"Auxesia might be rephacked hostile to Core for obvious reasons but that doesn't mean if presented the oppertunity Core won't work with them. Core diplomacy can be very fluid and dynamic. Factions such as Auxesia aren't Omicron natives and therefore don't conflict with their objectives within that region. It's in the same sense where there's a precedent for Core and Nomad cooperation. Core are oppertunists.
This all culminates into a reason why The Core, unlike other lawful IDs, doesn't have a "cannot partake in unlawful actions" or "cannot ally with unlawfuls" line on their ID, due to their roleplay. Lawful evil is in this area that effectively borders on quasi-lawful."