directed_edges_Q3
plain-language theorem explainer
The theorem establishes that the directed edge count for the three-dimensional hypercube ledger equals 24. Researchers studying the Ramanujan discriminant or Leech lattice would cite this result to trace the origin of the number 24 to double-entry flux on the Q3 structure rather than extra dimensions. The proof proceeds by a direct simplification that invokes the definition of directed edge count and the established count of twelve undirected edges at dimension three.
Claim. The three-dimensional hypercube ledger $Q_3$ possesses exactly 24 directed edges, obtained by doubling the 12 undirected edges of the cube at spatial dimension 3 under the double-entry rule.
background
The module deciphers the classical appearances of the number 24 in Ramanujan's modular discriminant, the Leech lattice dimension, and bosonic string theory. Recognition Science locates this count in the directed flux modes of the double-entry ledger on the Q3 hypercube for forced dimension D=3, not in additional spatial dimensions. The upstream theorem edges_at_D3 states that the cube has 12 edges when D=3, while the sibling definition directed_edge_count sets the directed total to twice the undirected count.
proof idea
The term-mode proof applies simplification to the definition of directed_edge_count, which doubles the cube edge count, together with the theorem edges_at_D3 that fixes the undirected count at 12 for D=3. This reduces the claim directly to the arithmetic identity 2 times 12 equals 24.
why it matters
This result supplies the numerical value 24 used in the downstream theorems leech_dimension_eq_directed_flux and tau_2_coefficient. It realizes the framework step from the eight-tick octave and forced dimension three to the count of independent flux modes on the Q3 ledger, thereby explaining the classical appearances of 24 without invoking 26 spacetime dimensions.
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