Detailed Analysis

Blank (i): derivative
- Context: The phrase "At once pioneering and ________ " suggests two contrasting qualities. The semicolon clause clarifies the second quality: the work "owes a substantial debt to her predecessors."
- Fit: If the work is original ("pioneering") but also owes a massive debt to past works, the word in the blank must mean unoriginal or copied. Derivative means based on another source, lacking originality. This sets up the perfect paradox.

Blank (ii): much
- Context: The second half of the sentence resolves the tension. Although the work is derivative (i.e., it relies on previous work), the predecessors "grant she has done _______ to advance the field."
- Fit: Since the work is also described as pioneering, it must have had a significant, positive impact. Therefore, she must have done much to advance the field. If the answer were "little" or "nothing," it would contradict the description of her work as "pioneering."

The completed sentence reads:

At once pioneering and derivative, her work owes a substantial debt to her predecessors, many of whom grant she has done much to advance the field.