I like Glorfindel's answer as it takes you through an example solution, and I recommend his answer. Just to show some underlying beauty and complexity of this puzzle, I created a diagram (directed multigraph) that shows all possible results (that yield integers) of permuting these operations. You'll have to open the image in another tab and magnify to follow ...
I don't think there's anything in the story that shows that the (fictional) Chinese didn't fake this right, but here's a thing that seems like it might be easy to get wrong and possible to detect:
Also, day 7:
The locations are
The location of Day 7
Credit where due: at least two other people, MOehm and Omega Krypton, figured out the "what" before I even saw the question. (I solved it independently.)
I say you are
I can be found near gentle green hills and stony mountains,
Alongside the gas in the clouds and the iron of the earth,
At times I can be white and frosty, red and fiery, or blue and stormy,
The hints to what the list actually represents are:
These all give the secret real reason for the list:
So, how to begin constructing the diagram?
So, what has Bob been "crowing about all week"? Well,