Pessach, or Posokh: A Krein-Operator Reformulation of the Triangle Decomposition for the Riemann Zeta Function

A Krein-space operator-theoretic reformulation of the geometric triangle decomposition of the Riemann zeta function (Rakhman, February 2026). The trivial-zero / non-trivial-zero pairing supports a (+, −) -signature Krein space with explicit 2×2 block structure and a PT discriminant trichotomy. Under a ceiling-normalized assignment, the Brit Milah theorem of the February paper is exactly the statement that the PT discriminant is non-negative, with the first block PT-critical and all subsequent blocks PT-unbroken. The Hilbert–Pólya spectral parameter λ_ρ = −i (ρ − ½) is adopted as the RH-neutral spectral object. A local-orbit lemma, a transverse-defect quantitative reformulation of RH, and a sign-convention audit are included. The paper is a reformulation, not a proof of RH; five explicit gaps are named.