The paper presents a Bayesian analysis of cosmic inflation models using third-order slow-roll power spectra. It assesses the compatibility of inflation with recent Cosmic Microwave Background (CMB) and Baryonic Acoustic Oscillation (BAO) data. The study involves 287 single-field inflation models, evaluating their Bayesian evidence, posterior distributions, and reheating parameters. Key findings include that the third Hubble-flow function ε₃ is within two sigma of [-0.4, 0.5], consistent with slow-roll predictions. The fourth Hubble-flow function ε₄ remains unbounded. The analysis also finds a residual excess of B-modes in BICEP/Keck data, suggesting non-zero primordial tensor modes. The Bayesian evidence for reheating parameters shows an information gain of 1.3 ± 0.18 bits, a significant improvement over previous data. Over 40% of models are now strongly disfavored, indicating that cosmological data are increasingly constraining. About 20% of models have evidences within the most probable region. The study highlights the importance of specifying or marginalizing over reheating kinematics for accurate inflationary predictions. The analysis uses a rescaled reheating parameter R_reh to reduce degeneracies between reheating kinematics and scalar perturbation amplitude. The results demonstrate that the landscape of inflation models is being increasingly constrained by data, and that Bayesian methods are essential for model comparison. The paper also introduces new inflation models and discusses their parameters, emphasizing the role of Bayesian evidence in determining the most probable scenarios. The study underscores the need for a unified framework to analyze inflationary models and their compatibility with observational data.The paper presents a Bayesian analysis of cosmic inflation models using third-order slow-roll power spectra. It assesses the compatibility of inflation with recent Cosmic Microwave Background (CMB) and Baryonic Acoustic Oscillation (BAO) data. The study involves 287 single-field inflation models, evaluating their Bayesian evidence, posterior distributions, and reheating parameters. Key findings include that the third Hubble-flow function ε₃ is within two sigma of [-0.4, 0.5], consistent with slow-roll predictions. The fourth Hubble-flow function ε₄ remains unbounded. The analysis also finds a residual excess of B-modes in BICEP/Keck data, suggesting non-zero primordial tensor modes. The Bayesian evidence for reheating parameters shows an information gain of 1.3 ± 0.18 bits, a significant improvement over previous data. Over 40% of models are now strongly disfavored, indicating that cosmological data are increasingly constraining. About 20% of models have evidences within the most probable region. The study highlights the importance of specifying or marginalizing over reheating kinematics for accurate inflationary predictions. The analysis uses a rescaled reheating parameter R_reh to reduce degeneracies between reheating kinematics and scalar perturbation amplitude. The results demonstrate that the landscape of inflation models is being increasingly constrained by data, and that Bayesian methods are essential for model comparison. The paper also introduces new inflation models and discusses their parameters, emphasizing the role of Bayesian evidence in determining the most probable scenarios. The study underscores the need for a unified framework to analyze inflationary models and their compatibility with observational data.