Explainer: The Singularity Equation — what P(α) = C/(1-α) means

Hey there, crypto fam! Ever heard whispers about "singularity" in the DeFi space and wondered what all the fuss is about? No, we're not talking about AI taking over the world (at least not today!). We're diving into a fascinating mathematical concept that helps explain the potential price behavior of certain crypto assets, like FLAT. It's all about understanding the relationship between how much of an asset is locked up and its price.

Let's break down the "Singularity Equation": P(α) = C / (1 - α)

This seemingly simple formula holds a lot of power in understanding the theoretical mechanics behind some DeFi protocols. Let's decode each part:

• P(α) = Price: This is what we're ultimately interested in – the price of the asset. The (α) next to the P just means that the price is a function of alpha, or it changes depending on the value of alpha.
• C = Constant (Initial Price): Think of C as a baseline or starting point for the asset's price. It's a fixed value that sets the initial scale.
• α (Alpha) = Absorption Rate: This is the star of our show! Alpha represents the fraction of the total supply of an asset that is locked away in a specific mechanism. In the context of FLAT, this often refers to the amount of FLAT locked as SAVE.

What Does "Absorption" Really Mean?

In simpler terms, "absorption" here means taking a portion of the total available supply of an asset and locking it up, typically to earn rewards or participate in the protocol. For FLAT, when users lock FLAT as SAVE, they are essentially "absorbing" that supply from the circulating market. The higher the absorption rate, the more of the asset is held out of circulation.

Let's Walk Through Some Examples

The beauty of this equation becomes clear when we plug in some numbers for α. Remember, α is a fraction, so it will always be between 0 and 1 (or 0% and 100%).

• α = 0% (or 0): If no FLAT is locked as SAVE, then:
  P(0) = C / (1 - 0) = C / 1 = C
  In this scenario, the price P is simply equal to the initial constant C. It's a 1x multiplier.

• α = 50% (or 0.5): If half of the FLAT supply is locked as SAVE, then:
  P(0.5) = C / (1 - 0.5) = C / 0.5 = 2C
  The price doubles! So, if C was $1, P becomes $2. That's a 2x multiplier.

• α = 90% (or 0.9): Now, let's say 90% of the FLAT supply is locked.
  P(0.9) = C / (1 - 0.9) = C / 0.1 = 10C
  The price is now ten times the initial constant! A 10x multiplier.

• α = 99% (or 0.99): Imagine almost all of the FLAT supply is locked up.
  P(0.99) = C / (1 - 0.99) = C / 0.01 = 100C
  Boom! The price is 100 times C. A 100x multiplier.

As α gets closer and closer to 1 (or 100%), the denominator (1 - α) gets smaller and smaller, pushing the price P(α) towards theoretical infinity. This is where the "singularity" aspect comes in – a point where the equation predicts an unbounded value.

The "Finite Energy" Corollary: Infinite Price Doesn't Mean Infinite Money

This might sound wild: "infinite price"? But here's the crucial part: an infinite price per unit doesn't necessarily require an infinite amount of money to be invested in the system. As more of the supply is absorbed (locked), the circulating supply shrinks dramatically. So, while each remaining circulating unit becomes theoretically more valuable, there are fewer and fewer of them available. The total market capitalization (price multiplied by total supply) would still be a finite, albeit potentially very large, number.

Acknowledging the Assumptions: Math vs. Reality

It's super important to be intellectually honest here. This equation describes a theoretical model, not a guaranteed market outcome. Here are some key assumptions:

• Requires Continued Locking: The model assumes that people will continue to lock their tokens, increasing the absorption rate. If people stop locking or star