I really feel like we've already explained this to you a couple threads ago, but I'll give you another chance:
basically, population = science. You get one science per person in your empire before modifiers. The only exceptions are specialists, and occasionally tile yields but population remains the biggest factor by far. Since wide empires tend to reach higher total populations than small empires they do BETTER on science, not WORSE provided you actually develop your cities and don't leave them as crappy 1-2 pop with no science buildings. So yes, wide AI do good at science. They aren't cheating other than having some perks that make happiness easier on them (aka it is easier on them to GO wide). Going wider results in better science provided you can develop those cities.
Now, what you may have heard is that each city has a science penalty. This is true, but I've found the penalty to be paltry most of the game. On standard: 5% increase in base tech cost, On large: 4%, on huge (best for wide and what I play) only 3%. This sounds bad until you realize most of the game the base science cost on techs is tiny. In the beginning techs cost very little (30-100 beakers). What is 5% of 50 science? only 2.5 science How many turns do you typically work on a tech? Let's say 8 to be generous. so 2.5/8 = 0.3 beakers. So in the ancient era, a city will overcome the science penalty just by being founded with population 1. The penalty worsens as techs cost more, but you also have tools to make your cities grow faster and more buildings to increase the base science yield (library, university, public school, observatory, research lab) . So basically, cities are worth it most of the game and will often be producing more science then they cost you just 10-20 turns later. The exception might be the atomic and information eras as tech costs are quite large and the city probably won't produce more than the penalty they cause until after the game will end via science victory.
A good rule of thumb that I use is I just build all the cities I can until about mid-industrial era. I've found any cities built after this time take a bit longer to overcome the penalty and often require a trade route and a lot of gold-buying of buildings as there are so many different ones starting around this time. If you put a lot of effort into growing them you could probably make them science positive even if they were founded in the Modern Era before the game ends, but it takes a lot of effort and gold and you lose science for a while so cities in the modern are probably just break-even--in my opinion not worth it. Save the gold for spaceship factories or CS's.
So there's the low-down. You're welcome to do whatever you want, and probably won't respond to this, but this is how the science penalty works, and as I said, it is very tiny. New cities are worth it most of the game. The bigger issue is happiness which the AI do cheat on a bit, however, they also aren't as effective at getting alternate sources so just do a lot of lux trading and go for the appropriate tenets for wide and you'll be fine. I found Order to be the best ideology for late-game settling. You can pick a policy that starts you off at 4 population automatically, and get extra smileys out of science and production buildings which you'll be building anyway. It results in about 7-8 extra happiness per city potentially.
Happy empire building!