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In a recent paper, Brendle showed the uniqueness of the Bryant soliton among3-dimensional $\kappa$-solutions. In this paper, we present an alternativeproof for this fact and show that compact $\kappa$-solutions are rotationalsymmetric. Our proof arose from independent work relating to our StrongStability Theorem for singular Ricci flows.

On the rotational symmetry of 3-dimensional $\kappa$-solutions