FAILURE MAP
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FA-86471 / Procedural level generation constraints / Open access

Platform jump reachability: Maximum-length jumps fail · case 01

A gap exactly equal to jump distance is unreachable.

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

ROOT CAUSE

The reach comparison is strict.

VERIFIED REPAIR

Restore `if gap <= reach:` at the gap boundary step.

Unsuccessful approach: Excluding zero gaps disconnects overlapping platforms.

Case contract

platforms [x1, x2, y] (y grows upward); the player starts on platform 0. From A the player reaches B when rise = yB-yA <= jump_h (any drop is allowed) and the horizontal gap max(0, xB1-xA2, xA1-xB2) <= jump_d - max(0, rise)//2. Reachability is transitive. Returns sorted reachable indices.

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(platforms, jump_h, jump_d):
    n = len(platforms)
    seen = {0}
    queue = [0]
    while queue:
        a = queue.pop(0)
        ax1, ax2, ay = platforms[a]
        for b in range(n):
            if b in seen:
                continue
            bx1, bx2, by = platforms[b]
            rise = by - ay
            if rise > jump_h:
                continue
            gap = max(0, bx1 - ax2, ax1 - bx2)
            reach = jump_d - max(0, rise) // 2
            if gap < reach:
                seen.add(b)
                queue.append(b)
    return sorted(seen)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('regression gap boundary #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression gap boundary #2', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[13, 18, 6], [20, 22, 7]], 2, 8], [0, 1]),
  ('control #2', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('regression gap boundary #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression gap boundary #2', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('partial repair boundary #2', [[[21, 21, 10], [16, 21, 3]], 4, 3], [0, 1]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0]),
  ('control #2', [[[17, 20, 8]], 4, 4], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site gap boundary #1',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('regression gap boundary #1',
   [[[18, 18, 5], [15, 19, 6], [21, 22, 3], [5, 9, 1], [14, 20, 6], [24, 29, 7]], 1, 5],
   [0, 1, 2, 3, 4, 5]),
  ('partial repair boundary #1', [[[7, 8, 6], [2, 8, 5], [20, 21, 2], [23, 28, 7]], 1, 5], [0, 1]),
  ('partial repair boundary #2', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[12, 14, 0], [26, 26, 2], [22, 27, 7], [0, 3, 1]], 5, 4], [0]),
  ('control #2',
   [[[19, 21, 8], [19, 19, 2], [21, 22, 10], [11, 17, 5], [11, 17, 9]], 3, 4],
   [0, 1, 2, 3, 4])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('fault site gap boundary #1',
   [[[8, 11, 3], [22, 23, 8], [13, 13, 5], [26, 27, 3], [16, 16, 5]], 5, 3],
   [0, 2, 4]),
  ('regression gap boundary #1',
   [[[3, 4, 8], [16, 18, 8], [9, 9, 2], [7, 12, 6], [19, 24, 7], [24, 27, 3]], 2, 5],
   [0, 1, 2, 3, 4, 5]),
  ('partial repair boundary #1', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1]),
  ('partial repair boundary #2', [[[25, 26, 5], [19, 25, 6], [15, 19, 7]], 3, 3], [0, 1, 2]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[5, 5, 2]], 4, 6], [0]),
  ('control #2', [[[27, 29, 10]], 3, 1], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site gap boundary #1',
   [[[11, 15, 6], [6, 8, 9], [28, 34, 2], [22, 24, 7], [4, 6, 5], [28, 34, 10]], 2, 5],
   [0, 4]),
  ('regression gap boundary #1',
   [[[29, 34, 5], [6, 11, 2], [26, 26, 4], [25, 31, 2], [0, 2, 0], [5, 11, 5]], 2, 1],
   [0, 2, 3]),
  ('partial repair boundary #1',
   [[[7, 9, 9], [10, 15, 0], [7, 10, 2], [9, 14, 4], [26, 30, 8], [15, 19, 1]], 5, 1],
   [0, 1, 2, 3, 5]),
  ('partial repair boundary #2',
   [[[19, 24, 5], [30, 34, 4], [9, 14, 9], [16, 22, 8], [6, 6, 9]], 3, 4],
   [0, 2, 3, 4]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[18, 20, 2], [24, 29, 0], [12, 17, 2], [30, 35, 0], [8, 12, 5]], 2, 7], [0, 1, 2, 3]),
  ('control #2', [[[21, 24, 2], [4, 5, 1], [12, 12, 2]], 1, 8], [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
platform to the left #1[0][0, 1]Failed
chain of hops #1[0][0, 1, 2]Failed
regression gap boundary #1[0, 1][0, 1, 3]Failed
regression gap boundary #2[0][0, 1, 3]Failed
partial repair boundary #1[0, 2][0, 2]Passed
deep drop #1[0, 1][0, 1]Passed
control #1[0, 1][0, 1]Passed
control #2[0][0]Passed

