Cerulean is a mod that optimizes Minecraft's advancement checking system, specifically the laggy InventoryChangeTrigger, which can cause heavy lag in modpacks with lots of modded advancements. It is a fork of Icterine, updated to modern versions and with additional features.

Aside from being updated to 1.21.1, Cerulean adds an option to only process advancements every few ticks, which is the strategy used by mods like Achievements Optimizer (which does not work with the original Icterine). This option is handled in a way that ensures the first time an item is picked up per player, it is always processed for achievements--preventing cases where advancements would stall until you moved items around.

From the original mod page:

Optimizes triggering advancements for obtaining items;
Might break parity with vanilla, but doesn't affect vanilla advancements and shouldn't affect the vast majority of mods/datapacks;
Even if it does affect something, advancement still should be obtainable by just dropping and picking up one of required items;
Currently, there are no known incompatibilities or issues;
Every injection into vanilla code can be disabled in config file.
All changes are server-side.