Does the Great Pumpkin really exist in the Peanuts Universe?

Recently my family was watching "It's The Great Pumpkin Charlie Brown" from 1966 and I recalled how the plot of the show came from comics that were written over time in the years before the cartoon game out. And one thing we talked about was whether Linus was correct that The Great Pumpkin actually exists, or was everyone else right and it was in his imagination.

It seems a reasonable question, because one thing about Linus is that he's usually the wisest character on the show. Like the rest of them, he has flaws but he tends to see things more clearly than the rest.
Well, I was looking for old Peanuts strips and I found one that seems to answer the question in this article:

https://screenrant.com/funniest-peanuts-comics-about-great-pumpkin-linus-disappointment/

It is under item 4, "Great Pumpkin, You're Going To Drive Me Crazy!" November 1 1961.
Here is a direct link to the comic in question, (not sure if it will work long term).

In the comic, Charlie Brown says: "Hey wake up, Halloween is over... You missed The Great Pumpkin. It just came over the radio... He appeared in a very sincere pumpkin patched owned by someone named Freeman in New Jersey!"

When I was a kid we had a book that had a lot of the older Peanuts comics in it, and I'm pretty sure that I had seen this one and just forgotten about it.

So I think one of the following is true:

• The Great Pumpkin really exists in the Peanut's world
• Charlie Brown is lying
• Charlie Brown is teasing
• The radio was lying, like when NORAD reports where Santa's sleigh is on Christmas eve
• Charlie Brown misunderstood the radio

This question may have been answered in a later strip a day or two later, but I don't currently have access to the strips in the order they appeared.

This question is mostly about whether Charles Schulz decided to have magic in his "universe" or not.
What do you think?