Jones polynomial skein relation ($t^{-1}{V}_{L_{+}}-t{V}_{L_{-}}=(t^{1/2}-t^{-1/2})V_{L_0}$)

Resolve the two crossings in a skein relation using the Kauffman bracket, then correct by the writhe of a link diagram. The other smoothing cancels, leaving the displayed coefficient of the oriented smoothing. This relation and the value one on the unknot determine the Jones polynomial: crossing changes give descending diagrams, which are unlinks, while the smoothing terms have fewer crossings.