FA-86761 / Procedural level generation constraints / Open access

Encounter pacing along the critical path: Proposals processed in input order · case 01

Gaps are checked against later positions, spacing encounters backwards.

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

ROOT CAUSE

Proposals are neither sorted nor deduplicated.

VERIFIED REPAIR

Restore `sorted(set(encounters))` at the proposal normalisation step.

Unsuccessful approach: Sorting without dedup accepts duplicate encounters when min_gap is zero.

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 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 = [[('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1',
   [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0],
   [6, 10, 12, 15, 20]),
  ('fault site proposal normalisation #2', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('regression proposal normalisation #1', [4, [1, -2, 1], 0, 7], [1]),
  ('regression proposal normalisation #2', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('fault site proposal normalisation #2', [40, [41, 39, 8, 9, 9, 32, 18, 41], 5, 0], [8, 18, 32]),
  ('regression proposal normalisation #1', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('regression proposal normalisation #2', [20, [16, 11, 18, 18, -2, 4, 21, 19, 21], 0, 0], [4, 11, 16, 18]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('fault site proposal normalisation #2', [37, [27, 33, 11, 14, 7], 0, 7], [11, 27, 33]),
  ('regression proposal normalisation #1', [30, [4, 23, 32, 22, 22, -1, 9, 2], 0, 0], [2, 4, 9, 22, 23]),
  ('regression proposal normalisation #2', [39, [36, 36, 16, 30, 0, 39, 8], 0, 5], [8, 16, 36]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('regression proposal normalisation #1', [4, [1, -2, 1], 0, 7], [1]),
  ('fault site proposal normalisation #1', [38, [27, 16, 11, 3], 0, 7], [3, 11, 16, 27]),
  ('partial repair boundary #1', [22, [23, 22, 5, 11, 5], 0, 0], [5, 11]),
  ('partial repair boundary #2', [14, [1, 12, 0, 1], 0, 0], [1, 12]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [36, [32, 33, 13], 2, 0], [13, 32]),
  ('fault site proposal normalisation #2', [29, [-2, 26, 19], 3, 0], [19, 26]),
  ('regression proposal normalisation #1', [15, [2, 8, 8, 11], 0, 5], [2, 8, 11]),
  ('regression proposal normalisation #2', [30, [17, 13, 17, -2, -2, 9, 32, 23], 0, 7], [9, 13, 17, 23]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('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 fixture	Actual	Expected	Outcome
duplicate proposals #1	`[3, 3, 4]`	`[3, 4]`	Failed
fault site proposal normalisation #1	`[20]`	`[6, 10, 12, 15, 20]`	Failed
fault site proposal normalisation #2	`[4, 9]`	`[4, 7, 8, 9]`	Failed
regression proposal normalisation #1	`[1, 1]`	`[1]`	Failed
regression proposal normalisation #2	`[6, 10]`	`[2, 4, 6, 9, 10]`	Failed
last legal tile #1	`[8]`	`[8]`	Passed
checkpoint resets gap #1	`[2, 7]`	`[2, 7]`	Passed
control #1	`[]`	`[]`	Passed

SHA-256 / 91b15f9f484c189b918beb917b22a5c6b1ca9d3d4e5c837cdc373dd3d84ec2bd

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(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 = [[('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1',
   [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0],
   [6, 10, 12, 15, 20]),
  ('fault site proposal normalisation #2', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('regression proposal normalisation #1', [4, [1, -2, 1], 0, 7], [1]),
  ('regression proposal normalisation #2', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('fault site proposal normalisation #2', [40, [41, 39, 8, 9, 9, 32, 18, 41], 5, 0], [8, 18, 32]),
  ('regression proposal normalisation #1', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('regression proposal normalisation #2', [20, [16, 11, 18, 18, -2, 4, 21, 19, 21], 0, 0], [4, 11, 16, 18]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('fault site proposal normalisation #2', [37, [27, 33, 11, 14, 7], 0, 7], [11, 27, 33]),
  ('regression proposal normalisation #1', [30, [4, 23, 32, 22, 22, -1, 9, 2], 0, 0], [2, 4, 9, 22, 23]),
  ('regression proposal normalisation #2', [39, [36, 36, 16, 30, 0, 39, 8], 0, 5], [8, 16, 36]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('regression proposal normalisation #1', [4, [1, -2, 1], 0, 7], [1]),
  ('fault site proposal normalisation #1', [38, [27, 16, 11, 3], 0, 7], [3, 11, 16, 27]),
  ('partial repair boundary #1', [22, [23, 22, 5, 11, 5], 0, 0], [5, 11]),
  ('partial repair boundary #2', [14, [1, 12, 0, 1], 0, 0], [1, 12]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [36, [32, 33, 13], 2, 0], [13, 32]),
  ('fault site proposal normalisation #2', [29, [-2, 26, 19], 3, 0], [19, 26]),
  ('regression proposal normalisation #1', [15, [2, 8, 8, 11], 0, 5], [2, 8, 11]),
  ('regression proposal normalisation #2', [30, [17, 13, 17, -2, -2, 9, 32, 23], 0, 7], [9, 13, 17, 23]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('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 fixture	Actual	Expected	Outcome
duplicate proposals #1	`[3, 3, 4]`	`[3, 4]`	Failed
fault site proposal normalisation #1	`[6, 10, 12, 15, 20]`	`[6, 10, 12, 15, 20]`	Passed
fault site proposal normalisation #2	`[4, 7, 8, 9]`	`[4, 7, 8, 9]`	Passed
regression proposal normalisation #1	`[1, 1]`	`[1]`	Failed
regression proposal normalisation #2	`[2, 4, 6, 6, 9, 10]`	`[2, 4, 6, 9, 10]`	Failed
last legal tile #1	`[8]`	`[8]`	Passed
checkpoint resets gap #1	`[2, 7]`	`[2, 7]`	Passed
control #1	`[]`	`[]`	Passed

