Physics-Informed Machine Learning for Dark Sector Field Inference: Methodology Validation on Synthetic Cosmological Data

A seven-stage computational pipeline for dark sector anomaly detection and field inference, combining Physics-Informed Kolmogorov-Arnold Networks (PIKAN), Neural ODE forecasting, ensemble anomaly detection, persistent homology, Wasserstein-Ricci geometry, and symbolic regression. All analysis stages operated on a physics-motivated synthetic redshift sequence (24 snapshots, z∈[0,6]) generated as an automatic fallback after CAMELS IllustrisTNG HDF5 snapshot downloads were unsuccessful. Results constitute methodology validation on synthetic data, not empirical cosmological findings. Data provenance, limitations, and failure modes are fully disclosed.