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The phrase "a demonstrable ability to" is correct and usable in written English.
It can be used when describing someone's clear and observable skill or competence in a particular area.
Example: "The candidate must demonstrate a demonstrable ability to lead a team effectively."
Alternatives: "a clear capability to" or "an evident skill in".
Exact(3)
In the chaos of the early days, a demonstrable ability to speak English sometimes in a chance encounter with a street patrol was enough to get you hired by an enterprising Marine captain.
In the chaos of the early days, a demonstrable ability to speak English — sometimes in a chance encounter with a street patrol — was enough to get you hired by an enterprising Marine captain.
The modified temperature index model (MTIM) accurately predicted salt-induced melt (R2 = 0.98 and 0.99, RMSE = 19.9 and 282.4 m3, CRM = −0.003 and 0.006 for calibration and validation sites respectively), and showed a demonstrable ability to calculate the Bare Pavement Regain Time (BPRT).
Similar(57)
The mRNA expressions of the nine genes examined had wide ranges, suggesting that quantitative Real-time RT-PCR is a highly sensitive method, with demonstrable ability to detect mRNA expression differences from less than 0.01-fold to more than 100-fold.
This fact is supported by the demonstrable ability to induce a variety of autoimmune diseases in rodents using appropriate immunization protocols.
Micrococcus sp NII-0909 isolated from the Western ghat forest soil in India had demonstrable ability to enhance soil fertility and promote plant growth (Dastager et al. 2010).
Green bio-nanotechnology has attracted substantial attention and has demonstrable abilities to improve cancer therapy.
For a child to be adopted with a no-contact order suggests there has been a high level of abuse and a demonstrable lack of ability to change.
Nuclear deterrence thus pushes to the forefront consideration of two facts that recent philosophy of coercion tends to obscure: one, the deep connection between the credibility of one's threats and the demonstrable ability and willingness to execute them; and two, the dynamic or strategic nature of coercive interactions.
Consistent with this small fiber neuropathy, Fabry mice also develop a demonstrable deficit in their ability to respond to a heat stimulus [22], [23].
Even if you do have a particular "genetically demonstrable" ability, what use is that knowledge when suggestion alone is enough to negate it.
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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