τTaosis

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

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 swap form's quote, so the screener and the form's "You receive" figure cannot disagree about the curve or which leg carries the fee. The same exit turns Locked α into Locked τ (realizable). The tolerance you set in the form 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 and Swap fee — and the Trader preset switches them on together. Root has no curve, so every depth figure is blank for SN0.