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That's part of the proposal, and I don't know if there is a hard limit. Personally I think this is actually a weakness in the system. There is a 10 SBD fee per proposal to reduce spam, but very long-lived proposals constitute a form of spam as well, and the fee should probably be per-month or something.

In practice I guess UIs will have to prioritize newer/active proposals in some manner. I don't know how that is going to work out.

Maybe they should have a sunset.
Same with witness votes?
If I can leave my proposal open forever the page is going to get cluttered.

I guess tomorrow will answer most of my current questions.

If I can leave my proposal open forever the page is going to get cluttered

Yes I agree. That's why I think the anti-spam fee should have a time component. Perhaps there is a role for multi-year proposals, but most do not need to be that long.