Separation persists for the two vanishing-viscosity families

separatedChains_of_inputs: SeparatedChainsContract β C₀ conditional on the statements VelGradContract β C₀ and CosineDatumContract.

For a cosine mode n with L_n = 1/(2πn) in the window [ε_m^{1+γ/2}, c₁ ε_m^{1+γ/2-δ/2}]: level m of the two chains topped at ½ ε_M^p, 2 ε_M^p is separated by ≳ ε_m^δ ‖θ₀‖ (flip-flop + short-time separation at t = c′ ε_m^{2-β}); the telescoped step-down increments to level M = 2j+1 cost ≲ ε_m^δ ‖θ₀‖, and the top tail θ − θ_M is o(1) as j → ∞.

theorem AVenhance.Infra.FullTheorem.NoSel.kappaSeq_top {β : ℝ} (I : Ingredients β) (κ : ℝ) (M : ℕ) : I.kappaSeq κ M M = κ

theorem AVenhance.Infra.FullTheorem.separatedChains_of_inputs (β C₀ : ℝ) (hV : VelGradContract β C₀) (hC : CosineDatumContract) : SeparatedChainsContract β C₀