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Stardate: 49373.4
Captain’s log. After mining some super-special dilithium that can handle higher warp frequencies, Torres, Kim, and Paris start tinkering with a transwarp drive that can hit warp ten, a theoretical impossibility, but which would enable them to get home in an instant since it’s, in essence, infinite velocity.
The problem is, every simulation they’ve run on the holodeck has failed. Talking with Neelix in the mess hall actually prompts an idea on how to fix the problem, though Neelix himself didn’t understand a word they said.
Their simulation works once they make that fix, and they put it to Janeway and Chakotay to move on to a practical test. Everyone is thrilled at the notion, and they get to work.