GUFT - A Reformulation of the Geometric Unified Framework Theory and its Fundamental Action

This document presents a reformulation of the Geometric Unified Framework Theory (GUFT) based on a covariant action in which a nonlocal scalar degree of freedom is coupled through a curvature-regulated kinetic sector. The previous formulation of GUFT introduced nonlocal gravitational effects through a hysteresis tensor added to the Einstein equations. The present work replaces that description with a variational framework defined by a fundamental action. No claim of phenomenological completeness is made. The purpose of this document is to fix the fundamental action, state the physical motivation, summarize the analytical results obtained so far, and clearly delimit what remains open. Note: This foundational action formulation completely supersedes the earlier phenomenological approach previously published under DOI: 10.5281/zenodo.18375550.