{"abstract":"Chunk contents differ between 32-bit and arbitrary-precision builds.","category":"Procedural level generation constraints","checks":8,"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].","evaluation_group":"w2-procedural-level-generation-constraints-chunk-seed","failed_approach":"A 28-bit mask truncates valid state bits.","family":"w2-procedural-level-generation-constraints-chunk-seed-left-shift-mask","id":"FA-86516","implementations":{"attempt":{"sha256":"6598b75e4d7409a619b0bf9486dd8123963976399c1905828a7c52fea22796c9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(world_seed, cx, cy):\n    def zz(v):\n        return v * 2 if v >= 0 else -v * 2 - 1\n    s = (world_seed * 1000003) & 0xFFFFFFFF\n    s ^= (zz(cx) * 73856093) & 0xFFFFFFFF\n    s ^= (zz(cy) * 19349663) & 0xFFFFFFFF\n    x = s or 1\n    for _ in range(3):\n        x ^= (x << 13) & 0xFFFFFFF\n        x ^= x >> 17\n        x ^= (x << 5) & 0xFFFFFFFF\n    return [s, x % 100]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),\n  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87])],\n [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),\n  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #6', [0, 2, -3], [341807727, 72])],\n [('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('regression left shift mask #1', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #2', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #3', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #4', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #5', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #6', [1099511627779, -1, 3], [44085550, 32])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('regression left shift mask #1', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #2', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #3', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #4', [1099511627779, -1, 3], [44085550, 32]),\n  ('regression left shift mask #5', [2147483655, -2, 0], [2371752642, 72]),\n  ('regression left shift mask #6', [1, -2, 1], [259333738, 52])],\n [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #2', [1099511627779, -1, 3], [44085550, 32]),\n  ('regression left shift mask #3', [2147483655, -2, 0], [2371752642, 72]),\n  ('regression left shift mask #4', [1, -2, 1], [259333738, 52]),\n  ('regression left shift mask #5', [42, -1, -303], [3206913376, 67]),\n  ('fault site left shift mask #1', [17601332116874, -1, 1], [1431083645, 95])]]\nfor label, args, expected in cases[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"5ca06a93e079ac57ed3df2054ad77fb06de9562f0ebe0290a31dc86e2ebfa6ba","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(world_seed, cx, cy):\n    def zz(v):\n        return v * 2 if v >= 0 else -v * 2 - 1\n    s = (world_seed * 1000003) & 0xFFFFFFFF\n    s ^= (zz(cx) * 73856093) & 0xFFFFFFFF\n    s ^= (zz(cy) * 19349663) & 0xFFFFFFFF\n    x = s or 1\n    for _ in range(3):\n        x ^= x << 13\n        x ^= x >> 17\n        x ^= (x << 5) & 0xFFFFFFFF\n    return [s, x % 100]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),\n  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87])],\n [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),\n  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #6', [0, 2, -3], [341807727, 72])],\n [('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('regression left shift mask #1', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #2', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #3', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #4', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #5', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #6', [1099511627779, -1, 3], [44085550, 32])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('regression left shift mask #1', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #2', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #3', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #4', [1099511627779, -1, 3], [44085550, 32]),\n  ('regression left shift mask #5', [2147483655, -2, 0], [2371752642, 72]),\n  ('regression left shift mask #6', [1, -2, 1], [259333738, 52])],\n [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #2', [1099511627779, -1, 3], [44085550, 32]),\n  ('regression left shift mask #3', [2147483655, -2, 0], [2371752642, 72]),\n  ('regression left shift mask #4', [1, -2, 1], [259333738, 52]),\n  ('regression left shift mask #5', [42, -1, -303], [3206913376, 67]),\n  ('fault site left shift mask #1', [17601332116874, -1, 1], [1431083645, 95])]]\nfor label, args, expected in cases[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"a7a27f20ae28a2f8401e97c285d2f3d181cf59e5e78eb02b4e6e0d1992507e97","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(world_seed, cx, cy):\n    def zz(v):\n        return v * 2 if v >= 0 else -v * 2 - 1\n    s = (world_seed * 1000003) & 0xFFFFFFFF\n    s ^= (zz(cx) * 73856093) & 0xFFFFFFFF\n    s ^= (zz(cy) * 19349663) & 0xFFFFFFFF\n    x = s or 1\n    for _ in range(3):\n        x ^= (x << 13) & 0xFFFFFFFF\n        x ^= x >> 17\n        x ^= (x << 5) & 0xFFFFFFFF\n    return [s, x % 100]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),\n  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87])],\n [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [42, -1, 1], [78162845, 87]),\n  ('regression left shift mask #2', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #3', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #4', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #5', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #6', [0, 2, -3], [341807727, 72])],\n [('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('regression left shift mask #1', [0, 0, 3], [116097978, 65]),\n  ('regression left shift mask #2', [1099511627779, -1, 155], [1640198686, 4]),\n  ('regression left shift mask #3', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #4', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #5', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #6', [1099511627779, -1, 3], [44085550, 32])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('regression left shift mask #1', [1099511627779, 1, 1], [179220301, 79]),\n  ('regression left shift mask #2', [1099511627779, -374, 0], [3628518806, 87]),\n  ('regression left shift mask #3', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #4', [1099511627779, -1, 3], [44085550, 32]),\n  ('regression left shift mask #5', [2147483655, -2, 0], [2371752642, 72]),\n  ('regression left shift mask #6', [1, -2, 1], [259333738, 52])],\n [('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('regression left shift mask #1', [0, 2, -3], [341807727, 72]),\n  ('regression left shift mask #2', [1099511627779, -1, 3], [44085550, 32]),\n  ('regression left shift mask #3', [2147483655, -2, 0], [2371752642, 72]),\n  ('regression left shift mask #4', [1, -2, 1], [259333738, 52]),\n  ('regression left shift mask #5', [42, -1, -303], [3206913376, 67]),\n  ('fault site left shift mask #1', [17601332116874, -1, 1], [1431083645, 95])]]\nfor label, args, expected in cases[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-procedural-level-generation-constraints-chunk-seed-left-shift-mask","generated_at":"2026-09-29T14:50:50.218391+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"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.","repair":"Restore `x ^= (x << 13) & 0xFFFFFFFF` at the left shift mask step.","root_cause":"The first left shift is not masked to 32 bits.","sha256":"3af591eadeb6f4244a35fbb304c0581039a0948c92222f2c8447d7e15b08a9fe","title":"Chunk seed derivation: Xorshift state grows beyond 32 bits · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.451,"exit_code":1,"observations":[{"actual":[0,5],"check":"origin with zero seed #1","expected":[0,61],"passed":false},{"actual":[115747491,99],"check":"negative neighbour chunk #1","expected":[115747491,56],"passed":false},{"actual":[294384589,76],"check":"mirrored coordinates #1","expected":[294384589,20],"passed":false},{"actual":[78162845,80],"check":"regression left shift mask #1","expected":[78162845,87],"passed":false},{"actual":[116097978,8],"check":"regression left shift mask #2","expected":[116097978,65],"passed":false},{"actual":[1640198686,52],"check":"regression left shift mask #3","expected":[1640198686,4],"passed":false},{"actual":[179220301,24],"check":"regression left shift mask #4","expected":[179220301,79],"passed":false},{"actual":[3628518806,30],"check":"regression left shift mask #5","expected":[3628518806,87],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"origin with zero seed #1\", \"actual\": [0, 5], \"expected\": [0, 61], \"passed\": false}, {\"check\": \"negative neighbour chunk #1\", \"actual\": [115747491, 99], \"expected\": [115747491, 56], \"passed\": false}, {\"check\": \"mirrored coordinates #1\", \"actual\": [294384589, 76], \"expected\": [294384589, 