Quantum Spacetime Geometry: A Standalone Exploratory Framework for Finite QFT and Non-Perturbative Yang-Mills Structure

This standalone document provides a pedagogical, self-contained introduction to Quantum Spacetime Geometry (QSG)—an exploratory framework that models ultraviolet finiteness and non-perturbative Yang-Mills phenomena via spatial ball averaging, non-commutative momentum geometry, and entire regularizing operators. Designed for first-time readers, this manuscript contains explicit notation definitions, comprehensive step-by-step proofs of coincident propagator convergence, one-loop bubble integrals, non-Abelian curvature derivations, and BRST consistency. We conclude by exploring a candidate mechanism for non-perturbative Yang-Mills mass generation, outlining how spatial form factors generate linear Wilson loop behavior and effective glueball scales. *Author DisclaimerAll underlying concepts, frameworks, and core research directions are the original work of the author. Generative AI tools were used strictly for assistance in manuscript drafting, code generation, and figure preparation. All theoretical formulations and mathematical proofs included herein are unverified AI-generated drafts shared as preliminary proposals for discussion and community review.