Atomic clock frequency ratios with fractional uncertainty leq 3.2 times 10^-18

We report high-precision frequency ratio measurements between optical atomic clocks based on ²⁷Al^+, ¹⁷¹Yb, and ⁸⁷Sr. With total fractional uncertainties at or below 3.2 times 10^-18, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in ⁸⁷Sr ratios at approximately 1times10^-16 and the Al^+/Yb ratio at 1.6times10^-17 in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this work is the use of a common ultrastable reference delivered to all clocks via a 3.6 km phase-stabilized fiber link between two institutions. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of 1.3 times 10^-16 at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.