**Core Concept**
Recurrent fractures and multiple bony deformities in an infant suggest a congenital or metabolic bone disorder. Osteogenesis imperfecta (OI) is a genetic disorder characterized by brittle bones, skeletal deformities, and frequent fractures due to defective collagen synthesis.

**Why the Correct Answer is Right**
The correct diagnosis is **Osteogenesis imperfecta** (OI). OI is caused by mutations in the COL1A1 or COL1A2 genes, which code for the alpha-1 and alpha-2 chains of type I collagen. Type I collagen is essential for bone strength and structure. Mutations in these genes lead to the production of defective collagen, resulting in brittle bones that are prone to fractures and deformities. The clinical presentation of OI can vary, but it often includes blue sclerae, hearing loss, and dental abnormalities.

**Why Each Wrong Option is Incorrect**
**Option A:** Rickets is a disease caused by vitamin D deficiency, leading to softening of bones in children. While it can cause skeletal deformities, it does not typically present with recurrent fractures.

**Option B:** Osteopetrosis is a rare genetic disorder characterized by overly dense bones. While it can cause skeletal deformities, it is not typically associated with recurrent fractures.

**Option C:** Achondroplasia is a genetic disorder that affects bone growth, leading to dwarfism and skeletal deformities. However, it is not typically associated with recurrent fractures.

**Clinical Pearl / High-Yield Fact**
OI can be diagnosed through genetic testing, which looks for mutations in the COL1A1 or COL1A2 genes. Early diagnosis and management can help prevent fractures and improve quality of life.

**Correct Answer:** A. Osteogenesis imperfecta.