vp_360_three
plain-language theorem explainer
The exponent of prime 3 in the factorization of 360 equals 2. Recognition Science modelers cite this arithmetic anchor when building bridge lemmas that reference constants such as 360 and 840. The proof is a direct native_decide evaluation of the factorization definition.
Claim. The exponent of 3 in the prime factorization of 360 is 2.
background
This module assembles small decidable arithmetic facts about integers that recur in Recognition Science derivations, including 8, 45, 360, 840 and selected primes. The function vp p n extracts the exponent of prime p in the factorization of n, implemented directly as n.factorization p. The present theorem supplies one such fixed fact for 360, keeping later lemmas free of repeated arithmetic.
proof idea
The proof is a one-line wrapper that invokes native_decide to evaluate the definition of vp on the concrete inputs 3 and 360.
why it matters
The result supplies a stable arithmetic anchor inside the RSConstants module, supporting readable bridge lemmas that reference 360 in factorizations and wheel constructions. It sits alongside sibling facts such as the factorization of 840 and the prime markers 11, 17, 37, 103 and 137. No downstream theorems are recorded yet, so its role remains that of a foundational constant fact.
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