A 48-year-old woman is admitted following a fall from a height of 4 meters. On examination, she has severe left-sided chest wall pain, paradoxical breathing (inward movement of a segment during inspiration), and crepitus over the left anterior chest wall. Arterial blood gas shows pH 7.28, PaCO₂ 52 mmHg, HCO₃⁻ 22 mEq/L. Chest X-ray confirms multiple rib fractures (ribs 3–6) with fractures in two places on each rib. What is the primary pathophysiologic consequence of her condition, and what is the most important component of management?