The paper makes a strong distinction between money, credit, and cash without explaining the importance or relevance of the distinction.
The importance is implicit in the fact that it is an objective distinction, based on the properties of gold versus credit tokens.
Credit and cash are generally considered forms of money, so it seems to me that asserting that the three are different would require some explanation.
In science, definitions should adhere to objective criteria, not to what is generally considered. The paper does not try to refute cultural convention (similar to tomatoes being 'vegetables') but to provide objective definitions (tomatoes are fruits in biology). The criterion is shown at the beginning of Section 2, besides the included citation.
I believe that the paper is making the point that the importance of a "naturally unique" item is that it cannot be duplicated. But, that characteristic does not necessarily depend on the item being "natural". There are "natural" things that can be duplicated, such as the color blue.
The colour blue is not an item. Even if it were, the fact that it can be duplicated means that it is not naturally unique. The relevant distinction is natural vs. artificial origin, and the context is signal or item reception, not production. Duplication ability refers to production.
The term "tangible" comes to mind, but that term is not sufficient. I think "distinct" is the term that more aptly describes the property being described.
Two 'distinct' (artificially unique) credit signals (e.g. bills) can be received for every naturally unique signal (gold piece).
The paper conflates a chain of blocks with a chain of transactions.
A chain of (transaction) blocks is a chain of transactions.
A chain of blocks
contains chains of transactions, but they are not the same. The links between the blocks are not the same as the links between transactions.
What is relevant to my argument of transaction uniqueness, and the provided example, is that the links between transactions correspond to links between blocks.