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FA-86721 / Procedural level generation constraints / Open access

Heightmap smoothing and biome classes: Left edge wraps to the right edge · case 01

The first column is smoothed with values from the opposite side.

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

ROOT CAUSE

The column window is not clamped at zero, so index -1 wraps.

THE FAILURE

The column window is not clamped at zero, so index -1 wraps.

Unsuccessful approach: Clamping at one excludes column zero from windows.

Case contract

Each cell height becomes floor(mean) of the in-bounds cells in its 3x3 window (input values only). Class: '~' when v < sea, 's' beach when v < sea+2, 'g' when v < mountain, otherwise '^'. Returns strings per row.

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(heights, sea, mountain):
    h = len(heights)
    w = len(heights[0])
    out = []
    for r in range(h):
        row = []
        for c in range(w):
            total = 0
            cnt = 0
            for rr in range(max(0, r - 1), min(h, r + 2)):
                for cc in range(c - 1, min(w, c + 2)):
                    total += heights[rr][cc]
                    cnt += 1
            v = total // cnt
            if v < sea:
                row.append('~')
            elif v < sea + 2:
                row.append('s')
            elif v < mountain:
                row.append('g')
            else:
                row.append('^')
        out.append(''.join(row))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('regression column window start #2',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('partial repair boundary #1',
   [[[8, 6, 12, 10, 8], [6, 1, 1, 7, 5], [1, 6, 12, 6, 0], [3, 8, 3, 6, 0], [1, 7, 3, 2, 0]], 6, 9],
   ['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']),
  ('regression column window start #3', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg']),
  ('control #1', [[[0, 9], [7, 2]], 2, 11], ['gg', 'gg']),
  ('control #2', [[[9, 5, 6], [9, 0, 4]], 6, 10], ['~~~', '~~~'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('regression column window start #2', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg']),
  ('regression column window start #3', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('partial repair boundary #1',
   [[[8, 6, 12, 10, 8], [6, 1, 1, 7, 5], [1, 6, 12, 6, 0], [3, 8, 3, 6, 0], [1, 7, 3, 2, 0]], 6, 9],
   ['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']),
  ('control #1', [[[10, 11], [1, 0]], 3, 9], ['gg', 'gg']),
  ('control #2', [[[9, 7]], 2, 6], ['^^'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1',
   [[[2, 9, 4, 10, 11], [7, 7, 11, 1, 10], [11, 5, 12, 1, 12], [9, 4, 1, 0, 2]], 6, 8],
   ['ssss^', 'sss^s', 'ss~~~', 'ss~~~']),
  ('regression column window start #2',
   [[[0, 3], [6, 9], [0, 3], [3, 12], [7, 10]], 5, 6],
   ['~~', '~~', 'ss', 'ss', '^^']),
  ('partial repair boundary #1',
   [[[8, 6, 12, 10, 8], [6, 1, 1, 7, 5], [1, 6, 12, 6, 0], [3, 8, 3, 6, 0], [1, 7, 3, 2, 0]], 6, 9],
   ['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']),
  ('regression column window start #3', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg']),
  ('control #1',
   [[[4, 3, 3, 1], [4, 1, 10, 9], [2, 2, 10, 5], [0, 0, 7, 2]], 6, 8],
   ['~~~~', '~~~s', '~~~s', '~~~s']),
  ('control #2', [[[7, 8], [6, 2], [5, 5], [4, 11]], 2, 11], ['gg', 'gg', 'gg', 'gg'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1', [[[11, 0, 4, 12]], 2, 7], ['ggg^']),
  ('regression column window start #2',
   [[[4, 5, 6, 9, 9], [8, 11, 8, 5, 5], [10, 12, 11, 0, 3]], 6, 11],
   ['sssss', 'ggss~', 'ggs~~']),
  ('regression column window start #3',
   [[[2, 9, 4, 10, 11], [7, 7, 11, 1, 10], [11, 5, 12, 1, 12], [9, 4, 1, 0, 2]], 6, 8],
   ['ssss^', 'sss^s', 'ss~~~', 'ss~~~']),
  ('partial repair boundary #1', [[[1, 2, 10]], 6, 9], ['~~s']),
  ('control #1', [[[7, 6], [5, 12], [1, 6], [10, 10], [8, 3]], 3, 6], ['^^', '^^', '^^', '^^', '^^']),
  ('control #2', [[[5, 3, 0, 8]], 6, 7], ['~~~~'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1', [[[0, 3, 3], [0, 1, 5], [4, 0, 5]], 2, 6], ['~ss', '~ss', '~ss']),
  ('regression column window start #2',
   [[[12, 10, 4, 10], [2, 0, 12, 2], [9, 12, 4, 8], [3, 9, 11, 3], [12, 5, 11, 6]], 5, 10],
   ['sssg', 'ggss', 'ssss', 'gggg', 'gggg']),
  ('partial repair boundary #1', [[[0, 1], [3, 5], [10, 1]], 3, 10], ['~~', 'ss', 'ss']),
  ('partial repair boundary #2',
   [[[1, 2, 0, 4], [12, 1, 9, 7], [9, 3, 6, 5]], 2, 11],
   ['ggsg', 'gggg', 'gggg']),
  ('control #1', [[[5, 9, 0, 8, 5], [12, 12, 0, 1, 8]], 2, 11], ['gggsg', 'gggsg']),
  ('control #2',
   [[[6, 10, 8, 0], [6, 10, 7, 12], [10, 7, 5, 3], [4, 11, 0, 1], [1, 2, 7, 12]], 2, 7],
   ['^^^g', '^^gg', '^ggg', 'gggg', 'gggg'])]]
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
single row #1['ss^']['^s^']Failed
corner cell average #1['gg', 'gg']['gg', 'gg']Passed
regression column window start #1['s^ss~', 's^ss~']['^^ss~', '^^ss~']Failed
regression column window start #2['ggggg', 'ggggg', 'g^ggs']['ggggg', 'ggggg', '^^ggs']Failed
partial repair boundary #1['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']Passed
regression column window start #3['gg', 'gg', 'sg']['gg', 'gg', 'gg']Failed
control #1['gg', 'gg']['gg', 'gg']Passed
control #2['~~~', '~~~']['~~~', '~~~']Passed

