A Three-Phase Generative Structure Model v2.0: Adaptive Dynamics, Background Conditions, and Structural Purity
Year: 2026
Type: preprint
Abstract: A Three-Phase Generative Structure Model v2.0: Adaptive Dynamics, Background Conditions, and Structural Purity This work extends the Three-Phase Generative Structure Model originally formulated through Dynamic, Static, and Breathing phases. Version 1.0 introduced the minimal generative cycle Dynamic → Static → Breathing as a structural grammar of differentiation, stabilization, and reintegration. Version 2.0 preserves this three-phase architecture while refining its mathematical formulation and extending it toward adaptive generative dynamics. The principal developments are: Refined convergence theorem: fixed-point convergence is reformulated under an explicit cycle-level contraction condition. Separation of convergence and self-similarity: convergence of a single three-phase operator is distinguished from self-similar attractors generated through a contractive iterated-function-system extension. Adaptive Three-Phase Dynamics: the fixed operator cycle is generalized to time-dependent Dynamic, Static, and Breathing operators whose behavior may vary with the evolving state. Background Conditions: persistent generative conditions are introduced as a layer that modulates the three phases rather than as a fourth phase. Structural Purity: a bounded structural variable is introduced to represent preservation of specified structural relations and to modulate phase dynamics. Adaptive stability: the model includes conditions for convergence to a common equilibrium and for tracking a moving equilibrium. Falsifiability and ablation: the full three-phase cycle can be compared with two-phase and single-phase alternatives to test whether each component contributes measurable explanatory or functional value. Version 1.0 is recovered as the fixed-operator regime of the adaptive formulation. The basic Dynamic–Static–Breathing grammar is therefore retained, while the conditions under which convergence, self-similarity, adaptation, and structural stability may be claimed are made more explicit. The resulting framework shifts the Three-Phase Generative Structure Model from a fixed descriptive cycle toward an adaptive, mathematically conditioned, and experimentally falsifiable generative framework. This release remains theoretical. Application-specific operator definitions, empirical validation, parameter identification, and comparative testing are reserved for future work.
Author: Nomura, Akio
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162783114
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