Oracle

Cube-Root TWAP (cbrtTWAP) — An innovative variant of TWAP oracle that balances arithmetic and geometric means.

Design Trade-off

Traditional TWAP oracles force a trade-off:

Approach	Pros	Cons
Arithmetic	Captures short-term price moves	Vulnerable to price spikes
Geometric	Smooths out volatility	Slow to reflect real-time changes

As highlighted in research by Delphi Digital, choosing between these approaches involves significant trade-offs.

Introduce cbrtTWAP Oracle

Our AMM invents cbrtTWAP. It utilizes cube-root transformation to achieve:

• Responsive — Captures immediate market changes better than Geometric TWAP
• Resistant — Harder to manipulate than Arithmetic TWAP
• Stable — Follows broader trends, not noise.

How It Works

Step 1: Transform Apply cube root to each price observation:

$$\sqrt[3]{P_t}$$

Step 2: Average Calculate time-weighted average of transformed prices:

$${\sqrt[3]{P}}_{t_0,t_1}=\frac{{\text{cumulativeCbrtPrice}}_{t_1}-{\text{cumulativeCbrtPrice}}_{t_0}}{t_1-t_0}$$

Step 3: Finalize Cube the result to get the final oracle price:

$${\text{cbrtTWAP}}_{t_0,t_1}={\left({\sqrt[3]{P}}_{t_0,t_1}\right)}^3$$

This final result combines the responsiveness of arithmetic means with the stability of geometric means.