Autological Recursion as a Law Hypothesis: Scope, Decidability, and Falsifiability Conditions

This paper formalizes the epistemic status of autological recursion Ψ=∂𝑆/∂𝑅 as a scope-limited law hypothesis. It does not introduce new operators, domains, or empirical claims. Instead, it specifies the formal conditions under which Ψ is admissible, decidable, and falsifiable. The paper establishes (i) a canonical definition of structural sensitivity to recurrence, (ii) the Rule–State Separation Axiom (RSSA) as a necessary admissibility criterion, (iii) null, negative, and undefined regimes of Ψ, and (iv) an explicit set of falsification conditions. A strict separation between the law itself and its empirical operationalizations is enforced. The result is a formally closed, domain-general law hypothesis whose critique is restricted to defined attack surfaces. This paper marks the transition of autological recursion from a descriptive framework to a law-grade theoretical construct. Note on Objectivity The present law hypothesis does not define objectivity. However, once Ψ is treated as a law-grade operator, objectivity can be formally reconstructed as the invariant subset of S under R → ∞. This reconstruction is carried out in [Non-Ascriptive Objectivity, Elbasan 2025]. --- 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 --- 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.