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FA-86771 / Procedural level generation constraints / Open access

Encounter pacing along the critical path: Only the first checkpoint resets pacing · case 01

Later rest stops do not give breathing room.

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

ROOT CAUSE

The anchor uses the first checkpoint instead of the latest one before pos.

VERIFIED REPAIR

Restore `anchor = max(anchor, pos // rest_every * rest_every)` at the checkpoint anchor step.

Unsuccessful approach: Overwriting the anchor forgets encounters placed after the checkpoint.

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, 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 checkpoint anchor #1', [21, [-2, 16], 2, 5], []),
  ('fault site checkpoint anchor #2', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('partial repair boundary #1', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('regression checkpoint anchor #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('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 checkpoint anchor #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('fault site checkpoint anchor #2', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('regression checkpoint anchor #1', [15, [3, 15, 2, 13], 2, 5], [2, 13]),
  ('regression checkpoint anchor #2', [24, [21, 26, 23, 10, 18, 9, 17, 19], 2, 4], [10, 18]),
  ('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 checkpoint anchor #1', [4, [1, -2, 1], 0, 7], [1]),
  ('fault site checkpoint anchor #2', [38, [27, 16, 11, 3], 0, 7], [3, 11, 16, 27]),
  ('regression checkpoint anchor #1', [22, [4, -1, 2, 3, 22], 2, 7], [2, 4]),
  ('regression checkpoint anchor #2', [23, [13, 20, 7, 12, 21, 15, 11, 19, 5], 2, 7], [5, 11, 13, 19]),
  ('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 checkpoint anchor #1', [29, [13, 16], 3, 5], [13]),
  ('regression checkpoint anchor #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('regression checkpoint anchor #2', [14, [5, 13, 6, 10, 8, 8], 3, 7], [5, 10]),
  ('regression checkpoint anchor #3', [13, [11, 14, 8, 0, 6, 4, 3, 10, 7, 5], 3, 7], [3, 6, 10]),
  ('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 checkpoint anchor #1', [14, [11, 0, 11, 6, 13, 15, 15, 3], 5, 7], [6]),
  ('fault site checkpoint anchor #2', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('regression checkpoint anchor #1', [22, [12, -2, 3, 4, 2, 14, 15, -1, 15, 16], 2, 4], [2, 14]),
  ('regression checkpoint anchor #2', [34, [32, 28, 21, 18, 3, 26, 15, 19, 3], 3, 5], [3, 18, 28]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [40, [3, 4], 3, 0], [3])]]
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[7][2, 7]Failed
fault site checkpoint anchor #1[16][]Failed
fault site checkpoint anchor #2[11, 25, 30][]Failed
partial repair boundary #1[15, 19, 34][15, 19, 34]Passed
regression checkpoint anchor #1[15, 17][2, 17]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 / 2ca31f1ae334da723c44d7e4503536efe6c468d9f3d7524a6740db110d92e11a

