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Ordinary inverse for the canonical endpoint arithmetic operator

Proved
Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.exists_fineMesh_cutoff_eventually_canonical_ordinaryProjectedRaw_inverse_compact

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

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

There exist Cref>0, meshTol>0 and W₀ such that for W≥W₀ and any relative mesh M with δ>0 and δ+M.ratio≤meshTol, eventually n>1 and scale separation hold. For the canonical prime partition P and its endpoint certificate, let T be the projected raw map formed from the endpoint arithmetic diagonal and kernel, with weights P.mass and centers P.center. Every q in its raw gauge satisfies the bound below. The constants are chosen before the mesh, and the norm is the ordinary supremum norm.

∥q∥∞≤Cref∥Tq∥∞.\|q\|_\infty\le C_{\rm ref}\|Tq\|_\infty.∥q∥∞​≤Cref​∥Tq∥∞​.
Preamble
import Definitions.Def_erdos390_analytic_compact_goals_006
Formal statement
theorem Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.exists_fineMesh_cutoff_eventually_canonical_ordinaryProjectedRaw_inverse_compact : Erdos390.AnalyticCompactBatch006Goal001 := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/Full/CanonicalEndpointOrdinaryProjectedRawInverseEventually.lean#L49-L827

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