The phrase "assertions around" is correct and usable in written English.
It can be used when discussing claims or statements that are related to a particular topic or context.
Example: "The report includes several assertions around the effectiveness of the new policy."
Alternatives: "claims regarding" or "statements about".
A US assertion that around 200 bombs have been dropped in "self-defence" on Iraqi military installations since Operation Desert Fox ended is "far below reality" according to one independent observer.
The British campaign featured assertions and allegations tossed around with little regard to the facts.
On this Sunday's "GPS," CNN host Fareed Zakaria blasted Glenn Beck's assertion that around ten percent of Muslims are terrorists.
"It's very easy to sling around assertions about benefactors," she says.
It added that these and related matters had been reported by the news media "with considerable hype around assertions of long-term harm to players from head injuries".
In the modern wired world, the company's activities will not simply fall under the microscopic scrutiny of advocacy groups, the report says, those same groups will spread their assertions and criticism around the world within seconds on the Internet.
Museveni's assertions raised eyebrows around the world.
It's also difficult for any deeply detailed truth-squad reports to compete with the reverberation of rumor and explosive but unsubstantiated assertions that bounce around social media.
If you're going to make amusing indefensible assertions, don't then turn around and defend yourself laboriously, endlessly, when, inevitably, some dim-bum Carl doesn't understand what you're talking about.
Jobs's assertion that "The info circulating around is false" is hard to analyse, given that he does not say which information he is referring to.
