congruence_primes_sum_eq_flux
plain-language theorem explainer
The sum of Ramanujan congruence primes 5, 7, 11 together with offset 1 equals the directed flux of the Q₃ graph. Researchers linking mock theta orders to partition congruences would cite this to tie the prime sets to the geometric count of 24. The proof is a one-line simplification that unfolds the definitions of directed flux and edge count.
Claim. $5 + 7 + 11 + 1 = 24$, where the right-hand side is the directed flux of the Q₃ cube graph, defined as twice its 12 undirected edges.
background
The CongruenceQ3Bridge module unifies Ramanujan's mock theta orders {3,5,7} and congruence primes {5,7,11} through the single value 24. Q₃ has 12 undirected edges by the upstream theorem Q3_edge_count from CubeSpectrum, which applies the handshaking lemma Q3_edges = Q3_degree * Q3_vertices / 2. Directed flux doubles this count via the double-entry ledger, producing exactly 24 directed edges.
proof idea
One-line wrapper that applies simp to unfold directed_flux_Q3 as 2 * Q3_edge_count and Q3_edge_count as 12, reducing both sides to the numeral 24.
why it matters
This equality anchors the congruence primes to the Q₃ flux of 24 that arises from the eight-tick octave. It supports the module claim that the primes are forced by Q₃ geometry, with 5 as the discriminant of the φ-equation, 7 as non-DC DFT modes, and 11 as passive edges. No downstream theorems are recorded, leaving the arithmetic side of the Ramanujan bridge as a supporting lemma.
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