Please, check more things.
1. Other wonders that might give science/great people/trade routes.
2. What is exactly doing his religion?
3. You didn't say if he has same number of policies, and what difficulty you are playing on.
4. Did you take too long to go for public schools?
5. Can you say if he has planted academies or has any natural wonder with science yields?
6. What is his monopoly? It's too early for corporations, but monopoly bonuses may give something.
7. Who has more militaristic CS allied?
8. Has he got many friends that could sign research agreements?
If he is focusing on great people, and has fewer cities, it is quite posible that his tech progress is faster than yours. And if his total population is smaller, then I'd swear that Pachacuti is focusing heavily on great people. Quite probably, his military cap is smaller.
and don't forget inca has got a mountain bias
which mean that his observatories give him a high amount of science.
Moreover the mountain are super science/gold tiles for inca only
Great questions:
2. He has 19 cities in his, I have 36 in mine:Theocratic Rule/Cooperation/Pagodas/
Sainthood +
Jesuit Education vs Apostolic/Churches/
Mastery/Pacifism, +TGoG.
3. Playing on Emperor, same number of policies (3 in Rationalism).
4. I don't think I took too long going for PS, but the point is he's pulling awa now, when I have them.
5. I don't see any academies with my diplomat -- mostly mountains and water.
6. Too early for corporations.
7. He has 2 allies, both militaristic.I have 1 -- and 10 overall vs his 2.
8. He has no Friends.
* He has no observatories -- I have x. But he is getting science and faith from mountains.
** He has a Military Academy in the capital.
More facts: Cusco is putting out 183 science; carthage is putting out 250. But in raw science (InfoAddict) he leads 1502 to 957 -- even though I'm in a GA. (He might be, too -- I don't know.) He has a mosque and pagodas, and got Sankore as well as Himeji (no Oxford). Again, I had Halicarnassus, Porcelain Tower, no friends, Oxford, Oracle.
Let's say all 10 of his cities have a Mil. Academy, but no observatories. 10 cities means 100 beakers.
Sainthood from 9 foreign cities (say average size 25) gives him another 20 or so.
Jes. Education, if he has uni's and PS's in all 10 cities, gives him 100.
I have a PS in 9 cities, uni's in all. I also have Mastery. That's 13 libraries and uni's, plus 9 PS: 70.
And, during a GA for me, he is putting out 1502 science vs my 957. We accounted for over 220 above, minus 70 Mastery -- a lead of about 150.
Aso, I was wrong about pop: he has 100 vs my 74.
Would that pop edge in 3 less cities, plus Tradition, Pagodas and mountains, give him an additional 400 or so beakers?