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

This work presents a complete, self-consistent ontological framework for theoretical physics built upon a discrete, finite-capacity quantum information network. The universe is modeled as a 3D lattice of 6-dimensional qudit pixels (C³_color ⊗ C²_spin) whose collective dynamics generate classical spacetime, gauge symmetries, the Standard Model particle spectrum, fermion mass hierarchies, and dark energy as emergent phenomena.

### Core Contributions
- **Chapter 1**: Establishes the irreducible 6D pixel axiom and variational projection principle that enforces local commutativity, deriving the structural debt formalism.
- **Chapter 2**: Derives emergent Lorentzian geometry, the Einstein equations, and dark energy directly from minimization of graph Dirichlet energy (structural debt).
- **Chapter 3**: Reproduces fractional electric charges via trace projections and explicit SU(2)×U(1) operators; demonstrates topological origin of three generations.
- **Chapter 4**: Introduces the calibrated Kramers escape mass mechanism with fractal dimension and fuzzy algebra, providing an exact fit to the charged lepton mass hierarchy and a geometric "shatter limit" proof for exactly three generations.
- **Chapter 5**: Resolves the black-hole information paradox by treating event horizons as topological phase transitions (shatter transitions at wrapping number w=4) that destroy classical geometry while strictly preserving underlying quantum information (unitarity).

The companion Jupyter notebook (`lattice_sim (5).ipynb`) implements the full unified dynamical engine: 3D lattice initialization, internal symmetry operators, non-perturbative mass hierarchy calibration, Hamiltonian time-evolution with overdamped Langevin integration, emergent Newtonian potential verification, and black-hole unitarity test.

**Version**: 7.0 (29 May 2026) — Final red-team compliant edition with explicit derivations, quantitative calibrations, and dynamical simulation.

**Keywords**: quantum gravity, discrete spacetime, emergent geometry, Standard Model, fermion generations, black hole information paradox, structural debt, fractal ontology, non-commutative geometry, lattice simulation

**License**: Creative Commons Attribution 4.0 International (CC BY 4.0)

This monograph and its executable companion constitute a complete, simulation-validated proposal for a unified physics engine grounded in information-theoretic principles.