The Blue Signal Log is obtained near the end of the “To: The Faint Star”. It’s given to you by Bernard as part of the quest.
This log contains a lie and is the opposite of the Red Signal Log which contains the truth. You can deliver it to Rocky, who was the young man that started this quest by asking you to log into some old records.
For the purpose of this guide, you can pick “The Blue Lie” to deliver the Blue Signal Log.
As far as we know, it doesn’t actually matter which log you give him. The quest will be completed either way and the rewards will be the same too.
You also have no use for the Blue Signal Log if you choose to deliver the red one instead. You can’t give it to any other character in the game, at least currently.