Tithi Pravesha takes the natal Sun-Moon angular separation Δ (the natal tithi position to within ~12°) and finds the instant near your N-th solar return when Δ recurs with the Sun back in its natal sign — restoring the lunar phase you were born under. The Sun’s degree is not restored, and for a few Vrischika, Dhanu and Makara births no such instant exists, so the match nearer the solar return is taken, with the Sun in the adjacent sign.

Compared with Varshaphala (solar return alone), Tithi Pravesha is a tighter anchor — useful for native-with-multiple-children/sibling/spouse-event readings where the lunar phase carries weight.

The algorithm follows Sanjay Rath’s Tithi Pravesha note and PVR Narasimha Rao’s Saptarishis Astrology essay: locate the solar return first, then take the nearest instant at which the Sun-Moon difference is back at the natal Δ, matched to under a second. If the Sun is outside its natal sign at that instant but inside it at the match a lunar month away on the other side of the solar return, that match is taken instead, so the chart can fall up to about four weeks before or after the solar return.