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I found these from 2024:

  - https://arxiv.org/pdf/2412.17199 
  - https://academic.oup.com/imrn/article/2024/16/11865/7704606
and re the Liouville function: https://en.wikipedia.org/wiki/Liouville_function
 help



Thanks. I couldn't find anything in literature suggesting this case was previously worked on. I'm also a pure math PhD candidate so I guess I'm just coping..



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