The Rithmatist takes place on an alternative version of Earth. One where the United States are the United Isles, for example.
Also that Earth is (I think) half the size of our own? Or possibly less? Brandon says it has a denser core to make up the difference.
Really? This is the first time I hear this, but it's pretty cool news. You know the man, find out specifics for us :P
Brandon and I discussed it when we put together the map of the United Isles... there was some hand-wavery in terms of total numbers, but the scale on the map legend is more-or-less accurate. As you can see, that puts the Isles themselves at about 1500 miles (give or take a few hundred, I'm eyeballing it) from the cliffs of the western California Archipelago to the eastern shores of New Guernsey.
In comparison, the continental United States is about 3000 miles across from shore to shore. So, loosely speaking, it's a half-sized planet with a core of something denser than iron to make the mass mostly the same. Perhaps gold?
Aside from the map, which I'm not surprised if it was overlooked, we also get some clues in the travel times and distances described during Joel and Fitch's trip.
All of those clues would require me to pay attention and think about things, though - which is something I find difficult to do when my hand is racing to turn the pages :)
On the topic of distances and masses though, I was looking into possible easy solutions, but it actually looks like there is some serious sciencing that needs to happen for the numbers to work out. But eyeballing, if you shrink the radius of the planet in half, this drops the volume (including the core volume) by a factor of 8, which - assuming the same density, which is not a safe assumption because lower mass makes lower density more likely - means that the core has to be about 8 times more massive to maintain the same gravity. Which is a problem, because such element doesn't exist naturally, and is even less likely to fuse in a small planet. So. Heavy sciencing and/or handwavium :)
Maybe a denser metal and a larger core? Our iron core is only about 10% of the planet's diameter, but I have no idea how a larger core would affect the physics of the planet.
Handwavium. Unobtanium. Impossibillium. :)