There are several sites for the fundamental categories as well. Having a site on the internet means nothing. Anyone can make a site or a post explaining something.

https://www.zevulsarcanum.com/post/soup-sandwich-or-salad---the-trifecta-of-food-theory
https://dishtaxonomy.com/

The Salad Theory even has a github.io page... although it goes a bit far in trying to say sandwiches are also an un-tossed salad, which is clearly crazy. They flew too close to the sun there.

nigiri sushi is obviously a toast, and pigs in blanket is obviously a sushi Those two examples are built differently despite what you're trying to claim... you chose nigiri sushi which is not like pigs in a blanket, the equivalent would actually be a sushi roll because they are both encased... and yet both of those examples are still clearly sandwiches. The cube rule isn't fundamental, it is still one layer abstracted from the simplest categories.

Nigiri sushi is clearly an open-faced sandwich, especially since you can easily rearrange it into a sushi roll without changing the ingredients. Pigs in a blanket would be classified the same as a burrito or corn dog, which again is a sandwich the same way a wrap is... just using a tortilla or corn batter instead of bread.

When you break it down... you get to these four fundamental food classifications, and that's what matters. The cube rule isn't wrong per se.... it's just more complicated than it needs to be. It's not broken down as far as it can go. Using the fundamental categories, you can chart any food. Between these four categories you can have sub-categories that fall between them, which most of the cube categories do.