FAILURE MAP
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FA-86516 / Procedural level generation constraints / Open access

Chunk seed derivation: Xorshift state grows beyond 32 bits · case 01

Chunk contents differ between 32-bit and arbitrary-precision builds.

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

ROOT CAUSE

The first left shift is not masked to 32 bits.

VERIFIED REPAIR

Restore `x ^= (x << 13) & 0xFFFFFFFF` at the left shift mask step.

Unsuccessful approach: A 28-bit mask truncates valid state bits.

Case contract

Coordinates are zigzag encoded (v >= 0 -> 2v, v < 0 -> -2v-1). seed = (world_seed*1000003 mod 2^32) xor (zz(cx)*73856093 mod 2^32) xor (zz(cy)*19349663 mod 2^32). The generator state is seed, or 1 when seed is 0, advanced by three 32-bit xorshift rounds (<<13, >>17, <<5, each left shift masked to 32 bits). Returns [seed, state % 100].

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(world_seed, cx, cy):
    def zz(v):
        return v * 2 if v >= 0 else -v * 2 - 1
    s = (world_seed * 1000003) & 0xFFFFFFFF
    s ^= (zz(cx) * 73856093) & 0xFFFFFFFF
    s ^= (zz(cy) * 19349663) & 0xFFFFFFFF
    x = s or 1
    for _ in range(3):
        x ^= x << 13
        x ^= x >> 17
        x ^= (x << 5) & 0xFFFFFFFF
    return [s, x % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),
  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87])],
 [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),
  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #6', [0, 2, -3], [341807727, 72])],
 [('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('regression left shift mask #1', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #2', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #3', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #4', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #5', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #6', [1099511627779, -1, 3], [44085550, 32])],
 [('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('regression left shift mask #1', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #2', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #3', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #4', [1099511627779, -1, 3], [44085550, 32]),
  ('regression left shift mask #5', [2147483655, -2, 0], [2371752642, 72]),
  ('regression left shift mask #6', [1, -2, 1], [259333738, 52])],
 [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #2', [1099511627779, -1, 3], [44085550, 32]),
  ('regression left shift mask #3', [2147483655, -2, 0], [2371752642, 72]),
  ('regression left shift mask #4', [1, -2, 1], [259333738, 52]),
  ('regression left shift mask #5', [42, -1, -303], [3206913376, 67]),
  ('fault site left shift mask #1', [17601332116874, -1, 1], [1431083645, 95])]]
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
origin with zero seed #1[0, 21][0, 61]Failed
negative neighbour chunk #1[115747491, 8][115747491, 56]Failed
mirrored coordinates #1[294384589, 4][294384589, 20]Failed
regression left shift mask #1[78162845, 83][78162845, 87]Failed
regression left shift mask #2[116097978, 46][116097978, 65]Failed
regression left shift mask #3[1640198686, 28][1640198686, 4]Failed
regression left shift mask #4[179220301, 27][179220301, 79]Failed
regression left shift mask #5[3628518806, 79][3628518806, 87]Failed

