A 4.13ct unheated blue sapphire typically refers to a high-quality gemstone that has not been subjected to heat treatment, which is a common process to enhance color and clarity. Unheated sapphires are highly prized for their natural beauty and rarity, as they maintain their original properties.

For a 4.13ct blue sapphire, the description would likely highlight:

- Color: The blue hue, which can range from light to deep, vivid blue. The more intense and rich the color, the more valuable the stone.

- Cut: The sapphire may be cut into a round, oval, cushion, or other shapes, with attention to maximizing the stone's brilliance and symmetry.

- Clarity: Unheated sapphires typically retain natural inclusions, which are sometimes visible under magnification. These inclusions can serve as a characteristic that confirms the stone's authenticity.

- Size: At 4.13 carats, this sapphire would be considered a substantial size, making it an eye-catching piece.

- Origin: Often, the country of origin is mentioned (e.g., Sri Lanka, Madagascar, Kashmir, or Burma), as certain regions are known for producing sapphires of exceptional quality.

Overall, the description of this sapphire would emphasize its natural, unaltered state, highlighting its color, size, and rarity, which contributes to its value.