So…
Because I assumed that I was doing something wrong, I thought that I would start again from scratch with a test site. I followed these steps:
1. Install WordPress
2. Upload Genesis 2.1.2
3. Upload and activate Epik 1.4
4. Set permalinks to “Day and name”
5. Add widgets to Welcome Feature #1, #2 and #3
6. Add page “Home”, with Template “Home”
7. Add page “Blog”, with Template “Blog”
At this point the home and blog pages work as expected.
8. Change “Reading settings” to “A static page” using “Home” and “Blog” for the “Front” and “Posts” page, respectively.
At this point the home page works as expected, but the blog page is also widgetised:
http://epik.royaltenniscourt.com
http://epik.royaltenniscourt.com/blog/
I can’t describe or reproduce it any more simply than that, and I can’t see what is wrong with step 8 (or any of the others).
Does this mean that the WP static page option is not compatible with Epik?
If that is the case then I can’t (easily) add the Jetpack sharing to the home page because, with a non-static home page, the sharing code thinks that the blog page is current.
