What is actually solved?
ℒtoy = −¼ FμνFμν + (DμΦ)* DμΦ − λ(|Φ|² − v²/2)²
DμΦ = (∂μ − igAμ)Φ
Φ̈ = DiDiΦ − 2λ(|Φ|² − v²/2)Φ
Äi = − δEmagnetic/δAi + 2g Im(Φ* Ui Φneighbor)
The link phase Uᵢ = exp(−igAᵢ Δx) makes the discrete scalar gradient gauge-covariant. The Gauss-law residual monitors ∇·E − 2g Im(Φ* Φ̇). The magnetic energy is computed from plaquettes. This is a reduced Abelian model; the Standard Model Higgs is an SU(2) doublet, not this single U(1)-charged complex scalar.
The quench starts near an unstable symmetric-field configuration; vortex pair seeds opposite phase windings; pulse creates a radial Higgs displacement. These are initial conditions, not measurements or predictions.