Why act so childishly? Just give us some specific examples.
Interesting.
What we can show is that Riemannian geometry accurately predicts the precession in planetary orbits while Newton's model using Euclidean geometry did not. Therefore, we don't need to assume. We have the test showing that one is better than the other.
Yes, Riemannian geometry better predicts precession. But what happens when the model that best predicts case A is not the one that best predicts case B? That is the reason I included the GR/QM example.
That is not a measurement. The measurements are the data points. Whether those data points fall into a Guassian curve or not has nothing to do with the ability to measure those data points.
Is that a concession of the point (even though you think it an irrelevant point)? I don't think it's irrelevant, and I explained why. Suppose I measure a parameter and obtain a value of 3.2. My assumed Gaussian model tells me the noise is 0.2. So, I conclude the "actual" value of the parameter is 3.0. That's an oversimplification of the math, but I did it for the sake of the example.
So, what is the "measurement"? IMO it's 3.2. But do I use that number? No. The number I use (3.0) is based on the Gaussian assumption.
But you don't like that example.
In fact, I have already cited numerous papers that test the very things you claim are assumptions. I see that you chose to ignore them. Why is that?
Did you read the full text of the sources I cited? If so, then I'll admit you're one up on me. I skimmed(*). If you didn't read them, I don't understand why you're expecting me to do that. My experience in the past has been that people refuse to read an entire text that I cite. The pace of the conversation makes that unrealistic, it's too difficult to read 10s or 100s of pages and know what message one is supposed to extract from the source, etc.
I can understand that. Do you? It's the reason I quoted the specific passage that made my point. So, if you would do the same, it would help the conversation along.
Or, if you want me to try offering another example - one that you might think is closer to a discussion of "actual measurement" - I'll suggest acceleration. Are you familiar with accelerometers?
[edit] (*) And after skimming (not ignoring) I replied that they didn't seem to address my point.