A 28-year-old woman from Delhi presents with a 3-year history of irregular menstrual cycles, amenorrhea for 4 months, and progressive weight gain (BMI 32 kg/m²). She reports hirsutism on the face and lower abdomen. On examination, she has acne and dark velvety patches on the neck (acanthosis nigricans). Pelvic ultrasound shows multiple small follicles arranged peripherally in both ovaries (>12 follicles per ovary, each 2–9 mm). LH:FSH ratio is 3.5:1. Fasting insulin is elevated at 18 mIU/mL (normal <12). Free testosterone is mildly elevated. What is the most likely diagnosis?