# Merkle path authentication

In point 4 of the Algorithm 4.2 (Classic Merkle Tree Traversal) of *"Post_Quantum_Cryptography.pdf"* shows *"Stack_h.update(2)"* each stack receives two updates. I am trying understand to understand why there are "two updates" but I don't. There is an example on page 19 of *"Boris_Ederov.bachelor.Merkle-Tree-Traversal-Techniques.pdf"*. In that thesis, it only updates one time. For example in the step 1. Why update stack one time?

Step 1: leaf=0
"For h=0 we run 0 Stack_0.update  , which only computes P_n(3), puts it onto the stack and stops."

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