Obligations recorded, weighed, coined, audited and lent.
Write down who owes what, before anyone mints anything.
Needs first: Start the record (Knowledge), Decide how you decide (Society), Plant staples (Food)
Give every market a balance whose readings can be checked and a set of reference weights within published tolerances, held to a master by an office that verifies, stamps and re-inspects them.
Needs first: The debt record, Blacksmithing (Tools), Writing and the durable record (Knowledge), Arithmetic for everyone (Knowledge), Published rule and the court (Society)
Keep accounts a stranger can check.
Needs first: Paper (Knowledge), Arithmetic for everyone (Knowledge), The debt record
Strike coins of a weight, fineness and size fixed in law, at one mint working under seal, and prove every year, in public, that they meet the standard.
Needs first: Standard weight, Smelting: first metal (Materials), Blacksmithing (Tools), Published rule and the court (Society), Double entry and the auditable enterprise
Move purchasing power across time, and survive the moment everyone wants it back at once.
Needs first: Double entry and the auditable enterprise, Published rule and the court (Society), The debt record
Let anyone form a company by registering it, let thousands of people invest in it while risking only what they put in, and pay for that protection with a public register, audited accounts and a board bound by duties to the shareholders.
Needs first: Credit, interest and the bank, The register: land, birth, company (Society), Double entry and the auditable enterprise, The enforceable promise (Society), Published rule and the court (Society)
Measure the price level every month, give an independent central bank a published inflation target and the tools to meet it, and make banks safe enough that a run on one does not become a run on all.
Needs first: Credit, interest and the bank, Fungible token and the mint, Pooled capital and limited liability, Count before you administer (Society), Telegraph (Computing)
Every guide, build, reference sheet and book reached from the steps above.
The 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 3Four-figure logarithms and trigonometry, square roots by Newton's method, and the two instruments that did the world's arithmetic before electronics.