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Once mine failed, the mechanic then bled some propane into the carb, and it passed. It was getting extra air from somewhere. I found a leaky hose that was sucking in the extra air.
The weirdest thing, bleeding in the propane cause the HC's , and CO to go down.
That pipe supplies fresh air to the cat to help it burn unspent fuel. Without it, the cat will burn out. It cannot be had new any longer. See if you can weld or even JB Weld that back on. It's going to be hard though. You can also place a WTB. But be warned, most are in pretty bad shape.
Also to add, the Federal and the California emissions spec RX-7's all had the three catalytic converter setup. You should have tow pre cats and one main cat. The split air tube will have a flange on the exhaust end that bolts to a flange on the main cat. If you have an aftermarket cat, you will have to weld a 90 degree bent tube with a flange to it so that the split air pipe can bolt to it.
You will also have to ensure that your air control valve is working properly and that the internal diaphragm is not full of carbon or had not ripped. The diaphragm was still available new the last time I checked.