Geometric Information Dynamics Construction D: The Physical Landscape Below the Planck Scale—The Ultimate Structure of Information Ontology

This paper explores the fundamental issues of physical description below thePlanck scale within the unified framework of Geometric Information Dynamics.When scales fall below the Planck length or energies exceed the Planck energy, theclassical spacetime background breaks down. This work posits that in this extremeregime, the core of the information hierarchy does not vanish but manifests as apurely algebraic, non-geometric discrete network structure, whose symmetries andtopological properties are strictly constrained by the Jones discrete spectrum insubfactor theory. We argue that under the limit of physical operability, the nestedtower structure of information levels converges to a finite-depth or periodic “algebraic primitive,” which can be effectively described by a finite-dimensional fusioncategory (such as the Fibonacci category Fib). Its quantum dimension correspondsto the Jones index d = √2 derived from the minimal unit of information gain∆µmin = ln2. In this picture, concepts such as spacetime, causality, and matter donot exist as fundamental entities but emerge as collective phenomena arising fromthis algebraic primitive through specific dynamical processes (e.g., coarse-graining,symmetry breaking) at higher information levels. The paper further constructs anemergent dynamics framework from the algebraic primitive to macroscopic spacetime geometry and causal structure, and discusses potential pathways for indirectlytesting this theory through astrophysical and cosmological observations, such asultra-high-energy cosmic ray spectral distortions, primordial black hole evaporationremnants, and non-Gaussianities in the cosmic microwave background radiation.