The site labels the problem DISPROVED. The status-defining source is Theorem 1 of Erdős and Fuchs (J. London Math. Soc. 31 (1956), 67--73, refereed): for no sequence and no $c>0$ does the number of pairs with $a_i+a_j\le n$ equal $cn+o(n^{1/4}(\log n)^{-1/2})$, so a bounded error term is impossible and the answer is no (the 1954 technical-report printing of the paper, the copy read, states the theorem with the weaker exponent $-1/2-\varepsilon$; see References). Montgomery and Vaughan [MoVa90], after unpublished work of Jurkat, extended the impossibility to an error term $o(N^{1/4})$, which answers the question on its own. The claim pages are Erdős–Fuchs (accepted on the refereed publication and the site's credit), which also pins the 2026 Lean formalization of the bounded-error case in the lean-proofs repository, a development the corpus has not built, and Montgomery–Vaughan (accepted on the site's credit; the paper appeared in an edited tribute volume whose refereeing is not documented).