Nice writeup. One thing I've been exploring is how information-theoretic measures connect to physics — specifically, the KL divergence between a "true" vacuum distribution and a perturbed one gives you coupling constants. In the Fibonacci- structured potential V(s) = v⁴(s−s₀)²/(1−s−s²), the strong coupling αₛ = 1/(2φ³) emerges exactly as the curvature at the vacuum divided by 2. The information- geometric interpretation is that αₛ measures how "distinguishable" the vacuum is from the pole — a Fisher metric on the space of potentials.

Probably a stretch, but it's interesting how divergence measures keep showing up in unexpected places.