boundary_dimension
plain-language theorem explainer
The declaration establishes that the boundary of any region in D spatial dimensions has dimension exactly 2. Researchers deriving holographic entropy bounds or ledger-based information scaling in Recognition Science cite it to fix the surface exponent at 2/3. The proof is a one-line simplification that substitutes the definition of D as 3 forced by the T8 step of the chain.
Claim. In three spatial dimensions the boundary of a region is two-dimensional: $D-1=2$ where $D=3$ is the integer dimension forced by the Recognition Science chain.
background
The module derives the Bekenstein-Hawking bound from ledger capacity on the integer lattice ℤ³. D is introduced as the spatial dimension fixed at 3 by the forcing chain (T8). The boundary of a region in D dimensions is therefore (D-1)-dimensional, which for D=3 yields a two-dimensional surface whose measure scales as volume to the power 2/3. This supplies the geometric input for the claim that accessible information flows only through the boundary rather than the bulk volume.
proof idea
The proof is a one-line wrapper that applies the definition of D as 3, reducing the arithmetic expression D-1 directly to 2.
why it matters
The result supplies the dimensional reduction step inside area_not_volume_certificate, which completes the chain to S_BH = A/4 in RS units where Gℏ=1. It also appears in brain_holography_fully_forced to confirm surface scaling. The declaration therefore closes the geometric prerequisite for T8 (D=3) inside the Bekenstein derivation and the brain-holography argument.
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