The Logic Breakdown
- The Pivot: The word "paradoxical" tells us there is a contradiction between the "widespread respect" and the nature of the theory.
- The Clue: The phrase "few could ever hope to master its claims" describes something that is not easily accessible, known only to a few, or hidden from general understanding.
- The Matches:
- Arcane (D): Understood by few; mysterious or secret. This perfectly matches the idea of a theory that is too specialized for most to master.
- Obscure (E): Not clearly expressed or easily understood. In an academic context, an "obscure" theory is one that remains difficult to grasp even for those in the field.

Why the others fail:
- Intractable (A): This means "hard to control or deal with." While String Theory might be mathematically intractable (hard to solve), the clue is about understanding/mastering claims, not just solving problems.
- Confusing (B): While the theory is certainly confusing, "confusing" lacks a synonym pair in the list. More importantly, it is a "low-level" word. The GRE prefers "arcane" to describe specialized academic difficulty.
- Elevated (C): This means lofty or high-ranking. While true, it doesn't explain why it's nearly impossible to master.
- Rigorous (F): This means extremely thorough. Rigorous theories are often easier to master because they follow strict logic; the difficulty here is the "hidden" or "mysterious" nature of the claims.