FAILURE MAP
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FA-86461 / Procedural level generation constraints / Open access

Platform jump reachability: Gap measured between left edges · case 01

Wide platforms appear far apart even when overlapping.

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

ROOT CAUSE

The gap compares left edges instead of the facing edges.

THE FAILURE

The gap compares left edges instead of the facing edges.

Unsuccessful approach: Measuring only rightward gaps makes platforms to the left look adjacent.

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 = abs(bx1 - ax1)
            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 = [[('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('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 horizontal gap #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('partial repair boundary #1', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0]),
  ('control #1', [[[13, 18, 6], [20, 22, 7]], 2, 8], [0, 1]),
  ('control #2', [[[17, 20, 8]], 4, 4], [0]),
  ('control #3', [[[5, 5, 2]], 4, 6], [0])],
 [('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 horizontal gap #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression horizontal gap #2',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('control #1', [[[27, 29, 10]], 3, 1], [0]),
  ('control #2', [[[7, 8, 6], [2, 8, 5], [20, 21, 2], [23, 28, 7]], 1, 5], [0, 1]),
  ('control #3', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('fault site horizontal gap #1', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('regression horizontal gap #1',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('partial repair boundary #1', [[[12, 14, 0], [26, 26, 2], [22, 27, 7], [0, 3, 1]], 5, 4], [0]),
  ('partial repair boundary #2', [[[21, 24, 2], [4, 5, 1], [12, 12, 2]], 1, 8], [0]),
  ('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', [[[2, 8, 1], [20, 22, 2]], 3, 6], [0]),
  ('control #3', [[[12, 15, 1]], 4, 3], [0])],
 [('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('fault site horizontal gap #1',
   [[[19, 21, 8], [19, 19, 2], [21, 22, 10], [11, 17, 5], [11, 17, 9]], 3, 4],
   [0, 1, 2, 3, 4]),
  ('fault site horizontal gap #2', [[[21, 21, 10], [16, 21, 3]], 4, 3], [0, 1]),
  ('partial repair boundary #1', [[[15, 16, 9], [5, 6, 2], [27, 30, 3], [22, 27, 8]], 1, 1], [0]),
  ('partial repair boundary #2', [[[25, 26, 6], [12, 14, 7], [7, 12, 10], [2, 2, 7]], 2, 8], [0]),
  ('control #1', [[[2, 4, 10], [13, 13, 1], [20, 20, 10]], 4, 1], [0]),
  ('control #2', [[[22, 26, 3], [24, 27, 10], [20, 26, 9]], 5, 5], [0]),
  ('control #3', [[[10, 11, 4], [28, 31, 2]], 1, 3], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site horizontal gap #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]),
  ('fault site horizontal gap #2', [[[25, 26, 5], [19, 25, 6], [15, 19, 7]], 3, 3], [0, 1, 2]),
  ('partial repair boundary #1', [[[15, 18, 6], [9, 13, 6]], 5, 1], [0]),
  ('partial repair boundary #2', [[[20, 24, 10], [6, 8, 1], [30, 30, 5]], 5, 5], [0]),
  ('control #1', [[[16, 18, 9]], 4, 8], [0]),
  ('control #2', [[[30, 31, 6]], 2, 6], [0]),
  ('control #3', [[[4, 8, 6], [16, 22, 0]], 3, 4], [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
deep drop #1[0][0, 1]Failed
platform to the left #1[0][0, 1]Failed
chain of hops #1[0][0, 1, 2]Failed
regression horizontal gap #1[0][0, 1, 3]Failed
partial repair boundary #1[0][0]Passed
control #1[0, 1][0, 1]Passed
control #2[0][0]Passed
control #3[0][0]Passed

