This paper presents a comprehensive study of the equation of state (EoS) of isospin-dense matter using lattice quantum chromodynamics (LQCD) calculations. The authors combine LQCD results with perturbative QCD (pQCD) and chiral perturbation theory (χPT) to determine the EoS over a wide range of isospin chemical potentials. Key findings include: 1. ** Agreement with χPT**: At small isospin chemical potentials, the LQCD results agree with χPT at next-to-leading order (NLO). 2. ** Superconducting Gap**: By comparing LQCD pressure with pQCD predictions, the authors extract the superconducting gap, which agrees with perturbative calculations but is more precise. 3. ** Speed of Sound**: The speed of sound in isospin-dense matter exceeds the conformal limit of \( c_s^2/c^2 \leq 1/3 \) over a wide range of isospin chemical potentials, suggesting that this assumption may be questionable in baryonic matter. 4. ** Bayesian Model Mixing**: A Bayesian model mixing approach combines χPT, LQCD, and pQCD to determine the zero-temperature EoS for isospin-dense matter, providing a rigorous bound on the nuclear EoS. 5. ** Constraints on Nuclear EoS**: The isospin-dense EoS bounds the nuclear EoS, offering new constraints relevant for astrophysical environments such as neutron stars and pion stars. 6. ** Systematic Uncertainties**: The study quantifies systematic uncertainties through model averaging and bootstrap resampling, ensuring the robustness of the results. 7. ** Additional Thermodynamic Quantities**: The GP model is used to compute additional thermodynamic quantities, including pressure, energy density, and squared speed of sound, providing a comprehensive understanding of the EoS. 8. ** Hyperparameter Dependence**: The model's sensitivity to hyperparameters is analyzed, showing mild dependence and consistency with the available LQCD data. This work provides a significant advancement in the understanding of dense hadronic matter and its implications for astrophysical phenomena.This paper presents a comprehensive study of the equation of state (EoS) of isospin-dense matter using lattice quantum chromodynamics (LQCD) calculations. The authors combine LQCD results with perturbative QCD (pQCD) and chiral perturbation theory (χPT) to determine the EoS over a wide range of isospin chemical potentials. Key findings include: 1. ** Agreement with χPT**: At small isospin chemical potentials, the LQCD results agree with χPT at next-to-leading order (NLO). 2. ** Superconducting Gap**: By comparing LQCD pressure with pQCD predictions, the authors extract the superconducting gap, which agrees with perturbative calculations but is more precise. 3. ** Speed of Sound**: The speed of sound in isospin-dense matter exceeds the conformal limit of \( c_s^2/c^2 \leq 1/3 \) over a wide range of isospin chemical potentials, suggesting that this assumption may be questionable in baryonic matter. 4. ** Bayesian Model Mixing**: A Bayesian model mixing approach combines χPT, LQCD, and pQCD to determine the zero-temperature EoS for isospin-dense matter, providing a rigorous bound on the nuclear EoS. 5. ** Constraints on Nuclear EoS**: The isospin-dense EoS bounds the nuclear EoS, offering new constraints relevant for astrophysical environments such as neutron stars and pion stars. 6. ** Systematic Uncertainties**: The study quantifies systematic uncertainties through model averaging and bootstrap resampling, ensuring the robustness of the results. 7. ** Additional Thermodynamic Quantities**: The GP model is used to compute additional thermodynamic quantities, including pressure, energy density, and squared speed of sound, providing a comprehensive understanding of the EoS. 8. ** Hyperparameter Dependence**: The model's sensitivity to hyperparameters is analyzed, showing mild dependence and consistency with the available LQCD data. This work provides a significant advancement in the understanding of dense hadronic matter and its implications for astrophysical phenomena.