Accessible-State Descriptors Transfer Across Families but Fail at Larger Scales

Can descriptions of the states visited during quantum dynamics predict product-formula simulation requirements beyond physical and Hamiltonian controls, and do those relationships survive a change of scale? In a frozen nested leave-one-family-out evaluation of finite matter–light models, normalized accessibility and a combined state-space representation reduced equal-family mean absolute step-count error from 7.4512 to 5.5334 and 4.6771, respectively, although effects were heterogeneous and the primary accessibility increment on a separately registered external family was marginal. On the subsequent strict large-simulation-dimension endpoint, frozen R6 and the later R7 representation each performed worse than the already inaccurate Phase IV physical baseline, with the resolved-fraction support gate remaining inconclusive. These results support a bounded predictive association within the tested finite regime, not a state-space complexity law, a causal explanation, or an extrapolatable hardware-resource estimate.