spb/prime-mystery-engine
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Python 64.3%
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Thu, Aug 6, 2026 3
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Journal: cycle 5 (10^14) aborted by user; nodes cleaned; predictions remain on record
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Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Paper v4: figures (scaling law, race, histogram, certificate map), Gallagher/Brent/Rankin/Lemke Oliver-Soundararajan math and references; cycle 5 launch infra (SEG env, idempotent workers)
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Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Prime Mystery Engine: cycles 1-4 — certified desert, refuted race conjecture, twice-confirmed correlation scaling law to 10^13
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- Verification-first pipeline (4-role protocol), 37-check validation gate - Cycle 1: C2 race conjecture REFUTED (minimal counterexample 80966861/80966933); certified 260-gap desert at a 25-digit prime (hybrid covering system) - Cycles 2-4: scaling law rho(x)·ln x = c + d/ln x, c = -0.4835(2), d = -1.777; out-of-sample predictions confirmed at 10^12 and 10^13 (lag-1 and lag-2) - Distributed mergeable-statistics scans (exact integer accumulators, bit-identical cross-machine); custom Metal GPU sieve kernel validated byte-identical vs CPU - All 53 published maximal gaps below 10^13 reproduced (OEIS A005250/A002386) - LaTeX paper (13 pp.) with robustness checks and threats-to-validity Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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