radical
plain-language theorem explainer
The radical of a natural number n is the product of its distinct prime factors. Number theorists and researchers modeling radical distributions in cost algebras cite this definition for square-free kernel calculations. It is realized as a direct one-line product over the primeFactors Finset using the identity map.
Claim. For a natural number $n$, the radical is defined by $rad(n) := prod_{p prime, p | n} p$.
background
This module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. The radical provides a basic interface for distinct prime factors before deeper Dirichlet algebra is layered on. Upstream identity morphisms from CostAlgebra, ArithmeticOf, and Octave supply the id map applied in the product.
proof idea
One-line definition that applies the product operation to n.primeFactors using the identity function.
why it matters
This definition feeds theorems on radical distributions in N-dimensional cost models, including affineShift_mem_LevelSet and radical_integrable_by_affine_leaves. It fills the arithmetic functions section that supports prime calculations in the Recognition framework, connecting to the forcing chain and phi-ladder structures.
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