In the attached screenshot, I see that the AI has constructed 3 industry and 1 science at Celaeno. But in the empire view, it still has the original 30/30/4 of the starting position, so it didn’t have those built last tick? That suggests to me that I’m seeing infrastructure in the same tick that it was built…
Note that if it built 3 industry last tick, there would be 11 ships (not the initial 10) at the star, since 3 industry will produce 1.13 ships/tick.
I don’t know if this has anything to do with the fact that this screenshot was taken in tick 48, and the player went AI in tick 47 (according to the event log). I’ve never seen this before. I checked with another player, and he can’t see my current builds, so it’s not a general info leakage.
(BTW, I’ve also noticed that my carrier counts don’t visibly increase until the turn runs, even though the econ/ind/sci numbers update as I build.)
On your screenshot, Yellow human player icookbabys never changed any orders into his empire, because he never breathed for 47 ticks.
Each star began with 10 ships. Each empire began with 6 stars. At tick 48, empire yellow circle has 600 ships = ( 6 stars ) * 10 ships + 30 IND * ( 5 + manuf tech 1 ) / ( 16 ticks per production ) * 48 ticks. All of this happened on sequence of events step 3, which is before step 8 when AI bought infrastructure.