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Claim. Infinite $r$-Powerful Sums, a one-page manuscript whose author line reads GPT-5.5 Pro, shared by Liam Price in a post of 24 May 2026 on the site's thread for Problem 939; the post attributes the argument to GPT-5.5 Pro and links a Lean file that, it says, Aristotle autoformalized from the argument. The manuscript's single theorem, stated on the library's result page: for every integer $r\geq6$ there are infinitely many tuples $(a_1,\ldots,a_{r-2},N)$ of positive integers with $a_1+\cdots+a_{r-2}=N$ such that $a_1,\ldots,a_{r-2},N$ are distinct $r$-powerful numbers and $\gcd(a_1,\ldots,a_{r-2})=1$. The proof expands $(X+Y)^r-(X-Y)^r$, splits the $j=3$ term into $\lfloor r/2\rfloor-2$ distinct positive multiples of $X^{r-3}Y^3$ to reach exactly $r-2$ summands, and takes $X=q^r$, $Y=B^r$ with $B$ the product of the primes in the coefficients and $q>B$ prime. The manuscript does not argue the distinctness of the summands, which follows from their $q$-adic valuations, and the Lean proof handles it explicitly. Read as the Formulation on the problem page reads the question (joint coprimality, each $r\geq4$), the theorem answers the first question yes and the second no at every $r\geq6$.

Covers. Every $r\geq6$: an $r$-powerful sum of $r-2$ jointly coprime $r$-powerful numbers exists, and there are infinitely many. Not covered: $r=4$ and $r=5$, where the construction has too many terms, so neither of the first two questions is settled as a whole; and the third question.

Depends on. No page of this wiki; the argument is the manuscript's own.

Standing. Claimed. The manuscript is unrefereed and undated; the site adopted the construction into its remarks on 28 May 2026 while keeping the label OPEN, which is not acceptance. Lines 1--676 of the Lean file that Conjectures.io kernel-checked coincide with the autoformalization linked from the post, and that file proves infinite_rpowerful_sums for every $r\geq6$ with positive, distinct, jointly coprime summands; but the certification's target was the catalog statement without positivity, the site's review states that the record does not settle the problem and that the $r\geq6$ construction was not checked line by line, so no reviewed is listed (the Conjectures.io card). This corpus has not built the Lean, so no formalized is listed.