I got a (nearly) new MIM Fender Standard Telecaster a couple of weeks ago. For some reason the strings are constantly pulling about 1/4 step sharp. If I retune and play, they last about 10-15 minutes before all being sharp again. If I leave the guitar alone, either in a stand or in its case, after 24 hours the strings have gone sharp. The strings, which are regular EB .10s, are about two and a half, three weeks old now, they've had more than enough time to stretch out and not enough time to rust or significantly weaken. The nut seems cut cleanly, I put some nut sauce in there and it did nothing to fix this problem. Checked the saddles, same deal, they seem fine. The action is good, the neck relief measures perfect. I restring by locking the string against itself, just like the stickies here say.

So I don't know what could be going on. The strings are stretched, restrung properly, not old, not brand new, the nut is cut well, the saddles are clean, everything looks to be set up right, the guitar can be tuned perfectly but after a short while playing or a day left alone all the strings are uniformly 1/5-1/4 of a step sharp. Anybody got any ideas what it could be?
the only thing in the world that I can imagine is that if youre using the whammy bar the string is binding in the nut.

if thats the case a liberal dose of graphite would help that

presuming you even have a trem on your tele
Well no, it's a standard Tele, it's a hardtail. And I already try lubing the nut with nut sauce. I doubt graphite will be any better, usually I find it's ineffective. That's what I don't get. If this was a Strat with a roughly cut nut then I'd understand the strings all going equally sharp. But this is a Tele, it's bizarre.