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Yes, x86:

https://www.intel.com/content/www/us/en/developer/articles/t...

Oooh has it shipped anywhere already ?

Everywhere. The constant-time bit defaults to "1" because the current x86 CPUs follow all of the promises of this already. The particular feature here is to allow Intel to make optional optimizations that are not constant-time on the particular subset of instructions.

ARM cores also have a similar set of promises.

No, this Zkt is part of the application profiles, so expected to be implemented by high perf OoO cores. It just defines that a list of instructions must have "data-independent timing".

Zkt is probably widely implemented even if not declared. Since most RISC-V cores are towards the lower end of the spectrum (in order etc.) you'd have to go to extra effort not to implement it.