sigma_two_fortyfive
plain-language theorem explainer
σ₂(45) evaluates to 2366 and functions as a fixed Recognition Science constant in divisor arithmetic. Number theorists auditing RS constants or implementing arithmetic functions would reference the result. Direct computation via native_decide confirms the equality without intermediate lemmas.
Claim. $σ_2(45) = 2366$, where $σ_2(n)$ denotes the sum of the squares of all positive divisors of $n$.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. This declaration computes a concrete instance of the divisor sum σ_k(n) as an RS constant. Upstream results include the definition of σ as the gap between private and public reports for an agent, the balanced property of ledgers, and the future set of uncommitted ledger states.
proof idea
One-line wrapper that applies the native_decide tactic to evaluate the arithmetic expression directly.
why it matters
The theorem supplies a verified value for the RS constant σ₂(45) = 2366 inside the arithmetic functions module. It supports concrete computations ahead of deeper Dirichlet algebra or Möbius inversion. No downstream uses are recorded, leaving open its integration with the forcing chain landmarks such as J-uniqueness and the eight-tick octave.
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