The phrase "a unique condition for" is correct and usable in written English.
It can be used when describing a specific requirement or circumstance that is distinct or one-of-a-kind for a particular situation or outcome.
Example: "The study established a unique condition for the growth of the rare plant species in the laboratory."
Alternatives: "a distinct requirement for" or "a specific criterion for".
Intergenerational co-residence is a particularly unique condition for exchange of support (Hayashi 1995; Pezzin and Schone 1997); and a co-residing child and child-in-law tend to play a critical role in providing and receiving support from older parents (Koyano 1994).
The Honours Scrutiny Committee, which had a veto over life peerages at the time, attached a unique condition that "to meet the requirements for a working peer, Mr Michael Ashcroft has given his clear and unequivocal assurance that he will take up personal residence in the United Kingdom again before the end of the calendar year".
This leads to a simulation of ∼28 million unique conditions for 99 different readouts and nearly a 2.8 billion total predicted readouts over all models, a scale inaccessible by most experimental screening methods.
It may be that the postwar decades, with a booming mixed economy, middle-class prosperity, and an agreed-upon enemy, created unique conditions for Americans to address some of the country's deepest problems, such as a century of Jim Crow.
The planned heavy ion synchrotron SIS100 will provide unique conditions for heavy ion plasma physics experiments at FAIR (Facility for Antiproton and Ion Research).
Furthermore, they perform the role of local closed sediment basins, creating unique conditions for the preservation of soils and colluvial sediments, along with the record of the evolution of the Holocene landscape, occurring under the influence of climate changes and human activity.
At the same time, this implies that the lack of a living spouse presents a unique family condition for older adults, where the availability of support from adult children may become especially critical.
But then Lewis cannot use his convention of truthfulness and trust to underwrite a unique truth-condition for \(S\).
