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I will just try to answer the question as logical as I can, going from the code:
In the code the mentioned trigger is "core_percentage", obsiously the only thing counting against "core_percentage" are provinces that are not distand overseas. This most likely means that distant overseas provinces are ignored alltogether.

Its quite easy to test: Just play as holland on very easy, cheat lots upon lots of colonists and gold and just go bonkers with colonizing in the new world, cheat yourself some cores there and move your capital overseas, just make sure you have the right conditions.
 
Yes, core_percentage only considers non-overseas provinces.
The separate num_of_cities conditions would count all provinces.

EDIT: core_percentage was tested while investigating ANO1453's bug report.
 
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Are you really sure of this, or did you just do something like having 10 colonies as Navarra? You need to keep in mind that there is a minimum amount of cities needed for overextension to even be possible.

And i doubt you will get an answer to your original question, so you will have to test it yourself. Usually, people expect the code to be true, and while there might be some rare cases where it is not, in the overwhelming majority of situations it is. So if you assume it isn't, you should do some accurate testing to prove that. This means not just some thing you remember from a game you played half a year ago, but where you can't find the safegame.
I am sure. I even filed a bug report over it, and I was assured they don't count.
 
I'm playing as Cherokee and I recently opened up Andalucia as a market. I monopolized it, but am getting 5 ducats/year for it (the CoT value is 900). For comparison, I have a monopoly on Mexico, which is ~650 in value and I am getting 60 ducats a year from that. Is this just a matter of time or is there a penalty on overseas markets?
 
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I'm playing as one of the Japanese daimyos, and i have a mission to recruit a trader, but that options is greyed out on the culture screen. What are the requirements to recruit a trader?
 
I'm playing as Cherokee and I recently opened up Andalucia as a market. I monopolized it, but am getting 5 ducats/year for it (the CoT value is 900). For comparison, I have a monopoly on Mexico, which is ~650 in value and I am getting 60 ducats a year from that. Is this just a matter of time or is there a penalty on overseas markets?

The number is only updated at the beginning of the month so when you first monopolize it the number will be wrong.

It is also not unlikely that there are fewer than maximum traders in Mexico (depending on your game settings) so you are getting a higher % there...
 
I'm playing as one of the Japanese daimyos, and i have a mission to recruit a trader, but that options is greyed out on the culture screen. What are the requirements to recruit a trader?

You have to have at least some navy tradition, I think 5% but it might be lower than that, as well as cultural tradition.
 
That sucks. How am i supposed to get naval tradition when i'm a japanese daimyo and the only other surviving daimyo is in a personal union with me? My cultural tradition is practially always 100% at least.
 
I have another question. What factors determine whether or not you will inherit in a personal union? I keep seeing it say i will inherit upon ruler death and then at some random point later it turns to "the personal union will contiue". My prestige and relation with them are only getting better so its very confusing why the personal union result is getting worse.
 
That sucks. How am i supposed to get naval tradition when i'm a japanese daimyo and the only other surviving daimyo is in a personal union with me? My cultural tradition is practially always 100% at least.

You could hire an advisor (Naval Reformer sounds right) or build a Naval College with the right tech. Unfortunately, that's your only real option without fighting.

I have another question. What factors determine whether or not you will inherit in a personal union? I keep seeing it say i will inherit upon ruler death and then at some random point later it turns to "the personal union will contiue". My prestige and relation with them are only getting better so its very confusing why the personal union result is getting worse.

The tooltip is wrong. There's no real science to inheriting PUs; sometimes it happens and sometimes it doesn't. You have to stay out of wars if you think your leader might die; you can't inherit during a war. Other than that? It's kind of a mystery.
 
That sucks. How am i supposed to get naval tradition when i'm a japanese daimyo and the only other surviving daimyo is in a personal union with me? My cultural tradition is practially always 100% at least.

Depending on how far you are willing to go, you also get a small amount of naval tradition when building ships and for exploring uncharted seazones.
 
I have another question. What factors determine whether or not you will inherit in a personal union? I keep seeing it say i will inherit upon ruler death and then at some random point later it turns to "the personal union will contiue". My prestige and relation with them are only getting better so its very confusing why the personal union result is getting worse.

Random die roll but the following factors do influence the chances (there may well be other factors):

1) number of provinces-you will never inherit a nation that owns more provinces than you
2) is the junior partner at war?-you will never inherit a nation that is at war (you can inherit while you are at war, they cannot be)
3) diplomacy value of the heir
4) relative prestige levels
5) your legitimacy
6) your infamy

Relations between the two nations do not appear to affect the chance to inherit with the caveat that you must not have negative relations as the union will break in that case 100% of the time
 
Random die roll but the following factors do influence the chances (there may well be other factors):

1) number of provinces-you will never inherit a nation that owns more provinces than you
...

actually I did inherit a 3 province Hesse as OPM Burbonnais not long ago so are You sure about this one?
 
I'm playing as Cherokee and have westernized and keep getting into wars with the european powers. Why is it that whenever I annihilate their armies (I have killed a good 100K of troops in the last war), this does not get added to the warscore? Neither do they get any WE, even though they run around my country getting attrition and then getting owned. by my technologically superior troops. Yet despite the fact that I keep occupying all of their colonies, annihilating every invasion on my American territory, their stupid couple of ships blockading my ports are enough to bring the warscore in their favor. What the heck?
 
What difficulty are you playing on? On higher difficulties, AI is pretty much immune to WE. Warscore is not really important, and if you are already technically superior, just build a few ships and smash their small blockading fleets one by one. You will not get lasting peace until you are significantly stronger then them, and pretty much the only way to get a good peace out of them is usually invading europe. Once you can keep your costs clear, they are not really doing anything to you anymore even if you are at war, and you can maybe even get a few colonies of them without invading europe once the war takes long enough, but building up a good fleet should always be your goal.
 
What difficulty are you playing on? On higher difficulties, AI is pretty much immune to WE. Warscore is not really important, and if you are already technically superior, just build a few ships and smash their small blockading fleets one by one. You will not get lasting peace until you are significantly stronger then them, and pretty much the only way to get a good peace out of them is usually invading europe. Once you can keep your costs clear, they are not really doing anything to you anymore even if you are at war, and you can maybe even get a few colonies of them without invading europe once the war takes long enough, but building up a good fleet should always be your goal.

Ah, that's what it is. I'm playing on very hard. Yea I'm in the process of building ships, but it takes time and when I'm at war with all the major European naval powers it's a bit hard to take them all on. But yea, that makes sense, thanks :)