Uniform-amplitude R46 wiring and its closed datum producer #
theorem
AVenhance.Infra.Section5.Contracts.r46Source_of_TGradient_uniform_amplitude
(β C₀ A : ℝ)
:
∃ (C₁ : ℝ),
Integration.OnA7Instances β C₀ C₁
fun (I : Ingredients β) (_Φ : ℕ → ℝ → Homogenization.Vec 2 → ℝ) (hΦ : IsStreamSeq I _Φ) (κ : ℝ) (M : ℕ) (_R : ℝ)
(_θ₀ : Homogenization.Vec 2 → ℝ) (m : ℕ) (_θprev : ℝ → Homogenization.Vec 2 → ℝ)
(T : ℕ → ℝ → Homogenization.Vec 2 → ℝ) =>
∀ (B : ℝ),
Integration.TGradientContract β (I.kappaSeq κ M (m - 1)) T A B →
Integration.R46SourceContract I hΦ m (I.kappaSeq κ M m) T A B
R46's coefficient is uniform in the amplitude, chosen before the instance.
theorem
AVenhance.Infra.Section5.Contracts.r46Source_datum_closed_contract
(β Ccut : ℝ)
:
∃ (C : ℝ) (C₁ : ℝ),
Integration.OnA7Instances β Ccut C₁
fun (I : Ingredients β) (_Φ : ℕ → ℝ → Homogenization.Vec 2 → ℝ) (hΦ : IsStreamSeq I _Φ) (κ : ℝ) (M : ℕ) (_R : ℝ)
(θ₀ : Homogenization.Vec 2 → ℝ) (m : ℕ) (_θprev : ℝ → Homogenization.Vec 2 → ℝ)
(T : ℕ → ℝ → Homogenization.Vec 2 → ℝ) =>
Integration.R46SourceContract I hΦ m (I.kappaSeq κ M m) T C √(l2NormSq θ₀)
Exact datum R46 source contract, with its T-gradient input discharged.