FAILURE MAP
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FA-86586 / Procedural level generation constraints / Open access

L-shaped corridor carving: Vertical leg on the source column · case 01

Horizontal-first corridors leave the corner disconnected.

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

ROOT CAUSE

The vertical leg is carved on the source column.

VERIFIED REPAIR

Restore `add(bx, y)` at the corner column step.

Unsuccessful approach: Offsetting the column by one step misses the corner.

Case contract

Carve from centre a [x, y] to b. Horizontal-first walks x from ax to bx on row ay, then y from ay to by on column bx; otherwise y first on column ax, then x on row by. Both legs include their endpoints; returns cells [x, y] in walk order without duplicates.

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(a, b, horizontal_first):
    ax, ay = a
    bx, by = b
    path = []
    def add(x, y):
        if [x, y] not in path:
            path.append([x, y])
    sx = 1 if bx >= ax else -1
    sy = 1 if by >= ay else -1
    if horizontal_first:
        for x in range(ax, bx + sx, sx):
            add(x, ay)
        for y in range(ay, by + sy, sy):
            add(ax, y)
    else:
        for y in range(ay, by + sy, sy):
            add(ax, y)
        for x in range(ax, bx + sx, sx):
            add(x, by)
    return path
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[8, 6], [4, 5], True], [[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]),
  ('regression corner column #2',
   [[8, 4], [1, 0], True],
   [[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]),
  ('regression corner column #3', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #4',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1', [[6, 4], [8, 5], False], [[6, 4], [6, 5], [7, 5], [8, 5]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1',
   [[8, 4], [1, 0], True],
   [[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]),
  ('regression corner column #2', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #3', [[8, 6], [4, 5], True], [[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]),
  ('regression corner column #4',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1', [[6, 4], [8, 5], False], [[6, 4], [6, 5], [7, 5], [8, 5]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('regression corner column #2', [[2, 4], [4, 5], True], [[2, 4], [3, 4], [4, 4], [4, 5]]),
  ('regression corner column #3', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #4', [[5, 1], [4, 5], True], [[5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[3, 2], [8, 8], False],
   [[3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[5, 1], [4, 5], True], [[5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5]]),
  ('regression corner column #2',
   [[5, 0], [7, 4], True],
   [[5, 0], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]),
  ('regression corner column #3', [[2, 4], [4, 5], True], [[2, 4], [3, 4], [4, 4], [4, 5]]),
  ('regression corner column #4', [[0, 3], [4, 4], True], [[0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [4, 4]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[3, 5], [8, 1], False],
   [[3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[0, 3], [4, 4], True], [[0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [4, 4]]),
  ('regression corner column #2', [[7, 0], [8, 2], True], [[7, 0], [8, 0], [8, 1], [8, 2]]),
  ('regression corner column #3',
   [[5, 0], [7, 4], True],
   [[5, 0], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]),
  ('regression corner column #4',
   [[1, 3], [0, 8], True],
   [[1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[1, 4], [6, 1], False],
   [[1, 4], [1, 3], [1, 2], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 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
leftward corridor #1[[5, 1], [4, 1], [3, 1], [2, 1], [5, 2], [5, 3]][[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]Failed
single cell #1[[4, 4]][[4, 4]]Passed
regression corner column #1[[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [8, 5]][[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]Failed
regression corner column #2[[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [8, 3], [8, 2], [8, 1], [8, 0]][[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]Failed
regression corner column #3[[6, 2], [7, 2], [8, 2], [6, 1], [6, 0]][[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]Failed
regression corner column #4[[3, 8], [4, 8], [5, 8], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [3, 0]][[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]Failed
same column #1[[3, 0], [3, 1], [3, 2]][[3, 0], [3, 1], [3, 2]]Passed
control #1[[6, 4], [6, 5], [7, 5], [8, 5]][[6, 4], [6, 5], [7, 5], [8, 5]]Passed

