A Traced Kreĭn Bridge and Spectral Determinant Identification for a Hilbert–Pólya Operator Model of the Completed Xi-Function

This preprint presents Paper A of the TEBAC Hilbert–Pólya program for the completed Riemann xi-function. The paper isolates a compact downstream operator-theoretic theorem chain: a traced Kreĭn bridge, exact heat-trace matching, spectral determinant identification, spectral divisor transfer, and the resulting critical-line implication under a stated Hilbert–Pólya input package. The manuscript is intentionally written as a conditional core paper rather than as a complete standalone proof of the Riemann Hypothesis. The upstream construction and closure burden is separated into five theorem-level inputs, denoted G1–G5: spectral operator realization, squared Kreĭn bridge, CT-admissible defect-kernel extraction, endpoint zero-mass forcing, and completed determinant comparison with a divisor-safe reference factor. The main result proves that, once these inputs are supplied as independent theorem-level mathematics with no use of RH, zero-location information, or circular determinant identification, the downstream chain identifies the completed xi-divisor with the spectral divisor of a nonnegative compact-resolvent operator square. The critical-line conclusion then follows from the quadratic parameter relation \(\sigma=(s-\frac12)^2\). This version should be cited as the conditional downstream core manuscript of the broader TEBAC RH/HP submission package. Companion works are intended to supply the independent proofs of the upstream inputs G1–G5.