ALADIN ∞ ℂ(t): G₂ An Entropy-Regularized GLM-MHD Solver with G₂-Inspired Octonion Fields

This upload presents the ALADIN-G₂ computational framework, a GPU-accelerated numerical solver for magnetohydrodynamics (MHD) implemented in CuPy and CUDA. The code extends a standard GLM-MHD formulation with additional auxiliary fields inspired by octonion algebra and G₂-structured symbolic interactions. The solver includes: A 3D GLM-MHD evolution system with divergence cleaning (ψ-field) GPU-accelerated volume operator kernel (CUDA RawKernel) High-order time integration (SSP-RK3) Positivity-preserving and stabilization limiters Auxiliary “octonion-inspired” fields for structured nonlinear coupling Optional entropy-motivated dissipation and variational regularization terms The goal of this framework is to explore alternative structured regularization strategies in plasma simulation, rather than to propose a physically complete or experimentally validated model. Content This repository includes: Python/CuPy implementation of the solver CUDA kernel for volume operator computation Octonion-inspired algebraic utilities Time-stepping and stabilization routines Example configuration for small-scale simulations Methodological Notes The formulation combines: Classical ideal MHD conservation laws GLM divergence cleaning Artificial dissipation for numerical stability Additional nonlinear correction terms based on: scalar 3-form φ(O) associator norm |[O,O,O]| gradient-like penalty terms (optional) These additions are numerical and structural in nature, and should not be interpreted as a first-principles physical theory of G₂ geometry or octonion physics. Intended Use This code is intended for: Experimental numerical physics research GPU kernel design exploration Testing stability effects of algebraic augmentation in PDE systems Educational and prototyping purposes in computational MHD It is not intended as a production-grade astrophysical solver or validated physical model. Requirements Python ≥ 3.10 CuPy (CUDA-compatible GPU required) NumPy NVIDIA GPU (tested on A100-class hardware) Notes on Reproducibility This implementation is a research prototype. Results may depend on: grid resolution (Ni) stabilization parameters (α, λ) boundary conditions GPU architecture Users are encouraged to treat outputs as qualitative behavior experiments rather than physical predictions. License MIT (code reuse allowed)