1D Anyonic Statistics from Confined Hopf Solitons

Hidalgo-Sacoto, Busch, and Blume (2025, Phys. Rev. A) recently demonstrated 1D identical particles obey generalised exchange statistics parameterised by α ∈ [0, 1]. We show a Hopf soliton confined to a 1D quantum wire has two programme-derivable exchange phases applying in distinct confinement regimes. B-Lite (Wilczek-Zee + Finkelstein-Rubinstein spin-statistics chain): in weak confinement (σ ≳ 0.3 μm), α_H^(B-Lite) = H bmod 2 — pinned at endpoints {0, 1}. B-Full-B (SU(2)_(k=H) Chern-Simons descent): in strong confinement (σ ∈ [0.05, 0.1] μm), the F₂ Hopf invariant identifies with level-k=H SU(2) CS (Faddeev-Niemi 1997), descends via Witten's CS-WZW correspondence (Witten 1989) to SU(2)_(k=H) WZW j = 1/2 primary, giving the closed-form boxedα_H^(B-Full-B) = 3 / [2(H+2)]. For H = 1, 2, 3, 4: 1/2, 3/8, 3/10, 1/4 — non-endpoint values in the interior of the Hidalgo-Sacoto range. Both predictions are pinned across the scattering length a_any in their regimes. Protocol E2b cold-atom experiments at tunable H discriminate three scenarios — Hidalgo-Sacoto generic, B-Lite, B-Full-B — providing a uniquely diagnostic signature of the F₂-Hopf-CS structure.