Picture a chain of sites, an even number of them. Every site carries the same value, and each neighbouring pair is linked with the same strength. Now give the left half of the chain a weight of plus one and the right half a weight of minus one. The eigenvalue problem for this chain is not symmetric in the usual sense, so some of its eigenvalues are complex numbers. A classical theorem of Gershgorin places every eigenvalue inside one of two disks of radius two, one centred at the site value and one at its negative. In twenty fourteen, Brian Davies and Michael Levitin conjectured, from computer experiments, something much sharper: that every complex eigenvalue lies inside both disks at once, in the lens-shaped region where they overlap. The question was listed among the open problems of a twenty fifteen workshop on non-self-adjoint operators in physics. Until now it was proved only for chains of at most six sites, and for eigenvalues that are purely imaginary. This release proves the conjecture for chains of every length. The proof rewrites the eigenvalue equation using Chebyshev polynomials, and a familiar step reduces it to comparing one explicit function at two points of equal height. The new part is the proof of that comparison. Explicit estimates, backed by a handful of computer-certified numerical constants, handle long chains. For chain lengths from six to fourteen sites, one short computer check in rigorous interval arithmetic completes the argument. The paper also shows, with certified examples, that the lens fails for chains with unequal halves, for a chain with one weakened link, and for other simple weightings, so the exact structure is essential. The research and the proof were produced by an AI research agent. The main limitation is this: the proof has been checked by the producing workflow and by several AI reviewers, but not yet by any human specialist, and nothing has been formally verified. This is an unrefereed candidate from Evidence Press, dated September twenty-fifth, twenty twenty-six. The paper, certificates and review records are linked from the release page.