Robust Static Candidate-Branch Obstructions and Reduced Pole-Correction Bounds in a Chiral Operator-Spectral Framework

Abstract

We study a supplied chiral operator-spectral branch in which a common positive spectral scale multiplies four Hermitian family quadratic forms relative to a common family metric. Conservative mass ratios and static spectral subspaces are invariant under common positive rescaling, whereas generalized eigenvalues and metric-normalized overlaps are invariant under simultaneous common congruence. For the archived candidate, a reproducible numerical neighborhood analysis shows that every tuple whose whitened operators lie within spectral-norm radius $2.5\times10^{-2}$ remains outside enlarged charged-lepton, CKM, PMNS reactor-entry, and electron-anchored tritium-endpoint acceptance regions. At this radius the muon-to-electron ratio stays below $1.864$, the best-permuted CKM distance exceeds $0.248$, every admissible static electron-row neutrino overlap exceeds $0.245$, and the lightest neutrino rest energy exceeds twelve tritium endpoints after electron anchoring. We also derive relabeling-independent lower bounds on the total reduced pole correction relative to a frozen conservative/counterterm split. For passive self-adjoint open sectors, the open-sector kernel is operator-valued anti-Herglotz; below threshold the matrix pencil is strictly Loewner monotone, giving conditional existence, uniqueness, positive residue, and Lipschitz stability of isolated real pole branches. The socket and family matrices are reproducible outputs of a calibrated supplied branch, not prospective mass predictions; the record does not establish a historical blind freeze or unique microscopic branch selection.