DISPROVED (LEAN), the site's label: the answer is no. Coloring each integer up to Hough's minimum-modulus bound with its own color and all larger integers with one more color leaves no color class containing the moduli of a covering system, and the same bound answers no to the density version Erdős and Graham asked. The deduction is the site's, resting on Hough's refereed theorem, and is recorded on its claim page (Hough, 2013), accepted on that publication and the site's credit, not on any review by this project. The label's Lean mark is traced to a Lean development in Boris Alexeev's lean-proofs repository, linked on the claim page and not built here; Formalization below records it.