The phrase "attack on the core" is correct and usable in written English.
It can be used in contexts discussing a direct assault or criticism aimed at the fundamental aspects of something, such as an organization, belief, or system.
Example: "The recent scandal was seen as an attack on the core values of the organization, prompting a reevaluation of its mission."
Alternatives: "assault on the foundation" or "strike at the essence".
Merkel described it as an attack on "the core elements of our free democratic culture".
"An attack on the holy prophet is an attack on the core belief of 1.5 billion Muslims," Prime Minister Raja Pervez Ashraf said in an address at a religious conference Friday morning in Islamabad.
Blockchain technologies have a well-earned reputation for hacking and fraud, but the recent theft of more than $20 million of second-tier cryptocurrencies like Bitcoin Gold, Verge and ZenCash was a fundamental attack on the core mechanisms that allow cryptocurrencies to function.
We spoke shortly after Trump had his press conference with Vladimir Putin — setting off this week's cycle of criticism, denial and missing double negatives — and Takei told me, "No augmented reality could have created the true reality of what we saw this morning: Donald Trump standing shoulder-to-shoulder with Vladimir Putin … his denial of the attack on the core activity of our democratic system".
Scott Walker will try to make the case that he's the biggest GOP disruptor for having survived his attack on the core Democratic legacy of public employee pensions.
University of Waterloo professor Emmett Macfarlane wrote in Maclean's that the school's tweet is a "reprehensible attack on the core of the academic mission, and specifically on academic freedom".
After discovering that they themselves were mere simulations in a deterministic computer universe, the Martians decided to launch a surprise attack on the galactic core.
It desecrates our history and is a repugnant attack on the very core of our nationhood.
To now presume because of his sexual orientation that he was mistaken, or worse, and based his ruling on personal, not legal, considerations, is a serious accusation, and an attack on the very core of the Judge's integrity.
ISIS supporters in Brussels killed 35 in a major attack on the city's core infrastructure and an offshoot of the Taliban killed more than 70 in an attack targeting Lahore's Christian minority.
But the "love yourself above all" philosophy of Rand and Ryan not only represents a direct attack, as Rand understood, on the core message of Christianity (and therefore Christmas).
