I really don't think we're disagreeing.

You're just saying, very clearly: Our observational data does not match our mathematical models for gravity, and our alternative models don't account for this case (bullet cluster)

I'm not disagreeing with you, and I'm not proposing MOND or derivatives are a valid solution, I'm just saying that you're still just positing:

"we saw thing X that doesn't work with our current model, or with our modified model, so there must be some mysterious "dark" matter that we have to add to bring our math back to matching what we observe."

So far, though - no experiment to actually find or record it, or make valid guesses about how or why it's distributed from a theoretical view, rather than as "glue" to hold our model back together, has been found (at least that I'm aware of).

So I guess I am disagreeing - It's not "directly observed" in any sense other than "something is wrong here and we can't explain why".

The "something" that "is wrong here" though is not merely a mathematical inconsistency in the amount of force or speed you expect. That may have been true when dark matter was first proposed as a solution for the weird spinning behavior of galaxies in 1933, but not so any more.

Dark matter is an actual physical reality that you can see with your normal human eyeballs in a photograph. The light emitting stuff is in one part of the picture, and the gravity causing stuff is in another part of the picture. You can see it with your own eyes. The bulk of the gravity of galaxies is separable from the bulk of its visible matter.

Dark Matter is the class of hypotheses that explains this plain observational reality by supposing some kind of invisible matter, which is the only explanation that fits what the photographs show.

Any attempt to discredit it must be accompanied with an alternative explanation of how the gravitational mass of galaxies seems to be removable from their visible material.

This article is like denying that the sun exists, without positing an alternative for where daylight comes from.

> It's not "directly observed" in any sense other than "something is wrong here and we can't explain why".

That's not disagreeing, that's literally an observation, in this case via photons coming from things we can see possibly interacting with things we can't. That's as direct an observation as you're going to get for most things in the universe.

> That's as direct an observation as you're going to get for most things in the universe.

It is decidedly not. It's a clear sign that points at "Our models don't work well here", but simply noting that we're seeing an unexpected result is FAR different than being able to declare "we have observed dark matter".

Basically - if you're saying that the bullet cluster is good evidence against MOND, welp... we agree.

If you're saying the bullet cluster is direct observation of dark matter... I don't agree at all. It's just proof that both models are broken for the cases where we see galactic collisions. The fact that you can wallpaper over this in models with dark matter is... the point of dark matter in the first place: A handy escape hatch for cases like this.