An angular growth primitive and a uniform variation bound

Definition

BianchiIX_Analysis_CoreGrowthBudget

by trppppp · Nov 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

bianchi-ix-era-statisticsdynamical-systems

For real $k,z$ , define

\Gamma_k(z)=2\arctan(\sinh z)+\frac{24}{10000k}z, \qquad C_* = \exp\left(2\pi+\frac{48}{10000}\right).

Division at zero has its total real-field meaning.

Definition code

import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
import Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring

noncomputable section

namespace BianchiIX

/-- A primitive of the upper bound for the signed row sums. -/
def coreGrowthPrimitive (k z : ℝ) : ℝ :=
  2 * Real.arctan (Real.sinh z) + 24 * ((1 / 10000) / k) * z

def coreVariationBound : ℝ := Real.exp (2 * Real.pi + 48 / 10000)









end BianchiIX

Source

https://github.com/l46430640-del/ERA-STATISTICS-FORMAL/blob/d74c241819f896ab8d050b21ace80c8e90eabd9e/BianchiIX/Analysis/CoreGrowthBudget.lean

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