M Theory Lesson 238
This quandle can be thought of as a group ring for a field with one element. Additively, there is only one choice for the coefficients of $\sigma_X$, $\sigma_Y$ and $\sigma_Z$, and so the formal sum $\sigma_X + \sigma_Y + \sigma_Z$ represents the three element set as the union of labelled one element sets. Multiplicatively, the cyclic quandle rules hold, and these are the only rules.
What does it mean to take the fundamental group (or groupoid) not of the trefoil, but of the Pauli quandle? What is the complement of the quandle in MUB space? A truncated braid group of type $B_3$ naturally arises for the $3 \times 3$ operators. Moreover, M theory is very interested in how the Pauli operators interact with this three dimensional case. Somehow M theory doesn't mind that $B_3$ is specialised to truncated knots when considering three objects. After all, the fundamental group is really about maps of a circle into a space, but a circle is what one obtains only after considering (at least) an infinite number of objects.