The finite-generation conjecture for identities of n-ary intermolecular recombination

Let $R$ denote the degree-$3n-2$ identity described in the degree-$3n-2$ consequence conjecture: it has all coefficients equal to $\b11$ and expresses every monomial of the second association type as a linear combination of monomials of the first association type.

Finite-generation conjecture. Every polynomial identity satisfied by $n$-ary intermolecular recombination, with no restriction on the degree, is a consequence of complete symmetry in degree $n$ together with the identity $R$ in degree $3n-2$.

This conjecture would give a complete finite description of all polynomial identities for general $n$-ary intermolecular recombination. The ternary computations in the paper support the proposed generators in the degrees examined, but the unrestricted-degree assertion remains open.