Yes, the problem seems to be that ArbNumerics needs to overload Serialization.serialize for ArbFloat (similar to e.g. how BigInt is serialized).
Right now, it is using the default serialize method, which just writes the contents of the Julia struct. Since this probably contains a C pointer, that won’t work.
I filed an issue for further discussion of this: implement Serialization serialize/deserialize · Issue #77 · JeffreySarnoff/ArbNumerics.jl · GitHub