Cores of Binary 3-Qualitative Independence Hypergraphs

Abstract

We prove that the binary 3-qualitative independence hypergraph 3-QI(n,2) is a core for every n >= 8, resolving an open problem of Thomas and Akhtar. The main structural result is a balanced-layer lift: if the most balanced layer is a core, then so is the full hypergraph. The package includes the preprint, LaTeX source, finite certificate verifiers, deterministic build tooling, and independent AI review reports. The verifiers check the n=12 certificate, the n=16 boundary instance of the general construction, and small instances of the balanced-layer lift. Manuscript and prose documentation: CC BY 4.0. Verification code: MIT.