{"abstract":"The origin chunk rolls the same value forever.","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":"Forcing the low bit changes every even seed, not just zero.","family":"w2-procedural-level-generation-constraints-chunk-seed-zero-state-guard","id":"FA-86511","implementations":{"attempt":{"sha256":"3da1a7fc5c87bdb4a861688ec4255b138a6d065f669eb29984b0ce96a6085239","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 | 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  ('partial repair boundary #1', [0, 0, 3], [116097978, 65]),\n  ('partial repair boundary #2', [1099511627779, -1, 155], [1640198686, 4]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [42, -1, 1], [78162845, 87]),\n  ('control #2', [1099511627779, 1, 1], [179220301, 79]),\n  ('control #3', [0, 2, -3], [341807727, 72])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [1099511627779, -374, 0], [3628518806, 87]),\n  ('partial repair boundary #2', [1099511627779, -1, 3], [44085550, 32]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1099511627779, 1, 1], [179220301, 79]),\n  ('control #2', [0, 2, -3], [341807727, 72]),\n  ('control #3', [17601332116874, -1, 1], [1431083645, 95])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [2147483655, -2, 0], [2371752642, 72]),\n  ('partial repair boundary #2', [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  ('control #1', [0, -22, 3], [3147860005, 93]),\n  ('control #2', [3799470242044, -1, 0], [3783972265, 71]),\n  ('control #3', [0, 2, -405], [3029395203, 17])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [42, -1, -303], [3206913376, 67]),\n  ('partial repair boundary #2', [1099511627779, -1, 0], [72037012, 17]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1099511627779, -1, -450], [144497865, 51]),\n  ('control #2', [42, 1, -1], [191526619, 48]),\n  ('control #3', [1099511627779, -2, -3], [148723909, 87])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [1099511627779, -2, 1], [257399520, 7]),\n  ('partial repair boundary #2', [34120951125993, -2, 3], [4279618902, 0]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1, 1, 3], [237578563, 58]),\n  ('control #2', [1099511627779, 420, 1], [1941083871, 61]),\n  ('control #3', [2147483655, -2, -3], [2291814873, 91])]]\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":"6ebaa149e49538662bbc66cc250c867414d39658d6621e83a014b2744a30749b","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\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  ('partial repair boundary #1', [0, 0, 3], [116097978, 65]),\n  ('partial repair boundary #2', [1099511627779, -1, 155], [1640198686, 4]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [42, -1, 1], [78162845, 87]),\n  ('control #2', [1099511627779, 1, 1], [179220301, 79]),\n  ('control #3', [0, 2, -3], [341807727, 72])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [1099511627779, -374, 0], [3628518806, 87]),\n  ('partial repair boundary #2', [1099511627779, -1, 3], [44085550, 32]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1099511627779, 1, 1], [179220301, 79]),\n  ('control #2', [0, 2, -3], [341807727, 72]),\n  ('control #3', [17601332116874, -1, 1], [1431083645, 95])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [2147483655, -2, 0], [2371752642, 72]),\n  ('partial repair boundary #2', [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  ('control #1', [0, -22, 3], [3147860005, 93]),\n  ('control #2', [3799470242044, -1, 0], [3783972265, 71]),\n  ('control #3', [0, 2, -405], [3029395203, 17])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [42, -1, -303], [3206913376, 67]),\n  ('partial repair boundary #2', [1099511627779, -1, 0], [72037012, 17]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1099511627779, -1, -450], [144497865, 51]),\n  ('control #2', [42, 1, -1], [191526619, 48]),\n  ('control #3', [1099511627779, -2, -3], [148723909, 87])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [1099511627779, -2, 1], [257399520, 7]),\n  ('partial repair boundary #2', [34120951125993, -2, 3], [4279618902, 0]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1, 1, 3], [237578563, 58]),\n  ('control #2', [1099511627779, 420, 1], [1941083871, 61]),\n  ('control #3', [2147483655, -2, -3], [2291814873, 91])]]\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":"7f0cdf97bb6a47e4d3fdd2d3ebe27fa4b36d973db53067d53f5093a0a4307561","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  ('partial repair boundary #1', [0, 0, 3], [116097978, 65]),\n  ('partial repair boundary #2', [1099511627779, -1, 155], [1640198686, 4]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [42, -1, 1], [78162845, 87]),\n  ('control #2', [1099511627779, 1, 1], [179220301, 79]),\n  ('control #3', [0, 2, -3], [341807727, 72])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [1099511627779, -374, 0], [3628518806, 87]),\n  ('partial repair boundary #2', [1099511627779, -1, 3], [44085550, 32]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1099511627779, 1, 1], [179220301, 79]),\n  ('control #2', [0, 2, -3], [341807727, 72]),\n  ('control #3', [17601332116874, -1, 1], [1431083645, 95])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [2147483655, -2, 0], [2371752642, 72]),\n  ('partial repair boundary #2', [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  ('control #1', [0, -22, 3], [3147860005, 93]),\n  ('control #2', [3799470242044, -1, 0], [3783972265, 71]),\n  ('control #3', [0, 