The algebraic framework of Hamiltonian sectors describes a multiverse of decohered, inequivalent quantum field theories via a direct-sum Hilbert space, a stability functional that dynamically selects a universal fixed point in coupling-constant space, and a gradient flow governing sector collisions. This paper proposes a geometric completion in which the bulk is a D-dimensional pseudo-Riemannian manifold and each decohered Hamiltonian sector is a dynamical 3-brane. Coupling constants are promoted to bulk scalar fields, decoherence rates arise from inter-brane propagators, and the stability functional emerges as an effective potential from bulk-mediated brane self-interaction. The formalism yields a geometric derivation of D=4 spacetime dimensionality from decoherence cost scaling and preserves all previously derived cosmological predictions. An algebraic–geometric dictionary maps every structure of the original framework onto bulk geometric counterparts. Appendices provide explicit mappings and a schematic derivation of the brane intersection operator. This work is a geometric companion to the Master Compendium of Core Derivations and Proofs, to which it serves as a conceptual completion.
Robert Clark (Sat,) studied this question.