Octonion Jordan-Shadow Decomposition as a Perception Layer for Sequential Data

Description: A method for applying octonion (hypercomplex, 8-dimensional, non-associative) algebraic decomposition as a general-purpose perception layer over sequential data. Input sequences are encoded as 24-dimensional feature vectors, passed through entropy-gated transponders, projected into octonion pairs, and decomposed via Jordan-Shadow decomposition into three orthogonal components: Jordan (symmetric/convergent intent), Commutator (anti-symmetric/directional momentum), and Associator (non-associative chaos). Two applications are demonstrated: (a) semantic text analysis — extracting structural subtext from natural language without language models, and (b) dynamical systems — regime classification of Collatz hailstone trajectories, revealing that powers of 2 are algebraically most chaotic, Mersenne numbers are smoothest, and the entropy wall between short and long trajectories is inverted. No prior work applies hypercomplex/octonion algebraic decomposition as a perception layer over sequential data. Dependencies: Python >= 3.10, NumPy only.