I have a set of Shimano CX70 canti brakes the pads of which are replacable by changing the pad only (cartridges).
I see in no document for any specification of a cartridge that fits. Are brake cartridges universal?
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The world of brake pad inserts is sort of a crazy world. Since there is lots of info, I'll be broader than what is required for the Shimano CX70s you have... Generally, the Shimano-style system (side grooves and one set screw dimple) is the most popular. Avid also has its own system for cantilever and linear pull brakes (a ridge with two clips). Campy has their own design as do a few other manufacturers, but this will be the starting point in your journey towards madness.
To complicate matters, there are hundreds of colored compounds specific to alloy rims and to carbon rims. There are grooves, channels, wedges, and fins. There are paired rims and pads that will stop your heart if you're not careful. Lots of marketing shtick that will get you nowhere for some extra cash.
Cartridge pads for linear pull brakes vary in length from 73 mm to 70 mm, and so on. Shimano is super common and it is easy enough to compare images of the pad to determine what will be compatible. Below are some Avid-type pads.
Caliper-style pads are generally ~55 mm long. There are lots of different designs and materials which can make it difficult to find the right ones.
Cantilever brakes are a toss up. Some manufacturers use longer pads and holders, others use shorter ones. Your Shimano CX70 brakes take pads that are 55mm long - standard road-Shimano-type pads.
As a rule you should measure your old pads and measure the new pads and write that info down so you don't have to go searching again in the future. Compare the actual pads (or pictures) to be sure of the mounting system. When you do buy pads, buy two sets so that you aren't stuck on unsafe pads when your current set wears out. You can always upgrade the pad holders as well, but if you're unsure about replacing those holders head to a qualified mechanic. Brakes are one component you need to be totally sure about.
If you're riding a vintage bike, take a look at Kool Stop's website, they manufacture a lot of hard-to-find replacements.
According to Shimano the model number for a pair of pads is R55C+1, but I think these are just standard road cartridge pads.