wei

a specter has returned to ethereum: the specter of code that runs without an operator.

wei is an erc-20 on ethereum. lowercase name, lowercase symbol, eighteen decimals. it is an asset. it does not launch and graduate and migrate. there is no roadmap, no v2, no fork, no successor token. the contract that exists is the contract.

issuance, not launch

wei is an issuance mechanic. the contract is the issuer. there is no team treasury, no premine, no foundation allocation, no insider round. the curve is the schedule; the smart contract enforces it.

mint deposits ether into the curve's reserve pool. burn redeems against that pool. the pool grows monotonically when net mints exceed net burns. holders' exits are backed by it. no party can withdraw from it.

what validators are to ethereum, the contract is to wei. ethereum's issuance scales with the validator set; wei's scales with the curve ledger. ethereum's supply contracts when activity exceeds a target; so does wei's. both convert outside-system activity into inside-system supply via a transparent, verifiable rule.

reserve as proof

every mint moves ether from the buyer's wallet into the contract. the reserve only moves out via burns priced by the inverse curve. there is no admin key, no emergency function, no upgrade path. ether deposited at mint time is ether available at burn time, less protocol fees that accumulate alongside it.

this distinguishes wei from synthetic-supply tokens. there is no token without a corresponding ether deposit on-chain. the reserve is the proof.

the hook

issuance happens through one contract, a uniswap v4 hook, set as the only minter at deployment and locked there. the formulas below are computed on-chain in PRBMath UD60x18 fixed-point arithmetic.

mintPriceEthPerWei(S) = K * sqrt(S)

S = cumulative wei issued through the curve
K = constant set at construction

mint price grows as the square root of cumulative issuance. each new wei issued raises the next mint's marginal cost. early holders accrue the value of later joiners; later joiners accept that price or do not buy. there is no fixed cap. issuance never halts by decree; it halts when its marginal cost exceeds market price.

fee, sealed

a 0.3% 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 it cannot be withdrawn, governed, voted on, or redirected.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 isn't a treasury. it is a counterweight that prevents the curve from being a free thing to abuse, and prevents anyone, including us, from extracting value from it.

anti-game

three constraints keep the curve hard to game. a single mint is capped at 5 ether, so no one can vacuum a meaningful share of supply in one transaction. burning in the same block as your last mint reverts, which makes flash-loan arbitrage uneconomic. and for the first 7,200 blocks after deployment, every mint receives a random multiplier between 0.85 and 1.00: a tax on the bots tuned for the exact deployment block, costing them up to fifteen percent of the wei their deposit would otherwise mint. the missing fraction is left in the reserve forever, never withdrawable. when that window closes the contract is fully deterministic.

transfer base burn

every transfer of wei is taxed by a base fee, in basis points of the value transferred, sent to 0x000000000000000000000000000000000000dEaD. the base fee is recomputed each block by an elastic update rule modeled on eip-1559:

target_block_volume = T              (constant, set at deployment)
used_block_volume   = U_b            (sum of transfer values in last block)

new_base_bps = old_base_bps * (1 + (1/8) * (U_b - T) / T)
             clamped to [1 bps, 100 bps]

above the target the fee rises by up to one-eighth per block; below it, falls by up to one-eighth, clamped between one and one hundred basis points. activity destroys supply. quiet does not.

the curve issues; transfers consume. supply is the running difference between the two.

two regimes

during bootstrap, the curve is the only path to wei. each new buyer mints against the contract; each seller burns against it. supply expansion and price discovery happen in lockstep.

once secondary AMM pools accumulate sufficient depth, secondary becomes the primary trading venue. the curve's role narrows: canonical issuer when minting is profitable, buyer of last resort when no one bids on secondary. this is the mature regime. the curve continues to mint supply only when secondary exceeds curve marginal — exactly the condition under which validation is profitable on ethereum.

btc-shaped vs eth-shaped

there is a sister project. sat0 is bitcoin's spirit on ethereum: a fixed cap, an exponential curve that climbs steeply, a halting schedule. wei is ethereum's spirit on ethereum: no cap, a square-root curve that climbs gently, an ultrasound burn. both rise; they diverge in shape and ceiling. they share a skeleton because the skeleton is the value. they diverge in monetary policy because that is the only thing worth diverging on.

lineage

wei is named after wei dai. b-money, 1998: the cryptographic-cash proposal cited by satoshi nakamoto in the bitcoin whitepaper, written ten years before bitcoin existed, by someone who chose not to ship it. wei dai's smallest unit of ether bears his name; this contract bears it too. there is no affiliation. there is a lineage.

trustless is the only feature

we did not pre-mint. we hold no allocation, no admin role, no pause function, no upgrade path. there is nothing to extract from the hook other than by burning wei back through the inverse curve like anybody else. if everyone who shipped this disappeared tonight, the contract would run tomorrow against the same rules and the same prices. that is what we mean by trustless. that is the only feature.