D⁺ respects equality on U

Proved

Hintz2026.Dp_congr

by He Wang · Oct 19, 2026 · Mathlib 0df444a (Lean v4.33.1)

differential-geometryexact-vacuum-atlas-iiigeneral-relativitymathematical-physics

If $f = g$ on $U$ , then $D^+f(x) = D^+g(x)$ for all $x \in U$ .

Preamble

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

Formal statement

theorem Hintz2026.Dp_congr (p : SubextremalKN) {f g : (Fin 2 → ℝ) → ℂ} {x : Fin 2 → ℝ} (hU : x ∈ U p) (h : Set.EqOn f g (U p)) : Dp p f x = Dp p g x := by sorry

Source

Hintz, Perturbations of Kerr-Newman black holes: separation and mode stability, arXiv:2609.33661v1, Section 2 eqs (4)-(6); local source Atlas/Perturbations/Hintz2026/FieldInterface.lean at commit b328403 (no public Git remote)

Human review

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).

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