Shortest paths — an illustrative studyRun 9: 228 synthetic points in 8 clusters; each cluster's hub links to the members near it, and every point to its nearest neighbours. 14 origins start in turn and grow waves at one speed; 13 trees meet another and join the network, and 1 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.