Transmission as the Physical Basis of Persistence: An Exploratory Test of the LOP-T Hypothesis Using Quantum Darwinism Experiments

The emergence and persistence of observable structures remain central questions in physics, information theory, and complex systems. This work proposes the Law of Persistence through Transmission (LOP-T), a minimal informational hypothesis stating that the persistence of a physical structure is proportional to its ability to transmit information to an environment capable of recording it redundantly. The hypothesis is tested against three independent experimental Quantum Darwinism platforms — a photonic quantum simulator (Chen et al., 2019), a nitrogen-vacancy (NV) center in diamond coupled to its nuclear spin bath (Unden et al., 2019), and a superconducting quantum processor (Zhu et al., 2025) — comprising a total of 65 independently analyzed states across static and time-resolved regimes. Transmission is estimated operationally from the Holevo bound normalized by its saturation value, and from redundancy-based estimators of increasing fragment order; persistence is estimated both from a record-based proxy built from Holevo information and quantum discord, and from an independent pointer-state tomography proxy. Across every platform and every estimator tested, transmission predicts persistence with strong and statistically significant explanatory power, reaching R^2=0.928 (operational persistence, N=55, p=5.62×10^(-32)) and R^2=0.997 (pointer-state persistence, N=10, p=2.12×10^(-11)) in the static regime, and up to R^2=0.985 in the early-time regime and R^2=0.924 over the full temporal window in a 601-point time-resolved analysis of the NV-center system. Four redundancy-order estimators are compared systematically against two coarser discretized alternatives, and the finer estimators are consistently found to explain more variance, closely tracking the redundancy plateau characteristic of the quantum Darwinism regime. Null and alternative control models are used throughout to rule out circular or trivial explanations. The results support the operational form of LOP-T as a robust, cross-platform empirical regularity, while its stronger temporal and microphysical formulations remain open theoretical extensions for future work.