In natural science, an educated guess at scientific fact is called a hypothesis. Hypotheses are rigorously tried by experiments conducted repeatedly under carefully controlled conditions. This is called the scientific method.
In mathematics, an educated guess at mathematical fact is called a conjecture. Conjectures are rigorously tried by deductive logic proceeding from a small body of fundamental axioms and a large, ever-growing body of previously proven theorems. This is called the axiomatic method.
In the study of history, an educated guess at historical fact is called a narrative. Narratives are rigorously tried by studying the historical record—the soundest narrative is the one that is supported by the greatest number of independent primary sources.
Does this method have a name? Moreover, is it the one method used to rigorously determine historical fact in the same way that the scientific and axiomatic methods are each the one method used to rigorously determine scientific and mathematical fact, respectively, or do there exist other, equally important methods?