The phrase "remaining core" refers to the central or essential parts that are left or still existing after some parts have been removed or lost. Full definition
Music must remain a core part of the teaching curriculum. (edutopia.org)
The access mission has remained a core value, even as student loans have become the centerpiece of the aid structure. (accesslex.org)
Specifically, they maintained, the concept of «common but differentiated responsibilities» remains a core principle of the climate negotiations. (scientificamerican.com)