Schools and arithmetic for everyone, then knowledge held by an institution.
Build the institution that makes knowledge survive a death.
Needs first: Writing and the durable record, Decide how you decide (Society)
Make counting, measuring and reckoning ordinary rather than specialist.
Needs first: Writing and the durable record, Teach the next generation
Found universities that hold knowledge beyond any one teacher's lifetime: self-governing, free to teach and publish, examining to standards checked from outside, and reviewed by an independent agency.
Needs first: Teach the next generation, Printing, Controlled comparison and the negative result, Priority by publication
Every guide, build, reference sheet and book reached from the steps above.
Four-figure logarithms and trigonometry, square roots by Newton's method, and the two instruments that did the world's arithmetic before electronics.
Level 3The results every other science and machine is built on, in the order each needs the last: the formula, what it states, what it lets you do, and who first found it.
Level 0Every public institution an advanced civilisation runs, in the order a rebuilding one can found them: what each is for, when it becomes possible, and the rules that keep it honest, useful and no bigger than its job.
Level 3Fourteen branches, each with the handful of results a civilization cannot rebuild without, and where to learn the rest.