There may be some confusion between "don't discharge beyond" and "consider your battery "dead" at".... As a general rule, most battery companies recommend not to discharge beyond 12 VDC on a regular basis in order to preserve the "lead acid battery lifespan"....
There's a lot of good information at this website:
https://www.solar-electric.com/learn...%20electrolyte
Given the "recommendation" not to discharge deep cycle batteries beyond 50% (on a regular basis) and that voltage being 11.96 at 40% and 12.10 at 50%, the "generally accepted term" of 12 volts being "dead" makes sense. In other words, never discharge below 12 volts if possible.
Here's a voltage chart that is "good to have on hand" information.