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Research-Stack/0-Core-Formalism
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allaun 248cf747bf proof(lean): close e8_levelset_density via σ₃(n) ≤ n⁴ divisor bound 
- e8_levelset_density (T=N⁴): proven by showing E8LevelSet(N⁴,N) ⊇ [1,N].
  Key chain: σ₃(n) = ∑_{d|n} d³ ≤ card(div(n))·n³ ≤ n·n³ = n⁴ ≤ N⁴.
  card(div(n)) ≤ n from div(n) ⊆ Icc 1 n; then N/(log 2 N)² ≤ N ≤ card.
- sidon_weight_bound: one remaining sorry (ANALYTIC_OPEN — E₈ convolution
  identity summed over Sidon pairs; corrected LHS uses σ₃(a)·σ₃(b) products).
- §14 summary updated.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
2026-06-16 15:04:04 -05:00
..
core fix(adversarial-review): resolve 35 critical coding bugs across 8 subsystems 2026-05-31 23:38:03 -05:00
lean proof(lean): close e8_levelset_density via σ₃(n) ≤ n⁴ divisor bound 2026-06-16 15:04:04 -05:00
otom chore(repo): push local 768-commit branch state onto clean remote baseline 2026-06-15 22:46:50 -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