CRUD
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CRUD refers to the ability to Create, Read, Update and Delete comments and posts. Also referred to specifically as "comment CRUD" or possibly "webmention CRUD".
There are also notions of POSSE CRUD and reply-context CRUD
Why
If you post a reply to another post, and possibly later update it or delete it, you should implement CRUD by sending (another) webmention to the post you've replied to so it can create, make available for reading, update, and possibly delete your comment inline on the original post.
If you support receiving webmentions and displaying comments, you should implement CRUD to enable commenters to edit and delete their comments.
How to
Create
Read
Update
Delete
IndieWeb Examples
IndieWeb Examples of people and their sites (and software) that support automatically updating and/or deleting their replies to others' posts, and/or receiving updates and delete webmentions from replies and updating the comments/interactions on their posts accordingly.
Kyle Mahan
Kyle Mahan uses RedWind which supports receiving Update webmentions on kylewm.com since at least 2014-12-15. E.g. the first comment from 
Ben Roberts was updated automatically on kylewm's site when it received a second webmention:
- https://kylewm.com/2014/12/signed-up-for-huffduffer-loving-the-quietly-magic
- note that Ben's reply POSSE tweet has the uncorrected first version of his reply to Kyle.