The popularity penalty for publishing a scene for a girl too close the to the previous one is not working as I would expect. It seems that the penalty ALWAYS lasts for 14 days, even though the displayed value is shorter. Below is a table showing the results of a test.
I shot a scene with a certain girl and published it from 1 to 14 days after her previous scene was published (reloading the save at "day 1" and waiting the appropriate number of days), and the results are summarized in the sheet .
The "Unadjusted Score" is the sum of scores shown on the Scene information screen, the "Actual score" is the score assigned by the game and the ratio is the "Actual Score" divided by the "Unadjusted Score". "Wait Days" is the value shown on the girl's information screen for how many days you need to wait to avoid the penalty, "Popularity Penalty" is if the girl appears in the Popularity Penalty section of the girls list, and "Highlighted in Studio List" is if the girl's name is highlighted in the list of girls on the studio production screen.
Here is the girl's info at the start of the test
As you can see, the penalty lasts for the full 14 days, not the 10 days indicated.
Also, the "Wait Days" shown on the girls information screen seems to be based on her current popularity, not her popularity when the scene was published. I'm not sure if this is by design nor not.