Ψ-CRITICAL REGIMES: Formal Boundary Conditions for Structural Decision Validity

This paper establishes the formal backbone for decision classification under structural recurrence within the KOGNETIK framework. Assuming the operator law Ψ = ∂S/∂R as law-grade, it introduces the concept of Ψ-critical regimes as admissibility boundaries for decisions under recurrence. The paper does not present applications, examples, or empirical claims. Instead, it defines what constitutes a decision, specifies conditions under which structural validity can be meaningfully assessed, and formalizes a closed typology of boundary violations (G₁–G₅). These regimes function as necessary and sufficient exclusion criteria for structural admissibility and serve as the sole reference framework for all subsequent case, system, and instantiation papers. The paper is neither normative nor explanatory; it is a jurisdictional infrastructure for structural decision analysis. --- 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.