SHA-256 / cc1f9baa2e4759f5b3e323bef15e390c1eead2acea44e7144fef945ceef0f5ee

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(a, b, horizontal_first):
    ax, ay = a
    bx, by = b
    path = []
    def add(x, y):
        if [x, y] not in path:
            path.append([x, y])
    sx = 1 if bx >= ax else -1
    sy = 1 if by >= ay else -1
    if horizontal_first:
        for x in range(ax, bx + sx, sx):
            add(x, ay)
        for y in range(ay, by + sy, sy):
            add(bx - sx, y)
    else:
        for y in range(ay, by + sy, sy):
            add(ax, y)
        for x in range(ax, bx + sx, sx):
            add(x, by)
    return path
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[8, 6], [4, 5], True], [[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]),
  ('regression corner column #2',
   [[8, 4], [1, 0], True],
   [[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]),
  ('regression corner column #3', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #4',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1', [[6, 4], [8, 5], False], [[6, 4], [6, 5], [7, 5], [8, 5]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1',
   [[8, 4], [1, 0], True],
   [[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]),
  ('regression corner column #2', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #3', [[8, 6], [4, 5], True], [[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]),
  ('regression corner column #4',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1', [[6, 4], [8, 5], False], [[6, 4], [6, 5], [7, 5], [8, 5]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('regression corner column #2', [[2, 4], [4, 5], True], [[2, 4], [3, 4], [4, 4], [4, 5]]),
  ('regression corner column #3', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #4', [[5, 1], [4, 5], True], [[5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[3, 2], [8, 8], False],
   [[3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[5, 1], [4, 5], True], [[5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5]]),
  ('regression corner column #2',
   [[5, 0], [7, 4], True],
   [[5, 0], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]),
  ('regression corner column #3', [[2, 4], [4, 5], True], [[2, 4], [3, 4], [4, 4], [4, 5]]),
  ('regression corner column #4', [[0, 3], [4, 4], True], [[0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [4, 4]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[3, 5], [8, 1], False],
   [[3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[0, 3], [4, 4], True], [[0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [4, 4]]),
  ('regression corner column #2', [[7, 0], [8, 2], True], [[7, 0], [8, 0], [8, 1], [8, 2]]),
  ('regression corner column #3',
   [[5, 0], [7, 4], True],
   [[5, 0], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]),
  ('regression corner column #4',
   [[1, 3], [0, 8], True],
   [[1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[1, 4], [6, 1], False],
   [[1, 4], [1, 3], [1, 2], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 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
leftward corridor #1[[5, 1], [4, 1], [3, 1], [2, 1], [3, 2], [3, 3]][[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]Failed
single cell #1[[4, 4], [3, 4]][[4, 4]]Failed
regression corner column #1[[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [5, 5]][[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]Failed
regression corner column #2[[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [2, 3], [2, 2], [2, 1], [2, 0]][[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]Failed
regression corner column #3[[6, 2], [7, 2], [8, 2], [7, 1], [7, 0]][[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]Failed
regression corner column #4[[3, 8], [4, 8], [5, 8], [4, 7], [4, 6], [4, 5], [4, 4], [4, 3], [4, 2], [4, 1], [4, 0]][[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]Failed
same column #1[[3, 0], [3, 1], [3, 2]][[3, 0], [3, 1], [3, 2]]Passed
control #1[[6, 4], [6, 5], [7, 5], [8, 5]][[6, 4], [6, 5], [7, 5], [8, 5]]Passed