2, -405], [3029395203, 17])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [42, -1, -303], [3206913376, 67]),\n  ('partial repair boundary #2', [1099511627779, -1, 0], [72037012, 17]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1099511627779, -1, -450], [144497865, 51]),\n  ('control #2', [42, 1, -1], [191526619, 48]),\n  ('control #3', [1099511627779, -2, -3], [148723909, 87])],\n [('origin with zero seed #1', [0, 0, 0], [0, 61]),\n  ('partial repair boundary #1', [1099511627779, -2, 1], [257399520, 7]),\n  ('partial repair boundary #2', [34120951125993, -2, 3], [4279618902, 0]),\n  ('negative neighbour chunk #1', [42, -1, 0], [115747491, 56]),\n  ('mirrored coordinates #1', [7, 3, 5], [294384589, 20]),\n  ('control #1', [1, 1, 3], [237578563, 58]),\n  ('control #2', [1099511627779, 420, 1], [1941083871, 61]),\n  ('control #3', [2147483655, -2, -3], [2291814873, 91])]]\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-zero-state-guard","generated_at":"2026-09-29T14:50:50.198472+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 = s or 1` at the zero state guard step.","root_cause":"A zero seed is fed to xorshift, which stays at zero.","sha256":"0bfd5531231e25c07c467793932b2c6af510c8589810c190bd699239b5d6ffa8","title":"Chunk seed derivation: Zero seed locks the generator · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.935,"exit_code":1,"observations":[{"actual":[0,61],"check":"origin with zero seed #1","expected":[0,61],"passed":true},{"actual":[116097978,84],"check":"partial repair boundary #1","expected":[116097978,65],"passed":false},{"actual":[1640198686,49],"check":"partial repair boundary #2","expected":[1640198686,4],"passed":false},{"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":"control #1","expected":[78162845,87],"passed":true},{"actual":[179220301,79],"check":"control #2","expected":[179220301,79],"passed":true},{"actual":[341807727,72],"check":"control #3","expected":[341807727,72],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"origin with zero seed #1\", \"actual\": [0, 61], \"expected\": [0, 61], \"passed\": true}, {\"check\": \"partial repair boundary #1\", \"actual\": [116097978, 84], \"expected\": [116097978, 65], \"passed\": false}, {\"check\": \"partial repair boundary #2\", \"actual\": [1640198686, 49], \"expected\": [1640198686, 4], \"passed\": false}, {\"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\": \"control #1\", \"actual\": [78162845, 87], \"expected\": [78162845, 87], \"passed\": true}, {\"check\": \"control #2\", \"actual\": [179220301, 79], \"expected\": [179220301, 79], \"passed\": true}, {\"check\": \"control #3\", \"actual\": [341807727, 72], \"expected\": [341807727, 72], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.513,"exit_code":1,"observations":[{"actual":[0,0],"check":"origin with zero seed #1","expected":[0,61],"passed":false},{"actual":[116097978,65],"check":"partial repair boundary #1","expected":[116097978,65],"passed":true},{"actual":[1640198686,4],"check":"partial repair boundary #2","expected":[1640198686,4],"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":"control #1","expected":[78162845,87],"passed":true},{"actual":[179220301,79],"check":"control #2","expected":[179220301,79],"passed":true},{"actual":[341807727,72],"check":"control #3","expected":[341807727,72],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"origin with zero seed #1\", \"actual\": [0, 0], \"expected\": [0, 61], \"passed\": false}, {\"check\": \"partial repair boundary #1\", \"actual\": [116097978, 65], \"expected\": [116097978, 65], \"passed\": true}, {\"check\": \"partial repair boundary #2\", \"actual\": [1640198686, 4], \"expected\": [1640198686, 4], \"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\": \"control #1\", \"actual\": [78162845, 87], \"expected\": [78162845, 87], \"passed\": true}, {\"check\": \"control #2\", \"actual\": [179220301, 79], \"expected\": [179220301, 79], \"passed\": true}, {\"check\": \"control #3\", \"actual\": [341807727, 72], \"expected\": [341807727, 72], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.052,"exit_code":0,"observations":[{"actual":[0,61],"check":"origin with zero seed #1","expected":[0,61],"passed":true},{"actual":[116097978,65],"check":"partial repair boundary #1","expected":[116097978,65],"passed":true},{"actual":[1640198686,4],"check":"partial repair boundary #2","expected":[1640198686,4],"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":"control #1","expected":[78162845,87],"passed":true},{"actual":[179220301,79],"check":"control #2","expected":[179220301,79],"passed":true},{"actual":[341807727,72],"check":"control #3","expected":[341807727,72],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"origin with zero seed #1\", \"actual\": [0, 61], \"expected\": [0, 61], \"passed\": true}, {\"check\": \"partial repair boundary #1\", \"actual\": [116097978, 65], \"expected\": [116097978, 65], \"passed\": true}, {\"check\": \"partial repair boundary #2\", \"actual\": [1640198686, 4], \"expected\": [1640198686, 4], \"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\": \"control #1\", \"actual\": [78162845, 87], \"expected\": [78162845, 87], \"passed\": true}, {\"check\": \"control #2\", \"actual\": [179220301, 79], \"expected\": [179220301, 79], \"passed\": true}, {\"check\": \"control #3\", \"actual\": [341807727, 72], \"expected\": [341807727, 72], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}