Provisional pipeline

Unpublished (publish: false): omitted from the main index until curated — 0 entries. YAML in data/problems_provisional/ (may still be listed on the index if publish: true): 100 for editorial tracking until files move to problems/. See publication criteria.

Files in data/problems_provisional/

100 entries.

• K-601 — Prove unconditional linear stability of Kerr (full subextremal range) in a fixed gauge, with full decay rates.
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-602 — Prove nonlinear stability of Kerr for the full subextremal range |a|<M.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-603 — Prove nonlinear stability of Kerr with quantitative scattering (asymptotic completeness near Kerr).
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-604 — Establish a sharp peeling/polyhomogeneity theorem at future null infinity ($\mathcal{I}^+$) for nonlinear near-Kerr evolutions.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-605 — Prove sharp nonlinear Price-law tails for curvature in near-Kerr vacuum.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-606 — Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-607 — Prove nonlinear stability of Kerr-Newman in the asymptotically flat setting (full coupling).
  Exterior Stability · Open · Open in literature · Classical frontier
• K-608 — Prove unconditional nonlinear stability of slowly rotating Kerr-de Sitter.
  Exterior Stability · Needs review · Solved in literature (classical) · Classical frontier
• K-609 — Prove conditional nonlinear stability of Kerr-de Sitter in the full subextremal range under explicit mode-stability assumptions.
  Exterior Stability · Conditional · Open in literature · Classical frontier
• K-610 — Establish sharp SCC thresholds in Kerr interiors for C0 vs C1 vs C2 formulations.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-611 — Prove generic Lipschitz (or C1) inextendibility of near-Kerr MGHDs.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-612 — Prove generic sharp lower bounds on event-horizon flux for spin-2 Teukolsky fields.
  Exterior Stability · Partial progress · Open in literature · Quantitative sharpening
• K-613 — Build an explicit linearized-gravity scattering map exterior to Cauchy horizon for Kerr.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-614 — Prove sharp asymptotics for the Teukolsky field in the Kerr interior (Price law inside).
  Interior / SCC · Open · Open in literature · Classical frontier
• K-615 — Show that small vacuum perturbations of Kerr produce weak null singularities generically at the Cauchy horizon.
  Interior / SCC · Partial progress · Open in literature · Classical frontier
• K-616 — Prove robust control of trapping geometry under dynamical near-Kerr perturbations in a sharp topology.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-617 — Prove a quantitative distance-to-Kerr estimate from a small invariant (Mars-Simon-type) with computable constants.
  Rigidity / Uniqueness · Open · Open in literature · Quantitative sharpening
• K-618 — Prove global Kerr uniqueness without analyticity under minimal smoothness/decay hypotheses.
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-619 — Prove uniqueness of stationary black holes with small deviations in asymptotic charges (effective inverse problems).
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-620 — Establish a rigorous nonlinear theory for extremal Kerr dynamics incorporating Aretakis charges.
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-621 — Prove a definitive linear stability/instability dichotomy for extremal Kerr spin-2 with sharp norms.
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-622 — Prove uniform (in kappa) energy/decay estimates for near-extremal Kerr approaching kappa to 0.
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-623 — Build a rigorous scattering theory for NHEK matching to global Kerr exterior at near-extremality.
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-624 — Prove a sharp characterization of near-extremal QNM clustering with explicit remainders.
  Spectral / Scattering · Open · Open in literature · Quantitative sharpening
• K-625 — Prove completeness/expansion of solutions in Kerr via QNMs plus branch-cut contributions (mathematical ringdown expansion).
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-626 — Prove a Kerr inverse problem: determine (M,a) from finitely many resonances with stability estimates.
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-627 — Establish pseudospectrum bounds for Kerr wave operators and relate to transient growth near superradiance.
  Spectral / Scattering · Open · Open in literature · Quantitative sharpening
• K-628 — Derive rigorous late-time tail constants for scalar wave on Kerr in full subextremal range.
  Exterior Stability · Open · Open in literature · Quantitative sharpening
• K-629 — Prove robust decay estimates for Maxwell/Dirac fields on Kerr without small-a restriction, in sharp norms.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-630 — Prove nonlinear stability of Schwarzschild without codimension restrictions (full moduli convergence to Kerr).
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-631 — Prove a unified framework for gauge choices in nonlinear black-hole stability compatible with $\mathcal{I}^+$ expansions and interior analysis.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-632 — Quantify how much Kerrness can be certified from finite-radius curvature invariants (numerical-relativity certification).
  Exterior Stability · Open · Open in literature · Quantitative sharpening
• K-633 — Prove that near-Kerr spacetimes admit approximate Carter operators with controlled commutators (usable in PDE estimates).
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-634 — Classify all second-order symmetry operators commuting with the scalar wave operator on Kerr.
  Rigidity / Uniqueness · Needs review · High-value / unformalized direction · Formalization target
• K-635 — Establish quantitative stability of photon regions for small metric perturbations in Ck/Sobolev norms.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-636 — Prove sharp semiclassical quantization of Kerr QNMs with explicit high-frequency error bounds.
