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Claim. The particular question of Problem 130, whether the chromatic number of the integer-distance graph can be infinite, is answered yes. The Lean 4 theorem Erdos130.erdos130_infinite_chromatic, in Research/Basic.lean of the starfleet/erdos-130 folder of the williamjblair/lean-proofs repository, states that there is an infinite set $A$ of plane points, with no three collinear and no four concyclic in the development's GeneralPosition predicate, such that for every natural number $k$ the graph on $A$ joining the pairs at positive integer distance has no proper coloring with $k$ colors. The folder's entry describes the construction: for each $k$ a finite block of rational points in strong general position whose integer-distance graph has no $k$-coloring, built from circle tangencies, a Hales--Jewett booster and rational inversion; the blocks are translated along the curve $(t,t^3)$, every mixed degeneracy between blocks (a collinear triple, a concyclic quadruple, a center collision) being the vanishing of a nonzero univariate polynomial, so that one rational parameter avoids them all; a recursive prefix state assembles the countable union and proves general position on every finite prefix. The hosting repository's README credits the proof to Colin Snyder of Star Fleet Math (starfleetmath.com), whose site describes its harness as agents running GPT-5.6 Sol max; that is the AI system named here. Star Fleet Math posted the result on its site by 15 July 2026, the date this page carries, with a written report and the development as the archive linked above; the entry's own header is dated 2026-07-10, and the lean-proofs repository hosted a copy on 2026-07-23.

Covers. The second, particular question: the chromatic number of the graph can be infinite, and, since the chromatic number never exceeds $\aleph_0$, the chromatic-number half of the first question. The first question's clique-number part is not addressed, as the catalog's docstring also says; the development states no clique number for its set. The same particular question is answered yes, by a different construction, in Lloyd.H's forum proof claim of 17 July 2026 (its claim page), two days after Star Fleet Math's posting; neither cites the other.

Depends on. No page of this wiki.

Standing. Claimed. The hosting repository's README says that each hosted Star Fleet proof was rebuilt on its continuous integration against the pinned Mathlib, that #print axioms of the terminal theorem reports only propext, Classical.choice and Quot.sound, and that the statement was read against the site's wording; the folder's entry reports the same axioms. The formal-conjectures statement of the problem has linked Research/Basic.lean at the pinned revision as its formal_proof since 2026-08-07 (the record link is pinned at the catalog's commit of that day), marking the problem research solved with the answer true; the community database records the formal statement, which the catalog added on 2026-08-07, but lists the problem as open and its formal status as unformalized. Nothing was built, replayed or audited in this corpus. Star Fleet Math's write-up, linked above, builds the finite blocks from rational circle-tangency families whose chromatic number a Hales--Jewett construction raises, makes their centers generic by a rational inversion and scales them to integer distances; the referee summary on that page comes from Star Fleet's own review harness and is not outside review. The formal GeneralPosition and HasKColoring predicates were not compared with the problem's wording by this corpus, so the page lists no formalized evidence. The site's label is OPEN and its page does not credit the result; no journal record, arXiv posting or outside review of the development is known.