His __________ pursuit of the truth led to the __________ that solved the long-standing mystery.

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**Solution:**

1. The word **tenacious** means being persistent and determined, which fits well with the idea of a strong pursuit of truth.

2. **Breakthrough** refers to a significant discovery or advancement, which aligns perfectly with solving a mystery.

3. **Ultimately** means finally or in the end, indicating the resolution of the mystery after persistent effort.

4. Other options do not fit the context:
   - *Preserving* means maintaining something, which does not suit the pursuit of truth.
   - *Dimension* is a measurement, irrelevant here.
   - *Apologetically* means with regret, which does not fit the sentence.
   - *Conundrum* means a puzzle, not a pursuit.
   - *Hesitation* and *indifferent* imply lack of action or interest, which contradicts the sentence.
   - *Breach* means a gap or violation, unrelated to discovery.
   - *Gradually* and *mistakenly* do not fit the context of a final solution.

**Answer:** (b) tenacious, breakthrough, ultimately

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