D
plain-language theorem explainer
The definition fixes the spatial dimension D to 3 as required by the linking condition in the Recognition Science forcing chain. Researchers deriving the fine-structure constant from the cubic ledger geometry cite this value to obtain 8 vertices, 12 edges, and 6 faces in the unit cell Q3. The assignment is a direct constant definition with no further computation or proof steps.
Claim. The spatial dimension is fixed at $D = 3$.
background
Recognition Science derives all physics from a discrete ledger on Z^3 whose fundamental unit cell is the cube Q3. The module derives α^{-1} from the geometry of this cube during one atomic tick, distinguishing one active edge from the remaining passive field edges. Upstream structures establish that Q3 simultaneously forces the gauge content SU(3) × SU(2) × U(1), exactly three particle generations from face-pair count, and 24 chiral fermion flavors (= D × 2^D).
proof idea
This is a direct definition that assigns the natural number 3 to D. No lemmas are applied and no tactics are used; the value is supplied as the fixed input for all subsequent geometric counts in the alpha derivation.
why it matters
This definition supplies the dimension D=3 required for the cubic ledger in the alpha derivation module. It implements the T8 step of the forcing chain that sets D=3 spatial dimensions. The value enables the calculation of 4π from Gauss-Bonnet on Q3 and the passive edge count of 11 used in the geometric seed for α^{-1}.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.