Lume-Dimensional: Deterministic Substrate for Higher-Dimensional Physics Governance in Autonomous Systems

Modern theoretical physics operates in spaces with more than the four dimensions of ordinary experience. String theory requires 10 dimensions. M-theory requires 11. Supergravity, Kaluza-Klein compactification, and braneworld scenarios all involve higher-dimensional manifolds, compactified geometries, and inter-brane dynamics that govern the observable physics of our universe. Any computational system that simulates, governs, or reasons about higher-dimensional physics must manage dimensional state transitions, brane interactions, and compactification maps with the same rigor that the DAIGS ecosystem brings to every other governed domain. Yet no existing framework provides deterministic governance over dimensional operations. I introduce Lume-Dimensional, a deterministic substrate for higher-dimensional physics governance. Lume-Dimensional defines dimensional state as a governed primitive — not a continuous manifold read from simulation output, but a certified, invariant-enforced, policy-governed representation of spatial structure managed by the Lume runtime. Every dimensional state transition is indexed by a DimIndex, recorded in the Dimensional Chain (D-Chain), and certified by the Dimensional Certificate Authority. Brane interactions are modeled as governed state transitions between dimensional configurations. Compactification maps — the mathematical machinery that curls extra dimensions into unobservable geometries — are treated as certified, reversible, deterministic transformations within the governance substrate. I formalize the Dimensional model, define seven dimensional invariants, specify four certificate types, present the Brane Interaction Engine and Compactification Engine, and demonstrate integration with the broader physics substrate (Lume-Quantum, Lume-Chronos, Lume-Identity, Lume-Causal). Lume-Dimensional does not claim to solve string theory. It claims that if you are building systems that operate in, simulate, or govern higher-dimensional spaces, you need a deterministic substrate to do it — and Lume-Dimensional is that substrate.