What question did this study set out to answer?

This research aims to elucidate the geometric relationship between protons and electrons using the Elastic Diffusive Cosmology framework.

March 27, 2026Open Access

Projection from Plenum to Brane: The Proton–Electron Geometric Relation in Elastic Diffusive Cosmology (Paper 5)

Key Points

This research aims to elucidate the geometric relationship between protons and electrons using the Elastic Diffusive Cosmology framework.
Establishment of three independent signal connections between proton and electron.
Utilization of M6 lattice geometry for analysis.
Self-consistency tests conducted to evaluate electron radius within lattice framework.
Mass ratio of proton to electron found to be approximately 6π5 to 0.002%.
Brane identity established with an accuracy of 0.02%.
Projection hypothesis correlates directly with the predicted nuclear saturation density of 0.1631 fm−3.

Abstract

We establish the geometric relation between the proton (anchor junction in the 5D Plenum) and the electron (loop state on the 3D Brane) within the Elastic Diffusive Cosmology (EDC) framework. Three independent signals connect the two particles through M6 lattice geometry: (1) the mass ratio mp/me ≈6π5 to 0.002% Der-M, (2) the brane identity σjun r3e= ℏc to 0.02% Dc, and (3) the projection hypothesis re/aM6 = 8/(3√3) to 0.64% P-nova. The third signal is algebraically equivalent to the holonomy γ = 2/3 that generates the Koide relation (Paper 6). A self-consistency test eliminates the possibility that the electron radius is determined by a closed loop within the lattice framework (Der-neg: fixed point r∗e = 0.0004 fm ̸= re = 2.818 fm). These results support the interpretation that the electron and proton inhabit different geometric spaces—the Plenum and the Brane—connected by a Z3-geometric projection constant. If re/aM6 = 8/(3√3) holds exactly, the nuclear saturation density is predicted: ρ0 = 0.1631 fm−3 .

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