Which term refers to the act of asserting something earnestly?

The term that refers to the act of asserting something earnestly is "asseverate." This word comes from the Latin "asseverare," which means to declare positively or to affirm. When someone asseverates, they are not just mentioning a point casually; rather, they are expressing it with a strong conviction or sincerity, indicating that they truly believe in what they are stating. Using this term suggests a level of seriousness and assurance in the declaration being made.

The other options do not convey the same meaning. For example, "assay" typically refers to testing or analyzing something, often in the context of assessing the quality or value of a material. "Asperity" denotes harshness or sharpness of tone or manner, which does not relate to assertion. "Cadge" means to obtain something by asking or begging, which also lacks the context of earnestness in assertion.