Will the connective constant of any new lattice be known by the end of June 2031?
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The connective constant of a lattice is defined as the limit as n approaches infinity of cₙ^(1/n), where cₙ is the number of n-step self-avoiding walks on the lattice.
Currently, the exact values of the connective constant are only known for two lattices: For the hexagonal lattice, it is √(2+√2), and for a related lattice called the (3.12²) lattice, it's equal to the largest real root of a certain polynomial.
Will there be any other lattice for which the exact value of the connective constant is proven?
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