Proofs of the Closure Targets (T1)–(T8) for the Balanced TEBAC Operator Companion preprint: a referee-proof Hilbert–Pólya pipeline from microlocal prime correspondences to a completed ξ-determinant
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| Format: | Recurso digital |
| Langue: | anglais |
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2025
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| _version_ | 1866901034863951872 |
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| author | Karadzhov, Tosho Lazarov |
| author_facet | Karadzhov, Tosho Lazarov |
| contents | <p><strong>A companion manuscript designed for referee-checkability and mechanical dependency auditing.</strong><br>This preprint provides a modular, proof-oriented verification of the closure targets <strong>(T1)–(T8)</strong> in the <strong>balanced TEBAC geometry</strong>, supplying the analytic and microlocal “input packages” required by a Hilbert–Pólya-style strategy and the subsequent identification of the associated completed spectral determinant with the <strong>Riemann ξ-function</strong> within the stated framework.</p> <h3>What makes this preprint different</h3> <ul> <li> <p><strong>Closure-target architecture (T1–T8):</strong> each target is proved in a dedicated section with explicit dependencies and a checklist of lemmas.</p> </li> <li> <p><strong>Referee-facing risk register:</strong> critical “black-box” points are isolated, audited, and either proved or reduced to sharply stated deliverables.</p> </li> <li> <p><strong>Explicit GL(1) end-normal form (Variant B):</strong> a consolidated end package enabling a fully checkable heat-trace subtraction and archimedean normalization.</p> </li> <li> <p><strong>Microlocal prime correspondences:</strong> prime(-power) correspondences are treated as properly supported graph FIOs, with clean fixed-point trace input and uniform trace-smoothing control.</p> </li> <li> <p><strong>Non-circular identification strategy:</strong> the bridge to ξ is engineered via <strong>log-derivative matching on Re(s) > 1</strong>, avoiding reliance on “same zero set” arguments.</p> </li> </ul> <h3>Scope and intended audience</h3> <p>This document targets readers in <strong>operator theory, microlocal analysis, spectral geometry,</strong> and <strong>analytic number theory</strong>, and is written to be traceable by label lookup with minimal narrative overhead.</p> <p><strong>Companion to:</strong> <em>“A GL(1) Trace–Prime Identity for the Balanced TEBAC Operator”</em> (main preprint).<br>If a persistent identifier (arXiv/DOI) exists for the main preprint, it should be added in “Related identifiers” below.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18102960 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Proofs of the Closure Targets (T1)–(T8) for the Balanced TEBAC Operator Companion preprint: a referee-proof Hilbert–Pólya pipeline from microlocal prime correspondences to a completed ξ-determinant Karadzhov, Tosho Lazarov Riemann ξ-function, Riemann Hypothesis (framework), Hilbert–Pólya program, spectral determinant, zeta-regularized determinant, trace formula, heat kernel, asymptotics microlocal analysis, Fourier integral operators (FIO), fixed-point trace / Lefschetz factor prime correspondences, GL(1) channel reduction, compact resolvent trace, class semigroup analytic continuation, functional equation <p><strong>A companion manuscript designed for referee-checkability and mechanical dependency auditing.</strong><br>This preprint provides a modular, proof-oriented verification of the closure targets <strong>(T1)–(T8)</strong> in the <strong>balanced TEBAC geometry</strong>, supplying the analytic and microlocal “input packages” required by a Hilbert–Pólya-style strategy and the subsequent identification of the associated completed spectral determinant with the <strong>Riemann ξ-function</strong> within the stated framework.</p> <h3>What makes this preprint different</h3> <ul> <li> <p><strong>Closure-target architecture (T1–T8):</strong> each target is proved in a dedicated section with explicit dependencies and a checklist of lemmas.</p> </li> <li> <p><strong>Referee-facing risk register:</strong> critical “black-box” points are isolated, audited, and either proved or reduced to sharply stated deliverables.</p> </li> <li> <p><strong>Explicit GL(1) end-normal form (Variant B):</strong> a consolidated end package enabling a fully checkable heat-trace subtraction and archimedean normalization.</p> </li> <li> <p><strong>Microlocal prime correspondences:</strong> prime(-power) correspondences are treated as properly supported graph FIOs, with clean fixed-point trace input and uniform trace-smoothing control.</p> </li> <li> <p><strong>Non-circular identification strategy:</strong> the bridge to ξ is engineered via <strong>log-derivative matching on Re(s) > 1</strong>, avoiding reliance on “same zero set” arguments.</p> </li> </ul> <h3>Scope and intended audience</h3> <p>This document targets readers in <strong>operator theory, microlocal analysis, spectral geometry,</strong> and <strong>analytic number theory</strong>, and is written to be traceable by label lookup with minimal narrative overhead.</p> <p><strong>Companion to:</strong> <em>“A GL(1) Trace–Prime Identity for the Balanced TEBAC Operator”</em> (main preprint).<br>If a persistent identifier (arXiv/DOI) exists for the main preprint, it should be added in “Related identifiers” below.</p> |
| title | Proofs of the Closure Targets (T1)–(T8) for the Balanced TEBAC Operator Companion preprint: a referee-proof Hilbert–Pólya pipeline from microlocal prime correspondences to a completed ξ-determinant |
| topic | Riemann ξ-function, Riemann Hypothesis (framework), Hilbert–Pólya program, spectral determinant, zeta-regularized determinant, trace formula, heat kernel, asymptotics microlocal analysis, Fourier integral operators (FIO), fixed-point trace / Lefschetz factor prime correspondences, GL(1) channel reduction, compact resolvent trace, class semigroup analytic continuation, functional equation |
| url | https://doi.org/10.5281/zenodo.18102960 |