DyadicBoxRegularity.lean`

2 declarations, 0 contain sorry, 0 declared as axioms

Regularity loss for the manuscript's concrete dyadic amplification weight

theorem OAI.JointDickman.dyadic_tensor_box_conditions line 12

theorem OAI.JointDickman.dyadicBox_signed_regularity_loss line 44

Source documentation

The actual smooth summand loses only a vanishing error plus the explicit regularity tail, with the uniform 1/(B*T) normalization on each dyadic box.

theorem dyadicBox_signed_regularity_loss
    (hFord : PublishedInputs.FordUpperSieveInput)
    (hM : PublishedInputs.PrimeReciprocalMertensInput) :
    ∃ K : ℝ, 0 < K ∧ ∀ L : ℕ, ∀ τ : ℝ, 0 < L → 0 < τ →
      ∃ ε : ℕ → ℝ, (∀ B, 0 ≤ ε B) ∧ Tendsto ε atTop (𝓝 0) ∧
        ∀ᶠ B : ℕ in atTop, ∀ T : ℝ, 1 ≤ T → Real.log T ≤ (B : ℝ)/10 →
          ∀ k ∈ dyadicBoxIndices (dyadicBoxLower B T) (dyadicBoxUpper B T),
          ∀ (C : ℝ) (j : ℕ), 0 ≤ C → j ≠ 0 →
          ∀ g h : (auxiliaryPrimes B → Bool) → ℝ,
          (∀ x, |g x| ≤ 1) → (∀ x, |h x| ≤ 1) →
          let N := Real.exp ((k : ℝ)*Real.log 2)
…

Mentions: OAI.JointDickman.PublishedInputs.FordUpperSieveInput, OAI.JointDickman.PublishedInputs.PrimeReciprocalMertensInput, OAI.JointDickman.dyadicBoxIndices, OAI.JointDickman.dyadicBoxLower, OAI.JointDickman.dyadicBoxUpper, OAI.JointDickman.auxiliaryPrimes