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It is proved that task-predictive equivalence induces the unique minimal sufficient quotient $\mathcal{H}/\!\sim_\tau$, leaving active observability complexity strictly invariant while eliminating superfluous distinctions.
Before a machine can discover a physical law, it must discover what its measurements are: which observations live on cells, which are intensive or extensive, which sectors are dual, and which distinctions are merely gauge. We introduce physical representation-language discovery, the problem of recovering this hidden on...
Recurrent models must preserve information that changes future behavior while suppressing hidden-state error. These objectives conflict: contraction improves stability, but contraction along a future-distinguishing direction destroys memory. We formalize this boundary through the predictive quotient of a recurrent stat...
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