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Claim. The set of $x>0$ for which the best $n$-term underapproximations $R_n(x)$ by distinct unit fractions are eventually built greedily has Lebesgue measure zero. The assertion of Problem 206, that this holds for almost all $x$, is therefore false: it fails for almost every $x$.

Result. Kovač's Theorem 1 (J. Number Theory 268 (2025), 39--48; arXiv:2406.07218v3, PDF p. 2; paged at theorem_1) states that the set of positive reals with eventually greedy best Egyptian underapproximations has Lebesgue measure zero. The paper's property, the existence of one strictly increasing sequence of denominators whose prefixes are the best $n$-term underapproximations for every large $n$, is the site's recursion $R_{n+1}(x)=R_n(x)+1/m$ with $m$ the least unused denominator keeping the sum below $x$; the equivalence is written on the result page. The paper states that it answers the problem in the negative. The proof is a recursive reduction to two-term underapproximations: for every $i\ge1000$ at least one per mille of the numbers in $(1/i,1/(i-1)]$ have a non-greedy best two-term underapproximation (Lemma 3), and this uniform share drives a geometric decay of the measure of the set of numbers whose best sums are nested over a growing range of $n$. Its Corollary 2 gives, non-constructively, a transcendental number without the property. The theorem says nothing about rational or algebraic $x$, which remain the problem's companion questions on the problem page.

Acceptance. Refereed: the paper appeared in the Journal of Number Theory, volume 268 (March 2025), with the arXiv comment on v3 (26 September 2024) recording that it incorporates the referee's suggestions; the published text has not been compared with the arXiv version. Reviewed: the site's curator, Thomas Bloom, marks the problem disproved and credits Kovač's paper in the commentary, an acceptance independent of the claimant. The library records Theorem 1, Corollary 2 and Lemma 3 as checked statements and the proof as a structural summary; the proof is not rewritten and has not been independently reviewed, a proof-coverage gap and not a doubt about the result.

Formalization. The linked Lean 4 file declares itself a formalization of a solution to Problem 206, names Kovač as its informal author and the AI system Aristotle and Matteo Del Vecchio as its formal authors, and proves, without sorry, that the set of eventually greedy reals has measure zero; its recorded axioms are propext, Classical.choice and Quot.sound. Del Vecchio announced the file in the site's discussion thread on 28 April 2026 as an autoformalization of Kovač's proof by Aristotle. This corpus has not built or audited the file, so it is a posting of the result and not formalized evidence; the site's Lean suffix is a catalog label, and the formal-conjectures statement file for the problem carries a sorry body.