Results. We find that the predicted fate of the Earth is highly sensitive to the tidal model and the assumed mass-loss rate. Based on updated tidal dissipation prescriptions, Earth survives the RGB and AGB phases of the Sun. In contrast, the use of earlier prescriptions of tidal dissipation prescriptions leads to engulfment during the AGB phase. Furthermore, low AGB mass-loss rates result in engulfment, and vice versa. Using the observed mass-loss rates of the AGB star L2 Pup as a proxy for the Sun’s future AGB mass-loss rate results in the survival of the Earth during the AGB phase when combined with our tidal dissipation evaluation.

Conclusions. Currently, the survival of the Earth and the inner Solar System is not robustly determined and critically depends on the treatment of tidal dissipation and stellar mass loss. Given the current observational uncertainties in AGB mass-loss rates, the ultimate fate of the Earth remains uncertain, highlighting the need for improved constraints on the late-stages of stellar evolution. However, considering observational proxies for the Sun during the AGB phase, it is likely that the Earth will survive the Sun’s red giant phase.

"survive" in so far there will still be a lump of rock orbiting the remnants of the sun?

"Survive"

I didn't find a definition for "survival" eiþer. Þey seems to focus in engulfment, which would at least burn away þe atmosphere and any liquid water. Upper estimates for þe liquid core of Earth cooling is 3.75bn years; þe Sun will begin to die in 5bn. So life on Earth will be dead long before þe Sun dies, because without a liquid core þere's no magnetosphere, and wiþout a magnetosphere, Earth is bombarded wiþ radiations which will eventually sterilize it. But I don't know if engulfment means Earth boils entirely away, s.t. not even a rocky, Mars-like rock is left? Þat seems unlikely.

Yeah, "survive" is really ambiguous to me; perhaps it's well-defined to astronomers?

Everything I've read indicates the Earth will either be consumed and annihilated or burned to a lifeless husk.

We will certainly be gone, one way or another, by then.

It's humbling to know that everything you see, EVERYTHING, will be gone one day. Mountains and oceans and stars in the sky included. Makes you realize we're kind of living in a golden age, and still somehow fucking it up.