FA-86776 / Procedural level generation constraints / Open access
Encounter pacing along the critical path: First encounter ignores the start gap · case 01
Enemies appear right at the level entrance.
ROOT CAUSE
The anchor starts before the level start.
VERIFIED REPAIR
Restore `last = 0` at the initial anchor step.
Unsuccessful approach: Anchoring at tile one shifts the first gap by one.
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 = -min_gap
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]),
('regression initial anchor #1', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
('fault site initial anchor #1', [5, [-1, 1, 7, 5, -2], 3, 0], []),
('partial repair boundary #1', [40, [3, 4], 3, 0], [3]),
('partial repair boundary #2', [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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('fault site initial anchor #1', [14, [2], 5, 0], []),
('regression initial anchor #1', [5, [4, 3, 1, 6, 0, 1, 3, 4], 3, 0], [3]),
('regression initial anchor #2', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
('partial repair boundary #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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('regression initial anchor #1', [8, [3, 2, 8, 9, 7, -2, 0, 1], 2, 0], [2]),
('fault site initial anchor #1', [12, [2, 1, 11], 5, 0], []),
('partial repair boundary #1', [23, [2], 2, 0], [2]),
('partial repair boundary #2', [13, [4, 11, 8, 5], 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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('regression initial anchor #1', [13, [15, 4, 0, 6, 1, 2, 1, 14, 11], 2, 0], [2, 4, 6, 11]),
('fault site initial anchor #1', [20, [21, 8, 21, 2, -2, 8, 7], 5, 0], [7]),
('regression initial anchor #2', [5, [4, 3, 1, 6, 0, 1, 3, 4], 3, 0], [3]),
('partial repair boundary #1', [5, [5, 0, 4, 3, 7], 3, 0], [3]),
('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 initial anchor #1', [11, [3, 1, 9, 8, 7, 12], 5, 0], [7]),
('fault site initial anchor #2', [21, [4, 11, 0, 3, 11, 4, 4, -1, 23], 5, 0], [11]),
('partial repair boundary #1', [33, [17, 5, -1], 5, 7], [5]),
('partial repair boundary #2', [24, [5], 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', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], [])]]
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 |
|---|---|---|---|
| checkpoint resets gap #1 | [2, 7] | [2, 7] | Passed |
| regression initial anchor #1 | [1, 6] | [3, 6] | Failed |
| fault site initial anchor #1 | [1] | [] | Failed |
| partial repair boundary #1 | [3] | [3] | Passed |
| partial repair boundary #2 | [2, 17] | [2, 17] | Passed |
| duplicate proposals #1 | [3, 4] | [3, 4] | Passed |
| last legal tile #1 | [8] | [8] | Passed |
| control #1 | [] | [] | Passed |
SHA-256 / 6b9a912394204a0fa7fedc2de6df5710bbb2c556cf3deb132866019f533593b3
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 = 1
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]),
('regression initial anchor #1', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
('fault site initial anchor #1', [5, [-1, 1, 7, 5, -2], 3, 0], []),
('partial repair boundary #1', [40, [3, 4], 3, 0], [3]),
('partial repair boundary #2', [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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('fault site initial anchor #1', [14, [2], 5, 0], []),
('regression initial anchor #1', [5, [4, 3, 1, 6, 0, 1, 3, 4], 3, 0], [3]),
('regression initial anchor #2', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
('partial repair boundary #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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('regression initial anchor #1', [8, [3, 2, 8, 9, 7, -2, 0, 1], 2, 0], [2]),
('fault site initial anchor #1', [12, [2, 1, 11], 5, 0], []),
('partial repair boundary #1', [23, [2], 2, 0], [2]),
