The proton-to-electron mass ratio m_p/m_e ≈ 1836.15 is one of the most precisely measured dimensionless ratios in physics. It is known to ten significant figures. Its value determines the entire architecture of atomic chemistry. And it has no derivation in standard physics — it is measured and inserted.
BFUT Paper 16 derives the electron mass from the condensation geometry of the 3+e threshold.
The Derivation
The electron is the balancing branch of the 3+e bifurcation — a single condensation unit generated by the three-core with opposite internal circulation. Its mass follows from the geometric connecting identity established in the three-sphere packing analysis of the 3+e configuration:
Evaluating: m_e = 938.272 MeV / (6 × 306.019) = 938.272 / 1836.115 = 0.511009 MeV. Measured: 0.510999 MeV. Agreement: essentially exact — the residual 0.002% reflects the demonstrative coefficient approximation.
What 6π⁵ Means
The factor 6π⁵ is a pure geometric quantity arising from the three-sphere packing that defines the 3+e configuration. It is the ratio of the cooperative three-core's binding geometry to the single-unit balancing branch geometry. It contains no free parameters — it is determined entirely by the topology of three packed spheres in the Spaticle substrate condensation.
The Mass Ratio Is Constant
A further consequence of the derivation is that m_e/m_p = 1/(6π⁵) is a pure geometric constant, independent of ρ_s. If the Spaticle substrate density were different — in a different universe or in a hypothetical region of this one — both m_e and m_p would scale together with ρ_s, but their ratio would remain fixed at 1/(6π⁵). The ratio is geometry, not density.
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