Comment on correlation 
The year 140 AD is leap year so if Thoht 1 is July 20 in 139 AD
it is July 19 for the next 3 years, all 4 years claimed as the rise of Sothis.
The year 2773 BC is likewise a Thoth 1 on July 17 whose previous year is July 18.
4241 BC is a July 19 date for Thoth 1.
As for correlation placing Egypt's earliets dates as 2170 BC and 2030 BC and 2001 BC etc;
the date for Thoht 1 is Jan 6 in 2001 BC and the winter solstice.
The wprt name for new year has been used for sothis but also for solstice
and not clear whether winter or summer. Connecting it to Nile flood doesnt help
when the myth of Noah's flood is at winter solstice. Further, if Thot is the 7th month
then Epagum days begin July 5 in 2001 BC so that the July 10 solstice is Pamenot 1 not 6.
Every disagreement in short Genesis has a counterpart application in Egypt.
Example, reunification in year 955. If Flood is year 600, and Noah dies in year 350,
he dies in the year 350 that the Pharaoh was created.
If using a 360-day calendar for those 350 years, then from year 600 it is year 955.
Unification of dynasties 1-5 is then the same year and event for dynasties 6-10.
The 5th being dead in Genesis in year 340, but in LXX in year 768.
The date 1872 BC July 17 is Memphis. But what if its at Fort Quban where
sothis rises on July 10 the solstice during the 12th dynasty. That blows those
who try to trace July 20 back to a Gregorian solstice in 4242 BC.
And at the time of that July 10 date in the year 120 of the 12th dynasty,
let's say 1824 BC July 10 as second month Parmuti 16 (versus 8th month 22)
we have Paopi 16 on Jan 6, so which is the wprt sopken of in record, winter or summer sothic.