After a period of inactivity your session is removed even if you don't log out, and the dotted lines show up under posts that were posted since that logout time.
Sozobe mentioned read tracking on top of this, where if you do visit a thread it won't have the new indicator anymore unless it's posted to again, but that doesn't yet work here. I think it's the single biggest usability drawback on the new software, even if few realize it and it'll eventually work the way it used to on the previous software.
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