# # Nebula Token

The Nebula Token (symbol: NEB) is the governance token given as a reward to users for maintaining the liveness properties that keep the protocol operational. Actions that receive NEB tokens as rewards include:

• staking NEB tokens for voting power
• providing liquidity to cluster token markets
• successfully rebalancing clusters

## # Governance

The Nebula Token (NEB) is Nebula Protocol's governance token and has the following functions:

• Polls: NEB tokens must be deposited to create governance polls.
• Staking: Users can stake NEB to vote on polls and earn NEB rewards.
• Voting: Users staking NEB receive voting power to vote on governance polls

The NEB token captures value from the cluster rebalancing fees across the protocol: the fees are collected and used to purchase NEB off Astroport, then distributed to NEB stakers pro-rata to their voting power.

## # Rewards

There are several ways through which a user can earn NEB token rewards through interactions with the protocol. This yield is paid to the users as NEB tokens that are newly minted through inflation, which gradually increases the total supply of NEB until the end of 4th year. See the distribution schedule for a specific breakdown.

### # LP Staking

Users can stake CT-UST LP tokens for various clusters to accrue NEB tokens for each LP staking pool to which they provide liquidity. These LP tokens can be unstaked at any time to be traded back for deposited liquidity, with the potential of impermanent loss depending on the pool state.

### # Governance Staking

Users can stake NEB in the Governance contract. This allows them to vote on polls with voting power proportional to the number of tokens they have staked. In addition, they earn NEB token rewards accrued come from protocol fees incurred during rebalancing operations, which are accumulated by the protocol and used to purchase NEB tokens off the Astroport NEB-UST liquidity pool.

## # Token Supply

There are planned to be a total of 1,000,000,000 NEB tokens to be distributed over 4 years. Beyond that, there will be no more new NEB tokens introduced to the supply.

### # Distribution Schedule

Number in millions Launch Y1 Y2 Y3 Y4
LUNA Staking Airdrop 10 0 0 0 0
Community Launch 20 0 0 0 0
Rebalancing Rewards 0 75 75 75 75
Cluster Token LP 0 50 50 50 50
Community Pool 153 0 0 0 0
Investors 0 39 39 39 0
External Contributors 0 33 33 33 0
Team 0 25 25 25 25
Token Supply 183.00 405.30 627.60 849.90 1000.00
Annual Inflation (%) - 121.48% 54.85% 35.42% 17.66%

### # Airdrop

At protocol genesis, the NEB token will be airdropped to users on Terra that stakes LUNA to one or more of the network's validators, excluding those validators in the top 5 by voting power at the time of the airdrop snapshot.

The airdrop methodology is calculated as follows:

#### # Notation

• $A$: Total Airdrop Amount
• $V$: Validator
• $x$: Staker
• $D_{v,x}$: Staker $x$'s delegation to validator $v$
• $T_v$: Total delegation to validator $v$
• $P_{v}$: Voting Power of Validator $v$

#### # Methodology

First, we calculate the share of the total airdrop amount $A$ allocated to each validator $V$

The ratio of tokens allocated $R_{v}$ to each valdiator is proportional to the ratio of their voting power to the network's total, both raised to the power of 0.75.

The 0.75 is the normalization factor intended to reduce the difference in share amount received by the validator with the highest and lowest voting power, generally making the distribution slightly more uniform.

$R_{v} = \frac{P_{v}^{0.75}}{\sum_{i=1}^{n} P_{v}^{0.75}}$

The share $S$ is then:

$S_{v} = AR_{v}$

$S_{v} = \frac{AP_{v}^{0.75}}{\sum_{i=1}^{n} P_{v}^{0.75}}$

Next, we calculate the total amount of airdrop tokens eligible for claiming by a user address $I$

Starting by getting the claimable amount assuming $I$ only stakes to a single validator

$I_{v,x} = \frac{S_{v}D_{V,x}}{T_v}$

Lastly, we generalize this for all delegations by user $I$ across validators $V_1,V_2,...,V_d$

$I_{x} = \sum_{i=1}^{d} I_{i,x}$

$I_{x} = \sum_{i=1}^{d} \frac{S_{i}D_{i,x}}{T_{i}}$

$I_{x} = \sum_{i=1}^{d} \frac{AD_{i,x}P_{i}^{0.75}}{T_i \sum_{j=1}^{n}P_{j}^{0.75}}$

$I_{x} = A\sum_{i=1}^{d} \frac{D_{i,x}P_{i}^{0.75}}{T_{i}\sum_{j=1}^{n}P_{j}^{0.75}}$

Updated on: 4/28/2022, 7:21:28 AM