I'd be careful with this anthropomorphizing language. GPT doesn't have beliefs. It's interesting that the training data contains enough of this kind of writing to steer/plagiarize its way into a course correction. But if you scold it, it will go back to "proving" something false. Would a human?

But (x y)^n ≠ Σx^i y^(n-i).

I actually reread Huck Finn *after* James, and I can recommend that. It made some moments especially chilling, but also I think it enhanced my appreciation of Twain's humor and humanity.

(Similar argument for an all-yellow column.)

Good point. A 7x3 contains either an all-white column or all-yellow column, or else a matching pair of the remaining 6 patterns.

If there's an all-white column, either one other column has two whites and we're done, or the other four possibilities for the other 6 columns must have a matching pair.

If it was a 3xn grid, each column could be colored one if 2^3=8 ways. If n=9, by the pigeonhole principle two columns must be identical, and by the PHP again, must have a repeated color. That repeated color in two columns gives our rectangle.

So n≤8 is a bound in the 3xn and hence the 4xn case...

A lower-tech solution: once you're looking at the cropped/obscured picture you want to post, take a screenshot of that, and post the screenshot.

(Or cropped screenshot, acknowledging that things like your battery percentage could potentially be extracted by someone who cared.)

I'm not an astronomer; is this "in depth analysis," or is meta just paraphrasing and rounding values?

Wait... how do we know it's dead?

I wonder if this number has other interesting properties...

Cool! So if I want more accuracy I can just enter more primes to www.wolframalpha.com/input/?i=%28...

Is the starting number defined as the one *such that* this happens? Like if I run this process and eventually get a composite, is it because I needed to start with more of the digits of 0.432...?

Okay but hear me out, then Kamala drops out making Walz the candidate, then Vance drops and his VP is the new candidate, and then Walz...

Ping!

I won't be able to make it to this but I'm quite interested! Do you know if a recording will be made available afterwards?

Is that raw hamburger?

I think about this too. I'd be interested to read your piece!