Ticks

Last modified: April 22, 2026

Ticks

In CenturionDEX v3, a liquidity position is defined over a bounded price interval. The endpoints of that interval are not arbitrary real numbers; they must coincide with protocol ticks. Ticks are indexed by integers $i \in \mathbb{Z}$ , and the price associated with tick $i$ is

p(i)=1.0001^i.

We refer to $i$ as the tick index of the price level $p(i)$ . Since adjacent ticks differ by $0.01\%$ , the grid of admissible prices is extremely fine and, in practice, covers a very broad range of relevant market prices.

For the concentrated-liquidity model, it is convenient to use canonical notation. Let $x$ and $y$ denote the virtual reserves of tokens $X$ and $Y$ , let $L$ denote the liquidity parameter, and let $p$ denote the spot price of token $X$ in units of token $Y$ . These quantities satisfy

x \cdot y = L^2, \qquad p=\frac{y}{x}.

Therefore, the virtual reserves can be written as

x=\frac{L}{\sqrt{p}}, \qquad y=L\sqrt{p}.

Hence, the pair $(L,\sqrt{p})$ completely determines the virtual state of the position.

Since

\sqrt{p(i)}=1.0001^{i/2},

the tick index associated with a price $p>0$ is the largest integer $i$ such that $p(i)\le p$ . Equivalently,

i(p)=\left\lfloor \log_{1.0001}(p)\right\rfloor = \left\lfloor 2\log_{1.0001}(\sqrt{p})\right\rfloor.

Here, $\lfloor \cdot \rfloor$ denotes the floor function.

Example

Consider a CenturionDEX v3 pool between CTN and USDC. Suppose that its current virtual balances are

x=24 \quad \text{(CTN)}, \qquad y=60{,}000 \quad \text{(USDC)}.

Then the current spot price is

p_0=\frac{y}{x}=\frac{60{,}000}{24}=2{,}500 \quad \text{USDC/CTN}.

The corresponding liquidity parameter is

L=\sqrt{xy}=\sqrt{24\cdot 60{,}000}=1{,}200.

Using the tick-index formula above, the current price is associated with the tick index

i(p_0)=\left\lfloor \log_{1.0001}(2500)\right\rfloor = 78{,}244.

Indeed, the neighboring tick prices are

p(78{,}244)=1.0001^{78{,}244}\approx 2499.906990,

and

p(78{,}245)=1.0001^{78{,}245}\approx 2500.156980.

Now suppose that a liquidity provider wants to create a position over the target price interval

[p_a,p_b]=[2300,3100].

To obtain a tick-aligned interval that contains this target range, we choose the lower boundary as the greatest tick price not exceeding $2300$ , and the upper boundary as the smallest tick price not below $3100$ . Thus,

i_a=\left\lfloor \log_{1.0001}(2300)\right\rfloor = 77{,}410, \qquad i_b=\left\lceil \log_{1.0001}(3100)\right\rceil = 80{,}396.

The neighboring tick prices around these bounds are

p(77{,}410)\approx 2299.881723, \qquad p(77{,}411)\approx 2300.111711,

and

p(80{,}395)\approx 3099.816056, \qquad p(80{,}396)\approx 3100.126037.

These values are summarized in the following table:

\begin{array}{c|cccc} \text{Tick index} & 77{,}410 & 77{,}411 & 80{,}395 & 80{,}396 \\ \hline \text{Tick price (approx.)} & 2299.882 & 2300.112 & 3099.816 & 3100.126 \end{array}

Therefore, a tick-aligned interval that contains the desired range $[2300,3100]$ is

[p(77{,}410),\,p(80{,}396)] \approx [2299.882,\;3100.126].

Thus, in practice, the liquidity provider would implement the position using these discrete tick bounds rather than the continuous target interval $[2300,3100]$ .