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Hi CML.
I don't think 'Paperweights of the World' is correct on this particular matter. There are a number of Caithness millefiori designs without a CG cane.
Regarding Caithness Moonflower paperweights (and other designs such as Maydance), I have had several examples with no marking on the base - most likely early examples which only carried stickers that went missing. Remember too that there is also the possibility that seconds, marked 'CIIG', have the base re-polished.
Alan