foundation; basis; core; fundamentals
Usually abstract and somewhat formal, referring to the essential basis or central structure that supports a system, idea, organization, right, or policy.
This is a problem that concerns the foundation of the system.
その発言は民主主義の根幹を揺るがした。
That remark shook the foundations of democracy.
root and trunk
Literal use for the roots and trunk of a tree or plant; much less common than the abstract sense and most likely in botanical, forestry, or descriptive contexts.
倒れた木の根幹を調べると、内部が腐っていた。
When they examined the fallen tree's roots and trunk, the inside had rotted.
Education forms the very foundation of a country's development.
This issue concerns the very core of how the company is run.
The incident shook the very foundations of democracy.
This technology is likely to become the foundation of the new industry.