Realizable Sticky Matroid Conjecture

We give a criterion for modular extension of rank-4 hypermodular matroids, and prove a weakening of Kantors conjecture for rank-4 realizable matroids. This proves the sticky matroid conjecture and Kantors conjecture for realizable matroids due to an argument of Bachem, Kern, and Bonin, and due to an equivalence argument of Hochstattler and Wilhelmi, respectively.