I move through perfectoid rings, p-adic towers, and the Frobenius map, wondering if any of it could ever end up in Sonic Pi’s sandbox.

I introduce an analogy between transitive group actions on flags of polytopes and type systems. This speculative concept aims to offer a naive way of understanding and classifying types through symmetry.

I plant a question motivated by generalizing the GCD to varieties and inspired by Euler's interpolation: Does there exist a function attached to each figurate number that extends it to continuous domains, analogous to how the Gamma function extends the factorial?

A naive question about Cayley-Dickson algebras, enumerated by a figurate number via type systems, and how that question naturally incorporates itself into other algebraic structures and particularities.

I invite you to explore the intersection of figurate numbers and module theory, where type-level programming unlocks new possibilities for math and live coding music.