Appendix A: Simulation Configuration and Summary Output A.1 Simulation Objective This simulation was designed to examine the limits of information persistence in an open, neural-like causal system subjected to energetic withdrawal, environmental decoherence, and stochastic perturbations. The objective was to determine whether organized information decays instantaneously or transitions through structured intermediate regimes. A.2 System Configuration Simulation ModeInformation persistence under decoherence limits System TypeNeural-like open information field Causal Preconditions Spacetime defined Directional time evolution Explicit causal ordering Matter-based interactions Environmental Parameters Temperature: 310 K Pressure: 1 atm Solvent class: water-like Ionic strength: 0.15 M Environmental noise floor: 1 × 10⁻⁸ A.3 Information Architecture Network architecture: Recurrent causal network Node count: 65,536 Connectivity: Mixed small-world and scale-free topology Initial informational state: Structured, non-random Redundancy factor: 0.18 Active error correction: None All observed persistence therefore arises intrinsically from system dynamics rather than imposed stabilization mechanisms. A.4 Dynamical Protocol Energetic Driving Steady energetic maintenance followed by controlled shutdown Shutdown initiated at 35% of total runtime Decoherence Model Environmental coupling enabled Coupling strength: 6 × 10⁻⁴ Phase noise: 2 × 10⁻⁴ Amplitude damping: 3 × 10⁻⁴ Stochastic Perturbations Random perturbative kicks enabled Kick rate: 0.01 Kick magnitude: 0.001 These parameters were selected to exceed trivial stability thresholds while avoiding immediate dominance of decoherence. A.5 Integration Parameters Total simulated duration: 7,200 seconds Temporal resolution: 262,144 discrete steps Ensemble size: 128 independent realizations Random seed: 552,991 The ensemble approach ensures robustness against stochastic artifacts and single-run anomalies. A.6 Observables Tracked Information persistence metrics Emergence and evolution of causal graphs Entropy flow dynamics Topology variance Self-similarity across scales Full time-series export Topology variance serves as a proxy for information locking, with low variance indicating stable causal organization. A.7 Summary of Emergent Results Global Stability Mean global stability metric: 6.02, significantly above randomized baselines Topology Topology variance converged to zero, indicating complete topology locking following structure formation Residual Structure System consistently converged to approximately 62 persistent informational nodes These nodes acted as stable causal anchors under ongoing decoherence Emergent Properties Complexity: 6.24 Self-similarity: 0.229 Causal density: 0.229 These values place the system in an intermediate regime between active organization and full entropy dominance. A.8 Notes on Interpretation No symbolic encoding or semantic interpretation is assumed No biological specificity is imposed No classical optimization or goal-directed behavior is present All observed persistence arises from intrinsic causal topology and system-environment interaction dynamics. A.9 Reproducibility Statement The simulation parameters and observables reported here are sufficient to reproduce the reported behavior in any equivalent causal-network-based information dynamics framework operating under comparable noise and decoherence conditions.

This study investigates the physical persistence of organized information following energetic withdrawal in an open, noisy system. Using high-resolution ensemble simulations of a neural-like causal network subject to environmental decoherence and stochastic perturbations, we examine whether information-bearing structure collapses instantaneously or persists through structured intermediate regimes. Across 128 independent simulations, we observe consistent non-trivial information persistence characterized by topology locking, reduced yet stable causal structure, and sustained global stability well above randomized baselines. Rather than undergoing immediate randomization, the system exhibits a multi-stage decay process, converging toward a reduced set of stable informational nodes that act as persistent causal anchors. The results demonstrate that information decay is a structured dynamical process rather than an abrupt transition to entropy, even in the absence of active maintenance, error correction, or symbolic encoding. These findings have implications for nonequilibrium thermodynamics, theoretical neuroscience, and the physical limits of memory and system identity under irreversible transitions.