When I was a freshman I got caught cheating on a homework (really just looked at a similar question online trying to figure out how and filled in the wrong number) and got a 0 on the assignment. I'm now working on grad school apps and am being asked if I ever had a sanction against me, if I've ever been found guilty of academic dishonesty, etc.
It's not on my transcript and I don't think they'd find out, but I don't feel right about lying here. Do I have any shot at getting in to a top grad school (CMU, MIT, Stanford, and Cornell are where I'm applying first). My understanding right now of this is good programs are basically off the table, now it's a question of how far down the ladder I have to go to find somewhere that doesn't just reject me right away. Is there any way to fix this or am I just screwed and not welcome in good academia? It seems like there's an attitude of "once a cheater, always a cheater" and people want nothing to do with somebody who was "convicted" of this.