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Brandon Schneider 61ee34b58f feat(lean): genus-1 torus carrier — winding numbers, surface braids, and C1/C2 lane formalization 
Three interconnected additions resolving the genus-1 vs genus-3 topology
question through structural derivation from the gap-6 prime lane pair:

(a) Burgers-PhiNUVMAP bridge (PistSimulation.lean):
  • `burgersSpatialWinding`: net circulation Σu[i]·dx around torus spatial cycle
  • `burgersTemporalWinding`: t/dt phase-step count (quarter-turns of T²)
  • dims 14-15 now hold (w_space, w_time) instead of reserved zeros
  • Eval witnesses: smooth parabola w_space=10, shock step w_space=4

(b) Torus surface-braid enrichment (BraidEigensolid.lean):
  • `TorusWinding` structure with a, b cycle counts (spatial + phase)
  • `TorusBraidCarrier`: wraps BraidState with torus topology
  • `torusCrossStep`: crossing step with phase winding increment
  • Each crossStep round at step_count mod 4 = 0 adds one phase increment
  • Preserves all existing eigensolid_convergence / receipt_invertible proofs

(c) Genus1TopologyMetaprobe.lean (new module):
  • χ = 0, b₁ = 2 theorems for genus 1
  • C1 = 6k−1 / C2 = 6k+1 lane predicates and gap-6 pair structure
  • Torsion-as-time: 4 steps = 1 torus wrap, phaseAngle in Q16_16 turns
  • Temperature-entropy reciprocity T·S = 1 for single handle
  • Symplectic intersection ω(a,b) = +1, ω(b,a) = −1
  • Surface braid group on T²: winding generators a, b with commutator relation

Build: lake build Semantics green at 3541 jobs.

Generated with [Devin](https://cli.devin.ai/docs)

Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
2026-05-21 01:06:37 -05:00
..
core Remove legacy Python prototypes superseded by Lean formalization 2026-05-19 15:34:17 +00:00
lean feat(lean): genus-1 torus carrier — winding numbers, surface braids, and C1/C2 lane formalization 2026-05-21 01:06:37 -05:00
otom docs: add external research import maps 2026-05-20 18:41:21 -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
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