edges_QD
plain-language theorem explainer
The edge count for the D-dimensional hypercube equals D times 2 to the power D minus 1. Recognition Science researchers cite this to obtain the 24 directed flux modes on the Q_3 ledger from the double-entry J-symmetry. The proof is immediate reflexivity on the definition of the edge count.
Claim. The number of undirected edges in the $D$-dimensional hypercube $Q_D$ is $D · 2^{D-1}$.
background
Recognition Science counts the directed flux degrees of freedom on the double-entry Q_3 ledger, where J-symmetry forces debit-credit pairs on each edge. The hypercube Q_D has 2^D vertices corresponding to the eight-tick octave positions and D · 2^{D-1} undirected edges. The upstream definition states: Number of edges in the D-hypercube: D · 2^(D-1), given explicitly by cube_edges d := d * 2^(d-1).
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of cube_edges.
why it matters
This supplies the base count that doubles to 24 directed edges on Q_3, matching the exponent in the modular discriminant Δ(τ) = η(τ)^24 and the Leech lattice dimension. It fills the combinatorial step in the RS reinterpretation of the Ramanujan number 24 as directed flux rather than extra dimensions, consistent with T7 eight-tick octave and T8 forcing D = 3. No open questions are addressed.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.