leech_dimension_eq_directed_flux
plain-language theorem explainer
The theorem equates the dimension of the Leech lattice to the count of directed edges on the three-dimensional hypercube Q3. Recognition Science researchers cite it to reinterpret the Ramanujan modular discriminant exponent as flux modes on a double-entry ledger rather than extra dimensions. The proof is a one-line simp that unfolds the definitions of leech_lattice_dimension and directed_edges_Q3 to the common value 24.
Claim. The dimension of the Leech lattice equals the number of directed edges on the three-dimensional hypercube: $24 = 2D2^{D-1}$ evaluated at $D=3$.
background
The module treats the number 24 as the count of directed flux modes on the Q3 hypercube under double-entry J-symmetry. The hypercube has 8 vertices and 12 undirected edges given by $D2^{D-1}$, but each edge carries flow in both directions, producing 24 independent variables whose partition function recovers the modular discriminant. This setting is local to the RamanujanBridge and rests on the upstream definitions of directed_edge_count and directed_edges_Q3 together with the Leech lattice dimension constant.
proof idea
The term proof is a one-line wrapper that applies simp to the pair leech_lattice_dimension and directed_edges_Q3, reducing both sides to the integer 24 by definition unfolding.
why it matters
The result anchors the Leech lattice dimension inside the Recognition Science counting of directed flux on the Q3 ledger, reinforcing the T8 claim that D equals 3 rather than the string-theory value 26. It supplies the explicit numerical bridge between the eight-tick octave structure and the Ramanujan tau function without introducing new hypotheses.
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