directed_edges_eq_double_entry
plain-language theorem explainer
The equality establishes that the directed flux count on a D-dimensional hypercube equals twice the undirected edge count D · 2^(D-1). Researchers tracing the exponent 24 in the modular discriminant Δ(q) = η(τ)^24 back to the Recognition Science ledger would cite this to replace the string-theory interpretation of extra dimensions. The proof is a one-line reflexivity that follows immediately from the definition of the directed count as double the cube edges.
Claim. For spatial dimension $D$, the directed flux count on the hypercube equals twice the undirected edge count: directed_edge_count$(D) = 2 ·$ cube_edges$(D)$, where cube_edges$(D) := D · 2^{D-1}$.
background
The module reinterprets the classical exponent 24 in Ramanujan's modular discriminant as the number of directed flux modes on the double-entry Q_3 ledger. For D = 3 the hypercube has 8 vertices and 12 undirected edges; J-symmetry (debit/credit pairing) requires each edge to carry flow in both directions, producing exactly 24 directed edges. The upstream cube_edges definition supplies the base count D · 2^(D-1) and is used verbatim in the equality.
proof idea
The proof is a one-line term-mode wrapper that applies reflexivity on the definitional equality between directed_edge_count and twice cube_edges.
why it matters
This supplies the counting step that identifies 24 with 2 × edges(D=3), grounding the modular discriminant bridge and the Leech-lattice reinterpretation inside the RS framework. It directly supports the claim that the 24 arises from the eight-tick octave and double-entry ledger rather than from 26 spacetime dimensions. The equality closes the arithmetic link between T8 (D=3) and the partition-function exponent without introducing new hypotheses.
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