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 & 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.
Serkan Elbasan (Wed,) studied this question.