This is a shot in the dark: In twf:202, an isomorphism $T\cong T^{7}$ between binary trees $T$ and seven tuples of binary trees T^{7} is mentioned. The argument for this isomorphism starts with the observation that the sixth root of unity is obtained from the categorified version of the statement "a planar binary tree is either the tree with one leaf or a pair of planar binary trees."

What implications (or extant research has been done?) would complex solutions to either Chaitin's exponential diophantine system (which is essentially a lisp implementation) or Matiyasevich's system have?