X2 every machine has a weak point and on our bikes (VN750) the stator is the weakest link. Just like a car alternator but a major job to replace.If its only getting 12V at 4,000 rpm, then the charging system is messed up. Possibly requiring a new stator, which requires the engine to be pulled from the frame to replace.
Seeing the voltage rise smoothly and consistently with every 1,000 rpm rise in engine speed is an ideal situation. My bike does not exhibit this ideal, but stays charged up none the less, and does not require use of a battery charger through the riding season, (unless I do something stupid, like forgetting to turn the key off after working on it. )X2 every machine has a weak point and on our bikes (VN750) the stator is the weakest link. Just like a car alternator but a major job to replace.
People have been known to charge the battery up with a charger before selling the bike to someone. Since the bike can start and run about 15 miles on battery power alone the "buyer" doesn't know there's a problem until they've gotten the bike home and ridden a few miles.
While there are several ways to test the stator the easiest way is to take a 10mm socket wrench with an extension and remove the seat with by opening the tool box behind the seat and unbolting the 2 small bolts that hold the seat in place revealing the battery which is under the seat. Lift the set out (this all takes 1 minute) to do this. Start the bike in neutral and while 1 person keeps the throttle / engine at 3000+ rpm put a voltage meter on the battery. If at 3000 rpm you don't see at least 14v walk away.
Realize that at 1000 rpm the voltage may be as low as 11.8v but when the engine is reving the voltage should go up.