Disproved here; the site's label is OPEN (page last edited 8 April 2026, no proof claim recorded there as of 2026-10-06); its commentary expects the answer no and records the Elsholtz--Harper square-root bounds on a hypothetical decomposition as the best result in that direction. One accepted full claim is recorded on the OpenAI release's claim page (2026): a manuscript of 24 September 2026 proves Ostmann's inverse Goldbach conjecture, that no sumset $A+B$ with $|A|,|B|\ge2$ differs from the primes in finitely many elements, which answers the question in the negative. Its Lean proofs, of that conjecture and of the case of two infinite summands that the question asks about, were built by this corpus with only the three standard axioms, their fingerprints identical to the release's comparator challenges, and the statement audit found the latter exactly the question with the answer no over the nonnegative integers. The claim has no outside review or refereed publication; the frontmatter standing is the accepted claim's.