Book 11 of the Geometric Series

Geometric AI

Alignment, Safety, and the Structure-Preserving Path to Superintelligence

A volume in the Geometric Series by Andrew H. Bond.

Contents

  1. Geometric AI: Alignment, Safety, and the Manifold Structure of Machine Values
  2. Chapter 1: The Scalar Alignment Trap
  3. Chapter 2: A Brief History of Alignment --- and Its Geometric Mistake
  4. Chapter 3: The Case for Geometric Alignment
  5. Chapter 4: The Value Manifold
  6. Chapter 5: The Reward Irrecoverability Theorem
  7. Chapter 6: The Four Alignment Failures as Geometric Pathologies
  8. Chapter 7: The Alignment Gauge Group
  9. Chapter 8: The No Escape Theorem --- and What Escapes It
  10. Chapter 9: The Bond Index for AI
  11. Chapter 10: The Five Cognitive Signatures --- What the Measuring AGI Benchmarks Revealed
  12. Chapter 11: Adversarial Probing as Manifold Exploration
  13. Chapter 12: The Sycophancy Manifold
  14. Chapter 13: Gauge-Invariant Reward Models
  15. Chapter 14: Constitutional Geometry
  16. Chapter 15: Scalable Oversight as Gauge Verification
  17. Chapter 16: Geometric RLHF
  18. Chapter 17: Superalignment as Parallel Transport
  19. Chapter 18: Multi-Agent Alignment as Equilibrium
  20. Chapter 19: What AI Teaches the General Theory
  21. Chapter 20: Open Questions
  22. Appendix A: Mathematical Prerequisites
  23. Appendix B: The DEME V3 Architecture --- Code Walkthrough
  24. Appendix C: The Alignment Probe Suite
  25. Appendix D: Proofs of Headline Theorems
  26. Appendix E: Notation and Conventions
  27. Bibliography
  28. Index
  29. Table of Contents
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