I have a few questions related to Invitation.

1.) Is there a cooldown on ‘bargain purity’?
2.) Is there a chance that ‘bargain purity’ fails, or does it always reduce your Invitation in the background (even if it doesn’t reduce the number)
3.) Is there a cap on how high your Invitation can rise from RPing with high-tiers? If so, does it vary by tier?
4.) Generally, at what sort of rate does RPing with high-tiers raise invitation? Is the expected rate 1-2 points a scene? 1-2 points over a week of regular scenes? 1-2 points of a month?