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How Does a Stablecoin Pool (Like a Constant Sum Market Maker) Manage the ‘K’ Value Differently?

A Constant Sum Market Maker (CSMM) uses x + y = k. In this model, 'k' is the sum of the reserves, and the price remains near 1:1 until one reserve is nearly depleted.

More advanced stablecoin AMMs, like Curve, use a hybrid function that combines the CSMM near the peg for low slippage and the CPMM at the extremes to ensure deep liquidity and prevent full depletion. This hybrid approach effectively manages 'k' to keep the price stable.

Can a Stablecoin Be Both Algorithmically Managed and Partially Collateralized (A Hybrid Model)?
How Do Hybrid Models Attempt to Combine the Efficiency of CEXs and the Decentralization of DEXs?
Are There Hybrid Legal Agreements That Combine Smart Contracts with Traditional Law?
Name a Common Mathematical Formula Used by AMMs besides $x Y = K$