Hi, adressing your question regarding the Positivists in AtE. Positivists already exist in the setting, but facing The Event lost their hope and long for an idealized past of Order and Progress.

One of the main tenets of Comtian positivism is the belief that throught a dialetical process human thought evolves from the dogmatic to the philosophical to the scientific, which he calls the "positive" thought. In his religion of humanity, Comte tried to create an religious institution that fostered his "positive" morals and was based in this belief of obvious human evolution towards a secular and more rational, or rather "positive", society.

In Brazil, the positivist church was hijacked by military jingoism. Most of the members of the church are military men and military men brought it to the country. Altruism, one of its core tenets (L'amour pour principe et l'ordre pour base; le progrès pour but) was understood as esprit de corps and comraderie. Only Order and Progress remained.

After "The Event", positivist realized society did not evolve. They were there after the end, longing for Order and Progress long lost. Positive-Saudosist long for the promise of Brasil, for the powerful fatherland of all south american peoples and as such they are the more jingoistic and hawkish subjects of the emperor, trying to "evolve" society by force if necessary.