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Epochal date of "Vira Nirvana Samvat"?

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This page gives the epochal date of "Vira Nirvana Samvat" as "7 October 527 BCE" (and earlier it was given here as "15 October 527 BCE"). However, I think that this date should rather be given as "14 September 527 BCE" (i.e. cJDN 1529193), which, according to the "Surya-Siddhanta" lunisolar Indian calendar system, was "1 Kartak" (or "1 Kartika") that year. I believe that someone has tried to calculate the date of the "Vira Nirvana" epoch from the statement that "the Nirvana occurred 603 years, 5 months and 11 [or 10, or 12] days before the Saka era", but without thinking too much about which kind of "years", "months" and "days" are meant by this statement. As the Jain era is counted together with the Indian lunisolar "Surya-Siddhanta" calendar, "years" should be lunisolar years, "months" lunar months and "days" probably "tithis". The epochal date of the (solar) Shaka era is "15 March 78 CE" (i.e. cJDN 1749621). Then 12 solar days earlier would be "3 March 78 CE", which was "1 Chaitra" in the Indian lunisolar calendar. And then, five lunar months earlier would be "6 October 77 CE", which indeed was "1 Kartak" in the Indian lunisolar calendar. Finally, 603 lunisolar years earlier would be "14 September 527 BCE", which also was "1 Kartak" in the lunisolar Indian reckoning, according to "Surya-Siddhanta". And if the Jain year nowadays begins on "1 Kartak" lunisolar reckoning (as the Gujarati "version" of the Hindu "Vikrama" era does, and also the Nepali "Newar" calendar era does), then its back-calculated epochal date should also be on "1 Kartak" lunisolar, or am I wrong in some way? /Erik Ljungstrand (Sweden).