COLLET

In watchmaking, the collet is a slotted brass ring that secures the balance spring (hairspring) to the balance staff. The slot allows the spring to be held in a fixed position and adjusted as needed during regulation (indexing). A lateral hole is used to firmly secure the inner end of the spring. The hairspring is attached to the collet using a brass pin, adhesive, or even laser-welded in place.

Useful links:

Balance spring/hairspring
Setting
The balance wheel