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Claim. Let $A$ be the set of integers whose base-$3$ digits are all $0$ or $1$ and $B$ the set of integers whose base-$4$ digits are all $0$ or $1$. Then $A+B$ does not have a positive asymptotic density: the ratio $\lvert (A+B)\cap[1,x]\rvert/x$ has no positive limit as $x\to\infty$. The Lean statement proved is the negation of (A + B).HasPosDensity in the formal-conjectures file, theorem erdos_125 at the linked commit.

Why it is rejected. The claim answers the question the site asked when it was posted, whether $A+B$ has positive density. The site now asks whether $A+B$ has positive lower density, the question Problem 125 states, and the result settles no instance of it: the inequality $\overline{d}(A+B)\geq\tfrac{6}{5}\,\underline{d}(A+B)$ rules out a positive density but says nothing about whether the lower density is positive, which DeepMind's proof that the lower density is zero settles. The result itself is not in question, and the problem page credits it.

Argument, in outline. As Terence Tao recast it on the thread (post 4469, 2026-02-25), a Kronecker-type approximation aligns a power of $3$ with a power of $4$, and the digit structure then forces a gap in $A+B$ that yields $\overline{d}(A+B)\geq\tfrac{6}{5}\,\underline{d}(A+B)$. This page records that outline only; the argument has not been reconstructed in this corpus.

Standing. The claimant is DeepMind, which the site's commentary credits; the result was posted on 2026-02-25 by George Tsoukalas, who reports that a DeepMind prover agent found the Lean proof autonomously on 2026-02-21 from the formal statement alone. The system is named here as the thread names it, a DeepMind prover agent. The site's curator, Thomas Bloom, records in the problem's commentary that the argument gives the $\tfrac{6}{5}$ inequality between the two densities and so rules out a positive density for $A+B$, and the formal-conjectures statement file, at its commit of 2026-09-18, marks erdos_125 solved with the linked commit as its formal proof: that curator record and Tao's reconstruction review the result itself. No informal write-up or refereed publication exists. Boris Alexeev's repository copy, linked above, declares itself a formalization of a solution with a DeepMind prover agent as informal author, names post 4448 and the pinned commit, and also proves not_erdos_125, the statement of this claim. Nothing has been built or audited in this corpus, so the page lists no formalized evidence.