Dating
Four months in, you know her apartment, her coffee order, and her work schedule. You don't know any of her friends. You haven't met her family. You don't appear on her social media. When you mention wanting to meet people in her life sometime, she's warm and vague. A few days later she goes to a birthday party without mentioning it.
You're not sure if you're her boyfriend or her secret.
The game
Introducing you to her social circle costs her something. It creates accountability. Her friends know about you, exits become complicated, the relationship acquires weight that's harder to put down. It signals that this is real.
Not introducing you preserves her options. She gets the benefits of the relationship (companionship, intimacy, someone to spend time with) without paying the social cost of commitment. You're available when she wants you. Nobody in her life knows to ask about you when she doesn't.
The equilibrium
The stash works because it's gradual. In the early weeks, not meeting anyone is normal. By the time the absence is notable, you're invested enough to make excuses for it. She's busy. The timing hasn't been right. It'll happen soon.
The situation is stable as long as you keep waiting. She has little incentive to change it. Integration would cost her flexibility and she's currently paying nothing for the arrangement.
Dominated strategies
Waiting for a natural moment to be introduced is the dominated strategy. The natural moment doesn't arrive on its own. If it were going to, it already would have.
Ask directly. Not as an ultimatum, but as a simple question: why haven't you met anyone in her life? The answer will tell you whether you have a relationship or a stash. Most people can't answer that question and maintain the ambiguity at the same time.