This paper presents a mechanized formal semantics for the Linux eBPF instruction set architecture (ISA). We develop a small-step semantics in Rocq that faithfully formalizes all 153 sequential in-kernel instructions of the eBPF ISA. The semantics is fully executable and has been validated against the official Linux eBPF test suite. This extensive testing revealed inconsistencies in our original formalization. Using this semantics, we have designed, implemented, and verified the soundness of the bit-level abstract domain employed by the Linux eBPF verifier. Our semantics also complements the existing Linux eBPF documentation by providing a rigorous formal specification. During the formalization process, we have discovered previously unknown bugs in the Linux eBPF implementation, and developed new verifier optimizations; the corresponding kernel patches have been upstreamed.