The phrase "represents the core" is correct and can be used in written English.
This phrase is used to emphasize that something is the most important element of a concept, idea, problem, etc. For example, "The mission statement of this new company represents the core values of the organization."
For him early music represents the core of the repertory, with contemporary music a close second.
"Annika is a champion who so wonderfully represents the core values of our great game, sportsmanship and integrity".
His case represents the core issue of what kind of role the nation's courts should have, if any, in reviewing the government's imprisonment of someone charged with something akin to a war crime.
In a lengthy editorial, the Record argued that Corbyn best represents the "core Labour values" required to build a fairer country and thus improve the lives of Scottish people.
To many Iranians, this setup represents the core betrayal of the revolution, whatever the elements of democracy — including a June presidential election — that have emerged around the Constitution's incorporation of the contested idea of a God-given guide.
The EU represents the core of what could be called "Wider Europe" – a Brussels-centric vision that extends into the heartlands of what had once been an alternative great-power system centred on Moscow.
With its stress on everyday objects, the design collection represents the core philosophy of the museum as it evolved in its early days: to extend modernism into the lives of ordinary people.
The formula below represents the core of the BLUiR approach.
Actually, it represents the core computation cost of these highly advanced seismic processing methods.
Moisture maximization represents the core concept of the proposed methodology; precipitable water being the key variable.
Situational crime prevention represents the core of prevention practices under the framework of environmental criminology.
