Abstract. We apply the UNNS Laboratory v0.9.1 τ-Coupling Engine to real spectroscopy data for YbF and SrF — heavy diatomic molecules central to electron EDM searches and laser-cooling programmes. Unlike RaF, these systems do not resolve into clear hyperfine manifolds in the τ-MSC comparison engine. Instead, they appear as single-shell τ-objects: their spectra are fully matched, but manifold structure is absent and χ²-normalization collapses to a trivial manifold count. Nevertheless, YbF and SrF exhibit reproducible and distinct τ-curvature and τ-phase profiles. We interpret this as a first glimpse of a hyperfine-silent τ-class of molecules — where recursion structure is present, but encoded primarily in rotational and centrifugal τ-deformation rather than in multi-manifold topology.