SHA-256 / 48054b064fc6b70e0bfdb66332a4ae0ccb3d9db6123ff681373f0676b0e9c912

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(platforms, jump_h, jump_d):
    n = len(platforms)
    seen = {0}
    queue = [0]
    while queue:
        a = queue.pop(0)
        ax1, ax2, ay = platforms[a]
        for b in range(n):
            if b in seen:
                continue
            bx1, bx2, by = platforms[b]
            rise = by - ay
            if rise > jump_h:
                continue
            gap = max(0, bx1 - ax2, ax1 - bx2)
            reach = jump_d - max(0, rise) // 2
            if gap <= reach and gap > 0:
                seen.add(b)
                queue.append(b)
    return sorted(seen)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('regression gap boundary #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression gap boundary #2', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[13, 18, 6], [20, 22, 7]], 2, 8], [0, 1]),
  ('control #2', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('regression gap boundary #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression gap boundary #2', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('partial repair boundary #2', [[[21, 21, 10], [16, 21, 3]], 4, 3], [0, 1]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0]),
  ('control #2', [[[17, 20, 8]], 4, 4], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site gap boundary #1',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('regression gap boundary #1',
   [[[18, 18, 5], [15, 19, 6], [21, 22, 3], [5, 9, 1], [14, 20, 6], [24, 29, 7]], 1, 5],
   [0, 1, 2, 3, 4, 5]),
  ('partial repair boundary #1', [[[7, 8, 6], [2, 8, 5], [20, 21, 2], [23, 28, 7]], 1, 5], [0, 1]),
  ('partial repair boundary #2', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[12, 14, 0], [26, 26, 2], [22, 27, 7], [0, 3, 1]], 5, 4], [0]),
  ('control #2',
   [[[19, 21, 8], [19, 19, 2], [21, 22, 10], [11, 17, 5], [11, 17, 9]], 3, 4],
   [0, 1, 2, 3, 4])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('fault site gap boundary #1',
   [[[8, 11, 3], [22, 23, 8], [13, 13, 5], [26, 27, 3], [16, 16, 5]], 5, 3],
   [0, 2, 4]),
  ('regression gap boundary #1',
   [[[3, 4, 8], [16, 18, 8], [9, 9, 2], [7, 12, 6], [19, 24, 7], [24, 27, 3]], 2, 5],
   [0, 1, 2, 3, 4, 5]),
  ('partial repair boundary #1', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1]),
  ('partial repair boundary #2', [[[25, 26, 5], [19, 25, 6], [15, 19, 7]], 3, 3], [0, 1, 2]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[5, 5, 2]], 4, 6], [0]),
  ('control #2', [[[27, 29, 10]], 3, 1], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site gap boundary #1',
   [[[11, 15, 6], [6, 8, 9], [28, 34, 2], [22, 24, 7], [4, 6, 5], [28, 34, 10]], 2, 5],
   [0, 4]),
  ('regression gap boundary #1',
   [[[29, 34, 5], [6, 11, 2], [26, 26, 4], [25, 31, 2], [0, 2, 0], [5, 11, 5]], 2, 1],
   [0, 2, 3]),
  ('partial repair boundary #1',
   [[[7, 9, 9], [10, 15, 0], [7, 10, 2], [9, 14, 4], [26, 30, 8], [15, 19, 1]], 5, 1],
   [0, 1, 2, 3, 5]),
  ('partial repair boundary #2',
   [[[19, 24, 5], [30, 34, 4], [9, 14, 9], [16, 22, 8], [6, 6, 9]], 3, 4],
   [0, 2, 3, 4]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[18, 20, 2], [24, 29, 0], [12, 17, 2], [30, 35, 0], [8, 12, 5]], 2, 7], [0, 1, 2, 3]),
  ('control #2', [[[21, 24, 2], [4, 5, 1], [12, 12, 2]], 1, 8], [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
platform to the left #1[0, 1][0, 1]Passed
chain of hops #1[0, 1, 2][0, 1, 2]Passed
regression gap boundary #1[0][0, 1, 3]Failed
regression gap boundary #2[0, 1][0, 1, 3]Failed
partial repair boundary #1[0][0, 2]Failed
deep drop #1[0, 1][0, 1]Passed
control #1[0, 1][0, 1]Passed
control #2[0][0]Passed

