--Search for top width or height caps at 4096--

order:width and order:heigth return tops from 4'096 down.

But order:mpixels reveals far greater out there, such as 16'918×24'138 for post #2889454.

4'096 is suspiciously a binary round number.
There could also be confusion between pixel and print dimensions.

There are no order:width and order:height metatags so they are ignored.

Ah ok.
They just return the latest images uploaded, and "4096" was just a coincidence.

I would rather have had an error message.

I found out the cheat sheet lists supported orders.