Bonding Curve

Core formula

$$x \cdot y = k$$ $$price = \frac{x}{y}$$

• x = virtual GOR reserves
• y = virtual token reserves
• k = constant product

Buy path

When a user buys $\Delta y$ tokens, the curve removes those tokens from the reserve and solves for the new GOR reserve.

$$y' = y - \Delta y$$ $$x' = \left\lceil \frac{k}{y'} \right\rceil$$ $$\text{gross GOR in} = x' - x$$

After that, protocol and creator fees are added on top of the gross curve cost.

Sell path

When a user sells $\Delta y$ tokens back into the curve, the token reserve increases and the quote reserve is solved again.

$$y' = y + \Delta y$$ $$x' = \left\lfloor \frac{k}{y'} \right\rfloor$$ $$\text{gross GOR out} = x - x'$$

The user receives the gross output minus protocol and creator fees.

What actually matters when you integrate

• Price is entirely deterministic from the curve reserves.
• Buy and sell previews must match the protocol's ceiling and floor rounding.
• Once the curve is complete, trading logic needs to switch to DumpsterSwap.