1819 Large Cent, Odd Pattern On Reverse

But a mesh pressed into a large cent would leave raised diamonds, not incuse.

There are many hand tools that could displace the copper in this cent in this fashion, I'm thinking a file like tool, leaving the copper metal raised and not incuse. The damage wouldn't necessarily be displaced down into the coin but most likely to the sides

Welcome to Coin Community, Lustre.

I am utterly fascinated by this one, and as yet unwilling to commit to any certainty regarding how it came to be.

An experiment: Take a compass or (preferably) a divider, and carefully adjust it to perfect vertical when observing from the side. A divider by nature should do this. Set one leg on one of the "hollows" in the waffle, and one leg on the field of the coin. I think the field southwest of the O on ONE - below and right of the large leaf, the darker area - would be the most consistent location for the second leg. With the coin on a flat surface, if your divider can rest in those two places and still appear perfectly vertical - meaning the field and the place inside the waffle are at the same level - I think a strong argument can be made that the waffle was originally on the die. If the divider is not level, further thinking is necessary.

Either way, Occam's Razor says that we have to assume PMD is the cause. I'm not yet ready to embrace that assumption, though.

The experiment with a caliber was inconclusive - the caliber too big, the hollows too shallow.
But if you look at the area at northwest of "N" on the coin, the indentations
appear to be pressed deeper than the surrounding plain. Also IMHO the mesh pattern is
definitely the result of pressing (or hit by a powerful blow) and not cutting.

It's not a vice, or we'd see damage in the exact same place on the obverse. The fact that it is raised stumps me. Maybe a peice of foreign material (mesh, something hard) came in between the die and the coin, pressed into the die instead of the coin, and became dislodged soon after a few more coins were struck, thus giving this raised pattern seen here. That is just a hypothesis. I don't see how Newcomb would have missed this one.

Another posibility is that is also a piece of copper mesh melded to the coin. In that case, it may be PMD.

I do not the mesh/cloth would have been uniform back then so that is why I am leaning towards something that happened during the minting process. The picture does not look like PMD to me.

PMD no doubt, not to say a new variety of a Large Cent couldn't come to light, but they are the most studied coin series in the entire history of United States coinage. To me it looks like PMD as well, now if this coin was in AU condition I think we could see easily how the damage was done, but the wear has made it appear to be more than it really is. I think it was likely squeezed in a vice - leather or wood on the other side to protect the obverse, IMO.