Catalytic Converter hose?
 

Anyone know what that hose that attaches to the cat does? I lost the nuts that connect it to the cat, and I'm due for emissions. Also, anyone happen to know what size these nuts are off the top your head? Thanks a bunch.

It supplies air to the cat from the airpump.
Without it, the cat will pretty much clog up.

You're absolutely correct that it is the air supply hose. But I'm not sure that it will clog if left disconnected. Since its purpose is to supply oxygen to the catalytic converter, if it's not connected then the converter will not be as effective in reducing the emissions. I don't think that makes the converter more prone to clogging, I think it just means that the emissions won't be as clean as they would be if the air supply pipe were connected. I don't know what the chemical reaction is, but the oxygen has to be supplied for it to take place. A little bit takes place anyway, but when you add the oxygen in large quantities, then the converter really cleans up the NOX or emissions or whatever it is that the EPA hates. Bottom line is, if your going for an emissions test, you'd better get it hooked up.

Cool, thanks a bunch guys

my understanding is that it supplies oxygen to the cat to keep it warm during low rpms. the rx7 cat needs to be hotter than normal cats because the rx7 injects oil into the engine. Im no expert, but it seems that the oil can collect in the cat and clog it up if the cat is not hot enough to burn it.

in any case, there is no benefit for having the hose disconnected, unless you have you air pump disconnected also. also, it will affect your emmissions (i think) so bolt it back on.