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Given the nature of caching, the Cache Stabilization should only be considered semi-stable. Cache expires, cache can be cleared, and, depending on your driver, old cached items can be swept to make space for new items.
Because of those realities, the Cache Stabilizer should not be used for long-term stabilization.
When to Consider
The primary use case for Cache Stabilization is to provide your user with a semi-stable URL while they are working on or building up a filter, or when filtering is mostly transactional. Most of the time you should pair automatic stabilization via cache with a long term solution such as the Database Stabilizer.
One way you can do that is offer a "Save" button in your application's interface. As the user is editing and perfecting their filter, you may run all of those filters through the Cache Stabilizer, and then when the user finally clicks "Save", you persist the filter in a more long term way.