The Multiverse of Geometry: A Phase-Space Taxonomy of Vacuum Geometries via Axiomatic Physical Homeostasis

We propose a new cosmological classification scheme based on the Axiomatic Physical Homeostasis(APH) framework. We posit that the Vacuum is not a monolith, but a dynamic fluid characterized bytwo order parameters: Geometric Stiffness (β) and Associator Hazard (A). By mapping the phase spaceof these parameters, we identify four distinct cosmological phases: (I) The Associative Desert (β = 1),(II) The Crystalline Void (β → ∞), (III) The Sedenion Chaos (β → 0), and (IV) The Life Zone (β ≈1.91). We reinterpret the Big Bang not as a singularity, but as a Vacuum Crash—a catastrophic failureof a high-dimensional pregeometry that triggered a reboot into the stable G2 configuration. Finally, wedemonstrate that Black Holes and Room-Temperature Superconductors are Pocket Cosmoses—localizedbubbles of alternative vacuum phases embedded within our own spacetime.