Canonical two-sided slow variance from fixed-witness base outputs

Fix cMesh>0 and Creg≥0. There are meshTol,γslow,Cvar>0 and 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 W≥W₀ and a permitted mesh with δ>0 and w=δ+η≤meshTol, eventually the following holds for every point z and every raw-band equivalence e. Assume its actual regression satisfies ‖q‖sharp≤Creg w and the same partition has |dev|≤w, L₁≤7w, w²≤(456/cMesh²)V, V≤4w² and V≤centerEnergy. Then its two-stage compensated variance obeys the following two-sided bound. The result needs no additional analytic-error assumptions.