Derivation of the bare electron mass from {ε₀, μ₀, ℏ} via Cosserat-functional minimization: m_e^bare = 446.279 keV

The electron rest energy mec² = 510.99895000 ± 0.00000015 keV (CODATA 2018) is treated by the Standard Model as an empirical input. No first-principles calculation derives it from more fundamental constants. This work derives the bare electron mass numerically from three vacuum constants — {ε₀, μ₀, ℏ} — by Nelder–Mead minimization of the Cosserat functional E[n, u] of the unit-vector director field n: ℝ³ → S² over a three-parameter Hopf ansatz with topological charge QH = −1. The construction uses the structural identities and dimensional reduction of the preceding work (SI Reduction via the Cosserat-continuum hypothesis, Zenodo DOI: 10.5281/zenodo.20187199) to fix all five parameters of the functional (K₁, K₂, K₃, μ_c, c₄) algebraically from {ε₀, μ₀, ℏ}; no parameters are tuned. Numerical minimization on a stretched cylindrical grid of resolution 1024 × 2048 (dyadic box L = 17 × 33 l₀) yields a hopfion of bare mass mebarec² = 446.279 keV The Hopf invariant is preserved to numerical precision (|QH| = 1 to better than 5·10⁻⁵). The energy decomposes into three physically distinct sectors: Frank–Oseen elastic (49.7 %), Skyrme stabiliser (49.4 %), and screened Cosserat coupling (0.8 %); the Frank–Oseen and Skyrme terms balance at the Derrick fixed point. Sensitivity analysis confirms the predicted scaling mec² ∝ ℏ3/4·ε₀−5/8·μ₀−3/8, excluding accidental cancellation. The dimensionless minimum Êmin ≈ 1039 matches a dyadic closed form, me/m₀ = x² + x/2 − 1 with x = α⁻¹/4: at the bare αbare⁻¹ = 128 it gives 2¹⁰ + 2⁴ − 1 = 1039, and the same shift of x that runs α⁻¹: 128 → 137 takes the bare mass to the physical me ≈ 511 keV (numerical observation). This is the bare value — a direct output of the bare functional, with zero free parameters available to absorb any discrepancy; it is deliberately not compared with the physical (measured) electron mass. Companion repository with full reproducibility recipe (Python script, stretched-grid module, requirements): github.com/igorevsiev-cmyk/cosserat-program Verifications: verifications/electron_mass_minimization/ — Nelder–Mead minimization on a 1024×2048 grid, dyadic box 17×33 (this paper) verifications/canonical_derrick/ — independent Derrick-stability scan of the same configuration