If you are starting from zero PAI, you will find that your daily PAI points earned adds up to your total 7-day PAI score. However, after 7 days, when your points begin to expire, your PAI score will no longer be a simple sum of the past 7 days' PAI points earned.
This is because the PAI algorithm is dynamic, and adjusts based on your activities over the past 7 days. Your PAI points earned each day may become worth slightly more points as time passes, until they expire after 7 days.