FAILURE MAP
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FA-86781 / Procedural level generation constraints / Open access

Encounter pacing along the critical path: Encounters one tile too far apart · case 01

Levels contain fewer encounters than designed.

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

ROOT CAUSE

The gap comparison is inclusive.

VERIFIED REPAIR

Restore `if pos - anchor < min_gap:` at the gap measure step.

Unsuccessful approach: Measuring from the last encounter ignores checkpoints.

Case contract

Proposed positions are deduplicated and taken ascending. A position is legal when 1 <= pos <= length-2, is not a rest checkpoint (pos % rest_every == 0 when rest_every > 0), and lies at least min_gap after the anchor: the later of the last accepted encounter (initially the start, 0) and the last checkpoint at or before pos. Returns accepted positions.

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(length, encounters, min_gap, rest_every):
    out = []
    last = 0
    for pos in sorted(set(encounters)):
        if pos < 1 or pos > length - 2:
            continue
        if rest_every and pos % rest_every == 0:
            continue
        anchor = last
        if rest_every:
            anchor = max(anchor, pos // rest_every * rest_every)
        if pos - anchor <= min_gap:
            continue
        out.append(pos)
        last = pos
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('fault site gap measure #2', [40, [3, 4], 3, 0], [3]),
  ('partial repair boundary #1', [21, [-2, 16], 2, 5], []),
  ('partial repair boundary #2', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [40, [3, 4], 3, 0], [3]),
  ('fault site gap measure #2', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('partial repair boundary #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('regression gap measure #1', [29, [13, 16], 3, 5], [13]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
  ('regression gap measure #1', [29, [13, 16], 3, 5], [13]),
  ('regression gap measure #2', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('partial repair boundary #1', [14, [11, 0, 11, 6, 13, 15, 15, 3], 5, 7], [6]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('regression gap measure #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('fault site gap measure #1', [38, [26, 15, -2, 19, 22, -1, 7, 23], 1, 0], [7, 15, 19, 22, 23, 26]),
  ('regression gap measure #2', [13, [4, 11, 8, 5], 5, 7], [5]),
  ('regression gap measure #3', [30, [32, 12, 17, 27, 6, 20], 3, 4], [27]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [40, [41, 39, 8, 9, 9, 32, 18, 41], 5, 0], [8, 18, 32])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [29, [18, 24, 20, 17, 15], 2, 0], [15, 17, 20, 24]),
  ('fault site gap measure #2', [27, [24], 3, 7], [24]),
  ('partial repair boundary #1', [37, [38, 25, 36, 9, 26, 10, 25, 2, 27, -2], 3, 5], [9]),
  ('regression gap measure #1', [33, [17, 5, -1], 5, 7], [5]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [37, [27, 33, 11, 14, 7], 0, 7], [11, 27, 33])]]
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
checkpoint resets gap #1[][2, 7]Failed
fault site gap measure #1[4, 7, 9][4, 7, 8, 9]Failed
fault site gap measure #2[4][3]Failed
partial repair boundary #1[][]Passed
partial repair boundary #2[][]Passed
duplicate proposals #1[3, 4][3, 4]Passed
last legal tile #1[8][8]Passed
control #1[6, 10, 12, 15, 20][6, 10, 12, 15, 20]Passed

