This v6 preprint presents a strengthened, claim-safe version of the TEBAC Hilbert--Pólya program for the Riemann Hypothesis. The manuscript develops a non-circular spectral-determinant framework aimed at the identity₂₎₌ (s) = (s), \ (D₂₎₌\) is the completed TEBAC Hilbert--Pólya determinant and \ (\) is the completed Riemann \ (\) -function. Compared with earlier versions, the present manuscript hardens the terminal analytic layer by isolating the remaining obstruction in a shifted prime-trace form rather than in ordinary determinant or unshifted phase form. In particular, the unresolved local analytic burden is organized around the shifted obstruction package and its trace-level realization through finite truncation, shell/tail control, and compatibility of the trace-lift mechanism. The official terminal front is therefore no longer an ordinary relative-determinant closure statement, but a shifted prime-trace closure problem expressed through the finite-level and limiting behavior of the shifted prime-trace terms. The manuscript also records the finite shifted prime-trace structure in explicit theorem-facing form, including the truncated shifted prime-power contribution\㵮 ₍ C, ₊^sh (s), with the associated shell, tail, and compatibility reductions that make the remaining analytic gates referee-checkable rather than schematic. The final spectral-square Hilbert--Pólya implication is retained in a claim-safe form: if the upstream determinant identity is established non-circularly, then the nontrivial zeros of \ (\) are transferred to the spectral-square condition\ (s-12) ² R₀, hence lie on the critical line. This version should therefore be read as a near-terminal proof manuscript and analytic hardening stage, not as a final completed unconditional proof of the Riemann Hypothesis. The remaining global verification is concentrated in the determinant-identification and trace-lift compatibility gates explicitly recorded in the manuscript.
Tosho Lazarov Karadzhov (Tue,) studied this question.