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"found at the same time" is a perfectly correct and usable phrase in written English.
It is usually used to describe a situation where two objects or events were discovered at the same time. For example, "The researchers were excited to discover two new species of bacteria found at the same time in the same pond."
Exact(17)
Lost and found at the same time.
Lost and found at the same time, I guess.
(Similar results were found at the same time by American astronomers Vera Rubin and W. Kent Ford).
The movements had to be found at the same time as the answers to the questions were found; they couldn't be grafted on afterwards.
The bodies of Kosovo Albanians recovered in recent months from the Danube at Batajnica, where they were apparently taken by truck during the Kosovo war, have been found at the same time as dozens of bodies around Visoko, in Bosnia.
In PLLA/Bio-TPU/L101 (90/10/0.3, 90/10/0.3) blends, excellent ductility and high tensile strength were found at the same time owing to largely improved compatibility and much higher crystallinity.
Similar(42)
On a long enough timescale, we'd get there anyway: the raw economics will win out as oil and gas is getting more costly to find at the same time as renewables are becoming cheaper.
Similar relationship of CTC presence was found at the same sampling time with advanced invasion of tumor (pT3-4); however, it did not reach statistical significance.
The body of a 15-year-old, Lisa Norrell, was also found at around the same time.
Note that the maximum in the ITS for ϕ 0=0° and ϕ 0=50° is found at almost the same time.
We also found at about the same time that the care given to patients with established moderate-to-severe BPD was highly variable and often lacked a neurodevelopmental focus during the initial NICU stay.
More suggestions(13)
defined at the same time
studied at the same time
discovered at the same time
founded at the same time
characteristics at the same time
discover at the same time
in at the same time
studies at the same time
searched at the same time
find at the same time
information at the same time
identifying at the same time
study at the same time
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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