  Using the light ladder basis for Kuperberg's $C_2$ webs, we derive triple
clasp formulas for idempotents projecting to the top summand in each tensor
product of fundamental representations. We then find explicit formulas for the
coefficients occurring in the clasps, by computing these coefficients as local
intersection forms. Our formulas provide further evidence for Elias's clasp
conjecture, which was given for type $A$ webs, and suggests how to generalize
the conjecture to non-simply laced types.
