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Claim. Let $R(N)$ count the ordered pairs $(u,v)$ of positive powerful integers with $u+v=N$, where an integer is powerful if each of its prime divisors occurs to exponent at least two, and $1$ is powerful. For every $\varepsilon>0$ there is $C_\varepsilon$ such that

$$R(N)\le C_\varepsilon N^{2/5+\varepsilon}$$

for all integers $N\ge2$. In the notation of the problem, $1_A\ast1_A(N)\le N^{2/5+o(1)}$.

Covers. A partial bound toward a positive answer on Problem 943, which asks whether $1_A\ast1_A(n)=n^{o(1)}$. The bound leaves the exponent $2/5$ and does not answer that question.

Credit. The proof's three-way dyadic interpolation is the one used in Section 2.5 of Tao's Products of consecutive integers with unusual anatomy for a real-quadratic difference equation, which the proof cites as methodological context. The uniform imaginary-quadratic norm count that the sum of two powerful numbers needs is supplied in the proof. No novelty is claimed. The same bound, $1_A*1_A(n)\ll_\varepsilon n^{2/5+\varepsilon}$, is Theorem 1.2 of Przemek Chojecki's unrefereed write-up, posted on the erdosproblems.com forum thread on 2026-03-18, a pending claim recorded on its claim page.

Standing. L24 is tier 0: author-recorded by Plasma AI, with a complete written proof and no independent examination or Lean proof. Catalog acceptance is pending.

Depends on. L24 (tier 0), which uses no other native claim.