Examples

Every page here is a runnable story: problem, data, an API walkthrough with executed snippets, and a discussion of which task, door, criterion, and solver were in play. The first three enter through each of the three doors in turn; the shootout puts every solver and baseline on one problem; the next five are theory demonstrations — a nuisance-parameter criterion, a soft relaxation, two counterexamples, and global certification; the last is a pointer into the one study that runs on real data.

Nine of the ten pages have a matching notebook under examples/notebooks/ that runs the same story at a larger, more decisive scale. See Three doors for what a door is, and Choosing your workflow for a task-first decision guide.

Page	Demonstrates	Task(s)	Door	Notebook
door1-score-events	Precomputed (event, score) rows, an exchange-stability certificate, and the compile bridge from a partition into a reusable rule	Both	1	door1_score_events.ipynb
door2-mixture-densities	Analytic component densities to a binned mixture-fraction measurement, with a two-parameter IntegrationSource fit	Space quantization	2	door2_mixture_densities.ipynb
door3-classifier	Classifier-derived density ratios turned into scores, retention against classifier quality, the ratio-closure check, and the surrogate-information caveat	Space quantization	3	door3_classifier.ipynb
solver-shootout	Every solver the library dispatches, and the three canonical baselines, on one two-parameter problem	Both	1	solver_shootout.ipynb
nuisance-profiled-ds	Plain D against profiled \(D_s\) for a signal fraction with a floating background shape, an efficient-score ceiling, and a DP initializer	Sample partitioning	1	nuisance_profiled_ds.ipynb
soft-purification	Responsibility-space relaxation, a temperature schedule, the hardening gap, and purification	Space quantization	1	soft_purification.ipynb
lloyd-nonmonotone	The manuscript's non-monotone Lloyd step, and the guard's acceptance trace rescuing it	Sample partitioning	1	lloyd_nonmonotone.ipynb
ds-geometry-counterexample	An exact rational fixture whose globally optimal profiled-\(D_s\) partition violates its own induced geometry, and why there is no compile bridge	Sample partitioning	1	ds_geometry_counterexample.ipynb
global-certification	Branch-and-bound optimality certificates and a multi-restart hit-rate study	Sample partitioning	2	global_certification.ipynb
flowcyt-teaser	A pointer into the complete real-data FlowCyt study: 600,000 real cells, a classifier-derived score, and a full population-fraction measurement	Space quantization	3	— see the FlowCyt study