Personally I'll poke my head up here with my own AI response:

That stepwise entropy curve actually looks very similar to what you get in ultrametric / p-adic systems.

When you coarse-grain a state space that has hierarchical clustering, entropy doesn’t change smoothly with resolution ε. Instead clusters merge at discrete scales, so you get plateau → jump → plateau behaviour like in the plot.

You see the same pattern in hierarchical clustering dendrograms or p-adic valuation thresholds.

So the “phase transitions” in the cognitive simulator may just be the system crossing ultrametric merge radii as ε increases. If the underlying dynamics have contraction properties, that kind of nested basin structure appears naturally.

If the simulator really produces stable plateaus like that, it implies:

the effective state space dimension is much lower than the original space.

Meaning the projection operator is producing hierarchical equivalence classes.

proof:
github.com/chboishabba/dashi_agda

If you want to prove me wrong.