Remark: Family 239. Sharp singularity rates for symmetric sign matrices

Determines the sharp exponential singularity rate of symmetric random sign matrices with independent entries on and above the diagonal. Uniform signs give $\mathrm{Pr}(\det A_n=0)=(1/2+o(1){)}^n$; for fixed bias $p\in (0,1)\setminus \{1/2\}$, the rate is $(p^2+(1-p{)}^2+o(1){)}^n$. In the biased case, agreeing rows attain this rate.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.