#', '~#.~~~.'],
    [[0, 0], [1, 3], [3, 0], [7, 1], [6, 3], [5, 2], [2, 0], [2, 6], [1, 1], [7, 1], [1, 2], [7, 4]],
    1,
    2],
   [[1, 3], [3, 0], [6, 3], [5, 2], [2, 0]]),
  ('partial repair boundary #1',
   [['......#', '~~..#~.', '.~.~~..', '#......', '..~..~#'],
    [[5, 3], [1, 2], [0, 3], [4, 0], [1, 4], [4, 3], [0, 3], [3, 4], [1, 3], [7, 5]],
    1,
    3],
   [[5, 3], [4, 0], [1, 4], [4, 3], [3, 4], [1, 3]]),
  ('partial repair boundary #2',
   [['~.#...', '......', '.~#~~#', '..~..~', '~#~#~#', '.~~...', '......'],
    [[4, 0], [3, 1], [1, 1], [1, 3], [3, 1], [5, 2], [3, 4]],
    1,
    2],
   [[4, 0], [3, 1], [1, 1], [1, 3]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['..', '~.'],
    [[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]]),
  ('control #2', [['.'], [[0, 0], [0, 0], [1, 0], [1, 1]], 1, 2], [[0, 0]])],
 [('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['.#..#..', '.#.~...', '.###..~', '~#..#.#', '.......', '...##~.'],
    [[2, 4], [6, 3], [0, 2], [6, 0], [2, 1], [4, 3], [4, 4], [0, 0], [4, 3], [0, 3]],
    1,
    3],
   [[2, 4], [0, 2], [6, 0], [2, 1], [4, 4], [0, 0]]),
  ('partial repair boundary #2',
   [['~~.....', '..#...~', '....#..', '.~.....', '#...~~~', '....~..'],
    [[1, 1], [3, 5], [5, 5], [5, 4], [4, 4], [1, 0], [0, 0], [1, 4], [3, 1], [4, 1], [6, 0], [3, 4]],
    2,
    2],
   [[1, 1], [3, 5], [5, 5], [1, 4], [3, 1], [6, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 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]])]]
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
fault site quota increment #1[[1, 1], [0, 1], [4, 2]][[1, 1], [0, 1], [4, 2]]Passed
fault site quota increment #2[[2, 1], [3, 1], [5, 0]][[2, 1], [3, 1], [5, 0]]Passed
partial repair boundary #1[[7, 4], [6, 2], [4, 1], [6, 5], [2, 5]][[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]]Failed
partial repair boundary #2[[0, 0], [4, 0]][[0, 0], [4, 0], [5, 0]]Failed
exact radius spacing #1[[0, 0], [2, 0]][[0, 0], [2, 0]]Passed
diagonal within radius #1[[0, 0]][[0, 0]]Passed
quadrant full #1[[0, 0], [3, 0]][[0, 0], [3, 0]]Passed
control #1[[3, 1], [1, 2], [1, 1]][[3, 1], [1, 2], [1, 1]]Passed

