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The phrase "after initial acceptance" is correct and usable in written English.
It can be used to refer to a point in time or a condition that follows the first approval or agreement in a process.
Example: "The project will proceed after initial acceptance from the stakeholders."
Alternatives: "following preliminary approval" or "subsequent to first acceptance".
Exact(1)
After initial acceptance, 439 workers participated to the initial assessment, 51 were returned to work and 325 refused (participation rate = 439/(439 + 325) = 57%.
Similar(56)
Nor does the law prohibit patients (or families) from changing their minds and requesting aggressive measures after an initial acceptance of palliative care.
I had no way of knowing just how much more pain was to come after my initial acceptance of that diagnosis.
But after some initial acceptance by directors, distributors, exhibitors and audiences, the rating fell deeply out of favor with filmmakers and moviegoers alike.
The FBI declined to further investigate after its initial acceptance of the case, stating that it had not been able to find evidence that Debbie Swenson's accepting of gifts for "Kaycee" constituted a dollar amount above their threshold for financial crimes.
In the case of compact discs, in 1987, after CDs had gained initial acceptance, CBS Records was the big chasm buster.
Due to the large number of markers segregating in the population, in Joinmap we used maximum likelihood mapping with the map order optimization parameters: chain length of 5000, initial acceptance probability 0.250, cooling control parameter of 0.001 stopping after 30,000 chains without improvement.
Computer software glitches and other problems have held up its initial acceptance by the government.
Its initial acceptance by 19th-century judges was halting and skeptical.
There is a higher level of initial acceptance to the notion of crunch.
In Vidin, he said, despite initial acceptance of desegregation, the struggle is not yet over.
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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