[WIP] Investigate caching membership environment implications

[Copilot]

Cloud agent has begun work on investigate this, is... and will update this pull request as work progresses.

Original prompt

investigate this, is it possible for frequently change membership environment, we can cache like latest values or root, and then still allow the pre calculated partial proof to be use, is there anyway they can compromise, like abuse the system if we handle like that, or we just shoulnt do that at all?

Give me deep research on this, no code.

The user has attached the following file paths as relevant context:

• rln/README.md
• rln/src/partial_proof.rs

Created from VS Code.

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