Shortest paths — an illustrative studyRun 7: 234 synthetic points in 9 clusters; each cluster's hub links to the members near it, and every point to its nearest neighbours. 13 origins start in turn and grow waves at one speed; 11 trees meet another and join the network, and 2 stop at 25 branches and fade. The result is checked against a formal specification in Lean. Decorative geometry, not measured data or evidence of a verified pipeline.