Blueperp: Leveraged Longs on a Bonding Curve

A bonding curve is a price function: given how much ETH has flowed into a pool, the curve tells you exactly what one unit of the token is worth. There is no spread, no market maker, no order book — just a formula. Blueperp uses a constant-product bonding curve (the same family as Uniswap) to price BLUE, and then adds one thing on top: leverage.

When you open a leveraged long, you put up ETH collateral and the protocol borrows additional ETH from the curve's liquidity, buys BLUE with the combined amount, and holds that BLUE as your position. If BLUE goes up, you profit on the full leveraged size. If it falls far enough, the position is liquidated — theBLUE is sold, the borrowed ETH is repaid, and you keep whatever is left (usually close to nothing). The whole thing settles on-chain with no counterparty.

The rest of this paper is the math. Throughout, we write E for the cumulative ETH that has been bought into the curve (we call this the curve level), P for the price of one BLUE in ETH, and L for leverage (2, 3, 4, or 5).

The curve is built around a constant product. Picture two reserves: an ETH reserve and a BLUE reserve. Their product never changes:

Here realBLUE is how much BLUE is still inside the curve, E is the cumulative ETH bought in, and V is a virtual ETH reserve — a phantom amount of ETH that exists only in the math. V does two jobs: it sets the launch price, and it acts as depth, damping how violently the price moves on small early buys. Blueperp uses:

(K is just total supply × V, which makes realBLUE = 1,000,000 at launch when E = 0 — all supply starts inside the curve.)

The price of one BLUE, in ETH, falls straight out of the constant-product rule:

Price grows with the square of the curve level. Double the ETH that has flowed in and the price quadruples-ish. The amount of BLUE still inside the curve, and the amount already sold to buyers, are:

At a reference ETH price of $2,300, the curve walks through these levels (FDV = fully-diluted value = total supply × price):

Where the curve ends. The 1,500-ETH level is the curve's natural top — past it the curve has no more BLUE to sell into, so the bonding-pool price stops climbing there. Think of it as the graduation point: beyond it, BLUE keeps trading freely on the open market (ordinary AMM pools, exchanges) with no curve involvement, and leveraged longs on Blueperp are available up to this level. The bonding pool then becomes a price floor — if BLUE ever trades back down into the curve's range, the pool comes alive again and operates exactly as before, leverage included. The curve isn't a cage; it's the launch ramp on the way up and the floor underneath on the way down.

A plain buy of ΔE ETH (no leverage) moves the curve level from E toE + ΔE and hands you the difference in BLUE reserves:

Selling is the same in reverse: feed BLUE back, the curve level drops, you receive ETH. Because price is convex, you always sell into a falling price — the bigger the sale, the worse the average fill. A 1% LP fee, taken in ETH, applies to every direct spot trade like this — buys and sells routed straight through the pool (see §8). Swaps the protocol performs internally for leverage (the leveraged buy on open, the sell-back on close, the forced sale on a liquidation) do not pay this fee — leverage has its own fee schedule.

You open a position with two inputs: collateral C (in ETH) and leverage L ∈ {2, 3, 4, 5}. The protocol then:

1. Borrows B = C · (L − 1) ETH from the curve's liquidity (§7 explains where).
2. Takes a 1% origination fee on the borrow — f = 0.01 · B — and routes it to stakers. Your effective collateral becomes C′ = C − f.
3. Buys BLUE with C′ + B ETH, receiving H BLUE. This leveraged buy is performed by the protocol internally — it does not pay the 1% spot LP fee.
4. Holds H BLUE as your position; you owe a debt D = B ETH back to the curve.

So your exposure is roughly L × your collateral, financed by a one-time origination fee — no running funding rate. The position's value at any later price P is just H · P. We track its safety with a health ratio:

Ignoring fees for intuition, at the moment you open: H ≈ L·C / P_entry andD = (L−1)·C, so

Higher leverage = thinner buffer between your entry health and the liquidation line.

A position is liquidated the moment its health falls to 1.05 (105%):

Plugging the entry approximation into Health = (H·P)/D = 1.05 and solving for the price at which that happens gives a clean result that depends only on leverage:

In words — the percentage drop from your entry price that triggers liquidation:

The health check uses a 5-minute time-weighted average price (TWAP), not the instantaneous spot. A single-block price spike — a flash dump, a sandwich — moves spot but barely budges a 5-minute average, so it cannot manufacture liquidations out of healthy positions. The forced sale that follows a real liquidation is itself rate-limited (a bounded number per block, and a price-impact cap on the sale) so a cascade cannot spiral.

Partial closes make a position safer. Closing part of a position repays debt first, which lowers the debt-to-holding ratio and pushes P_liq down. Your live liquidation price always reflects the current debt and holding, not the leverage you opened with:

Bad debt. In a severe drawdown a liquidation sale can recover less ETH than the debt owed. The shortfall is a realized loss to the protocol — it is recorded transparently on-chain (a public bad-debt counter) rather than hidden, and can be repaid later by the protocol depositing fresh ETH back into the curve. It never touches other users' funds or claimable balances.

