Local well-posedness for transport-noise Navier--Stokes with $B^{-1/2}_{6,4}(\R^3)$ initial data

We prove local well-posedness of the three-dimensional incompressible Navier--Stokes equation with prescribed smooth, compactly supported, divergence-free Ito transport noise and deterministic initial velocity in the inhomogeneous space $B^{-1/2}_{6,4}(\R^3)$. Under strict stochastic parabolicity, with no further smallness assumption, the solution is heat-mild and belongs almost surely to $C_tB^{-1/2}_{6,4}\cap L^4_tL^6_x$ up to a positive stopping time. Pathwise uniqueness holds in this entire class, and initial-data dependence is continuous in probability in both norms on common local intervals. The proof combines the published linear stochastic Stokes maximal-regularity theorem of Agresti and Veraar with a cutoff depending on the accumulated $L^4_tL^6_x$ norm. This gives a nonlinear local theory at the negative-half endpoint without treating the derivative noise as a small perturbation.