Are Pedantry and Pedanticism synonyms?

Solution 1:

The OED defines them as follows:

Pedantry, n.

1. The character, habit of mind, or practice of a pedant.
   a. Mere academic learning, without judgement or discrimination; excessive reverence for or display of learning or technical knowledge; intellectual conceit.
   b. Excessive or undue concern for petty details; slavish adherence to formal precision, rules, or literal meaning.
2. As a count noun: an instance of pedantic behaviour; a pedantic form of expression.

Pedanticism, n.

   Pedantry; a piece of pedantry, a pedantic expression or idea.

So...yes. They are both words that are recognized by the OED. Pedantry has been around since the 1600s and pedanticism since the 1800s, which means to me that the former is the proper (original) word and the latter is one derived by the people that was used often enough that it has been adopted into the standard language.