The Solution to the Is-Ought Problem: Ontology of General Persistence with Dual-Operator Dynamics and a Global Budget Indexed p(Γ)-Laplacian Law for System Stability

This manuscript proposes a solution to Hume’s is–ought problem by reframing it as a question about persistence. Instead of starting from moral intuitions or specific physical theories, it assumes only five ontological conditions: there are systems with internal representations, they receive feedback from an environment, they must remain within a viability set, they operate under finite resources, and their environment is non-stationary and partially beyond their control. From these assumptions, the paper derives a dual-operator dynamics: an Update role that revises internal representations in response to discrepancies, and an Optimize role that selects trajectories expected to minimise future discrepancy under resource constraints. At the field level, this recursion forces a structural correction term on top of any empirical Lagrangian, yielding a budget-indexed p (Γ) -Laplacian law of the form ℰu + λ ∇· (|∇u|^p (Γ) −2∇u) = 0, where p (Γ) encodes a global finite budget. The accompanying addendum sketches toy 1D–3D “universes” to illustrate how varying the budget parameter drives behaviour from diffusion to filamentation and collapse. A technical note explores if the correction role is structural and substrate-translatable, then, as a conjecture, inputs a term into the WDW equation. The text was originally drafted as a stand-alone chapter in a larger philosophical project and is presented here as a conceptual, domain-agnostic framework for system stability, rather than a completed empirical theory. It is intended primarily as a stake in the ground: a compact ontology of general persistence that can be tested, refined, or rejected by future work in philosophy, physics, and complexity science.