An aside on the topic of partial orders in currency: perhaps we can take inspiration to what humans did in the past when (totally-ordered) bullion money was scarce but still needed to do commerce: we often relied on recording transactions with others through [tally sticks]( and other forms of credit. You could even make it effectively tamper-proof by recording transactions in which two halves of a stick, forging the exact locations of notches natural grain of the split stick would have been practically impossible. Debt in this form [could then be traded as currency]( and someone to try to collect on that debt.

This is partially ordered because a mark on one set of sticks is not necessarily fungible or comparable with another: one person's debt might not be perceived as being able to pay back their debt, so in exchange, it might not be perceived worth the nominal value.