Quai block rewards are proportional to “bits” of difficulty, which can be approximately represented by the number of leading zeros in each hash that “finds” a valid block. Quai has an effectively fixed supply, as inflation trends towards zero over time.

BlockRewardQuailog2(Difficulty)Block Reward_{Quai} ∝ log_{2}(Difficulty)

Qi block rewards are linearly proportional to “hashes” of difficulty, or the expected number of hashes needed to mine a block at the current difficulty.

BlockRewardQi(Difficulty)Block Reward_{Qi} ∝ (Difficulty)

This logarithmic versus linear relationship produces the significant difference between Quai scarcity and Qi expansion. For every doubling (2x) in difficulty or hashes, there is only one added unit (+1) in bits. Over time, this ensures Quai’s scarcity, while Qi is naturally connected to the miner cost of production and thus functions as a loose measure of energy or electricity pricing.

Importantly, these block reward functions only define how many Quai/Qi tokens can potentially be emitted. Actual, realized supply emissions from block rewards are determined by the choices miners must make to receive only either Quai or Qi, a selection they may change going forward at any time.

Note that there are proportionality constants/variables in each of the block reward functions provided above. The exact calculus for these constants/variables will be shared publicly closer to Mainnet launch.