I'd be poor if I replaced every tire that had a cut like that....and I get them at wholesale.

Ride it. If it freaks you out then just keep an eye on it. You will either get more flats quickly or it will slowly start to bulge (over many rides) if that cut is truly through the cords and begins to propagate. It isn't going to leave you stranded from the looks of it. I can assure you I probably have 3 or 4 mounted and currently ridden tires that have multiple cuts that look like that with no issues.

For those of you who recommended to absolutely swap it out.....have you seen my website?