Short answer: no
Longer answer: if you can live with meeting those jitter requirements most of the time, but with an occasional flub, you can probably take a basic Linux distro and remove almost everything that yes running, add back in just what you need, and see what happens.
Longer still: a Linux kernel with the real-time patch applied does better still but is still not hard real-time. However, I suspect on a modern system you can meet your 10ms jitter requirement.
Provably meets the spec: you're gonna need an rtos.