Calculating root proportion

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Where we are — step 5 of the emission flow

How we got here:

1. TAO emission — TAO split across subnets.
2. Alpha emission — each subnet mints alpha_in + alpha_out.
3. Split alpha_out among participants — owner / miners / validators.
4. Parent / child hotkeys — aggregate each validator's dividends.

This page (step 5): divide the validator's dividends into a root proportion and an alpha proportion.

In the Bittensor ecosystem, holders of tao may stake to a validator in a subnet in two different ways:

• Root stake : Staking to a validator in subnet 0, the root subnet.
• Alpha Stake: Staking to a validator in a subnet, exchanging your tao for alpha token.

The ratio of root: alpha staked is calculated using the root_proportion.

root proportion is calculated from 3 values:

• tao on root: The total amount of tao on root.
• alpha issued: The sum of alpha_in and alpha_out (all alpha emitted)
• tao_weight: a variable set by the chain. The current tao_weight is 0.18.

Current Root prop

Root proportion will change every block, as the tao and alpha values will have increased. The results can be charted over time:

The chart will vary on the amount of tao available at the moment the subnet is created. The above chart shows day 0 = 6 million tao.

On day 0 of the subnet, 100% of emission will go to root stakeholders.

50% root: 50% alpha is met at approximately day 70 (this is highly variable, and just an estimate).

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Each Subnet has a statistics page showing the Root proportion chart for the subnet.

https://beta.taostats.io/subnets/75/statistics

In this second chart, the yellow/green subnet is created 100 days after the blue/red subnet (9,720,000 tao, and 0 alpha for the 2nd subnet):

What's next

The validator's dividends are now split into a root share and an alpha share. The final step distributes each to stakeholders:

• Step 6a — Stakeholder emissions: root
• Step 6b — Stakeholder emissions: alpha