Local matrix and interval-certificate research around the Riemann hypothesis

Three-point spectral-defect bounds, a second-moment saturation obstruction and finite interval probes of Weil kernels.

Read historical manuscripts, supporting audits and notes according to their roles; consult the handoff for evidence and stage boundaries.

Why we tried it

Seek checkable matrix inequalities and rigorous falsification certificates relevant to zeta-zero questions.

What the evidence shows

Local derivations and bounded positivity certificates exist; failure to find a counterexample is not positivity at all heights or on the full space.

Where the work stands

The transfer from local matrix extrema to global bounds on actual zeros is incomplete, and no new global zero-proportion record is established.

Possible next steps

Specify kernel-specific attainability, error enclosures and global transfer steps; seek a rigorous negative witness or close the missing reasoning instead of declaring RH from a larger finite scan.

Suggested next steps are untested research questions, not new experimental results. The archive records manuscript provenance, licensing and status.