---

Claim. Let $f(N)$ be the extremal function of Problem 301. The README of the claimant's repository, at the linked commit of 30 July 2026, states

$$f(N)\le\Bigl(\frac{15437}{19344}+o(1)\Bigr)N\approx0.7980\,N ,$$

the first claimed constant below $4/5$, below Wang's $667/806$ and the thread's $319/390$. The route as the README describes it: with $M=5040=2^4\cdot3^2\cdot5\cdot7$, every integer is written $n=bd$ with $d\mid M$ and every exponent $v_p(b)$ divisible by $e_p+1$, where $e_p$ is the exponent of $p$ in $M$; the fibers $b\,D(M)$, with $D(M)$ the $60$ divisors of $M$, are pairwise disjoint, and the admissible $b$ have density $105/403$; multiplying a relation inside one fiber by $M/b$ turns it into a distinct-subset-sum relation among the integer weights $M/d$, so the problem inside a fiber is a finite optimization over relations of every length; an exhaustive exact-integer certificate shows that no $18$-element subset of the divisor block is relation-free, exhibits a free $17$-element set and pins the maxima of all $60$ divisor prefixes, and summing gives $(105/403)\cdot(15437/5040)=15437/19344$. The intermediate blocks $M=720$, $1680$ and $2520$ give the constants $667/806$ (Wang's), $4865/5952$ and $839/1040$.

Covers. The upper bound $f(N)\le(15437/19344+o(1))N$ only. It does not bear on the particular question, whether $f(N)=(1/2+o(1))N$, which the same claimant's lower-bound claim addresses, and it bounds $\limsup f(N)/N$ above by $15437/19344$ without determining the constant.

Standing. Claimed. The claimant is Donald Della Pietra, whose repository announces the bound beside the lower bound of the claimant's partial proof claim filed on the site's proof-claim tab the same day; the tab's claim and its summary state the lower bound only, and no manuscript states the upper bound: its write-up is a section of the README, with the C++ certificate at $M=5040$ (exact integer arithmetic, no floating point; transcripts in the repository's supplement folder) as its certificate. The README says that both bounds are unrefereed and audited only on the author's side, and that AI systems provided substantial assistance with literature search, adversarial proof audit, exploration, parameter search, the certificates, the Lean implementation and the exposition. The repository's Lean development formalizes the upper bound only in part: the $M=60$ divisor-block certificate (block maximum exactly $7$, proved by decide) and the bridge from a relation-free set to its divisor coordinates; the fiber partition, the density asymptotic and the prefix summation are not formalized, so there is no Lean theorem of the form $f(N)\le(c+o(1))N$, and the formalized block corresponds to the constant $145/168\approx0.8631$, not to $15437/19344$. Nothing was built here and no formalized evidence is listed. The result has no arXiv version, no journal record and no independent review; the site's label is OPEN (page last edited 16 January 2026; as of 2026-10-07), and its commentary records the bound $25/28$ of van Doorn's claim page.