How does Apple verify who I am at the Genius Bar appointment?

I have an Apple Store appointment to replace the usb sync cable for my two-month-old iPhone (cable is starting to fray). Will this work fine if I don’t have the iPhone itself with me, just the cable? I have an Apple account with my email address (same address I used to buy the iPhone) and I will have the same credit card with me that I used to buy the iPhone. Should I bring also the serial number of my iPhone?