Fragility of DeFi: Rigorous Maths of Infinite Apples and Oranges
Exploring how stable coin, meme coins, and circular dependencies highlight the unstable foundations of DeFi.
Reading The Block should come with a warning—to myself, I mean: “Reading this article may leave you confused and consume your afternoon until you’ve resolved this quagmire in your brain.” But even that wouldn’t be a good deterrent against having a look.
Take this one, for example, about a project from Eonia Labs: “Research Unlock: Where Mathematics Meets Memes.” I hope the person who recently put the idea in my head that I should look more carefully at memes feels at least some remorse for causing all of this. Because the buzzword meme made me look, and the hookline said this:
“The project represents a unique blend of serious DeFi infrastructure and cultural relevance, incorporating features like on-chain chat while maintaining technical rigor through mathematical first principles.”
Something that describes itself as serious, with technical rigor and mathematical soundness (I am not sure exactly what they mean)—well, I have to admit, the term mathematical first principles already raised an eyebrow—and cultural relevance? It sounds like they’re fellow art-tech fusionists, which would be superb.
The cultural ‘significance’ (at this rate I’ll run out of apostrophes before the article is finished) is described as follows:
“The platform allows users to create and trade assets with emoji ticker symbols instead of traditional alphanumeric ones, democratizing the creation of culturally relevant digital assets.”
It reminds me of watching a scene in a movie about medieval times where people sign contracts with xxx because they’re otherwise illiterate. But I’m not here to judge how replacing writing and numbers with emojis somehow brings relevant cultural advancement. 🤔🤐
“The emojicoin CPAMM follows the constant-product equation popularized by Uniswap v2: X⋅Y=K”
The way they represented the formula caught my interest because this isn’t exactly the Uniswap formula which goes like this:
“The automated market making algorithm used by Uniswap. See x*y=k.”
CPAMM (Constant Product AMM) is a mechanism underpinning many DeFi applications, including Uniswap and other decentralized exchanges (DEXs). It establishes the relative value between two assets while ensuring liquidity by allowing trades to occur that change the ratio of assets in the pool. However, it does not establish their absolute value (e.g., in USD). Let’s break it down with a simple example:
Imagine you have 5 apples (x=5) and 10 oranges (y=10) in a "fruit pool." The product of the quantities must always remain constant:
x⋅y=K so 5⋅10 =50
This 50 is not the number of apples or oranges but rather the "unit of account" for the apple-orange pool, which must remain stable.
Now, suppose a friend says, "I have oranges, but I’d rather have an apple instead." Time for some DeFi trading! Here's how it works:
Current price:
In your bowl, there are 5 apples and 10 oranges, so the price of apples in terms of oranges is:Price of 1 apple is established by the ratio of 10 oranges to 5 apples = 2 oranges per apple.
The trade:
Your friend wants 1 apple. If they were to trade 2 oranges (based on the current price), the new quantities would be:x=4 apples, y=12 oranges
However, this would violate the constant product rule, because:
4⋅12=48 (not 50!)
To maintain K=50, the price must adjust dynamically.
Recalculating the price:
If there are 4 apples left, the pool requires:50 / 4 = 12.5 oranges.
Therefore, your friend needs to add:
12.5−10=2.5 oranges
The actual price of 1 apple is 2.5 oranges, not 2 oranges.
This way, the ratio adjusts automatically based on supply and demand in the pool, constantly updating the relative price between apples and oranges at which my fruit bowl operates. This mechanism works under the assumption that these assets can be traded in fractional volumes. And don’t think you can shut me down by investing in an orange farm and trying to completely deplete me of apples. The fewer apple slices that remain in the apple-orange bowl, the steeper the price increase—which will approach infinity—because the pool cannot allow zero apples. If that happened, K would be reduced to zero, breaking the entire system. That’s not allowed!
This is an infallible system as long as we are only interested in such pairings: apples and oranges, or BMW and Mercedes cars. But you need a unit of account to make conversions between these pairings. If I know the relative price of apples to oranges and the relative price of BMW cars to Mercedes cars, I still cannot answer how many apples it would take to buy a BMW. I could set up a pairing, but any ratio would be as valid as any other: 1 apple to 1 BMW or 1 million apples to 1 BMW would create a functioning and coherent DeFi market—assuming, for a moment, this setup exists in isolation without reference to an external world where these products are produced, valued, and traded.
Many DeFi protocols use USD-pegged stablecoins like USDT or USDC as their unit of account, quoting token prices, yields, and portfolio values in USD terms. On Uniswap, for example, the price of ETH might be quoted as $1,800 in a USDC/ETH pool. This creates a consistent unit of account (USD), even if participants are trading ETH and USDC directly.
So why wouldn’t DeFi use crypto as a unit of account? Well, sometimes they do. In a DAI/ETH pool on Uniswap, the price of ETH might be 2,000 DAI/ETH, reflecting the relative quantities of DAI and ETH in the pool. Here, USD (via DAI) is indirectly the unit of account. And this is the problem: without a common standard (e.g., USD), pricing assets across protocols becomes chaotic. The entire system's reliability hinges on the trust and stability of the stablecoin used as the anchor.
While DeFi markets tout their independence from intermediaries, they are not truly decentralized. My concern isn’t so much with the reliance on oracles to feed prices but with the ecosystem’s principal dependence on centralized components—chiefly, a regulated currency like USD, albeit via a derivative, i.e., a stablecoin. This arrangement, especially when involving stablecoins like Tether, makes the system highly fragile.
Stablecoins like USDT rely on confidence and reserves to maintain their peg:
DeFi protocols use stablecoins to stabilize their own value.
If confidence in Tether wavers, it triggers a feedback loop without redundancy or resilience.
This creates a circular dependency where each layer assumes the stability of the other.
I’ve written about this before, but Tether’s legal terms explicitly state that it reserves the right to refuse or delay redemption for any reason—or even "no reason"—at its discretion.
From a strict financial theory perspective, USDT should theoretically be worth zero because:
No Legal Claim to Reserves
Unverified Reserves
No Regulation
USDT provides no meaningful legal claim, protection, or enforceable right to get your dollars back, and its value depends entirely on market perception, utility, and liquidity. However, stablecoins like USDC (issued by Circle) operate under ‘some regulatory oversight’. The degree of fragility depends on the stablecoin in question perhaps.
Returning to Emojicoin.fun and their claims of mathematical rigor to set a new standard for DeFi projects, I’d say this: My concerns about the risks in stablecoins are nothing new, of course. But here is a project claiming mathematical rigor while dealing with unresolved circular dependencies. And the ‘research’ by The Block doesn’t even mention this. That deserves 😭😭🤦♂️.