Same-State Pairs Make One JEPA Proof of the Platonic Representation Hypothesis Vacuous

In a Joint-Embedding Predictive Architecture (JEPA), the JEPA proof of the Platonic Representation Hypothesis (PRH) assumes that every observation determines the world state and that a spectral gap makes minimizers unique up to rotation. Under the hard-whitening population objective, same-state positive pairs make the induced world kernel the identity: every centered whitened state function is a global minimizer, and, when dz-1≥ 2k, two minimizers can have best-rotation squared residual $2k$. The uniqueness claim is conditional; for $k