Reflected-Packet Interactions in the Semilocal Weil Form: An Exact Zero Expansion and Unconditional Infinite Oscillation

We freeze one explicit real, even, compactly supported smooth packet and compute the interaction of two widely separated reflected translates in the complete semilocal Weil preform. The pole and all-prime-power sectors combine into a Stieltjes pairing against the Chebyshev-error distribution. Its canonical bilateral Laplace transform is expressed through the logarithmic derivative of the Riemann zeta function together with the required pole subtraction. A rigorous contour displacement gives an absolutely convergent expansion over all nontrivial and trivial zeros. The archimedean term and the remaining pole term cancel the complete trivial-zero series, leaving an exact zero-only expansion for the full reflected cross interaction. The frozen packet coefficient vanishes exactly on an explicitly determined imaginary lattice. Conrey's unconditional positive-proportion theorem supplies infinitely many visible critical-line poles. A Laplace-transform version of Landau's theorem then excludes either eventual sign. Consequently, both the arithmetic interaction and the even-minus-odd energy splitting take positive and negative values arbitrarily far to the right. This is not a proof of the Riemann hypothesis. It is a fixed-packet theorem. It does not identify, approximate, or determine the parity of an actual semilocal ground state. The numerical computations supplied with the paper are diagnostics only and are not premises of the analytic proof. The deposit includes the paper PDF, complete LaTeX sources, the frozen mathematical specification, independent audit records, two numerical implementations, all retained prime-power data, finite certificates, tests, and reproducibility instructions.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21512461
Primary Topic
Mathematical functions and polynomials
Type
preprint
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preprint

Reflected-Packet Interactions in the Semilocal Weil Form: An Exact Zero Expansion and Unconditional Infinite Oscillation

Leonard van Hemert
Zenodo (CERN European Organization for Nuclear Research)
Mathematical functions and polynomials
preprint

Reflected-Packet Interactions in the Semilocal Weil Form: An Exact Zero Expansion and Unconditional Infinite Oscillation

Leonard van Hemert
preprint en

Abstract

We freeze one explicit real, even, compactly supported smooth packet and compute the interaction of two widely separated reflected translates in the complete semilocal Weil preform. The pole and all-prime-power sectors combine into a Stieltjes pairing against the Chebyshev-error distribution. Its canonical bilateral Laplace transform is expressed through the logarithmic derivative of the Riemann zeta function together with the required pole subtraction. A rigorous contour displacement gives an absolutely convergent expansion over all nontrivial and trivial zeros. The archimedean term and the remaining pole term cancel the complete trivial-zero series, leaving an exact zero-only expansion for the full reflected cross interaction. The frozen packet coefficient vanishes exactly on an explicitly determined imaginary lattice. Conrey's unconditional positive-proportion theorem supplies infinitely many visible critical-line poles. A Laplace-transform version of Landau's theorem then excludes either eventual sign. Consequently, both the arithmetic interaction and the even-minus-odd energy splitting take positive and negative values arbitrarily far to the right. This is not a proof of the Riemann hypothesis. It is a fixed-packet theorem. It does not identify, approximate, or determine the parity of an actual semilocal ground state. The numerical computations supplied with the paper are diagnostics only and are not premises of the analytic proof. The deposit includes the paper PDF, complete LaTeX sources, the frozen mathematical specification, independent audit records, two numerical implementations, all retained prime-power data, finite certificates, tests, and reproducibility instructions.

Zenodo (CERN European Organization for Nuclear Research)
Mathematical functions and polynomials
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Reflected-Packet Interactions in the Semilocal Weil Form: An Exact Zero Expansion and Unconditional Infinite Oscillation — Leonard van Hemert · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS