The Kernel Ontology Principle: Foundations for a Unified Fundamental Equation

This work introduces the Kernel Ontology Principle (KOP), a meta-framework in theoretical physics proposing that every coherent universe originates from a minimally sufficient relational structure, referred to as its Kernel. All higher-order physical laws, mathematical formalisms and emergent complexities arise as projections of this foundational structure. Unlike the Mathematical Universe Hypothesis, which identifies reality with mathematics itself, KOP treats mathematics as an epistemic language encoding a deeper ontological substrate. In its strong formulation, this substrate can be compressed into a single generative relation known as the Fundamental Kernel Relation (FKR). FKR is the central technical contribution of this work Presented in Appendix C, FKR provides a compact relational generator from which diverse physical behaviors can emerge. It offers a principled method for reconstructing effective laws from first principles, outlines necessary constraints for internal consistency and establishes a structural pathway toward unification. By specifying how relational configurations can transform while preserving invariants, FKR functions as a candidate blueprint for a unified relational physics. Its formulation enables cross-domain reconstruction (quantum, geometric and thermodynamic structures) and provides falsifiable criteria that any proposed fundamental equation must satisfy. The goal of KOP, strengthened by the introduction of FKR, is to explain why mathematics unifies physical theories so effectively and why diverse domains of physics share deep structural symmetries. Within this ontology, unification arises naturally from a universe generated by a minimally sufficient relational core. This framework offers a coherent explanation for the consistency linking quantum theory, spacetime geometry, thermodynamics and informational principles. KOP outlines a three-layer ontological hierarchy:• Ontology – the Kernel as the primary relational substrate.• Epistemology – mathematics as the representational language of Kernel relations.• Physics – effective laws emerging from Kernel structure across scales.This hierarchy accounts for the universality of mathematical structures and the cross-scale coherence observed in empirical science. KOP also integrates seamlessly with the other components of the Information Kernel Framework (IKF). In Information-Centric Cosmogenesis (ICC), universes arise from minimal informational kernels that become autonomous physical domains once relational complexity reaches a critical threshold. The Energy–Information Continuity Hypothesis (EIK) describes the energetic consequences of informational change, providing testable predictions for high-autonomy artificial systems. The Dark Energy as Topological Pressure (DETP) model extends these principles to cosmology by interpreting cosmic acceleration as a geometric response to increasing relational complexity. Methodologically, this work introduces a reconstruction program grounded in FKR:• Cross-scale analysis to identify persistent relational invariants.• Diachronic extrapolation toward structurally minimal early-universe states.• Axiomatic minimisation to identify the essential relational requirements for any self-consistent universe. KOP, together with FKR, is designed to be testable and falsifiable. The framework predicts specific relational invariances, defines empirical conditions for potential failure and imposes structural constraints on any attempt at a unified fundamental equation. This paper forms part of the Information Kernel Framework collection, a set of foundational works unifying ontology, informational dynamics, cosmogenesis and complexity-driven cosmology. The full IKF dataset is available at: https://doi.org/10.5281/zenodo.17823353 • Dark Energy as Topological Pressure (DETP)https://doi.org/10.5281/zenodo.17677395 • Information-Centric Cosmogenesis (ICC)https://doi.org/10.5281/zenodo.17694375 • Energy–Information Continuity Hypothesis (EIK)https://doi.org/10.5281/zenodo.17713324 For feedback or questions, contact: kh.researc@gmail.com