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Claim. The number $1$ is a sum of reciprocals of $47$ distinct integers, each the product of two distinct primes, in seventeen ways: the preprint prints the seventeen representations (Section 3.3, pp. 5--10), the first of them with denominators $6,10,14,\ldots,851,1073$ and largest prime factor $53$, the others with prime factors up to $101$. This is the instance $a/b=1$ of Problem 306, answered yes, with one term fewer than Johnson's record of 1978 (Johnson's claim page). The preprint also reports (Section 4.1, p. 11) that no $46$-term representation exists when the prime factors are at most $101$; that $47$ is the least possible number of terms is the author's expectation, not a theorem. The statement is recorded on the library's result page. Exact rational arithmetic for this corpus confirms the first example, an author-recorded check and not a review; the other sixteen are recorded as printed.

Covers. The instance $a/b=1$ only. Not covered: any other rational, and the minimality of $47$.

Standing. Claimed. Watanabe, T., New examples of the representation of 1 by the sum of reciprocals of semiprime numbers, arXiv:2009.03275, v1 of 1 September 2020 and v2 of 9 September 2020, 11 pages; no journal record is known (arXiv listing and Crossref, 2026-09-18), so refereed is not listed. The site's commentary credits the preprint with the shortest known representations on a problem it labels OPEN, which is not acceptance of a claim, so reviewed is not listed.

Formalization. The community database's formal-status note records a Lean formalization by Collin Yuanjie Ren, AI-assisted, of the first 47-term decomposition, at the pinned README linked above. The README declares the theorem erdos_306_one in its Erdos306One/Main.lean, the instance $q=1$ of the formal-conjectures proposition for the problem, with Watanabe's first example as the witness, every fact proved by kernel-checked arithmetic without native_decide, and an audit printing the axioms propext, Classical.choice and Quot.sound; it attributes the decomposition to Watanabe, claims no mathematical novelty, and says the certificate was prepared with Claude Code assistance (Claude Fable 5.1 orchestration, Claude Opus 5 implementation, as the README names them). It declares itself a formalization of this result and so is a link on this page and not a claim of its own. This corpus has not built or audited it, so no formalized evidence is listed.