pat0 is an erc20 on robinhood chain. it is issued by one contract, deployed once, with no owner and no admin path. eth enters the contract through mint and leaves through burn. the contract keeps the eth in a reserve called the cistern and every token is a claim on a share of it.
two prices govern the machine. the curve price is what the next token costs to mint, a cubic function of how much eth has ever entered the curve. book is what a token is worth to burn, the cistern divided by supply. the curve price is never below book, so the contract cannot be drained by round trips. a third quantity, pressure, sits between a minter and the curve and diverts part of every crowded mint straight into the reserve.
this document walks through the arithmetic in the order the contract executes it, then through the storage, the invariants, and what can be checked on the explorer. the plates are drawn from the formulas. once the contract address is configured, live values from the chain appear as markers on them and as rows in the tables.
| word | meaning |
|---|---|
| cistern | the eth reserve the contract holds |
| curve | the rational supply function q(e) |
| position | e, cumulative eth that has entered the curve, in wei |
| curve price | marginal price of the next token along the curve |
| book | cistern divided by supply, eth per token |
| pressure | the per block congestion multiplier π |
| budget | the maximum tokens that may issue in one block |
| pat | one mint transaction, capped at 2 eth of curve entry |
| cooldown | the 64 block wait between a wallet's mint and its burn |
| headroom | asymptote minus supply |