SHA-256 / 021a7f6cccf802a956c5e77b9d8658e6479217a79d668101099685cbfdaea49d

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)
            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 = [[('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('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 horizontal gap #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('partial repair boundary #1', [[[23, 29, 1], [3, 9, 0]], 4, 3], [0]),
  ('control #1', [[[13, 18, 6], [20, 22, 7]], 2, 8], [0, 1]),
  ('control #2', [[[17, 20, 8]], 4, 4], [0]),
  ('control #3', [[[5, 5, 2]], 4, 6], [0])],
 [('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 horizontal gap #1',
   [[[5, 9, 8], [7, 13, 0], [0, 2, 9], [13, 13, 2], [25, 31, 3]], 2, 1],
   [0, 1, 3]),
  ('regression horizontal gap #2',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('partial repair boundary #1', [[[29, 30, 8], [13, 15, 5], [30, 33, 8]], 4, 6], [0, 2]),
  ('control #1', [[[27, 29, 10]], 3, 1], [0]),
  ('control #2', [[[7, 8, 6], [2, 8, 5], [20, 21, 2], [23, 28, 7]], 1, 5], [0, 1]),
  ('control #3', [[[30, 35, 8], [29, 34, 7]], 1, 4], [0, 1])],
 [('chain of hops #1', [[[0, 1, 0], [3, 4, 2], [6, 7, 4]], 2, 3], [0, 1, 2]),
  ('fault site horizontal gap #1', [[[23, 29, 6], [19, 22, 0], [30, 32, 8], [15, 20, 1]], 3, 1], [0, 1, 3]),
  ('regression horizontal gap #1',
   [[[23, 25, 6], [15, 16, 2], [21, 21, 7], [27, 33, 3], [2, 8, 3]], 2, 2],
   [0, 2, 3]),
  ('partial repair boundary #1', [[[12, 14, 0], [26, 26, 2], [22, 27, 7], [0, 3, 1]], 5, 4], [0]),
  ('partial repair boundary #2', [[[21, 24, 2], [4, 5, 1], [12, 12, 2]], 1, 8], [0]),
  ('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', [[[2, 8, 1], [20, 22, 2]], 3, 6], [0]),
  ('control #3', [[[12, 15, 1]], 4, 3], [0])],
 [('deep drop #1', [[[0, 2, 10], [3, 5, 0]], 2, 2], [0, 1]),
  ('fault site horizontal gap #1',
   [[[19, 21, 8], [19, 19, 2], [21, 22, 10], [11, 17, 5], [11, 17, 9]], 3, 4],
   [0, 1, 2, 3, 4]),
  ('fault site horizontal gap #2', [[[21, 21, 10], [16, 21, 3]], 4, 3], [0, 1]),
  ('partial repair boundary #1', [[[15, 16, 9], [5, 6, 2], [27, 30, 3], [22, 27, 8]], 1, 1], [0]),
  ('partial repair boundary #2', [[[25, 26, 6], [12, 14, 7], [7, 12, 10], [2, 2, 7]], 2, 8], [0]),
  ('control #1', [[[2, 4, 10], [13, 13, 1], [20, 20, 10]], 4, 1], [0]),
  ('control #2', [[[22, 26, 3], [24, 27, 10], [20, 26, 9]], 5, 5], [0]),
  ('control #3', [[[10, 11, 4], [28, 31, 2]], 1, 3], [0])],
 [('platform to the left #1', [[[10, 12, 0], [4, 7, 0]], 1, 3], [0, 1]),
  ('fault site horizontal gap #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]),
  ('fault site horizontal gap #2', [[[25, 26, 5], [19, 25, 6], [15, 19, 7]], 3, 3], [0, 1, 2]),
  ('partial repair boundary #1', [[[15, 18, 6], [9, 13, 6]], 5, 1], [0]),
  ('partial repair boundary #2', [[[20, 24, 10], [6, 8, 1], [30, 30, 5]], 5, 5], [0]),
  ('control #1', [[[16, 18, 9]], 4, 8], [0]),
  ('control #2', [[[30, 31, 6]], 2, 6], [0]),
  ('control #3', [[[4, 8, 6], [16, 22, 0]], 3, 4], [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
deep drop #1[0, 1][0, 1]Passed
platform to the left #1[0, 1][0, 1]Passed
chain of hops #1[0, 1, 2][0, 1, 2]Passed
regression horizontal gap #1[0, 1, 2, 3][0, 1, 3]Failed
partial repair boundary #1[0, 1][0]Failed
control #1[0, 1][0, 1]Passed
control #2[0][0]Passed
control #3[0][0]Passed

SHA-256 / cb712503c465de5167934b8e19822a34d8d3fbb3f0bc8df7b94d01e32f249b85

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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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 2026-09-29T14:50:49.833381+00:00.

Case digest / 441b86960c0837febe35858407e2b1753d2eea7b9851979dde6650b3230c9343