> It appears that it might be possible for CTV to create on-chain AMM-style marketplaces. On chain marketplaces create arbitrage opportunities which motivate people to pay for faster transactions:

That article doesn't mention AMMs at all. It mentioned inscription marketplaces, like Magic Eden, which is running today, where you need to construct a PSBT to create an "ask" for a Rune (you can't even do bids). They were talking about that creating some MEV. 

> Please show me where the non-technical risks were discussed. I haven’t been able to find anything other than Peter identifying the risk of cheaper OOB payments.

Great question. Let's see what folks say: 

https://x.com/matthewjablack/status/1838340344607355010

utxos.org is obviously a great resource. And mailing list for previous iterations of CTV

OpTech had some things to say: https://utxos.org/analysis/optech/

> We were previously discussing AMM style marketplaces.

AMM style marketplaces can't be built with CTV.

> I suggested that perhaps specific UTXOs could represent points on the hyperbolic constant product curve (x * y = k) that’s used in AMM marketplaces.

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

> You haven’t yet shown me why it’s impossible to create AMM style marketplaces using CTV.

You haven't shown me how you can! 

First of all, you need to do multiplication to do x * y = k. You don't have OP_MUL in Bitcoin script since it was disabled back in 2010 by Satoshi. You can emulate OP_MUL using CAT in order 1400 bytes. But you cannot emulate it with just CTV. 

Bitmatrix ran into this problem when they were building an AMM on Liquid. They were able to get MUL working using OP_SUBSTR and OP_CAT:

https://medium.com/bit-matrix/technical-how-does-bitmatrix-v1-multiply-two-integers-in-the-absence-of-op-mul-a58b7a3794a3

However CTV doesn't enable MUL in any capacity. You cannot create an AMM if you cannot calculate the price after a swap occurs.