20], \"passed\": false}, {\"check\": \"regression left shift mask #1\", \"actual\": [78162845, 80], \"expected\": [78162845, 87], \"passed\": false}, {\"check\": \"regression left shift mask #2\", \"actual\": [116097978, 8], \"expected\": [116097978, 65], \"passed\": false}, {\"check\": \"regression left shift mask #3\", \"actual\": [1640198686, 52], \"expected\": [1640198686, 4], \"passed\": false}, {\"check\": \"regression left shift mask #4\", \"actual\": [179220301, 24], \"expected\": [179220301, 79], \"passed\": false}, {\"check\": \"regression left shift mask #5\", \"actual\": [3628518806, 30], \"expected\": [3628518806, 87], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.216,"exit_code":1,"observations":[{"actual":[0,21],"check":"origin with zero seed #1","expected":[0,61],"passed":false},{"actual":[115747491,8],"check":"negative neighbour chunk #1","expected":[115747491,56],"passed":false},{"actual":[294384589,4],"check":"mirrored coordinates #1","expected":[294384589,20],"passed":false},{"actual":[78162845,83],"check":"regression left shift mask #1","expected":[78162845,87],"passed":false},{"actual":[116097978,46],"check":"regression left shift mask #2","expected":[116097978,65],"passed":false},{"actual":[1640198686,28],"check":"regression left shift mask #3","expected":[1640198686,4],"passed":false},{"actual":[179220301,27],"check":"regression left shift mask #4","expected":[179220301,79],"passed":false},{"actual":[3628518806,79],"check":"regression left shift mask #5","expected":[3628518806,87],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"origin with zero seed #1\", \"actual\": [0, 21], \"expected\": [0, 61], \"passed\": false}, {\"check\": \"negative neighbour chunk #1\", \"actual\": [115747491, 8], \"expected\": [115747491, 56], \"passed\": false}, {\"check\": \"mirrored coordinates #1\", \"actual\": [294384589, 4], \"expected\": [294384589, 20], \"passed\": false}, {\"check\": \"regression left shift mask #1\", \"actual\": [78162845, 83], \"expected\": [78162845, 87], \"passed\": false}, {\"check\": \"regression left shift mask #2\", \"actual\": [116097978, 46], \"expected\": [116097978, 65], \"passed\": false}, {\"check\": \"regression left shift mask #3\", \"actual\": [1640198686, 28], \"expected\": [1640198686, 4], \"passed\": false}, {\"check\": \"regression left shift mask #4\", \"actual\": [179220301, 27], \"expected\": [179220301, 79], \"passed\": false}, {\"check\": \"regression left shift mask #5\", \"actual\": [3628518806, 79], \"expected\": [3628518806, 87], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.206,"exit_code":0,"observations":[{"actual":[0,61],"check":"origin with zero seed #1","expected":[0,61],"passed":true},{"actual":[115747491,56],"check":"negative neighbour chunk #1","expected":[115747491,56],"passed":true},{"actual":[294384589,20],"check":"mirrored coordinates #1","expected":[294384589,20],"passed":true},{"actual":[78162845,87],"check":"regression left shift mask #1","expected":[78162845,87],"passed":true},{"actual":[116097978,65],"check":"regression left shift mask #2","expected":[116097978,65],"passed":true},{"actual":[1640198686,4],"check":"regression left shift mask #3","expected":[1640198686,4],"passed":true},{"actual":[179220301,79],"check":"regression left shift mask #4","expected":[179220301,79],"passed":true},{"actual":[3628518806,87],"check":"regression left shift mask #5","expected":[3628518806,87],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"origin with zero seed #1\", \"actual\": [0, 61], \"expected\": [0, 61], \"passed\": true}, {\"check\": \"negative neighbour chunk #1\", \"actual\": [115747491, 56], \"expected\": [115747491, 56], \"passed\": true}, {\"check\": \"mirrored coordinates #1\", \"actual\": [294384589, 20], \"expected\": [294384589, 20], \"passed\": true}, {\"check\": \"regression left shift mask #1\", \"actual\": [78162845, 87], \"expected\": [78162845, 87], \"passed\": true}, {\"check\": \"regression left shift mask #2\", \"actual\": [116097978, 65], \"expected\": [116097978, 65], \"passed\": true}, {\"check\": \"regression left shift mask #3\", \"actual\": [1640198686, 4], \"expected\": [1640198686, 4], \"passed\": true}, {\"check\": \"regression left shift mask #4\", \"actual\": [179220301, 79], \"expected\": [179220301, 79], \"passed\": true}, {\"check\": \"regression left shift mask #5\", \"actual\": [3628518806, 87], \"expected\": [3628518806, 87], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}