Refine direct Davidson Rayleigh quotients

[benjipeng]

Summary

• recompute each Rayleigh quotient from the authoritative direct Hpsi action before sealing Davidson residuals
• remove the residual component parallel to each vector without another Hamiltonian application or FFT
• add a deterministic stale-eigenvalue regression test
• refresh the current MgO q10 failed evidence without changing its locked gate

Evidence

• 118 impacted Davidson and periodic SCF regressions pass
• injected parallel residual is removed while the orthogonal residual is preserved
• MgO q10 seeded direct residual improves from 4.5987e-6 to 3.0126e-6
• the 2e-6 MgO gate still fails, so no full-mesh oracle or EOS was run