Phi Week starts on the Solar Golden Ratio date where the proportion of numbers of days left in the solar year to the number of days that have passed is equal to the proportion of the days passed to the total number of days in a Solar year. The Solar year starts on the Winter Solstice (December 21st) which makes the Solar Golden Ratio date August 3rd.
Phi Week Ends on the Julian Golden Ratio date, as the Julian year starts on January 1st and the Golden ratio date is August 14th (day 226 of the year).
Unsophisticated Golden Rationalist like to use the Pi Day convention of just using numbers to mark their day (March 14 or 3.14) by denoting June 18th (6/18? How does that work again?) as their Phi Day. More dedicated Phiologist actually divide the year up into the Golden Ratio (365 x .618 = 225.57 days, which rounded up to 226 days. 226 x .618 = 139.67 or 140 so 226+140 = 366 days, the length of a Leap Year).
Phi Week falls squarely within the sign of Leo, which is ruled by our wonderful golden orb, the Sun, without which none of us would be here. Phi day is August 8th or 8/8 which represents the dual infinite proportion of the Golden Ratio (.618:1:1.618), as Phi week is 12 days long (August 3rd through August 14th), we just split the difference between the Solar and Julian Golden Ratio dates to arrive at 8/8.
May 20th is the 140th day of the year, but we already have a major holiday that time of year, there are no major holidays in August, so Phi Day fills this void.