Negotiation doesn't just happen in the room. Negotiation is heavily affected by what you do before you enter the room. Someone who is, for example, looking at multiple offers and who wants a high salary is going to "negotiate" a better salary than someone who has only one offer -- not because of some magical skills of course.

https://en.wikipedia.org/wiki/Search_theory

It's possible that society better equips men for job searching in general, and too much focus is placed on the very moment of agreeing to a salary.

Negotiation starts from a base point though. It is exceptionally difficult to right a lifetime of wrong. By that I mean, women with work experience have lower salaries from the get go and when negotiating for pay at a new employer she starts with a lower pay history than males. Most employers will not jump a salary from say $78,000 to $100,000 AND most women are fearful of pricing themselves out by asking for such a jump. For those who will ask will rarely get the salary they deserve but may make up a little ground is they have been underpaid for an extended period of time.

True, but it could support the idea that women don't negotiate for promotions as well or as often. Or that they are less likely to be promoted in general, for whatever reason. Whether the underlying reason is innate personality, socially-conditioned personality, or sexism, this seems like the simplest explanation for why the pay gap looks the way it does.

That definitely seems possible. I have also read some interesting stuff around how women tend to end up a few years behind their male counterparts due to child care, maternity leave, and them choosing not to take less demanding positions to spend more time with kids. There is a lot in there to unpack and you could still argue it is a societal discrimination thing (women are expected to do more child care duties), but that is not an argument supporting pay discrimination at a corporate level, but more of a societal shift that has to happen between child rearing partners. I don't know if this matches up with data and studies, but just logically, it is inevitable for a woman to have to take at least a little more time out than a man due to the biology of child birth and child rearing.

I think all of this points to women not attaining the same rank/position as the key factor in gender differences, not a discriminatory pay gap.

my wife does not know how to negotiate, multiple times have i said to her that she should fight for more, but she will not or does not know how to do it.

but there is also another side. women that i have worked with have used social norms to ask for more. like in some conversation make a joke about how they deserve promotion and pay incrase, like hehe im such a great team member/worker i deserve a pay incrase, wink wink, and such comments multiple times. I never heard a man use this method. If its from a man then he asks to speak to you and directly says what he wants.

No, not really. At lower grades, salaries are often not negotiated. At the higher grades where you see the differences they are.

So the data from the article corroborates that idea.