TL;DR
I booted Debian Linux on a 4-bit intel microprocessor from 1971 - the first microprocessor in the world - the 4004. It is not fast, but it is a real Linux kernel with a Debian rootfs on a real board whose only CPU is a real intel 4004 from the 1970s. The video is sped up at variable rates to demonstrate this without boring you. The clock and calendar in the video are accurate. A constant-rate video is linked below.
At first I was not very impressed. Then I read that that 4004 does not have any AND, OR, or XOR instructions. Yikes.