Noun form of "aver"?

The noun form is

averment

• (Law) A formal statement by a party in a case of a fact or circumstance which the party offers to prove or substantiate.

(ODO)

Origin of averment:

1400–50; late Middle English averrement < Middle French. See aver, -ment.

-ment suffix usage origin:

suffix forming nouns, originally from French and representing Latin -mentum, which was added to verb stems sometimes to represent the result or product of the action.

There are two noun forms. The everyday one is averral, meaning an act of averring; but there is also averment, which has more of a legalistic flavour, as described in user240918's answer.

Edited to add: It seems from the comments that I am wrong about averral, at least as far as all the dictionaries in the world are concerned. I shall just have to stop using it, I suppose.

By the way, aversion is by no means the obvious noun form of aver. For example, from infer we get inference; from deter we get deterrence; from confer we get conferral or conferment. If you tried to use infersion, detersion or confersion, nobody would even know what you were trying to say!