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FA-86716 / Procedural level generation constraints / Open access

Heightmap smoothing and biome classes: Window skips the row below · case 01

Smoothing is biased toward northern neighbours.

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

ROOT CAUSE

The row range stops at the current row.

THE FAILURE

The row range stops at the current row.

Unsuccessful approach: Clamping to h-1 drops the bottom row from every window.

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 + 1)):
                for cc in range(max(0, 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 = [[('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #1', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('fault site row window #1',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('partial repair boundary #1', [[[3], [4], [0]], 4, 10], ['~', '~', '~']),
  ('partial repair boundary #2', [[[6], [4], [8], [4], [8]], 5, 9], ['s', 's', 's', 's', 's']),
  ('control #1', [[[0, 9], [7, 2]], 2, 11], ['gg', 'gg']),
  ('control #2', [[[9], [8]], 6, 6], ['^', '^']),
  ('control #3', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('fault site row window #1',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('regression row window #1', [[[9, 5, 6], [9, 0, 4]], 6, 10], ['~~~', '~~~']),
  ('regression row window #2', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('partial repair boundary #1', [[[6], [4], [8], [4], [8]], 5, 9], ['s', 's', 's', 's', 's']),
  ('control #1', [[[7, 8], [6, 2], [5, 5], [4, 11]], 2, 11], ['gg', 'gg', 'gg', 'gg']),
  ('control #2', [[[7, 6], [5, 12], [1, 6], [10, 10], [8, 3]], 3, 6], ['^^', '^^', '^^', '^^', '^^']),
  ('control #3', [[[0, 3, 3], [0, 1, 5], [4, 0, 5]], 2, 6], ['~ss', '~ss', '~ss'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #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 row window #2', [[[10, 11], [1, 0]], 3, 9], ['gg', 'gg']),
  ('regression row window #3', [[[9, 5, 6], [9, 0, 4]], 6, 10], ['~~~', '~~~']),
  ('regression row window #4',
   [[[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~~~']),
  ('control #1', [[[10], [5], [3], [6]], 3, 11], ['g', 'g', 's', 's']),
  ('control #2', [[[5, 4], [0, 5]], 3, 6], ['ss', 'ss']),
  ('control #3', [[[4, 9], [5, 10]], 2, 10], ['gg', 'gg'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #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 row window #2', [[[0, 1], [3, 5], [10, 1]], 3, 10], ['~~', 'ss', 'ss']),
  ('regression row window #3', [[[10, 11], [1, 0]], 3, 9], ['gg', 'gg']),
  ('regression row window #4',
   [[[1, 2, 0, 4], [12, 1, 9, 7], [9, 3, 6, 5]], 2, 11],
   ['ggsg', 'gggg', 'gggg']),
  ('control #1', [[[5], [6], [8], [8]], 2, 8], ['g', 'g', 'g', '^']),
  ('control #2', [[[4], [0]], 6, 11], ['~', '~']),
  ('control #3', [[[8, 8, 12], [11, 3, 6]], 3, 11], ['ggg', 'ggg'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #1',
   [[[1, 2, 0, 4], [12, 1, 9, 7], [9, 3, 6, 5]], 2, 11],
   ['ggsg', 'gggg', 'gggg']),
  ('regression row window #2',
   [[[0, 3], [6, 9], [0, 3], [3, 12], [7, 10]], 5, 6],
   ['~~', '~~', 'ss', 'ss', '^^']),
  ('regression row window #3', [[[0, 1], [3, 5], [10, 1]], 3, 10], ['~~', 'ss', 'ss']),
  ('regression row window #4',
   [[[4, 3, 3, 1], [4, 1, 10, 9], [2, 2, 10, 5], [0, 0, 7, 2]], 6, 8],
   ['~~~~', '~~~s', '~~~s', '~~~s']),
  ('control #1', [[[11], [11], [6], [6]], 3, 9], ['^', '^', 'g', 'g']),
  ('control #2', [[[4, 12, 12, 8, 8], [5, 10, 5, 10, 2]], 5, 6], ['^^^^^', '^^^^^']),
  ('control #3', [[[3, 2], [6, 0], [0, 5]], 4, 7], ['~~', '~~', '~~'])]]
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
corner cell average #1['^^', 'gg']['gg', 'gg']Failed
regression row window #1['^^^ss', '^^ss~']['^^ss~', '^^ss~']Failed
fault site row window #1['gsggg', 'ggggg', '^^ggs']['ggggg', 'ggggg', '^^ggs']Failed
partial repair boundary #1['~', '~', '~']['~', '~', '~']Passed
partial repair boundary #2['s', 's', 's', 's', 's']['s', 's', 's', 's', 's']Passed
control #1['gg', 'gg']['gg', 'gg']Passed
control #2['^', '^']['^', '^']Passed
control #3['gg', 'gg', 'gg']['gg', 'gg', 'gg']Passed

