Green (ground), got it.Black (positive), got it.White (common), got it.Gray wire with like a black fiber in it, what is this? This is a pendant light so my guess is its just a filler wire to bulk up the cord it hangs from, am I right?
Dan is probably right, the extra cable would be called a messenger, cable have small letters printed on them, if you can identify the multi-letter UL cable designation and submit it here or google it.
Cut it loose,wire up the other three,it will work fine.
The gray wire is not a wire that you need. The black is your HOT wire, your white is your NEUTRAL wire (don't call it common/wrong term) and your green is your ground. Those three will make your light work. You are right!...
The gray wire is used as a physical support for the light fixture. You tie each end to the light fixture and to the box where the power wires are connected. This is so that you don't use the power wires as a physical support (hanger) to hold the light in place. Think of a swag lamp from years ago. The lamp hung from a chain connected between the lamp and the ceiling. The power cord never supported the weight of the lamp fixture. The black fiber in the gray wire is a strong cord.
