A 42-year-old male presents to the emergency department with acute onset of severe pain, swelling, and erythema of the right big toe that started 6 hours ago. He reports a history of similar episodes over the past 2 years, each lasting 7–10 days. On examination, the first metatarsophalangeal joint is warm, tender, and markedly swollen. Serum uric acid is 8.2 mg/dL (normal <6.8). Synovial fluid analysis shows needle-shaped, negatively birefringent crystals. Which enzyme deficiency is the PRIMARY metabolic basis for this patient's recurrent attacks?