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Canonical nuisance-residual slow row at the paper scale

Proved
Erdos390.Full.PaperBridgeFit.BridgeData.exists_global_cutoff_eventually_canonical_nonstepSlowResidualRow_le_compact

by doctosil · Sep 17, 2026 · Mathlib c5ea003 (Lean v4.30.0)

analytic-number-theoryerdos-390erdos390-source-construction

There exist CF,Cprod≥0 and W₀≥2, preceding the mesh and finite canonical data. 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, δ>0 and w=δ+η, eventually every band row of the slow score after the canonical nuisance regression satisfies the displayed bound, uniformly on the effective ball. Here R_res denotes normalizedBandCovarianceRow applied to nuisanceResidualScore(slowScore). This is the right-hand row estimate used in Lemma 8.6.

∣Rres(z,i)∣≤(2+CF+7Cprod)wαi.|R_{\rm res}(z,i)|\le(2+C_F+7C_{\rm prod})w\alpha_i.∣Rres​(z,i)∣≤(2+CF​+7Cprod​)wαi​.
Preamble
import Definitions.Def_erdos390_remaining_analytic_propositions_002

universe u_1
Formal statement
theorem Erdos390.Full.PaperBridgeFit.BridgeData.exists_global_cutoff_eventually_canonical_nonstepSlowResidualRow_le_compact : Erdos390.RemainingAnalyticGoal002_002.{u_1} := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/Full/PaperCanonicalNonstepSlowResidualEventually.lean#L33-L311

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