A Hilbert–Pólya Program for the Riemann Hypothesis via TEBAC: Conditional Reduction, Trace Identities, and an Unconditionality Audit

A companion manuscript designed for referee-checkability and mechanical dependency auditing. This preprint develops a Hilbert–Pólya-type program for the Riemann Hypothesis (RH) in the balanced TEBAC framework. It provides a modular, proof-oriented verification of the closure targets (T1)–(T8) and the associated input packages (GS1/GS3/GS5/GS6) required for a Hilbert–Pólya-style strategy. Within the stated framework, the goal is to identify the completed spectral determinant D_comp(s) with the Riemann ξ-function via log-derivative matching on the half-plane Re(s) > 1. Core closure mechanism (conditional): once the prime-power trace expansion and the determinant package yield-∂_s log D_comp(s) = -ξ'(s)/ξ(s) on Re(s) > 1,one obtains D_comp(s) = C·ξ(s) by analytic continuation, and self-adjointness forces the nontrivial zeros onto the critical line. The present version includes an unconditionality audit and a referee-oriented dependency walkthrough; several critical modules remain open and are recorded explicitly as targets. What makes this preprint different Closure-target architecture (T1–T8). Each target is treated in a dedicated section with explicit dependencies and a checklist of lemmas. Referee-facing risk register. Critical “black-box” points are isolated, audited, and either proved or reduced to sharply stated deliverables. Explicit GL(1) end-normal form (Variant B). A consolidated end package enabling fully checkable heat-trace subtraction and archimedean normalization. Microlocal prime correspondences. Prime(-power) correspondences are modeled as properly supported graph Fourier integral operators, with clean fixed-point trace input and uniform trace-smoothing control. Non-circular identification strategy. The bridge to ξ is engineered via log-derivative matching on Re(s) > 1, avoiding reliance on “same zero set” arguments. Scope and intended audience This document targets readers in operator theory, microlocal analysis, spectral geometry, and analytic number theory, and is written to be traceable by label lookup with minimal narrative overhead. Companion to: “A GL(1) Trace–Prime Identity for the Balanced TEBAC Operator” (main preprint). If a persistent identifier (arXiv/DOI) exists for the main preprint, it should be added in “Related identifiers”. Version: 2026-01-09 (v1)