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Claim. Let $\lambda_*>0$ be the unique solution of $\int_0^1 dx/(x(1+e^{\lambda_*/x}))=1$ and $\gamma_*=\lambda_*+\int_0^1\log(1+e^{-\lambda_*/x})\,dx$. Theorem 1.2 of the paper states that the number of sets $B\subseteq\{1,\ldots,N\}$ with $\sum_{b\in B}1/b=1$ is $\exp(\gamma_*N+o(N))$ as $N\to\infty$; its proof's upper bound counts the sets with reciprocal sum at most one, so that family has the same rate. The paper reports $\gamma_*\approx0.631573$ and $e^{\gamma_*}\approx1.88057$; the corpus has not certified the decimals. This fixes the exponential growth rate asked for and nothing finer: no multiplicative asymptotic and no finite-$N$ formula.

Acceptance. The paper is refereed: On further questions regarding unit fractions, International Mathematics Research Notices 2026, no. 2, rnaf382, received 28 October 2025, accepted 23 December 2025 and published online 14 January 2026. The site's curator, Thomas Bloom, marks the problem solved and credits this theorem, independently of the authors, as one of two proofs of the rate. The arXiv record lists one version, v1 of 10 April 2024,; the published text has not been compared with it, and the library's locators are v1 locators. The counting theorem has a complete rewritten proof on the theorem page, through the restricted form of the paper's Proposition 3.2; the library records a two-adic counterexample to the printed unrestricted period statement and shows that the target one is unaffected.

Formalization. The file src/latest/ErdosProblems/Erdos297.lean of Boris Alexeev's lean-proofs collection, linked at its pinned commit, declares itself a formalization of a solution to Problem 297, names Liu and Sawhney as informal authors and Codex and GPT-5.6 Sol as formal authors, and proves erdos_297: there is a unique critical parameter $\lambda_*$, and the logarithm of the exact-sum count divided by $N$ tends to $\gamma_*$; it also proves the base-two form of the rate and that the base-two exponent is below one. It is not among the Lean this corpus built and audited, so the claim carries no formalized evidence.

Independent proofs. Conlon, Fox, He, Mubayi, Pham, Suk and Verstraëte proved the same rate, as $2^{c_1N+o(N)}$ with $c_1=\gamma_*/\log2$, by an entropy method; their result is the page Conlon and collaborators' Theorem 1.

Related. Liu and Sawhney's paper also proves Theorem 1.3, which settles Problem 300 and has its own claim page there, and Theorem 1.1, which sharpens Bloom's reciprocal-mass threshold, the subject of Problem 47, where it is the accepted claim page Liu and Sawhney's four-fifths threshold; Problem 298 records it as a refinement.