Bracket smoothing state
= Bracket smoothing state
A bracket smoothing state chooses one of the two unoriented smoothings at every crossing of a <link diagram>. Its weight is $A^{a-b}\delta^{s-1}$ in the reduced <Kauffman bracket>, where $a,b$ count the smoothing types and $s$ counts resulting circles. The all-$A$ and all-$B$ states choose the same smoothing type at every crossing.