Strixformes: Relational Viability Under Incomplete and Changing Knowledge

Abstract This research investigates whether an observer can preserve an intended action by understanding and modifying the relationships between the parameters of a dynamic system, rather than necessarily reversing the original action when an undesirable outcome becomes possible. The investigation originates from the relational-coherence hypothesis: outcomes emerge through interacting conditions, actions, environmental relationships, and available corrective mechanisms. It examines the distinction between present safety and future viability, including how information, timing, physical resources, uncertainty, actuator failures, and changing relationships influence whether a safe continuation remains possible. The paper introduces the proposed Strixformes future-safety functional: SF_H(I₀) = max_π min_ω min_(t,i) [hᵢ(Zₜ^(π,ω)) / sᵢ] The functional expresses the greatest minimum normalized safety margin that an observer can guarantee across admissible future conditions using an information-respecting control strategy. The investigation synthesizes established robust viability, feedback control, set-membership estimation, and fault-tolerant planning methods within a relational framework. It presents formal definitions, conditional safety propositions, counterexamples, and selected computational findings. One verified synthetic result demonstrates that exact information reduces the minimum viable starting clearance from 7 to 3 units when a relationship remains stable. When the relationship may change adversarially before the next action, the same information provides no guaranteed improvement under the tested conditions. The central deduction is that an observer's present safety does not establish future viability. Preserving an intended outcome depends on the relationships that determine which safe corrections remain possible, the availability of sufficient physical control, and whether the observer's information remains useful when a decision must be made. The Strixformes formulation is proposed as a named research synthesis of existing mathematical concepts. It is not presented as a proven new physical law or an independently established novel mathematical operator. Research status: Preprint for independent mathematical criticism and verification. Not peer-reviewed. Research author: Olusehinde Elijah Kolawole (Strixformes). Declaration of AI-Assisted Research : OpenAI's ChatGPT was used to support mathematical modelling, computational experimentation, code development, and manuscript preparation. The research questions and conceptual direction were initiated by the author. The author assumes responsibility for independently verifying the mathematical claims, computational results, references, and final published content.