('partial repair boundary #2', [13, [4, 11, 8, 5], 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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('regression initial anchor #1', [13, [15, 4, 0, 6, 1, 2, 1, 14, 11], 2, 0], [2, 4, 6, 11]),
('fault site initial anchor #1', [20, [21, 8, 21, 2, -2, 8, 7], 5, 0], [7]),
('regression initial anchor #2', [5, [4, 3, 1, 6, 0, 1, 3, 4], 3, 0], [3]),
('partial repair boundary #1', [5, [5, 0, 4, 3, 7], 3, 0], [3]),
('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 initial anchor #1', [11, [3, 1, 9, 8, 7, 12], 5, 0], [7]),
('fault site initial anchor #2', [21, [4, 11, 0, 3, 11, 4, 4, -1, 23], 5, 0], [11]),
('partial repair boundary #1', [33, [17, 5, -1], 5, 7], [5]),
('partial repair boundary #2', [24, [5], 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', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], [])]]
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 |
|---|---|---|---|
| checkpoint resets gap #1 | [7] | [2, 7] | Failed |
| regression initial anchor #1 | [6] | [3, 6] | Failed |
| fault site initial anchor #1 | [] | [] | Passed |
| partial repair boundary #1 | [4] | [3] | Failed |
| partial repair boundary #2 | [17] | [2, 17] | Failed |
| duplicate proposals #1 | [3, 4] | [3, 4] | Passed |
| last legal tile #1 | [8] | [8] | Passed |
| control #1 | [] | [] | Passed |
SHA-256 / 3e4dfc1ab1bbcb9c3eebbe2351e84b97eb0b0491d94e2c876162e2dd4af3743d
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]),
('regression initial anchor #1', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
('fault site initial anchor #1', [5, [-1, 1, 7, 5, -2], 3, 0], []),
('partial repair boundary #1', [40, [3, 4], 3, 0], [3]),
('partial repair boundary #2', [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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('fault site initial anchor #1', [14, [2], 5, 0], []),
('regression initial anchor #1', [5, [4, 3, 1, 6, 0, 1, 3, 4], 3, 0], [3]),
('regression initial anchor #2', [10, [1, 3, 6, 0, 12, 9, 7, -1], 3, 0], [3, 6]),
('partial repair boundary #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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('regression initial anchor #1', [8, [3, 2, 8, 9, 7, -2, 0, 1], 2, 0], [2]),
('fault site initial anchor #1', [12, [2, 1, 11], 5, 0], []),
('partial repair boundary #1', [23, [2], 2, 0], [2]),
('partial repair boundary #2', [13, [4, 11, 8, 5], 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', [21, [-2, 16], 2, 5], [])],
[('checkpoint resets gap #1', [20, [2, 6, 7], 2, 5], [2, 7]),
('regression initial anchor #1', [13, [15, 4, 0, 6, 1, 2, 1, 14, 11], 2, 0], [2, 4, 6, 11]),
('fault site initial anchor #1', [20, [21, 8, 21, 2, -2, 8, 7], 5, 0], [7]),
('regression initial anchor #2', [5, [4, 3, 1, 6, 0, 1, 3, 4], 3, 0], [3]),
('partial repair boundary #1', [5, [5, 0, 4, 3, 7], 3, 0], [3]),
('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 initial anchor #1', [11, [3, 1, 9, 8, 7, 12], 5, 0], [7]),
('fault site initial anchor #2', [21, [4, 11, 0, 3, 11, 4, 4, -1, 23], 5, 0], [11]),
('partial repair boundary #1', [33, [17, 5, -1], 5, 7], [5]),
('partial repair boundary #2', [24, [5], 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', [34, [-1, 30, 25, 20, 1, 11, 0], 5, 4], [])]]
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 |
|---|---|---|---|
| checkpoint resets gap #1 | [2, 7] | [2, 7] | Passed |
| regression initial anchor #1 | [3, 6] | [3, 6] | Passed |
| fault site initial anchor #1 | [] | [] | Passed |
| partial repair boundary #1 | [3] | [3] | Passed |
| partial repair boundary #2 | [2, 17] | [2, 17] | Passed |
| duplicate proposals #1 | [3, 4] | [3, 4] | Passed |
| last legal tile #1 | [8] | [8] | Passed |
| control #1 | [] | [] | Passed |
SHA-256 / 4b4177be5313237f4553e042ae672e88c80823b01f70a80c234ce60c00af2693
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 2026-09-29T14:50:52.719434+00:00.
Case digest / f7410f1cbc159e138970514dbcfe0e32f4985b404edac2358c7a1327d2a65268