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Research-Stack/0-Core-Formalism
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Devin AI 38b61fc790 feat(lean): add E8Sidon module — Eisenstein coefficient identity and Sidon framework 
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>
2026-06-15 01:06:22 +00:00
..
core fix(adversarial-review): resolve 35 critical coding bugs across 8 subsystems 2026-05-31 23:38:03 -05:00
lean feat(lean): add E8Sidon module — Eisenstein coefficient identity and Sidon framework 2026-06-15 01:06:22 +00:00
otom Add Phys.org May 2026 source intake for bees, biocoatings, THz, and diamond membranes 2026-05-23 19:27:37 -05:00
receipts docs: add bio optical witness living light equations 2026-05-09 20:53:51 -05:00
rust/ftdi_gimbal initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
scripts chore: commit accumulated working tree changes 2026-05-30 00:10:02 -05:00
README.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00

README.md

0-Core-Formalism

Purpose: Formal foundations for the entire Research Stack — Lean modules, bind primitive, Triumvirate consensus, core source.

No external dependencies. All other layers depend on this.

Contents (Target)

Source Destination
0-Core-Formalism/lean/Semantics/ 0-Core-Formalism/lean/Semantics/
core/ 0-Core-Formalism/core/

Concepts

  • bind — State → (State → Action) → State
  • TriumvirateClock — ternary consensus (ADD/PAUSE/SUBTRACT)
  • Builder/Judge/Warden — roles mapped to hardware registers
  • OTOM — Ordered Transformation & Orchestration Model

Build

cd "0-Core-Formalism"
lake build