Possible Clues:

• Moon’s age at New Year, something agreed on by earth
• Excess of solar year over lunar year
• Solar-lunar equalizer
• Last bit of the agreement is a matter of astronomical significance
• Difference in days between the lunar and solar year
• End of the formal agreement in a certain number of days
• Solar-lunar calendar discrepancy
• Solar year/lunar year differential
• Treaty of Rome? It refers to the moon!
• Excess of calendar month over lunar month