How to tell if I permanently unlocked Bad Moon? I just completed my first Bad Moon run, and it was 100&amp;#37; Black Cat. (torture)

I *did* keep the cat with me from the very first adventure until I stepped through the gash. I did not abandon the kitty after freeing the king, as I had been warned not to. I also have the pet sweater available to me in Valhalla now, which I did not before, another verification that this was a 100&amp;#37; kitty run. But there doesn't seem to be any message verifying that I've permanently unlocked Bad Moon, and I'm terrified that I'm going to have to go through that torture AGAIN for NO REASON. What am I missing? What have I done?