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 = 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 checkpoint anchor #1', [21, [-2, 16], 2, 5], []),
  ('fault site checkpoint anchor #2', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('partial repair boundary #1', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('regression checkpoint anchor #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('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 checkpoint anchor #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('fault site checkpoint anchor #2', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('regression checkpoint anchor #1', [15, [3, 15, 2, 13], 2, 5], [2, 13]),
  ('regression checkpoint anchor #2', [24, [21, 26, 23, 10, 18, 9, 17, 19], 2, 4], [10, 18]),
  ('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 checkpoint anchor #1', [4, [1, -2, 1], 0, 7], [1]),
  ('fault site checkpoint anchor #2', [38, [27, 16, 11, 3], 0, 7], [3, 11, 16, 27]),
  ('regression checkpoint anchor #1', [22, [4, -1, 2, 3, 22], 2, 7], [2, 4]),
  ('regression checkpoint anchor #2', [23, [13, 20, 7, 12, 21, 15, 11, 19, 5], 2, 7], [5, 11, 13, 19]),
  ('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 checkpoint anchor #1', [29, [13, 16], 3, 5], [13]),
  ('regression checkpoint anchor #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('regression checkpoint anchor #2', [14, [5, 13, 6, 10, 8, 8], 3, 7], [5, 10]),
  ('regression checkpoint anchor #3', [13, [11, 14, 8, 0, 6, 4, 3, 10, 7, 5], 3, 7], [3, 6, 10]),
  ('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 checkpoint anchor #1', [14, [11, 0, 11, 6, 13, 15, 15, 3], 5, 7], [6]),
  ('fault site checkpoint anchor #2', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('regression checkpoint anchor #1', [22, [12, -2, 3, 4, 2, 14, 15, -1, 15, 16], 2, 4], [2, 14]),
  ('regression checkpoint anchor #2', [34, [32, 28, 21, 18, 3, 26, 15, 19, 3], 3, 5], [3, 18, 28]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [40, [3, 4], 3, 0], [3])]]
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 checkpoint anchor #1[][]Passed
fault site checkpoint anchor #2[][]Passed
partial repair boundary #1[15, 19, 34, 35][15, 19, 34]Failed
regression checkpoint anchor #1[2, 17, 18][2, 17]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 / 12f0c01920aceb8aa08fbdb7a6d0f972a0b5a622de2edae6d16b0d49a43488a7

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 checkpoint anchor #1', [21, [-2, 16], 2, 5], []),
  ('fault site checkpoint anchor #2', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('partial repair boundary #1', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('regression checkpoint anchor #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('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 checkpoint anchor #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], []),
  ('fault site checkpoint anchor #2', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('regression checkpoint anchor #1', [15, [3, 15, 2, 13], 2, 5], [2, 13]),
  ('regression checkpoint anchor #2', [24, [21, 26, 23, 10, 18, 9, 17, 19], 2, 4], [10, 18]),
  ('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 checkpoint anchor #1', [4, [1, -2, 1], 0, 7], [1]),
  ('fault site checkpoint anchor #2', [38, [27, 16, 11, 3], 0, 7], [3, 11, 16, 27]),
  ('regression checkpoint anchor #1', [22, [4, -1, 2, 3, 22], 2, 7], [2, 4]),
  ('regression checkpoint anchor #2', [23, [13, 20, 7, 12, 21, 15, 11, 19, 5], 2, 7], [5, 11, 13, 19]),
  ('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 checkpoint anchor #1', [29, [13, 16], 3, 5], [13]),
  ('regression checkpoint anchor #1', [22, [17, 15, -1, 24, 7, 1, -2, 18, 2], 2, 7], [2, 17]),
  ('regression checkpoint anchor #2', [14, [5, 13, 6, 10, 8, 8], 3, 7], [5, 10]),
  ('regression checkpoint anchor #3', [13, [11, 14, 8, 0, 6, 4, 3, 10, 7, 5], 3, 7], [3, 6, 10]),
  ('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 checkpoint anchor #1', [14, [11, 0, 11, 6, 13, 15, 15, 3], 5, 7], [6]),
  ('fault site checkpoint anchor #2', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('regression checkpoint anchor #1', [22, [12, -2, 3, 4, 2, 14, 15, -1, 15, 16], 2, 4], [2, 14]),
  ('regression checkpoint anchor #2', [34, [32, 28, 21, 18, 3, 26, 15, 19, 3], 3, 5], [3, 18, 28]),
  ('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('control #1', [40, [3, 4], 3, 0], [3])]]
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 checkpoint anchor #1[][]Passed
fault site checkpoint anchor #2[][]Passed
partial repair boundary #1[15, 19, 34][15, 19, 34]Passed
regression checkpoint anchor #1[2, 17][2, 17]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 / d006388202eb5ffe1b2ddffd6875a6ac486dd12cc4ceb7e87f017e19bc1418f0

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 2026-09-29T14:50:52.717252+00:00.

Case digest / 0bd8ce530f239fc2a33806931d08c263eac377568a1585742ead177a119c7537