Fukui–Kurdyka–Paunescu conjecture on real analytic multiplicity modulo 2

Let $X,Y\subset\mathbb{R}^n$ be two germs at the origin of irreducible real analytic subsets. Let $h\colon(\mathbb{R}^n,0)\to(\mathbb{R}^n,0)$ be a germ of a subanalytic, arc-analytic and bi-Lipschitz homeomorphism such that $h(X)=Y$. Fukui–Kurdyka–Paunescu's conjecture. Then

$$m(X,0)\equiv m(Y,0)\pmod{2}.$$

The conjecture concerns invariance of real analytic multiplicity modulo $2$ under subanalytic arc-analytic bi-Lipschitz equivalence. The paper states that it gives a complete positive answer, so the conjecture is solved; earlier results covered curves, hypersurfaces, and additional special cases.