SHA-256 / 25caad51b1bdbb360774660b30c9d25bfc0479656e508fda8e4b9597fac20db6

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 - 1, r + 2)):
                for cc in range(max(0, 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 = [[('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #1', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('fault site row window #1',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('partial repair boundary #1', [[[3], [4], [0]], 4, 10], ['~', '~', '~']),
  ('partial repair boundary #2', [[[6], [4], [8], [4], [8]], 5, 9], ['s', 's', 's', 's', 's']),
  ('control #1', [[[0, 9], [7, 2]], 2, 11], ['gg', 'gg']),
  ('control #2', [[[9], [8]], 6, 6], ['^', '^']),
  ('control #3', [[[5, 5], [10, 3], [7, 0]], 2, 10], ['gg', 'gg', 'gg'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('fault site row window #1',
   [[[5, 4, 2, 6, 4], [12, 10, 8, 2, 4], [4, 10, 11, 2, 6]], 2, 8],
   ['ggggg', 'ggggg', '^^ggs']),
  ('regression row window #1', [[[9, 5, 6], [9, 0, 4]], 6, 10], ['~~~', '~~~']),
  ('regression row window #2', [[[10, 11, 6, 11, 0], [9, 0, 9, 4, 4]], 5, 7], ['^^ss~', '^^ss~']),
  ('partial repair boundary #1', [[[6], [4], [8], [4], [8]], 5, 9], ['s', 's', 's', 's', 's']),
  ('control #1', [[[7, 8], [6, 2], [5, 5], [4, 11]], 2, 11], ['gg', 'gg', 'gg', 'gg']),
  ('control #2', [[[7, 6], [5, 12], [1, 6], [10, 10], [8, 3]], 3, 6], ['^^', '^^', '^^', '^^', '^^']),
  ('control #3', [[[0, 3, 3], [0, 1, 5], [4, 0, 5]], 2, 6], ['~ss', '~ss', '~ss'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #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 row window #2', [[[10, 11], [1, 0]], 3, 9], ['gg', 'gg']),
  ('regression row window #3', [[[9, 5, 6], [9, 0, 4]], 6, 10], ['~~~', '~~~']),
  ('regression row window #4',
   [[[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~~~']),
  ('control #1', [[[10], [5], [3], [6]], 3, 11], ['g', 'g', 's', 's']),
  ('control #2', [[[5, 4], [0, 5]], 3, 6], ['ss', 'ss']),
  ('control #3', [[[4, 9], [5, 10]], 2, 10], ['gg', 'gg'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #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 row window #2', [[[0, 1], [3, 5], [10, 1]], 3, 10], ['~~', 'ss', 'ss']),
  ('regression row window #3', [[[10, 11], [1, 0]], 3, 9], ['gg', 'gg']),
  ('regression row window #4',
   [[[1, 2, 0, 4], [12, 1, 9, 7], [9, 3, 6, 5]], 2, 11],
   ['ggsg', 'gggg', 'gggg']),
  ('control #1', [[[5], [6], [8], [8]], 2, 8], ['g', 'g', 'g', '^']),
  ('control #2', [[[4], [0]], 6, 11], ['~', '~']),
  ('control #3', [[[8, 8, 12], [11, 3, 6]], 3, 11], ['ggg', 'ggg'])],
 [('corner cell average #1', [[[9, 9], [9, 0]], 3, 8], ['gg', 'gg']),
  ('regression row window #1',
   [[[1, 2, 0, 4], [12, 1, 9, 7], [9, 3, 6, 5]], 2, 11],
   ['ggsg', 'gggg', 'gggg']),
  ('regression row window #2',
   [[[0, 3], [6, 9], [0, 3], [3, 12], [7, 10]], 5, 6],
   ['~~', '~~', 'ss', 'ss', '^^']),
  ('regression row window #3', [[[0, 1], [3, 5], [10, 1]], 3, 10], ['~~', 'ss', 'ss']),
  ('regression row window #4',
   [[[4, 3, 3, 1], [4, 1, 10, 9], [2, 2, 10, 5], [0, 0, 7, 2]], 6, 8],
   ['~~~~', '~~~s', '~~~s', '~~~s']),
  ('control #1', [[[11], [11], [6], [6]], 3, 9], ['^', '^', 'g', 'g']),
  ('control #2', [[[4, 12, 12, 8, 8], [5, 10, 5, 10, 2]], 5, 6], ['^^^^^', '^^^^^']),
  ('control #3', [[[3, 2], [6, 0], [0, 5]], 4, 7], ['~~', '~~', '~~'])]]
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
corner cell average #1['^^', '^^']['gg', 'gg']Failed
regression row window #1['^^^ss', '^^^ss']['^^ss~', '^^ss~']Failed
fault site row window #1['ggggg', 'ggggg', '^^ggs']['ggggg', 'ggggg', '^^ggs']Passed
partial repair boundary #1['~', '~', 's']['~', '~', '~']Failed
partial repair boundary #2['s', 's', 's', 's', '~']['s', 's', 's', 's', 's']Failed
control #1['gg', 'gg']['gg', 'gg']Passed
control #2['^', '^']['^', '^']Passed
control #3['gg', 'gg', 'gg']['gg', 'gg', 'gg']Passed

SHA-256 / c17c15905a57bcc2efa668532c0c334f931507fdf237f8bfe08da54271e91a51

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 2026-09-29T14:50:52.170547+00:00.

Case digest / 72d967b37b027ff203ea7cddcff3fd2bfbe83a8366c485402d70a13a34a2c1e6