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-5101 Low-degree integral curves on the Fermat fourfold
- Math-5102 A local-defect lower bound for the 3-Selmer group over cyclic cubic fields
- Math-5103 A PAC counterexample and the projectivity boundary
- Math-5104 A fiberwise harmonic bridge on the quintic del Pezzo torsor
- Math-5105 Arakelov replacement and a surface exponent-transfer lemma
- Math-5106 A transfer principle and the full Banach range for lacunary rotation-coupled circle averages
- Math-5107 Near-sharp trilinear convolution range on transverse patches of the 3-sphere
- Math-5108 The critical logarithmic endpoint model
- Math-5109 Normalization and the constant-one multilinear Kakeya question
- Math-5110 Pure-state extensions across a split ideal
- Math-5111 Directional hyperbolic families and the obstruction to a uniform leaf
- Math-5112 Sharp root motion for a first-order stability preserver
- Math-5113 Exact lower witnesses in the complete-edge Weaver family
- Math-5114 Facewise strongly-Rayleigh completion and a sharp marginal packing threshold
- Math-5115 Exact finite Feichtinger partition count and a sharp ceiling obstruction
- Math-5116 Equal-measure sets can have different exponential-frame partition data
- Math-5117 Constructive syndetic partitions via restricted DFT matroids and irrational rotations
- Math-5118 A mixed-discriminant reconstruction of the five-way spanning problem
- Math-5119 Quantitative counts of Weaver-good bipartitions
- Math-5120 Generating interlacing families by real-rootedness preservers
- Math-5121 Fixed-diagonal geometry and an exact 4x4 two-paving profile
- Math-5122 A support-discrepancy formulation for zonotope generator partitions
- Math-5123 A one-sided endpoint criterion for largest-root selection
- Math-5124 A CUE critical-point sum rule and the small-exponent Jensen bridge
- Math-5125 A constant-intensity obstruction to negatively correlated GAF zeros
- Math-5126 Covariance, diagonal, and normalized-kernel criteria for Gaussian entire functions
- Math-5127 Exact GUE-zero insertion amplitudes and a coefficient-space obstruction
- Math-5128 Stationary zero-process obstruction to reconstruction from real zeros
- Math-5129 Weight-only modularity recognition has a finite-data obstruction
- Math-5130 A finite-theta certificate for sum-side modularity
- Math-5131 Torsion continuous q-Hermite expansions as Siegel modular units
- Math-5132 Coupled rank-two Nahm sums as modular units and partition series
- Math-5133 An exact q-dilogarithmic action and finite-q Nahm equation
- Math-5134 Character-phase evidence for Elliott--Halberstam and a sparse twisted-psi diagonal
- Math-5135 Exact indicator extremizers for complete-grid large sieve inequalities
- Math-5136 A spliced large-sieve/zeta record and a local 1-line zeta certificate
- Math-5137 A quantitative short-interval transfer for small values of ap-q
- Math-5138 Alternative GPY weights: exact perturbation geometry and a radial escape
- Math-5139 Primitive balanced proper triples of sums of two squares
- Math-5140 Gauss-inseparability strata and a Frobenius plane-curve family
- Math-5141 A tangent-weight criterion for rational Hilbert components
- Math-5142 Known irreducibility regions and the explicit q=1 component decomposition
- Math-5143 Hyperplane lifting defects and a Gorenstein Rao-module obstruction
- Math-5144 A rank-three flat family where the restricted Gröbner fan jumps
- Math-5145 Monomial signatures distinguish components through affine length eight
- Math-5146 A sharp uniqueness threshold and conductor-preserving flag criterion
- Math-5147 A support-deficit criterion and the fold-singularity test family
- Math-5148 A fixed-locus criterion and an obstruction in the standard nonreduced toric chart
- Math-5149 A stabilizer-aware speciality obstruction to rigid projective curves
- Math-5150 A Pfaffian-colon reducedness certificate for Hilb^8(A^4)