Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 095-01. Hyperbolicity Cones Without Semidefinite Lifts
Manuscript map · lines 4305–4314
OpenAI@2026-10-07#rem:oai-p-095-01
Authors: OpenAI. Family 095.
Title: Hyperbolicity Cones Without Semidefinite Lifts.
Abstract: We prove that not every hyperbolicity cone is a spectrahedral shadow: some closed hyperbolicity cones admit no finite affine semidefinite lift, even with arbitrary real coefficients and any finite number of auxiliary variables. This disproves the Projected Lax Conjecture and hence the generalized Lax conjecture.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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