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We present preliminary results for B-physics from a combination ofnon-perturbative results in the static limit with relativistic computationssatisfying $am_{\mathrm{heavy}}\ll 1$. Relativistic measurements are carriedout at the physical b-quark mass using the Schr\"{o}dinger Functional in a $0.5\ \mathrm{fm}$ box. They are connected to large volume observables through stepscaling functions that trace the mass dependence between the physical charmregion and the static limit, such that B-physics results can be obtained byinterpolation; the procedure is designed to exactly cancel the troublesome$\alpha_s(m_{\mathrm{heavy}})^{n+\gamma}$ corrections to large mass scaling.Large volume computations for both static and relativistic quantities use CLS$N_f=2+1$ ensembles at $m_u=m_d=m_s$, and with five values of the latticespacing down to $0.039$ fm. Our preliminary results for the b-quark mass andleptonic decay constants have competitive uncertainties, which are furthermoredominated by statistics, allowing for substantial future improvement. Here wefocus on numerical results, while the underlying strategy is discussed in acompanion contribution.

$m_B$ and $f_{B^{(\star)}}$ in $2+1$ flavour QCD from a combination of continuum limit static and relativistic results