To core is the Unix equivalent of a Windows application "fatal error" or whatnot. It's not an error, it's a way for whoever wrote the application to get feedback on the state of the app when it crashed, kind of like a picture of the car at the exact moment it died, so mechanics can figure out what it was missing.

In windows, this is done via log dumps, in Unix it's a core dump (saving the memory of the app to disk). An application core dump is the result of an error and, the term got shortened to "to core". As trivia, Windows also dumps core on some components that crash, when the logging mechanism is compromised. E.g., in a kernel crash or a general BSOD and the core is dumped completely (aka all the RAM).

Also, this is probably the most useless post on this thread, since I'm fresh out of ideas. I'm fairly sure it's not the broadcast messages. Mainly, because those flow through all the time and on all phones with no ill effects.

Right now, the only correlation I found is that it cores immediately after plugging it and leaving it alone. If this is repeatable, this might be it. For example, I think phone is locked at a frequency while charging (actually, while in mass storage but it is possible).

Try to get brightness display applet and leave the screen on at low setting (so it won't heat up) overnight when charging. This prevents device sleep - if that fixes it's it's likely sleeping is at fault.

If it still cores, it might be the charger itself - a problem with the SMPSU could fery well put bad, bad juice through the phone and while sane enough to charge battery, might prove too much for an undervolted CPU.

No warning reboots smell like hardware faults.

So:

* does it happen overnight but not in the day?
* does it happen if left on with no auto-TKlock?
* does it happen if left locked but not on charger?

Let's go from here.