vp_eight_five
plain-language theorem explainer
The declaration establishes that the exponent of prime 5 in the factorization of 8 is zero. Number theorists maintaining stable arithmetic anchors for Recognition Science constants would cite this to keep bridge lemmas free of repeated computation. The proof is a one-line term that resolves the equality by direct native computation of the prime exponent.
Claim. The exponent of the prime 5 in the prime factorization of 8 is zero: $v_5(8)=0$.
background
The module collects small, decidable arithmetic facts about integers that appear repeatedly in the reality repo, such as 8, 45, 360, 840 and prime markers like 11, 17, 37, 103, 137. These serve as boring but stable anchors that keep later bridge lemmas readable and avoid re-proving the same arithmetic in many places. The function vp, imported from the Factorization module, returns the exponent of a given prime in the factorization of an integer.
proof idea
The proof is a one-line term that applies native_decide to evaluate the prime exponent directly by computation.
why it matters
This supplies a foundational arithmetic fact for RS constants involving the number 8. It anchors the eight-tick octave (T7) in the forcing chain, where 8 = 2^3 appears as the period tied to D = 3 spatial dimensions. Although no direct downstream uses are recorded, the fact supports readability of bridge lemmas in NumberTheory.Primes without re-deriving basic factorization properties.
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