ALETHEIA: Autonomous Loop for Experimental Theory and HEP Inference Across-data

ALETHEIA is a self-completing tool for monitoring the learning of manifolds in physics foundation models from data. It provides a method to automatically build physics foundation models for permutation-invariant per-event representations of unknown physics manifolds. This process is demonstrated here for dimension-six Standard Model Effective Field Theory (SMEFT) content of four operators in neutral-current Drell-Yan, whose input is unordered event-level features, and we drive it with an active-learning loop that separates two jobs that the literature usually conflates. Active learning completes a representation: given a fixed operator content, an acquisition rule chooses the working points that pin the model's coefficients fastest. The physics expands it: which new operator to switch on is read from the residual structure, ordered by SMEFT power counting, never guessed by the acquisition. The representation is the ManifoldInformer, a permutation-invariant per-event encoder $\psi_\theta$ pooled into a closed-form ridge head; its latent recovers the analytic morphing tangents ($R^2=0.999$) and curvatures ($R^2=0.954$) of the SMEFT cross section. The loop monitors a residual-operator fingerprint: when a single out-of-span direction dominates, it appends that direction to $\psi_\theta$ ($\psi$-extension) and refits. The acquisition arm unlocks new operators through an Arize-Phoenix span, such that the concepts of ``learning correctly'', in which each extension collapses $\sigma_1$; and ``learned completely'', in which $\sigma_1$ is below the noise floor; are read directly off the monitored trace.