Random symmetric matrix singularity reference

Family 239: Sharp singularity rates for symmetric random sign matrices. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Numerical probability researchers can compare uniform or biased symmetric sign-matrix sampling against the claimed exponential singularity rates.

Applicability and commercial boundary

The o(1) term is asymptotic, determinant zero is an exact arithmetic event, and floating-point near-singularity is different. The claim does not certify numerical conditioning of arbitrary matrices.

Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

Next verification action

Use exact integer rank on small fixtures and inspect effective error bounds before estimating finite failure probability.

Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Main source

The sharp exponential rate of singularity for symmetric Bernoulli matrices.