Relativistic calculation of the hyperfine-quenching rate of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mmultiscripts> <mml:msub> <mml:mi mathvariant="bold-italic">P</mml:mi> <mml:mn mathvariant="bol

We present a relativistic ab initio determination of the hyperfine-induced spontaneous decay corresponds to transitions between the hyperfine levels of and in the clock transition of . Although this transition is strictly forbidden by electric-dipole selection rules in the absence of nuclear spin, the hyperfine interaction admixes nearby odd-parity states into the level, thereby enabling a weak E1 decay channel to the ground state. Using calculated hyperfine mixing coefficients and reduced electric-dipole matrix elements, we evaluate the hyperfine-induced spontaneous decay rate of 5.253 , corresponding to a natural lifetime of approximately 190 s. The decay is found to be dominated by admixture with the state, while contributions from higher-lying triplet and singlet configurations are strongly suppressed. Our result is in good agreement with previous theoretical studies and confirms the extreme metastability of the clock state, reinforcing its suitability for high-precision optical lattice clock applications. • A relativistic ab initio calculation of the hyperfine-induced decay of the clock state in is presented. • Hyperfine interaction enables a weak electric-dipole decay channel for the nominally forbidden transition. • The hyperfine-induced natural linewidth is found to be 5.253 mHz, corresponding to a lifetime of approximately 190 s. • The decay is dominated by admixture with the state, while higher-lying contributions are strongly suppressed. • The results are in good agreement with previous theoretical studies and confirm the extreme metastability of the clock state.