D⁻v=0 iff D⁻(Xv)-A(Xv)=0 (pointwise)

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

theorem Hintz2026.Dm_v_zero_iff_Xv_residual_zero (p : SubextremalKN) {x : Fin 2 → ℝ} (hx : x ∈ U p) (v : (Fin 2 → ℝ) → Fin 2 → ℂ) (hX : ∀ i j k, DifferentiableAt ℝ (fun u => X p (update x k u) i j) (x k)) (hv : ∀ j k, DifferentiableAt ℝ (fun u => v (update x k u) j) (x k)) : (fun j => Dm p (fun z => v z j) x) = 0 ↔ (fun i => Dm p (fun z => (X p z *ᵥ v z) i) x) - A p x *ᵥ (X p x *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).