45-year-old woman complains of bleeding gums. The bleeding occurs when she brushes her teeth or eats hard food. Objectively, in the frontal area of her lower jaw the gums are hyperemic, edematous, and bleed when palpated. In the other areas, her oral mucosa is normal. The woman has a deep bite. Her teeth are stable, except for teeth 41 and 31 (the I degree of mobility). X-ray shows resorption of the interalveolar septa in the area of teeth 41, 42, 31, and 32 to 1/3 of the root length. What is the most likely diagnosis?