Exact Localized Information Capacity of a Local Observable in a Hilbert-Space-Shattered System
This paper establishes a rigorous, closed-form expression for the exact localized information capacity of local observables in Hilbert-space-shattered systems, demonstrating that this capacity is determined by the projection onto the exact commutant algebra and yields specific, non-universal bit densities (such as bits/site for the dipole-conserving chain and bit/site for the - chain) that explain why complete memory in these systems arises from statistically localized data rather than strictly local integrals of motion.