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Vol. 1 · Fragile Mechanics

Overview
Part I - Foundations
- The Control Loop: Representation and Control
Part II - The Sieve (Runtime Safety)
Part III - Implementation Architecture
Part IV - Control & Belief
- Belief Dynamics: Prediction, Update, Projection
- Implementation Note: Entropy-Regularized Optimal Transport Bridge
Part V - Geometric Dynamics
Part VI - Holography & Field Theory
- The Reward Field: Value Forms and Hodge Geometry
- The Causal Information Bound
Part VII - Cognitive Extensions
Part VIII - Multi-Agent Gauge Theory
Part IX - Economics
Appendices
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
Architecture
Part II — Finite-Particle Convergence
Part III — Mean-Field Limits and Equilibrium
Part IV — Entropy, Regularity, and Bounds
Part V — Fractal Set and Continuum Limits
Part VI — Fields and Emergent Physics
Part VII — Computation and Experiments
Reference Material
- Frequently Asked Questions
- FractalAI: Research Lineage and Empirical Comparisons
Conclusion

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By Guillem Duran-Ballester