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The phrase "assumption that the current" is correct and usable in written English.
It can be used when discussing a belief or expectation regarding the present situation or state of affairs.
Example: "The assumption that the current economic conditions will improve is optimistic but not guaranteed."
Alternatives: "belief that the present" or "expectation regarding the current".
Exact(19)
In economics, political science and the study of international relations there has been, for about three decades, a general assumption that the current framework is permanent.
It was based on an assumption that the current flow measured at Lee's Ferry, just south of Lake Powell, could fall short of demand by as much as 500,000 acre-feet a year.
Tramnesia Waking up from a deep sleep on the train, not knowing what stop you're at, and bolting for the door in the assumption that the current stop is yours.
The simplest ones use statistical relations based on the typical paths of hurricanes in a region, along with the assumption that the current observed motion of the storm will persist.
As the nation tries in this cynical age to avoid "generational chauvinism" -- the assumption that the current generation is morally superior to all past generations -- we can still learn from history the invaluable lesson that an enormously powerful and profitable evil can be overcome.
Central to this methodology is the assumption that the current wetlands are fragments of the larger past wetland.
Similar(40)
The third one is the observation independence assumption; that is, the current observation is statistically independent of previous observations.
To test this hypothesis, we exposed embryos to X-rays with a range of energies for various periods of time, guided roughly by the assumptions that i) the current (j) is constant and ii) the average energy of the X-rays is proportional to the voltage setting (in units of kV).
Our results challenge the conventional assumption that wound electric currents are merely ion leakage due to breakdown of the epithelial barrier that short-circuits the trans-epithelial potential at the wound site.
When a random interleaver is used, the Markov assumption, stating that the current state is only dependent on a finite history of previous states, is violated since the interleaver randomizes the encoded data according to some predetermined random permutation.
The presented analytical model is free from the assumption that the generated current is identically distributed over all the piezoelectric layers, which has been widely used by the existing models in literature.
More suggestions(15)
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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