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The phrase "they certified that" is correct and usable in written English.
You can use it when indicating that a person or organization has officially confirmed or validated a statement or fact. Example: "They certified that the documents were authentic and met all legal requirements."
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Earlier this month, family members of missing demonstrators were taken to a morgue in southwest Tehran where they reported seeing "hundreds of corpses" and were not allowed to retrieve bodies unless they certified that the deaths were of natural causes, according to accounts relayed on Web sites and to human rights workers.
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"When nursing homes submit claims, they certify that they comply with all laws and regulations.
Under the bill, no money "may be made available for any purpose" to Planned Parenthood clinics unless they certify that they will not perform abortions.
They certify that "in those regions there are mountains, plains, rivers, lakes, brooks, rills, trees, flowers, birds, beasts and every attribute of the most admired portions of this lower sphere".
Clarification of existing federal law that guarantees freedom of conscience to health care providers and institutions would not expand the reach of those laws; it would merely remind state and city governments of the First Amendment rights of their citizens by requiring that they certify that they are in compliance.
They certify that they had no relationship with companies that may have a financial interest.
The authors certify that no party having a direct interest in the results of the research supporting this paper has or will confer a benefit on them or on any organization with which they are associated and, if applicable, they certify that all financial and material support for this research (e.g., VA) and work are clearly identified in the title page of the paper.
Chinese doctors can declare a person dead only after they have certified that the heart has stopped.
First, they do testing to discover vulnerabilities in the system and they certify sites that are secure.
Last December's change allows companies that handle those chemicals to use the shorter reporting form, but only if they can certify that they are not releasing them into the environment.
And at least some of the illegal Mexicans already in the United States could earn permanent lawful status if they could certify that they had been living and working in the country for a specified time, and had been paying taxes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com