SHA-256 / 0cc8d942360913ca4ce961a7f99f26838a9c0a96e130fbd6b5aa1866713864c6

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(length, encounters, min_gap, rest_every):
    out = []
    last = 0
    for pos in sorted(set(encounters)):
        if pos < 1 or pos > length - 2:
            continue
        if rest_every and pos % rest_every == 0:
            continue
        anchor = last
        if rest_every:
            anchor = max(anchor, pos // rest_every * rest_every)
        if pos - last < min_gap:
            continue
        out.append(pos)
        last = pos
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('fault site gap measure #2', [40, [3, 4], 3, 0], [3]),
  ('partial repair boundary #1', [21, [-2, 16], 2, 5], []),
  ('partial repair boundary #2', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [40, [3, 4], 3, 0], [3]),
  ('fault site gap measure #2', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('partial repair boundary #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('regression gap measure #1', [29, [13, 16], 3, 5], [13]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
  ('regression gap measure #1', [29, [13, 16], 3, 5], [13]),
  ('regression gap measure #2', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('partial repair boundary #1', [14, [11, 0, 11, 6, 13, 15, 15, 3], 5, 7], [6]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('regression gap measure #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('fault site gap measure #1', [38, [26, 15, -2, 19, 22, -1, 7, 23], 1, 0], [7, 15, 19, 22, 23, 26]),
  ('regression gap measure #2', [13, [4, 11, 8, 5], 5, 7], [5]),
  ('regression gap measure #3', [30, [32, 12, 17, 27, 6, 20], 3, 4], [27]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [40, [41, 39, 8, 9, 9, 32, 18, 41], 5, 0], [8, 18, 32])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [29, [18, 24, 20, 17, 15], 2, 0], [15, 17, 20, 24]),
  ('fault site gap measure #2', [27, [24], 3, 7], [24]),
  ('partial repair boundary #1', [37, [38, 25, 36, 9, 26, 10, 25, 2, 27, -2], 3, 5], [9]),
  ('regression gap measure #1', [33, [17, 5, -1], 5, 7], [5]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [37, [27, 33, 11, 14, 7], 0, 7], [11, 27, 33])]]
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
checkpoint resets gap #1[2, 6][2, 7]Failed
fault site gap measure #1[4, 7, 8, 9][4, 7, 8, 9]Passed
fault site gap measure #2[3][3]Passed
partial repair boundary #1[16][]Failed
partial repair boundary #2[11, 25, 30][]Failed
duplicate proposals #1[3, 4][3, 4]Passed
last legal tile #1[8][8]Passed
control #1[6, 10, 12, 15, 20][6, 10, 12, 15, 20]Passed

SHA-256 / c07266f3a497df9fea3cb34bda4cee3af1d9048ba7e8b9718f424f893bf5b5ca

3 / The verified repair

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

N = 1
observations = []
def solve(length, encounters, min_gap, rest_every):
    out = []
    last = 0
    for pos in sorted(set(encounters)):
        if pos < 1 or pos > length - 2:
            continue
        if rest_every and pos % rest_every == 0:
            continue
        anchor = last
        if rest_every:
            anchor = max(anchor, pos // rest_every * rest_every)
        if pos - anchor < min_gap:
            continue
        out.append(pos)
        last = pos
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('fault site gap measure #2', [40, [3, 4], 3, 0], [3]),
  ('partial repair boundary #1', [21, [-2, 16], 2, 5], []),
  ('partial repair boundary #2', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [40, [3, 4], 3, 0], [3]),
  ('fault site gap measure #2', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('partial repair boundary #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('regression gap measure #1', [29, [13, 16], 3, 5], [13]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
  ('regression gap measure #1', [29, [13, 16], 3, 5], [13]),
  ('regression gap measure #2', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('partial repair boundary #1', [14, [11, 0, 11, 6, 13, 15, 15, 3], 5, 7], [6]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0], [6, 10, 12, 15, 20])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('regression gap measure #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('fault site gap measure #1', [38, [26, 15, -2, 19, 22, -1, 7, 23], 1, 0], [7, 15, 19, 22, 23, 26]),
  ('regression gap measure #2', [13, [4, 11, 8, 5], 5, 7], [5]),
  ('regression gap measure #3', [30, [32, 12, 17, 27, 6, 20], 3, 4], [27]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [40, [41, 39, 8, 9, 9, 32, 18, 41], 5, 0], [8, 18, 32])],
 [('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('fault site gap measure #1', [29, [18, 24, 20, 17, 15], 2, 0], [15, 17, 20, 24]),
  ('fault site gap measure #2', [27, [24], 3, 7], [24]),
  ('partial repair boundary #1', [37, [38, 25, 36, 9, 26, 10, 25, 2, 27, -2], 3, 5], [9]),
  ('regression gap measure #1', [33, [17, 5, -1], 5, 7], [5]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [37, [27, 33, 11, 14, 7], 0, 7], [11, 27, 33])]]
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
checkpoint resets gap #1[2, 7][2, 7]Passed
fault site gap measure #1[4, 7, 8, 9][4, 7, 8, 9]Passed
fault site gap measure #2[3][3]Passed
partial repair boundary #1[][]Passed
partial repair boundary #2[][]Passed
duplicate proposals #1[3, 4][3, 4]Passed
last legal tile #1[8][8]Passed
control #1[6, 10, 12, 15, 20][6, 10, 12, 15, 20]Passed

SHA-256 / b8d2b06c558fe22cb81d569f9dfe582d52ca2d90602061863597327ba33cd0eb

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 2026-09-29T14:50:52.734265+00:00.

Case digest / d6fb6acafac10c8d8e58bb784fb7002af60ce58327c22f42d0681af6b7b32668