No. To be serious. A challenge, like sailing round the world for a stably employed sailor, is to derive a TOE from logic. I've known doing so had to have a kind of 'geometric logic' somehow.
We've made a few attempts we were not proud of. By attempts I mean thinking in few-hour timeframes for a day or two. By proud - recalling favorably for a week or so. Yet nothing had really done it 'till your conundrum's stating.
The approach beyond your handle, has to do with stacking negations interminably. Yet surprisingly this time the geometry was a resolution instead of progenitor.
That is one was not trying to show that ⊠=⊠⊗ was especially relevant from the start. I think there are still writings on my headboard for THAT!