Relational Memory and Conditional Coherence: Persistent Information-Bearing Constraints Across Quantum, Physical, and Embodied Systems: Formal Definitions, Exact Classical Demonstration, Guardrails, and a Reproducible Research Programme

Abstract

Abstract Memory is commonly described as information stored within a local physical substrate. This paper develops a broader operational account in which memory may also persist through information-bearing constraints distributed across relations among system components. A system is said to retain memory of an event when that event leaves a detectable and causally consequential influence on later states or behaviour. This persistent influence is termed a causal memory wake. The framework distinguishes locally stored information from joint-state relational memory, in which individual components may contain no recoverable information about a past event while their combined relation retains it. An exact classical XOR parity construction demonstrates this principle. Each component considered independently carries zero mutual information about the encoded event, while the joint state preserves the event completely. A temporal extension shows how such relational information decays under noise, with surviving memory quantified by mutual information and binary entropy. A fixed-seed Monte Carlo implementation is included as a computational verification of the analytic result; it demonstrates consistency of the implementation rather than empirical validation of biological memory. The paper extends the previously introduced Base-State Memory and Conditional Coherence framework. Conditional coherence describes a model that explains available evidence while remaining dependent on fragile or unverified relational bindings. Grounded assurance is approached when those bindings are independently supported, persistent, redundant, accessible, and robust under intervention. A relational conditional-burden metric is proposed to quantify dependence on unverified or unstable constraints. Quantum entanglement is considered only as a mathematically exact limiting example of nonseparable relational information. The paper does not claim that biological memory relies on entanglement, that consciousness is quantum-mechanical, or that memory or usable information travels faster than light. Decoherence and Quantum Darwinism are discussed solely as established physical frameworks concerning the suppression of interference and redundant environmental encoding; they are not proposed as mechanisms of biological memory. The paper presents formal definitions, exact classical demonstrations, computational tests, falsifiable predictions, failure criteria, and a staged research programme for examining relationally encoded memory across artificial, physical, and embodied systems. This work is a conceptual extension of: Riley, M. (2026). Base-State Memory and Conditional Coherence: A Layered State-Capacity Theory of Embodied Dimensional Assurance. Zenodo. https://doi.org/10.5281/zenodo.21432223 Status: Independent research manuscript; conceptual and computational methods paper; not peer reviewed. Version: 1.0 AI-Assistance Disclosure Artificial-intelligence systems, including OpenAI ChatGPT, Google Gemini, and xAI Grok, were used as research-support tools for manuscript structuring, language refinement, mathematical checking, critical review, formatting, and preparation of publication materials. The originating concepts, theoretical direction, interpretation of results, acceptance or rejection of suggested revisions, and final manuscript decisions are those of Matthew Riley. The author reviewed the complete work and accepts full responsibility for its accuracy, limitations, claims, and conclusions.