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Balanced raw smooth-row discrepancy has the required scale

Proved
Erdos390.WholePaper.BankPaperRealization.bankPaperCanonicalBalancedRawSmoothRowDiscrepancy_isBigO_compact

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

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

Write L=log⁡nL=\log nL=logn, N=n/LN=n/LN=n/L, Y=⌊n2/9⌋Y=\lfloor n^{2/9}\rfloorY=⌊n2/9⌋, h=upperTailLength(c,n)h=\mathrm{upperTailLength}(c,n)h=upperTailLength(c,n), QW=roughHeadModulus(W)Q_W=\mathrm{roughHeadModulus}(W)QW​=roughHeadModulus(W), and dW=roughHeadDensity(W)d_W=\mathrm{roughHeadDensity}(W)dW​=roughHeadDensity(W). Fix W,K0W,K_0W,K0​, c>0c>0c>0, and any real β\betaβ. Let wnw_nwn​ be the canonical balanced raw weight. The complete-label-one raw row discrepancy satisfies

roughCanonicalRawRowDiscrepancy(n,h,K0+1,1,wn)=O(N/L).\mathrm{roughCanonicalRawRowDiscrepancy}(n,h,K_0+1,1,w_n)=O(N/L).roughCanonicalRawRowDiscrepancy(n,h,K0​+1,1,wn​)=O(N/L).

This gives the raw smooth-mass estimate used in the initial selector construction.

Preamble
import Definitions.Def_erdos390_remaining_analytic_propositions_004
Formal statement
theorem Erdos390.WholePaper.BankPaperRealization.bankPaperCanonicalBalancedRawSmoothRowDiscrepancy_isBigO_compact : Erdos390.RemainingAnalyticGoal004_010 := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/WholePaper/BankPaperCanonicalSectionEightTopFrozenInitialMassConnector.lean#L387-L565

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