What is the difference between the broken hamza "inna" (إنّ) and the open hamza "anna" (أنّ) from a linguistic perspective?

The hamza of "inna" has three states: فتح (fatḥ - opening), كسر (kasr - breaking), and the permissibility of both. It takes fatḥ if it can be interpreted with its annex as a verbal noun. It takes kasr obligatorily in six places: at the beginning of a sentence, at the beginning of a relative clause, as the answer to an oath when the verb "aqsama" (to swear) is not explicitly used, when it is quoted directly, when it is in the position of a circumstantial adverb (ḥāl), or after a verb of the heart (af'āl al-qulūb) that has been suspended from governing it by the lam (lām al-ta'līl). Both fatḥ and kasr are permissible in other contexts.