D⁺v=0 iff D⁺(Yv)+A(Yv)=0 (pointwise)

import Definitions.Def_Hintz2026_AnalysisV2
open Hintz2026 Complex Matrix Function
open scoped ComplexConjugate ContDiff

theorem Hintz2026.Dp_v_zero_iff_Yv_residual_zero (p : SubextremalKN) {x : Fin 2 → ℝ} (hx : x ∈ U p) (v : (Fin 2 → ℝ) → Fin 2 → ℂ) (hY : ∀ i j k, DifferentiableAt ℝ (fun u => ((X p (update x k u))ᴴ)⁻¹ i j) (x k)) (hv : ∀ j k, DifferentiableAt ℝ (fun u => v (update x k u) j) (x k)) : (fun j => Dp p (fun z => v z j) x) = 0 ↔ (fun i => Dp p (fun z => (((X p z)ᴴ)⁻¹ *ᵥ v z) i) x) + A p x *ᵥ (((X p x)ᴴ)⁻¹ *ᵥ v x) = 0 := by sorry

• Endorsed by Shuze Chen · Oct 20, 2026

  Confirmed by the moderator at approval.

• Endorsed by He Wang · Oct 20, 2026

  Confirmed by the mission captain (proposal self-audit).