Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT) exhibit spectral dimension ds ≈ 2.0–2.2 at UV scales, computed numerically from spin-network coarse-graining and Monte Carlo path integrals. The geometric origin of this dimensional reduction has remained an open question for 15 years. We derive ds = ln 8 ≈ 2.0794 algebraically from a single axiom: the quantum vacuum maximizes holographic entropy density by selecting tetrahedral coordination (z = 4). Orientation duality (bidirectional information flow along network links) yields ds = ln(2z) exactly. This prediction, made independently of LQG/CDT data, falls within their empirical range with discrepancy < 4% and is obtained with zero adjustable parameters and zero numerical input from LQG or CDT simulations. The oriented heat-kernel formalism recently developed for directed Bethe lattices Delporte 2024 provides rigorous support for the key derivation step. Originality: We present the first purely algebraic derivation of the spectral dimension from a geometric vacuum axiom. Previous results (LQG: Modesto 2009; CDT: Ambjørn et al. 2005) were numerical. The tetrahedral vacuum axiom and its connection to dimensional reduction are novel contributions not appearing in prior literature.
miguel angel franco leon (Sun,) studied this question.