PacketDataPhysicalResidualNorm.lean`

3 declarations, 0 contain sorry, 0 declared as axioms

A residual sees only the parent angular cell. Its cone, rather than the slopes of the whole packet family, supplies the single-scale bound.

theorem OAI.LipschitzHilbert.PacketLatticeData.physicalMaskedValue_eq_complex_cross line 22
theorem OAI.LipschitzHilbert.PacketLatticeData.physical_parent_residual_norm line 35

theorem OAI.LipschitzHilbert.PacketLatticeData.eventually_physical_parent_shifted_residual_norm line 111

Source documentation

Source stopping and the rounded block length absorb every constant in the physical single-block estimate before a family is chosen.

theorem eventually_physical_parent_shifted_residual_norm
    (q D M : ℝ) (hD : 0 ≤ D) (hM : 0 ≤ M) (K H : ℕ) :
    ∀ᶠ L : ℝ in atTop,
    ∀ (N : ℕ) (κ : Type) (Label : Fin N → Type) (Item : ∀ j, Label j → Type)
      [Fintype κ] [∀ j l, Fintype (Item j l)]
      (P : PacketLatticeData N κ Label Item), 6 ≤ P.order → P.referenceEnvelopeConstant ≤ L^q →
    ∀ (alt : ∀ j (l : P.labels j), Item j l → κ → SchwartzMap (ℝ×ℝ) ℂ)
      (hAlt : ∀ j l u k, planarProfileConstant (alt j l u k) (2*P.order) ≤ P.profileBound)
      (t : ℝ) (d radius : Fin N → ℝ), (∀ j, 0 < d j) → (∀ j, radius j ≤ K) →
      (∀ j, SourceSlopeLabels.LocalMultiplicity Finset.univ
        (fun l : P.labels j => t+P.rowSlope j l) (d j) H) →
    ∀ (b : ∀ j, P.labels j → κ → ℝ → ℂ),
…

Mentions: OAI.LipschitzHilbert.PacketLatticeData, OAI.LipschitzHilbert.planarProfileConstant, OAI.LipschitzHilbert.SourceSlopeLabels.LocalMultiplicity