Understanding what happened on your phone at a particular time can be challenging, especially when it comes to something like a sent SMS message. Android doesn't have built-in detailed logs that would provide this level of information for user-level events.

The adb shell dumpsys command you're using can provide a lot of information about the system, but it doesn't usually include a detailed log of all user-level events like sending SMS messages.

The Android system does have logs (logcat) that could potentially include this information, but these logs are not persistent -- they're stored in a circular buffer that only holds a certain amount of data and older information is lost as new data comes in. Unless you had been continuously saving these logs to a file at the time of the event, the information about what happened at that specific time has likely been overwritten by now.

If you have root access on your device, there are some more options available -- for example, there may be detailed SMS database files or logs that you can access. However, these typically aren't accessible on non-rooted devices due to Android's security model.

If you have concerns about the security of your device (for example, if you think the SMS message may have been sent by malware), one option would be to use an antivirus app to scan your device. Most major antivirus companies offer Android apps, and these can detect and remove many types of malware.

Finally, it's worth noting that sometimes mobile providers' records can have errors or discrepancies. It's not common, but it does happen. If you're sure that you didn't send the message and can't find any evidence of it on your device, it may be worth contacting your mobile provider to ask about it.