Choose a reading path
Choose a starting point: an example you can see, or the definitions of spaces and maps. Both routes meet at finite encodings. From “Why two parameters?”, you can continue directly or explore the full definitions first.
Installation is only needed to run the notebook; you can read its saved figures without it. Arrows suggest continuations, not prerequisites.
After finite encodings, inspect the square in code or learn how regions and a matrix describe it. Either route leads to the question of when finite descriptions exist.
Lesson cards open pages on this site, including the ring and square inspection notebooks. On a narrow screen, scroll sideways or use the linked outline below the map.
To run the notebook: Install and reopen
Read the map as a linked outline
- A hole appears and disappears (Site page · starting point)
Start with an example. When is the hole alive? Continue to: Why two parameters? Alternatively: Ordinary persistence.
- Persistence modules (Site page · starting point)
Start with definitions. What are spaces and maps? Continue to: Finite encodings.
- Install and reopen (Site page)
To run the notebook. How do I run a lesson? Continue to: A hole appears and disappears.
- Why two parameters? (Site page)
Which parameters can we compare? Continue to: Finite encodings. Optional: Explore the full definitions: Persistence modules.
- Finite encodings (Site page)
How can finite data recover a module? Continue to: Inspect spaces and maps. Alternatively: Indicator presentations.
- Inspect spaces and maps (Site page)
What does the square's encoding contain? Continue to: Tameness and scope. Alternatively: Visualization and export.
- Indicator presentations (Site page)
How do regions and a matrix define spaces? Continue to: Tameness and scope. Optional: Or inspect the result: Inspect spaces and maps.
- Tameness and scope (Site page)
When do finite descriptions exist? Continue to: Why computations stay tame.
- Why computations stay tame (Site page)
Why do finite computations stay finite? Continue to: Categories and derived computations.
- Ordinary persistence (Site page)
Supporting reference. Which conventions do intervals use? Continue to: Why two parameters?
More questions to pursue
Bring in data
Start with the choices that determine an ingested module. For radius and coverage depth, continue through multicover construction, exact grades, and depth windows.
- Ingestion options (Site page)
- Multicover computation (Site page)
- Exact radius grades (Site page)
- Coverage-depth windows (Site page)
Work with the retained algebra
First identify the category in which a calculation takes place. Then choose which objects to materialize and, for floating coefficients, how to assess numerical rank decisions.
- Categories and derived computations (Site page)
- Exploring spaces and maps (Site page)
- Inspection and explicit computation (Site page)
- Numerical derived algebra (Site page)
Compare and show results
Use the visualization guide to choose a view of the encoded object. For comparing two compatible encodings, the matching-distance guide explains the finite-window question and its hypotheses.
- Ordinary persistence (Site page)
- Visualization and export (Site page)
- Exact matching distance (Site page)
Choose tools and reproduce work
Add the integration your task needs, check what its options change, and use the benchmarking methodology when measuring computational cost.
- Optional integrations (Site page)
- Option contracts (Site page)
- Benchmarking methodology (Site page)
Use the grouped guides for further questions about data, algebra, figures, and reproducibility. Repository destinations are labeled on their links.
To find different kinds of treatment of the same subject, use the topic map. It groups documents by subject without prescribing a reading order.