Did you mean to delete this demo? If you meant to, then whats the rationale? EDIT: oops, sorry I see it above...

So I guess I'm not sure if we should have every fcn used by every example listed like this... Are you curating this at all?

I'm curating this a bit indeed. But I may have been inconsistent in doing so in some places.
In general I'm aiming at putting those functions/methods classes in the references that are important for the example. E.g. if the example treats some complex histogram plotting, I won't put ax.set_xlabel in the references. If the example aim is to to show some basic plotting, I'm putting the basic functions in. So far I've also tried to make sure there is at least one example for each new method I came accross, so the whole process surely depends a bit on the order of processing the examples - which is admitedly arbitrary.
But there might be cases where I deviated from that strategy - it's always a bit handwavy.

In this particular case I guess the logic was that the example is rather basic and those methods had not been covered previously as far as I remember.

That being said, I guess it's beneficial to be slightly more inclusive with references for now. Later, once all examples have a reference section, the aim would be to inversely go through the docs and see if there are overcrowded gallery sections - in which case one can easily remove some references in those examples, as well as see if there are still methods or classes which do not have an example, but should - in which case one can either add a new example or find an existing one which can be modified.

At the end one benefit of those references will also be to manually check example coverage of the library.

At this point I'm wondering if there is not a way to automate this block of text that is cut and pasted between 52 files here. If we decide the change the heading from "References" to "Methods in this example" we will have to go through all these changes and edit by hand. I'm not familiar enough w/ Sphinx/gallery to know if there is a macro definition possible, but maybe we should check if there is?

As far as I can tell there is no way to manipulate the way sphinx-gallery processes the .py files - other than monkey-patching sphinx-gallery. I took this approach in #11169. However since here we need to change the content of this "Reference" section manually, such approach would be really complicated.

However, I think it should be relatively easy to change the section heading via search&replace (possibly with regex) in case that would be needed in the future.

For the record I have a work in the plans to make this kind of referencing completely automated (using a rewrite from scratch of s-g, as there are a bunch of things I don't like in their design anyways).
(The idea being to inject an AST transformer to transform foo.bar to logged_getattr(foo, "bar") at the AST level, so that I know what is the actual name that needs to be linked at what point in the source.)

@anntzer On what timescale do you plan to do this? In how far should this prevent us from continuing adding the backreferences manually?

I "should" have something by the end of the month.