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The phrase "a precisely defined" is correct and usable in written English.
It can be used when referring to something that has been clearly and accurately specified or described.
Example: "In scientific research, it is essential to have a precisely defined hypothesis to guide the study."
Alternatives: "a clearly defined" or "a well-defined".
Exact(60)
In statistics, error is a precisely defined term.
He had developed a precisely defined compositional technique involving total serialization (i.e., of every musical element).
Only in a "flat" universe, containing a precisely defined amount of matter and energy, do the rays remain parallel.
The most successful collaborations seem to have been those in which the participants had a precisely defined role.
(A gender-bending "True West"?) More than her company peers Ms. Lemp has proven that an operatic style can adjust to fit into a precisely defined character.
It was a visionary idea: by ceding some of their national sovereignty in a precisely defined era, pooling their resources and using them more efficiently (the reasoning went) war would become, in Schuman's words, "not only unthinkable but materially impossible".
Casting an established actor (De Silva) opposite a talented newcomer (Duarte), Giorgelli conjures an extraordinary balance between an air of unaffected naturalism and a precisely defined, acutely observed dissection of human interaction.
The United States has declared war on cancer, on pornography, and on terror, and the lesson to be gleaned from those campaigns is that, unlike most other wars, those declared against common nouns seldom come to a precisely defined conclusion.
"She was the first person to lay down in rigorous fashion a precisely defined system of rules for reasoning with modal and quantificational notions," said Kit Fine, Silver professor of philosophy and mathematics at New York University.
In this approach, very high doses of radiation are delivered to a precisely defined volume of tissue in a short period of time, effectively killing tumour cells and reducing the size of the tumour mass.
In the relaxed aftermath of victory, General Napier applies to imperialism the old Scots adage "Ye canna dae right for daein' wrang!" Advantageously, the Abyssinian campaign had a precisely defined objective, the rescue of the British prisoners, who included Her Majesty's envoy to the court of the Emperor Theodore, Captain Douglas Cameron.
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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