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Hi, Marie!  You don't say where you are, but is there a University nearby?  Such an institution should have a Math department that might assist.

Hi Marie - One of my writing coaching clients is a now-retired math professor -- this isn't in her field, but she does know someone who may be able to help:

Tim Flaherty, Associate Teaching Professor, Carnegie Mellon University, 412-268-8171, tim@andrew.cmu.edu 

https://www.cmu.edu/math/people/faculty/flaherty.html

Good luck!

Judy

Judy Fort Brenneman
Greenfire Creative, LLC

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Electric Lemons: Interpretation and the Art of Writing

I do not have an answer, sorry, but thank you for making me look up the "Feigenbaum Constant!" Interesting phenomenon. I'm really curious what you're working on!

my BIL is an actuary and they are incredible at math! maybe look up one in your town? or find a math professor at a local university? could also see if there's an FB group devoted to this (I am betting so!)

I second Vivian’s point about a University. Another option is to reach out to CERN via their website or (better) on LinkedIn. They are very supportive of Museums. My daughter is a physicist there but she’s in the Alps mountain climbing right now so not available. 

For whom and what purpose you need this will, of course, have a bearing on what response you may get, but I am agreeing that you should explore the academic route. More specifically you might want to reach out to the Courant Institute of Mathematics, which is part of NYU in New York City. I think there's a high probability of finding "Someone familiar with the Feigenbaum Constant. Verification" there, whether among the staff or the grad students working towards advanced mathematics degrees.
https://cims.nyu.edu/dynamic/

I reached put to LSU and the professor there was unwilling to even help. The assistant was rather nice and said he would try someone else but I have not heard back. I am in Orlando near UCF but have had no success with the university. I have a friend in one of the local colleges but there is no one woth that degree of math knowledge. Same with Rollins College. But thank you for the assistance and I will check out your leads. 

One of my science guys who at times helps me with verification and text creation has a paper that needs someone other than himself to verify. Pretty cool and very very smart guy