Which term indicates an authoritative assertion without proof?

The correct term that indicates an authoritative assertion without proof is "dogmatic." This term is often used to describe statements or beliefs that are presented as undeniably true, regardless of evidence or opposition. When someone is dogmatic, they assert their views in a way that suggests there is no room for debate or questioning, even if those views lack solid justification or empirical support.

In many contexts, particularly in discussions of philosophy, politics, and religion, dogmatism can lead to rigid thinking and an unwillingness to consider alternative perspectives. This characteristic is significant as it emphasizes the importance of critical thinking and the need to substantiate claims with evidence in discussions or arguments.

The other terms do not fit this description. For instance, "dormant" refers to something that is inactive or not currently in use, "divest" relates to the process of selling off assets or investments, and "eloquence" describes the ability to express ideas fluently and persuasively. None of these terms carry the same connotation of making authoritative assertions without proof, making "dogmatic" the most appropriate choice.