**Core Concept**
Papillary thyroid carcinoma is a type of thyroid cancer that can spread to lymph nodes and distant organs. The TNM staging system is used to classify the extent of cancer spread, which includes the primary tumor size (T), lymph node involvement (N), and distant metastasis (M).

**Why the Correct Answer is Right**
The tumor is 4 cm in size and has invaded the strap muscles, which is classified as T4a. Since lymph node involvement is negative, it is classified as N0. Therefore, the stage of the disease is T4aN0M0. The T4a classification indicates that the tumor has grown beyond the thyroid gland and has invaded nearby structures, such as the strap muscles.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not a valid stage for papillary thyroid carcinoma based on the given information.
**Option B:** This option does not accurately describe the stage based on the tumor size and invasion of strap muscles.
**Option C:** This option is incorrect because it implies the presence of distant metastasis (M1), which is not mentioned in the scenario.

**Clinical Pearl / High-Yield Fact**
When staging papillary thyroid carcinoma, it's essential to remember that T4a classification indicates a more advanced tumor with invasion of nearby structures.

**Correct Answer:** D. T4aN0M0