Can outside observers discern graduate student agency from a CV or papers?
I think that what it is possible to do in doctoral studies varies a lot by field. In some fields, if a student were required to come up with their own problem it would be nearly impossible to get started until many many years had passed. In others, it is much more natural for students to propose feasible projects. But even in those fields in which it is difficult, there are a few students able to do it and have their idea accepted by the advisor. The latter may be a stiff hurdle in many cases.
But, to answer the question, I think it may be a mistake for the individual to try to do this themself. It is likely to come across as bragging that can't easily be validated. On the other hand, if others are willing to make such a claim about your &quot;agency&quot; it will serve you well, especially if it comes from a well-respected researcher, perhaps your advisor.
Whether this can be discerned from the CV or not is less important IMO, than how it sounds to the reader. If you say (implicitly) &quot;I'm smarter than you...&quot; it isn't likely to help your career.
And for the most explicit answer to your question, it depends on the reader. A very sophisticated reader may realize that a problem solved is truly fresh and provides new directions for research. But most won't be able to do that sort of analysis, I think.
And, I think this only matters at the beginning of your career, which makes the advisors statements both helpful and sufficient. After you have been &quot;in the game&quot; for a while it will be obvious if you have &quot;agency&quot; or not.
And even if the advisor proposes (or insists on) the problem to be solved, it can still be very challenging to complete it successfully. I worked on three problems leading up to my degree. The first was too easy to be significant. The second was to hard to make any progress. The last was both significant and successful. But still hard enough.