Why is this not a Postnikov diagram?

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I am following this paper on Grassmannians and Cluster Structures. I drew the following diagram for $Gr(2,6)$:

An invalid Postnikov diagram for Gr(2,6)

However, it doesn't satisfy the property that each alternating region is labelled by a $2$-subset, indicating that I have violated some rule while drawing the diagram. I cannot spot my mistake.

For reference, I am listing the rules here:

  1. The strands have no self-intersections.
  2. There are finitely many intersections and they are transversal of multiplicity $2$.
  3. Crossings alternate (following any strand, the strands crossing it alternate between crossing from the left and crossing from the right).
  4. There are no “unoriented lenses”: if two strands cross, they form an oriented disk.
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I think I got it: the meeting of in-paths and out-paths at boundary vertices are also crossings—the diagram above therefore violates the condition about alternating crossings.

Even if you are using the alternate definition of a Postnikov diagram (as in Marsh's Lecture Notes on Cluster Algebras) where there are two vertices $i$ and $i'$ corresponding to each index, one for the in-path and one for the out-path, you can assume the boundary itself to have a clockwise orientation to 'complete' your boundary oriented cells.