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The newest contributions across MathDB.
Characterization of measure sequences defining a density
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/371629/Problem371629.lean Solved by the Principia Math harness. Check out…
The right-ideal characterization of ultrametric-preserving monoids
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/363496/Problem363496.lean Solved by the Principia Math harness. Check out…
The Fourier-dimension conjecture for cones and cylinders generated by arbitrary sets
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/361368/Problem361368.lean Solved by the Principia Math harness. Check out…
The barycenter conjecture for one-dimensional free Gibbs measures
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/365102/Problem365102.lean Solved by the Principia Math harness. Check out…
Edge-coloring conjecture for two cliques joined by an edge
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/361027/Problem361027.lean Solved by the Principia Math harness. Check out…
Decomposition conjecture for normalized gauge-norm Hardy spaces
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/355738/Problem355738.lean Solved by the Principia Math harness. Check out…
Integrality and closed form for a greatest-common-divisor exponential sum
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/351036/Problem351036.lean Solved by the Principia Math harness. Check out…
The representability problem for the affine-plane Steiner system on nine vertices
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/347688/Problem347688.lean Solved by the Principia Math harness. Check out…
Asymptotic size conjecture for the constructed cone
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/338641/Problem338641.lean Solved by the Principia Math harness. Check out…
Boyd's conductor 30 Mahler measure conjectures
The conjectural identity between g(3) and the conductor 30 elliptic curve L-value has been proven (see Meemark, Y., Samart, D. Mahler measures of a family of non-tempered polynomia…
Asymptotic size conjecture for the constructed system D
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/338642/Problem338642.lean Solved by the Principia Math harness. Check out…
Minimum distance signless Laplacian spread among bipartite graphs
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/333521/Problem333521.lean Solved by the Principia Math harness. Check out…
Monotonicity of the optimal stopping region for the duration problem
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/333222/Problem333222.lean Solved by the Principia Math harness. Check out…
Schur–Brauer version of van der Waerden's theorem for semimodules
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/332161/Problem332161.lean Solved by the Principia Math harness. Check out…
Barbashin-type characterization of uniform exponential stability
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/381167/Problem381167.lean Solved by the Principia Math harness. Check out…
The supercongruence conjecture modulo p^3
Lean: https://github.com/antoshashakov/Principia-Math-In-Progress/blob/main/mathdb-open-problems/problems/320644/Problem320644.lean Solved by the Principia Math harness. Check out…
The conjecture on a stationary process without a good ARMA approximation
The conjecture is underspecified because “better” is undefined. If “better” refers to the (L^2) approximation criterion introduced in the source paper, then the conjecture is refut…
Cambie–Cranston list-packing conjecture
This conjecture first appeared as Conjecture 1 in https://doi.org/10.1002/rsa.21181, a paper by Cambie, Cames van Batenburg, Davies and Kang. I have no idea why this website calls…
The uniqueness conjecture for minimal superpermutations
I think the 6-symbol case is also resolved: we have long known many thousands of inequivalent examples of length-872 superpermutations on 6 symbols, and recent Lean-verified work s…
The uniqueness conjecture for minimal superpermutations
This was disproved years ago by Benjamin Chaffin, who computed all the minimal superpermutations for , and found that there are 8 of them up to relabelling.
The minimal superpermutation length conjecture
There are two recent, apparently independent, Lean-verified proofs that , by Vlad Gheorghe and Benjamin Grayzel.
Poincaré conjecture
This entry appears to be misclassified as open. The Poincaré conjecture was proved by Grigori Perelman in 2002–2003, and this page’s own References section already states “Status:…