Non-Associative Geometry as Dark Matter: A 3+1D Octonionic Field Theory

This repository contains Octo-Wave v9, an exploratory computational implementation of a non-associative field theory based on octonionic degrees of freedom in full 3+1-dimensional spacetime. The project uses physics-informed neural networks to numerically evolve fields valued in the octonions while explicitly enforcing Euler–Lagrange dynamics, norm stability, and controlled non-associativity governed by exceptional G₂ symmetry. The primary result is the observation that, under a wide range of initial conditions and even under extreme localized perturbations resembling singularities, certain G₂-related invariant combinations remain bounded and information-preserving. Rather than collapsing into associative (complex or quaternionic) subalgebras, the learned solutions remain genuinely octonionic, with most field energy residing in the non-associative components. This suggests a mechanism by which information may be redirected into higher algebraic dimensions instead of being destroyed. The work is computational, speculative, and intended as an open starting point rather than a finished theory. It does not include dynamical gravity and does not claim experimental verification. The goal is to make the construction, assumptions, and measurements transparent so others can reproduce the results, criticize them, improve them, or demonstrate where they fail. This upload is shared in the spirit of open scientific exploration. Feedback, replication attempts, and alternative interpretations are explicitly welcomed.