Abstract We present a 4D Euclidean lattice path integral computation for the Faddeev-Niemi Hopf field theory with per-site topology constraint, measuring the vacuum-subtracted soliton energy across five lattice sizes $N^3 \times 16$ ($N = 16, 20, 24, 32, 40$) at couplings $\beta = \kappa = 10, 20, 50$. The vacuum-subtracted energy $E_\text{sol} = E(H{=}1) - E(H{=}0)$ is positive at $N = 16$ (finite-volume artifact) but negative for $N \geq 20$, reaching $-124.73 \pm 2.63$ at $N = 40$ ($47\sigma$). Raw energies scale as $E(H{=}1) \sim 0.333 N^2$ and $E(H{=}0) \sim 0.507 N^2$ --- the unconstrained vacuum grows 52% faster than the topologically constrained soliton sector. At $N = 32$, the soliton sector is the ground state at all three couplings ($27\sigma$ at $\beta = 10$, $48\sigma$ at $\beta = 20$, $84\sigma$ at $\beta = 50$). A continuum extrapolation yields $\Delta E(\beta \to \infty) = -2.78$, confirming the ground state ordering survives the continuum limit. The $H = 1$ topological sector is the true ground state of the Faddeev-Niemi theory: the per-site Hopf charge constraint organizes quantum fluctuations, reducing the free energy below the unconstrained vacuum. This is the lattice analogue of topological order. The result resolves the $F_2$ saddle-point problem that has been the central open question of the soliton programme. Type Preprint License CC BY 4.0 Date 2026-04-05 Subject Theoretical Physics DOI 10.5281/zenodo.19430204 © 2026 Alexander Novickis. Licensed under Creative Commons Attribution 4.0 International.