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Research-Stack/0-Core-Formalism
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Brandon Schneider 4965029758 feat: integrate May 2026 math papers into Research Stack 
1. Singer Sidon Sets (2605.03274):
   - New SidonSets.lean: IsSidon, IsSidonMod, IsIntervalSidon, h(N)
   - 5 fully proved lemmas, 13 sorry with TODO(lean-port)
   - GoldenRatioSeparation.lean: singer_density_lt_golden (proved)
   - lake build: 3303 jobs, 0 errors

2. Hexagonal lattice + RG (2605.09974):
   - New test_hexagonal_lattice_rg() in unified_rg_tests.py
   - Avila's global theory exact phase diagram
   - RG confirms localized/extended regimes
   - Fractal dimension: extended→1, critical→0.5, localized→0
   - 7 tests, all pass

3. Burgers + Hopf-Cole + Fokas (2605.11788):
   - Added solve_heat_fokas() — unified transform method
   - Added solve_burgers_fokas() — full Burgers via Hopf-Cole + Fokas
   - Added solve_heat_fourier_series() — comparison solver
   - Fokas converges in ~64 quadrature points vs Fourier 2000 terms
   - Hopf-Cole FFT: 8-208x faster than finite differences
2026-05-30 18:16:57 -05:00
..
core Remove legacy Python prototypes superseded by Lean formalization 2026-05-19 15:34:17 +00:00
lean feat: integrate May 2026 math papers into Research Stack 2026-05-30 18:16:57 -05:00
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