| 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 | |