SHA-256 / c994992985b97d92ab7815acccadd3bb0a93a8634bfe31722af3e41088bd2706

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 = [[('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1',
   [27, [20, 6, 10, 15, 26, -2, 12, 27, -1], 0, 0],
   [6, 10, 12, 15, 20]),
  ('fault site proposal normalisation #2', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('regression proposal normalisation #1', [4, [1, -2, 1], 0, 7], [1]),
  ('regression proposal normalisation #2', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [14, [4, 9, 16, 9, 16, 7, 8, 16, 0, 13], 1, 5], [4, 7, 8, 9]),
  ('fault site proposal normalisation #2', [40, [41, 39, 8, 9, 9, 32, 18, 41], 5, 0], [8, 18, 32]),
  ('regression proposal normalisation #1', [19, [6, 20, 0, 10, 4, 6, 2, 14, 9], 0, 7], [2, 4, 6, 9, 10]),
  ('regression proposal normalisation #2', [20, [16, 11, 18, 18, -2, 4, 21, 19, 21], 0, 0], [4, 11, 16, 18]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [39, [34, 15, 35, 19, 4], 2, 4], [15, 19, 34]),
  ('fault site proposal normalisation #2', [37, [27, 33, 11, 14, 7], 0, 7], [11, 27, 33]),
  ('regression proposal normalisation #1', [30, [4, 23, 32, 22, 22, -1, 9, 2], 0, 0], [2, 4, 9, 22, 23]),
  ('regression proposal normalisation #2', [39, [36, 36, 16, 30, 0, 39, 8], 0, 5], [8, 16, 36]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [21, [-2, 16], 2, 5], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('regression proposal normalisation #1', [4, [1, -2, 1], 0, 7], [1]),
  ('fault site proposal normalisation #1', [38, [27, 16, 11, 3], 0, 7], [3, 11, 16, 27]),
  ('partial repair boundary #1', [22, [23, 22, 5, 11, 5], 0, 0], [5, 11]),
  ('partial repair boundary #2', [14, [1, 12, 0, 1], 0, 0], [1, 12]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('control #1', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], [])],
 [('duplicate proposals #1', [10, [3, 3, 4], 0, 0], [3, 4]),
  ('fault site proposal normalisation #1', [36, [32, 33, 13], 2, 0], [13, 32]),
  ('fault site proposal normalisation #2', [29, [-2, 26, 19], 3, 0], [19, 26]),
  ('regression proposal normalisation #1', [15, [2, 8, 8, 11], 0, 5], [2, 8, 11]),
  ('regression proposal normalisation #2', [30, [17, 13, 17, -2, -2, 9, 32, 23], 0, 7], [9, 13, 17, 23]),
  ('last legal tile #1', [10, [8, 9], 1, 0], [8]),
  ('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
  ('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 fixture	Actual	Expected	Outcome
duplicate proposals #1	`[3, 4]`	`[3, 4]`	Passed
fault site proposal normalisation #1	`[6, 10, 12, 15, 20]`	`[6, 10, 12, 15, 20]`	Passed
fault site proposal normalisation #2	`[4, 7, 8, 9]`	`[4, 7, 8, 9]`	Passed
regression proposal normalisation #1	`[1]`	`[1]`	Passed
regression proposal normalisation #2	`[2, 4, 6, 9, 10]`	`[2, 4, 6, 9, 10]`	Passed
last legal tile #1	`[8]`	`[8]`	Passed
checkpoint resets gap #1	`[2, 7]`	`[2, 7]`	Passed
control #1	`[]`	`[]`	Passed

SHA-256 / c48b55b02cc78bb951b3035c2b8c19c67fd7a69ff13acf50a28d8eba4878709d

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 2026-09-29T14:50:52.561731+00:00.

Case digest / faec22a173f0979ed04637cb206032345a9bc6c19ebf03cf941d479b5b6202ed