Canonical geometry and regression coefficients for Lemma 8.6

For cMesh>0 there are meshTol,Csharp,Cordinary>0, Crow≥0 and W₀, all preceding the permitted 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. If W≥W₀, δ>0, w=δ+η≤meshTol and M is permitted with constant cMesh, then eventually the canonical partition has |dev|≤w, L₁≤7w, w²≤(456/cMesh²)V, V≤4w² and V≤centerEnergy. On the same ball there is an equivalence e_z equal to the actual nuisance-Schur operator, with sharp and ordinary inverse bounds Csharp and Cordinary. Its slow residual row is bounded by Crow·wα_i. Writing Creg=2Csharp Crow, the corresponding actual regression q_z solves its literal normal equation and its compensated coefficients d_p satisfy the following bounds. This package preserves a single inverse witness throughout.