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-5301 Exact membership of the origin in an ideal amoeba
- Math-5302 Prime integral counterexamples to adelic halfspace intersection
- Math-5303 Affine phase retrieval and a same-matroid obstruction
- Math-5304 Stable contour graphs and their toric ends
- Math-5305 A finite recognition certificate for planar tropical fans
- Math-5306 Convention-safe six-dimensional Q-curvature decomposition
- Math-5307 Einstein factorization and the trace-free-Ricci obstruction to Paneitz positivity
- Math-5308 Dimension four bounds total Q above and determines its exact range
- Math-5309 Spinorial nullities, Yamabe sign, and Lorentzian finiteness
- Math-5310 Exact spin-tractor holonomy formula for the twistor-spinor dimension
- Math-5311 Spin-lifted null dynamics and a parity correction on Lorentzian tori
- Math-5312 A conformal-factor cocycle proof of fact 2
- Math-5313 The Paneitz factor as a conformal gauge companion
- Math-5314 The Branson cocycle and its Weyl-scale obstruction
- Math-5315 Branson's cocycle as an action, polarization, and kernel detector
- Math-5316 The critical Q-density fibre and the kernel of P
- Math-5317 Affine conformal densities from form Q-operators
- Math-5318 Zero-section intersections in a 1-jet space
- Math-5319 Stein nonfillability of a torus prequantization
- Math-5320 Even-dimensional intersection theorem and conditional odd case for Lagrangian spheres in quadrics
- Math-5321 Pullback Hamiltonians, maximality, and toric Floer resonances
- Math-5322 A convex support-function obstruction for holomorphic curves in R x T^3
- Math-5323 Globality, Lee-cover volume, and mapping-torus resonance for lcs forms
- Math-5324 A non-exact l.c.s. family on a Sol mapping torus
- Math-5325 A uniformity hierarchy and universal-fiber reduction for DPRM over finite-characteristic polynomial rings
- Math-5326 A positive-existential definition of nonzero rationals
- Math-5327 Equal degree in polynomial rings: parameters and the place at infinity
- Math-5328 Finite-cover coordinates for a strongly minimal group
- Math-5329 Effective nonforking sections in stable theories
- Math-5330 One-jump selection and a pure-equality obstruction for the definition map
- Math-5331 What a computable nonforking section computes
- Math-5332 A finite-support obstruction to definable isomorphisms with the complex field
- Math-5333 Finite uncountable spectra and computable presentations
- Math-5334 Effective isolation and descent to the prime model
- Math-5335 Uniform principal types and computable prime models
- Math-5336 From stable norms to stable theories
- Math-5337 Randomized finite-field vector spaces solve the beautiful-pair problem
- Math-5338 A central-quotient obstruction to metric ample generics
- Math-5339 Quantitative bridge from Vershik genericity to existential closure
- Math-5340 Displacement classification and a two-level obstruction for a generic Urysohn involution
- Math-5341 Definable sets reconstruct types in omega-stable theories
- Math-5342 Compactness transfer from exact isometry to uniform almost isometry
- Math-5343 Fermat's little theorem and a bounded modular-factorial code
- Math-5344 Diophantine additive polynomials and the failure of finite Artin--Schreier tests
- Math-5345 Effective semilinearity for polynomial zeros at powers of two
- Math-5346 Effective simple-set transfer and an obstruction from noneffective localizations
- Math-5347 An inert-prime lifting criterion for the Cornelissen K3 equation
- Math-5348 Density-zero localizations do not force rank-small integral points
- Math-5349 A Prym criterion for rank preservation under Denef base change
- Math-5350 A corrected algebraic p-adic field with definable valuation and algebraically closed residue