Three canonical ordinary perturbation estimates

Fix Cref>0 and Rproj≥0. There is a cutoff W₀ chosen before the finite head family, physical intervals, guard ledger and effective ball. Head primes need only be at most W. For W≥W₀, 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. 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 an arbitrary finite nonempty band type assume ∑H_jα_j≤Rproj∑H_jα_j². Eventually, for every raw-gauge q and every band i, the squarefree/reference and full/squarefree row differences are bounded by the canonical ordinary row tolerance τ=canonicalOrdinaryRowTolerance(Cref,Rproj). The actual nuisance-Schur/full-map difference is bounded by σ=canonicalOrdinarySchurTolerance(Cref).