The same faith with or without charity: common Roman view, not dogma
Common Roman teaching even allows the same numerical faith to be formed or unformed as charity comes and goes — Peter's faith intrinsically the same under either label.
Same-species living/dead faith is defined dogma; same-number continuity is common and approved by modern doctors, but not equal in certainty and not a dogma — some older Scholastics opposed it.
Latin
XIII. Imo communis Scholae Romanae doctrina est eandem numero fidem modo formatam & vivam, modo mortuam & informem esse posse. Nempe Petri fides eadem in se & intrinsece manens, alias fides informis & mortua dicitur absente charitate, alias vero fides viva & formata si charitas adsit. Sed prior sententia quae statuit fidem vivam & mortuam ad eandem fidei speciem pertinere, est in Ecclesia Romana definita, & inter dogmata fidei recensetur: Posterior vero quae ponit eandem numero fidem modo formatam, modo informem esse, non est paris certitudinis, nec tanquam dogma fidei habetur: & contrarium tenuerunt quidam veteres Scholastici, licet Doctores hodierni calculo suo illam communiter approbent.