Persistent Information Surviving Reinitialization in an Untrained Neural Network

This preprint investigates information retention, instance-specific signatures and persistent organization in ZEUS, an untrained neural network and the research substrate underlying X1, X3 and X-Crypt. Behind a single-neuron bottleneck, the measured downstream activations follow a shared rank-one signal, with residuals consistent with single-precision rounding. The study distinguishes redundancy within a processing step from information retained across time. Across 50 campaigns using stored weights and new inputs, global information efficiency remains at 76.3% ± 0.4%, while retention from the bottleneck neuron into the sub-network ranges from 96.5% to 99.2%. Across five freshly initialized instances, 7,061 specific layer pairs remain strongly coupled, while their correlation signs vary between instances. These measurements distinguish a shared coupling structure from the sign patterns associated with individual instances. The paper also examines coupled neurons in the main network, changing amplitude regimes, an observed state carry-over following full reinitialization, and task-dependent divergence recorded in operational campaigns. An outlier instance is reported separately, and the observational status of the task-binding records is explicitly identified. Methods include singular-value analysis, numerical reference computations, entropy and mutual-information estimation, correlation analysis, binary-signature comparisons and untrained conventional control networks. Interference visualizations are assessed against random references to distinguish properties of the rendering procedure from instance-specific arrangements. The work connects the measured properties of ZEUS with its role as the research foundation for live authentication, live identity for AI agents and drone swarms, and neural amplitude cryptography through X1, X3 and X-Crypt. This preprint focuses on the underlying neural substrate; security validation of the derived systems is addressed in separate publications.