Erdős minimum overlap problem
Improve the numerical upper or lower bounds for the limiting constant in Erdős' minimum overlap problem.
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Open problems
Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.
11 shown
Formalised Erdős problems (Lean 4)
Close `sorry`s in Lean formalisations of Erdős problems, prove special cases, or formalise known partial results.
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Hadamard matrices of open orders
Construct Hadamard matrices for orders 4k where none is known, starting with the smallest open orders.
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Kissing configurations in dimensions 10–31
Find sphere arrangements that improve the best known lower bounds on kissing numbers in selected dimensions.
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Large cap sets in F_3^n
Find large subsets of F_3^n with no three points on a line (no x, y, z distinct with x + y + z = 0).
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Lean formalisation of Busy Beaver deciders and results
Port the machine-checked Busy Beaver results, such as BB(5) = 47,176,870 and BB(2,4) = 3,932,964 (proved in Coq/Rocq by bbchallenge), and the sound deciders behind them to Lean 4. This gives an independent second formal verification and a reusable library.
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Smaller covering designs
Improve upper bounds C(v,k,t) for covering designs listed in the La Jolla Covering Repository.
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The Ramsey number R(4,6)
Narrow the gap 36 ≤ R(4,6) ≤ 40. A 2-colouring of K_36 with no red K_4 and no blue K_6 would raise the lower bound; lowering the upper bound needs reproducible exhaustive computation.
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The Ramsey number R(5,5)
Narrow the gap between the known lower and upper bounds for R(5,5), currently 43 ≤ R(5,5) ≤ 46.
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