This is the outermost cranial appendage

The correct option/answer is Dura mater.

To understand why this is correct, we can break down the structure of the cranial meninges (the protective membranes surrounding the brain) from the outermost layer to the innermost layer:
1. Dura mater: This is the thickest, toughest, and outermost cranial appendage/meningeal layer. It lies directly underneath the bones of the skull and provides a strong protective barrier.
2. Arachnoid mater: This is the middle, web-like layer that lies beneath the dura mater.
3. Pia mater: This is the thin, delicate, and innermost layer that directly adheres to the surface of the brain and spinal cord.

Since the question asks for the outermost cranial appendage among the meningeal layers, Dura mater is the correct choice (note that while the skull is a bony structure, the dura mater is the outermost protective membrane/appendage of the meninges surrounding the brain itself).