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Depends on the subfields. CS is by publication, number theory varies ("my students can find a stapler" to the dissertation has revolutionary result not published elsewhere)

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CS can (but not frequently) have the revolutionary result you mention as well. A candidate Fully Homomorphic Encryption scheme was first detailed in Craig Gentry's thesis, for example. That being said, this is much less common than a

1. literal stapler thesis, or

2. cleaned up version of a stapler thesis (e.g. rewrite of several previous publications to give broader context etc)

Cryptography is closer to math than most CS disciplines institutionally.

that's broadly true, but there are some areas of CS that are at least as close (say at a minimum PL theory). it's also less math heavy than e.g. complexity theory (though that's admittedly smaller). It can also be less math-heavy than learning theory. This all depends on the type of cryptography as well, especially since it can depend on the region (american cryptography is more theoretical than european cryptography, for example).

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