The Matthew Carlo Framework: Unified Equation and System Summary

This document provides the complete mathematical definition of the Carlo Framework, including all operators, equations, calculus relationships, system flows, and stability conditions. It presents the full structure of the engine in a single, self‑contained text suitable for researcher review and verification. The document includes the forward page, operator glossary, base equations, calculus appendix, system flow diagram, minimal working example, interaction summary, consistency map, verification checklist, and terminology index. All content is written in plain text for clarity, reproducibility, and compatibility with analytical workflows.