Mathematics
Open problems, research attempts and community review.
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-2851 Uniqueness of admissible periodic hard-sphere Boltzmann evolution
- Math-2852 Halting detection by a fixed particle under initialized periodic solenoidal forcing
- Math-2853 Computation under rapidly vanishing force in one fixed spatial box
- Math-2854 Halting detection under reciprocal-time decaying torus forcing
- Math-2855 Smooth anisotropic conductivity uniqueness from a single proper patch
- Math-2856 Full-boundary recovery of both smooth isotropic elastic moduli
- Math-2857 Strict hot spots and absence of critical points for smooth planar Neumann ground modes
- Math-2858 Classification of every bounded stable Allen–Cahn solution in dimension seven
- Math-2859 The Boltzmann–Grad limit throughout a regular kinetic lifespan
- Math-2860 Strong diffeomorphic approximation of three-dimensional homeomorphisms above exponent two
- Math-2861 Strong diffeomorphic approximation of three-dimensional Sobolev homeomorphisms up to exponent two
- Math-2862 GOE bulk statistics for weakly disordered regular-graph operators
- Math-2863 The joint GFF and cluster limit of critical Ashkin–Teller currents
- Math-2864 The exact GFF variance of balanced six-vertex heights
- Math-2865 The sharp singularity exponent of biased symmetric sign matrices
- Math-2866 A directional zero–one law for finite-range-dependent random environments
- Math-2867 The exact hierarchical cavity pressure for dilute even-arity spin glasses
- Math-2868 The nested CLE limit of half-plane double-dimer loops
- Math-2869 Strict convexity and differentiability of the exponential planar passage shape
- Math-2870 Metric–measure universality of subcritical FK and tree-weighted maps
- Math-2871 Conformal geometry of spherical FK maps at weight four
- Math-2872 Conformal metric and loop convergence of FK maps below four
- Math-2873 Joint metric, spectrum and heat-trace limit for FK–Ising maps
- Math-2874 Liouville Brownian motion as the walk limit on FK–Ising maps
- Math-2875 Natural occupation measures of critical FK interfaces
- Math-2876 Joint SLE and CLE limits at FK weights from one through four
- Math-2877 The continuum tree limit of FK maps above weight four
- Math-2878 Critical square-lattice FK interfaces below random-cluster weight one
- Math-2879 A nonlinear-capacity criterion for four-state reconstruction on arbitrary trees
- Math-2880 The exact reconstruction threshold of the ferromagnetic four-state channel
- Math-2881 The exact IID-factor threshold for free Ising laws on regular trees
- Math-2882 One root-independent IID factor for all free uniform spanning forests
- Math-2883 The all-temperature spherical Gaussian perceptron pressure
- Math-2884 BKT scaling and the endpoint stiffness for finite-range integer heights
- Math-2885 The mass and mean length of critical bridges in a fixed-width corridor
- Math-2886 The fugacity-dependent cylinder exponent for critical honeycomb loops
- Math-2887 Diameter, local mass and covering exponents of fixed-length honeycomb walks
- Math-2888 Critical honeycomb polygon diameter and length exponents
- Math-2889 The length exponent of critical honeycomb chords with fixed endpoints
- Math-2890 Partition and mean-length exponents for macroscopic triangular honeycomb chords
- Math-2891 The all-temperature pressure of orthogonally invariant Ising disorder
- Math-2892 Spherical perceptron pressure with orthogonally invariant disorder
- Math-2893 The thermodynamic pressure of every bounded Gaussian Ising perceptron activation
- Math-2894 Universal gap and force exponents at negative spherical-perceptron jamming
- Math-2895 Finite critical two-point operator norm and nonuniqueness for nonamenable graphs
- Math-2896 A non-Gaussian massive continuum theory from the planar O(3) model
- Math-2897 An isolated lightest particle in the continuum O(3) spin field
- Math-2898 The exact low-temperature transfer gap of the planar O(4) model
- Math-2899 A GFF limit for triangular odd heights with two boundary arcs
- Math-2900 Critical nonpercolation on locally finite quasi-transitive graphs below one