Geometric Reasoning

From Search to Manifolds

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

Spring 2026 · Book 2 of the Geometric Series

Front Matter

  1. Preface
  2. Core Objects at a Glance

Part I: The Search-Geometry Connection

  1. Chapter 1: Reasoning as Search
  2. Chapter 2: When the Space Has Shape
  3. Chapter 3: The Heuristic Field
  4. Chapter 4: Geodesics and Optimal Reasoning

Part II: Failure Modes as Geometric Pathologies

  1. Chapter 5: Heuristic Corruption
  2. Chapter 6: Sycophancy as Search Hijacking
  3. Chapter 7: Local Minima, Premature Convergence, and Dead Zones
  4. Chapter 8: Gauge Invariance and Symmetry

Part III: The Control Layer

  1. Chapter 9: Metacognition as Search Control
  2. Chapter 10: The Robustness Surface
  3. Chapter 11: Alignment as Heuristic Shaping

Part IV: Empirical Program

  1. Chapter 12: Benchmarks as Geometric Probes
  2. Chapter 13: The Five Convergent Measurements
  3. Chapter 14: From Theory to Engineering

Part V: Horizons

  1. Chapter 15: Open Questions
  2. Chapter 16: Geometric Reasoning as a Field