We will briefly introduce some background works on Kapustin-Witten equation and Witten's conjecture on the relation of its moduli space and Jones polynomials. We will prove Yang-Mills energy is bounded for the moduli space of Kapustin-Witten solutions on with empty knot:

 

for any . We will also discuss the formula and the boundedness for the first Pontryagin number for the moduli space of Kapustin-Witten solutions.