Structural reduction of the SI base of units via the Cosserat-continuum hypothesis: electromagnetic and gravitational quantities as mechanical objects of an elastic medium

We propose a unified Cosserat-continuum interpretation of electromagnetism and gravitation in which the SI base of units {m, kg, s, A} reduces to a single energy dimension. Four identifications of medium parameters with fundamental constants of nature (P1: ρ ≡ μ₀; P2: G_shear ≡ 1/ε₀; P3: ℏ as the action quantum of microrotations; P4: G via the Kleinert gauge mechanism) yield: — the speed of light as the transverse Cosserat-wave speed: c = 1/√(ε₀μ₀); — the charge as a defect cross-section: [Q] ↔ [m²]; — the Planck length as a derived scale: l_P = l₀²/(2√2 · l_G). Combined with the hopfionic identification of the electron, geometry yields a bare fine-structure constant α_bare = 1/128 = 2⁻⁷, agreeing with the measured α(M_Z) = 1/128.9 to within 0.7%; the QED running to the low-energy 1/137 is the standard vacuum-polarization shift. The canonical set of fundamental constants reduces to {ε₀, μ₀, ℏ, G}. The linearized Cosserat metric reproduces all five classical tests of General Relativity; deviations from pure GR appear only as torsion at Planckian densities (Einstein–Cartan) and as a massive Cosserat mode at the nanometer scale.Derrick scan of the full canonical functional confirming the canonical configuration is a true energy minimum (E_tot=510.93 keV at λ=1, Δ=0.014%) First preprint of a planned series. License: CC-BY 4.0.