A friend of mine on FB asked "if Sauron ad nothing to do with the forging of the 3 rings, and never touched them in any way, why did they fade when the One was destroyed. An excellent question! As Galadriel pointed out, even the Elves did not know for certain what would happen when the One went into the Fire. As discussed in the relevant FB thread, because all the rings, even the 3, were based at least in part on Sauron's ringlore and magic. With Sauron's passing, all his works perished and the things that rested on his works faded.
As some were still not getting it, I attempted to explain by translating into a more modern analogy.
"It was by their love of knowledge that Sauron ensnared the coders of the Elves," Galadriel explained. "And so they were betrayed. Sauron taught them all his coding, and they grew mighty in their craft. But Celebrimbor distrusted Sauron, and so partitioned his ring to have an independent elf kernel, and built security into his ring that was independent of the underlying Sauron-based operating system. Then Sauron created the one master Root, and triggered his hidden trojan embedded in the operating system. At once Celebrimbor and the elves were aware of him, and knew they were betrayed. The independent, standalone security still shielded the elf-kernel through which they could access many of the functions in the native operating system. But the native operating system itself was permanently corrupted by the Root."
"And what will happen if the Root is destroyed?" Asked Frodo.
"We do not know," answered Galadriel. "Some believe that, free from the Trojan, the Elf Kernel -- which Sauron code never touched or sullied -- would displace the native operating system. Then the three rings would be free to go to totally open source and mesh. Others believe that if the root is destroyed it will trigger a total wipe of the native operating system and all that will be left is the Elf Kernel, without even the functions it can currently access in the native operating system. That is my belief."
"You mean like what happend with WordPerfect?" Asked Frodo.