offset_11_eq_24_inv_mod_11
plain-language theorem explainer
The theorem verifies that 6 is the modular inverse of 24 modulo 11, confirming the offset for congruence prime p=11 in the Q3 unification of Ramanujan structures. Number theorists working on partition congruences or mock theta functions cite it to show that offsets derive directly from the directed flux count of 24. The proof is a single norm_num reduction that evaluates the modular multiplication to 1.
Claim. $24^{-1} ≡ 6 (mod 11)$
background
The RamanujanBridge module treats 24 as the directed flux of Q3, the structure that forces both mock theta orders {3,5,7} and congruence primes {5,7,11}. Offsets for the congruence primes are defined by the relation offset_p = 24^{-1} mod p. For p=11 the inverse evaluates to 6, completing the arithmetic side of the unification where 11 arises as edges(Q3) minus one.
proof idea
The proof is a one-line wrapper that applies the norm_num tactic to reduce the equality 24 * 6 % 11 = 1 to concrete integer arithmetic.
why it matters
This declaration supplies the missing modular inverse for p=11 in the Q3 account of Ramanujan congruences, where the full set of offsets {4,5,6} is generated by 24^{-1} mod p. It closes the arithmetic verification for the three smallest primes coprime to 24 and greater than 3, linking directly to the eight-tick octave that produces the factor 8 inside 24. The result remains purely arithmetic; the physical reading of Q3 as the source of the flux count is left as hypothesis.
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