Geometric Theory of Gravity: A Horizon-Induced Framework for Galaxy Rotation and Gravitational Lensing

About this Monograph This document presents the complete fundamental conceptual formulation of the Geometric Theory of Gravity (GTG 3.1 - fundamental). It is intentionally concise. Rather than reproducing every mathematical derivation, it explains the complete logical architecture of the theory, the canonical chain connecting first principles with physical observables, and the methodology required for independent validation. The complete mathematical specification—including formal derivations, theorem chains, dependency graphs, consistency audits and operator definitions—is provided separately in the accompanying GTG 3.1 AI Ingestion Package (JSON Repository). Together, these documents constitute the complete public specification of GTG. Instead of introducing dark matter as an additional matter component, GTG attributes the observed deviations from Newtonian gravity in weak-field regimes to the geometric response of spacetime itself. Within this framework, gravitational phenomena emerge from a single canonical geometric reconstruction rather than from additional unseen sources. The theory develops a continuous logical chain beginning with a fundamental variational principle and proceeding through the field equations, geometric response, effective geometry and predicted gravitational field to measurable astrophysical observables. Within their respective domains of validity, the framework recovers the Newtonian and General Relativistic limits while providing geometric explanations for galaxy rotation curves, the baryonic Tully–Fisher relation, the Radial Acceleration Relation, weak gravitational lensing and related weak-field gravitational phenomena. This monograph provides the conceptual and physical architecture of GTG 3.1, while the accompanying repositories contain its complete formal mathematical specification suitable for independent verification, numerical implementation and AI-assisted analysis.