Part 2a (Concurrence of two eagles/co-regency) has shown that there is a strong chronological correlation of co-regency with two-eagle coin production.  Also, during times in which there was no co-regency there are no two-eagle coins known.  These conclusions are reviewed at the end of Part 2a and can be viewed here.
Click  Review conclusions of Part 2a 
 
 In addition to such direct evidence from chronological correlations,  further support for the co-regency / two-eagle hypothesis is found from consideration of an unusual type of Ptolemaic coin with three eagles.
 
Click  Review three-eagle coin 
 
The two-eagle hypothesis predicts that two-eagle coins would not be produced during a reign without co-regency.  A situation that tests this prediction has occurred.
 
Click  Review prediction