That sign is real.

"A sign that's... fake? As in, not real?" don't think about that too hard, you may have a seizure.

"In this case, it means that the signs were not posted by the authorities." well, i think in this case it really means a sign that lies, because if they were posted by the authorities or not, if they tell the truth, who would call them fake?

but then, a sign is anything that can be used to tell a lie...

i think i just had a seizure.