KO-6 Spectral Solver

A lightweight spectral solver for finite spectral triples of KO-dimension 6, with canonical benchmarks from mathematical physics.

This repository provides a Python implementation of the core solver for finite spectral triples, together with a suite of canonical benchmarks (B1–B3) that validate the numerical scheme independently of any physical model.

Author: Patrice Portemann — ORCID: 0009-0009-4016-8389

Solver Core

The solver implements the update iteration

X_{t+1} = X_t + η(L X_t + M F(X_t) + D(S))

with Strang splitting for stability:

• Half-step dissipative (L, D)
• Full-step conservative M via exact rotation or midpoint rule (symplectic)
• Half-step dissipative (L, D)

This preserves the structure that the spectral triple formalism demands and removes the instability of explicit Euler (item 8 of the dimensional-closure checklist).

Benchmarks

#	Benchmark	What it verifies	Pass criterion
B1	Taylor–Green vortex (2D, damped analytic solution)	Diffusion term L, conservation	L² error < 10⁻⁴ at reference resolution
B2	Sine–Gordon / KdV soliton	Term M F(X), stable localised structures	Soliton propagated without distortion (< 1%) over 10⁴ steps
B3	2D Ising model	Phase transition (Landau formalism)	Tc numerical within ±2% of exact value

Related Repositories

Repository	Role
noetic-machine	Core solver — SU(2) Georgi–Glashow implementation with 5 confirmed predictions (P0–P4)
noetic-applications	14 experimental case studies (P7–P20) applying the finite-core solver
spectral-triple-minimality	Mathematical foundations — 4 theorems and the KO-6 arithmetic law

Citation

@software{portemann2027ko6,
  author = {Portemann, Patrice},
  title  = {KO-6 Spectral Solver: Canonical benchmarks for finite spectral triples},
  year   = {2027},
  url    = {https://github.com/PORTEMANN/ko6-spectral-solver}
}

See CITATION.bib for cross-repository entries.

Quick Start

git clone https://github.com/PORTEMANN/ko6-spectral-solver.git
cd ko6-spectral-solver
pip install -r requirements.txt
pytest tests/
python -m benchmarks.taylor_green --verify
python -m benchmarks.kdv --verify
python -m benchmarks.ising --verify

License

MIT License — see LICENSE.