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Prof. Aron Dotan explained to me that by understanding the relationships between different kinds of dagesh and nikkud, then it is possible to mark vocalized Hebrew text with replacement Hebrew grammar symbols, such as the shvah-na/shvah-nach and the kamatz-katan/kamatz gadol.
Hence, I seek to understand clearly what causes a shvah to be either na or nach, or a kamatz to be either katan or gadol, or a dagesh to be either kal or chazak.
After that, the remaining 7 nikkud must be understood accordingly.
(Apparently, there are three forms of each nikkud and dagesh. That totals 10 x 3 = 30, or if the cholam haser dot is included, this the total would be 33.)