Certification of the core's positive-definiteness status

Determine whether the fixed cuDSS general-matrix factorization used for the reported large systems corresponds to a symmetric positive-definite material--volumetric core, so that the conditional Togeari spectral and optimality results can be certified for those systems.

Background

The mathematical spectrum, inverse-error identity, and selector-optimality results require $M=M^T\succ0$. The experiments instead use a cuDSS general-matrix factorization and do not record a global Cholesky factorization or inertia.

Thus the preconditioner remains algebraically meaningful under weaker nonsingularity assumptions, but the paper cannot verify whether the stronger SPD hypotheses hold for the reported numerical systems.