Li Gan

Ri Gan (Regan in the anime) is the Sage of Mirror Lake and a dedicated researcher on magic.

Background
Although he is a mage, his interest lies on magical research especially a global-level magic. His knowledge is vast, one of a few people who recognised that Elder Tale has been altered by magic three times in its history, and he named it World Fraction. In the archive, he found that Shiroe first appeared 98 years ago and believed that he must be an archmage based on the frequency and activeness, leading him to contact the guild master of Log Horizon directly to discuss the World Fraction and the Spirit Theory.

An Invitation from Eastal
During the Round Table Alliance's arrival at the Ancient Palace of Eternal Ice, Ri Gan sensed the person he had been looking for has arrived while inside his private library.

Shield and Freedom
Ri Gan appeared to Shiroe and Akatsuki through a portal at the balcony, though his entrance made them ready their weapons in self-defense.