Final Report on the Measurement of the Positive Muon Anomalous Magnetic Moment at Fermilab to 127 ppb

This report details the final measurement of the muon magnetic anomaly, $a_{\mu }=(g_{\mu }-2)\mathrm{/}2$, by the Muon $g-2$ experiment at Fermi National Accelerator Laboratory (FNAL), using positive muons collected from 2021 to 2023. The value of $a_{\mu }$ is determined from the ratio of the anomalous spin precession frequency to the shielded proton precession frequency in the muon storage ring magnetic field, combined with external constants known at the 22 ppb level. The new dataset, containing over $2.5$ times the statistics of our previous results, yields $a_{\mu }=1165920710(162)\times {10}^{-12}$ (139 ppb), or $a_{\mu }=1165920705(148)\times {10}^{-12}$ (127 ppb) when combined with our previous results. The new experimental world average, dominated by the measurements at FNAL, is $a_{\mu }^{\text{Exp}}=1165920715(145)\times {10}^{-12}$ (124 ppb).