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What category would this chip go in?

It is hard for me to give you advise but I would put with my Pentium/Mac Ceramic chips.

The reaso why is that it has all the characteristics for that grade with the exception of the shape (square vs. rectangular). The Pentium Ceramic Chips have gold plated pins and a ceramic body with no gold caps.

I'm guessing closer to 386 class given it's an 8088 chip....
Much more pm content than a p4/p5 or k6 line chip. .

It's missing the gold cap for 8086/8088 class.

Honestly I'd put it aside in your shipment for a special quote since it's higher than p4 but has no cap.

while that is a 8086 class chip they only give that classification to chips that have the gold legs AND gold cap.

I am pretty sure you will get better than the pentium/mac classification but you would have to check with them to make sure. Most of those types of chips have gold brazing and/or contacts inside the IC case that make them more valuable.