**Core Concept**
Ataxia-telangiectasia is a rare, complex genetic disorder characterized by a combination of neurological, immunological, and chromosomal abnormalities. Phacomatoses are a group of rare hereditary disorders that affect the skin, nervous system, and other organs. Autosomal recessive inheritance means that a person must inherit two copies of the mutated gene (one from each parent) to express the condition.

**Why the Correct Answer is Right**
Ataxia-telangiectasia is indeed the only phacomatosis among the given options to be inherited on an autosomal recessive basis. This is due to the mutation in the ATM gene, which is responsible for the regulation of the cell cycle and DNA repair. Individuals with ataxia-telangiectasia have a defect in the double-strand break repair pathway, leading to genomic instability and a high risk of cancer. The other phacomatoses listed are inherited in an autosomal dominant manner.

**Why Each Wrong Option is Incorrect**
**Option A:** Sturge-Weber syndrome is a phacomatosis characterized by a port-wine stain on the face and neurological abnormalities, but it is inherited in an autosomal dominant pattern.
**Option B:** von Hippel lindau syndrome is a phacomatosis that predisposes individuals to develop tumors in various organs, but it is also inherited in an autosomal dominant pattern.
**Option C:** Neurofibromatosis is a phacomatosis that affects the nervous system and is characterized by the development of neurofibromas, but it is also inherited in an autosomal dominant pattern.

**Clinical Pearl / High-Yield Fact**
Ataxia-telangiectasia is a classic example of a genetic disorder that affects multiple organ systems, and it often presents with a combination of neurological, immunological, and chromosomal abnormalities. The condition is often diagnosed in childhood, and early recognition is essential for providing appropriate management and supportive care.

**✓ Correct Answer: A. Ataxia-telangiectasia**