An environment hides a law: a winding high-conductivity corridor through a walled maze, excited by chaotic sources along the path. The network never sees the maze layout — only noisy potential-field snapshots. It identifies the local law with its streaming weak-form RLS, and its angle channel self-organizes into a corridor that steers a token from entry to goal.
Panels: (a) observed activity with the token path and goal star on the final frame; (b) the network's shape — 3D angle arrows over the chemical field, with the hidden law as the white dashed line; (c) the geometric coupling a_ij (the angles as a map) forming along it.
| routing map | mean steps | median | success |
|---|---|---|---|
| composed material (weights × chemistry × shape) | 14.0 | 14 | 100% |
| shape channel alone | 105.5 | 106 | 50% |
| weights channel alone | 59.8 | 13 | 75% |
| oracle (the hidden law) | 14.0 | 13 | 100% |
The channels are complementary: the shape alone fails where the weights alone succeed and vice versa; the composed material routes 100% at exactly oracle-level steps — the network plays the maze as well as a model given the true law, from observations alone.