This paper presents the first non-perturbative QCD constraint on the nuclear equation of state (EoS) for isospin-dense matter, with complete quantification of systematic uncertainties. Using lattice QCD calculations, the authors compute thermodynamic quantities and the EoS of QCD over a wide range of isospin chemical potentials. The results agree with chiral perturbation theory (χPT) at small chemical potentials and with perturbative QCD (pQCD) at large chemical potentials. The calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter EoS over a wide range of baryon densities. The study addresses the challenge of determining the internal structure of neutron stars, which has long been a problem in nuclear theory. The results show that the speed of sound in isospin-dense matter significantly exceeds the conformal limit of 1/3 over a wide range of isospin chemical potentials. A Bayesian model mixing approach combining χPT, LQCD, and pQCD provides a determination of the zero-temperature EoS for isospin-dense QCD matter valid at all values of the isospin chemical potential for the first time. The paper also discusses the implications of the results for nuclear phenomenology, including the existence of pion stars and the isospin effects that distinguish pure neutron matter from symmetric nuclear matter. The results provide a systematic-controlled QCD bound at all densities and have important implications for astrophysical environments. The study uses lattice QCD calculations to determine the pressure, energy density, and speed of sound of isospin-dense matter. The results are compared with pQCD and χPT predictions, and the superconducting gap is determined by subtracting the pQCD calculation of the pressure in the absence of the gap. The results show that the gap extracted from the LQCD calculations is in agreement with the perturbative gap for μ_I in [1500, 3250] MeV but is considerably more precisely determined than the uncertainty from perturbative scale variation. The paper also discusses the constraints on the nuclear EoS derived from the GP-model of the isospin-dense EoS. The results show that the isospin-dense EoS bounds the EoS for symmetric nuclear matter, and the bounds become tight at large quark chemical potentials where pQCD is valid. The results provide important insights into the behavior of dense hadronic matter and the nature and dynamics of astrophysical objects such as supernovae and neutron stars.This paper presents the first non-perturbative QCD constraint on the nuclear equation of state (EoS) for isospin-dense matter, with complete quantification of systematic uncertainties. Using lattice QCD calculations, the authors compute thermodynamic quantities and the EoS of QCD over a wide range of isospin chemical potentials. The results agree with chiral perturbation theory (χPT) at small chemical potentials and with perturbative QCD (pQCD) at large chemical potentials. The calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter EoS over a wide range of baryon densities. The study addresses the challenge of determining the internal structure of neutron stars, which has long been a problem in nuclear theory. The results show that the speed of sound in isospin-dense matter significantly exceeds the conformal limit of 1/3 over a wide range of isospin chemical potentials. A Bayesian model mixing approach combining χPT, LQCD, and pQCD provides a determination of the zero-temperature EoS for isospin-dense QCD matter valid at all values of the isospin chemical potential for the first time. The paper also discusses the implications of the results for nuclear phenomenology, including the existence of pion stars and the isospin effects that distinguish pure neutron matter from symmetric nuclear matter. The results provide a systematic-controlled QCD bound at all densities and have important implications for astrophysical environments. The study uses lattice QCD calculations to determine the pressure, energy density, and speed of sound of isospin-dense matter. The results are compared with pQCD and χPT predictions, and the superconducting gap is determined by subtracting the pQCD calculation of the pressure in the absence of the gap. The results show that the gap extracted from the LQCD calculations is in agreement with the perturbative gap for μ_I in [1500, 3250] MeV but is considerably more precisely determined than the uncertainty from perturbative scale variation. The paper also discusses the constraints on the nuclear EoS derived from the GP-model of the isospin-dense EoS. The results show that the isospin-dense EoS bounds the EoS for symmetric nuclear matter, and the bounds become tight at large quark chemical potentials where pQCD is valid. The results provide important insights into the behavior of dense hadronic matter and the nature and dynamics of astrophysical objects such as supernovae and neutron stars.