KOGNETIK is constituted as a discipline for the admissible classification of structural claims under recurrence. Its object is neither cognition nor meaning, neither explanation nor mechanism, but the conditions under which claims about structural change remain well-posed when systems repeatedly re-encounter their own generative operations. The discipline is post-law with respect to the operator relation Ψ = ∂S/∂R and therefore neither re-derives nor justifies Ψ. Instead, it specifies the admissibility gates that determine when Ψ is classifiable at all and when a claim must be returned as null or formally undefined. Structure is constrained to non-semantic form: an equivalence class of generative rule-objects under explicitly declared invariances within an admissibility model. Recurrence is treated as an exposure condition rather than a motor-driven phenomenon. The central admissibility gate is Rule–State Separation (RSSA): a claim of structural change is admissible only when rule change is separable from state evolution under recurrence. Where this separation cannot be enforced or is undecidable in principle, KOGNETIK classifies the claim as undefined rather than permitting semantic substitution. This paper provides: (i) a membership test for admissible KOGNETIK claims, (ii) a regime logic separating null, non-null, and undefined outcomes, (iii) a strict separation between the law Ψ and any operational proxy, (iv) a closed boundary-case typology (G₁–G₅), and (v) a critique protocol specifying valid falsification and attack surfaces. KOGNETIK explains nothing and proposes no models or applications. It determines only when structural explanations under recurrence are admissible at all. --- Intellectual Property & ContactKOGNETIK® is a registered trademark of Serkan Elbasan (Germany).The KOGNETIK Research Series is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0). All scientific works within the series are open for citation and derivative research under proper attribution.For partnerships, translations, or applied development inquiries:✉️ research@kognetik.de · 🌐 https://www.kognetik.de 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 is a transformation rule, not a content or level. Domain-independent operator:Valid across biological, cognitive, artificial, social, industrial, and geophysical systems. Non-ascriptive, empirically testable:Ψ compares systems by observable structure and recurrence. Higher-order phenomena as specifications:Learning, adaptation, consciousness, governance, and identity are structured regimes of Ψ.