➡️ “That article doesn't mention AMMs at all.”

The term “AMM” appears 19 times in that article. 🤷‍♂️

➡️ “You can't do transaction introspection with CTV, so this isn't possible”

You don’t need introspection if the addresses are preregistered. Scanning the address will list all the UTXOs. Once you know the UTXOs then you also know the amounts. 

➡️ “First of all, you need to do multiplication to do x * y = k.”

No, you don’t need multiplication if you can determine the product in another way. You might be able to create a state machine through a chain of predefined UTXOs that represent the AMM’s balance ratio. 

Specifically, I’m suggesting to model the AMM's pricing curve through output UTXOs. Each UTXO represents a specific state of the liquidity pool at a point on the curve, with predefined balances of Bitcoin and tokens. 

Trades are executed by consuming a state UTXO and creating a new one corresponding to the next state along the curve, effectively moving the liquidity pool's balances according to the AMM's pricing function. 

CTV would enforce that only valid state transitions can occur by committing to specific transaction templates. If input A and input B, then move to point on the curve #1. But if input A and input C, then move to point #2. You’re determining the product based on the inputs provided. It has the same effect as multiplication, just doesn’t require computation or introspection. 

➡️ “Great question. Let's see what folks say”

Looks like nobody responded with any information showing the non-technical risks were considered. I still haven’t seen anything either. It’s on the proponents to show safety. It would be negligent to not fully consider all risks.