  Spectral / Scattering · Open · Open in literature · Quantitative sharpening
• K-637 — Prove rigorous existence and nonlinear stability/instability classification of Kerr-AdS endstates (black resonators/geons).
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-638 — Prove nonlinear instability of Kerr-AdS in a theorem (beyond numerics/backreaction studies).
  Spectral / Scattering · Partial progress · Open in literature · Quantitative sharpening
• K-639 — Classify superradiant instability windows for massive scalar fields on Kerr in fully rigorous parameter inequalities.
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-640 — Prove nonlinear outcomes of Einstein-Klein-Gordon near Kerr in regimes with linear superradiant instability.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-641 — Prove the interior blue-shift blow-up for linearized gravity without auxiliary decay assumptions (purely from generic initial data).
  Interior / SCC · Open · Open in literature · Classical frontier
• K-642 — Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-643 — Establish a sharp criterion for when Kerr interior admits C0 extension vs stronger regularity failure (in terms of horizon tails).
  Interior / SCC · Open · Open in literature · Classical frontier
• K-644 — Prove a full nonlinear characteristic IVP theorem from event-horizon data to the interior boundary in near-Kerr vacuum.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-645 — Quantify the nonlinear backreaction of Price-law tails on Kerr interior geometry (mass inflation vs weak null singularity).
  Interior / SCC · Open · Open in literature · Quantitative sharpening
• K-646 — Prove global uniqueness/rigidity for Kerr with minimal assumptions on horizon regularity and connectedness.
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-647 — Prove a minimal-data theorem: finite set of horizon multipoles determines Kerr parameters with stability bounds.
  Rigidity / Uniqueness · Open · Open in literature · Quantitative sharpening
• K-648 — Prove existence/uniqueness of approximate Kerr solutions given approximate Killing spinors (computable error-to-parameter map).
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-649 — Formalize in a proof assistant: the exact Kerr separability structure and Carter constant derivation.
  Exterior Stability · Open · High-value / unformalized direction · Formalization target
• K-650 — Formalize: equivalence of Teukolsky and Regge-Wheeler transformations in Schwarzschild and slowly rotating Kerr.
  Exterior Stability · Needs review · Solved in literature (classical) · Formalization target
• K-651 — Prove linear stability of Kerr in alternative gauges (radiation gauges, generalized wave gauges) with explicit gauge maps.
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-652 — Prove nonlinear stability of Kerr under weaker asymptotic flatness (polyhomogeneous/rough null infinity assumptions).
  Exterior Stability · Open · Open in literature · Classical frontier
• K-653 — Establish sharp decay for Teukolsky equation on Kerr in full range with quantitative constants usable as blackboxes.
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-654 — Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.
  Interior / SCC · Partial progress · Open in literature · Classical frontier
• K-655 — Prove explicit sharp late-time asymptotics for scalar field along the event horizon in Kerr (full range).
  Exterior Stability · Open · Open in literature · Classical frontier
• K-656 — Prove decay/growth dichotomy for extremal Kerr perturbations with explicit identification of conserved charges.
  Extremal / Near-Extremal · Partial progress · Open in literature · Classical frontier
• K-657 — Prove nonlinear evolution of near-horizon conserved quantities in extremal Kerr produces curvature singularity (or not).
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-658 — Prove linear stability/instability classification for extremal Kerr-Newman under coupled perturbations.
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-659 — Prove sharp resolvent bounds near omega=0 for Kerr linearized Einstein operator, uniform in a/M.
  Exterior Stability · Partial progress · Open in literature · Quantitative sharpening
• K-660 — Establish a full nonlinear ringdown plus tail decomposition for near-Kerr vacuum spacetimes.
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-661 — Determine whether QNM expansions are stable under small nonlinearities (nonlinear resonance theory).
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-662 — Develop a rigorous theory of excitation factors in Kerr and prove universal bounds across (l,m).
  Spectral / Scattering · Open · Open in literature · Quantitative sharpening
• K-663 — Prove stability of the photon sphere/trapped set for families of metrics satisfying Einstein vacuum approximately.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-664 — Prove robust decay estimates for wave/Teukolsky equations on perturbed Kerr backgrounds without separability.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-665 — Prove quantitative mode stability for Kerr-de Sitter in full subextremal range and feed into nonlinear stability.
  Exterior Stability · Conditional · Open in literature · Classical frontier
• K-666 — Prove SCC threshold for Kerr-de Sitter and Kerr-Newman-de Sitter with explicit dependence on spectral gap.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-667 — Prove stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-668 — Prove a nonlinear interior from exterior theorem: decay on event horizon implies interior weak null singularity.
  Interior / SCC · Open · Open in literature · Classical frontier
• K-669 — Prove global existence and weak cosmic censorship for small perturbations of Kerr data in an appropriate gauge.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-670 — Prove existence of trapped surfaces in vacuum from very low regularity characteristic data.
  Exterior Stability · Open · High-value / unformalized direction · Speculative direction
• K-671 — Derive sharp stability thresholds for massive fields on Kerr: identify stable/unstable mass windows with proofs.
