IsMockOrder
plain-language theorem explainer
Mock theta orders are defined as primes p that are coprime to 8 and strictly less than 8. Researchers studying Ramanujan's mock theta functions cite the predicate to recover exactly the set {3,5,7}. The definition is a direct conjunction of primality, coprimality to 8, and the bound p<8 with no reduction steps.
Claim. A natural number $p$ is a mock theta order when $p$ is prime, $p$ is coprime to 8, and $p<8$.
background
The module CongruenceQ3Bridge unifies Ramanujan's mock theta orders {3,5,7} with partition congruence primes {5,7,11} through the single number 24 = directed_flux(Q3). The eight-tick octave (period 2^3) from the forcing chain supplies the bound 8, while coprimality to 8 ensures a k-periodic pattern cannot close inside one window and therefore yields only mock modular symmetry. Upstream the Prime abbreviation is the transparent alias for Nat.Prime; the remaining upstream lists of seven narrative geodesics, seven kinship systems, seven ore classes and seven Greek modes illustrate the seven-fold structures that recur inside the same 8-tick window.
proof idea
The declaration is a direct definition that conjoins the primality predicate, coprimality to 8, and the strict inequality p<8.
why it matters
The predicate appears in the biconditional IsMockOrder_iff and supplies the mock-order half of the unification theorem mock_and_congruence_unified_by_Q3. That theorem shows both Ramanujan phenomena are governed by the single directed flux count 24, with 3 mock-only because it divides 24 and 11 congruence-only because it exceeds the 8-tick bound. The definition therefore closes the structural gap between the mock-only and congruence-only primes inside the Recognition Science eight-tick octave.
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