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-4701 Hurwitz class numbers, CM enumeration, and local conductor layers
- Math-4702 Formal, Jacobi, and wave-function transformations of the string coupling
- Math-4703 Mirror-quintic periods, modular-type structures, and a conifold obstruction
- Math-4704 Functional equations and an Euler-product obstruction for mixed mock L-series
- Math-4705 Hauptmodul differential equations for an even-weight mixed-mock class
- Math-4706 Mock modularity, geometric invariants, and finite pole tomography
- Math-4707 A two-vertex counterexample to color-number monotonicity
- Math-4708 Equatorial symmetry and a Jacobian-jet test for local Kerr caustic cusps
- Math-4709 An invariant certificate for caustic-forming Kerr rays
- Math-4710 Melrose's answer, compact Sobolev embedding, and escape of mass
- Math-4711 Why gravitational instantons arise from monopoles
- Math-4712 A synchronized heat-kernel construction on eight-dimensional hyperkähler products
- Math-4713 Audible primitive two-torus areas on a flat three-torus
- Math-4714 Centered asymptotics for a Gibbons--Hawking subfamily
- Math-4715 A quantified Gibbons-Hawking N-body cluster model
- Math-4716 The L2-signature of toric hyperkahler quotients
- Math-4717 A smoothness criterion for projective conic compactifications of ALF twistor models
- Math-4718 Topology and character sectors in monopole L2-cohomology
- Math-4719 The signed Hill threshold for binary exchange
- Math-4720 A gauge-invariant action-gap certificate for barbell transit orbits
- Math-4721 The four-body super-eight and the rotating-square obstruction
- Math-4722 Fixed winding numbers: exact pair bounds, graph coercivity, and collision loss
- Math-4723 Homology-only escape and a strict zero-winding choreography gap
- Math-4724 Coercivity and collision boundaries for the Broucke-Henon class (1,0,1)
- Math-4725 Coercivity, collision support, and the identity braid for the class (1,0,-1)
- Math-4726 Syzygy-word parity and the angular-momentum holonomy obstruction
- Math-4727 When constrained minimizers gain symmetry
- Math-4728 Quantitative simplex and dimension bounds for minimum-potential equal-mass configurations
- Math-4729 Circulant mass compatibility and a six-body temporal Fourier obstruction
- Math-4730 Fourier obstructions to unequally phased single-trace motions
- Math-4731 Effective full-isotropy constraints for time-space-label symmetries
- Math-4732 Matrix virial decomposition and a collision-free tensor stress test
- Math-4733 An affine-defect test for Newtonian motions
- Math-4734 The syzygy-free three-body solution and quantitative crossing certificates
- Math-4735 Closure-area limit sets and geometric phase on the shape sphere
- Math-4736 Constant normalized area in the three-body problem
- Math-4737 A logarithmic-volume identity and zero-angular-momentum obstruction
- Math-4738 Zero-total-mass reduction and obstruction to the Euler integral
- Math-4739 Level-orbit potentials: quantifier audit, speed criterion, and transnormal rigidity
- Math-4740 A Jacobi-Maupertuis and McGehee scale-shape dictionary
- Math-4741 Limits of action minimization: collisions, constraints, stability, and fixed energy
- Math-4742 Quantitative collinear finiteness and maximal-dimensional simplex rigidity
- Math-4743 Normal Hessian blocks, an exact four-body index jump, and stability obstructions
- Math-4744 Compatibility and reversible shooting for connections between relative equilibria
- Math-4745 Exact reversible shooting criterion for halo-orbit bifurcation
- Math-4746 A feasibility sieve for negative-energy binary-single direct scattering
- Math-4747 Full-space mass-splitting criterion for prograde relative periodic orbits
- Math-4748 Multipartite Dense-Coding Capacity
- Math-4749 LOCC Dense-Codeability of the Four-Qubit W State
- Math-4750 Facial Structure of Classical and Quantum Correlation Sets