Block Production and Emissions

Proof-of-Liquidity governs block rewards and token emissions on Berachain using the $BGT token. This page explains the mathematical principles behind validator selection, block rewards, and emissions calculations.

Validator Selection

The network maintains an active set of N validators who are eligible for block production. Selection criteria include:

• Only top N validators by $BERA stake are included in active set
• Block proposal probability is proportional to staked $BERA and does not affect reward amounts
• Stake limitations per validator:
  • Minimum: 250,000 $BERA
  • Maximum: 10,000,000 $BERA

$BGT Emissions Structure

When a validator produces a block, $BGT tokens are emitted through two emission components:

1. Base Emission

   • Fixed amount equal to a base rate parameter (B)
   • Paid directly to block-producing validator

2. Reward Vault Emission

   • Variable amount dependent on validator's boost (x)
     • i.e. percentage of total $BGT delegated to the validator
   • Distributed to Reward Vaults selected by validator
     • Proportional to weights configured in the validator's Reward Allocation
     • Valdators receive Incentives from projects based on amounts directed to their Reward Vaults

Validator Boosts

Boost is a crucial metric that determines a validator's reward emissions:

• Calculated as the percentage of $BGT delegation a validator has compared to the total $BGT delegated in the network
• Expressed as a decimal between 0 and 1
• Example: If a validator has 1000 $BGT delegated and the network has 10000 total $BGT delegated, their boost would be 0.1 (10%) Higher boost leads to higher reward emissions, subject to the emission formula

$BGT Emissions Per Block

The total $BGT emitted per block is calculated using the following formula:

$$emission=[B+max(m,(a+1)(1-\frac{1}{1+a{x}^b})R)]$$

Parameters

Parameter	Description	Impact
x (boost)	Fraction of total $BGT delegated to validator (range: [0,1])	Determines $BGT emissions to Reward Vaults
B (base rate)	Fixed amount of 0.5 $BGT for block production	Determines baseline validator rewards
R (reward rate)	Base $BGT amount for reward vaults	Sets foundation for reward emissions
a (boost multiplier)	Boost impact coefficient	Higher values increase boost importance
b (convexity parameter)	Boost impact curve steepness	Higher values penalize low boost more severely
m (minimum boosted reward rate)	Floor for reward vault emissions	Higher values benefit low-boost validators

Sample Emissions Chart

Using the following sample parameters, we can visualize how emissions scale with $BGT delegation:

$$B=0.5,R=1.5,a=3.5,b=0.4,m=0$$

Max Block Inflation

$BGT emissions grow with the amount of boost a validator has, up to a cap. The Maximum theoretical block emission occurs at 100% boost:

$$max\mathbb{E}[\text{emission}]=[B+max(m,aR)]$$