vp_360_two
plain-language theorem explainer
The exponent of prime 2 in the factorization of 360 is exactly 3. Researchers handling Recognition Science constants cite this when confirming the prime spectrum of 360 for LCM-based derivations. The result follows from a direct decision procedure applied to the exponent definition.
Claim. Let $v_p(n)$ denote the exponent of prime $p$ in the prime factorization of natural number $n$. Then $v_2(360) = 3$.
background
The module gathers small decidable arithmetic facts about integers recurring in Recognition Science, including 8, 45, 360, 840 and marker primes such as 11, 17, 37, 103, 137. These serve as stable anchors that keep later bridge lemmas readable without repeated arithmetic proofs. The function $v_p(n)$ extracts the exponent of prime $p$ in $n$, implemented as the factorization count.
proof idea
The proof is a one-line wrapper that applies a native decision procedure to the equality after unfolding the definition of the prime exponent.
why it matters
This result fills the prime spectrum entry for 360, confirming involvement of primes 2, 3 and 5 in its LCM. It supplies a stable arithmetic anchor for bridge lemmas in the Recognition Science constants file. No downstream uses are recorded, so it remains a foundational fact rather than a direct link to the forcing chain or phi-ladder.
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