Dynamic Matrix Logic: Duality, Path Multiplicity, and the Structure of Apparent Paradox

This work presents Version 4 of Dynamic Matrix Logic (DML), focusing on the concepts of duality, path multiplicity, and anti-directional reconstruction within indexed numerical systems.Unlike earlier versions that introduced the foundational structure of DML, this version emphasizes the symmetrical relationship between forward and backward operators and explores how identical target indices can be reconstructed through multiple valid pathways. Particular attention is given to paired operators (such as DML-2/3, DML-4/8, and DML-6/7), highlighting structural duality rather than physical opposition.This manuscript does not propose new physical laws or empirical claims. Instead, it offers a conceptual framework for interpreting apparent paradoxes—such as identity persistence, reversibility, and multi-path convergence—through a deterministic yet non-unique construction process.Version 4 is intended as a focused, interpretative extension of Dynamic Matrix Logic, aimed at readers interested in mathematical structure, logical symmetry, and the emergence of order from multiple valid pathways.