Fix minor broken link

learn/S-two-book/air-development/index.mdx

@@ -6,5 +6,5 @@ title: "Introduction"
 > This section is intended for developers who want to create custom proofs using S-two (proofs of custom VMs, ML inference, etc.). It assumes that the reader is familiar with Rust and has some background knowledge of cryptography (e.g. finite fields). It also assumes that the reader is familiar with the concept of proof systems and knows what they want to create proofs for, but it does not assume any prior experience with creating them.
 
 <Note>
-All the code that appears throughout this section is available [here](../stwo-examples/index).
+All the code that appears throughout this section is available [here](https://github.com/starknet-io/starknet-docs/tree/main/learn/S-two-book/stwo-examples/examples).
 </Note>

learn/S-two-book/how-it-works/lookups.mdx

@@ -19,7 +19,7 @@ We can use the idea that two sets of values will have the same cumulative produc
 
 ### Step 3: We want to check that all values in `col_2` are in `col_1`, but each value appears an arbitrary number of times.
 
-_(Note that this is a generalization of the second step in that for the second step,all values in `col_2` appear exactly once in `col_1`)_
+_(Note that this is a generalization of the second step in that for the second step, all values in `col_2` appear exactly once in `col_1`)_
 
 Supporting this third step is actually pretty simple: when creating the running cumulative product, we need to raise each value in `col_1` to its multiplicity, or the number of times it appears in `col_2`. The rest of the constraints do not need to be changed.
 
@@ -29,13 +29,13 @@ Finally, we want to create many more columns that contain values from `col_1`. F
 
 To support this, we can use the same idea as the third step: when creating the running cumulative product, we need to raise each value in `col_1` to the power of the number of times it appears in `[col_2, col_3, ...]`.
 
-<Callout type="info">
-In summary, lookups support the following use-cases:
+<Info>
+**In summary, lookups support the following use-cases:**
 
 1. Prove equality: we want to prove that the values of the first column are equal to the values of the second column.
 2. Prove permutation: we want to prove that the values of the first column are a permutation of the values of the second column.
 3. Prove permutation with multiplicities: we want to prove that each value of the first column appears a certain number of times over multiple columns.
-</Callout>
+</Info>
 
 ## Technique: LogUp
 
@@ -63,37 +63,41 @@ Let's walk through how LogUp is implemented in S-two using a simple example wher
 
 First, we create columns in the original trace, where all values are from the preprocessed trace $A$.
 
+<div id="figure-1" style={{ textAlign: 'center', maxWidth: '100%', height: 'auto', margin: '0 auto',  }}>
 ![](./figures/lookups-1.png)
-
 *Figure 1: Create original trace columns that look up values from a preprocessed trace*
-
+</div>
 Then, we add a multiplicity column to the original trace indicating the number of times each value in $A$ appears in the original trace.
 
+<div id="figure-2" style={{ textAlign: 'center', maxWidth: '100%', height: 'auto', margin: '0 auto',  }}>
 ![](./figures/lookups-2.png)
-
 *Figure 2: Add a multiplicity column*
+</div>
 
 Next, we create LogUp columns as part of the interaction trace, one for the preprocessed trace and the multiplicity column, and another for the batch of all lookups.
 
+<div id="figure-3" style={{ textAlign: 'center', maxWidth: '100%', height: 'auto', margin: '0 auto',  }}>
 ![](./figures/lookups-3.png)
-
 *Figure 3: Create LogUp columns*
+</div>
 
 To create a constraint over the LogUp columns, S-two modifies the LogUp columns to contain the cumulative sum of the fractions in each row. This results in columns that look like the following:
 
+<div id="figure-4" style={{ textAlign: 'center', maxWidth: '100%', height: 'auto', margin: '0 auto',  }}>
 ![](./figures/lookups-4.png)
-
 *Figure 4: Cumulative sum columns*
+</div>
 
 A constraint is created using the values of two rows of the cumulative sum LogUp column. For example, as in **Figure 5**, we can create a constraint by subtracting $row_1$ from $row_2$ and checking that it equals the LogUp fraction created using values $a_2$ and $m_2$:
 
 $$
 \frac{m_2}{X - a_2} = row\_2 - row\_1
 $$
 
+<div id="figure-5" style={{ textAlign: 'center', maxWidth: '100%', height: 'auto', margin: '0 auto',  }}>
 ![](./figures/lookups-5.png)
-
 *Figure 5: Constraint over two rows*
+</div>
 
 However, this constraint actually does not hold for the first row since $\frac{m_1}{X - a_1} \neq row_1 - row_n$. A typical solution to this problem would be to disable this constraint for the first row and create a separate constraint that is enabled only on the first row.
 
@@ -105,9 +109,10 @@ $$
 
 Where $\text{avg}$ is a witness value provided by the prover.
 
+<div id="figure-6" style={{ textAlign: 'center', maxWidth: '100%', height: 'auto', margin: '0 auto',  }}>
 ![](./figures/lookups-6.png)
-
 *Figure 6: Trick to not create a separate constraint for the first row*
+</div>
 
 The right column in **Figure 6** is the final form of the LogUp column that S-two commits to as part of the interaction trace.