Mathematical Foundations of the Stiffness Field Theory

This work provides the mathematical backbone of the Stiffness Field Cosmol- ogy (SFC), a non-metric framework in which all physical phenomena arise from the dynamical response of a single scalar vacuum field. We formulate a covariant trans- port theory for the vacuum stiffness field K(x) and the associated stiffness-contrast potential ϕ(x), from which amplitude scaling, finite propagation speed, dissipation, and feedback-driven cyclic behavior emerge. Photon-like excitations appear as stable, finite-amplitude oscillatory pulses sup- ported by the stiffness background, while redshift, time drift, and large-scale cos- mic evolution are described as consequences of slow background stiffness evolution rather than spacetime expansion. No FRW metric, geodesic principle, or thermal- equilibrium assumption is employed. This document is intended as a technical reference that formalizes the dynamical structure underlying the phenomenological and observational sectors developed in the companion SFC papers.