Superdense Ether Theory: A Parameter-Free Derivation of Nuclear Radii, Particle Masses, and Fundamental Constants from αEM, G, ħ, c

Abstract We present a complete, parameter-free derivation of nuclear and particle physics observables from four fundamental constants αEM, G, ħ, c and two topological in- tegers Hp = 3, He = 1. The physical vacuum is modelled as a Superdense Ether (SET) - a superfluid 4D elastic continuum with Planck density ρP = c5/(ħG2) ≈ 5.15 × 1096 kg m−3 whose topological excitations are elementary particles. The density hierarchy from the Planck scale to ordinary matter is governed by ρ(k) = ρP · βk where β = 2α2 is derived from the Z2 degeneracy of Hopf ground EMstates. A fundamental identity lP4 ρPc2 = ħc is proved analytically. Fiveequationsfullyclosethesystem: (I)xIHf(xI,H)=1fromvortexcirculation and angular-momentum quantisation; (II) x2II ln(8/xII − 7/4) = 1/(48π3αEM) from electromagnetic equilibrium; (III) β = 2α2 ; (IV) xtrue = xIκH/(H2+1) from the EM Ginzburg-Landau functional minimum; (V) R0 from the vortex energy minimum at kbg = 20. The results are: R0 = 1.20002 fm (experiment: 1.2000 fm, error 0.001%); mp and me reproduced exactly; mp/me = 1836.15 exact. No free parameters. The theory also predicts δγ = γ − 1 = −2 × 10−5 for the Shapiro parameter, testable by BepiColombo.