Problem detail · source-aware
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The Smith-Ward theorem realizes the first $k$ essential matrix ranges of an operator as the matrix ranges of a compact perturbation. The classical Smith-Ward problem asks whether that perturbation can be chosen independently of $k$, equivalently whether the identity map on a three-dimensional operator system $\mathrm{span}\{1,q(D),q(K)\}$ in the Calkin algebra always lifts. It need not: an explicit three-dimensional hyperrigid operator system has no unital completely positive lift, and its dual is the first three-dimensional operator system that fails to be exact.
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The one-line disclosure says the model was used to perform literature search and to accelerate the search for the operator system. Since that operator system is the counterexample, the contribution touches the mathematics, but the wording does not say the model found it.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint (v2), isolating and strengthening an argument of Harris; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Harris had settled the generalized problem in dimension four; this reaches dimension three
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.