Constant-product Total Supplies

Greetings. I desire feedback on this concept, and have not seen it specifically referred to; if it has already been discussed in the past few days, please point me to the discussion.
(I am unsurprised if there are holes, and which to know them if they exist.)

I note that this might require a unique balancer for each stablecoin (rather than a single balancer absorbing volatility from stablecoins with different pegs).
[Edit: One way to effectively keep LUNA as the single balancer supporting multiple currencies would be to to have 1:1 transformation between distinct balancers, for instance LUNA-UST, LUNA-EUR, LUNA-KRW; transforming LUNA forms from one to the other would be how market cap was moved between the currency groups, all currency-to-currency transformations being through LUNA rather than Terra-to-Terra.]

To note my biases, I am in favour of keeping the UST/LUNA brand recognition (both fame and infamy contributing to future weight). With so much thought and code and analysis already as a foundation, and especially having paid so much for this learning experience, ‘Let’s Do It Better This Time’.

The thoughts in this post are solely my own and should not be taking as representing any other entity (person or organisation).

Looking back at Total Supply measurements ( ),
Terra began with a 10 million UST supply and a 1 billion LUNA supply.
At peak UST supply, UST supply had grown to over 18 billion (18,000x) while LUNA had not fallen below 700 million (0.7x).
In recent days, UST supply did not fall below 11 billion (~0.6x) while LUNA supply rose to over 6 trillion (~8,000x).

It is a strong appeal of an algorithmic stablecoin that as more money enters the ecosystem (summed market cap), the stablecoin supply can expand indefinitely without requiring centralised management of collateral. What has stood out to me most in these few days has been the importance of this being reversible, money able to exit the ecosystem without unlimited hyperinflation.

In more concrete terms: If UST total supply did not fall below 10m, it should not have been possible for LUNA supply to exceed 1b. If any group (TFL or otherwise) had previously destroyed forever (true burn of) 1b UST, it should not have been possible for LUNA supply to exceed 10m. The maximum possible inflation should have been knowable.

Decimals are certainly a consideration, in ensuring sufficient liquidity when the balancer gets so deflationary it starts running out of decimals (e.g. copper/silver for gold, non-Bitcoin for Bitcoin); an approach if or when that becomes an issue is spawning another stablecoin-balancer pair with the same peg.

As for the peg itself, transformation (burn-mint) perhaps possible only in the direction which (and to the extent which) supports the peg. (UST supply only able to shrink when priced below 1 USD, and only able to increase when priced above 1 USD, opposite-direction trades taking place (with no burn-mint transformation) in exchanges (DEXs or CEXs).)
Tobin tax perhaps in the form of slippage-based transformation fee, such that incremental transformations which changed supply ratio negligibly would cost a negligible percentage, while large swaps which changed supply ratio considerably would cost a considerable percentage.
(This thus encouraging transformations to be carried out slower, giving the rest of the ecosystem more time to react, or viewable as allowing those in a hurry to pay a premium for speed.)
(Credit for the concept to the formulas at Liquidity Model - THORChain Docs )

To summarise: Total supplies of UST and LUNA could change, but only in whichever direction that adjusted UST supply in the direction of 1 USD per UST, and while transformations of a small percentage of the UST total supply would mint a similar small percentage of the LUNA total supply, large percentages transformed would mint less-large percentages, such that the product of the two supplies (the two total supplies multiplied by each other) never exceeded its initial value.
(Deflationary decrease would still be possible through permanent burning of either the stablecoin or the balancer.)

I am happy if this has been in any way food for thought; please share with me your thoughts on this.

Looks like a solid idea - however, LUNAs supply is currently 6 trillion - not 6B as stated in this proposal.

A welcome correction of my understanding, thank you @FromTheAshes ! Altering now.