THE CRYSTALLISATION OF SPACETIME: A Unified Theory of Geometric Emergence from Non-Hermitian Algebraic Substrates

EXECUTIVE SUMMARY Spacetime does not exist a priori. It is an emergent phenomenon—a thermodynamic phase that crystallises from a pre-geometric substrate when certain informational thresholds are crossed. This capstone article consolidates a research programme spanning ~54 frontier papers across seven thematic clusters, unified by a single theoretical hypothesis: **spacetime geometry is not fundamental, but emerges as a thermodynamic phase transition from a deeper Non-Hermitian Algebraic substrate.** The MTN-G (Modular Tensor Network Genesis) framework proposes that at the cosmic Exceptional Point (EP^d)—when the universe's informational processing bandwidth becomes exhausted—eigenvectors of the pre-geometric Type III₁ von Neumann algebraic network coalesce, and spacetime crystallises as the first stable eigenstate. The signature of this transition is a k²-suppressed primordial power spectrum at ℓ < 40, directly observable in CMB anomalies.The Temporal Layering (TL) conjecture extends this to the spatial domain: heterogeneity in the pre-geometric network produces directional CMB scars. Keywords: Emergent spacetime; Non-Hermitian Algebraic Gravity (MTN-G); Exceptional Point (EP^d); Type III₁ von Neumann algebra; Pre-geometric substrate; Sparse-Reservoir Substrate Memory (SRSM); Modular tensor network; Phase transition mechanism; Bandwidth exhaustion; Geometric crystallization; Thermodynamic emergence