THE SIX SHAPES

Forget the numbers — keep only the shape. Every window of 3 samples is replaced by its ordinal pattern (which sample is smallest, middle, largest): only 6 shapes exist. Count how shapes follow shapes and you get a transition network; a walk on that network is a reservoir — no random weights, no continuous state, the substrate is inferred from the data itself. The readout is embarrassingly small: the average next-step change seen after each shape. (Potratzki, de Jong, Small & Bröhl, arXiv:2610.21973, Oct 2026 — this piece is a labelled toy model, not their data or their code.)

current shape – · steps 0
one-step RMSE — symbolic – · persistence (just repeat last value) –
toy symbolic reservoir · canvas 2d
dashed gold = greedy walk rollout (most-likely transitions)