Causal Holographic Dynamics (CHD): A Discrete Quantum Gravity Framework Based on Geometric Aliasing and Causal Chain Statistics

This paper introduces Causal Holographic Dynamics (CHD), a theoretical framework for discrete quantum gravity that is rigorously grounded in numerical empirical evidence. The core of CHD is derived from two key phenomena identified in Monte Carlo simulations of 2D discrete spacetimes: first, the geometric recoverability of continuous Riemannian curvature from causal chain statistics, evidenced by the exceptional sensitivity of the Benincasa-Dowker action (Cohen’s d=2.47); second, the geometric aliasing effect, a statistical breakdown in geometric resolution that arises when the curvature radius approaches the fundamental discreteness scale. We conjecture that this observed aliasing boundary corresponds to a fundamental physical limit, wherein spacetime evolution is constrained to avoid regimes of irreversible information loss. Within the CHD framework, this constraint is formalized via an information capacity functional, which yields modified gravitational field equations and emergent dynamical behavior. CHD provides a unified, phenomenologically motivated explanation for the holographic principle (manifest as area-law entropy), a kinematic mechanism for cosmic dark energy as a necessary consequence of evading the aliasing bound, and a natural ultraviolet cutoff at the Planck scale. Importantly, CHD is presented as an empirically guided exploratory framework—not a complete or final theory of quantum gravity. We elaborate its mathematical structure, present an open-source validation platform for numerical verification, and rigorously address its key theoretical limitations, including unresolved challenges related to general covariance and covariant energy-momentum conservation. The primary contribution of this work is methodological: it demonstrates a transparent, numerically driven approach to constructing and constraining quantum gravity theories, bridging phenomenological numerical results with theoretical dynamical modeling.