SHA-256 / 4cc54ad8107e077d6b9ac0515fb999350a967fbff2f0612c57965448611c4f21

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(heights, sea, mountain):
    h = len(heights)
    w = len(heights[0])
    out = []
    for r in range(h):
        row = []
        for c in range(w):
            total = 0
            cnt = 0
            for rr in range(max(0, r - 1), min(h, r + 2)):
                for cc in range(max(1, c - 1), min(w, c + 2)):
                    total += heights[rr][cc]
                    cnt += 1
            v = total // cnt
            if v < sea:
                row.append('~')
            elif v < sea + 2:
                row.append('s')
            elif v < mountain:
                row.append('g')
            else:
                row.append('^')
        out.append(''.join(row))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('regression column window start #2',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('partial repair boundary #1',
   [[[8, 6, 12, 10, 8], [6, 1, 1, 7, 5], [1, 6, 12, 6, 0], [3, 8, 3, 6, 0], [1, 7, 3, 2, 0]], 6, 9],
   ['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']),
  ('regression column window start #3', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg']),
  ('control #1', [[[0, 9], [7, 2]], 2, 11], ['gg', 'gg']),
  ('control #2', [[[9, 5, 6], [9, 0, 4]], 6, 10], ['~~~', '~~~'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('regression column window start #2', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg']),
  ('regression column window start #3', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('partial repair boundary #1',
   [[[8, 6, 12, 10, 8], [6, 1, 1, 7, 5], [1, 6, 12, 6, 0], [3, 8, 3, 6, 0], [1, 7, 3, 2, 0]], 6, 9],
   ['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']),
  ('control #1', [[[10, 11], [1, 0]], 3, 9], ['gg', 'gg']),
  ('control #2', [[[9, 7]], 2, 6], ['^^'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1',
   [[[2, 9, 4, 10, 11], [7, 7, 11, 1, 10], [11, 5, 12, 1, 12], [9, 4, 1, 0, 2]], 6, 8],
   ['ssss^', 'sss^s', 'ss~~~', 'ss~~~']),
  ('regression column window start #2',
   [[[0, 3], [6, 9], [0, 3], [3, 12], [7, 10]], 5, 6],
   ['~~', '~~', 'ss', 'ss', '^^']),
  ('partial repair boundary #1',
   [[[8, 6, 12, 10, 8], [6, 1, 1, 7, 5], [1, 6, 12, 6, 0], [3, 8, 3, 6, 0], [1, 7, 3, 2, 0]], 6, 9],
   ['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']),
  ('regression column window start #3', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg']),
