OAI/NumberTheory/TotientAsymptotic/NormalizedShell.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Additive boundary slices vanish after the smooth-cofactor cost.

  1. def OAI.TotientAsymptotic.normalizedShellLoss line 14
  2. lemma OAI.TotientAsymptotic.normalizedShellLoss_tendsto line 18
  3. theorem OAI.TotientAsymptotic.normalized_additive_shell_loss line 31

    Source documentation

    All retained boundary slices have negligible normalized volume, even after paying for every admissible smooth cofactor.

    theorem normalized_additive_shell_loss (hren : FordRenewalInput) (K : ℝ) :
        ∃ δ : ℕ → ℝ, Tendsto δ atTop (nhds 0) ∧
          ∀ᶠ H : ℕ in atTop, ∀ᶠ x : ℝ in atTop,
          ∀ hRN : R x H ≤ L x H,
          Real.exp (K*cofactorScale H)*
            volume.real (additiveBoxShell x (R x H) (L x H) hRN)/G x (m x) ≤ δ H := by
    …

    Mentions: OAI.TotientAsymptotic.FordRenewalInput, OAI.TotientAsymptotic.R, OAI.TotientAsymptotic.L, OAI.TotientAsymptotic.cofactorScale, OAI.TotientAsymptotic.additiveBoxShell, OAI.TotientAsymptotic.G, OAI.TotientAsymptotic.m