Charging voltage is WAY too low. As stated, optimum is around 14-14.25 volts. The way the system works is the battery holds a charge that is released as a demand (load) occurs for current (amps)to flow from the battery to the starter(for instance, or the lights) as the engine runs it turns the fan belt and the alternator sends current back to the battery to keep it charged. Batteries are nominal (name only) 12 volt. In order to keep them charged the alternator must supply more current to the battery than any load removes. That is why you have to have higher readings than 13volts (potential), or the battery will eventually die and leave you stranded when you least expect it to.
As to the fix, I suspect one of several things. First make sure your fan belt is good and tight but has some deflection in the belt between the water pump pulley and the alternator pulley. You don't want slippage of the belt under load, but you don't want it so tight as to damage a bearing in the alternator or the water pump. Once verified, then look for any loose or bad grounds. The battery must have a good chassis ground which may have been compromised by the corrosion of the bad battery that you just replaced. The negative post ground cable needs to be traced to the chassis and determined whether it sustained any corrosion, especially where it attaches to the chassis. If it did or looks like it did than have it replaced by the dealer under warranty.
Once you have a known to be solid ground to the chassis and the fan belt is adjusted to specs then see what charge is being supplied to the battery at idle, AND with a load on it like headlights, etc.
If it still fails to give you the proper voltage range 14-14.25volts then suspect your alternator is faulty. It could be an intermittent diode starting to fail or the bridge rectifier which converts the ac which the alternator produces to dc voltage which the tractor needs to feed the battery. No matter what the problem with the alternator, assuming this turns out to be the problem it should be rebuilt or replaced with a known good one.
Most likely the problem is the old battery was just bad and had a problem with a cell across its plates, but the 'boil over' condition could just as likely come from a 'runaway' alternator deciding to supply over voltage one day and undervoltage hte next. Since I am not familiar with the CK 20 and whether it has a separate voltage regulator that limits voltage sent back to the battery- I would say, if the voltage regulator IS separate from the alternator than check it too, because it could easily be faulty. Most alternators these days use a built in voltage regulator, however, but you dealer can determine that for you.
Good luck and have them fix the whole problem, not just the symptoms! And require then to remedy the corrosion problem too. They may want to blame the battery and say it is covered under a separate warranty which does not cover consequential damages from the acid, etc. Hopefully they will come through for you!
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CM