Uniform sharp inverse for the canonical actual nuisance-Schur operator

There exist positive constants meshTol and Cschur and a cutoff W₀, chosen before the mesh, head family, and effective ball. For W ≥ W₀, let M be a relative mesh with δ > 0 and δ + M.ratio ≤ meshTol. Suppose its nonempty anchor cells have lower endpoints greater than 1/8, upper endpoints at most 7/8, and total width at least 1/4. Here a canonical bridge means the guarded canonical sample at the indicated n and W, with separated physical intervals, a nonempty remainder in each cell, and the canonical mesh prime partition. The finite nonempty head family has exactly the primes at most W in each head pattern. Physical interval endpoints lie between 1 and a fixed upper bound; guard ledgers have fixed promotion and bank parameters. The barycentric target has cell-mass margin at least a fixed positive marginFloor, and its baseline equals the bridge baseline. Conclusions are uniform on the closed effective-parameter ball of any fixed radius a ≥ 0. Eventually in n, every such bridge with W > 1 admits linear equivalences e_z equal to its actual nuisance-Schur band operator S_z, whose inverses satisfy the following bound in the paper sharp norm. This supplies an actual, rather than reference, inverse for the later regression construction.