Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 239-02. The sharp singularity rate for biased symmetric sign matrices
Manuscript map · lines 7195–7204
OpenAI@2026-10-07#rem:oai-p-239-02
Authors: OpenAI. Family 239.
Title: The sharp singularity rate for biased symmetric sign matrices.
Abstract: Let An be a symmetric random matrix whose entries on and above the diagonal are independent signs, equal to 1 with fixed probability $p{}in(0,1){}setminus{}{1/2{}}$. We prove that ${}mathbb P({}det A_n=0)=(p{}2+(1-p){}2+o(1)){}n$. The rate is attained by the event that two rows agree.
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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