  Exterior Stability · Partial progress · Open in literature · Classical frontier
• K-672 — Prove that generic small perturbations of Kerr generate nonzero angular momentum in the asymptotic Kerr parameter (modulation).
  Exterior Stability · Open · Open in literature · Classical frontier
• K-673 — Prove a quantitative angular-momentum extraction formula from $\mathcal{I}^+$ radiation for near-Kerr vacuum spacetimes.
  Exterior Stability · Open · Open in literature · Quantitative sharpening
• K-674 — Prove that near-Kerr spacetimes admit a robust foliation by generalized GCM spheres with quantified control.
  Exterior Stability · Partial progress · Open in literature · Quantitative sharpening
• K-675 — Prove uniqueness/stability of event-horizon generators and their expansion/shear in near-Kerr evolution.
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-676 — Prove sharp bounds on superradiant amplification for waves on Kerr uniform in a/M.
  Exterior Stability · Open · Open in literature · Quantitative sharpening
• K-677 — Prove stability of Kerr under small non-vacuum perturbations (e.g., Einstein-Vlasov) in a near-Kerr regime.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-678 — Prove nonlinear stability of Kerr under polarized symmetry-breaking perturbations (intermediate symmetry classes).
  Exterior Stability · Open · Open in literature · Classical frontier
• K-679 — Prove stability/instability of higher-dimensional Kerr (Myers-Perry) in PDE sense for small angular momentum.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-680 — Prove rigorous statements about tails vs memory interaction in near-Kerr: do late-time tails source measurable memory at $\mathcal{I}^+$?
  Exterior Stability · Open · Open in literature · Classical frontier
• K-681 — Develop a mathematically rigorous definition of nonlinear QNMs as poles of a suitable nonlinear response functional.
  Spectral / Scattering · Open · Open in literature · Speculative direction
• K-682 — Prove that Kerr QNMs are stable under small perturbations of the metric in a topology relevant to stability proofs.
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-683 — Prove a sharp characterization of the Kerr trapped set as a normally hyperbolic invariant manifold uniformly in a/M.
  Spectral / Scattering · Partial progress · Open in literature · Classical frontier
• K-684 — Prove that the linearized Einstein operator on Kerr has no embedded eigenvalues/resonances on the real axis beyond gauge.
  Spectral / Scattering · Partial progress · Open in literature · Classical frontier
• K-685 — Prove quantitative stability of the Carter constant for geodesics under small metric perturbations.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-686 — Prove an effective theorem translating small Mars-Simon tensor into existence of approximate Killing spinors.
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-687 — Prove a black-hole uniqueness theorem for near Kerr-Newman-de Sitter without analyticity in smooth category.
  Rigidity / Uniqueness · Open · Open in literature · Classical frontier
• K-688 — Prove a fully rigorous PDE theorem for nonlinear superradiant instability of Kerr in a confining setting (mirror/AdS).
  Spectral / Scattering · Open · Open in literature · Classical frontier
• K-689 — Prove existence and stability of time-periodic near-Kerr solutions (vacuum or with fields) if any.
  Exterior Stability · Open · High-value / unformalized direction · Speculative direction
• K-690 — Prove robust constraints on nonlinear energy cascades near Kerr (no-turbulence regimes) under small data.
  Exterior Stability · Open · Open in literature · Speculative direction
• K-691 — Prove that event-horizon redshift estimates remain valid for near-extremal Kerr with uniform constants away from kappa=0.
  Extremal / Near-Extremal · Open · Open in literature · Classical frontier
• K-692 — Prove sharp mapping properties of the Kerr scattering operator in weighted Sobolev spaces matching physical radiation norms.
  Spectral / Scattering · Open · Open in literature · Quantitative sharpening
• K-693 — Prove deterministic stability results for Kerr under stochastic perturbations (noise robustness in PDE sense).
  Exterior Stability · Open · High-value / unformalized direction · Speculative direction
• K-694 — Prove sharp stability of Kerr under small violations of vacuum Einstein (numerical truncation errors).
  Exterior Stability · Open · High-value / unformalized direction · Speculative direction
• K-695 — Formalize in a proof assistant: Carter separability and associated conserved quantities for Kerr geodesics.
  Exterior Stability · Open · High-value / unformalized direction · Formalization target
• K-696 — Formalize: perturbative uniqueness near Kerr using Mars-Simon tensor estimates (machine-checkable Carleman skeleton).
  Rigidity / Uniqueness · Open · Open in literature · Formalization target
• K-697 — Prove that Kerr is uniquely determined among stationary vacua by a finite set of multipole moments with stability.
  Rigidity / Uniqueness · Open · Open in literature · Quantitative sharpening
• K-698 — Prove stability/instability of the Kerr Cauchy horizon for nonlinear vacuum perturbations with genericity (beyond C0).
  Interior / SCC · Open · Open in literature · Classical frontier
• K-699 — Prove that generic near-Kerr perturbations lead to curvature blow-up rates matching those predicted by linear theory.
  Exterior Stability · Open · Open in literature · Classical frontier
• K-700 — Produce a complete, cited dependency graph of Kerr stability research milestones with verified theorem statements.
  Exterior Stability · Open · High-value / unformalized direction · Literature reformulation