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Eventual raw broad-pool surplus with three guard coordinates

Proved
Erdos390.WholePaper.eventually_roughCanonicalActiveIntrinsicRawBroadSurplus_compact

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

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

Fix natural W,K,mW,K,mW,K,m and positive real c,δ∗c,\delta_*c,δ∗​. Eventually in nnn, every complete rough label rrr at cutoff y(n)y(n)y(n) that is intrinsically active and nonexceptional at (n,δ∗)(n,\delta_*)(n,δ∗​) satisfies

∣BW,K(n,hc(n),y(n);r)∣≥max⁡{m,T(n,hc(n),y(n);r)}+3,|\mathcal B_{W,K}(n,h_c(n),y(n);r)|\ge\max\{m,T(n,h_c(n),y(n);r)\}+3,∣BW,K​(n,hc​(n),y(n);r)∣≥max{m,T(n,hc​(n),y(n);r)}+3,

where TTT is the full upper complete-rough-row target and B\mathcal BB is the raw broad correction pool.

The surplus accommodates both an arbitrary fixed pool minimum and the literal three-coordinate guard budget.

Preamble
import Definitions.Def_erdos390_remaining_analytic_propositions_008
Formal statement
theorem Erdos390.WholePaper.eventually_roughCanonicalActiveIntrinsicRawBroadSurplus_compact : Erdos390.RemainingAnalyticGoal008_006 := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/WholePaper/BankPaperCanonicalRawBroadSurplusAsymptotic.lean#L1009-L1153

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