Title: Paper XXXV: Electroweak Symmetry Breaking from Hopf Vacuum Structure Author: Alexander Novickis (alex.novickis@gmail.com) The Standard Model's electroweak sector --- $SU(2)_L \times U(1)_Y$ gauge symmetry, spontaneous breaking to $U(1)_\text{em}$, three massive and one massless gauge boson, and a scalar Higgs field --- is conventionally built from an ad hoc scalar doublet with two free parameters ($\mu^2$, $\lambda$). We show that this entire structure emerges from the topology of the Hopf fibration $S^3 \xrightarrow{S^1} S^2$. The $S^3$ isometry group $SO(4) \cong SU(2)_L \times SU(2)_R$ provides the gauge symmetry; squashing the Hopf fiber reduces $SU(2)_R$ to $U(1)_Y$. When the soliton vacuum condenses --- selecting a point on $S^2$ --- the pattern $SU(2)_L \times U(1)_Y \to U(1)_\text{em}$ follows without any scalar potential. The $W^\pm$ mass arises from the Skyrme term's energy cost for fiber reorientation; the $Z^0$ mass from electroweak mixing; the photon remains massless as the unbroken $U(1)_\text{em}$ generator. The Weinberg angle $\sin^2\theta_W = 3/13$ is derived geometrically. The electroweak scale is fixed non-circularly from $\alpha$ and the electron mass through the derived top-quark mass, $v = \sqrt2\,m_e\,\alpha^{-44/17} = 245$ GeV (0.4%), and the Higgs mass then follows as $m_H = \sqrt{2\lambda}\,v \approx v/2 \approx 123$--$125$ GeV with a near-critical quartic. A direct Coleman--Weinberg evaluation on the Berger-sphere moduli space yields $m_H \approx 125.8$ GeV as a geometrically-motivated estimate, with open items stated explicitly (the curvature-cutoff value and the fermion-loop sign). All precision electroweak observables are reproduced at the per-mille level. Apparent Planck-scale relations for the Higgs ($m_H/M_P \approx \alpha^8$) are numerical coincidences, not derivations. Keywords: physics, electroweak, higgs, soliton, topology, symmetrybreaking, hopf, weinberg, topquark, electroweakscale, vacuumexpectationvalue, quasifixedpoint, nearcriticality, higgsquartic, planckmass, bergersphere, kaluzaklein, colemanweinberg, fermiconstant DOI: 10.5281/zenodo.19626044 Series: Paper XXXV in the Hopf Soliton Programme