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The phrase "a sole solution and" is correct and usable in written English.
It can be used when discussing a unique answer or resolution to a problem, often in a context where alternatives are being considered.
Example: "After extensive research, we concluded that there is a sole solution and it is to implement the new software system."
Alternatives: "a single solution" or "the only solution".
Exact(1)
Thus, the linearly constrained basis pursuit problem has a sole solution and its dual problem is smooth.
Similar(59)
It is shown that the revised algorithm provides a sole solution under the proportional and non-proportional loading by application of the Matake and Papadopoulos criteria.
The scientists viewed these options as a much bigger wild card that is clearly not ready for prime time, saying it would be "irrational and irresponsible" to implement as a sole solution without also reducing emissions or removing CO2, or pursuing all three.
It is true that civic groups in Nassau and Suffolk Counties have expressed opposition to mass-burning incinerators as a sole solution to garbage disposal.
Imagine the world leagues coming together to discuss a sole solution to synchronising our leagues for the 2022 World Cup in Qatar.
Unfortunately, research has shown that despite their ubiquity, when offered as a sole solution, sleep hygiene simply does not work.
But "struggle" would at least have acknowledged that warfare is not the sole solution, and "violent extremism" would have recognized a motive behind the method.
Fancy talk about data and apps will never serve as the sole solution in city government and we strongly believe that nothing will ever replace being in our neighborhoods, meeting people and hearing first-hand of their concerns.
It is a great achievement and an important advance, but they know that this partially protective vaccine is not the sole solution to the control and elimination of malaria".
The paper presents research data of lipid peroxidation and lectin activity in wheat seedlings at seed treatment with solution of metal nanoparticles (Zn, Ag, Fe, Mn, Cu) and sole solution of copper nanoparticles under the high pathogen infection background of Pseudocercosporella herpotrichoides (Fron) Deighton (synonym: Oculimacula yallundae (Wallwork & Sponer) Crous & W. Gams).
In this sense, technical infrastructure and system development is not the sole solution for promoting data sharing and open access.
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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