the curve is the schedule. everything left of the current position has been paid for in ether that sits in the reserve; everything right of it costs more than everything left of it did.
rat0 is an issuance mechanic. the contract is the issuer. there is no team allocation, no premine, no foundation tranche, no insider round. the curve is the schedule and the contract enforces it.
a mint deposits ether into the curve's reserve. a burn redeems against that reserve. the pool grows monotonically while net mints exceed net burns, and every holder's exit is backed by it. no party can withdraw from it, including whoever deployed it.
what miners are to bitcoin, the contract is to rat0. bitcoin gates issuance with hash power; rat0 gates it with curve price. both convert effort outside the system into supply inside it through one transparent, verifiable rule. on this chain the ether arrives over the canonical bridge and pays gas natively, so the mechanic runs in its own denomination end to end.
every mint moves ether from the caller's wallet into the contract. the reserve leaves only through burns priced by the inverse curve. there is no admin key, no pause switch, no emergency function, no upgrade path. ether that entered at mint time is ether available at burn time, less the protocol fee that accumulates beside it.
this is what separates rat0 from synthetic supply. a token cannot exist without a corresponding ether deposit recorded on chain. the reserve is the proof.
issuance flows through one contract, a uniswap v4 hook, set as the sole minter at deployment and locked there. everything below is computed on chain in prbmath ud60x18 fixed point arithmetic.
a 0.3 percent protocol fee is taken on each side of every mint and every burn. it stays in the hook permanently. it cannot be withdrawn, governed, voted on, or redirected. it is not a treasury. it is a counterweight that makes the curve expensive to abuse and impossible to extract from, by anyone, including whoever wrote it.
three constraints keep the curve hard to game. a single mint is capped at 5 ether, so no transaction can vacuum a meaningful share of supply. burning in the same block as your last mint reverts, which breaks flash loan round trips even at 100 millisecond blocks, because atomicity lives in the block, not the clock. and for the first 36,000 blocks after deployment, roughly the first hour at this chain's cadence, every mint receives a random multiplier between 0.9 and 1.1: a tax averaging ten percent on bots tuned to the deployment block. the chain itself sharpens this defense in a way ethereum could not: sequencing is first come, first served, so a sniper cannot buy priority into the opening blocks at any price.
drawn at multiplier parity. real drift between forward and inverse positions widens this band; it never closes it.
after block 36,000 the contract is fully deterministic, forever.
mint price grows exponentially; each new mint costs more ether than the last. eventually the marginal cost of issuance exceeds the market price and minting halts on its own. burns continue to redeem against the reserve.
the curve is asymptotic. reachable supply is bounded near 20.5 million rat0 and declines slightly with each burn. anything plotted past cumulative ether of roughly 2,302 is theory, not territory.
the curve transitions from active issuance to dormancy. the reserve persists.
bitcoin pays less for each epoch of work; the curve charges more for each tranche of supply. mirrored mechanisms, same conclusion: issuance ends not by decree but by arithmetic, and in both systems the schedule was public before the first unit existed. hover any bar for exact figures.
during bootstrap, the curve is the only path in. each new buyer mints against the contract; each seller burns against it. supply expansion and price discovery happen in lockstep.
once secondary pools accumulate real depth, secondary becomes the primary venue and the curve's role narrows: canonical issuer whenever minting is profitable, buyer of last resort whenever no one bids. this is the mature regime, and it is bitcoin's condition restated: new supply appears only while the market pays more than the marginal cost of producing it. each successful mint advances the curve and raises the cost basis for everyone after.
the bonding curve is a uniswap v4 pool with a hook attached. the secondary market is a separate v4 pool, rat0 against usdg, robinhood's dollar, with no hook. both live under the same poolmanager; they are not the same pool. a trade touches the curve only when its pool key is selected.
most venues that list rat0 will not route through the curve. they will route through aggregators, which call into the poolmanager and quote whichever pools they support. aggregators that understand v4 custom hooks can discover the curve pool and price it; the rest will trade the plain pool.
burning is a property of the pool, not a privilege of any site. any caller that swaps rat0 to eth through the curve pool decrements totalSupply against the inverse curve and is paid from the hook's reserve. any caller that swaps through the usdg pool trades amm liquidity and leaves supply and reserve untouched. the burn quote at any moment:
the curve answers what the formula owes at this position. the secondary answers what someone will pay right now. the two diverge, and the fixed point drift between forward and inverse positions keeps the burn quote structurally below the mint quote even traded back to back. when secondary bids are thin, depressed, or the pool leans heavy with rat0, the curve's algorithmic bid is the better exit, and it never runs out of inventory before the reserve does. when makers quote tight, secondary wins. the quotes panel above prints both numbers and prefers neither.
there is no premine. there is no allocation, no admin role, no pause function, no upgrade path. nothing can be extracted from the hook except by burning rat0 back through the inverse curve like anyone else. if everyone who shipped this vanished tonight, the contract would run tomorrow against the same rules and the same prices.
the chain beneath it has an operator; the sequencer has a name and a compliance department. the token does not. it cannot be paused by its authors because its authors kept nothing, and its state cannot be forged by the sequencer because every transition is checkable on ethereum. that is what no operator means here. it is the only feature.