Jus sanguinis is the general framework for citizenship by blood, our version of it is one implementation. As I stated earlier, our interpretation is matrilineal linage or a formal naturalization (“conversion”) process. Nothing difficult here.
As for the Stat of Israel, the Law of Return allows anyone with even 1/4th Jewish heritage to gain citizenship but that is separate from the rabbinic authority recognizing religious status as a Jew. There are other paths towards naturalization besides the Law of Return. As for recognition by the rabbinic authorities that sometimes involves providing birth certificates, marriage contracts or other documentary proof going back several generations. The rabbinic authority is under Ultra Orthodox control so they are very strict on this.
Anyway, its a few hours till shabbos here in Tokyo so I’m going off line now to prepare for things. Be happy to answer other questions when I get back.
