Chronic Bronchitis: Given the patient's history of smoking and a 3-month duration of cough with clear sputum, chronic bronchitis is a highly plausible diagnosis. The presence of advanced coronary arterial calcification and atherosclerotic calcifications of the aortic arch also supports a diagnosis related to long-term smoking.

Pulmonary Fibrosis: Although the pulmonary parenchyma is described as well-aerated with no airspace disease, the minimal left lower lobe soft tissue density pulmonary nodularity could suggest early or mild pulmonary fibrosis, especially in the context of a history of granulomatous exposure indicated by calcifications in the left hilum.
Asthma or COPD Exacerbation: These conditions could present with a chronic cough, especially in a former smoker. However, the lack of specific findings like airway abnormalities or significant pulmonary nodularity makes them less likely but still possible.

Lung Cancer: Despite the CT findings not specifically indicating a mass, the history of smoking mandates consideration of lung cancer. The minimal left lower lobe soft tissue density pulmonary nodularity, although small (0.3 cm), warrants further investigation to rule out malignancy.
Tuberculosis (TB) or Fungal Infections: The extensive calcifications in the left hilum suggest prior granulomatous disease, which could be due to TB or fungal infections. Although less likely given the clinical context, these conditions can have severe consequences if not diagnosed and treated properly.

Sarcoidosis: This condition can cause granulomatous changes and could explain the calcifications in the left hilum. However, the lack of other systemic symptoms or specific pulmonary findings makes it less likely.
Histoplasmosis or Other Fungal Infections: Similar to TB, these infections can cause granulomatous changes and calcifications. They are less common and would typically be associated with specific exposure histories or systemic symptoms.