SHA-256 / 2ed333ea620d2dcef2702bef7bc223966d8e13bcbaa04a6c153ca468d9871c34

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(a, b, horizontal_first):
    ax, ay = a
    bx, by = b
    path = []
    def add(x, y):
        if [x, y] not in path:
            path.append([x, y])
    sx = 1 if bx >= ax else -1
    sy = 1 if by >= ay else -1
    if horizontal_first:
        for x in range(ax, bx + sx, sx):
            add(x, ay)
        for y in range(ay, by + sy, sy):
            add(bx, y)
    else:
        for y in range(ay, by + sy, sy):
            add(ax, y)
        for x in range(ax, bx + sx, sx):
            add(x, by)
    return path
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[8, 6], [4, 5], True], [[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]),
  ('regression corner column #2',
   [[8, 4], [1, 0], True],
   [[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]),
  ('regression corner column #3', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #4',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1', [[6, 4], [8, 5], False], [[6, 4], [6, 5], [7, 5], [8, 5]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1',
   [[8, 4], [1, 0], True],
   [[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]),
  ('regression corner column #2', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #3', [[8, 6], [4, 5], True], [[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]),
  ('regression corner column #4',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1', [[6, 4], [8, 5], False], [[6, 4], [6, 5], [7, 5], [8, 5]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1',
   [[3, 8], [5, 0], True],
   [[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]),
  ('regression corner column #2', [[2, 4], [4, 5], True], [[2, 4], [3, 4], [4, 4], [4, 5]]),
  ('regression corner column #3', [[6, 2], [8, 0], True], [[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]),
  ('regression corner column #4', [[5, 1], [4, 5], True], [[5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[3, 2], [8, 8], False],
   [[3, 2], [3, 3], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 8], [5, 8], [6, 8], [7, 8], [8, 8]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[5, 1], [4, 5], True], [[5, 1], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5]]),
  ('regression corner column #2',
   [[5, 0], [7, 4], True],
   [[5, 0], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]),
  ('regression corner column #3', [[2, 4], [4, 5], True], [[2, 4], [3, 4], [4, 4], [4, 5]]),
  ('regression corner column #4', [[0, 3], [4, 4], True], [[0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [4, 4]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[3, 5], [8, 1], False],
   [[3, 5], [3, 4], [3, 3], [3, 2], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1]])],
 [('leftward corridor #1', [[5, 1], [2, 3], True], [[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]),
  ('single cell #1', [[4, 4], [4, 4], True], [[4, 4]]),
  ('regression corner column #1', [[0, 3], [4, 4], True], [[0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [4, 4]]),
  ('regression corner column #2', [[7, 0], [8, 2], True], [[7, 0], [8, 0], [8, 1], [8, 2]]),
  ('regression corner column #3',
   [[5, 0], [7, 4], True],
   [[5, 0], [6, 0], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]),
  ('regression corner column #4',
   [[1, 3], [0, 8], True],
   [[1, 3], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8]]),
  ('same column #1', [[3, 0], [3, 2], False], [[3, 0], [3, 1], [3, 2]]),
  ('control #1',
   [[1, 4], [6, 1], False],
   [[1, 4], [1, 3], [1, 2], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 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
leftward corridor #1[[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]][[5, 1], [4, 1], [3, 1], [2, 1], [2, 2], [2, 3]]Passed
single cell #1[[4, 4]][[4, 4]]Passed
regression corner column #1[[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]][[8, 6], [7, 6], [6, 6], [5, 6], [4, 6], [4, 5]]Passed
regression corner column #2[[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]][[8, 4], [7, 4], [6, 4], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4], [1, 3], [1, 2], [1, 1], [1, 0]]Passed
regression corner column #3[[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]][[6, 2], [7, 2], [8, 2], [8, 1], [8, 0]]Passed
regression corner column #4[[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]][[3, 8], [4, 8], [5, 8], [5, 7], [5, 6], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]Passed
same column #1[[3, 0], [3, 1], [3, 2]][[3, 0], [3, 1], [3, 2]]Passed
control #1[[6, 4], [6, 5], [7, 5], [8, 5]][[6, 4], [6, 5], [7, 5], [8, 5]]Passed

SHA-256 / 8aec0d4b8e2d852f3229b2cdbbb2294c947e8bf3f60e4e38c689a9865482e1d7

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 2026-09-29T14:50:50.855008+00:00.

Case digest / 87b1806d38d25f8dd957080fdbba5bf220149b81f34879cce80a293138595868