The ctrlX CORE can for sure run without an battery, as it is only buffering the date and time.
But Currently there is no possibility to switch of the battery low warning, so your ctrlX CORE with light up in yellow if you would remove it or it will be depleted.
See general information about battery in the online documentation "Battery change". There is mentioned "It is recommended to change the battery of the control ctrlX CORE every three years."
While ctrlX CORE is connected to the supply voltage there should nearly no depletion so battery life would be extended but without any estimation. Please beware that in quite old hardware versions there was a Problem that also while supplied the battery depleted. This was fixed from hardware index AG1 on.
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