What was the most frequently referenced single event in the DC Silver Age of Comics?
I'll give you a clue; although it was mentioned very frequently, the first time we learned of it, we did not see the event itself, we just heard about it.
The shrinking of Kandor by Brainiac (the renegade scientist mentioned) is undeniably the most commonly referenced event. It comes up constantly in the DC Silver Age, because Kandor turned into a very popular topic for the Superman writers.
Kandor had been the capital city of Krypton. When Brainiac originally shrank it and put it into a jar, it was obviously seen as a horrific crime. But it turned out to be a blessing in disguise as Kandor was (apparently) the only city to survive the destruction of Krypton.
Why did Kandor suddenly appear? It seems obvious from an editorial standpoint. Superman stories set on Krypton tended to sell, as did stories of other Supermen on Earth, and yet they were difficult to create given Mort Weissinger's simultaneous effort to establish continuity in the Silver Age Superman.
Kandor succeeded in creating many memorable Krypton-type adventures for Superman. It had some success in bringing other Supermen to Earth, although this part represented a mixed blessing.
The problem of Kandor is obvious. Superman had always been sold as the only survivor of an ancient race; now he was one of millions of survivors. It diminishes Supergirl's appearance the next year. And Superman's inability to expand the city (other than a convenient character or two at a time) was one of his few (but frequently mentioned) failures, like his inability to cure Mon-El of his reaction to lead poisoning.
But overall the positives of the new locale for stories outweighed the negatives. In many ways, Kandor is another way of weakening the Silver Age Superman. It's a place where he no longer has his powers and must survive instead on his wits.
Kandor spawned many fine stories. One of the best appeared in Lois Lane #15 (February 1960). Here's the "puzzle" cover:
Of course, it is a trick. It turns out that the Superman on the cover is Van-Zee, a Kandorian subbing for Superman, while the woman is Sylvia, an unrelated gal who's Lois' doppelganger. Van-Zee and Sylvia returned many times, starting with this mention in Lois Lane #21:
The Exchange Ray was a clever idea and although it was used fairly often it had one significant drawback; it required that one Kandorian come out of the bottle, which means effectively another Superman/Woman on Earth. As a result, other means were commonly used to get into and out of the bottle.
Van-Zee became an even more important character when he became a member of the Superman Emergency Squad. Here's a discussion of their function from Action #276:
In Superman Annual #5, we learned (from a brief text feature) that the leader of the Superman Emergency Squad is named Don-El. Another relative of Kal-El, perhaps?
There was another important squad in Kandor:
Whether they were helping out Superman and his friends or Weissinger and his writers, I can't say.
But the best Kandor stories were those that took place inside the bottle. As noted above, the idea of putting Superman on Krypton was irresistible to writers of the time, but it was becoming harder. In the Golden Age, I think there's one story where Superman just flies back in time to Krypton. By the Silver Age that was verboten since we all knew that Supes would lose his powers under the higher gravity and red sun of his home planet. So it became a challenge to the writers; how do you put Superman on Krypton without having him somehow then rescue his parents before the planet's explosion (or die himself)? Answer: Put a little bit of Krypton on Earth.
This also creates a place where ordinary humans can interact with Superman on an equal footing, creating a new dynamic in their relationships with the Man of Steel. Jimmy Olsen, for example, went from being the clown in the bowtie to Flamebird, the Boy Wonder:
And Batman established he was the alpha male in World's Finest #143:
This hits on a theme I've talked about before; one of the big changes that Weissinger made was to make Superman more vulnerable, because he realized a legitimately invulnerable character made the series rather dull and forced the more comical approach which he clearly did not favor. Kandor was a place where Supes placed his life on the line.
It also was a place where we got to observe the wonders of Kryptonian science and technology in action:
Lois gets the techno tour from yet another Superman double (Dik-Zee, Van's twin):
Jimmy samples the movies in Kandor:
I'll be adding to this post over time, as Kandor is a very involved and interesting topic.