Iterates Material Budget Normalized #
Support for the Armstrong–Vicol anomalous-diffusion formalization.
theorem
AVenhance.Infra.Section4.iterate_higher_material_budget_normalized
{κ Ccoef Cs Cv Cf N ρ q C₀ W Wprev : ℝ}
{i : ℕ}
(hκ : 0 < κ)
(hρ : 0 ≤ ρ)
(hρq : ρ ≤ q)
(hC₀ : 0 < C₀)
(hq : 0 < q)
(hsmall : C₀ * q ≤ 1)
(hi : 1 ≤ i)
(hW : 0 ≤ Wprev)
(hWle : Wprev ≤ W)
:
24 * iterateHigherMaterialBudget κ Ccoef Cs Cv Cf (N * iterateAmplitude (C₀ * q) i / √κ)
(N * iterateAmplitude (C₀ * q) (i - 1) / √κ) (N * iterateAmplitude (C₀ * q) i) ρ q W Wprev ≤ (24 * amnrMaterialMajorantConstant Ccoef Cs Cv Cf / C₀ + 2 * (24 * amnrMaterialMajorantConstant Ccoef Cs Cv Cf) / C₀ ^ 2) * N ^ 2 * iterateAmplitude (C₀ * q) (i + 1) ^ 2 * W ^ 2
The explicit higher material budget closes with the corrected C/C0 term. Only scalar coefficient scales and amplitudes enter this algebraic lemma.