Build a hypothetical post-apocalypse bicycle

Done.

These things last forever, are built like tanks, are mainatainable and fixable by basic (though not metric) tools, and have been proven (and consequently cloned) across the world, and tolerate an almost complete lack of maintenance extremely well.
Mine is nearly 40 years old and at the moment it's my daily rider.
And the wheels on it are 60 years old

And you've never had a puncture or replaced the tyres? The cables are still the original and never been replaced?

Welcome to the post-apocalypse, where you avoid cities for the gangs that roam around, and travel constantly and scavenge a living. There are no bike shops, and you don't carry more than a few basic things.

There are no replacement tubes after more than 5 years, and finding the right bearings and tools and then performing a service is difficult almost immediately... so as soon as you do need to perform maintenance you're screwed. (Oh, and brake pads, chain wear, etc too)

We're looking for the Mad Max of bicycles, something that will continue to work when all else fails. Something that 10 or 15 years after the apocalypse is still rideable. Something that means that 20 years after the apocalypse you can still manage 10mph average human powered speed rather than 3mph.