Why do systems repeatedly re-encounter themselves rather than dissipate into irrelevance?Across disciplines, recurrence is often explained by invoking an implicit motor: rotation, cyclic forcing, oscillation, or a privileged dynamical cause. This paper rejects that framing. It argues that recurrence requires no driver. Instead, recurrence arises as a structural default whenever minimal conditions are satisfied. The paper establishes three such conditions: partial conservation, output-to-input coupling, and effective boundedness. When a system cannot fully dissipate, cannot fully decouple its outputs from future inputs, and cannot expand without bound, repeated self-encounter is not an added hypothesis but the expected organization of process. Recurrence is treated not as a cause, force, or ontological principle, but as a structural consequence of constraint. A second upstream condition is then isolated: nonlinearity. While recurrence alone may be structurally neutral in idealized regimes, the presence of nonlinearity renders neutrality non-generic. Under recurrence, nonlinearity converts asymmetries, constraint couplings, thresholds, and saturation effects into cumulative structural consequences. As a result, repeated recurrence becomes a source of structural drift—not in a semantic or teleological sense, but as a change in the admissible structure of system behavior. The paper formulates these claims in a domain-agnostic manner and specifies explicit failure conditions under which recurrence or drift becomes negligible: full dissipation, strict feedforward organization, unbounded escape, global linearity, perfect cancellation, or complete independence of constraints. These conditions provide local falsifiability rather than metaphysical generalization. Finally, the paper clarifies the exact bridge to the law-level operator Ψ = ∂S/∂R. Once recurrence is structurally unavoidable and nonlinearity makes structural drift non-accidental, the question of measuring structural change per unit recurrence becomes coherent. This paper remains deliberately pre-law: it neither introduces nor justifies the law hypothesis, but establishes why recurrence should be expected and why recurrence cannot be assumed to be structurally inert. --- 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.