sato is an issuance primitive. one ether in, a deterministic quantity of sato out, priced by p(eth) = (S/K) · e^(eth/S). it is the cleanest base layer ethereum has produced for a bonded asset: no operator, no allocation, no oracle. its price at any moment is a closed-form expression of one observable variable.
that property, more than anything else, is what satocurve is built on. most derivative tokens on ethereum need an oracle, a TWAP, an off-chain feed. satocurve does not. the underlying's price is the curve itself, and the curve is tamper-proof.
satocurve (scv) is an erc-20 that mints against sato, not against ether. depositing N sato into the satocurve vault mints scv according to a convex function of the underlying's price growth since launch. the vault holds the deposited sato; the inverse function burns scv and returns sato to the holder.
r = p_sato(now) / p_sato(launch)the result is a token that amplifies sato's moves on the way up and bleeds value during stagnation. when sato rises to 5×, scv rises to roughly 8×. when sato sits flat, scv loses ~0.18% per day to decay. when sato falls, scv falls faster.
this is the part that needs to be said plainly, in the same voice sato uses for its own math.
satocurve does not create leverage out of nothing. there is no counterparty paying funding rates, no perp engine, no rebalancing trick that magically multiplies returns. the convexity comes from two sources, and only those two:
one. the sato held inside the satocurve vault is removed from the float. as long as scv exists, that sato is locked. burning scv releases it back. this means scv's redemption value tracks sato directly — but its market price, set by the scv/sato uniswap v4 pool, can trade at a premium when demand for leveraged exposure is high. that premium is the convex term. it is not free; it can also go negative.
two. the decay term e^(−λ·t) is paid by holders, to holders. every block, every scv is worth fractionally less in vault terms; the released sato accrues to a redemption pool that anyone burning scv can claim from. decay is not a fee taken by an operator — there is no operator. it is a transfer from passive holders to active redeemers, on-chain, deterministic, ungovernable.
satocurve is a bet that sato keeps moving. holding scv through a flat market loses money. holding scv through a rising sato market makes money faster than holding sato directly. holding scv through a falling sato market loses money faster than holding sato directly. there is no scenario in which scv is strictly safer than sato. that is the entire point of the instrument.
the satocurve vault is a single contract. set as the only minter at deployment. locked there. it accepts sato and emits scv; it accepts scv and burns it for sato. there is no admin role, no pause, no upgrade path, no migration. parameters k and λ are set at deployment and immutable.
a 0.3% fee is taken on every mint and every burn. the fee stays in the vault permanently, increasing the redemption ratio for everyone who has not yet exited. it is not a treasury. it is the same counterweight sato uses: a small automatic tax on round-trip activity that makes the curve hard to abuse, and prevents anyone — including us — from extracting value from it.
scv trades against sato on a uniswap v4 pool. not against ether. this is deliberate. by keeping the pair entirely inside the sato ecosystem, scv inherits sato's price discovery rather than competing with it. ether-denominated price is a derived quantity — scv → sato → eth — and the spread between vault NAV and pool price is what arbitrageurs close.
the pool uses a custom v4 hook that reads vault state. when pool price diverges from vault NAV by more than 2%, the hook routes excess fee to whichever side is closing the gap. this is the only mechanism by which scv stays loosely pegged to its convex formula. it is loose by design. a perfectly pegged leverage token is one trade away from a depeg event.
three constraints, copied from sato's playbook with modifications:
a single mint is capped at 5,000 sato. no one can vacuum a meaningful share of vault capacity in one transaction.
burning in the same block as a mint reverts. flash-loan arbitrage on the convex curve is uneconomic.
for the first 100 blocks after deployment, every mint receives a random multiplier between 0.9 and 1.1. a tax on the bots tuned for the exact deployment block. average cost: 10%. after block 100, fully deterministic.
it is not a stable product. it is not a yield product. it is not "sato but better." if you want pure exposure to the issuance curve, hold sato. if you want amplified exposure with explicit, on-chain decay, hold scv.
the decay is the price you pay for the convexity. the convexity is the entire reason scv exists. anyone who sells scv as "leverage without decay" is selling something else.
sato has a terminal state: when 99% of K is minted, selfDeprecated flips and issuance ends. satocurve's vault remains open after that point, because the underlying still trades — on uniswap pools, on exchanges, peer-to-peer. scv's mint function continues to work as long as someone is willing to deposit sato; its burn function continues as long as the vault holds reserves. the convex relationship persists.
if scv's circulating supply goes to zero, the vault is empty, the contract is inert, and scv can be redeployed against future sato flows by anyone with the bytecode. there is no privileged redeployment. there is nothing to extract. if everyone who shipped this disappeared tonight, the contract would run tomorrow against the same rules.
that is what satocurve borrows from sato. the rest is just math.