2025-293

The Galactic Federation maintains an interplanetary communication network connecting \(N = 1000\) colonies through hyperspace routes. Scientists from the Central Observatory have estimated:

\(\langle k \rangle = 4\), \(\langle k^2 \rangle = 100\)

During a cosmic particle storm, 800 colonies lost communication with the network.  Does the Galactic Federation’s network still maintain a giant component or has it collapsed?

1. The network remains connected, since the critical threshold is \(f_c = 0.96\).
2. The network has collapsed, since the critical threshold is \(f_c = 0.96\).
3. Communication has collapsed, since the critical threshold is \(f_c = 0.67\).
4. Communication is still possible, since the critical threshold is \(f_c = 0.67\).
5. None of the above

Original idea by: Aline Azevedo