Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. The file Erdos/Erdos1134/solution.lean of the repository
AxiomMath/erdos-public, at the commit linked above, proves
erdos_1134 : lowerDensity (setOf ErdosSetA) = 0: the smallest set of
positive integers containing and closed under ,
and , the set of
Problem 1134, has lower density
zero, so the problem's question is answered no. The file (714 lines,
importing Mathlib) defines the set inductively from under the three
maps, defines the lower density as the liminf of , and
reaches the theorem through a sublinear count with exponent ; its
text contains no sorry, axiom declaration or native_decide and prints
no axioms. The file carries no author header and names no informal author or
source, so it presents itself as an independent proof. The thread's first
post (19 June 2026) presents it as the work of AxiomProver, Axiom Math's
prover, as the post names it. The corpus has not built, kernel-checked or
audited the file.
Standing. Claimed: no outside acceptance of the file exists, since the
site's label DISPROVED (LEAN) credits Crampin and Hilton's answer as
published by Lagarias, recorded on
Lagarias's claim page,
and the corpus has not audited the formal statement. A copy of
this development in the repository plby/lean-proofs, whose header names
Crampin and Hilton as the informal authors, is linked from Lagarias's page
as a formalization of that result; the formal-conjectures file for the
problem points at that copy.
Depends on. No page of this wiki.