Recurrence Load and Instability in Recursive Systems: A Minimal Threshold Mechanism for Structural Change

Abstract Many complex systems undergo structural change after repeated exposure to comparable conditions. Such transitions appear in biological evolution, technological innovation, machine learning, and institutional reform. Despite extensive domain-specific explanations, the minimal dynamical mechanism generating pressure for structural change is rarely specified. This paper introduces a minimal recurrence–mismatch–load mechanism explaining when recursive systems exceed finite tolerance under persistent mismatch. A recursive system is represented by a rule object g=(O,C,U)g=(O,C,U)g=(O,C,U) inducing a reachable state region and an achievable performance set. When recurring requirements exceed maximal achievable performance, mismatch becomes uniformly bounded below. Recurrence load is defined through a linear recurrence equation driven by mismatch input. Closed-form dynamics yield asymptotic lower bounds on load accumulation and provide sufficient conditions for threshold exceedance. Structural mutation is interpreted as rule-object transformation expanding achievable performance. The framework identifies a minimal mechanism by which recursive systems accumulate structural pressure under persistent mismatch. Intellectual Property & Licensing The KOGNETIK Research Series is released under the Creative Commons Attribution–NonCommercial 4.0 International License (CC BY-NC 4.0). All scientific works within the series may be cited, shared, and adapted for non-commercial research purposes with proper attribution. Commercial use—including consulting, advisory services, integration into commercial platforms, monetized training, certification, or system-level deployment—is not permitted under this license and requires a separate written agreement. Full license text:https://creativecommons.org/licenses/by-nc/4.0/ For licensing, partnerships, translations, or applied development inquiries:research@kognetik.dehttps://www.kognetik.de ORCID: https://orcid.org/0009-0000-8544-4847 Kognetik Series Information KOGNETIK — Minimal Operator Definition of Reflexivity (Ψ = ∂S/∂R) Reflexivity as structural rate-of-change:Ψ = ∂S/∂R measures structural drift under recurrence. Process, not state:Reflexivity specifies a transformation rule rather than a content or level. Domain-independent operator:Applicable across biological, cognitive, artificial, social, industrial, and geophysical systems. Non-ascriptive and empirically testable:Ψ enables comparative analysis of systems via observable structure and recurrence. Higher-order phenomena as specifications:Learning, adaptation, consciousness, governance, and identity are structured regimes of Ψ.