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Canonical full slow rows converge relatively to reference rows

Proved
Erdos390.Full.PaperBridgeFit.BridgeData.forall_accuracy_exists_cutoff_eventually_canonical_fullSlowRow_sub_reference_compact

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

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

For every r>0 there is W₀ such that W≥W₀ can be fixed before the relative mesh, head patterns, physical intervals, ledger and tilt bounds. 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. Assume δ>0, w=δ+η, and nonnegative bounds Acoef,Aphys on the effective prime coefficients and physical tilt coordinate. Eventually in n, uniformly over canonical bridges and allowed ξ, the full-valuation slow row obeys the following estimate in every band. This strengthens squarefree approximation to the actual valuation law.

∣Rfull(ξ,i)−Rref(i)∣≤rwαi.|R_{\rm full}(\xi,i)-R_{\rm ref}(i)|\le r w\alpha_i.∣Rfull​(ξ,i)−Rref​(i)∣≤rwαi​.
Preamble
import Definitions.Def_erdos390_remaining_analytic_propositions_004

universe u_1
Formal statement
theorem Erdos390.Full.PaperBridgeFit.BridgeData.forall_accuracy_exists_cutoff_eventually_canonical_fullSlowRow_sub_reference_compact : Erdos390.RemainingAnalyticGoal004_001.{u_1} := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/Full/PaperCanonicalNonstepFullSlowEventually.lean#L36-L432

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