The phrase "assertions are based" is correct and usable in written English.
You can use it when discussing the foundation or reasoning behind certain claims or statements.
Example: "The conclusions drawn in the report are valid because the assertions are based on extensive research and data analysis."
Alternatives: "claims are founded" or "statements are grounded".
In the sections below we describe the steps the RAST server implements to automatically produce two classes of asserted gene functions: subsystem-based assertions are based on recognition of functional variants of subsystems, while nonsubsystem-based assertions are filled in using more common approaches based on integration of evidence from a number of tools.
They assert that there were no kingdoms in South East Asia called Kalinga and such assertions are based on erroneous readings of the Chinese name for a locality called Ho-ling which actually stood for Walain not Kalinga.
The Pentagon insists that his assertions are based on outdated information and ignorance of classified materials.
The Russian assertions are based in part on five hours of underwater videotape now being examined by an investigative commission headed by Deputy Prime Minister Ilya I. Klebanov.
Both assertions are based on a false premise, since it is clear that there are plenty of willing and informed women out there.
But her assertions are based on instinct, contemporary gossip and the matching up of dates, times and places rather than revelatory new documents.
None of those assertions is based on any academic understanding or knowledge".
He said the film-maker's assertions were based on court documents and news items from reliable media sources.
Dr. Abramowitz said his assertions were based on reports from more than 100 adult children, social workers, siblings and family lawyers.
But now, having read all the material – points and counterpoints, objections and defenses — I believe that some of the column's assertions were based on too little direct evidence or used statistical information that is, at the very least, open to interpretation.
This assertion is based on two main properties.
