Formalizing Freedom: Toward a Mathematical Principle of Maximal Freedom for Temporal Rate Ontology

Temporal Rate Ontology (TRO) proposes primitive succession as the ontological foundation of physical reality, with spacetime geometry and dynamical laws emerging as representational structures. Within this framework, the Principle of Maximal Freedom (PMF) has been introduced as a candidate dynamical principle selecting realized histories from the space of globally consistent successions. To date, however, the PMF has remained conceptually clear but formally schematic. This paper provides the first systematic mathematical formalization of the PMF. We define succession networks as growing directed acyclic graphs, formalize admissible future extensions under global consistency constraints, and introduce candidate freedom functionals Φ(G) measuring the global structural capacity for future branching. We analyze the axiomatic requirements such functionals must satisfy and address the intrinsic self-reference of the PMF through three complementary strategies: horizon-limited extremization, probabilistic selection, and global fixed-point consistency. A minimal worked example demonstrates calculability. The result is not a final dynamical theory, but a precise formal scaffold providing a foundation for investigating how emergent temporal rates, stability, and continuum behavior could arise from pre-geometric dynamics.