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And also don't underestimate the advantage of being behind in science. The AI researches these new technologies with a penalty, when they're an era behind that tech level. The other way around you're getting a cost reduction, if you research techs, that are outdated. That said it's not that bad to have some AI civs being ahead of you until the mid game, so that you can research many things faster, than the AI did.
"batteries"? If you have a resource called batteries in your game, it sounds like you are playing modded, and any potential issues become almost impossible to identify since mods can easily break the game in any number of ways.
For example: Does the AI cheat in science? We have no idea how much cheating the AI does or does not do in science when playing with your mods.
If you have just one mod then you could try asking the mod's author on the workshop page for that mod.
There has been a relatively recent change in the willingness of the AI to use special projects, including the science special project. That can have an impact on how quickly the AI is able to work through the tech tree, and also on how many great scientists they will earn. It can also be difficult to know how much of an impact that has had. For example, if you have twice the science output of an AI civ on turn 200, there's no way to know what amount of science output either of you has had in the earlier 199 turns. Perhaps the AI has been running a lot of science projects for the majority of the game, and actually has had an average science output that was nearly twice your average for that entire time, resulting in a tech lead over you. Then, on turn 200 it just so happens that the AI does not have any science projects running, and so its science output is deceptively low.
So, even if you were not using any mods, it would be impossible for us to conclude that the situation you have described meant that the AI was cheating at science. If we discount the expected cheating associated with difficulty level, the more likely explanation is that over the course of the game the AI has gotten more boosts and maintained a higher average level of science output, and so deserves to be ahead in tech. Your higher science now could be a sign that you are on the road to catching up, or it could be a clue that the AI is using projects to stay ahead of you.
Thanks again.