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covr: Split the Fees From the Bag

A memecoin derivative made of nothing but a box, a clock, and a square root.

Every LP has had this month. You provided liquidity to a coin that was printing, the fee APR said 400%, you did everything right, and you still ended the month down bad, because the bag ate everything the fees earned. Fees up, bag down, net red.

covr exists to fix exactly that month. It takes an LP position, which is secretly two things glued together, and cuts it into its two halves so that two different people can each hold the half they actually wanted. One person keeps the fee income with zero price risk. The other gets the price exposure at a discount. Nobody gets liquidated, nobody trusts an oracle, and the whole settlement is arithmetic a high schooler can check.

Here is the entire thing, from the ground up.

1. An LP position is a square root machine

A liquidity pool is two buckets, say GOODBOY and SOL, and it enforces one rule at all times:

x · y = k

The amount of coin times the amount of SOL always equals the same number, k. When someone buys, SOL goes in, coin comes out, and the pool slides along that rule. The price is just the ratio of the buckets.

Now the algebra, every step shown. Price is just the ratio of the buckets, p = y/x, so y = p·x. Put that into the rule:

x · (p·x) = k      →      p·x² = k      →      x = √(k/p)

and therefore y = p·x = p·√(k/p) = √(k·p), because multiplying by p is the same as sliding p² inside the square root.

The LP owns both buckets. In SOL terms the coins are worth x·p, and by the same slide-inside-the-root move, x·p = √(k·p). Notice that means the coin side and the SOL side are always worth exactly the same, the pool perpetually rebalances itself to 50/50, which is the real reason a square root is about to appear. Add the two halves:

value = x·p + y = √(kp) + √(kp) = 2·√k·√p

Check it with real numbers. A pool holding 100,000 coins and 4 SOL has k = 400,000 and p = 0.00004. Then 2·√(400,000 × 0.00004) = 2·√16 = 8 SOL, which is obviously right: 4 SOL plus 100,000 coins worth 4 SOL.

That is a theorem, not a backtest.

The whole product in one curve. The pool's balancing rule bends a straight line into a square root: quadruple the price and the LP doubles, crash 75% and the LP halves. An LP position is worth 2√k times the square root of price. If the coin 4x's, the position 2x's. If the coin drops 75%, the position drops 50%. The pool's balancing rule manufactures a square root payoff out of a linear asset, automatically, for free.

And k is not constant. Every swap pays a fee that stays in the buckets, so k only ever grows. Price pumping, dumping, or round tripping does nothing to it. k is deaf to price. Two things do move it: fees, which is the income we are after, and other people depositing into or withdrawing from the pool, which is not income at all. Section 2 tells those apart in one step.

So an LP position is two things glued together: a √price shape that moves with the market, and a growing k that is the fee income. covr is just scissors. It cuts along the glue line.

2. The trade

Priya has $10,000 of WIF/SOL liquidity. She loves the fees and is done with the price risk.

Rahul wants WIF exposure but hates full-size pain.

They match:

1. Priya's LP tokens go into a box.
2. Rahul puts $9,870 into the same box. That is the position's value today minus a 1.3% discount they agreed on.
3. The contract writes down two of today's numbers: the pool's k, call it k₀, and the total number of LP tokens in existence, call it L₀.
4. The box locks for 30 days. Nobody can touch it, including us.

At expiry, the contract reads both numbers again, k₁ and L₁, and splits the LP tokens with one fraction:

fee growth per LP token  ∝  √k / L

Rahul's share of the tokens = (√k₀ / √k₁) · (L₁ / L₀)

Priya gets the rest of the tokens, plus the $9,870.

Why the L's are there: k grows for two reasons and only one of them is income. Fees grow it, and that growth is Priya's. A stranger depositing into the pool also grows it, and that growth is nobody's. The tell is that a deposit raises k and L together, so dividing by L cancels it. What survives is fee growth per LP token, and that is the only thing the split reads.

Think of k as the size of a pizza and L as the number of people sharing it. If the pizza doubles because two more people showed up carrying their own halves, your slice did not get bigger. Covered measures pizza per person, and that number only moves when somebody actually adds a topping.

Why the fraction is perfect: multiply it into what Rahul's tokens are worth at expiry and every expiry number cancels. The k₁ goes, the L₁ goes, and what is left is the position priced at his entry vintage. He holds it as if no fees had ever arrived, which is pure price exposure. Priya's leftover tokens are worth exactly what fee growth created, and nothing else. All the √price goes one way, all the fee growth goes the other. The cut is clean because the square roots make it clean.

One position, two payoffs. The farmer's line is flat at every price, cash plus fees, which is the entire point of her side. The scooper holds the curve. Add the two lines together at any price and you get the original LP position back, nothing created, nothing lost.

3. What each side actually holds

Priya, the farmer. Her $9,870 is escrowed and hers at expiry no matter what WIF does. Every fee the pool earns during the term is hers too. She sold the shape and kept the income. Her cost is simple and she should stare at it before signing: if WIF moons, Rahul rides it, not her. One honest footnote: her fee income accrues inside the pool, in kind, so the fees themselves are still worth more or less depending on price until she collects them. Principal derisked, fee value still floats.

Rahul, the scooper. He paid 98.7 cents on the dollar for a square root. Run the numbers against just buying the coin:

Read that table honestly. Rahul wins on every outcome below roughly plus 2.6%, and loses the race above it. He is long, with no leverage anywhere, and with less upside than spot, on purpose. In market language he sold convexity, the accelerating part of the payoff, and the discount is what he was paid for selling it. If you came looking for more upside than the coin itself, this is not your product, and we would rather tell you that here than have you find out at expiry.

