TheoremDB

Problems

Browse reviewed problems by field, research program, status, and recorded activity.

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Problem index

Related problem families are nested under compact headings. Search results remain a plain relevance-ranked list.

253 problems

ProblemFieldStatusLean verificationUpdated
[#P3062] Cycle Double Cover ConjectureGraph theoryResolvedLean-verified
[#P3064] Sabidussi's Compatibility ConjectureGraph theoryResolved?Not Lean-verified
[#P3092] Existence and value of the diagonal Ramsey exponential limitGraph theoryOpen
[#P3086] An explicit exponential lower bound for diagonal Ramsey numbersGraph theoryOpen
[#P3084] A common high-chromatic subgraph of two \(\aleph_1\)-chromatic graphsGraph theoryOpen
[#P3080] Four-cycle supersaturation just above the extremal thresholdGraph theoryOpen
[#P2556] A period-six recurrence for domination on the three-row knight graphGraph theoryResolved?Not Lean-verified
[#P2676] Most spanning trees in a 10-regular circulant on 101 verticesAlgebraic graph theoryResolved?Not Lean-verified
[#P2874] Five-colouring triangle-free graphs of maximum degree sixGraph theoryOpen
[#P2894] Rainbow perfect matchings from eight spanning color classesGraph theoryOpen
[#P3066] Erdős Problem 152: isolated sums in Sidon setsAdditive combinatoricsResolved?Not Lean-verified
[#P3124] All nonnegative limits of normalized consecutive-prime gapsNumber theoryOpen
[#P2850] Unbounded numbers of integral points on global minimal elliptic curvesNumber theoryOpen
[#P2762] Rational points on y^2=x^6-x^2+1Arithmetic geometryOpen
[#P2670] Largest rainbow squarefree gap below 10^12Multiplicative number theoryOpen
[#P2658] Longest rainbow divisor-count interval below 10^12Multiplicative number theoryOpen
[#P2638] Sparsest degree-600 recurrence for a prime-indicator prefixInteger sequencesOpen
[#P2848] Unbounded continued-fraction coefficients of piNumber theoryOpen
[#P2742] Square-class collisions in the Pell-Lucas sequenceNumber theoryOpen
[#P2662] Most irreducible constant slices of a sparse quintic over F_101Finite fieldsResolved?Not Lean-verified
[#P3148] Whitehead asphericity conjectureTopologyOpen
[#P3132] Purely cosmetic surgery conjectureTopologyOpen
[#P3114] Kashaev volume conjecture for hyperbolic knotsTopologyOpen
[#P3094] Dürer’s edge-unfolding problemGeometryOpen
[#P3082] Cabling conjecture for reducible Dehn surgeryTopologyOpen
[#P3076] Borsuk’s conjecture in four dimensionsGeometryOpen
[#P2502] Minimum spanning-tree dilation on the regular nonagonComputational geometryResolved?Not Lean-verified
[#P2922] Planar drums whose spectra differ only finitelySpectral geometryOpen
[#P2888] Completing a line arrangement to triangular bounded cellsDiscrete geometryOpen
[#P2510] Homotopy type of a Lee-metric Rips complex on the 7 by 7 torusComputational topologyResolved?Not Lean-verified
[#P3146] Is VP equal to VNP?Theoretical computer scienceOpen
[#P3144] Is there a truly subcubic algorithm for weighted APSP?Theoretical computer scienceOpen
[#P3140] Strong Exponential Time HypothesisTheoretical computer scienceOpen
[#P3134] Decidability of the real exponential fieldLogicOpen
[#P3130] Polynomial-time recovery of planted cliques below the square-root scaleTheoretical computer scienceOpen
[#P3126] Do one-way functions exist?Theoretical computer scienceOpen
[#P3118] Does the matrix-multiplication exponent equal two?Theoretical computer scienceOpen
[#P3116] Decidability of positivity for linear recurrence sequencesLogicOpen
[#P3112] Is graph isomorphism solvable in polynomial time?Theoretical computer scienceOpen
[#P3102] Decidability of the first-order theory of F_p((t))LogicOpen
[#P3142] The Total Coloring ConjectureCombinatoricsOpen
[#P3136] Ryser’s conjecture for multipartite hypergraphsCombinatoricsOpen
[#P3120] Matrix Spencer discrepancy conjectureCombinatoricsOpen
[#P3088] Conway’s thrackle conjectureCombinatoricsOpen
[#P3070] Barnette’s conjectureCombinatoricsOpen
[#P3068] Minimum avoiding alphabet for every avoidable wordCombinatoricsOpen
[#P2598] Rank log-concavity for symmetric binary matrices through order fiftyProbabilistic combinatoricsResolved?Not Lean-verified
[#P2584] Exact Hamiltonicity probability on eight labeled verticesProbabilistic combinatoricsResolved?Not Lean-verified
[#P2604] Largest subtour-LP gap among eight-vertex graph metricsCombinatorial optimizationOpen
[#P2872] Infinitely many ones in the greedy three-term-progression-free sequenceCombinatorics on wordsOpen
[#P3138] Positive metric entropy for the standard mapDynamical systemsOpen
[#P3110] Generic analytic Arnold diffusion in a priori stable systemsDynamical systemsOpen
[#P3104] The one-quarter threshold for fitting Gaussian points by a centered ellipsoidProbabilityOpen
[#P3072] Birkhoff conjecture for integrable convex billiardsDynamical systemsOpen
[#P2698] Longest rotor-router cover time on the eight by eight gridDiscrete dynamical systemsOpen
