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 Michelson-phase page covers
the analytic ScoreFunction route and the NumPy backend at once; 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 two point into real data — a real classifier-to-score bridge on the
public FAIR Universe HiggsML dataset, and the complete FlowCyt population-fraction study.
Eleven of the twelve 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 Diagnostics and choosing a
method 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 |
| michelson-phase | An analytic ScoreFunction against a bounded IntegrationSource on the NumPy backend, a closed-form profiled ceiling, aliasing in a naive detector segmentation, the compiled D rule's comb, and the fragments of the profiled partition diagnosed |
Both | 2 | michelson_phase.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 |
| hep-classifier | A signal-vs-background classifier and a tes minus/plus classifier feeding two different ratio doors on the public FAIR Universe HiggsML dataset, profiled \(D_s\) against a certified ceiling, and a delta convergence study |
Both | 3 | hep_classifier.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 |