ObsCore is a library of functions that is required by ObsTrophies and ObsAoA.
Despite the name, ObsCore is NOT a "coremod", simply a library of functions used by multiple mods (two of which - ObsTrophies and ObsAoA - have been released).
ObsCore does have some tools to allow you to dump the details of all installed mods, entities and biomes to file. Look in obscore_client.cfg in your config/ directory to enable.