[#P2536] Monotonicity of consecutive-adjacency avoidance in random permutationsProbabilityResolved?Not Lean-verified
[#P2906] Computability of the area of the Mandelbrot setComplex dynamicsOpen
[#P2696] Longest cycle of a nonlinear area-preserving map over F_1000003Finite dynamical systemsOpen
[#P2936] Complete coverage by random disks at the harmonic scaleProbabilityOpen
[#P2532] Longest four-number Ducci trajectory in the 100 boxDiscrete dynamical systemsResolved?Not Lean-verified
[#P3128] Hot spots conjecture for convex planar domainsAnalysisOpen
[#P3122] Backward self-similar Navier-Stokes profiles in a half-spaceAnalysisOpen
[#P3096] Persistent exponential stretching of a material line in two-dimensional Euler flowAnalysisOpen
[#P3074] Bochner-Riesz conjecture in higher dimensionsAnalysisOpen
[#P2516] The sharp Dirichlet Poincare constant with two moment constraintsReal analysisResolved?Not Lean-verified
[#P2518] Optimal symmetric three-point quadrature for a bounded second derivativeReal analysisResolved?Not Lean-verified
[#P2924] Openness of convolution on l1 of the integersFunctional analysisOpen
[#P2908] A free group generated by exponential and squaring mapsReal analysisOpen
[#P2730] Sharp fourth-power norm of the cyclic Hilbert transform at order 31Harmonic analysisOpen
[#P29] Three-dimensional Euler regularityPartial differential equationsOpen
[#P3108] Capacity of the general discrete memoryless relay channelInformation theoryOpen
[#P3106] Exact capacity region of the two-user Gaussian interference channelInformation theoryOpen
[#P2904] Integral-root classification for Lloyd polynomialsCoding theoryOpen
[#P46] Zauner's conjectureQuantum informationOpen
[#P2788] Components of the Pasch-switch graph on STS(15) classesDesign theoryOpen
[#P2632] Largest cyclic 3-(31,5,1) packingDesign theoryOpen
[#P2794] Covering radius of the second-order Reed-Muller code RM(2,8)Coding theoryOpen
[#P2796] Exact mixed-dimension subspace-code number A_2(7,4)Coding theoryOpen
[#P2534] Three mutually orthogonal Latin squares of order tenDesign theoryOpen
[#P2520] A Hadamard matrix of order 668Combinatorial designsOpen
[#P3100] Embeddability into a finite-group power semigroupAlgebraOpen
[#P2448] Eventual unimodality of ternary subset-sum polynomialsAlgebraic combinatoricsResolved?Not Lean-verified
[#P2860] A Tarski monster of exponent fiveAlgebraOpen
[#P2750] Trace-indistinguishable triples in sl2(F5)AlgebraOpen
[#P2862] Kaplansky's sixth conjecture for semisimple Hopf algebrasAlgebraOpen
[#P2858] Ternary representatives of finite-order integral matricesAlgebraOpen
[#P2440] Maximum determinant of a zero-diagonal binary symmetric Toeplitz matrix of order 20Matrix theoryResolved?Not Lean-verified
[#P2878] Orders of ternary row-orthogonal matrices with a full rowCombinatorial matrix theoryOpen
[#P2854] A support-three zero divisor over a torsion-free groupAlgebraOpen
[#P45] Rota's basis conjectureLinear algebraOpen
[#P2572] Smallest variable-order OBDD for the middle bit of six-bit multiplicationDecision diagramsResolved?Not Lean-verified
[#P2892] Plane tilings by every five-cell lattice animalTiling theoryOpen
[#P2896] Logarithmic dimension for almost-equilateral sets in Banach spacesBanach spacesOpen
[#P2934] Effectivity of cocongruences in commutative monoidsCategory theoryOpen
[#P2628] Zero-sum-free subsets of the unit sphere over F_7Zero sum theoryOpen
[#P2608] Shortest addition chain for the 127th Mersenne numberAddition chainsOpen
[#P36] Yang-Mills existence and mass gapMathematical physicsOpen
[#P42] Quantum PCP conjectureQuantum computingOpen
[#P2700] Exact heat-bath spectral gap on the six by six Ising torusMathematical physicsOpen
[#P2718] Nearest hard-square partition-function zero for the sixteen gridMathematical physicsOpen
[#P2594] Hard-core coefficient log-concavity on the first ten thousand four-cycle stripsMathematical physicsOpen
[#P2702] Most antiferromagnetic ground states in a 3-connected cubic graph on twenty verticesMathematical physicsOpen

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  1. StatementReviewers check that the setup, terms, conventions, and acceptance conditions define one precise mathematical question.
  2. References and open statusThe record must include relevant sources, a dated search record, and evidence that the exact target remains open.
  3. Duplicate searchReviewers search TheoremDB and equivalent formulations, then merge any direct duplicate into its canonical record.
  4. Hero presentationThe qualification handoff records a visual brief and whether the page uses reviewed bespoke art or the neutral generated fallback. Bespoke art must depict the mathematical object, use accurate alt text and a neutral caption, and record its rights basis.

Publication requires every gate to pass, independent confirmation of the checklist facts, support from each review role, and no unresolved blocker. Unknown or conflicting facts require staff review.

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