In Death's End, Luo Ji asks Sophon if there's a way to send out a 'safety notice' to the universe and she responds in the affirmative. But then proceeds to say that "I can tell you nothing more. I can never tell you anything again."
Why exactly could she not tell them how to send the safety notice?
Related question; What was the "safety broadcast"?
The Safety notice under discussion seems to be the conversion of the solar system to a Black Domain, essentially reducing the local speed of light to a point where advanced technology becomes non-functional.
One reason the Sophon might not want to tell them how to do this is the standard double edged sword of all technology, the Black Domain technology can be deployed locally as a safety notice, or in another star system as a weapon.
This however does not explain why the Sophon cannot tell them anything ever again.
I think Sophon would not tell them about converting the solar system into a "black domain", as it would also be in conflict with the Trisolarans' goal for Earth. Their interest in Earth was using it as a new home for their species - in particular, the subset thereof that was underway in the Trisolaran lightspeed fleet.
Transforming the solar system into a "black domain" would make it essentially unreachable for those lightspeed ships, assuming they are not equipped for significantly prolonging their journey by an additional sublight leg in the vicinity of the solar system (let alone possible countermeasures humanity might be able to put in place).
As for why Sophon can never say anything again, I presume that is a result of the book's "small, absolute decision graph" approach. Presumably, the in-universe assumption is that any further statement by Sophon would invariably lead to humanity quickly figuring out the "black domain" solution themselves.
I really like this question, it kinda hints at what the safety notice turns out to be.
In the past outside of time chapter directly after the way of tea conversation, Cheng Xin reasons that after the broadcast Trisolaris should no longer care about the progress of human technology, as humans aren't their greatest threat anymore.
However, Trisolaris knows that humanity won't shy away from taking revenge on them if given the chance, given that Trisolaris really were the aggressors at every turn of this war. Not blocking human technology is one thing, but if Sophon were to outright give humanity lightspeed technology for the purpose of creating a black domain, there will be nothing stopping humans from exacting revenge. We could just gather an army and launch it at the fleeing Trisolarian fleet, we'll have more than enough time to do that before the solar system's destruction.
Cheng Xin concedes that Trisolaris won't give us tools that could lead to us chasing after them, and in the very next paragraph wonders why they won't share with us the tools we need to create a black domain. In hindsight it's very damning evidence that lightspeed travel is the key for creating a safety notice.
Well maybe more like a bearing coordinate than evidence :).
