Documentation

Calculating emissions for Parent/Child hotkeys

Parent hotkeys are validators that do not run infrastructure in a subnet. They use their stake as a parent hotkey to a validator running infrastructure (the child hotkey).

Parent hotkeys have all of the same abilities as child hotkeys.

  • Delegators may stake alpha on a parent hotkey inside a subnet.
  • Delegators staked on root receive root stake from parent hotkeys.
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Where we are — step 4 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 18% / miners 41% / validators 41%.

This page (step 4): aggregate each validator's dividends across its parent and child hotkeys.

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Example

Taostats is the validator

Spreadsheet row with columns for child, root stake, alpha stake, child hotkey take, amount parent staked, and dividends used in parent/child emission calc

There are two parent hotkeys:

Spreadsheet listing parent hotkeys with root stake, alpha stake, and stake-percentage columns as inputs to an emission calculation

The validator running the child hotkey (running the validation infrastructure) can impose a child hotkey take on any validator running a parent hotkey. In the screenshot above the child hotkey take is set at 4.5%.

Step 1: Find the tao and alpha staked to the hotkey

First, we determine the amount of tao and alpha each validator has on this hotkey:

  • Taostats has 8/9 of its stake
  • parent_1 has 50% of its stake on this child hotkey
  • parent_2 has 100% of its stake on the child hotkey.
Spreadsheet mapping accounts (validator and two parents) to their tao and alpha stake columns for finding stake on a hotkey

Step 2: Determine the total stake of each validator

tao_weight = 0.18

formula
Spreadsheet with tao, alpha, and total-stake columns per validator, combining the two token stakes into one weighted total

Step 3: Find the Percentage of total stake, and apply it to the dividends.

The 0..15 dividends are split based on the % of total stake for each validator

Spreadsheet splitting a fixed dividend pool across validators proportionally by each one's percentage of total stake

Step 4: Apply child hotkey take to parents

Taostats has a 4.5% child hotkey take. Remove 4.5% of the dividends from each parent, and apply the proceeds to taostats.

Spreadsheet applying a child hotkey take to each parent's dividends, showing dividends, take, and final dividends columns

0.000102 and 0.003372 are taken from parent_1 and parent_2, and added to taostats' final dividends.

Step 5: Repeat this math for all child hotkeys.

Taostats has 1/9 of its stake on another validator.

Parent_1 has 50% of its stake on other validators.

Sum these dividends for all hotkeys in a subnet to get the final dividends for a validator on a subnet.

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Child Hotkey Take

Note that the child hotkey take collected by the child hotkey is added to the dividends of the validator.

This means that most of the child hotkey take is distributed to the stakeholders of the validator, and it is not directly deposited to the validator's wallet.

What's next

Step 5 — Root vs alpha split: the validator's remaining dividends are divided into a root proportion and an alpha proportion, then distributed to stakeholders (root / alpha).

Updated 18 days ago

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