Likwid runs spot, lending, and leverage on one curve:

$$(x+x^{\prime })(y+y^{\prime })=k$$

where x, y are the pool's real reserves and x', y' are mirror reserves — the internal "IOU" side that lets the pool be borrowed against and levered on without an external counterparty. Two user actions touch this curve very differently, and the difference explains why borrowing on Likwid cannot distort the price while leverage moves it on purpose.

Price comes from the expanded reserves

The quoted price is always read from the expanded reserves, not the raw ones:

$$\text{price}=\frac{x+x^{\prime }}{y+y^{\prime }}$$

When something is borrowed, the borrowed amount does not simply disappear from the books — it is recorded as a mirror reserve. So x + x' can stay constant even as real reserves move. That single fact is what separates lending from leverage.

Lending / borrowing — no swap, price unchanged

A pure loan is when a user posts collateral and borrows the other asset to take it away.

• No trade is executed against the curve.
• The borrowed amount leaves real reserves, but the same amount is added back as a mirror reserve.
• Because x + x' and y + y' are unchanged, the quoted price does not move.

This is the key safety property: borrowing on Likwid cannot be used to pump or dump the quote. A naive "lend straight out of an AMM" design would let a borrower drain real reserves and shift the price artificially; mirror reserves prevent that. Borrowing changes only who holds the assets, not what the pool quotes.

Leverage — a real swap, price moves

Opening a leveraged position is the opposite — a genuine trade against the pool.

• To build, say, a 3× long, the protocol borrows the quote asset and swaps it through the curve to buy the target.
• That swap moves the pricing point along the curve — x + x' and y + y' change — so price moves, exactly as any market buy or sell would.
• The borrowed leg is still tracked as a mirror reserve (it is the debt the position owes), and the position size is collateral × leverage.

So leverage is meant to move the price: it is a directional bet executed against real depth. The mirror bookkeeping here does not freeze the price — it records the borrowed obligation and bounds how far the pool can be extended.

Side by side

	Lending / borrowing	Leverage
Swap against the curve	No	Yes
Effect on quoted price	None — price is frozen	Moves along the curve
What the position holds	collateral + debt	a collateral × leverage directional position
Role of mirror reserves	offset the outflow → keep price still	record the borrowed leg (debt) and bound expansion

Bounded the same way

Both actions are limited so a single pool can never be over-extended: a cap on leverage, a cap on the mirror share of reserves, and time-smoothed reserve references for liquidation so a one-block price spike from a flash loan cannot force unfair liquidations or enable cheap manipulation. See Truncated Price and Margin Position Mechanics for the details.