AxCore Informational Bridge Model: A Complete Framework of Bounded Informational Dynamics

AxCore is a complete, self-contained mathematical framework for the dynamics of any system that processes information under finite resources. The framework establishes that a system operating under finite energy and finite compute cannot remain indefinitely exploratory. Energy scarcity yields an exact dispersion-contraction law. Sequential causality enters as a structural resource. Prior mismatch carries a thermodynamic cost. These are derived from the mathematics of bounded sequential operation under a discrete action principle. Organized around Theorem 1 (Thermodynamic Decoherence Bridge) and the unifying metric of route cost, this framework bridges quantum decoherence, thermodynamics, emergent gravity, time dilation, and the mass ladder.