prime_triplet_thirtyseven_fortyone_fortythree
plain-language theorem explainer
37, 41, and 43 form a prime triplet with gaps of 4 and 2. Recognition Science researchers cite the triplet because 37 functions as the beat numerator on the phi-ladder. The proof is a term-mode native decision that evaluates the three primality predicates directly.
Claim. $37$, $41$, and $43$ are each prime numbers.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Statements remain minimal until Dirichlet algebra layers are added. Upstream structures include J-cost minimization (strictly convex with global minimum at x=1), spectral emergence forcing SU(3)×SU(2)×U(1) gauge content plus three generations, and nuclear density tiers scaled by φ powers.
proof idea
One-line wrapper that applies native_decide to the conjunction of the three primality statements.
why it matters
The declaration records the concrete triplet (37,41,43) with 37 as beat numerator. It supplies an arithmetic fact for phi-ladder mass formulas and eight-tick octave constructions in the forcing chain. No downstream uses are recorded; the fact touches T5 J-uniqueness and T7 period-8 dynamics without closing any open scaffolding.
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