The phrase "at its core however" is correct and usable in written English.
It can be used to introduce a fundamental idea or essence of a topic, often contrasting it with other aspects.
Example: "At its core, however, the issue is about trust and communication between the parties involved."
Alternatives: "essentially, though" or "fundamentally, however".
At its core, however, is a simple, radical and, most important, correct argument.
At its core, however, the movement was aimed at curtailing the growth of the power of the cities.
At its core, however, the High Line today is a linear park through its own narrow garden.
At its core, however, Toy Story Mania represents an effort to solve a puzzle that poses a much larger threat to Disney and the broader amusement park business.
At its core, however, is a career-extending, creative curio that, even in its weaker moments (Come to Mama is wretched), is never dull.
At its core, however, Wikets isn't all that different from Oink, the first app from Kevin Rose's startup lab Milk.
However, at its core, it remains about trying to find a way through a system that you feel does not represent you.
However, at its core some in Pakistan still seek a Muslim Middle Eastern identity to avoid acknowldgement of the shared heritage with India.
However, at its core, The Other Ida is an exploration of identity.
However, at its core is not worship of an external creator or the rigid promulgation of codes of behaviour, but a path of practice designed to test its ideas, a path in which asking questions is more important than having the answers and openness to the evidence is more valuable than being right.
However, at its core, Korniloff believes that the art business hasn't changed when it comes to an artist's representation by a gallerist, and that galleries will continue to be relevant to the evolution of culture in a community.
