The Entropic Spacetime Hypothesis A Computational Derivation of 4D Spacetime from Causal Graph Dynamics

We present a comprehensive computational investigation demonstrating that the four-dimensional nature of spacetime emerges from the interplay between a discrete causal substrate and quantum vacuum fluctuations. Through a series of four interconnected milestones, we establish that: (1) a causal graph generated by the Golden-Fano Cellular Automaton possesses a well-defined arrow of time; (2) the fractal dimension of this graph exhibits scale-dependent flow, revealing a "missing dimension" of approximately 0.08 in 2D simulations; (3) in 3+1 dimensions, the geometric substrate yields D ≈ 3.80, with the remaining 0.208 arising from the entropic contribution of virtual particles, whose density is derived from first principles via the Fano TRB fraction and vacuum energy (derived from first principles via the Fano TRB fraction (1/7) and vacuum energy fluctuations (enhancement factor ≈ 1.4), giving a total effective dimension of D = 4.008; and (4) classical phenomena including inertial motion and gravitational lensing emerge naturally from geodesic computation in the entropic graph. This work provides the first quantitative link between quantum vacuum entropy and the macroscopic dimensionality of spacetime, offering a computational framework for reconciling quantum mechanics and general relativity.