Understanding LSTs

Jack is the first user to mint cAlgo by depositing his Algo on the CompX node. He places 1000 Algo on the node. Since he has a claim on all of the Algo in the pool, he's distributed 1000 cAlgo. He could burn this at any time and get his 1000 Algo back.

Jack hodls his cAlgo until the CompX node proposes a block and is rewarded with 10 Algo. Because Jack is the only person who has deposited into the node, he has a claim on all of the reward Algo. There is now 1010 Algo and he still has 1000 cAlgo. At this point cAlgo has appreciated in value by 1%

$$1 cAlgo = 1.01 Algo$$

Dianne sees how quickly his cAlgo has appreciated and wants in on the racket. She also deposits 1000 Algo onto the node, but due to the change in price of cAlgo, she'll receive a reduced number of cAlgo from the minting contract.

$$1000 Algo *(1cAlgo/1.01 Algo) = 990.099cAlgo$$

Note that despite not gaining cAlgo at a 1:1 rate anymore, if she were to turn around and immediately burn her cAlgo, she would get the full 1000 Algo that she's owed. To prove that to yourself, simply flip the direction of equation above.

After some period of time, the node proposes another block and is rewarded with another 10 Algo. There are now 2020 total Algo in the node and 1990.099 cAlgo in circulation. This means that the new price for cAlgo is

$$(2020 Algo/1990.099 cAlgo) = 1.015 Algo/cAlgo$$

Simple calculations show that if Jack pulls his entire stake, he will get a total of 1015 Algo, a profit of 1.5%. The same is true for Dianne, who would get 1005 Algo. A profit of 0.5%. Thinking about these simple numbers, it's not hard to come to the conclusion that the LST is tracking correctly by intuition. Jack gets all of the rewards the first block and gets half of the rewards the second block, netting him 15 Algo. Same is true for Diane, where she receives half of the second blocks rewards.

Complexity increases as more people add, get rewarded and we include the 8% fee in the calculation. However, it's sufficient to note that the smart contract, knowing the circulating supply and the amount of Algos on the node, can consistently and accurately price each minting transaction. Once the user has minted their cAlgo, they are locked in to get a piece of all subsequent rewards payouts from block proposal. The math is actually quite simple.

$$(Node\ Algo)/(Circulating\ cAlgo) =cAlgo\ Value$$

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