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Accepted · first revision · record

Title: Nonlinear stability of Kerr for all spins below extremal
Plain: Proofs that a spinning black hole is stable appeared only in 2021-2022, and only for slow spin. In June and September 2026 two independent proofs were posted that cover every spin below the maximum, and these await verification.
Precise: Prove that the maximal development of asymptotically flat vacuum data close to subextremal $\operatorname{Kerr}(a_0, M_0), \mid a_0\mid < M_0$, has complete future null infinity and a domain of outer communication converging to a nearby $\operatorname{Kerr}(a_f, M_f)$. Residual question: confirm the 2026 proofs and close the gap between their data classes (structured data with polyhomogeneous expansions plus an O(r^-3-eps) remainder in one, structureless O(r^-3/2-delta) decay in the other).
Settled by: Refereed acceptance of a proof for $\mid a \mid < M$ covering initial data with the physically expected decay rate.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: partially-resolved
Status note: Hintz (arXiv:2606.28253, June 2026) and Szeftel (arXiv:2609.40068, September 2026) posted proofs for $\left|a\right| < M$; both are unrefereed preprints as of October 2026.
Posed since: (empty)