SHA-256 / f2d203ec9b0e7ae4857b1e6a041210c66cedd3bbbcaa76bc660ee35d0eec20f6

3 / The verified repair

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

N = 1
observations = []
def solve(platforms, jump_h, jump_d):
    n = len(platforms)
    seen = {0}
    queue = [0]
    while queue:
        a = queue.pop(0)
        ax1, ax2, ay = platforms[a]
        for b in range(n):
            if b in seen:
                continue
            bx1, bx2, by = platforms[b]
            rise = by - ay
            if rise > jump_h:
                continue
            gap = max(0, bx1 - ax2, ax1 - bx2)
            reach = jump_d - max(0, rise) // 2
            if gap <= reach:
                seen.add(b)
                queue.append(b)
    return sorted(seen)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('regression gap boundary #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression gap boundary #2', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[13, 18, 6], [20, 22, 7]], 2, 8], [0, 1]),
  ('control #2', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('regression gap boundary #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression gap boundary #2', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('partial repair boundary #2', [[[21, 21, 10], [16, 21, 3]], 4, 3], [0, 1]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0]),
  ('control #2', [[[17, 20, 8]], 4, 4], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site gap boundary #1',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('regression gap boundary #1',
   [[[18, 18, 5], [15, 19, 6], [21, 22, 3], [5, 9, 1], [14, 20, 6], [24, 29, 7]], 1, 5],
   [0, 1, 2, 3, 4, 5]),
  ('partial repair boundary #1', [[[7, 8, 6], [2, 8, 5], [20, 21, 2], [23, 28, 7]], 1, 5], [0, 1]),
  ('partial repair boundary #2', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[12, 14, 0], [26, 26, 2], [22, 27, 7], [0, 3, 1]], 5, 4], [0]),
  ('control #2',
   [[[19, 21, 8], [19, 19, 2], [21, 22, 10], [11, 17, 5], [11, 17, 9]], 3, 4],
   [0, 1, 2, 3, 4])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('fault site gap boundary #1',
   [[[8, 11, 3], [22, 23, 8], [13, 13, 5], [26, 27, 3], [16, 16, 5]], 5, 3],
   [0, 2, 4]),
  ('regression gap boundary #1',
   [[[3, 4, 8], [16, 18, 8], [9, 9, 2], [7, 12, 6], [19, 24, 7], [24, 27, 3]], 2, 5],
   [0, 1, 2, 3, 4, 5]),
  ('partial repair boundary #1', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1]),
  ('partial repair boundary #2', [[[25, 26, 5], [19, 25, 6], [15, 19, 7]], 3, 3], [0, 1, 2]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[5, 5, 2]], 4, 6], [0]),
  ('control #2', [[[27, 29, 10]], 3, 1], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site gap boundary #1',
   [[[11, 15, 6], [6, 8, 9], [28, 34, 2], [22, 24, 7], [4, 6, 5], [28, 34, 10]], 2, 5],
   [0, 4]),
  ('regression gap boundary #1',
   [[[29, 34, 5], [6, 11, 2], [26, 26, 4], [25, 31, 2], [0, 2, 0], [5, 11, 5]], 2, 1],
   [0, 2, 3]),
  ('partial repair boundary #1',
   [[[7, 9, 9], [10, 15, 0], [7, 10, 2], [9, 14, 4], [26, 30, 8], [15, 19, 1]], 5, 1],
   [0, 1, 2, 3, 5]),
  ('partial repair boundary #2',
   [[[19, 24, 5], [30, 34, 4], [9, 14, 9], [16, 22, 8], [6, 6, 9]], 3, 4],
   [0, 2, 3, 4]),
  ('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('control #1', [[[18, 20, 2], [24, 29, 0], [12, 17, 2], [30, 35, 0], [8, 12, 5]], 2, 7], [0, 1, 2, 3]),
  ('control #2', [[[21, 24, 2], [4, 5, 1], [12, 12, 2]], 1, 8], [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
platform to the left #1[0, 1][0, 1]Passed
chain of hops #1[0, 1, 2][0, 1, 2]Passed
regression gap boundary #1[0, 1, 3][0, 1, 3]Passed
regression gap boundary #2[0, 1, 3][0, 1, 3]Passed
partial repair boundary #1[0, 2][0, 2]Passed
deep drop #1[0, 1][0, 1]Passed
control #1[0, 1][0, 1]Passed
control #2[0][0]Passed

SHA-256 / 94e7a3edf19382b94e1c8ef20cb570ff83d07c247487d3d5e9dc309a4ee984e9

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 2026-09-29T14:50:49.929014+00:00.

Case digest / 718fd9787ae6234b77888ca598e58c677cfbdd175814aeb6d2810f8a1d21e7a2