Theory Update 37

Let us recall the parity cube as it appears in Bar-Natan's account of the Khovanov invariant. His image shows all eight possible smoothings of the trefoil knot, which has three crossings. Each crossing is resolved into uncrossed strands in one of two distinct ways.

Since quarks also fit onto the central six vertices of a three qubit cube, their fractional charge is associated to the bit sum of a qubit word. The association of charge and braid strands is also familiar to us from the Bilson-Thompson braid spectrum. Some prefer to call these diagrams octupi.