A "core supporter" can be defined as someone who is unwavering in their support and loyalty towards a particular cause, person, organization, or political party. Some synonyms for this term are loyalist, staunch supporter, diehard fan, dedicated advocate, committed follower, ardent believer, devoted adherent, faithful ally, and steadfast proponent. These words all convey the idea of a person who is firmly committed to a particular idea or person, and who will stand by them no matter what. These types of supporters are essential for the success of any movement or organization, as they provide a solid base of support that can be relied upon in times of need.