Symmetry Compliance and a Determinant Octonion Engine

This companion note provides formal verification of three critical properties of "The Living Fold" theoretical physics framework: 1. Symmetry Compliance: Demonstrates that the framework's fixed rules operate within a Standard-Model-compatible symmetry structure (Spin(7,3) ⊃ SU(2)×SU(3))2. Dynamical Admissibility: Shows that gate decisions are invariant under triality flows within the allowed metric class3. Computational Reproducibility: Implements a table-free, determinant-based octonion multiplication engine that passes norm-multiplicativity and alternativity tests Key Features: · Uses fixed, untuned rules: registry variable L ∈ [0,1], coherence kernel f(L) = L(1-L)sin²(πL), and three gate policies· Reproduces nuclear magic number sequence (2, 8, 20, 28, 50, 82, 126, ...) using only public nuclear data (AME2020)· Includes materials sanity check with diamond, silicon, iron, and lead· Registers a falsifiable prediction: pressure-induced conductivity minimum in gold near 260 GPa· Provides complete reproduction package with Python code, datasets, and execution instructions Scientific Status: This is a verification companion - it certifies internal consistency and reproducibility of the framework but does not constitute experimental validation. The registered prediction provides a clear path for experimental falsification/verification. Contents: · Formal symmetry compliance proofs· Triality flow invariance demonstrations· Determinant octonion engine implementation· Standards recovery (nuclear magic numbers)· Materials integrity index analysis· Live prediction with falsification protocol· Complete reproduction code (Python/Jupyter)· Checksum-verified datasets Related Materials:Companion to"The Octomorphic Framework: A Unified Geometric Derivation of Physical Law" (Zenodo 17109790) https://zenodo.org/records/17109790 License: Octomorphic Open License v1.1