What’s even bigger than SIZECHAD?

The brand new TriCrypto pool from Curve represents a major mathematical and economic breakthrough. Just as Einstein’s theory of General Relativity refined Special Relativity, the Transformed Peg Invariant takes the already revolutionary StableSwap Invariant to the next level.

Like relativity, the white paper is also not for the faint of heart. Conceptually, the Transformed Peg Invariants allow for high liquidity among differently priced assets (5-10x greater than the product invariant used by other AMMs). The pool internally computes an “internal oracle” price that adjusts when the loss becomes smaller than the system’s profit.

To visualize the effect, consider the various curves produced by different invariants after applying a transformation to a constant price.

Blue is the existing stableswap for fixed price assets, with the dashed lines representing the largely archaic constant product invariants. The new orange curve provides the best of all worlds — adhering closely to the blue line to minimize slippage at small price movements, but demonstrating more asymptotic behavior to account for large fluctuations of differentially priced assets.

The new formula maintains the general form of the original stableswap, but with some adjustments to accommodate the case of differently priced assets.

The solution can be computed using Newton’s method, which when computed on EVM takes about 35K gas.

The paper describes great results from simulations, but ultimately the proof is in the actual implementation. Lucky enough, Curve has already launched a TriCrypto pool on Polygon for those brave enough to jump in. TriCrypto contains Bitcoin, Ethereum, and USD, arguably the three most important assets within the cryptocurrency space.

If we want to liken them to Hyrule’s Triforce:

Certainly any new pool has risk, so you should consult your neighborhood mathematician or review the source code before jumping into an experimental new pool.

Of course, Curve’s track record gives us a lot of confidence. The original StableSwap invariant has weathered three different assaults from at least one competitor:

It’s funny that this major breakthrough happens to be launching not just on Ethereum but also Polygon, a chain that only today discovered the concept of block explorers. This is a bit like a civilization discovering fire and splitting the atom on the same day.

Depending on how TriCrypto shakes out, we hope this gets the recognition it deserves. Some day Sweden will have to open the floodgates to recognizing cryptocurrency by issuing Satoshi Nakamoto the Nobel Prize for Economics. Once this occurs, we nominate this paper to be next in line for a serious look by the committee.

*For more info, check our live market data at https://curvemarketcap.com/ or our subscribe to our daily newsletter at https://curve.substack.com/. Nothing in our newsletter can be construed as financial advice, or even coding advice. Author is a $CRV maximalist.*

Thanks for the analysis, really enjoying the newsletter so far!