Tutorials

Executed notebooks from tutorials/, exported to HTML (outputs and figures included). They share the test cases of tutorial 0; the intrusive geometry and dynamics are tutorials 1–4.

	Notebook	What it covers
0	The test cases	The KS 1-D / 2-D cases: what they look like, how hard each is to reduce, signal-level analysis, attractor geometry, regime classification, bifurcation diagrams.
1	What a qlROM is, and where its charts come from	Why one global basis is not enough, quantization into charts, and every knob of fit_clusters / fit_charts (how many charts, kmeans_method, cluster_space, overlapping assignment, transition snapshots).
2	Building a local-chart ROM	The intrusive step: the governing equations projected onto each chart, one step / one chart, the chart machinery watched from outside, statistics for the chaotic case.
3	Diagnosing a qlROM	Representation vs forecast error, local vs global (\(K=1\)), \((K, r)\) sweeps, chart occupancy and transitions, characterization with ntsa.
4	Charts, transitions and the exact atlas	Chart, Atlas, TransitionMaps: why local → atlas → local is lossless and local → local is not, exact distances, the same identity for operators.

The notebooks themselves live in the repository (tutorials/*.ipynb, with their figures in tutorials/figs/); the HTML here is regenerated from them on every docs build.