Conservative Motion Theory – MB VI: Normality–Spacing Duality under Mellin–Free Fredholm Kernels

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Autore principale:	Kawasaki, Hideyo
Natura:	Recurso digital
Pubblicazione:	Zenodo 2025
Accesso online:	Acceder al recurso
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_version_	1866901160047149056
author	Kawasaki, Hideyo
author_facet	Kawasaki, Hideyo
contents	<p>We establish a duality between (i) normality of real-number expansions and (ii) GUE-type<br>zero spacing for automorphic L–functions, arising naturally from the Mellin-free Fredholm<br>framework of CMTMB I–V. The key observation is that both phenomena are governed<br>by the same Gaussian Fredholm deformation: finite–κ kernels enforce positive spacing and<br>uniform digit frequencies, while the limit κ → 0+ transmits these structural constraints<br>to the automorphic and arithmetic spectra. This provides a unified explanation of the<br>Montgomery–Dyson law and Borel’s normality conjecture.</p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_17658230
institution	Zenodo
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publishDate	2025
publisher	Zenodo
record_format	zenodo
spellingShingle	Conservative Motion Theory – MB VI: Normality–Spacing Duality under Mellin–Free Fredholm Kernels Kawasaki, Hideyo <p>We establish a duality between (i) normality of real-number expansions and (ii) GUE-type<br>zero spacing for automorphic L–functions, arising naturally from the Mellin-free Fredholm<br>framework of CMTMB I–V. The key observation is that both phenomena are governed<br>by the same Gaussian Fredholm deformation: finite–κ kernels enforce positive spacing and<br>uniform digit frequencies, while the limit κ → 0+ transmits these structural constraints<br>to the automorphic and arithmetic spectra. This provides a unified explanation of the<br>Montgomery–Dyson law and Borel’s normality conjecture.</p>
title	Conservative Motion Theory – MB VI: Normality–Spacing Duality under Mellin–Free Fredholm Kernels
url	https://doi.org/10.5281/zenodo.17658230

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