The Volumetric Beat: A Programmatic Discrete-Geometric Parameterization of Gravitational Redshift within a Constant-Density Ontology

This revised version corrects a formal inconsistency in the gravitational redshift relation of the previous version, clarifies the dimensionless definition of the Beat count N, and substantially narrows the scope of the paper. The Volumetric Beat is now presented as a programmatic discrete-geometric parameterization of gravitational redshift, not as a completed theory of gravitation. Additional limitations concerning the phenomenological status of the dilation field, Lorentz invariance, and relation to existing approaches have been added. The references are provided to situate the present proposal within broader discussions on discreteness, emergent geometry, and effective spacetime structures. They are not claimed to be fully integrated into the present framework. The present work should be read as a programmatic research note rather than as a completed physical theory. The author is not a professional physicist. The proposal originates from an ontological intuition concerning time, mass, geometry, and discrete physical change. Its mathematical formulation was developed with AI-assisted support and remains subject to expert verification. The aim of this paper is therefore not to claim a new established theory of gravitation, but to formulate a coherent hypothesis that may be critically examined, corrected, or further developed by qualified physicists.