Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 095-03. An Exact Semidefinite Lift of a Nonspectrahedral Hyperbolicity Cone
Manuscript map · lines 4325–4334
OpenAI@2026-10-07#rem:oai-p-095-03
Authors: OpenAI. Family 095.
Title: An Exact Semidefinite Lift of a Nonspectrahedral Hyperbolicity Cone.
Abstract: We construct an exact semidefinite lift of the explicit nonspectrahedral hyperbolicity cone in twenty-three variables defined in the companion paper. The lift is a homogeneous real symmetric pencil of size 100 with 307 auxiliary variables and represents the entire closed cone, including every point with singular X. Thus, although this cone has no semidefinite representation in its original coordinates, it admits one when auxiliary variables are allowed. The stated sizes are not claimed to be minimal.
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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