When you close (fully or partially): the protocol sells the requested amount of yourBLUE back into the curve (this sell-back is internal — no spot LP fee), uses the proceeds to repay your debt first, then credits the surplus to you minus a1% close fee on that surplus. You withdraw what's credited with a separate claim. Your profit on a full close is approximately:

The only frictions are the 1% origination fee at open (on the borrowed amount) and the 1% close fee at exit (on the surplus). Set profit to zero and the favorable price move needed just to get your collateral back works out to roughly:

It's about the same for every leverage because the round-trip friction lands at roughly 1% of the position notional regardless of L — bigger leverage means bigger fees in absolute terms, but a proportionally bigger position to spread them over. A losing close pays no close fee at all (no surplus → no fee). For a memecoin-style asset that routinely moves tens of percent, a ~1–2% break-even is small relative to the bet — but it's real, and a position that just drifts sideways bleeds it.

The smooth curve is realized as 300 stacked liquidity slices — bands — each covering a 5-ETH window of the curve level (band 0 covers levels 0–5, band 1 covers 5–10, …, band 299 covers 1,495–1,500). Each band is born holding only BLUE; as buyers push the curve level through a band's window, that band converts fromBLUE into ETH. A band the curve level has already moved completely past is therefore pure ETH — and that idle ETH is what leveraged longs borrow.

Borrowing walks these fully-passed bands farthest-first — it drains the deepest, most dormant ETH (band 0, then band 1, …), leaving the bands nearest the live price intact for ordinary trading. On a close or liquidation, repaid ETH is re-deposited nearest-first, restoring the bands that see the most traffic. No band is ever drained more than 40% of the way, and a single position can pull from at most a few bands — so the maximum any one position can borrow is on the order of10 ETH (≈ 2 ETH from each of ~5 bands).

One consequence: leverage is not available the instant the curve launches.Until the curve level has passed band 0 — i.e. until ~5 ETH of ordinary buys have flowed in (about $50k FDV) — there is no fully-passed band to borrow from, and leveraged opens revert. Each additional 5 ETH of organic volume unlocks another band of borrow capacity. Importantly, borrowing and refilling only ever touch fully-passed ETH-only bands, never the live band straddling the current price, so the curve's price function stays exactly intact — leverage never distorts the published price.

Three fees, each on a different event. No transaction ever pays more than one of them.

So a spot trader pays one fee (1% LP fee on their trade). A leverage traderpays one fee on the way in (1% origination on the borrowed amount) and one on the way out (1% on their surplus, if any) — both go to BLUE stakers, and the leveraged buy and the close sell-back themselves are fee-free. There is no funding rate; the borrow fee is one-time at open, not per hour. Example: a 5× position with 1 ETH collateral borrows 4 ETH, so it pays 0.04 ETH origination at open, plus 1% of its profit-plus-collateral surplus when it closes. Round-trip friction works out to roughly 1% of the position notional — see §6.

Stake BLUE to earn ETH. Both leverage fees flow here: the 1% origination fee on every open, and the 1% close fee on every profitable exit (close or liquidation). They're distributed to stakers pro-rata by stake, streamed as the fees arrive. Rewards accrue continuously; you claim them in ETH whenever you like, and you can unstake at any time. (The 1% spot LP fee is the one fee that doesn't come here — it goes to the pool's LP fee address.)

• Leverage cuts both ways. A 5× long is wiped out by a 16% drop inBLUE; a 2× long by 47.5%. Liquidation is automatic, on-chain, and final — there is no margin call to top up.
• You can lose your whole collateral. After a liquidation the typical remainder credited back to you is near zero; in a deep drawdown it is zero.
• Leverage lives inside the curve. Leveraged longs can only be opened while BLUE is trading within the curve's range. Right at the top of the curve (~1,500-ETH level) a leveraged open can't fully execute and reverts; onceBLUE graduates above the curve it stays freely tradable on open markets, just without Blueperp leverage. The bonding pool remains as a price floor and re-activates, leverage included, if BLUE ever trades back into the curve's range.
• Bad debt is possible. Extreme, fast drawdowns can leave a liquidation recovering less ETH than the borrowed amount. The shortfall is tracked openly on-chain and is isolated from user balances and claimable funds, but it is a real risk borne by the pool.
• Leverage is bootstrapped at launch. Until ~5 ETH of organic volume has flowed through the curve, no leverage can be opened (there's no idle band ETH to borrow yet). Position size is also capped by how much fully-passed band ETH exists at the time.
• Smart-contract risk. Like any on-chain protocol, bugs are possible. Use only funds you can afford to lose, and only on the network the app is configured for — signing on the wrong chain can route funds to an address that doesn't exist.