Cosmological Memory Networks & The Non-Unitary Entropy Pump

This research note presents Cosmological Memory Networks (CMN), a proposed theoretical framework that explores whether spacetime and gravitational structure can be modeled as a self-modifying, graph-based quantum associative memory network embedded on a non-Archimedean p-adic topological manifold. The central hypothesis of the framework is that physical spacetime may be interpreted not only through conventional geometric and metric descriptions, but also through an underlying information and memory architecture. Within this proposed model, nodes and connections represent elements of an evolving information structure, while p-adic distance provides a mathematical description of relationships between states or nodes within the network. The framework investigates the possibility that macroscopic physical behavior could emerge from the dynamics and resource constraints of such an information network. A principal component of the framework is the proposed Non-Unitary Entropy Pump. This mechanism is introduced as a theoretical process through which local entropy behavior may be altered by interactions with the proposed memory structure. The paper formulates a corresponding entropy expression and considers the possibility of local entropy reduction accompanied by information or entropy transfer within the larger network. The proposed mechanism is explored through a non-unitary evolution operator and through a coupling between memory dynamics and physical fields. The framework further introduces a Memory Stress Tensor, intended to represent the effective contribution of the proposed memory network to spacetime dynamics. This leads to a modified field-equation structure referred to as the Einstein-Memory equations, in which the conventional gravitational description is supplemented by a term associated with the dynamics of the proposed memory field. The paper presents an action-based formulation containing the p-adic curvature contribution, memory-field terms, and matter contributions, followed by a variational formulation for obtaining the corresponding field equations. The mathematical framework incorporates p-adic topology, graph and network concepts, information-theoretic quantities, entropy dynamics, tensor formulations, and gravitational field equations. A proposed relationship between network-node displacement, an internal clock scale, and the speed of light is also introduced as part of the model. These relationships are presented as components of the proposed CMN framework rather than as established physical laws. The paper additionally explores possible physical consequences of the proposed framework. One application is a theoretical model of propellant-free propulsion, in which interaction with the proposed memory structure is considered as a possible mechanism for generating effective momentum transfer without conventional propellant. A benchmark scenario involving a specified power input, resonance condition, system volume, and predicted thrust is presented as a theoretical example of the proposed mechanism. A second application considers relativistic interstellar travel. The paper examines a theoretical acceleration and energy-scaling scenario for travel to Alpha Centauri and discusses relativistic effects, including the difference between elapsed time measured by an Earth-based observer and the corresponding proper time experienced by a hypothetical crew. The calculations are presented as consequences of the proposed theoretical framework and are intended as benchmark scenarios rather than experimental demonstrations. The framework is also applied to a proposed model of wormhole stabilization. The paper introduces a throat-equilibrium condition and considers the possibility that memory-field dynamics could contribute to the stabilization of a wormhole geometry and the reduction of tidal effects. A theoretical traversal benchmark is provided for a specified throat size, initial velocity, and travel distance. Finally, the paper proposes an experimental verification blueprint intended to provide a possible route for testing selected predictions of the framework. The proposed setup involves a Rydberg-dressed Rubidium-87 Bose-Einstein condensate, low-temperature operation, ultraviolet laser excitation to a specified Rydberg state, a high-frequency pump, and measurement techniques involving optical absorption imaging and a micro-cantilever. The purpose of the proposed experiment is to investigate whether measurable effects corresponding to the theoretical memory-field and entropy-pump mechanisms could be observed. The paper therefore brings together concepts from theoretical physics, mathematical physics, quantum information, p-adic topology, gravitation, entropy, and information dynamics into a single proposed framework. Its objective is to formulate mathematical structures and experimentally testable scenarios around the hypothesis that information, memory, and network dynamics may play a deeper role in the structure and behavior of spacetime. This document represents the author's proposed theoretical framework and research hypothesis. The equations, mechanisms, numerical benchmarks, physical interpretations, and experimental predictions presented in this work have not been independently validated or established as accepted physical theory. The proposed models should therefore be interpreted as theoretical constructions intended for further mathematical analysis, critical examination, and potential experimental investigation.