edges_Q3
plain-language theorem explainer
The three-dimensional hypercube has exactly twelve edges under the formula D times two to the power of D minus one. Ledger modelers in Recognition Science cite this count when tallying directed flux variables on the Q3 structure. The proof is a direct one-line invocation of the specialized hypercube theorem at D equals three.
Claim. The three-dimensional hypercube possesses exactly twelve edges: $D · 2^{D-1} = 12$ for $D = 3$.
background
The Q3 hypercube encodes the eight-tick octave positions in three spatial dimensions forced by the unified forcing chain. Its edge count is given by the function that multiplies dimension by two raised to dimension minus one. At D=3 this produces twelve undirected edges, each of which splits into a debit-credit pair under the reciprocal automorphism that enforces J(x) equals J(1/x).
proof idea
The declaration is a one-line wrapper that applies the upstream theorem edges_at_D3, which itself reduces the general hypercube formula at D=3 via native decision.
why it matters
This supplies the base twelve-edge count that doubles to twenty-four directed flux variables, reproducing the exponent in the Ramanujan modular discriminant as the ledger's independent modes rather than extra dimensions. It completes the counting step inside the DirectedFlux24 module and aligns with T8 forcing D=3 together with the double-entry rule from J-symmetry. No scaffolding remains.
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