I have published online a short article saying that the set of funcoids is isomorphic to the set of filters on a certain lattice.
Then I found a counter-example and decided that my theorem was wrong. I was somehow sad about this.
But now I’ve realized that the counter-example is wrong.
So we can celebrate my new theorem. Now there is no reason to assume that it is false.
I will add more details to the article and keep you informed about it.