rs_spatial_dimension
plain-language theorem explainer
Recognition Science forces the spatial dimension to three via the T8 step of the unified forcing chain. Researchers deriving holographic properties of neural caches cite this constant to obtain surface-area scaling of accessible information. The definition is a direct assignment of the natural number three with no computation required.
Claim. The Recognition Science spatial dimension is defined to be three: $D = 3$.
background
The module derives brain holography from GCIC first principles, showing every local ledger region encodes global state and that accessible information scales with boundary size. Upstream results include the J-cost structure from PhiForcingDerived.of and LedgerFactorization.of, which enforce constancy on connected graphs at zero cost, and the continuum bridge from SimplicialLedger.ContinuumBridge.as that identifies the discrete Laplacian with continuum curvature. The module's derivation chain runs from T5 J-uniqueness through graph rigidity and local-cache optimality to surface-area scaling in D=3.
proof idea
This is a direct definition that assigns the natural number three, matching the value forced by T8 in the unified forcing chain.
why it matters
The definition supplies the dimension value required by boundary_scales_as_area and brain_holography_inevitable. It closes the module's derivation chain from T5 through GCIC graph rigidity to the surface-area scaling step, confirming that information in a local cache scales as R² in three dimensions. The result supports the master certificate that brain holography is inevitable under Recognition Science assumptions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.