Top Open Problems
The Top Open Problems editorial order restricted to Physics, with ranks numbered within this field. Unassessed entries retain their previous relative order. About rankings
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- Phys-1 Yang–Mills Existence and Mass Gap
- Phys-2 Prove the Penrose inequality or present a counterexample
- Phys-3 Entanglement Area Law for 2D Gapped Quantum Systems
- Phys-4 Extended States in the Anderson Model
- Phys-5 Conformal Field Theory Limit of the Critical Three-Dimensional Ising Model
- Phys-6 Non-Perturbative Construction and Non-Triviality of 4D Euclidean Phi4 Quantum Field Theory
- Phys-7 Bose-Einstein Condensation in Continuum Models
- Phys-8 Non-Triviality of the Three-Dimensional Ising Model
- Phys-9 The Haldane Conjecture on Spectral Gaps of Antiferromagnetic Quantum Spin Chains
- Phys-10 Quantum Unique Ergodicity on Negatively Curved Manifolds
- Phys-11 Prove the BKL locality conjecture in the general inhomogeneous context
- Phys-12 Polyakov Conjecture: Absence of a Phase Transition for Planar O(n) Models with n >= 3
- Phys-13 Long-Range Order in the Quantum Heisenberg Ferromagnet
- Phys-14 Global Dynamics of the Vlasov–Maxwell System
- Phys-15 Berry random-wave conjecture: real negative-curvature BS formulation
- Phys-16 Equivalence or Strict Containment of QMA and QMA(2)
- Phys-17 Exact Unassisted Quantum Capacity of the Qubit Depolarizing Channel
- Phys-18 Bound Entanglement with Negative Partial Transpose
- Phys-19 Secret key from all entangled states
- Phys-20 Néel Order for the Spin-1/2 Square-Lattice Heisenberg Antiferromagnet (Averaged Ground-State Order)
- Phys-21 Discontinuity of the q-State Potts Phase Transition on Z^d for d >= 3 and q >= 3
- Phys-22 Constant-Parameter Quantum Locally Testable Codes
- Phys-23 Mutually Unbiased Bases in Non-Prime-Power Dimensions
- Phys-24 Aaronson-Ambainis Conjecture
- Phys-25 Soft Phases in Two-Dimensional O(N) Models
- Phys-26 Long-Range Order for the Quantum Heisenberg Model
- Phys-27 Extended States with Extensive Disorder
- Phys-28 Localization in Two Dimensions
- Phys-29 Bounded Excess Electrons
- Phys-30 Asymptotics of Atomic Ionization Energy
- Phys-31 One-Dimensional Lieb-Thirring Constants
- Phys-32 Mutually Unbiased Bases in Dimension Six
- Phys-33 Non-self-adjoint spectral theory: completeness, reconstruction, and matrix-function bounds
- Phys-34 Strong Cosmic Censorship at Weak Regularity
- Phys-35 Hemisphere Partition Functions and Stability Across GLSM Phases
- Phys-36 Universal Bounds on Atomic Excess Charge
- Phys-37 Mass–Angular-Momentum Inequalities with Trapped and Multiple Horizons
- Phys-38 Maximum Excess Charge of Atoms
- Phys-39 Rigorous Mesoscopic Limits of Many-Particle Systems
- Phys-40 Low-Temperature Order in Quantum Heisenberg Ferromagnets
- Phys-41 AQFT Locality of Unitary Vertex Operator Algebras
- Phys-42 The numerical spacetime enclosing-area inequality in every dimension
- Phys-43 Single-letter classical capacity of generalized amplitude damping
- Phys-44 Unbounded positive point spectrum of relative SU(2) BFSS
- Phys-45 Exactly one threshold bound state in every relative SU(N) BFSS model
- Phys-46 QMA hardness of continuum electronic energy with binary nuclear charges
- Phys-47 The first lattice correction to quantum Bloch magnetization
- Phys-48 Polynomial quantum synthesis of any unitary using a suitable Boolean oracle
- Phys-49 A gap in the open spin-one chain with fixed same-sign boundary fields
- Phys-50 A conditional charged Penrose bound in spatial dimension at least four