Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 126-01. Exponential PSD rank of positively shifted matching matrices
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OpenAI@2026-10-07#rem:oai-p-126-01
Authors: OpenAI. Family 126.
Title: Exponential PSD rank of positively shifted matching matrices.
Abstract: For every fixed $0{}lt {}rho{}lt 1$, the matrix indexed by odd vertex sets U and perfect matchings M of Kn, with entries $|M{}cap{}delta(U)|-1+{}rho$, has real positive semidefinite rank $2{}{{}Omega(n)}$ as even n tends to infinity. Here ${}delta(U)$ is the edge cut of U. Consequently, every exact semidefinite lift of the perfect matching polytope has exponential size.
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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