SHA-256 / 9f4e6522ab23abb5d5e2c868e2f1ec2a98326bee82373bf43d0e78ae91d5e75d

3 / The verified repair

Exit 0
"""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 // w, y * 2 // h)
        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 = [[('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['......~.', '#..~.#.#', '~#..~..#', '..~...~#', '~.......', '....#~..'],
    [[0, 2], [7, 4], [6, 2], [5, 1], [4, 1], [5, 0], [6, 5], [7, 1], [2, 5], [4, 5], [2, 6]],
    1,
    3],
   [[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]]),
  ('partial repair boundary #2',
   [['.~~...'], [[2, 0], [0, 0], [4, 0], [4, 0], [3, 1], [6, 1], [5, 0], [3, 1]], 1, 2],
   [[0, 0], [4, 0], [5, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('control #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 quota increment #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]]),
  ('regression quota increment #2',
   [['~#...##', '...##..', '~..~~..', '#.#.~..', '..#...#', '~#.~~~.'],
    [[0, 0], [1, 3], [3, 0], [7, 1], [6, 3], [5, 2], [2, 0], [2, 6], [1, 1], [7, 1], [1, 2], [7, 4]],
    1,
    2],
   [[1, 3], [3, 0], [6, 3], [5, 2], [2, 0]]),
  ('partial repair boundary #1',
   [['#..~.##', '..~.#..', '#.~#..~'],
    [[3, 1], [7, 1], [4, 1], [0, 3], [6, 0], [5, 2], [5, 3], [6, 3], [1, 0], [6, 1], [2, 0], [6, 1]],
    1,
    3],
   [[3, 1], [5, 2], [1, 0], [6, 1], [2, 0]]),
  ('partial repair boundary #2',
   [['~..#.#', '~.#~..', '......', '.~.#.#', '..~...', '....#.', '..~~.#'],
    [[1, 5], [0, 0], [0, 4], [1, 3], [1, 0], [5, 1], [2, 6], [3, 0], [1, 1], [5, 1]],
    1,
    3],
   [[1, 5], [0, 4], [1, 0], [5, 1], [1, 1]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('control #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]]),
  ('control #2',
   [['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
   [[1, 2], [4, 3]])],
 [('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['.~....', '...~..'], [[0, 0], [5, 1], [6, 0], [4, 1], [0, 1], [3, 2], [1, 0]], 1, 2],
   [[0, 0], [5, 1], [4, 1], [0, 1]]),
  ('partial repair boundary #2',
   [['#.~', '.~#', '.~.', '...', '#..', '..~'],
    [[3, 5], [2, 2], [2, 6], [0, 2], [3, 1], [1, 2], [2, 2], [1, 0], [2, 1]],
    2,
    2],
   [[2, 2], [0, 2], [1, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 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]])],
 [('regression quota increment #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]]),
  ('regression quota increment #2',
   [['~#...##', '...##..', '~..~~..', '#.#.~..', '..#...#', '~#.~~~.'],
    [[0, 0], [1, 3], [3, 0], [7, 1], [6, 3], [5, 2], [2, 0], [2, 6], [1, 1], [7, 1], [1, 2], [7, 4]],
    1,
    2],
   [[1, 3], [3, 0], [6, 3], [5, 2], [2, 0]]),
  ('partial repair boundary #1',
   [['......#', '~~..#~.', '.~.~~..', '#......', '..~..~#'],
    [[5, 3], [1, 2], [0, 3], [4, 0], [1, 4], [4, 3], [0, 3], [3, 4], [1, 3], [7, 5]],
    1,
    3],
   [[5, 3], [4, 0], [1, 4], [4, 3], [3, 4], [1, 3]]),
  ('partial repair boundary #2',
   [['~.#...', '......', '.~#~~#', '..~..~', '~#~#~#', '.~~...', '......'],
    [[4, 0], [3, 1], [1, 1], [1, 3], [3, 1], [5, 2], [3, 4]],
    1,
    2],
   [[4, 0], [3, 1], [1, 1], [1, 3]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
  ('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
  ('control #1',
   [['..', '~.'],
    [[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]]),
  ('control #2', [['.'], [[0, 0], [0, 0], [1, 0], [1, 1]], 1, 2], [[0, 0]])],
 [('fault site quota increment #1',
   [['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
    [[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
    1,
    2],
   [[1, 1], [0, 1], [4, 2]]),
  ('fault site quota increment #2',
   [['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
   [[2, 1], [3, 1], [5, 0]]),
  ('partial repair boundary #1',
   [['.#..#..', '.#.~...', '.###..~', '~#..#.#', '.......', '...##~.'],
    [[2, 4], [6, 3], [0, 2], [6, 0], [2, 1], [4, 3], [4, 4], [0, 0], [4, 3], [0, 3]],
    1,
    3],
   [[2, 4], [0, 2], [6, 0], [2, 1], [4, 4], [0, 0]]),
  ('partial repair boundary #2',
   [['~~.....', '..#...~', '....#..', '.~.....', '#...~~~', '....~..'],
    [[1, 1], [3, 5], [5, 5], [5, 4], [4, 4], [1, 0], [0, 0], [1, 4], [3, 1], [4, 1], [6, 0], [3, 4]],
    2,
    2],
   [[1, 1], [3, 5], [5, 5], [1, 4], [3, 1], [6, 0]]),
  ('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
  ('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 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]])]]
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
fault site quota increment #1[[1, 1], [0, 1], [4, 2]][[1, 1], [0, 1], [4, 2]]Passed
fault site quota increment #2[[2, 1], [3, 1], [5, 0]][[2, 1], [3, 1], [5, 0]]Passed
partial repair boundary #1[[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]][[7, 4], [6, 2], [4, 1], [5, 0], [6, 5], [2, 5]]Passed
partial repair boundary #2[[0, 0], [4, 0], [5, 0]][[0, 0], [4, 0], [5, 0]]Passed
exact radius spacing #1[[0, 0], [2, 0]][[0, 0], [2, 0]]Passed
diagonal within radius #1[[0, 0]][[0, 0]]Passed
quadrant full #1[[0, 0], [3, 0]][[0, 0], [3, 0]]Passed
control #1[[3, 1], [1, 2], [1, 1]][[3, 1], [1, 2], [1, 1]]Passed

SHA-256 / 6d1fe659f31e111cd658b0493e4065fd1ac9e58c75fa14ddfc8b465c0614965d

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 2026-09-29T14:50:51.952493+00:00.

Case digest / 43c05b41294e38bf7ca059e42cd40ebbbb7b31b4935a312c220124955c4457d6