Fisherman:
How do you know or by what authority are the actual dates of the solstices for -568/-588?
The following is provided for honest readers who might also want to know about the method used. I installed Cartes du Ciel, (the program used by the 2011 Watchtower ‘researchers’) and made the observations for the required dates, and provided screenshots. Physics determines the correct dates. One can take two approaches. If you know the solstice date already, you can start from there. But even if you don’t know the correct date, you can pick a date in the required year and check the values for the sun, observe the ecliptic longitude and declination for that date, and then adjust the date until the measurements are 90° and 0, pinpointing the correct date for the solstice. I chose to keep all the observations at midday, but the exact time of day can be refined to precisely match if desired.