Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
versions View all 2 versions
addClaim

A Conjectural Proof of the Riemann Hypothesis

Authors: Frank, Karol;

A Conjectural Proof of the Riemann Hypothesis

Abstract

Tested with N=20000 and Wigner GEO Chaos https://www.filemail.com/d/tcwvvmkdjrgvagi The Riemann Hypothesis (RH) asserts that all non-trivial zeros of the zeta function ζ(s) lie on the critical line ℜ(s) = 1/2. The Hilbert-Pólya conjecture posits a spectral realization via a self-adjoint operator H whose eigenvalues match the imaginary parts t k of these zeros. In the Eternal Universe Theory (EUT), we construct an explicit candidate H on ℓ 2 (N), derived from the Frank field’s quantum foam dynamics: arithmetic via the von Mangoldt function and geometry via a “heartbeat” kernel K ϕ (u) from LQG-correlated noise. Numerical evidence for truncations up to N = 500 shows GOE-level repulsion and eigenvalue convergence to t k within 1.2% for the first 20 zeros (after proper unfolding). We conjecture that RH follows as a cosmological selection principle: Only critical-line zeros stabilize the foam vacuum. This framework ties RH to quantum chaos in cyclic cosmology, with falsifiable predictions via larger-scale computations.

Keywords

Millenium, Riemann, Millenium Puzzle, RH

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average