A Divisor-Safe Completed Determinant Comparison for the Riemann Xi-Function
Year: 2026
Type: preprint
Abstract: This companion paper isolates the completed determinant comparison used as input G5 in the conditional Hilbert–Pólya core framework for the Riemann \(\xi\)-function. It constructs the canonical completed determinant in the squared spectral variable\[\sigma=(s-\tfrac12)^2\]by evenizing the completed \(\xi\)-function, proves that the construction is entire and branch-independent, and records the logarithmic-derivative normalization criterion identifying any externally constructed canonical determinant with this completed determinant. The main conclusion is a divisor-safe completed determinant comparison\[\xi(s)=D_{\mathrm{ref}}(s)\cdot D_{\mathrm{can}}\bigl((s-\tfrac12)^2\bigr),\]with the reference factor forced to be\[D_{\mathrm{ref}}\equiv 1.\]Consequently, the reference factor is entire, zero-free, and cannot absorb hidden non-real zeros. The argument uses no Riemann-hypothesis input, no critical-strip zero-location theorem, and no fitted Hilbert–Pólya spectrum. This paper is intended as Paper~B / G5 in the TEBAC Hilbert–Pólya program. It is self-contained for the completed \(\xi\)-side determinant comparison and intentionally does not claim to discharge the other input lanes G1--G4, such as the construction of the Hilbert–Pólya operator or the identification of the Hilbert–Pólya determinant with the canonical determinant. Subjects:Mathematics; Analytic Number Theory; Spectral Theory; Complex Analysis; Mathematical Physics. MSC 2020:11M26; 11M06; 30D15; 47A10; 58J52.
Author: Karadzhov, Tosho
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166461998
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