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As I remember each magnetic path in closed. Path may be composed of ferrous material and non ferrous air part. Problem is how to calculate magnetic resistance in magnetic circuit carpenter has. I don't remember how.
With the air gap you're right, in the meantime, it also occurred to me (slow lines).
From the producers any support or data about the material can not wait, they are not public.
The magnetic permeability is materil constant and as such it can only be measured, unfortunately, I do not know how.
More precisely, I do not know how to measure it at the ROD core
You can't measure the permeability in an open path configuration without calculating the field geometry. But even if you have a rather accurate calculation, it will only give a very rough estimation of the permeabilty because most of the total reluctance is created in-air.
In a similar topology, I found that increasing core µr from 100 to 1000 raised the inductance only by 10%. There may be more sensitive differential measurement methods using multiple coils.