Clarification about definition of O(T,l)

In the white paper, a function O(T,l) is described as the “the Merkle opening for leaf with index l” and “value of sister nodes on the way from
leaf l to the root, denoted by R”

To me, this seems kinda like the Merkle Proof, which is a sequence of all the sister nodes along the path to the leaf node. Is this correct?

In the description of the statement of Knowledge, O is referred to as the the opening of H2(k||r) at position l to R. Does this refer to the fact that H2 is used to determine the value of each node along the path in the tree? Thanks!

That’s exactly what it is.

Looks like there is a mistake in the whitepaper, should be H1(k||r) (Pedersen commitment and not MiMC). This is what we call a commitment, a hash of secret+nullifier that gets inserted into commitment tree as a leaf. H2 is indeed used to hash nodes of the merkle tree.

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Ahh it is H1 not H2 - that makes more sense based on what I know. This is a lot more clear now, thanks!