Free Disturbance Propagation and the Primitive Analog of c in the Scalar Relational UEF Model

This paper examines free disturbance propagation in the scalar relational model of the Universal Energy Field (UEF), proposed within an energistic ontology. The UEF is treated as a pre-spatiotemporal substratum whose stable localized formations may later be described as condensates. The present study focuses on the undisturbed background sector and asks whether small perturbations of the UEF can obey a well-defined propagation law. Starting from the primitive dynamical equation, the analysis fixes the regime parameter, selects a stationary background, linearizes around that background, and uses spectral decomposition of the relational coupling matrix. It is shown that a spectrum alone is not sufficient to define propagation: a regular large-scale relational sector is also required, allowing normal modes to be labelled by an emergent wave number. Under a normalized positive Laplacian-type coupling, the long-wavelength limit yields a relativistic-type dispersion relation. In the gapless sector, the group velocity becomes constant. This constant is interpreted not as the speed of light in pre-given spacetime, but as a primitive precursor of c.