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1

Germany's BSI has produced AIS 31 that includes requirements on Physical True RNGs (PTRNGs). It is designed to fill a gap in the Common Criteria standard. Chapter 4 describes pre-defined classes for physical true, non-physical true, deterministic and hybrid random number generators. ... The basic concepts and evaluation criteria are illustrated by ...

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As far as I can tell, NIST has only one official document about entropy collection. SP-800-90B. The purpose of NIST Special Publication (SP) 800-90B is to specify the design and testing requirements for entropy sources that can be validated as approved entropy sources by NIST‘s CAVP and CMVP. It essentially defines a bunch of statistical tests to ...

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$\pi$ is the transcendental number 3.1415926... It's there in the formula to show this specific number was not chosen with a specific cryptographical backdoor in mind; it seems unlikely that anyone was able to select the value of $\pi$ (unless Carl Sagan was correct, of course :-)

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