A Structural Derivation of the Consciousness Dynamical System (CDS)

Note: A revised Version 2 of this work is available at DOI: 10.5281/zenodo.18851855. A Chinese version of this work is available at DOI: 10.5281/zenodo.18851253. The public repository for this work is available at: https://github.com/Li-Shaner/CDS-consciousness-dynamical-system. This paper proposes a formal mathematical framework for consciousness grounded in a set of foundational postulates. Within this framework, consciousness is characterized as a formalizable dynamical system (hereafter referred to as the Consciousness Dynamical System, CDS). Under a unified variable scheme, the system’s core equation—termed the consciousness dynamical equation—is derived: C = fd/(a + l) Here, C denotes coherence intensity. The variables f, d, a, and l represent the potential structural field, dynamical drive, information gradient, and information manifold, respectively. The term fd characterizes the generative contribution of the system, while a + l expresses the constraint and normalization conditions governing this generation. When the steady–state closed–loop condition a + l ≠ 0 is satisfied, the equation corresponds to the consciousness actualized state equation defined in this framework. This study addresses the following central question: Can consciousness be axiomatically characterized under minimal structural prerequisites and, from there, yield formal dynamical laws? The main contributions of the paper are as follows: (1) Research Objective: To construct a formalizable and derivable mathematical representation of consciousness; (2) Methodology: Postulate–based modeling, variable decomposition, and formal system derivation; (3) Result: Derivation of the consciousness dynamical equation C = fd/(a + l) under steady–state constraint conditions; (4) Significance: The framework provides a formally mappable variable structure applicable to life–information systems, cognitive dynamics, and artificial system design. This study does not aim to provide an empirical definition of consciousness. Instead, it offers an axiomatic theoretical pathway characterized by mathematical self–consistency, structural coherence, and potential testability. This preprint establishes a theoretical foundation, intended for further discussion, refinement, and future empirical investigation.