It's maybe an old thread but I wanted to give my contribution and some food for thought. I wanted to know how you wanted to do your tech progress, so I went on reddit and this is I think (correct me If I am wrong) how you want it in general terms :
-Pop Based discoveries and spread
-Multiples ways to achieve it
-A little like Victoria 2 (probabilities each month to discover a technology)
So I went to try to conceive a simple system to test some thing. It is mainly based on the pops stats which can be influenced in multiple ways, but here is the base :
Numbers : Numbers of pops
Culture : Determine cultural bonus and penalties
Species: Some species have it easier than others
(Un)Hapiness: Self-explanatory
Job/Function: A farmer and a merchant will not have the same free time nor interest in developing the same tech.
Others factors like the Tile environment, Infrastructure, Species Interaction, Desperation or already discovered tech can be accounted, But I didn't to make it too complicate to begin with. I think this is the bare minimum in order to have a good spreading and tech progress, so after some testing to make it somewhat realistic, the equation is like this :
X = (N/1000000+C+S+H+J)/100
With X being the base chance of breakthrough/spread of a Tech. (N = Numbers, C= Culture, S= Species, H= Happiness, J=Job/Function)
N is divided by a million because otherwise it will be too fast to research tech and all of this equation is divided by 100 for the same reason. (Of course you could tweak to make it simpler I guess, but I'm no mathematician so I worked with that).
So let's say your pops want to have a basic wood spear, it could go like this.
You need one simple discoveries to achieve it :
-Find a solid branch and carve it in a deadly spear : base chance of 1
See it like a reverse Victoria 2 tech, your pops need to research the discoveries before they got the tech. Since it's a simple object, the base chance is high enough to achieve it rather quickly and there is only one discovery. So lets say that X = 0.01 and that we have monthly research tick like in Vicky 2.
0.01 or 1% is the probability, you got it, it's quite low, but as soon as the months passes, the chance of you researching it increase tremendously.
In one year there is 11% of chance you research it.
in ten year there is 66% of chance you research it.
In fourty year there is 99 % of chance you research it.
So after this pops discover it, this technology will slowly begin to spread to your adjacents pops, they will have a good bonus, since this knowledge is knowed not far from them. Adding in the equation an infrastructure/adjacency variable would simulate it in practice.
The thing is I really don't know how you are gonna make it, it's just an idea I tried to have some kind of "base" to talk about since you didn't get too much into the details. The last thing I would add is since I've got no experience in development, I really don't know If this concept of mine will work out in terms of performance or objectives you fixed. I hope it helped you nevertheless.