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-4451 Multiple marked inputs: exclusion bounds and tight query regimes
- Math-4452 Finite-window reduction and binary-cost accounting for hidden shift on the integers
- Math-4453 A batch-fidelity obstruction in hidden-shift attacks on unique-SVP
- Math-4454 Exact period-quotient reduction and unary lift cost for hidden shift on Z^d
- Math-4455 Spectral laws for Gaussian multiple-shift states
- Math-4456 The cyclic core of Heisenberg hidden shift
- Math-4457 The real cost of the CSIDH hidden-shift attack
- Math-4458 Exact DDH leakage and sampler criteria for the CSIDH torsor
- Math-4459 Finite resource bounds for random spherical covering
- Math-4460 HHL, Macaulay conditioning, and presentation instability
- Math-4461 Offline Simon, explicit HSP instances, and a classical-transcript obstruction
- Math-4462 A localization-safe action of Weyl operators
- Math-4463 Degree-windowed Cech computation and the role of one b-function
- Math-4464 Fixed-ambient extraction of roots of finite Frobenius modules
- Math-4465 Random-access slices of free resolutions
- Math-4466 A fixed-basis semibasis certificate for DG-module interoperability
- Math-4467 Degree-local Hom computation and certified corner reuse
- Math-4468 Expected-Optimum Approximation for Random MAX $R$-3SAT
- Math-4469 Approximability and Parameterized Complexity of Steiner Forest
- Math-4470 Hardness of the $\varepsilon-Dense$ Steiner Tree Problem
- Math-4471 Complexity and Approximation of Planar Min-Bisection
- Math-4472 An FPAS for Constrained Bicriteria Spanning Trees
- Math-4473 Output-Polynomial Enumeration of Bicriteria Spanning Trees
- Math-4474 Polynomial-Time Computation of Ehrhart Periods
- Math-4475 Asymptotic Goodness of Function-Field-Tower Codes
- Math-4476 Recognition and Eutaxy Testing of Bacher Matrices
- Math-4477 Polynomial Complexity of Greedy Lattice Reduction
- Math-4478 Central-Trajectory Integral Bounds
- Math-4479 Nonadaptive Polynomial Stabilization of Minimum-Phase Linear Systems
- Math-4480 Stationary and Optimal Linear Differential Behaviors
- Math-4481 Computational Hardness of Learning Parity with Noise
- Math-4482 Quantum Hardness of Approximate Lattice Problems
- Math-4483 Three-Terminal Distance-Interdiction Complexity
- Math-4484 Characterization of Ideal $0$–$1$ Matrices
- Math-4485 Integral Primal Certificates for Submodular Minimization
- Math-4486 Recognition and Characterization of Leaf Powers
- Math-4487 Sampling Algorithms for Maximum-Cut Density
- Math-4488 Codegree Thresholds for Hypergraph Matchings
- Math-4489 Complexity of Dense Perfect Hypergraph Matching
- Math-4490 Separation of Constant-Free Valiant Classes
- Math-4491 Optimal Algebraic Immunity of Boolean Functions
- Math-4492 Explicit Polynomial Maps Escaping Low-Degree Images
- Math-4493 Half-Distance Decoding for Hypergraph Codes
- Math-4494 Multiplicity Decoding for Order-Domain Codes
- Math-4495 Quantitative Manipulability of Social Choice Functions
- Math-4496 Individual Manipulation Power in Neutral Social Choice
- Math-4497 Optimal Rates of Collusion-Secure Fingerprinting Codes
- Math-4498 Decidability of Simplicial-Complex Embeddability
- Math-4499 Rotational Matching Complexity for Planar Point Sets
- Math-4500 Convex-Hull Decomposition for Mixed-Integer Bipartite Systems