Please don't follow the original comments suggestion; I feel that "easily digestible" is not compatible with what makes the idea shine in the first place.
Your suggestion delegating such functionality to a local LLM is quite nice as a choice but adding it as a core functionality is quite antithetical to leverage the arXiv part, without which everything reverts back to a bland and generic whateverTok format.
Although the suggestion seems to be aware of the fact and provides both a good reasoning and a quite good solution (progressively deepening explanations), the implicit information and nuance lost in a summary by an unreliable LLM would undeniably turn this from a useful and interesting idea to a cool party trick no one uses for more than 5 minutes.