SHA-256 / 5ca06a93e079ac57ed3df2054ad77fb06de9562f0ebe0290a31dc86e2ebfa6ba

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(world_seed, cx, cy):
    def zz(v):
        return v * 2 if v >= 0 else -v * 2 - 1
    s = (world_seed * 1000003) & 0xFFFFFFFF
    s ^= (zz(cx) * 73856093) & 0xFFFFFFFF
    s ^= (zz(cy) * 19349663) & 0xFFFFFFFF
    x = s or 1
    for _ in range(3):
        x ^= (x << 13) & 0xFFFFFFF
        x ^= x >> 17
        x ^= (x << 5) & 0xFFFFFFFF
    return [s, x % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),
  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87])],
 [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),
  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #6', [0, 2, -3], [341807727, 72])],
 [('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('regression left shift mask #1', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #2', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #3', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #4', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #5', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #6', [1099511627779, -1, 3], [44085550, 32])],
 [('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('regression left shift mask #1', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #2', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #3', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #4', [1099511627779, -1, 3], [44085550, 32]),
  ('regression left shift mask #5', [2147483655, -2, 0], [2371752642, 72]),
  ('regression left shift mask #6', [1, -2, 1], [259333738, 52])],
 [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #2', [1099511627779, -1, 3], [44085550, 32]),
  ('regression left shift mask #3', [2147483655, -2, 0], [2371752642, 72]),
  ('regression left shift mask #4', [1, -2, 1], [259333738, 52]),
  ('regression left shift mask #5', [42, -1, -303], [3206913376, 67]),
  ('fault site left shift mask #1', [17601332116874, -1, 1], [1431083645, 95])]]
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
origin with zero seed #1[0, 5][0, 61]Failed
negative neighbour chunk #1[115747491, 99][115747491, 56]Failed
mirrored coordinates #1[294384589, 76][294384589, 20]Failed
regression left shift mask #1[78162845, 80][78162845, 87]Failed
regression left shift mask #2[116097978, 8][116097978, 65]Failed
regression left shift mask #3[1640198686, 52][1640198686, 4]Failed
regression left shift mask #4[179220301, 24][179220301, 79]Failed
regression left shift mask #5[3628518806, 30][3628518806, 87]Failed

SHA-256 / 6598b75e4d7409a619b0bf9486dd8123963976399c1905828a7c52fea22796c9

3 / The verified repair

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

N = 1
observations = []
def solve(world_seed, cx, cy):
    def zz(v):
        return v * 2 if v >= 0 else -v * 2 - 1
    s = (world_seed * 1000003) & 0xFFFFFFFF
    s ^= (zz(cx) * 73856093) & 0xFFFFFFFF
    s ^= (zz(cy) * 19349663) & 0xFFFFFFFF
    x = s or 1
    for _ in range(3):
        x ^= (x << 13) & 0xFFFFFFFF
        x ^= x >> 17
        x ^= (x << 5) & 0xFFFFFFFF
    return [s, x % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),
  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87])],
 [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),
  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #6', [0, 2, -3], [341807727, 72])],
 [('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('regression left shift mask #1', [0, 0, 3], [116097978, 65]),
  ('regression left shift mask #2', [1099511627779, -1, 155], [1640198686, 4]),
  ('regression left shift mask #3', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #4', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #5', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #6', [1099511627779, -1, 3], [44085550, 32])],
 [('origin with zero seed #1', [0, 0, 0], [0, 61]),
  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('regression left shift mask #1', [1099511627779, 1, 1], [179220301, 79]),
  ('regression left shift mask #2', [1099511627779, -374, 0], [3628518806, 87]),
  ('regression left shift mask #3', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #4', [1099511627779, -1, 3], [44085550, 32]),
  ('regression left shift mask #5', [2147483655, -2, 0], [2371752642, 72]),
  ('regression left shift mask #6', [1, -2, 1], [259333738, 52])],
 [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),
  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),
  ('regression left shift mask #1', [0, 2, -3], [341807727, 72]),
  ('regression left shift mask #2', [1099511627779, -1, 3], [44085550, 32]),
  ('regression left shift mask #3', [2147483655, -2, 0], [2371752642, 72]),
  ('regression left shift mask #4', [1, -2, 1], [259333738, 52]),
  ('regression left shift mask #5', [42, -1, -303], [3206913376, 67]),
  ('fault site left shift mask #1', [17601332116874, -1, 1], [1431083645, 95])]]
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
origin with zero seed #1[0, 61][0, 61]Passed
negative neighbour chunk #1[115747491, 56][115747491, 56]Passed
mirrored coordinates #1[294384589, 20][294384589, 20]Passed
regression left shift mask #1[78162845, 87][78162845, 87]Passed
regression left shift mask #2[116097978, 65][116097978, 65]Passed
regression left shift mask #3[1640198686, 4][1640198686, 4]Passed
regression left shift mask #4[179220301, 79][179220301, 79]Passed
regression left shift mask #5[3628518806, 87][3628518806, 87]Passed

SHA-256 / a7a27f20ae28a2f8401e97c285d2f3d181cf59e5e78eb02b4e6e0d1992507e97

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 2026-09-29T14:50:50.218391+00:00.

Case digest / 3af591eadeb6f4244a35fbb304c0581039a0948c92222f2c8447d7e15b08a9fe