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The phrase "a perfect equilibrium between" is correct and usable in written English.
It can be used when discussing a state of balance or harmony between two or more elements or factors.
Example: "The project aims to achieve a perfect equilibrium between environmental sustainability and economic growth."
Alternatives: "an ideal balance between" or "a harmonious relationship between".
Exact(2)
Perhaps the greatest madrigal composer of the 16th century was Luca Marenzio, who brought the madrigal to perfection by achieving a perfect equilibrium between word and music.
They also contributed to the show by creating a piece that they feel is "a perfect equilibrium" between their aesthetics, mixing Ms. Susplugas' focus on the medical field and Mr. Declercq's interest in authority.
Similar(58)
It treats the trade-offs between human needs for water, energy and food as a perfect equilibrium model, in which resource allocation can be decided.
Yet a perfect equilibrium implies stasis, and stasis is anathema to a city.
Loads more drones, loads of aircraft equipped with anti-drone death rays, all locked into a perfect equilibrium of mutually assured destruction?
Obviously, the thermodynamic data are based on a perfect equilibrium status which may require an extremely long term reaction.
This was observed by DMA analysis as a consequence of the perfect equilibrium between the contributions of TA as a compatibiliser and in the acidolysis of starch, resulting in films with a tensile strength of 5.93 MPa, a possible alternative to non-biodegradable packaging.
Clinically grisly but seraphic in its concentration, it had found the perfect equilibrium between inner and objective realities.
So, it's difficult to find the perfect equilibrium between privacy on the one hand, and other factors, such as innovation and security, on the other.
It struck a perfect balance between smart and dumb.
This is a subgame perfect equilibrium.
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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