I traded for Beam Miniaturization earlier in my current game. I just researched that specialization's precursor Beam Weapons. I am now unable to choose a specialization. I believe if I had not traded for Beam Miniaturization before researching Focused Beam Weapons or Low-Cost Beam Weapons I would then have been able to have chosen either specialization and then traded for Beam Miniaturization.
So it seems that trading for a specialization before researching one of the three techs in a particular set stops you from researching anymore in that group as if you had researched it your self. So you have to trade for the other two also. If you had researched one on your own you'd only have to trade for two.
Is this correct?