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Do you even Fixxer? The conversion replaces the freehub rotor on common Shimano rear hubs, using the large hollow central bolt for attachment and the splines on the hubshell for drive.
A Specialized/Hed with just 1.37"x24 threads on the hub is for a screw-on multiple freewheel. You can get adapters to move the chainline to suit fixed use, but the adapter unscrews off the hub when you try to brake, so it's still a suicide hub even though the adapter has lockring threads.
The front spok on my CAAD is a Specialized (I think) and it has threads that look like theyd fit a cog, assuming because it was converted from a rear. Surely this means a fixxer would work?