Mathematical Foundations of a Theory of Causal Graphs with Dynamic Trace

This document presents a mathematical formalism for the study of Causal Graphs with Dynamic Trace (GCTD). It defines their fundamental structures, their algebraic and topological properties, and explores the intrinsic dynamics of accumulation, dissipation, and generation of "novelty" of the causal trace. The goal is to establish the foundations for a new field of research in discrete mathematics and network theory, with potential intersections with category theory, algebraic topology, and complex dynamical systems. A particular focus is placed on structural covariance properties and the emergence of aggregate concepts such as measures of "volume," "depth," "entropy," and "expansion" from this discrete structure.