# Dynamic Penalty Function

For convenience, Dynamic Penalty Function is referred to as DPF in this paper.
Dynamic Penalty Function (DPF) is designed by TARS and followed by Claimer to limit adjusting token vesting during the period, which is calculated according to the following formula:
$z = k · ΣCeil(Abs(x-y))$
The symbol Σ (sigma) is used to denote a sum of multiple terms.
The Ceil() method rounds a number UPWARDS to the nearest integer and returns the result.
The Abs() function returns the absolute value of a number.
The z refers to the total amount of penalty that the proposer will pay if all adjustments to the token claim rules are completed by the Claimer smart contract.
The k refers to the specific fines per hour.
The x refers to the adjusted claim time of the specific batch.
The y refers to the initial claim time of the specific batch.
The unit to Abs(x-y) should be an hour/hours.
According to the DPF, as the proposer, the more times you adjust, or the larger adjustment range you make, the higher the penalty you will pay.

## Why DPF

When the crypto project party implements the token vesting schedule according to their original tokenomics, it is often seen that some project teams adjust or change it, and they attribute this to market factors or other reasons. There is a huge risk of centralization in this case and the token vesting schedule is adjusted without any cost and constraint, which seriously hurts people's trust in the project and harms the interests of investors.
Even if the project party develops a dedicated token claim page for investors, the claim contract is usually not open source and lacks auditing, which is still untrustworthy. At the same time, for investors, it would be a wonderful crypto journey to have a tool that enables them to aggregate and manage all (more) portfolios, as well as token vesting schedules, including claimable tokens, claimed tokens, etc.
We have noticed that the immutable token vesting schedule is not suitable for the healthy development of the crypto project. Therefore, the design of DPF fully considers the feasibility of adjusting the claim rules by the clients (usually referring to the project parties) and restricts them from adjusting the claim rules through a penalty mechanism. According to the DPF, only the Token Vesting Time of each batch can be adjusted. As the proposer, the more times you adjust, or the larger adjustment range you make, the higher the penalty you will pay.

## How DPF Works

The clients (usually referring to the project parties) can launch Claimer dApp to easily create Claim Rules for their token vesting schedules so that the investors will be able to claim tokens accordingly. Thus, once the clients (usually referring to the project parties) adjust the Claim Rules in Claimer, they will be automatically deducted fine by the smart contract, and most of the fine will be compensated to the investors who claim tokens, and the rest will be the revenue of TARS.
The initial compensation ratio we set is 70%, which means 70% of the total fine will be compensated to the investors and settled monthly. Before the TGE of \$TARS, the initial payment method for the penalty will be stable coins.
In an absolutely decentralized environment, the Claimer dApp that follows DPF provides a humane option for project parties and investors. Therefore, we hope that all investors can call on the project teams to use Claimer for token vesting, and promote and build a credible crypto investment environment for the Decentralized Society (DeSoc).