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The phrase "a solution once the" is correct and usable in written English.
It can be used when discussing a resolution or answer that is contingent upon a specific condition being met.
Example: "We will have a solution once the data is analyzed thoroughly."
Alternatives: "an answer after the" or "a resolution when the".
Exact(1)
Lew said he's optimistic lawmakers will make progress toward a solution once the House returns from recess this week.
Similar(58)
Unfortunately, it is projected that these roads will only be a temporary solution; once the lava flows over the highway, it will eventually cross down to the ocean, overtaking the new roads and cutting us off completely.
"I think we need to get to a solution once and for all for the over-crowding in Treganna which has been going on for too long.
Mr. Kushler thinks he has a solution once again.
He takes more than his fair share of beatings and sleights to find his way to the solution, but the solution is clearly not Chandler's aim (he was famously irked by "plotting" and once said that a solution, once arrived at, should seem inevitable).
It is proved that the Water Filling algorithm gives the globally optimal solution once the sufficient condition is satisfied.
The factory also makes professional dance shoes with pointes which are created by layering Hessian sheets covered in a plaster solution; once inside the pink satin slipper, the pointe has to be completely flat at the end so that the shoe will stand up by itself.
"During the crisis, it was clear that they were pulling out all of the stops to try to find a solution, and once the financial system stabilized and the problem was merely 10 percent unemployment, then they moved more slowly," said Laurence Ball, an economist at Johns Hopkins University, who wrote in a 2012 paper that Mr. Bernanke has lacked the courage of his convictions.
"I have been doing my best to try and find a solution but once the players are out on the pitch they have to do it by themselves.
Simply spraying spots with a vinegar solution once a week or so, as they begin to form, may be adequate.
We wish to stress that it is unlikely that the ANN will outperform an SVM solution once a good kernel will have been identified [35].
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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