Do you think is possible the use of surreal numbers to index a whole graph branch (with the desired depth-level determined by construction)?
Yes, it's theoretically possible. Surreal numbers are an extension of real numbers that allow for more complex arithmetic operations and have some interesting properties such as being able to represent negative integers.

In terms of indexing a whole graph branch with a given level of detail, this could be done using a combination of surreal numbers and binary trees. The tree would store information about which nodes in the branch should be included at each level of detail, while the surreal number indices would provide a way to quickly access specific parts of the branch based on their level of detail.

It may also be useful to consider using a different data structure than just a tree or list to store the branch, depending on your needs. For example, if you need to perform certain calculations on the branch, then a hash table might make sense instead of a simple list.