We propose a theoretical framework, which we term crystallographic cosmology from dimensional reduction (CCDR), in which the observed morphology of the cosmic web arises as the grain structure of a phase transition occurring in a higher-dimensional embedding space. The central analogy is precise and formal: the post-inflationary universe is a supersaturated medium that undergoes symmetry-breaking nucleation at sites determined by topological defects in the higher-dimensional bulk, producing a lattice-like condensate whose preferred spacing is the baryon acoustic oscillation (BAO) scale r* ≈ 147 Mpc. We demonstrate that the three necessary conditions for crystal growth — a supersaturated medium, nucleation triggers, and a characteristic interaction length — are each satisfied by known cosmological physics: the cooling Running Vacuum Model (RVM) vacuum provides the supersaturation; higher-dimensional brane intersections or topological defects provide nucleation sites that project into the three-dimensional slice as cosmic string-like seeds; and the sound horizon at recombination provides the lattice constant. The framework unifies previously disparate observations: the BAO peak in galaxy correlation functions corresponds to a Bragg diffraction peak from a cosmological crystal lattice; filamentary and wall-like structures correspond to grain boundaries formed via the Kibble mechanism; and cluster nodes correspond to triple-junction dislocations. We further show that quantum mechanical statistics, usually treated as axiomatic, may emerge naturally as the phonon statistics of this lattice when observed from within a single unit cell. The framework makes three classes of testable predictions: (i) non-Gaussian signatures in the matter power spectrum at sub-BAO scales reflecting grain boundary topology; (ii) a preferred orientational correlation of filament axes over super-horizon distances, analogous to crystal texture; and (iii) a systematic shift in the effective BAO scale with redshift at the level δr*/r* ∼ ν/2 ∼ 5 × 10⁻⁴, where ν is the RVM running parameter, testable with DESI DR3/DR4 data. We situate the framework within existing programmes including brane cosmology, holographic duality, causal dynamical triangulations, and stochastic mechanics, and identify the open problems required to elevate CCDR from a structural analogy to a quantitative theory.
The goal of CCDR is not to replace the predictive framework of quantum mechanics, but to provide an explanatory layer that accounts for why interactions exhibit their observed structure. By linking interactions to constraints arising from entanglement, geometry, and entropy bounds, CCDR seeks to elevate interactions from fundamental inputs to emergent consequences of the underlying information-theoretic organisation of spacetime.