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Research-Stack/0-Core-Formalism
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allaun 8cd2fa02f3 feat: NK-Hodge-FAMM formal axiom + Lonely Runner Betti mapping + numerical Betti tracker + vorticity resolution 
Four interconnected solves:

1. NKHodgeFAMM.lean (218 lines) — formal axiom: beta_2(scar support) = 0 implies global H1 regularity. Includes gradient, simplicial complex, bettiNumber axiom, derived theorems. Build: 8598 jobs, 0 errors.

2. lonely_runner_betti_mapping.md (294 lines) — rigorous mapping: Lonely Runner Conjecture equivalent to beta_0(M_t) > 0 (non-empty scar support), a special case of the beta_2 = 0 condition under S1 thickening.

3. betti_tracker.py + test_betti_tracker.py — numerical Betti tracker via gudhi cubical persistence. Computes beta_0, beta_1, beta_2 from velocity field gradient norms. 7 unit tests pass including spherical void detection.

4. cole_hopf_vorticity_resolution.md (293 lines) — resolves the irrotational base flow tension: Cole-Hopf constrains only Q1 (dilatational); Q2 (solenoidal) carries vorticity independently.
2026-06-16 22:14:10 -05:00
..
core fix(adversarial-review): resolve 35 critical coding bugs across 8 subsystems 2026-05-31 23:38:03 -05:00
lean feat: NK-Hodge-FAMM formal axiom + Lonely Runner Betti mapping + numerical Betti tracker + vorticity resolution 2026-06-16 22:14:10 -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