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So I've been looking at this rules and I do like them but I'm not 100% sure I've got them right. So before I attempt to create the enourmous library of an obsessive compulsive wizard (think library of Alexandria curated by someone who's happy to spend a month re-organizing the entire multi-floor library because they came up with a system that lets someone find a particular book 3 seconds faster on average and would do it in a heartbeat if anyone told them about the Dewey Decimal or Library of Congress system).
Anyway I've summarized the various statistics and how they interact below and just want to check that I'm right this is how they work.
Library CR: Any CR you want from 1-20.
XP: As appropriate for selected CR granted when knowledge in a field is reduced to 0.
Complexity: Not entirely sure, I think you can assign any (difficulty to find) value for checks based on how hard you want it to be for people to find information.
Research Checks: Assign a number of knowledge checks as appropriate to retrieve information from the library.
kp: 3 x CR points that represent the total amount of knowledge you can retrive from a libarary as you hit various point values.
Research Thresholds: The 5 point or 10 point thresholds where you retrieve more information on a subject.
Other: Any challenges such as different languages or creatures lurking in the stacks that increase difficulty.
To put in context if my understanding is right this is how it would work out.
Mythic Wizard’s Arcane Library CR 9
XP 2,700
Complexity 22 (easy, aside from some specific they deliberately try to make the library easy to use)
Research Check: Pick any 1-3 as appropriate for information saught. Knowledge Bonus +2
kp 20/27 (See other)
Research Thresholds
kp 25 Basic summary's about an area of research.
kp 20 Commonly known information on a subject that is known even by those who don't study it.
kp 15 General information on a subject that someone who studies it would know.
kp 10 Everything but obscure or high level theoretical knowledge.
kp 5 All non-restricted information for area of research.
kp 0 All information available in the library for area of research.
Other
The most dangerous or valuable information is stored in a hidden pocket plane more to protect those unprepared for this knowledge so without access to it (not recorded in the library is how to access it) the library only has 20 kp and you can't reduce it to 0.
The library contains a large number of tomes and scrolls in languages other than common, some of which are no longer even in use (especially Aztlanti relics) and it may be necessary to have the ability to read them depending on the area of research.