Top Open Problems
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2901 Critical honeycomb polygon diameter and length exponents
- Math-2902 The length exponent of critical honeycomb chords with fixed endpoints
- Math-2903 Partition and mean-length exponents for macroscopic triangular honeycomb chords
- Math-2904 The all-temperature pressure of orthogonally invariant Ising disorder
- Math-2905 Spherical perceptron pressure with orthogonally invariant disorder
- Math-2906 The thermodynamic pressure of every bounded Gaussian Ising perceptron activation
- Math-2907 Universal gap and force exponents at negative spherical-perceptron jamming
- Math-2908 Finite critical two-point operator norm and nonuniqueness for nonamenable graphs
- Math-2909 A non-Gaussian massive continuum theory from the planar O(3) model
- Math-2910 An isolated lightest particle in the continuum O(3) spin field
- Math-2911 The exact low-temperature transfer gap of the planar O(4) model
- Math-2912 A GFF limit for triangular odd heights with two boundary arcs
- Math-2913 Critical nonpercolation on locally finite quasi-transitive graphs below one
- Math-2914 A first-order temperature singularity for a stable radial continuum gas
- Math-2915 A limiting density threshold for every fixed random clause size
- Math-2916 Linear hitting-time variance for random clause size at least four
- Math-2917 Linear variance of the random 3-SAT unsatisfiability time
- Math-2918 Interface and field scaling limits of triangular real Lipschitz surfaces
- Math-2919 Critical SK mixing, relaxation and log-Sobolev exponents
- Math-2920 A universal joint critical SK equilibrium and quench autocorrelation law
- Math-2921 Critical SK mixing lower bounds from realized Gibbs states
- Math-2922 Glauber cutoff throughout the high-temperature SK phase
- Math-2923 A size-independent Gibbs Poincaré constant throughout high-temperature SK
- Math-2924 A limiting law for standardized low-temperature SK free energy
- Math-2925 The one-sixth free-energy fluctuation exponent in low-temperature SK
- Math-2926 Stretched-exponential mixing barriers for typical low-temperature SK starts
- Math-2927 A subexponential mixing bound from typical low-temperature SK starts
- Math-2928 A deterministic exact Hausdorff gauge for ordinary SLE
- Math-2929 The explicit logarithmic Hausdorff correction for SLE
- Math-2930 IID factors for invariant strongly Rayleigh laws on countable groups
- Math-2931 Massive interface limits under thermal FK–Ising perturbation
- Math-2932 Logarithmic total-variation mixing of the physical Thorp shuffle
- Math-2933 The exact weak-recovery threshold for the symmetric three-community SBM
- Math-2934 Oracle-free computation of the limiting random 3-SAT threshold
- Math-2935 The exact three-state reconstruction threshold including equality
- Math-2936 A deterministic linear walk clock on tree-weighted planar maps
- Math-2937 Cardy crossing probabilities for Poisson–Voronoi percolation
- Math-2938 Near-critical Voronoi universality conditional on Cardy limits
- Math-2939 The Voronoi pivotal-count amplitude under Cardy’s formula
- Math-2940 A quenched SLE limit for weakly disordered FK–Ising interfaces
- Math-2941 Conformal limits of all mixed Ising spin and energy correlations
- Math-2942 SLE interfaces for weakly interacting planar Ising models
- Math-2943 Quenched critical Ising interfaces under weak bond disorder
- Math-2944 Logarithmic relative fluctuations of disordered critical Ising correlations
- Math-2945 GFF limits of weighted integer Lipschitz surfaces
- Math-2946 Critical center magnetization in fixed-boundary XY boxes
- Math-2947 The essential singularity of the planar XY correlation length
- Math-2948 The logarithmic factor in critical planar XY correlations
- Math-2949 The critical correlation power of the nearest-neighbor planar XY model
- Math-2950 The full critical XY spin-field limit with fixed boundary