# EVO Protocol

> a micro-protocol, for protocols.

## Abstract

Utilize 'Fees' as a method of disincentivizing short positions and dumps by dynamically changing 'fee' rate,
where the fee rate is *zero* for those transfers **below** the trailing transfer average rate.
This means that transfer's exceeding the combined average transfer rate would have a fee imposed.
The vast majority of users would not incurr this fee or could simply wait between 'epochs'/'time periods'
to withdraw *feeless*.

## Potential Implementation

as a component either to high risk assets (to enable price protection against dumping)

as a module for vaults in general (this would require more extensive testing)

as an optional component with user opt-in

as a module for 'yUSD' (or some variation, e.g. yyUSD) so that additional stablecoins (i.e. yet to be proven) may be included

## Introduction
We propose a crypto-derived functional asset in which controllable volumetric functions are embedded
within the operational utility of the asset. As a result this function exhibits desirable properties
as a _unit of account_ for its underlying asset.

In essence by utilizing the _acceleration_ and _deceleration_ (i.e. **velocity**) that the speed of the ERC20
token transfers (e.g. average transaction rate/mean transaction rate) can help to _counter-balance_
and reduce the market price volatility of the faster base currency (\$ETH). Our focus is on
purely-virtual crypto currencies, which are based on computational assets e.g. as BTC, which is
based on "mining", or ETH, which is based on computational "GAS".

By utilizing small volume movements and disincentivizing the larger ones without compensation to
holders every exceeding unusual trade of the token is tracked by the smart contract and higher
"interest" fees are applied (re: withdraw, or 'consumption').

Transference of funds _below_ daily volume threshold does not impose any interest fee.

When the threshold has been exceeded some percentage of tokens gets burned, for the transfer, for
deposit or for withdraw of the base instrument (ETH).

Thresholds are tracked individually per address as the average rate and have a function by which
they operate on.

'evo-' tokens are minted and burned **on-demand** by deposit and withdraw operations directly via
the contract.

> Think of 'evo-' as a prefix/marker: much like 'aDai' or 'cDai', and of course, 'yDai'

## Initiated Protocol Operations

* Deposit
* Withdraw
* Transfer

These **operations** contribute to the *transfer rates*. Transfer rates are tracked both **in
aggregate** and **individually** (i.e. *per address*). The *period* of time for tracking is the last
`25 days`

**EVO Protocol** is determined both in aggregate (dynamically) and individually for each address
based on transactional (i.e. volumetric transactional information) stored and updated through the
smart contract during the previous transactions.

All three operations such as deposit, withdraw and transfer can equally contribute to the transfer
rates that are tracked totally and individually(as per holder) by the smart contract for the period
of the last 25 days.The token price is determined dynamically(and individually for each holder)
based on the information stored or updated in the smart contract during previous transactions:

{equation.EVO Protocol}

$$
P_{t+1}(h, a):=\sqrt{\frac{D_{t}}{S_{t}}}+I_{t+1}^{\prime}(h, a)
$$

The above equation will compute the price for a holder $$h$$ to purchase a certain amount of `EVO`
tokens in exchange for a base deposit in `ETH/WETH` at the given discrete time - $$t +1$$ , where
$$Dt$$ stands for the deposit of `ETH` in the smart contract at previous time - point and $$St$$
stands for the total supply of `EVO` tokens so far.

The first component with the token - base ratio $$Dt/St$$ under the square root is the *indicative
price* and **does not depend on the purchase/transferred** amount, ``$a$.``

Ergo, the component $$I_{t+1}^{\prime}(h, a)$$ is called the *discounted interest rate* and it can
grow *proportionally* to a within a range of $$[0, 0.24]$$ of ``$$a$$.``

Higher interest payouts can slow down, **deaccelerate**, the price movement. Interest rate
determines how fast, or **accleration**, such price can change depending on the market demand &
supply pressure for EVO-based tokens. Interest[#] is computed individually for each EVO holder.

*Note* that all interest payments are contributed to the same common deposit `Dt` on the smart
contract, which is supporting the indicative price. This means that interest is shared by all
holders that *choose not to trade their tokens* at the moment.

An ERC20 smart contract will contain the information about the balance of every address,

##### Address Information (i.e. wallets)
$$B(h) s.t. Bt + 1(h, a): = Bt(h) + a$$.

In addition to the individual balances, EVO Protocol contract keeps track about how much each holder
has transferred in the last epoch (i.e. 25days)

##### Total average transfer rate for an address
$$avg(Rt + 1(h, a)): = avg(Rt(h)) + a$$

##### Total average daily transfer rate for all holders
$$avg(R¯ t + 1(h, a)): = avg(R¯t(h)) + a$$.

### Calculations
More formally calculation of the individual interest rate as well as the applied ownership discount
can be described in following steps:

For: $$l := 4 , m := 26$$ are the *low* and *high* *transfer rate constants* and

$$\beta=\frac{\operatorname{avg}\left(B_{t+1}(h, a)\right)}{S_{t+1}}$$, the *future balance ratio*,
we resolve $$\tau=\frac{\operatorname{avg}\left(R_{t+1}(h,
a)\right)}{\operatorname{avg}\left(\bar{R}_{t+1}(h, a)\right)}$$ is the *future transfer ratio* and
$$\theta=\frac{B_{t}(h)}{S_{t}}$$ is the ownership ratio at a *discrete point in `block time`* then
we resolve the **interest rate**;

$$
P_{t+1}(h, a):=\sqrt{\frac{D_{t}}{S_{t}}}+I_{t+1}^{\prime}(h, a)
$$

thereby applying the ownership ratio for discount

$$l_{t+1}^{\prime}(h, a):=\frac{a \times \sqrt{l * \max \left(\min \left(\theta, l^{2}\right),
1\right)}}{100}$$

whereas %$$I`$$ is the *discount**, thereby computing the *discounted interest* as,

$$I_{t+1}^{\prime}(h, a):=\max \left(I_{t+1}(h, a), l_{t+1}^{\prime}(h,
a)\right)-l_{t+1}^{\prime}(h, a)$$

Price dynamics of equation (1) depends on the transactions volume conducted by all of the involved
market participants and bounded by $$O(sqrt(n))$$.

Therefore it can be expected that the demand for EVO Protocol based tokens like EVO Protocol will be
able to represent the *demand* for the value storage, whereas EVO Protocol represents the value of
storage as a derivative function of the underlying asset, Ethereum (i.e. gwei, or as a fixed unit of
account for contracting)