When might human help outweigh the penalty of not dismantling Earth? It requires these conditions:
1. The AGI can very quickly reach an alternative source of materials: AGI spaceflight is superhuman.
AGI spacecraft, once in space, can reach eg. the Moon within hours, the Sun within a day
The AGI is willing to wait for additional computational power (it can wait until it has reached the Sun), but it really wants to leave Earth quickly
2. The AGI’s best alternative to a negotiated agreement is to lie in wait initially: AGI ground operations is initially weaker-than-human.
In the initial days, humans could reliably prevent the AGI from building or launching spacecraft
In the initial days, the AGI is vulnerable to human action, and would have chosen to lay low, and wouldn’t effectively begin dismantling Earth
3. If there is a negotiated agreement, then human help (or nonresistance) can allow the AGI to launch its first spacecrafts days earlier.
Relevant human decision makers recognize that the AGI will eventually win any conflict, and decide to instead start negotiating immediately
Relevant human decision makers can effectively coordinate multiple parts of the economy (to help the AGI), or (nonresistance) can effectively prevent others from interfering with the initially weak AGI
I now think that the conjunction of all these conditions is unlikely, so I agree that this negotiation is unlikely to work.
Even if we’re already doomed, we might still negotiate with the AGI.
I borrow the idea in Astronomical Waste. The Virgo Supercluster has a luminosity of about 3×1012 solar luminosity ≈1039 W, losing mass at a rate of 1039/c2≈1022 kg / s.
The Earth has mass ∼6×1024 kg.
If human help (or nonresistance) can allow the AGI to effectively start up (and begin space colonization) 600 seconds = 10 minutes earlier, then it would be mutually beneficial for humans to cooperate with the AGI (in the initial stages when the AGI could benefit from human nonresistance), in return for the AGI to spare Earth (and, at minimum, give us fusion technology to stay alive when the sun is dismantled).
(While the AGI only needs to trust humanity for 10 minutes, humanity needs to trust the AGI eternally. We still need good enough decision-making to cooperate.)
We may choose to consider the reachable universe instead. Armstrong and Sandberg (2013) (section 4.4.2 Reaching into the universe) estimates that we could reach about 109 galaxies, with a luminosity of 1047 W, and a mass loss of 1029 kg / s. That is dwarfed by the 105 stars that becomes unreachable per second (Siegel (2021), Kurzgesagt (2021)), a mass loss of 1035 kg / s.
Starting earlier but sparing Earth means a space colonization progress curve that starts earlier, but initially increases slower. The AGI requires that space colonization progress with human help be asymptotically 10 minutes earlier, that is:
For any sufficiently large time t, progress with human help at time t≥ progress with human resistance at time (t+10 minutes).
I think the dramatic impact would be stronger without the “The end”, and instead adding more blank space.
Idea copied from a comment on the final chapter of Three Worlds Collide.