Geometric AI

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

Andrew H. Bond
Senior Member, IEEE · Department of Computer Science · San Jose State University

Spring 2026 · Book 11 of the Geometric Series

Part I: The Problem (Ch. 1–3)

  1. Chapter 1: The Scalar Alignment Trap
  2. Chapter 2: A Brief History of Alignment
  3. Chapter 3: The Case for Geometric Alignment

Part II: The Mathematical Framework (Ch. 4–8)

  1. Chapter 4: The Value Manifold
  2. Chapter 5: The Reward Irrecoverability Theorem
  3. Chapter 6: The Four Alignment Failures
  4. Chapter 7: The Alignment Gauge Group
  5. Chapter 8: The No Escape Theorem

Part III: Measurement (Ch. 9–12)

  1. Chapter 9: The Bond Index for AI
  2. Chapter 10: The Five Cognitive Signatures
  3. Chapter 11: Adversarial Probing
  4. Chapter 12: The Sycophancy Manifold

Part IV: Solutions (Ch. 13–16)

  1. Chapter 13: Gauge-Invariant Reward Models
  2. Chapter 14: Constitutional Geometry
  3. Chapter 15: Scalable Oversight
  4. Chapter 16: Geometric RLHF

Part V: The Frontier (Ch. 17–18)

  1. Chapter 17: Superalignment as Parallel Transport
  2. Chapter 18: Multi-Agent Alignment

Part VI: Synthesis (Ch. 19–20)

  1. Chapter 19: What AI Teaches the General Theory
  2. Chapter 20: Open Questions