bibkey: harris2016mosertardos
authors: "David G. Harris"
year: 2016
title: "New bounds for the Moser–Tardos distribution"
doi: 10.48550/arXiv.1610.09653
url: https://arxiv.org/abs/1610.09653
claim: "Under the stated Moser–Tardos and Shearer hypotheses, ordered-union probabilities admit bounds using the ambient probabilities of disjoint pieces."
strata_touched:
  - D5/S3/Arith/Congruence/TwoOddPrimeUncoveredDensity
license: citation-only
triage: anchor

Actual unions in the Moser–Tardos law

The inspected version is v7, dated 10 October 2019; first submission 30 October 2016. Checked 16 September 2026. Proposition 3.4 bounds an ordered union using disjoint ambient pieces. Section 1.1 defines adjacency by shared variables; Propositions 2.7 and 3.3 retain that dependency convention.

The bound can be applied to level sets of one complete test-layout load. It does not justify replacing shared-variable edges by assignment-conflict edges. The Erdős #7 dossier uses the separately verified commutative-resampling theorem of Iliopoulos for that finer graph. Neither source supplies an unconditional numerical head bound for the covering problem.

Citation and source-boundary note only; no source text or code is vendored.