The Root is Constantly Changing

Question

A negative sign is not a Peanuts character!

-264.66409225
-462.71021449
-20.60615236
-21.38877504
-92.13888121
-213.77948944
-58.14977536
-276.29420841
-242.07314569
-276.16789489
-373.92343641

Answer is a semi-thematic four word phrase.

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Hint 1

What operation(s) do you have to apply to the numbers?

Hint 2 (minor spoiler)

The phrase you get after applying the operation(s) in Hint 1, plus part of the title, can be used to find the knowledge you need to proceed.

Hint 3 (updated)

If you have the right knowledge, the decimal portion has all you need to finish off this puzzle.

Answer 1

Each of the given numbers...

...is the negative square of a number to exactly four decimal places.

$-264.66409225 = -(16.2685)^2$
$-462.71021449 = -(21.5107)^2$
$-20.60615236 = -(4.5394)^2$
$-21.38877504 = -(4.6248)^2$
$-92.13888121 = -(9.5989)^2$
$-213.77948944 = -(14.6212)^2$
$-58.14977536 = -(7.6256)^2$
$-276.29420841 = -(16.6221)^2$
$-242.07314569 = -(15.5587)^2$
$-276.16789489 = -(16.6183)^2$
$-373.92343641 = -(19.3371)^2$

The integer parts of these roots, when converted using A1Z26, spell PUDDING POPS.

A Google search for...

... "pudding pops" and "constantly changing" leads us to various results concerning "Square Root of Minus Garfield", a comic strip that parodies Garfield. (This aligns with the decoding mechanism from the previous step!)

One running gag there is to parody one particular Garfield strip...



... by replacing Garfield with something else in the second panel. These strips are typically titled "Garfield [blank] Garfield", where the blank is (usually) close to the word "minus". For example, the first instance of this is called "Garfield Linus Garfield":



Recall the puzzle's flavor text:

A negative sign is not a Peanuts character!

This makes much more sense now!

Armed with this knowledge...

... we note that the first three digits of the fractional parts of the roots above are strip IDs for some of these "Garfield [blank] Garfield" strips.

For example, the first root is 16.2685, with fractional part is "2685". The comic with strip ID 268 happens to be "Garfield Linus Garfield".

We can now use fourth digit to index into its associated [blank].

 268 → LINUS                        → index 5 → S
 510 → PINENUTS                     → index 7 → T
 539 → MENUS                        → index 4 → U
 624 → SPRINGSTEEN                  → index 8 → T
 598 → HISROYALHIGHNESS             → index 9 → H
 621 → MANUS                        → index 2 → A
 625 → SKYNET                       → index 6 → T
 622 → SWINUB                       → index 1 → S
 558 → THESQUAREROOTOFMINUSGARFIELD → index 7 → A
 618 → MYNOSE                       → index 3 → N
 337 → SINUS                        → index 1 → S

This yields the answer...

... STU THAT'S AN S, which, well—I'm not actually sure what this means (or whether I'm even parsing it correctly)!

_{This answer builds off of significant progress made by Gareth McCaughan in his answer. He deserves much credit!}

Answer 2

Very partial solution

Since this has been open for quite a while with no obvious progress, I'll post what I've found so far. Maybe someone else will see whatever I'm currently missing.

First of all,

the given numbers are exactly $-x^2$ for these values of $x$: 16.2685, 21.5107, 4.5394, 4.6248, 9.5989, 14.6212, 7.6256, 16.6221, 15.5587, 16.6183, 19.3371. If we convert the integer parts to letters via A1Z26 we get PUDDINGPOPS. "Pudding Pops", according to Wikipedia, are "frosty ice pop treats originally made and marketed by Jell-O", first sold in the 1970s but since discontinued. So, these are $\sqrt{-y}$ where the $y$ are the numbers given, which we might prefer to write as $i\sqrt{y}$; or, alternatively, the numbers given are $(ix)^2$ where the $x$ are the numbers I have listed above. This suggests some sort of phrase involving the word "I" along with "SQUARE" or "ROOT" and, of course, "PUDDING POPS" (and perhaps also something like FLOOR or ROUND or INTEGER??), but (1) I can't think of any such thing that makes any kind of sense and (2) those fractional parts still need to be accounted for somehow. I can't get anything out of them with A1Z26, nor as phone keypad codes; considered as 4-digit numbers they don't seem obviously interesting; the main thing that strikes me is that they're almost all a little over 1/2, the two exceptions being instead a little over 1/4 in one case and 1/3 in the other.

Now,

a bit of web searching turns up this peculiar thing. Title: "The square root of minus Garfield"; main content is a Garfield comic (I think a real one) where in the first panel Jon says "The world is constantly changing", nothing at all happens in the second, and in the third Garfield thinks "They haven't stopped making frozen Pudding Pops, have they?". It looks as if we've located the [knowledge] we're supposed to be using.

What I'm meant to do with this is currently beyond me.

It's tempting to take the fractional parts as page numbers on that site, but there aren't that many -- the latest is 3845 -- so almost all of them just yield the last page. I note with interest that mezzacotta.net has in the past run puzzle competitions, but there doesn't seem to be a current one. In any case, heavy dependence on external resources is generally frowned on around here and I'm guessing that solving this puzzle isn't meant to depend on exhaustive knowledge of everything on mezzacotta.net. "Mezzacotta" means "half-cooked" but the only thing I can think of to do with that fact is to halve those four-digit numbers and anagram them :-) which doesn't seem promising, especially as several of them are odd. Or maybe subtract one half from each of those fractional parts that are just over 1/2 and ... then use them as page numbers on TSROMG? Nope, that doesn't produce anything obviously useful.