**Core Concept**
The condylar guidance programming on an articulator is a critical aspect of removable partial denture design, particularly in cases of mandibular movement. This concept is based on the understanding of the mandibular condyle's movement and its relationship with the articular eminence.

**Why the Correct Answer is Right**
The minimum protrusion required for condylar guidance programming is crucial in accurately replicating the mandibular condyle's movement on the articulator. This is essential for ensuring proper occlusion and function of the denture. The correct answer is **2 mm**, as this is the minimum protrusion required to accurately replicate the mandibular condyle's movement and prevent unnecessary interference with the articular eminence.

**Why Each Wrong Option is Incorrect**
**Option A:** 1 mm is too minimal, as it may not accurately replicate the condyle's movement, leading to potential occlusal discrepancies.
**Option B:** 3 mm is excessive, as it may cause the articulator to deviate from the natural path of the mandibular condyle, resulting in inaccuracies in denture design.
**Option C:** 4 mm is also too much, as it may lead to an unnatural movement of the condyle, causing potential discomfort and occlusal issues for the patient.

**Clinical Pearl / High-Yield Fact**
A common mistake in condylar guidance programming is using a protrusion that is too small, leading to inaccurate replication of the mandibular condyle's movement. To avoid this, it is essential to use a minimum protrusion of 2 mm to ensure accurate denture design.

**Correct Answer:** C. 2 mm.