Iterates Higher Energy Budget

Support for the Armstrong–Vicol anomalous-diffusion formalization.

def AVenhance.Infra.Section4.iterateAnalyticWeight (n i : ℕ) (L : ℝ) : ℝ

The actual factorial weight at coordinate order n and increment i.

Equations

• AVenhance.Infra.Section4.iterateAnalyticWeight n i L = ↑(n + 2 * i).factorial * L ^ n

noncomputable def AVenhance.Infra.Section4.iterateHigherEnergyBudget (n i : ℕ) (κ D a e L Ccoef Cs Cv Cf Gcur Gprev Gprevprev Nprev ρ q : ℝ) (d : ℕ → ℝ) : ℝ

Explicit remainder of the differentiated higher-increment energy equation. It keeps the corrected term linear in q, both preceding amplitudes, and both lower current-order kernels. This is a real formula, not an assumed energy estimate.

Equations

• One or more equations did not get rendered due to their size.

noncomputable def AVenhance.Infra.Section4.iterateFirstEnergyBudget (n : ℕ) (κ D a e r L C Ccoef B Gcur N ρ q : ℝ) (d : ℕ → ℝ) : ℝ

Explicit exceptional first-increment budget. Its material terms have q squared; the lower current-order drift convolution is retained separately.

Equations

• One or more equations did not get rendered due to their size.