1969 Dodge Dart Engine Stutter

So I gave the dart a jump and took some measurements after I removed the jump cables. The battery was so dead that the engine wasn't even turning over.

The battery was reading 12.90 volts after jump and dropped slowly to 12.60. Shortly thereafter the car stalled and died.
The alternator was reading 12.61 volts.

I am going to charge the battery overnight and get the readings again tomorrow. But, if these numbers are correct then it would be the alternator is not putting out enough voltage to charge the battery. Right?

Thoughts?