I got a notification email that stated:

The following items were added to your inbox since you last checked it on 2015-04-19:

I know that is not true given that I have been checking it all throughout the year.

Here is the screenshot of http://stackexchange.com before clicking on the red "2" here:

stackexchange.com screenshot

So I am considering this as a bug, as the expected behavior is that notifications are sent, but not with the incorrect dates as to when I have checked the inbox.

Here are some of the email headers from the message. See the Date field for when this was received:

From: Stack Exchange <do-not-reply@stackexchange.com>
To: do-not-reply@stackexchange.com
Reply-To: do-not-reply@stackexchange.com
Subject: 2 new items in your Stack Exchange inbox
Date: Sun, 04 Dec 2016 03:12:49 +0000
Message-ID: <2.615c3af0158722959802@NY-WEB05>

Here is a screenshot of the gmail interface view of the message:

gmail inbox screenshot

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