Non-Algorithmic Reality and Emergent Law: Toward a Generative Framework for Cosmology and Physics

This paper examines the possibility that reality is not governed by a single closed, algorithmic rule set, but instead emerges from a deeper generative substrate. Building on undecidability arguments, non-computable collapse proposals, and layered ontology, the work motivates a shift from “final law” thinking toward “law formation” thinking. Drawing on prior discussions linking incompleteness and physics (e.g., Gödel-type arguments and undecidability analyses), the paper situates these ideas alongside Penrose’s Orch-OR proposal, where non-computable structure may already enter at the level of quantum state reduction. Rather than restricting non-algorithmicity to collapse events, the framework developed here embeds it within cosmology itself. Within the ψ₀–OCM (Osborne Cosmological Model), physical law is treated as an emergent phenomenon arising from redistribution processes operating on a non-algorithmic generative layer. Stabilised domains support familiar effective physics (GR, QFT, conservation structures), while anomalies, singularities, and regime transitions are interpreted not as failures of theory, but as transitions between layers. The paper develops the conceptual architecture, clarifies the operational meaning of non-algorithmicity, and outlines consequences for simulation, unification, and cosmology. It does not present a complete mathematical formulation; instead, it establishes priority for the claim that: • a non-algorithmic generative substrate precedes law,• physical law emerges through stabilisation,• observed physics represents only stabilised projections of deeper dynamics. A separate Supplement provides extended definitions, clarifications, and conceptual scaffolding supporting the broader ψ₀–OCM programme. Statement of Novelty This work advances the position that generative structure precedes physical law and that non-algorithmicity is a structural property of reality rather than a limit on knowledge. The ψ₀–OCM provides one concrete cosmological implementation of this view, integrating undecidability arguments, collapse-related proposals, and layer