Emissions

Emissions to nodes are calculated through levels:

1. Overall network inflation

2. Subnet distribution

3. Node distribution

Overall Network Inflation

The Hypertensor inflation mechanism is disinflationary. As the overall network's number of sub-network nodes increases, the inflation rate decreases.

Inflation is based on the activity of subnet validator nodes.

$$\text{inflation}(u) = r_t - (r_t - r_0) \cdot \begin{cases} \frac{1}{1 + e^{k \cdot |u - m|}}, & \text{if } u > m \\ \frac{e^{k \cdot |u - m|}}{1 + e^{k \cdot |u - m|}}, & \text{if } u \leq m \end{cases}$$

This function defines a sigmoid-shaped curve for yearly inflation based on network utilization:

• u: current node utilization ratio (active nodes / max nodes)

• m: midpoint of the curve (utilization where inflation changes fastest)

• k: steepness of the curve (higher = steeper transition)

• r₀​: initial (max) inflation rate

• r_t​: terminal (min) inflation rate

As utilization increases:

• Inflation starts high at r₀

• Decreases smoothly as more of the network is used

• Levels off near r_t​ when saturation is reached

This incentivizes early participation while gradually stabilizing rewards as network activity increases.

Subnet Distribution

From the overall inflation, the emissions are distributed to subnets based on economic and fundamental mechanisms.

The final subnet weights are calculated once per epoch based on the delegate staking weight and the node weight of each subnet.

Node Distribution

Node distribution is based on the consensus that a subnet comes to each epoch.