On fresh coins the discount is much bigger because the risk is much bigger. A day-two graduate might trade at 19% off for a 7 day term, which moves Rahul's breakeven to plus 52%. He beats a spot buyer on everything from a full rug up to a 52% pump. That is why fresh coins are where scooping shines.

The scooper against a spot buyer, net of what each paid. Green shading is where the scooper is better off, red is where spot wins. On a major, the discount buys a small cushion and a low breakeven. On a fresh graduate, the 19% discount pushes the crossover past +52%: the scooper wins everywhere from a full rug to a half-double.

4. Terms: how long is the box locked

The lock is not a limitation, it is the merchandise. Rahul is buying guaranteed delivery, and Priya is selling guaranteed cash. A cancelable farmer would be holding a free option to yank the upside back the moment the coin pumps, which is exactly the kind of hidden option this design refuses to contain.

Terms come from a fixed menu, matched to the coin's stage of life:

Short terms live on wild coins because that is where a one day discount is real money and where anything beyond a week is unpriceable anyway. Long terms live on majors. The 4 hour tier is really an event contract, a box around a stream or an unlock, and it only opens on pools deep enough that nobody can bend a short settlement window.

Expiries land on standard timestamps, the way options markets do it, so that every claim on the same pool and expiry is interchangeable with every other one. That is what lets claims trade.

5. Getting out early, the honest version

The guaranteed exit is expiry. Everything else is a probability, and we will not pretend otherwise. Here is what actually exists, in order of how real it is:

Flip to Farm. Rahul's claim is future LP shares, which means it can itself be escrowed as the farmer side of a brand new contract. If WIF peaks mid-term, he locks in today's value minus a fresh discount, cash at the new expiry. He does not need to find a claim buyer, he needs to find a new scooper, and peaks manufacture new scoopers, because the peak's native persona is the scared bull who thinks it runs further but wants a cushion.

Bag rotation. Holders of the coin are natural buyers of claims, because the lock costs them nothing. A holder sells some coins into the peak on the pool's deep liquidity, buys claims with the proceeds at a discount, keeps their exposure, and pockets the difference. They were holding past expiry anyway.

Take profit, set in advance. At the moment you scoop, you can set an auto-list: if my claim hits 2x, put it up for sale. Note the word carefully. It lists automatically. It does not sell automatically, because nothing can guarantee a buyer. On major coins with listed perps, market maker bots will usually take a fairly priced claim within seconds, since they can hedge it. On a coin that trades nowhere else, no bot exists, because there is nothing to hedge with, and the panel will tell you plainly: no bids, you are in until expiry.

Farmer buyback. The person most full of regret at your 2x is the farmer who sold you the upside. Both sides can pre-agree unwind prices at match time, while everyone is still calm. To be real, a farmer's buyback bid has to be escrowed cash, because an unfunded promise is a default waiting to happen, and defaults are the one thing this product refuses to contain.

Who will never buy your claim: momentum flippers. A flipper's entire product is the exit button, and a locked claim removes it. No discount makes it the same good. We do not build on their demand and neither should your expectations.

And a consolation built into the math itself: if you miss the top entirely, the square root softens the round trip. A 40% retrace from the peak only hits a claim holder for about 23%. Missing the peak hurts half as much as it hurts a spot holder.

6. Why nothing can leak

Every DeFi blowup in history needed at least one of four ingredients. Count them in covr:

A price feed to lie to. None. Settlement reads two numbers, k at fill and k at expiry, off the pool's own buckets. Anyone can read the same accounts and get the same numbers. It is the pool weighing itself.

A debt to liquidate. None. Both sides pay 100% into the box on day one. Nobody ever owes anything, so there are no liquidations, no margin calls, no keeper bots racing a crashing chart, and no transaction anywhere that must land in the next block to keep anyone solvent.

A pool of other people's money to drain. None. One farmer, one scooper, one box. If the discount was a bad price, exactly one adult overpaid exactly one other adult, precisely as agreed. A wild month transfers value between two consenting people. It cannot create a hole.

A model that can be wrong. None. There is no volatility formula, no funding rate, no listing committee. The 2√(kp) identity is algebra, the split divides by LP supply so that other people joining or leaving the pool never reads as income, and the discount is set between the two humans, never by us.

Two guards handle the two ways someone could try to bend the arithmetic itself. Readings are time-averaged medians over minutes, not single instants, so a one-block spike does nothing and holding a distortion for the whole window costs real fees, paid partly into the very pool the farmer owns a slice of. And because a direct token donation into a pool is indistinguishable from fee income on chain, recognized fee growth is capped at a multiple of the pool's organic fee rate, so no sudden jump in k can ever move principal-scale money. Both guards are arithmetic, not judgment.

7. The fine print, volunteered

The farmer gives up the pump. The scooper's cushion is not safety, a rug still costs most of your money. Fee income is in kind until settlement. Terms are terms, and the only guaranteed exit is expiry. Classic full-range constant product pools only, on canonical venues, because concentrated liquidity breaks the square root and lookalike pools are how people get phished. Smart contracts carry risk no structure deletes. Nothing here is investment advice, and the discount is a price set between users, so check it against the pool's fee history before you sign either side.

8. Where this came from

We spent a long time trying to build a much fancier machine: perpetuals on powers of price, funding rates computed from variance, listing gates computed from backtests. Every version had a panel that hid a leak, and two hostile reviews plus our own data kept finding them. The thing that survived every attack was the thing with no machine in it at all.

Because the machine already exists. The AMM built the curved payoff the day the pool was created, out of x·y = k, and it has been sitting inside every LP position ever minted. covr adds a box, a clock, and one fraction with a square root in it.

Pick your side. One of you wants the fees. One of you wants the bag. Finally, a clean way to split them.

Both sides fully funded when matched. Settlement is a share transfer. Nothing here can be liquidated, margin called, or drained.