mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-08-13 19:40:34 +00:00
38b61fc790
New module Semantics.E8Sidon formalizes the connection between E₈ lattice theta series, Eisenstein series identities, and Sidon set theory. Definitions (all proven/computable): - sigma3, sigma7: divisor sum functions via Mathlib ArithmeticFunction.sigma - convolutionLHS: Cauchy product convolution of σ₃ - IsSidonSet, sidon8, sidonSlack, additiveEnergy, r8 - bernoulli_four, bernoulli_eight: B₄ = B₈ = -1/30 (native_decide) - E4_normalization, E8_normalization: -(2k/B_k) = 240, 480 Computational witnesses (#eval): - σ₃(1..4) = 1, 9, 28, 73 - σ₇(1..3) = 1, 129, 2188 - E₄²=E₈ identity verified for n=2,3,4: (61920,61920), (1050240,1050240), (7926240,7926240) - sidon8.card = 8, sidonSlack = 128 Sorry inventory (12 total, all with TODO(lean-port)): - E4_sq_eq_E8_coeff: blocked on Mathlib missing valence formula / dim M₈=1 - Sidon theory: energy bound, collision theory, greedy extraction (4) - E₈ lattice: r8_via_sigma3, r8_one, levelset density (3) - Conditional: Singer improvement, Erdős bound, fiber partition (3) Axiom (1): e8_additive_completeness (open problem) Build: 3572 jobs, 0 errors (lake build) Co-Authored-By: Allaun Silverfox <bigdataiscoming+9i37y6j2@protonmail.com> |
||
|---|---|---|
| .. | ||
| conversions/hardware | ||
| external/OTOM | ||
| LeanGPT | ||
| Semantics | ||
| CHAIN_ALL_REVIEW_REPORT.md | ||