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tackle multiple eval todo
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source/starknet/merkle.md

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@@ -29,9 +29,9 @@ A vector commitment is simply a Merkle tree. It is configured with two fields:
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* `height`: the height of the Merkle tree
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* `n_verifier_friendly_commitment_layers`: the depth at which layers will start using the verifier-friendly hash.
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![tree indexing](/img/starknet/tree_indexing.png)
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<img src="/img/starknet/tree_indexing.png" style="max-width:100%">
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<img src="/img/starknet/vector_commit.png" style="max-width:100%">
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![vector commit](/img/starknet/vector_commit.png)
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## Table Commitments
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A vector decommitment/membership proof must provide a witness (the neighbor nodes missing to compute the root of the Merkle tree) ordered in a specific way. The following algorithm dictates in which order the nodes hash values provided in the proof are consumed:
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![vector decommit](/img/starknet/vector_decommit.png)
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<img src="/img/starknet/vector_decommit.png" style="max-width:100%">
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## Verifier-Friendly Layers
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A `n_verifier_friendly_layers` variable can be passed which dictates at which layer the Merkle tree starts using a verifier-friendly hash.
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In the following example, the height of the table commitment is $6$ (and the height of the vector commitment is $5$). As such, a `n_verifier_friendly_layers` of $6$ would mean that only the table would use the verifier-friendly hash. A `n_verifier_friendly_layers` of $5$ would mean that the last / bottom layer of the Merkle tree would also use the verifier-friendly hash. A `n_verifier_friendly_layers` of $1$ would mean that all layers would use the verifier-friendly hash.
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![vector decommit](/img/starknet/tree_height.png)
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<img src="/img/starknet/tree_height.png" style="max-width:100%">
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### Note on commitment multiple evaluations under the same leaf
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TKTK
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As can be seen in the previous diagram, a leaf can contain (using the technique in [table commitments](#table-commitments)) multiple evaluations of the same polynomial at different points. This is useful for the FRI layer commitments where the same polynomial is evaluated at $v$ and $-v$ (and potentially more values depending on skipped layers).

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