The challenge:
I am trying to setup a piece of hardware that is transparent to the network that transfers ip packets between two interfaces without adding a "hop".

Details
The particular problem I'm having is that one interface is ppp, the other is ethernet. It is trivial to setup a bridge between two ethernet devices but I am having trouble finding anything for ppp<->ethernet.

Here, the ppp link is an internet connection, and the ethernet connection has exactly one device attached. Once the ppp link is negotiated, I want the ppp peer to think it's talking directly with the device on my ethernet interface and I want the device on my ethernet interface to think it's talking directly to the ppp peer.

Current solution:
The best solution I currently have is to alter the routing table. When the ppp link is negotiated, I am given an ip address. I add a route that directs everything to that ip address to the eth0 device. I also set a default route to the ppp device. Now, anything that comes from the ethernet side gets forwarded to the ppp side, and anything directed towards my ip address gets forwarded to the eth0 side.

ppp isn't ethernet; it doesn't support any kind of bus but ONLY end-to-end communication. So, bridging won't work. You CAN create a bridged virtual network (using for example openvpn), but that's a lot of overhead. Why do you want your ppp peer appear bridged into your local ethernet segment? Maybe there is a better way to solve the problem.

What I want is to be completely transparent at layer 3. I want the box to only touch things from layer 2 down - that is, handle ppp<>ethernet interface, but leave IP alone completely.

It would be much easier to configure the device as router and use it as a gateway device. Plus, if you don't have an internet IP assigned for each host, you need to use NAT anyway. Plus, now you can configure the device as a firewall for your network.

I only have one host, and it should be assigned the address that comes from the ppp negotiation. The whole point is that I don't want a gateway - I want it to be invisible.