What question did this study set out to answer?

The aim is to derive all fundamental particle masses from a novel geometric framework using topological integers.

March 31, 20260 citationsOpen Access

The Complete Particle Mass Spectrum from Planck-Scale Foam Geometry: All 13 Fundamental Masses from Cell Integers

Key Points

The aim is to derive all fundamental particle masses from a novel geometric framework using topological integers.
Utilized the geometry of a truncated octahedron with zero free parameters.
Applied mathematical formulations relating hierarchical mass structures.
Calculated masses for leptons and quarks based on derived equations.
Identified 13 fundamental particle masses categorized from derived equations.
Established electron mass as 511.01 keV with minimal deviation.
Showed relationships among quark masses and lepton classifications through topological coefficients.

Abstract

All 13 fundamental particle masses derived from topological integers of the truncated octahedron with zero free parameters. Hierarchy: ln (MP/v) = (|G|+V+E+F+ (|G|-CA) √Δ) /8, v = 246. 24 GeV (0. 009%). Electron: mₑ = r₁MP exp (- (E-F) (2Δ+√Δ) /16) = 511. 01 keV (0. 002%). Leptons from Koide θ = 2/9 (0. 004%, 0. 009%). All six quarks as mq = mₑ exp ( (A+B√Δ) /C) with cell integer coefficients (0. 08-0. 23%). The up quark uses |G|-1 and V-F, the same quantities as the fine structure constant. Generation splittings: Gen 2 ΔA = Δ = 17, Gen 3 ΔA = -CA³ = -27. Part LV of the Unified Foam Field Theory.

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