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None of it is saved.As we're absorbing this idea... I've seen employment contracts for technical people that arguably might consider these handwritten notes to be IP artifacts, which must be preserved and made accessible to the company.
If that's your situation, you could scribble the date, your name, project, etc. in some margin of the piece of paper, and stick it in a pile/folder. To eventually be scanned, and the file put somewhere accessible, and/or the paper technically preserved.
In a startup, you might also want to preserve things like these for nostalgia, even if they have no IP value. One seed startup, I kept a folder of "nostalgia" photos, video clips, screenshots, etc., of early prototypes, people working late, incremental successes, etc., and it was quickly a good thing. It's amazing how well you can progress, and what positive feelings you have some of these things that quickly become nostalgic. Anyone can see the current state of the code in the repo, but here's the pencil sketch on quadrille paper (or a napkin) one evening that became our architecture.