Listing ORCiD in LaTeX papers The ORCiD unique author identifier, run by a non-profit organisation, has been around for a number of years now. Its stated goal is to become a de facto standard for uniquely identifying authors, even in cases where they have non-unique names, have changed their name, or have had their name appear in different variants on different publications. A large number of organisations, including the American Mathematical Society, have signed up to the system. (However, integration with MathSciNet has not happened so far.) 
At the moment, users maintain their own record manually, but there is a possibility that papers would eventually be added automatically to a record as they appear, as the functionality of publishers automatically updating records has recently been implemented. According to this link, the metadata provided by publishers to Crossref for assigning a DOI includes ORCiD identifiers, and Crossref will at some point start to automatically update corresponding the records of those users who have permitted this. 
However, this raises the question of how the ORCiD identifier is provided to the publisher in the first place. So far my experience has been that few journals have the option of including such an identifier either at submission or acceptance. (Of course, this may change with recent developments). At some point, I saw some advice - which unfortunately I am now unable to locate - to routinely list your ORCiD within the text of the paper. I wonder what the best way of doing so would be. 

Question. Is there by now an accepted way (in mathematics) of including an ORCiD as part of the author information, say when using LaTeX with the amsart article class? If so, what is it?

I would also be interested to hear whether this would actually be worthwhile: 

Is there any evidence that journals, as part of their processing, will pick up on ORCiD identifiers listed in papers and pass these on automatically as part of the metadata?

Nb. While my main question concerns LaTeX usage, I feel that it is not primarily a technical question, but rather one concerning academic practice, and specifically within mathematics. Hence mathoverflow seems an appropriate place for it, rather than tex.stackexchange or academiae.stackexchange. But of course if others disagree I am open to migrating.

(The lead-in to this question has been edited to be more factual, removing some of my personal opinions on the identifier system that may be irrelevant.)
 A: I recently had a paper accepted where I included the ORCiD in the address field of the LaTeX code, as suggested in my comment to Carlo's answer. The publisher did not ask me for any form-based entry as part of the publication process.
The publisher (Springer) did automatically recognise the ORCiD identifier from this and included it in the metadata. IIRC the paper was automatically added to my ORCiD record by Crossref upon publication as a result.
This may not be representative of other publishers, but I do conclude that it is a good idea to include an ORCiD in the address field, and that there is evidence that this is picked up as part of the publication process.
A: Several publishers (Wiley, Elsevier, Hindawi, more are listed here) allow you to attach your manuscript to your ORCID ID. Like other metadata, this ID is entered in a form at the submission stage, it is not part of the LaTeX code (which in most cases is converted to XML right away). The typical workflow is explained here.
If your manuscript is in MS Word, you can include the ORCID ID in the author list and the conversion to XML will pick it up (as explained here). I am not aware of a LaTeX implementation with the same functionality.
So I would say the answer to your first question is that form-based entry is presently the accepted way to tell a publisher about your ORCID ID, and the answer to your second question is "no".
