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f89a930 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | import OAI.NumberTheory.Jacobsthal.Estimates.SourceParentBenchmark
import OAI.NumberTheory.Jacobsthal.Estimates.SourceReferenceRemainders
namespace OAI
namespace Erdos970
open scoped _root_.Erdos970
section
open _root_.Filter
open scoped Topology
namespace ErdosSourceReferenceMargin
open ErdosCorrectionLimit ErdosContinuousAnomaly ErdosBoundaryIntegral
open NumberTheoryLean.ReferenceSourceDecomposition NumberTheoryLean.ReferenceLocalResidual
open Erdos970Dependency.InvariantCostBound
theorem root_sourceReference_tendsto (a : ℝ) :
Tendsto (fun z => (ErdosInverseBoxHeight.sourceB z)^2*
sourceReference (ErdosInverseBoxHeight.sourceW z) (sourceRootNode a z)) atTop
(𝓝 (Real.exp Real.eulerMascheroniConstant*(-a+2*signedCoefficientI/costMass))) := by
have hh := (((root_source_remainder_tendsto a).add (root_anomaly_replacement_tendsto a)).add
(root_nodeBenchmark_tendsto a)).add (floored_source_correction_tendsto a)
convert! hh using 1
· funext z
ring
· ring_nf
theorem actual_sourceReference_tendsto :
Tendsto (fun z => (ErdosInverseBoxHeight.sourceB z)^2*
sourceReference (ErdosInverseBoxHeight.sourceW z) (sourceRootNode (1/100) z)) atTop
(𝓝 (Real.exp Real.eulerMascheroniConstant*(-(1:ℝ)/100+2*signedCoefficientI/costMass))) := by
simpa only [neg_div] using! root_sourceReference_tendsto (1/100)
end ErdosSourceReferenceMargin
end
end Erdos970
end OAI
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