The whole fandom has heard of the aspect duality and inversion theories. As first suggested by BlastYoBoots, everything is set up in pairs and dichotomies, symmetry-within-symmetry. The class verbs are antonyms of each other, and the inverse of your class has the opposite passivity and the opposite verb. So, for example, if -Lord/+Muse was “one who creates” (a theory nobody supports) we’d see inversion patterns like the following:
BYB worked out a class layout based on this “antonym” idea, based on which trolljegus put together this neat graphic. Everything is pairs of pairs, and the arrows form X shapes all over the place. Simple.
I have a nit to pick with the antonym thing. It’s an outside assumption, based on a source unrelated to Homestuck. There’s no particular evidence in the text itself that this is how things work, and nothing about inversion itself that necessitates it. In a pair like destroy/create, there are clear antonyms, but as soon as you look at other verbs like the canon “steal,” the semantics get weird and the active/passive thing makes everything really hairy.
Instead, I want to suggest that inversion is circular. Classes arranged in a circle would be “neighbors” either if they’re active/passive pairs or if they invert to each other. For example, if there were three verbs in total such as “destroy,” “die,” and “attack,” we could show all six classes together, with dotted lines for inversions and solid ones for active/passive pairs:
Not all classes need be linked together in a giant chain. BYB’s setup is in fact a special case of this one with only two verbs per circle. Other layouts might use one-verb, three-verb, or four-verb circles, perhaps in combination with each other. I’m not advocating any particular layout over another, but I do want to point out that such layouts are conceivable.
If there’s a clear reason why this model cannot make sense, please let me know as soon as possible. Thanks!