Temporal Texture Gravity — Paper A: The Classical Core: Physical-Frame Action and the Stabilized General-Relativity Branch

What if gravity is fundamentally driven by variations in the local pace of time? This paper introduces the classical foundation of Temporal Texture Gravity, a theoretical framework where the local rate of time flow is treated as a dynamic physical field. Rather than inventing new unobserved forces, the model explores what happens when matter and space-time are directly locked to this local time-flow field. To test the physical validity of this concept, the paper subjects the framework to strict gravitational tests: Exact Match with General Relativity: The paper proves that whenever the local flow of time settles into a stable equilibrium, the field equations reduce identically to Einstein’s General Relativity with a cosmological constant. Solar System and Black Hole Safety: It establishes an exact "no-hair" theorem for static astronomical bodies. Stars and black holes do not generate unwanted extra forces in the surrounding space, satisfying precision tests (such as light deflection and planetary orbits) through clean geometric structure rather than fine-tuned parameters. Built-in Physical Stability: The framework demonstrates that the natural expansion of the universe acts as a protective buffer, preventing the physical system from ever reaching mathematical breakdown points. By establishing total compatibility with existing gravitational observations, this paper provides a rigorous, battle-tested classical core for exploring deeper questions in cosmology.