Here are the logs of "last full" and "remaining", as the battery finished charging and hit 100%:

last full capacity: 3781 mAh
remaining capacity: 3183 mAh

last full capacity: 3781 mAh
remaining capacity: 3408 mAh

last full capacity: 3781 mAh
remaining capacity: 3483 mAh

last full capacity: 3781 mAh
remaining capacity: 3589 mAh

last full capacity: 3781 mAh
remaining capacity: 3693 mAh

last full capacity: 3781 mAh
remaining capacity: 3705 mAh

last full capacity: 3781 mAh
remaining capacity: 3715 mAh

last full capacity: 3781 mAh
remaining capacity: 4800 mAh

Battery 0: Full, 100%
Battery 0: design capacity 4800 mAh, last full capacity 3781 mAh = 78%
AC Adapter 0: on-line
Thermal 0: ok, 43.5 degrees C
Cooling 0: Processor 0 of 10

last full capacity: 3781 mAh
remaining capacity: 4800 mAh

As you can see, remaining capacity creeps up towards 3781 and when it hits it, jumps to 4800 which is invalid for an old dead battery. The battery meter in LXDE showed 97/98/99% just fine then jumped to 126% when the bad reading occured, and stayed there forever as long as the AC adapter was plugged in.