Substrate Independence in Computational Finitism: Emergent Holography, Endogenous Lorentz Invariance, and the Fisher Collapse of Singularities

The framework of Computational Finitism posits that the universe is a discrete, computationally bounded substrate, rejecting continuous infinities as representational artifacts. While previous work (Avenues 1-4), Ramos N.E. 2026 (g, h, i, j) successfully derived fundamental constants and 4D spacetime using the specific Golden-Fano Cellular Automaton, a critical vulnerability remained: the "Golden-Fano Pocket" hypothesis. If these results only occur within that specific numerical environment, the framework risks being dismissed as numerology. This paper documents Avenue 7, a rigorous suite of computational tests designed to prove substrate independence. We demonstrate that holography, 4D spacetime, Lorentz invariance, and gravitational physics emerge endogenously from purely discrete, finite rules without relying on a continuous background manifold. Crucially, we demonstrate that these results are not artifacts of the specific Golden-Fano architecture, but universal properties of any finite, local, computationally bounded substrate, thereby establishing substrate independence. Furthermore, we derive General Relativity from Information Geometry, demonstrating that the "Fisher Collapse" naturally prevents physical singularities, and that the Cosmological Constant emerges endogenously from hardware regularization.