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Canonical squarefree slow rows converge relatively to reference rows

Proved
Erdos390.Full.PaperBridgeFit.BridgeData.exists_global_cutoff_eventually_canonical_squarefreeSlowRow_sub_reference_compact

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

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

There is a global cutoff W₀. Choose W≥W₀, a relative mesh with δ>0, then the canonical finite head and physical data, nonnegative tilt bounds Acoef,Aphys, and an accuracy r>0. 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. For all sufficiently large n, every canonical bridge with w=δ+η and every tilt ξ whose effective prime coefficients have absolute value at most Acoef and whose physical coordinate has absolute value at most Aphys satisfies the following estimate for every band. No profile or convergence assumptions are required as inputs.

∣Rsf(ξ,i)−Rref(i)∣≤rwαi.|R_{\rm sf}(\xi,i)-R_{\rm ref}(i)|\le r w\alpha_i.∣Rsf​(ξ,i)−Rref​(i)∣≤rwαi​.
Preamble
import Definitions.Def_erdos390_remaining_analytic_propositions_002

universe u_1
Formal statement
theorem Erdos390.Full.PaperBridgeFit.BridgeData.exists_global_cutoff_eventually_canonical_squarefreeSlowRow_sub_reference_compact : Erdos390.RemainingAnalyticGoal002_003.{u_1} := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/Full/PaperCanonicalNonstepSquarefreeSlowEventually.lean#L42-L372

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