D
plain-language theorem explainer
D is set to the integer 3 to fix the number of spatial dimensions on the ledger lattice. Workers deriving holographic entropy bounds from ledger capacity cite this when closing the G3 gap in the Bekenstein-Hawking derivation. The assignment follows at once from the T8 step of the forcing chain with no further reduction required.
Claim. The spatial dimension satisfies $D=3$.
background
Recognition Science places the ledger on a discrete lattice whose dimension is fixed by the forcing chain. T8 of that chain requires exactly three spatial directions. The present module works in that setting to obtain the entropy bound $S=A/(4Gℏ)$ from boundary information flow on ℤ³, using the RS-native constants $G=φ^5$ and $ℏ=φ^{-5}$. Upstream structures calibrate the J-cost on the multiplicative group and the spectral emergence of gauge content from the same lattice.
proof idea
One-line definition that directly assigns the constant 3, justified by the T8 forcing step already established in the chain.
why it matters
The definition supplies the lattice dimension required for the boundary scaling |∂S| ∝ |S|^{2/3} that yields S_BH = A/4 once Gℏ=1. It therefore anchors the main results of the module, including boundary_dimension and bekenstein_hawking_from_rs. The assignment closes the G3 gap referenced in the module header and aligns with the eight-tick octave and D=3 landmark of the overall framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.