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  • Lectures on Algorithmic Geometrodynamics

Vol. 1 · Fragile Mechanics

  • Overview
  • Part I - Foundations
    • The Control Loop: Representation and Control
  • Part II - The Sieve (Runtime Safety)
    • Limits: Barriers (The Limits of Control)
    • Failure Modes (Observed Pathologies)
    • Infeasible Implementation Replacements
  • Part III - Implementation Architecture
    • Computational Considerations
    • TopoEncoder Architecture: Attentive Atlas with Typed Latents
    • Optimization: Thermodynamic Governor and Stable Updates
  • Part IV - Control & Belief
    • Belief Dynamics: Prediction, Update, Projection
    • Implementation Note: Entropy-Regularized Optimal Transport Bridge
  • Part V - Geometric Dynamics
    • Wasserstein-Fisher-Rao Geometry: Unified Transport on Hybrid State Spaces
    • Radial Generation: Entropic Drift and Policy Control
    • The Equations of Motion: Geodesic Jump-Diffusion
  • Part VI - Holography & Field Theory
    • The Reward Field: Value Forms and Hodge Geometry
    • The Causal Information Bound
  • Part VII - Cognitive Extensions
    • Theory of Meta-Stability: The Universal Governor as Homeostatic Controller
    • Non-Local Memory as Self-Interaction Functional
    • Ontological Expansion: Topological Fission and the Semantic Vacuum
    • Computational Metabolism: The Landauer Bound and Deliberation Dynamics
    • Causal Discovery: Interventional Geometry and the Singularity of Action
    • The Metabolic Transducer: Autopoiesis and the Szilard Engine
    • The Inter-Subjective Metric: Gauge Locking and the Emergence of Objective Reality
    • Covariant Memory Attention: Self-Attention and Lorentzian Cross-Attention for Causal Retrieval
  • Part VIII - Multi-Agent Gauge Theory
    • The Standard Model of Cognition: Gauge-Theoretic Formulation
    • The Parameter Space Sieve: Deriving Fundamental Constants
    • The Geometric Micro-Architecture
    • Covariant Cross-Attention: The World Model as Geodesic Integrator
    • End-to-End Architecture: The Universal Geometric Network
  • Part IX - Economics
  • Appendices
    • Appendix B: Units, Parameters, and Coefficients (Audit Table)
    • Appendix C: WFR Stress-Energy Tensor (Full Derivation)
    • Appendix D: Frequently Asked Questions
    • Appendix E: Rigorous Proof Sketches for Ontological and Metabolic Laws
    • Appendix F: Loss Terms Reference
    • Appendix G: Architecture Modules Reference
  • Part XI - Implementation
    • The Covariant World Model: Geodesic Dynamics on the Poincare Ball
    • Geometric Dreamer — Model-Based RL on the Poincare Ball

Vol. 2 · Fractal Gas

  • Overview
  • Part I — Algorithms and Foundations
    • The Fractal Gas Algorithm Family
    • Variants of the Fractal Gas
    • Mathematical Foundations of Fragile
    • Euclidean Gas: Canonical Transition and Operator Estimates
    • Single Walker Observables and Probability Fields
    • Latent Fractal Gas: Algorithm and Analytic Conditions
  • Architecture
  • Part II — Finite-Particle Convergence
    • The Keystone Principle and the Contractive Nature of Cloning
    • Wasserstein-2 Control via Keystone-Based Variance Proxy
    • Hypocoercivity and Convergence of the Euclidean Gas
    • Convergence, Survival, and Parameter Dependence
  • Part III — Mean-Field Limits and Equilibrium
    • The Mean-Field Law of the Euclidean Gas
    • The Discrete Population Limit and Propagation of Chaos
    • Equilibrium Profiles and Their Analytical Characterization
    • Exchangeability, Empirical Laws, and Functional Inequalities
  • Part IV — Entropy, Regularity, and Bounds
    • Hypocoercive Entropy: From Kinetic Mixing to the Full Swarm
    • Mass, Hellinger, and Transport Convergence
    • C³ Regularity of the Fractal Gas Fitness
    • Smooth and Analytic Regularity of the Fractal Gas Fitness
    • Logarithmic Sobolev inequalities and entropy convergence
    • The Geometric Gas: Regularity, Stability, and Entropy
    • Quantitative Error Bounds
    • Parameter Constraints and Tuning
  • Part V — Fractal Set and Continuum Limits
    • The Fractal Set
    • Emergent Geometry from Adaptive Diffusion
    • Scutoid Spacetime: Moving Cells and Neighbor Changes
    • Continuum Limits: Hypotheses and Consistency
    • Fractal Set as Causal Set
  • Part VI — Fields and Emergent Physics
    • Direct Field Observables and Lattice QFT on the Fractal Set
    • Direct Observables and Standard Model Representations on the Fractal Set
    • Discrete Yang–Mills Actions, Noether Identities, and Quantum Reconstruction
    • Twistor Formulation of the Fractal Set
    • Curvature of the Algorithmic Fitness Metric
    • Field Equations and Pressure Dynamics
    • Algorithmic Thermodynamics, Graph Cuts, and Boundary Geometry
    • Expansion, Equilibrium, and Macroscopic Closure
    • Interactive experiments for Part VI: fields and algorithmic QFT
  • Part VII — Computation and Experiments
    • Measurement Operators on Scutoid Spacetime
    • Computational Proxies for Scutoid Geometry
    • Voronoi Wilson Loops on the Fitness Manifold
    • Empirical Validation of QFT Predictions
    • Fractal Gas QFT Calibration Notebook
    • QFT Calibration Report: Standard Model Parameter Mapping
    • QFT Calibration: Channel Knobs and Mass Plateaus
  • Reference Material
    • Frequently Asked Questions
    • FractalAI: Research Lineage and Empirical Comparisons
  • Conclusion
  • .md

Part VI — Fields and Emergent Physics

Part VI — Fields and Emergent Physics#

  • Direct Field Observables and Lattice QFT on the Fractal Set
  • Direct Observables and Standard Model Representations on the Fractal Set
  • Discrete Yang–Mills Actions, Noether Identities, and Quantum Reconstruction
  • Twistor Formulation of the Fractal Set
  • Curvature of the Algorithmic Fitness Metric
  • Field Equations and Pressure Dynamics
  • Algorithmic Thermodynamics, Graph Cuts, and Boundary Geometry
  • Expansion, Equilibrium, and Macroscopic Closure
  • Interactive experiments for Part VI: fields and algorithmic QFT

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Fractal Set as Causal Set

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Direct Field Observables and Lattice QFT on the Fractal Set

By Guillem Duran-Ballester

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