The Fractal Composition Operator Ψ: Definition, Axiomatic Foundation, and Implementation

Version 1.1 adds:- Python implementation (fractal_operator.py)- LaTeX appendix for integration with QO3/FIO papers The Fractal Composition Operator Ψ formalizes composition in complex systems with memory and scale dependence. This package includes: 1. Notation Note (PDF) — mathematical definition and 5 axioms2. Python module — full implementation with: - fractal_compose(A, B, D, H): main operator - estimate_parameters(): extract D, H from data - verify_axioms(): test axiom satisfaction - regime_transition(): QO3/FIO application3. LaTeX appendix — ready for inclusion in academic papers Reference: Chechelnitsky, I. (2026). The Fractal Composition Operator Ψ. Zenodo. https://doi.org/10.5281/zenodo.18143814