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-2751 An exponential threshold-repetition bound for arbitrary finite entangled games
- Math-2752 The entropy photon-number inequality for arbitrary finite-mode inputs
- Math-2753 Exact quantum factoring over one fixed finite gate set
- Math-2754 The exact Bloch coefficient for three-dimensional finite-range quantum ferromagnets
- Math-2755 The universal quantum-depletion constant for fixed bounded repulsions
- Math-2756 Polynomial-bond PEPS approximation of every gapped square-grid ground vector
- Math-2757 Thomas–Fermi asymptotics for growing atomic ionization number
- Math-2758 The Bogoliubov momentum law for the dilute hard-sphere ground state
- Math-2759 Condensation in every dilute hard-sphere ground state
- Math-2760 A spherical distribution of the low-temperature total quantum spin
- Math-2761 The area, charge and angular-momentum bound with controlled electromagnetic tails
- Math-2762 The Kerr–Newman area bound without electromagnetic-tail controls
- Math-2763 A Laughlin gap stable under every small bounded scalar perturbation
- Math-2764 A size-independent spectral gap above the spherical Laughlin line
- Math-2765 Every extremizer of the sharp matrix Lieb–Thirring bound
- Math-2766 The sharp one-dimensional finite-matrix Lieb–Thirring inequality
- Math-2767 A uniform bound on excess electrons in full Coulomb molecules
- Math-2768 Generic C1 future inextendibility near rotating subextremal Kerr
- Math-2769 Generic C2 future inextendibility near rotating subextremal Kerr
- Math-2770 Generic weak future inextendibility near a fixed rotating Kerr datum
- Math-2771 The nonmaximal anti-de Sitter enclosing-area inequality
- Math-2772 Conformal stress improvement in the finite-scaling-support operational framework
- Math-2773 The universal radius containing all but m electrons of neutral atoms
- Math-2774 A uniform gap in the periodic spin-one antiferromagnetic chain
- Math-2775 A parity lower bound for bounded-depth quantum circuits with polynomial ancillas
- Math-2776 QAOA reaches the SK ground value when thermodynamic size is taken first
- Math-2777 The Riemannian Penrose bound with minimizing frontiers in every dimension
- Math-2778 Full support of every zero-temperature SK minimizing order parameter
- Math-2779 Original-data rigidity at equality in spacetime Penrose bounds
- Math-2780 Conformal nets and representation equivalence for strongly rational unitary VOAs
- Math-2781 The optimal randomized-versus-quantum query exponent for total Boolean functions
- Math-2782 QMA hardness using only unit-charge nuclei in the continuum
- Math-2783 Elliptic-square intersections of Hodge-generic curves in A2
- Math-2784 Product-CM intersections of Hodge-generic curves in A2
- Math-2785 Quaternionic division intersections of Hodge-generic curves in A2
- Math-2786 Zilber-Pink for abelian varieties over Qbar
- Math-2787 Primitive-root infinitude for every admissible base
- Math-2788 Corrected binary Elliott for ordinary averages
- Math-2789 Integral-point density on curve character varieties
- Math-2790 The exact BSD formula at low Selmer corank
- Math-2791 Generic Ramanujan for exceptional groups over function fields
- Math-2792 An explicit asymptotic formula for the number of totients
- Math-2793 Odd regular Fontaine-Mazur over Q at two
- Math-2794 Full finite-level Ramanujan-Arthur decomposition
- Math-2795 Global Arthur enhancements of occurring excursion parameters
- Math-2796 Goldfeld analytic rank density over Q
- Math-2797 Mean analytic rank of quadratic twists over Q
- Math-2798 Modularity of elliptic curves over imaginary quadratic fields
- Math-2799 The joint Dickman law for consecutive integers
- Math-2800 Milnor K reconstruction at the characteristic prime