Modified log-Sobolev inequalities for the random field Ising model with unbounded fields

Unrefereed AI-assisted mathematical candidate. A sign-adapted localisation construction establishes a field-magnitude-independent continuous-time Dirichlet-form modified log-Sobolev bound under the stated strong-disorder anti-concentration assumptions on arbitrary bounded-degree graphs. Independent nonidentical field magnitudes are permitted under a common uniform bound. An attributed last-update warm-up gives tail-free continuous-time mixing. This does not establish Han's stronger one-step entropy-contraction constant or approximate tensorisation. The mixture comparison is known and attributed. Finite numerical checks are diagnostic, not universal proof certificates. Constants may be very large. Original prose/data are CC0-1.0; original code is MIT.