The present work is devoted to being an outline of the final part of a research program to describe the fundamental steps in the construction of a thermostatistics of occurrence probabilities. The work is also written to complement and sometimes correct the attempts made by many authors, many of them in the “not even wrong” style over the years since 1988. We have chosen to work with Sharma-Mittal entropy measures of two parameters, in all the developments and calculations shown here.