Foundations of Causal Holographic Dynamics: Axiomatic Emergence of Spacetime and the Dark Sector

This paper establishes the axiomatic theoretical foundation for Causal Holographic Dynamics(CHD), synthesizing results from our previous numerical experiments into a coherentframework. We propose that spacetime is not fundamental but emerges from a discretecausal network governed by three information-theoretic postulates: (1) Information Completeness,which induces the Lorentzian metric signature via Fisher information geometry;(2) Combinatorial Curvature, which recovers the Einstein-Hilbert action in the continuumlimit but predicts specific anomalous scaling; and (3) Holographic Horizon Saturation, whichleads to cosmic acceleration.Crucially, we argue that the "Dark Sector" is not composed of new particles, but is thephenomenological manifestation of discrete spacetime microstructure. Our comprehensivenumerical simulations, extended to N = 12, 800 with high-precision statistical bootstrapping(1000 iterations), reveal a robust anomalous scaling ⟨SBD⟩ ∝ Nγ with γ = 1.3231 ± 0.0016.This precision confirms the geometric aliasing effect at a confidence level exceeding 5σ,ruling out the null hypothesis of classical area-law scaling (γ = 1) with near-certainty. Thisgeometric aliasing exponent acts as a fundamental parameter governing the deviation fromclassical gravity, naturally giving rise to "phantom mass" effects at galactic scales withoutmodifying Newtonian dynamics at the fundamental level. This work unifies the scalinganomalies, causal deficits, and entropic forces observed in our simulations into a single,logically consistent theory of emergent quantum gravity.