Breezon's Law of Laws: Supplemental Theorem Framework

Breezon’s Law of Laws: Supplemental Theorem Framework This document provides a mathematically rigorous supplement to the official white paper on Breezon’s Law of Laws (DOI: 10.5281/zenodo.17149944). It formalizes the six-class partition of bounded deterministic recursions into: C (Collapse) Q (Quasi) F (Fractal) L (Limit) D (Divergent) H (Hybrid) Working under compact metric spaces with piecewise C1C^1C1 maps and invariant probability measures, this supplement: States clear system assumptions and ergodic decomposition framework. Defines pointwise observables (Lyapunov exponent, Kolmogorov–Sinai entropy, spectral type, permutation entropy, correlation dimension). Proves mutual exclusivity and exhaustiveness of the classification. Introduces precise structural lemmas (spectral trichotomy, entropy forcing, zero-entropy partition). Provides canonical and higher-dimensional examples (constant maps, irrational rotations, logistic map, Lorenz–63, Hénon map, Lotka–Volterra, gradient descent). Details a falsifiability protocol with hash-locked reproducible artifacts. Adds estimator consistency bounds and operational surrogates connecting abstract ergodic theory to finite-sample classification (\texttt{breezon_master.py}). Significance:This supplement bridges abstract ergodic theory, dynamical systems, and applied computation. It delivers a falsifiable and reproducible classification system with both theoretical proofs and algorithmic surrogates. The framework is closed, exhaustive, and directly testable by adversarial challenge submissions.