Systems frequently pursue declared targets: professional qualifications, technical capabilities, organizational capacities, or forms of expertise. In most descriptions these targets are framed in terms of motivation, planning, or intention. However, structural change does not arise from intention but from recurrence: the repeated exposure of a system to comparable operations or decision demands. Previous work within the KOGNETIK framework established that recurrence generates structural stabilization, drift, and mutation depending on the relationship between structure and recurring requirements. This paper introduces a complementary perspective: the inverse recurrence problem. Instead of asking which structures emerge from recurrence, we ask: Which recurrence regimes are necessary for a declared target structure to become reachable? We introduce a minimal structural model consisting of: • target structures 𝑆\*• structural floors defining minimal admissibility conditions• recurrence classes capable of inducing structural change• admissible recurrence paths connecting structures The framework defines structural reachability: a target structure is reachable from a given starting structure only if an admissible recurrence path exists that satisfies the floors of the target space. The result provides a minimal structural account of transformation processes across domains including learning, professional qualification, skill acquisition, and organizational capability development. 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 (Mon,) studied this question.