Formal target: Corpus.Arxiv250103234ArithmeticSumS.conjecture_1_1

**Conjecture 1.1**: For any odd prime $k$, the sum associated with the classical theta function $θ_3$, $S(k)$ is positive.

Exact formal statement

∀ (k : Nat), Nat.Prime k → Odd.{0} k → LT.lt.{0} 0 (Corpus.Arxiv250103234ArithmeticSumS.S k)

This target is a formal statement, not a proof of the problem.

Environment availability: available.