Thursday May 11

Hives define an associative ring; the octahedron recurrence provides an associator.
Henriques' theorem (statement only): the associator satisfies the pentagon identity.
The accessibility lemma from linear programming (statement only).
Consequence for hives: if we can figure out all the ways to add up rhombus functionals such that the dependence on the interior vertices cancels, we'll learn the possible boundaries of real hives.