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This is my addendum for an academic disciplinary warning:

In the spring semester of my second year at SCHOOL X, two classmates and I were cited for excessive collaboration on a homework assignment in our Computer Science 1315 course. We each received a zero on the assignment and a disciplinary warning in our disciplinary file. By no means do I wish to marginalize the gravity of error, but our intentions were not malicious. In fact, we admitted to the violation after the course’s policies were more explicitly explained to the class. After reviewing the class’s policy on collaboration, I admit that our method of collaboration was excessive and that we deserved to be disciplined. I sincerely regret this mistake, but I learned from the incident and have had no other such issues in my academic career.

How will this affect my applications?

The part about your intentions and such seems to be a little squirmy. It sounds like you self-reported your actions after discovering the depth of the policy, is that correct?

Why not something simpler such as:
"In the spring semester of my second year at SCHOOL X, two classmates and I were cited for excessive collaboration on a homework assignment in our Computer Science 1315 course. After understanding the depth to which the course's policies was applied, we voluntarily reported our wrongdoing and received zeros on the assignment and disciplinary warnings on our files. I sincerely regret this particular mistake and have had no other issues in my academic career."

^^Probably needs some touching up of phrases here and there, but it makes it sound that you #1 aren't downplaying the incident, and #2 actually did the trustworthy thing and reported it, in less words than your original addendum.

How doesthis sound?

In the spring semester of my second year at SCHOOL X, two classmates and I were cited for excessive collaboration on a homework assignment in our Computer Science 1315 course. After having the course’s collaboration policy explicitly explained to the class, we concluded that we had mistakenly violated the policy. We voluntarily reported our violation and each received a zero on the assignment and a disciplinary warning in our disciplinary file. I sincerely regret this mistake, but I learned from the incident and have had no other such issues in my academic career.