The paper presents a high-precision calculation of the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment ($a_\mu$). The authors improve upon their previous work by reducing uncertainties by 40%, achieving an unprecedented level of precision. They perform large-scale lattice QCD simulations on finer lattices, allowing for more accurate continuum extrapolation. The calculation includes a small, long-distance contribution obtained from low-energy experiments, which reduces the total uncertainty significantly. The final result for the HVP contribution to $a_\mu$ is $714.1(2.2)(2.5)[3.3] \times 10^{-10}$, with statistical, systematic, and total errors. When combined with other standard-model contributions, the total prediction for $a_\mu$ differs from the experimental measurement by only 0.9 standard deviations, validating the standard model to 0.37 ppm. The paper also discusses the challenges and improvements in the calculation, including the treatment of statistical uncertainties, finite lattice size effects, continuum extrapolation, and physical point determination. The results are compared with other lattice and data-driven determinations, showing good agreement with most lattice calculations but tensions with data-driven approaches. The authors expect further lattice collaborations to provide precise calculations of $a_\mu^{\text{LO-HVP}}$ to confirm or refute their results.The paper presents a high-precision calculation of the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment ($a_\mu$). The authors improve upon their previous work by reducing uncertainties by 40%, achieving an unprecedented level of precision. They perform large-scale lattice QCD simulations on finer lattices, allowing for more accurate continuum extrapolation. The calculation includes a small, long-distance contribution obtained from low-energy experiments, which reduces the total uncertainty significantly. The final result for the HVP contribution to $a_\mu$ is $714.1(2.2)(2.5)[3.3] \times 10^{-10}$, with statistical, systematic, and total errors. When combined with other standard-model contributions, the total prediction for $a_\mu$ differs from the experimental measurement by only 0.9 standard deviations, validating the standard model to 0.37 ppm. The paper also discusses the challenges and improvements in the calculation, including the treatment of statistical uncertainties, finite lattice size effects, continuum extrapolation, and physical point determination. The results are compared with other lattice and data-driven determinations, showing good agreement with most lattice calculations but tensions with data-driven approaches. The authors expect further lattice collaborations to provide precise calculations of $a_\mu^{\text{LO-HVP}}$ to confirm or refute their results.