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How likely is there to be a foam lining around the hose in the down tube?
Very unlikely. Almost all carbon frames are made using internal bladders to compress the carbon laminate against the outside of the mould, so they're hollow. There are some frames made with foam cores, but that's a pretty outdated method of construction. Anyway, there must have been some way of installing the hoses in the first place, so all you need to do is replicate that...
How likely is there to be a foam lining around the hose in the down tube?
Obviously I can’t pull anything through a piece of foam.
Sram could solve this with wireless brakes.