Dr.PathRoch said:

Keep the original post as written when you update it, and add the correction underneath.

Filing a mild objection. Mild because I might be wrong; an objection because nobody has addressed the case that does not fit. I would resist the confidence. Half of what this board was certain about two years ago has since been quietly dropped, and nobody went back to correct the threads.

Happy to go further on any of that.

Dr.PathRoch said:

Keep the original post as written when you update it, and add the correction underneath.

That is right, and it stops being right at the edges. The general case is well behaved; the interesting cases in this thread are all at the boundary where the general case breaks.

Happy to go further on any of that.

Dr.PathRoch said:

Keep the original post as written when you update it, and add the correction underneath.

Saving this. It is the first explanation that did not require me to already understand it. Printing the relevant bit and taking it with me.

Adding the clinical framing, because it changes how the question reads. It is worth asking what the claim would look like if it were false. If nothing would look different, it is not a claim about the world and no amount of discussion will settle it.

sophie_paris said:

It is worth asking what the claim would look like if it were false.

Same pattern here, and in the same order. Nothing to add that would improve it.