Mathematics catalogue
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-12101 A gauge-invariant action-gap certificate for barbell transit orbits
- Math-12102 The four-body super-eight and the rotating-square obstruction
- Math-12103 Fixed winding numbers: exact pair bounds, graph coercivity, and collision loss
- Math-12104 Homology-only escape and a strict zero-winding choreography gap
- Math-12105 Coercivity and collision boundaries for the Broucke-Henon class (1,0,1)
- Math-12106 Coercivity, collision support, and the identity braid for the class (1,0,-1)
- Math-12107 Syzygy-word parity and the angular-momentum holonomy obstruction
- Math-12108 When constrained minimizers gain symmetry
- Math-12109 Quantitative simplex and dimension bounds for minimum-potential equal-mass configurations
- Math-12110 Circulant mass compatibility and a six-body temporal Fourier obstruction
- Math-12111 Fourier obstructions to unequally phased single-trace motions
- Math-12112 Effective full-isotropy constraints for time-space-label symmetries
- Math-12113 Matrix virial decomposition and a collision-free tensor stress test
- Math-12114 An affine-defect test for Newtonian motions
- Math-12115 The syzygy-free three-body solution and quantitative crossing certificates
- Math-12116 Closure-area limit sets and geometric phase on the shape sphere
- Math-12117 Constant normalized area in the three-body problem
- Math-12118 A logarithmic-volume identity and zero-angular-momentum obstruction
- Math-12119 Zero-total-mass reduction and obstruction to the Euler integral
- Math-12120 Level-orbit potentials: quantifier audit, speed criterion, and transnormal rigidity
- Math-12121 A Jacobi-Maupertuis and McGehee scale-shape dictionary
- Math-12122 Limits of action minimization: collisions, constraints, stability, and fixed energy
- Math-12123 Quantitative collinear finiteness and maximal-dimensional simplex rigidity
- Math-12124 Normal Hessian blocks, an exact four-body index jump, and stability obstructions
- Math-12125 Compatibility and reversible shooting for connections between relative equilibria
- Math-12126 Exact reversible shooting criterion for halo-orbit bifurcation
- Math-12127 A feasibility sieve for negative-energy binary-single direct scattering
- Math-12128 Full-space mass-splitting criterion for prograde relative periodic orbits
- Math-12129 Multipartite Dense-Coding Capacity
- Math-12130 LOCC Dense-Codeability of the Four-Qubit W State
- Math-12131 Facial Structure of Classical and Quantum Correlation Sets
- Math-12132 Connections Between CGLMP Inequalities and Quantum Field Theory
- Math-12133 Positive Maps and Multipartite Bound Entanglement
- Math-12134 Systematic Multiscale Design of Hierarchical Materials
- Math-12135 Relationship Between Two-Species Condensates
- Math-12136 Physical Interpretation of Elliptic Partition Functions
- Math-12137 Physical Regularity Criteria for Massless Scattering Theory
- Math-12138 Bounded Local Observables in Factorizing Quantum Field Theories
- Math-12139 Renormalization through Langmann–Szabo Duality
- Math-12140 Geometric Spin–Statistics under Weakened Assumptions
- Math-12141 Spectral Geometry and Cyclic Homology of $SU_q(2)$
- Math-12142 Scaling Limits of Tensor Products in AQFT
- Math-12143 Heterotic Mirror Symmetry for Bundled Calabi–Yau Manifolds
- Math-12144 Deformations and Massless Spectra of Smooth Deligne–Mumford Stacks
- Math-12145 Infrared Equivalence of Stack Presentations
- Math-12146 Gauge Fixing for Quantum Vertex Algebra Deformations
- Math-12147 Hoop Conjecture for Black-Hole Formation
- Math-12148 Orthotropic Extensions of Anisotropic Creep-Damage Models
- Math-12149 Nonperturbative Infrared Behavior of Nonamenable Sigma Models
- Math-12150 Continuous-Spectrum Analysis of Nelson-Type Models