Spectral and Geometric Derivation of the Gravitational Coupling in Grand Consistency Theory
Year: 2026
Type: preprint
Abstract: This paper develops a spectral and geometric derivation of gravitational coupling within Grand Consistency Theory (GCT). The central objective is to obtain the gravitational interaction from the microscopic consistency structure of the theory rather than introduce Newton’s gravitational constant as an independent microscopic input. The construction begins with the Constraint Laplacian defined on a barycentrically refined four-dimensional simplicial carrier. The associated spectral decomposition separates the relevant geometric fluctuation sectors and provides a microscopic curvature response. Refinement drives this response toward a stable fixed-point structure, which is then converted into an extensive geometric curvature response. A boundary-to-geometry stiffness transfer connects the finite microscopic boundary sector with the four-dimensional infrared geometric sector. Normalized-stiffness preservation and infrared isotropy determine the corresponding geometric response within the canonical GCT realization. A simplicial-to-continuum curvature normalization then connects the microscopic spectral construction to the emergent Einstein-Hilbert curvature action. The paper also develops the boundary renormalization sector of GCT. The microscopic boundary stiffness determines an effective boundary coupling, while the symmetry structure of the canonical boundary sector supplies the renormalization coefficient responsible for dimensional transmutation. This produces a hierarchy between the microscopic consistency scale and the emergent cosmological curvature scale. Combining the gravitational and cosmological sectors eliminates the microscopic consistency length and produces a dimensionless gravitational-cosmological closure relation. The resulting construction provides an internally connected route from microscopic consistency geometry to gravitational coupling, cosmological suppression, and an emergent continuum curvature action. The results apply to the canonical realization developed in this work. The paper identifies universality under broader refinement classes, geometric realizations, and boundary dynamics as a central target for further theoretical testing.
Author: Awadelkareem, Saad Osman
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208820269
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