Disproved, the site's label. The status-defining source is Vaughan's theorem (J. Number Theory 4 (1972), 1--16, refereed): for no set and no $c>0$ does the three-fold representation count through $N$ equal $cN$ with an error $o(N^{1/4}(\log N)^{-1/2})$, the three-summand case of a general result on $h$-fold convolutions, so a bounded error term is impossible and the answer is no. The claim page is Vaughan (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.