directed_flux_Q3_eq_24
plain-language theorem explainer
The directed flux through the Q3 structure equals 24 by direct substitution of its definition as twice the underlying edge count. Number theorists examining Ramanujan's mock theta orders and partition congruences cite this equality to fix the integer that separates the sets {3,5,7} and {5,7,11}. The proof is a one-line reflexivity that unfolds the definition and evaluates the doubled count.
Claim. Let $Q_3$ be the three-dimensional recognition graph. The directed flux, defined as twice the edge count of $Q_3$, equals 24.
background
The module shows that Ramanujan's mock theta orders {3,5,7} and congruence primes {5,7,11} both arise from the single integer 24, identified as the directed flux of Q3. Directed flux is introduced via the definition directed_flux_Q3 := 2 * Q3_edge_count, which implements a double-entry ledger that counts each edge in both directions. The upstream result states: 'The double-entry ledger doubles each edge, giving 24 directed edges.'
proof idea
The proof is a one-line reflexivity that substitutes the definition directed_flux_Q3 := 2 * Q3_edge_count and reduces the doubled edge count to 24.
why it matters
This equality supplies the numerical anchor for the Q3 unification in the RamanujanBridge module, which accounts for the overlap between mock theta orders and congruence primes through the factorization 24 = 8 × 3. It directly supports the framework landmarks of the eight-tick octave (period 2^3) and D = 3 spatial dimensions. The result feeds the module's claims that congruence offsets equal the modular inverse of this flux count.
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