Temporal Texture Gravity — Paper C: Vacuum Structure and Discrete Scale Invariance

What if one of the greatest embarrassments in modern physics—the massive, $10^{50}$-fold overestimation of quantum vacuum energy—could be resolved through structural geometry rather than fine-tuned numbers? This paper explores the quantum vacuum and scale-invariant features of Temporal Texture Gravity. It focuses on how a multi-scale hierarchy of temporal fields interacts with the energy of empty space, tackling the infamous "vacuum catastrophe" where standard quantum field theory predicts an energy density vastly larger than what astronomical observations show. The paper establishes a rigorous algebraic framework and tests its observational consequences: Natural Cancellation of Vacuum Energy: The paper proves an exact algebraic mechanism where infinite quantum vacuum energy contributions cancel out naturally across the temporal field hierarchy. Even in curved spacetime, the leading mathematical divergences vanish identically, leaving behind a stable, finite energy shift rather than an infinite blow-up. Fractal Scale Structures: The geometric spacing of the temporal fields introduces "Discrete Scale Invariance"—a self-similar, fractal-like structure across energy scales. This architecture offers a unified way to study multi-scale physical phenomena from particle interactions to galactic dynamics. Rigorous Empirical Transparency: The paper subjects its scale-invariant predictions to observational data, maintaining complete transparency by reporting both positive fits and null results: Galactic Dynamics: Evaluates rotation curves against galaxy databases (SPARC), confirming a certified preference over standard dark matter halo models while accurately bounding the extent of the fit. Documented Null Findings: Includes certified tests where expected periodic modulations are absent (such as in supermassive black hole distributions), treating these null results as valuable physical constraints rather than hiding them. By uniting exact quantum vacuum algebra with transparent observational benchmarks, this paper provides a clean, mathematically sound foundation for scale-invariant temporal physics.