Someday, in an overhauled America...
A nationalized open-source voting machine will be needed. A facility builds the devices, inspectors from every single state verify the product before and after it gets shipped out. Each state is free to do unannounced checks, and to share their results with other states and the public.
Every machine produces a paper receipt for the voter. By using a QR code, the voter can make a digital record for their state and the national verification boards, if they so choose. When the physical receipt is being printed out, the voter can choose to have it laminated, so that they can keep it for a pretty darn long time.