The Universe Schema: Structural Prerequisites for Decohered Hamiltonian Sectors

This paper proposes a minimal set of structural conditions—the Universe Schema—that a Hamiltonian must satisfy to decohere into an autonomous universe. Rather than assuming a fixed spacetime or predetermined dynamical laws, we treat universes as decohered Hamiltonian sectors: self-consistent blocks of a larger Hilbert space whose internal dynamics, symmetries, and conserved quantities define their physical content. Nine structural conditions are identified, and a separate activation criterion requires that decoherence actually occur. From these conditions, a natural taxonomy emerges: monolithic universes without subsystem structure, dud universes with subsystem structure but non-mixing dynamics, and thermodynamic universes with mixing dynamics, entropy gradients, and arrows of time. We conjecture that thermodynamic universes bifurcate into two terminal fates—heat death and Big Crunch—determined by the curvature of a stability functional in Hamiltonian space. The Schema provides a principled foundation for separating structural necessity from dynamical contingency in cosmology. This is Paper 11 in the Hamiltonian Collision Framework series.