{ "generatedAt": "2026-10-08T09:27:47.298Z", "startedAt": "2026-10-08T09:27:11.882Z", "mathVersion": "demo-curved-rain-inclusive-97-12-v6", "roundsPerRegion": 100000000, "totalIndependentPaths": 300000000, "multiplierTargets": [ 1.1, 1.25, 1.45, 1.75, 2.1, 2.6, 3.25, 4.1, 5.2, 6.6, 8.2, 10 ], "sourceHashes": { "src/game/demo.ts": "ae96f2d002fba56cf7800f59007f47442f0c6551d42149088eb93cea777f4f1f", "src/game/curved-math.ts": "4b0b9a8520b2e77ae2f69a12378639c6204f7754c18a2bd47f2ccda9c52e394e", "scripts/curved-payout-analysis.ts": "2cf7f00fbd7a2bd48fe04325732a3c1254248ff6210f17f2fedc4cc72f425ff0" }, "auditSeed": "cclg-curved-three-regions-2026-10-08-v1", "command": "npx tsx scripts/curved-payout-analysis.ts 100000000 cclg-curved-three-regions-2026-10-08-v1", "method": { "strategy": "Start one 10-credit round; evaluate cashout after each specified successful steal. Losses return zero. Gross return includes stake. Rare earlier 10x automatic settlements are retained by later stopping policies.", "sharedPaths": "Each region has 100M independently seeded full paths when run with 100000000. The 12 stopping-policy rows reuse those paths and are correlated. Regions use different SHA-256-derived AES keys. This is 300M paths, not 3.6B independent policy runs.", "sampler": "AES-256-CTR with SHA-256(seed + NUL + region) key, zero IV, zero plaintext, 1 MiB chunks, little-endian Uint32 words; audit-only deterministic PRNG. Browser RNG remains crypto.getRandomValues.", "transitions": "Direct success Uint32 draw; after successful sub-cap ordinary result one Rain draw; only on Rain a size draw. Integer cutoff = ceil(threshold * 2^32), copied from imported curved probability functions. No draws after failure or cap.", "rounding": "Gross return rounded to nearest cent using imported payoutFor; half cents round up. Simulation stake10 credits. Exact state enumeration also covers1,1.1,2.5,10,100 credits.", "confidence": "Normal-approximation two-sided95% Monte Carlo intervals per row. Bonferroni simultaneous95% intervals across36 region/step RTP comparisons. Correlated policy rows do not invalidate Bonferroni. The pooled table is descriptive and is not included in that36-test family.", "familywiseComparisons": 36, "z95": 1.9599639861189817, "zFamilywise95": 3.1969502266105976, "scope": "Validates this mathematical model and implementation mapping; not production entropy certification, accredited laboratory testing, platform security, payout solvency, regulation, or real-money approval. Free-play play-credit RTP is the same gross-credits-returned / credits-staked measure." }, "quantizedRain": { "triggerWords": 30064772, "range": 4294967296, "triggerProbability": 0.007000000216066837, "smallBoundaryWords": 3221225472, "mediumBoundaryWords": 4080218932, "successBranches": [ { "extraHundredths": 0, "probability": 0.9929999997839332 }, { "extraHundredths": 5, "probability": 0.005250000162050128 }, { "extraHundredths": 10, "probability": 0.001400000044517219 }, { "extraHundredths": 20, "probability": 0.0003500000094994902 } ] }, "engineValidation": { "passed": true, "boundaryCases": 9080, "randomPaths": 5000, "randomStepsChecked": 28731, "payoutChecks": 9080, "boundaryScenarios": [ "caught exactly at survival boundary", "ordinary at Rain boundary", "Rain size boundary 0", "Rain size boundary 3221225471", "Rain size boundary 3221225472", "Rain size boundary 4080218931", "Rain size boundary 4080218932", "Rain size boundary 4294967295", "cap skips Rain draws" ], 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