On the iPhone under the Settings > General > About > Diagnostics & Usage Data > log aggregated, what does this mean?
Does it mean the number of text sent or received or both?
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It means that that program (the SMS application) was started 9 times on that day.
Whether that corresponds to someone checking the app in response to a message or simply entering the app isn't logged in that file. I don't know offhand if you can reconstruct that level of detail from any of the standard logs on iOS so you may need a forensic analysis of either the database the SMS app uses or the network / server side of things to track down delivery times or even something as detailed as a daily count of SMS messages.