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The phrase "and thus only" is correct and usable in written English.
It can be used to indicate exclusivity or limitation in a statement, emphasizing that something is true or applicable in a specific context.
Example: "This solution is effective for this problem and thus only for this scenario."
Alternatives: "and therefore solely" or "and consequently exclusively".
Exact(60)
LSZ strongly interacts with the hydroxyapatite particles and thus only forms thin films with very low elastic moduli.
And thus only the faithful are ever disappointed.
PingER uses the ICMP echo facility (ping) and thus only makes round trip measurements.
These results were generated numerically and thus only simulate a finitely large cubic phase plate.
In contrast, it was effectively repressed by pRB and thus only minimally active in nontransformed cells.
"As a Coventry City fan," Dominic adds, "I witnessed my team demolish Wise's Millwall 4-0, Wise Winjuredured and thus only involved in a managerial capacity.
Most of the common tests likely to be used measure traits under polygenic, genetically heterogeneous control, and thus, only large effects are likely to be detected.
Maximum Likelihood (ML) and Bayesian Inference (BI) analyses yielded identical tree topologies and thus only the tree inferred from the ML analysis is shown (Fig. 1).
The kinetic energy density is semilocal in the occupied orbitals, immediately available from common DFT calculations, and thus only adds moderate extra computational cost.
I assumed that the environment is large compared to the rendered scene, and thus only the direction is used in retrieving the radiance from the radiance map.
In many practical applications it is common and reasonable to assume that the nonlinearities are highly local and thus only affect a limited set of spatial coordinates.
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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