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-5201 The repeated-label reduction and its sharp threshold
- Math-5202 Repairing the safe-completion reduction from rainbow reachability to Sullivan-2
- Math-5203 The exact fresh-color safety criterion behind the Sullivan-2 reduction
- Math-5204 Rigidity of the deficit-one rainbow-cycle obstruction
- Math-5205 A surplus lattice for Seymour and Sullivan neighborhood inequalities
- Math-5206 The exact interpolation among second-neighborhood inequalities
- Math-5207 A two-vertex digon counterexample and an oriented local descent theorem
- Math-5208 A literal parallel-arc counterexample and a collision obstruction for the simple repair
- Math-5209 A convention-sensitive counterexample to Hamidoune's reverse local-connectivity conjecture
- Math-5210 A counterexample to the unqualified weak-weight formulation
- Math-5211 Reciprocal-weight cycles and a winding-number obstruction
- Math-5212 A parametric audit of a refuted logarithmic outdegree condition
- Math-5213 Minimal feedback arc sets and long paths
- Math-5214 Thomasse's path-girth conjecture: refutation and exact cyclic blow-ups
- Math-5215 Convention obstructions and an oriented-pseudoforest theorem
- Math-5216 The prime maximal Z15 boundary counterexample
- Math-5217 A missing threshold and an explicit Freiman-model repair
- Math-5218 Finite Beatty blocks and balanced gap words
- Math-5219 Balanced power-sum obstructions and the one-sign Behrend family
- Math-5220 Recognizing self-sumsets over finite fields
- Math-5221 An odd-order five-coset counterexample above the one-third threshold
- Math-5222 Bourgain's arbitrary-modulus theorem answers Chang's sum-product question
- Math-5223 A local mirrored-shadow law for sum representation functions
- Math-5224 Lacunary counterexamples to the asymmetric Freiman container question
- Math-5225 Minimal order-two bases and quantitative thinning
- Math-5226 Two-step product growth in SL_2(F_p)
- Math-5227 Small sums and products near the square-root scale
- Math-5228 A singleton obstruction to the Katz critical-set question
- Math-5229 Exact horizontal Plancherel identities for the diagonal Diffie--Hellman sum
- Math-5230 A weighted product of chordal distances
- Math-5231 A 21-vertex counterexample via the complement of the WBGKSF
- Math-5232 Perfect contractility and 1-amalgam blocks
- Math-5233 The chromatic-to-divisibility implication hidden in a source fragment
- Math-5234 An extraction fragment and an exact triangle-free list-coloring corollary
- Math-5235 A literal NP class for the P4-structure of proper 2-joins
- Math-5236 An existential NP class for P4-structures of M-join graphs
- Math-5237 Three-dimensional vertex index and the choice of center
- Math-5238 Finite-dimensional local rigidity from central-section perimeters
- Math-5239 Few-vertex Mahler bounds and pyramid cores
- Math-5240 Rigidity and a sharp halfspace benchmark for Gaussian cylinders
- Math-5241 An explicit iid-uniform counterexample to scalar entropy-power supermodularity
- Math-5242 The sharp Gaussian perimeter bound for ellipsoids
- Math-5243 Closedness, dimensional correction, and a dual certificate for polar-zonoid intersection bodies
- Math-5244 Small Fourier data do not force simplicial facets without local normalization
- Math-5245 Polynomial ridge completeness and switching obstructions for the four AIM directions
- Math-5246 A modewise rotating-AR analogue for discrete-time stochastic reaction-diffusion systems
- Math-5247 Variable-block coupling bounds for nonstationary statistics
- Math-5248 Chronological Lasota--Yorke bounds for nonstationary compositions
- Math-5249 Stable laws and diffusion clocks for nonstationary sums
- Math-5250 A gap-optimized Poisson approximation bound with a clustering obstruction