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Claim. On 2026-05-03 Svyable posted in the thread of Problem 881 the manuscript Infinite Deletions from Strongly Minimal Additive Bases, which claims a complete answer; the post links the ChatGPT conversation that generated the write-up and a Perplexity conversation used as its referee. For $k=1$ the answer is yes: removing a sparse infinite subset from a basis of order $1$ leaves a basis of order $2$ (Proposition 7). For every $k\ge2$ the answer is no (Main Theorem 6): some asymptotic basis $A$ of order $k$, minimal at order $k$ both in the ordinary sense and under infinite deletions, has $A\setminus B$ not an asymptotic basis of order $k+1$ for every infinite $B\subset A$, and $|A\cap[0,x]|=O_k(x^{1/k})$. formal-conjectures states the question for every order $k$ and every minimal basis (erdos_881, the record link), with a basis of order $k$ meaning that all large integers are sums of exactly $k$ elements, so one counterexample at some $k\ge2$ answers it no. The site's definitions page instead allows sums of at most $k$ elements. The source card is svyable_2026_infinite_deletions_strongly_minimal_additive_bases.

Standing. The site's curator wrote the same day that the proof appears to have been generated entirely by GPT and asked for the use of AI to be disclosed. A reader posted the same day an AI check, a ChatGPT conversation, reporting several major gaps. The check finds that the manuscript counts sums of exactly $k$ elements, so that it could settle at most that reading and not the site's; that the clause of the witness lemmas placing the witnesses in any prescribed subinterval (the 'Moreover' clause of Lemma 8, and its analogue for the booster witnesses) is false as stated, since a witness is a sum of $k$ chosen elements, while the construction relies on it; that the booster step's scale inequalities fail for $k\ge21$; that the recursion uses the next scale before choosing it and lacks a uniform estimate for its induction; and that the finite-booster normal form theorem is not proved. The thread records no reply to these points. No refutation of the stated result is recorded, so the claim stays claimed; it is not refereed, reviewed or formalized.

Depends on. No page of this wiki.