While there may be an existing and suitable name for the concept I am going to describe below, not knowing what it is and since I have not come across it, I am going introduce a new astronomy term in the context of Indian luni-solar calendar and also define it.
I have already referred to this concept for last 5+ years in my writings.
This would be easy to define with a lunar tithi of ‘purnima’ (full moon day). I will define it in the context of a lunar day when full mood day coincided with the day of winter solstice (21/23 December).
Around year 2650 CE, Median Tithi for the day of Winter solstice would be Margashirsha Purnima (full moon). This is because around 2650 CE, the point of summer solstice (180 degree opposite to that of winter solstice) would coincide with the point of (RA coordinates) Yogatara of nakshatra Mrigashirsha.
Thus, when sun is at the point of winter solstice in (~2650 CE), and if that day also happens to be the lunar day (tithi) of full moon, then the position of full moon would coincide with the point of summer solstice (180 degree opposite to the point of winter solstice and also the position of the sun) and we would say that winter solstice occurred on the day of Margashirsha Purnima.
Recall that a lunar year is short of solar year by 10.88 days and thus ‘lunar tithi’ recedes by about 10/11 days every year (for the same day on Gregorian Calendar, such as day of Winter solstice).
As a result, while the day of winter solstice would continue to occur, per Gregorian calendar, on about 21/23 December, this would not be (and was never) the case for corresponding Indian Lunar Tithi for this very day of winter solstice.
During ~2650 CE, lunar tithis would range from Margashirsha Shukla 1 through Margashirsha Vayda 15 (Amawasya). Occurrences for a specific ‘tithi’ would occur in the fashion of, more or less, uniform distribution whose range is defined by Margashirha Shukla 1 and Margashirsha Vadya 15 (Amawasya).
Such a stable picture for the lunar thithis, coinciding with the day of winter solstice, with Margashirsha Shukla 15 (full moon) as ‘Median Tithi’ would continue for about ~72 years.
At this time, the picture would not change drastically, but a slow shift for ‘Median Tithi’ from Margashirsha Shukla 15 (full moon) to Margashirsha Shukla 14 would occur (1 degree of change in about 72 years for the position and thus day of winter solstice)
Since Gregorian calendar is solely focused on matching the cardinal points (equinoxes and solstices) with fixed day on Gregorian calendar (23 March, 21 June, 23 September, 21 December, etc.), required corrections would be made (hopefully) as required.
On the other hand, the effect of ‘precession of equinoxes’ is unavoidable on Indian calendar lunar tithis and thus shift in ‘Median tithi’ of ‘one tithi’ every ~72 years is unavoidable. The unavoidable effect of ‘precession of equinoxes’ on ‘Median Tithi’ is not a limitation of Indian Luni-solar calendar, but rather a gift to humanity, in tracing ancient Indian (and thus world) history.
In our times (e.g. 2015 CE), the point of summer solstice is about 9 degrees away from (and to the east of) the point (RA coordinates) of Yogatara of Mrigashirsha Nakshatra (Bellatrix) and that means the ‘Median Lunar tithi’ for the day of Winter solstice, in our times is Margashirsha Vadya/Krishna 9.
While occurrences of lunar tithis that coincide with the day of winter solstice would continue to occur within a space of ~30 consecutive tithis, with ‘median tithi’ in the center, we must understand the change in nomenclature (especially of associated lunar month) for that lunar tithi. This is due to the insertion of ‘Adhika masa (intercalary month) and rare but real ‘Kshaya masa (elapsed month).
Thus during 2650 CE, depending on the position (for insertion) of Adhika masa (or Kshaya masa), associated lunar month for a lunar tithi (that coincides with the day of winter solstice) may be termed either Pausha (in case of ‘Adhika masa’) or Kartika (in case of ‘Kshaya masa’)
I understand that some readers will need to read and re-read, in order to understand the concept (s) of ‘Median Tithi’ and variation in nomenclature of lunar months (due to Adhika and Kshya masa), however, it is essential in order to comprehend and appreciate important consequences of ‘duration of Bhishma on bed of arrows’ for the ancient history of India.
‘Adhika masa’ correction is applied to the lunar calendar (on an average ~2.8 years), in order to synchronize lunar calendar with the solar calendar. Adhika masa occurs, about every ~2.8 years (on an average) when two ‘Amawasya’ occurs while sun is passing through area of single (specific) zodiac.
‘Kshaya masa’ does occur, albeit rarely, when sun passes through area of specific zodiac (one of the 12) without an ‘Amawasya’ during its transit through the zodiac.