Causal Memory Theory (CMT) proposes a radically discrete, relational, and historical foundation for physical reality. This ontological departure from the continuous structure of conventional physics raises fundamental questions regarding the applicability of classical concepts such as covariance and geometry. In this work, we present a formalized mathematical framework for CMT, investigating the meaning of covariance within the CMT framework and demonstrating how its absence in the traditional form naturally leads to the need for a new mathematical foundation. We introduce the conceptual and formal outlines of a Causal Algebra with Memory, founded on discrete causal networks with weighted dynamics, and formulate the first axioms for an emergent informational topology intrinsic to this framework. We define the central axioms for the discrete causal network and memory accumulation, analyzing the dynamics of memory growth and introducing a detailed model for ”mnemonic condensation” that explains how quantization, and the role of Planck’s reduced constant ℏ, can emerge from a fundamentally continuous accumulation of memory. Saturation and attenuation mechanisms, topological and metric structures, and how apparent criticalities can be resolved through emergent regimes are discussed. Finally, we explore potential avenues for experimental verification of the theory, with the aim of providing a robust mathematical basis for CMT, highlighting its unifying potential and internal consistency. AN UPDATED VERSION WITH NUMERICAL ERROR CORRECTIONS IS AVAILABLE HERE, PENDING THE PUBLICATION ON AUTHOREA OF THE VERSION UPDATED AS OF 08/12/2025: https://zenodo.org/records/17855005