This v5 release presents the latest Version B iteration of the TEBAC Hilbert--Polya program for the Riemann Hypothesis. The manuscript develops a non-circular trace-prime, shifted-trace, and determinant architecture aimed at identifying the completed Riemann xi-function with a compact-resolvent spectral determinant arising from a balanced GL(1) Hilbert--Polya channel. The main advance of v5 is the sharpening of the terminal C1 obstruction. Earlier versions isolated the actual/reference shifted-trace defect and showed that the Gaussian reference trace alone cannot justify the full prime-trace identity for the confining GL(1) channel. Version v5 develops this point into a precise terminal fork: either one proves a Null-Duhamel theorem for the shifted defect, or one constructs a shifted relative determinant / transmutation route whose relative factor is independently shown to be divisor-safe and zero-free. This release adds the shifted transmutation and shifted relative determinant framework, together with an index-closure/no-crossing package for the shifted relative Fredholm family. The new Stage 79 constructs the shifted relative determinant route and identifies the C1 discrepancy as the logarithmic derivative of a shifted relative factor. The new Stage 80 formulates the corresponding shifted relative index-closure theorem, reducing zero-freeness to explicit upstream checks: Euler anchor, trace-norm continuation, zero boundary winding, spectral-flow control, and divisor-neutral gluing. The manuscript also includes the earlier Version B hierarchy: ordinary relative index closure, ordinary divisor-stripped phase acyclicity, and Route C coefficient-table verification are treated as preparatory or backup mechanisms, while the genuinely shifted prime-trace obstruction remains the terminal theorem-target. The F2A divisor-stripped phase route, the Stage 66 no-crossing proof front, the Stage 67--68 phase-family construction, and the Stage 69--80 shifted C1 machinery together make the remaining obstruction mathematically explicit. This version remains claim-safe. It should be read as a highly developed near-terminal proof architecture and shifted-obstruction closure program, not yet as an externally validated unconditional proof of RH. The decisive remaining mathematical work is to discharge one of the two C1 terminal alternatives: prove the Null-Duhamel theorem, or prove the shifted relative determinant route through an independent zero-free/index-closure theorem. In parallel, the C2 weighted Hilbert--Schmidt completeness and C3 operator-square identity must also be fully established as independent theorem-level inputs before a final unconditional RH claim can be made.
Tosho Lazarov Karadzhov (Tue,) studied this question.