  ('control #1',
   [[[4, 3, 3, 1], [4, 1, 10, 9], [2, 2, 10, 5], [0, 0, 7, 2]], 6, 8],
   ['~~~~', '~~~s', '~~~s', '~~~s']),
  ('control #2', [[[7, 8], [6, 2], [5, 5], [4, 11]], 2, 11], ['gg', 'gg', 'gg', 'gg'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1', [[[11, 0, 4, 12]], 2, 7], ['ggg^']),
  ('regression column window start #2',
   [[[4, 5, 6, 9, 9], [8, 11, 8, 5, 5], [10, 12, 11, 0, 3]], 6, 11],
   ['sssss', 'ggss~', 'ggs~~']),
  ('regression column window start #3',
   [[[2, 9, 4, 10, 11], [7, 7, 11, 1, 10], [11, 5, 12, 1, 12], [9, 4, 1, 0, 2]], 6, 8],
   ['ssss^', 'sss^s', 'ss~~~', 'ss~~~']),
  ('partial repair boundary #1', [[[1, 2, 10]], 6, 9], ['~~s']),
  ('control #1', [[[7, 6], [5, 12], [1, 6], [10, 10], [8, 3]], 3, 6], ['^^', '^^', '^^', '^^', '^^']),
  ('control #2', [[[5, 3, 0, 8]], 6, 7], ['~~~~'])],
 [('single row #1', [[[0, 12, 0]], 3, 6], ['^s^']),
  ('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression column window start #1', [[[0, 3, 3], [0, 1, 5], [4, 0, 5]], 2, 6], ['~ss', '~ss', '~ss']),
  ('regression column window start #2',
   [[[12, 10, 4, 10], [2, 0, 12, 2], [9, 12, 4, 8], [3, 9, 11, 3], [12, 5, 11, 6]], 5, 10],
   ['sssg', 'ggss', 'ssss', 'gggg', 'gggg']),
  ('partial repair boundary #1', [[[0, 1], [3, 5], [10, 1]], 3, 10], ['~~', 'ss', 'ss']),
  ('partial repair boundary #2',
   [[[1, 2, 0, 4], [12, 1, 9, 7], [9, 3, 6, 5]], 2, 11],
   ['ggsg', 'gggg', 'gggg']),
  ('control #1', [[[5, 9, 0, 8, 5], [12, 12, 0, 1, 8]], 2, 11], ['gggsg', 'gggsg']),
  ('control #2',
   [[[6, 10, 8, 0], [6, 10, 7, 12], [10, 7, 5, 3], [4, 11, 0, 1], [1, 2, 7, 12]], 2, 7],
   ['^^^g', '^^gg', '^ggg', 'gggg', 'gggg'])]]
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
single row #1['^^^']['^s^']Failed
corner cell average #1['ss', 'ss']['gg', 'gg']Failed
regression column window start #1['ssss~', 'ssss~']['^^ss~', '^^ss~']Failed
regression column window start #2['ggggg', '^gggg', '^^ggs']['ggggg', 'ggggg', '^^ggs']Failed
partial repair boundary #1['~~sss', '~ssss', '~~~~~', 'ss~~~', 's~~~~']['~~sss', '~~sss', '~~~~~', '~~~~~', '~~~~~']Failed
regression column window start #3['gg', 'ss', '~~']['gg', 'gg', 'gg']Failed
control #1['gg', 'gg']['gg', 'gg']Passed
control #2['~~~', '~~~']['~~~', '~~~']Passed

SHA-256 / d33fbeddc60ead5305741d0d720442360bfcbed3558577a69079d63be8476616

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 2026-09-29T14:50:52.169921+00:00.

Case digest / 237e44f64e117c21cc9e008c6c31caf88f13ca7def05b75bd9f5f0865162f443