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ZENODO
Preprint . 2026
License: CC BY NC
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY NC
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY NC
Data sources: Datacite
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A Geometric Mass Formula for Charged Fermions from Heptagon Spectral Data

Authors: Mueller, Andreas;

A Geometric Mass Formula for Charged Fermions from Heptagon Spectral Data

Abstract

The note presents a compact geometric mass formula for the charged fermions based on regular-heptagon spectral data and a fixed cubic three-root spectrum. The three generations are identified with the roots of the polynomial alpha^3 + alpha^2 - 2 alpha - 1 = 0. Sector-dependent coefficients are generated from a common discrete label assignment for the fermion sectors. The charged-sector reference masses are not fitted independently, but are obtained from the Higgs vacuum expectation value v = 246.22 GeV through an exponential damping law M_ref^(f) = (v/sqrt(2)) exp(-Delta^(f)), with Delta^(f) = k0 - phi r_f - Q_f^2/sqrt(2) and k0 = 6 + 7u - 2u^2, where u = 2 sin(pi/7). For the nine charged fermions, the resulting predictions reproduce the observed hierarchy with a global root-mean-square deviation of 5.7%. This deposition contains the manuscript and a reference implementation used to generate the reported numerical results.

Related Organizations
Keywords

charged fermion masses, flavour hierarchy, Higgs vacuum expectation value, heptagon geometry

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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
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