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A few years ago, I got arrested for assault. There was a plea down to a non-criminal violation.

Unfortunately, the school initiated a proceeding (brought by my ex) regarding the incident and suspended me for a semester.

How do I disclose and spin this in an addendum? (I was stupid and I've definitely learned [cynical] things from it.)

There is no way to "spin" it. You simply say: "I did X. I accepted my punishment y. I learned Z. [Insert contrition] and I will never do it again."

Remove any sense of evasion or excuse-making from your effort. My guess would be if your proceeding contains the words 'Domestic' and 'Violence,' you are going to have a hell of a time with this.