Learn·Markets
How much τ it takes to move a subnet's price
Depth is the τ that moves a pool's price a given distance; a quote is the same curve read from the trader's side, with the fee on a different leg for buys and sells.
Published 2026-09-17 · updated 2026-09-28
Depth is a τ figure, not a score
Depth ±2% / ±5% is the TAO of net buying that would move the price up by that much, and the TAO of net selling that would move it down by that much. Up: τ reserve × (√(1+δ) − 1) ÷ (1 − swap fee). Down: τ reserve × (1 − √(1−δ)).
The square root is the constant-product curve: lifting the price by (1+δ) grows the τ side by √(1+δ). Only the τ reserve and the subnet's own swap fee are needed, which is what makes depth comparable across subnets — and why it is blank when the fee could not be read, since a depth without the fee is a different number, not a rounded one.
Why the down figure is always larger
The fee sits on the input of a swap. On a buy, τ is the input, so the fee comes off before the τ reaches the curve and a buyer must send the curve's step divided by (1 − fee). On a sell, α is the input; the down figure is τ leaving the pool, so there is nothing to divide.
Add the curve's convexity and the −2% figure sits a little above the +2% figure on every subnet. That is the arithmetic, not a bug.
A quote is the same curve from the other side
Selling α: the effective α is what you sell less the fee, k is τ reserve × α in pool, and you receive τ reserve − k ÷ (α in pool + effective α). Each further α fetches less; slippage is the gap between the spot price and what the order realises.
Taosis runs one port of that function for the depth columns, and the same exit turns Locked α into Locked τ (realizable). The slippage tolerance a wallet lets you set is a different thing — a limit on how far from the quote the chain may fill.
Depth against what could leave
A deep pool can still be small next to what holders own. ADR is max(α staked out − α burned, 0) ÷ α in pool: α held outside the pool for every α inside it. Above 1, holders own more than the pool could absorb, so a rush for the exit sells at a discount.
All of this sits in the screener's Liquidity group — TAO in pool, ADR, the four depth columns, Swap fee and the three sell-off columns. The Trader preset switches on TAO in pool, the depth columns and Swap fee; ADR is in the Risk preset. Root has no curve, so every depth figure is blank for SN0.
Read next
How the α price works
It is a ratio between two chain values, not an order book — which is why the price can move with no trade at all.
What a swap fee is
A per-subnet rate the pool takes on every trade, charged on what you send in — which is why the buy and sell depth figures never quite match.
Staking safely
Taosis never signs or sends anything: staking happens in your own wallet or on a staking platform. What to check there before you approve.