The Discrete Information Substrate: A Fractal Ontology for Quantum Gravity and the Standard Model

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Description (Abstract):

Modern fundamental physics is fractured by the incompatible ontologies of General Relativity and Quantum Field Theory. This monograph proposes a strict ontological shift: the universe is fundamentally a discrete, finite-capacity quantum information network rather than a continuous manifold.

Postulating a 6-dimensional qudit register ($\mathbb{C}^3_{\text{color}} \otimes \mathbb{C}^2_{\text{spin}}$) as the irreducible foundational pixel, this framework demonstrates that classical spacetime emerges dynamically via a variational projection operator that minimizes local non-commutativity. The entropic cost of enforcing this classical geometry—termed "structural debt"—naturally yields a zero-point resonant tension synonymous with Dark Energy.

Matter arises as topological defects (knots) within this network. By mapping the fermion mass hierarchy to the Kramers Escape Rate of these defects, the framework reproduces the qualitative structure of the Standard Model generations and provides a geometric proof for the existence of exactly three generations: a fourth generation exceeds the unitarity bound of the network, shattering the local spacetime projection. This phase transition resolves the Black-Hole Information Paradox, demonstrating that black holes destroy classical geometry, but strictly preserve quantum information.