DISPROVED (LEAN), the site's label: the answer is no, by Baumgartner's published 1975 theorem applied to $\mathbb R$ as a vector space over $\mathbb Q$, recorded on its claim page (Baumgartner, 1975) with its refereed and site evidence; the label's Lean mark refers to a Lean formalization of Baumgartner's proof posted in the site's discussion thread in February 2026 and linked by the catalog, listed on the claim page and not built by this corpus.