When do new buildings from research appear?

Solution 1:

Looking at the code, in buildings.js, there is the following:

var res = this.game.resPool.get(price.name);
if (res.value < price.val * unlockRatio){
    isEnabled = false;
    break;
}

Thus, to unlock a building, you need at least unlockRatio of each resource that is used in building it. The default is to require 30% of the cost of a building, with only one building having a non-default value.

For those looking to know, the religion-related Ziggurat is the one with non-default unlockRatio. It's set to 5%, partly so you don't need a ton of Megaliths before you ever know what they're good for; building a handful to see if they do anything is generally enough.

Building your first Academy will cost 50 Wood, 70 Minerals, and 100 Science, so you should only need 15 Wood, 21 Minerals, and 30 Science to unlock them. Mines should unlock once you have 30 Wood, and Pastures would have appeared once you had 30 Catnip and 3 Wood.