Relative prime-power variance estimate with the same regression witness

For cMesh>0 there are a positive mesh tolerance, positive sharp and ordinary inverse constants, Crow≥0, Creg=2Csharp Crow≥0, Crel>0 and a cutoff W₀ preceding the mesh. 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. For a permitted mesh with δ>0 and w=δ+η within that tolerance, there is an eventually nonnegative ε_rel(n) with ε_rel→0 and ε_rel log L→0. Eventually the partition satisfies |dev|≤w, L₁(dev)≤7w, w²≤(456/cMesh²)V, V≤4w² and V≤centerEnergy. There is one common equivalence e_z equal to the actual nuisance-Schur map, with sharp and ordinary inverse bounds Csharp and Cordinary, slow residual rows bounded by Crow·wα_i, and a regression solving the literal normal equation with sharp norm at most Creg w. Its compensated coefficients have supremum at most (1+Creg)w, L¹ sum at most (7+2Creg log 4)w, and squared-L² sum at most 2(4+2Creg² log 4)w². For its regression q_z, the full post-band prime score and squarefree post-band score additionally satisfy the displayed relative variance bound.