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Published November 19, 2025 | Version v1
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The Kernel Ontology Principle: Foundations for a Unified Fundamental Equation

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https://doi.org/10.5281/zenodo.17654165

Abstract
This work presents the Kernel Ontology Principle (KOP), a foundational proposal in theoretical physics and the philosophy of physical law. It introduces a unified meta-framework for understanding the relational ontology underlying all mathematical and physical structures.

KOP posits that every internally coherent universe is grounded in a minimal relational kernel, from which all mathematical formalisms, effective physical laws, and structural regularities emerge. In its strong formulation, this kernel is compressible into a single unified mathematical object - the Kernel Relation (HKR) - which functions as a candidate for a unified fundamental equation governing physical reality.

Theoretical Framework
The study develops a formal axiomatic foundation for KOP, encompassing:

  • Universality and Minimality
  • Compositional Invariance
  • Relational Structure and Mathematical Representability

It proposes that the kernel is encoded in one fundamental equation and introduces a three-path methodology for empirical and theoretical kernel reconstruction:

  1. Cross-scale invariance analysis
  2. Early-universe extrapolation
  3. Axiomatic minimization

These approaches provide a systematic methodology for identifying the minimal relational structure that must hold across all physical subsystems.

Ontological Distinction
The framework contrasts with the Mathematical Universe Hypothesis (MUH) by distinguishing ontology (the kernel as fundamental relational reality) from mathematical epistemology (formal descriptions). This distinction clarifies why unified laws in physics should exist. This meta-theoretical foundation connects naturally to the Energy–Information Continuity (EIK) hypothesis as a possible cosmogenetic mechanism, while remaining fully independent of EIK for its internal validity.

Key Contributions

  • Axiomatic Definition: A formal definition of the kernel as a minimal invariant relational structure.
  • The HKR: Introduction of the Kernel Relation (HKR) as the mathematically compressed representation of fundamental ontology.
  • Methodology: A structured approach for kernel identification across scales and cosmological epochs.
  • Empirical Survey: Analysis of invariants across quantum physics, relativity, thermodynamics, and information theory.
  • Falsifiability: Criteria for meta-theoretical unification and structural consistency.
  • Illustrative Model: A kernel example based on the 1D quantum harmonic oscillator.

Target Audience
Researchers in theoretical physics, fundamental physics, cosmology, mathematical physics, philosophy of physics, unification frameworks, and the ontology of physical law.

Significance
The Kernel Ontology Principle offers the first systematic ontological justification for the existence of unified physical laws. It opens a new direction in the search for a single fundamental relational equation that may underlie all physical phenomena, offering a conceptual and methodological foundation for future theoretical and empirical developments in the unification of physics.

Contact
For feedback or questions regarding this version: kh.researc@gmail.com

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