The Dandy Land Postulate: A Relational, Non-Numerical Framework for Void-Up Universe Bootstrapping, Spatial Extrusion, and Geometric Irreversibility

Traditional cosmology and quantum field theory treat three-dimensional space (R³) as a static volumetric background or container where matter and energy evolve against continuous coordinates. This treatise presents the Dandy Land Postulate, a bottom-up, non-numerical framework demonstrating that three-dimensional space is an inherently unstable, transient chiral extrusion rather than a static primitive. Rooted in the single foundational axiom that an absolute null void is informationally over-saturated and structurally untenable (The Imperfect Void), space emerges as an active boundary wavefront governed by a discrete balanced ternary state primitive (Σ ∈ \-1, 0, +1\). We formalize three core mechanisms: Cauchy Simplex Collapse: Volumetric 3D momentum cannot maintain equilibrium in isolation and is continually forced to project onto 2D triangular boundary slices (simplices) to register determinate observable states. Geometric Irreversibility via Chair44: Using the topological discovery of Chair44 (the first 3D strongly aperiodic monotile), we prove that aperiodic space-filling requires non-invertible hierarchical substitution rules (Chairs → Superchairs). Downscaling higher-tier structures loses boundary history, establishing an irreducible geometric arrow of time where entropy is the directional metabolic cost of preventing collapse into a trivial periodic lattice. The Boundary Law & Trit Erasure: The projection from 3D volumetric extrusion to 2D Cauchy surfaces acts as the fundamental information-loss mechanism, bounded by kB T ln(3) Landauer trit erasure. We integrate these principles with empirical benchmarks, demonstrating that discrete tetrahedral cavity boundaries (Td symmetry, $N=14$ recursion limit) naturally resolve the Planck CMB low-multipole power deficits (C₂, C₃) and derive the fine-structure invariant (α⁻¹ = 4π³ + π² + π = 137.036304) within $0.0002%$ of CODATA values without arbitrary scalar coefficients.