Part XXVII: Geometric Vortex Loop Gravity - A Geometric Mass Gap Theorem for Sobolev Mappings in Four Dimensions
Year: 2026
Type: article
Abstract: This paper establishes a geometric mass gap in a class of Sobolev mappings between compact, oriented manifolds of equal dimension. The model is built on a discrete backbone Λ₄ whose projection structure produces eight activation variants, each encoding a distinct geometric response mode. The analytic proof uses a quantitative degree–energy inequality for Sobolev maps, linking the topological invariant deg(F) to the gradient norm. This inequality shows that any configuration with nonzero degree must incur irreducible geometric distortion, enforcing a positive lower bound on the energy in every nontrivial sector. The mass gap follows from the energy decomposition and holds uniformly across all activation variants. The argument is purely geometric and topological, with no physical or field-theoretic claims.
Author: O'Kroley, Colin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203697387
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