So I'm still a little fuzzy on how technology works. (I did read the wikia entry). So, each county has its own level for each tech category. For some techs, the effects make obvious sense, for example Religious Customs grants an opinion bonus for the Bishop holding any given Church in that county. But for other techs, I'm not sure how to interpret the benefit... like with Siege Equipment, the bonus is to Siege Speed... is that applied to the troops raised from that county, or is it applied in some other way? Or is only the capital county's improved speed applied to your troops, but to all of them? Seems it would be the former.
The other question then is about advancing technology. Does the focus apply to all counties, or only to your capital county? The hint screen in the game implies that it only applies to advances in your capital, but the tooltip for the focus button just says it increases the chances of advancing the tech. So where does the focus apply? And if it applies only to your capital, then is it a better strategy to set a focus, set an advisor in your capital, then once you get the level up it will hopefully spread more easily from there to your other counties by virtue of being neighboring (and/or moving the advisor along to help the spread as well)?