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"Who knows? Maybe it really is just a messenger. But it's here to give humanity a different message," Ding Yi said, turning his gaze away from the droplet.

"What?"

"If I destroy you, what business is it of yours?"

The words were followed by a momentary silence as the three other members of the expeditionary team and the million members of the combined fleet ruminated over their meaning. Then, all of a sudden, Ding Yi said, "Run." The word was uttered softly, but then he raised his hands and shouted hoarsely, "Stupid children. Run!"

"Run where?" Xizi asked in fright.

Just seconds after Ding Yi, the lieutenant colonel realized the truth. Like Ding Yi, he shouted desperately: "The fleet! Evacuate the fleet!"

All they had deduced is that:

the probe had decelerated in the solar system, and that its surface was at absolute zero.

Did they simply mentally exhaust the other potential reasons for its behaviour?

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    -1 For gratuitous use of spoiler tags.
    – Lexible
    Feb 29 '20 at 17:03
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I don't think the thought process is explicit in the novels. They had deduced that the droplet was made of strong interaction material:

The droplet wasn’t fragile like a tear. Entirely the opposite: Its strength was a hundred times greater than the sturdiest material in the Solar System. All known substances were as fragile as paper by comparison. It could pass through the Earth like a bullet through cheese

They also knew the previous interactions with the Trisolarans; they had previously believed that they would surrender because humanity had an advantage over them, but realising that the droplets were in fact significantly in advance of Earth science and capable of being weapons, deduced that they were there to fight.

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  • > they had previously believed that they would surrender because humanity had an advantage over them I forgot about the emphasis give to this point, great answer, thanks. Feb 29 '20 at 22:53

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