A 28-year-old man with type 1 diabetes presents to the emergency department with severe hyperglycemia (680 mg/dL), pH 7.28, HCO₃⁻ 12 mEq/L, and prominent Kussmaul respiration. His serum osmolality is 315 mOsm/kg. A 35-year-old woman with undiagnosed diabetes presents with glucose 1100 mg/dL, pH 7.35, HCO₃⁻ 20 mEq/L, and no respiratory distress. Her serum osmolality is 340 mOsm/kg and she is drowsy. Which finding most reliably distinguishes the first patient's diagnosis (DKA) from the second patient's diagnosis (HHS)?