docs: Reorganize documentation into three-tier structure

**Three Manuals for Three Audiences:**

1. **User Manual** (docs/user/) - "Just Get It Done"
   - For end users, engineers, students
   - Simple, practical, step-by-step
   - Quick start, tutorials, examples, troubleshooting
   - Philosophy: Show me how to solve my problem

2. **Contributor Manual** (docs/contributor/) - "Show Me the Code"
   - For developers, contributors, advanced users
   - Technical, detailed, design rationale
   - Testing, architecture, performance, CI/CD
   - Philosophy: Explain HOW and WHY

3. **The JuliaFEM Book** (docs/book/) - "Let Me Show You How I Think"
   - For researchers, theory nerds, and Jukka
   - Comprehensive, educational, opinionated, personal
   - Math foundations, design philosophy, history, research
   - Philosophy: Mix theory, code, and personal experience

**Reorganization:**
- Moved: TESTING_PHILOSOPHY.md → contributor/testing_philosophy.md
- Moved: STATUS.md → contributor/status.md
- Moved: TEST_FIXES_NEEDED.md → contributor/test_fixes_needed.md
- Moved: lagrange_basis_functions.md → book/lagrange_basis_functions.md
- Moved: benchmarks/ → book/benchmarks/
- Created: docs/README.md (main index explaining structure)
- Created: README.md in each section explaining audience and contents
- Updated: All references in scripts and source files

**Naming:** All docs now lowercase (testing_philosophy not TESTING_PHILOSOPHY)

**Benefits:**
- Clear separation of concerns
- Users don't get overwhelmed with implementation details
- Contributors get technical depth
- Book preserves deep theory and personal insights
- Each manual optimized for its audience

**Next:** Populate each section with appropriate content

docs/book/README.md

@@ -0,0 +1,82 @@
+# The JuliaFEM Book
+
+**Audience:** Advanced researchers, theory nerds, those who want to understand the "why" and "how" at a deep level. And Jukka.
+
+This is the **JuliaFEM Bible** - a comprehensive manual mixing theory, philosophy, software design, and personal experience. It's educational, opinionated, and unapologetically deep.
+
+## What's Here
+
+- **Mathematical Foundations:** Lagrange basis functions, weak forms, contact mechanics
+- **Design Philosophy:** Why JuliaFEM exists, what problems it solves (and doesn't)
+- **Technical Vision:** Strategic mistakes from 2015-2019, lessons learned
+- **Research Directions:** Experimental ideas (nodal assembly, matrix-free, etc.)
+- **Personal Notes:** The journey, the failures, the "aha!" moments
+- **Theory + Code:** How mathematics becomes software
+
+## What's NOT Here
+
+- "How do I install?" (see `docs/user/`)
+- "How do I add a feature?" (see `docs/contributor/`)
+- Short answers (everything here is DEEP)
+
+## Philosophy
+
+**"Let me show you how I think about FEM."**
+
+This is:
+- **Educational:** Teach FEM through implementation
+- **Personal:** Written in Jukka's voice, reflecting 8+ years of experience
+- **Opinionated:** Strong views on what works and what doesn't
+- **Comprehensive:** From first principles to cutting-edge research
+- **Honest:** Documents failures as much as successes
+
+We assume you:
+- Love mathematics AND programming
+- Want to understand WHY, not just HOW
+- Have time to read deeply
+- Are curious about unconventional approaches
+- Might be me, 5 years from now, trying to remember why I did this
+
+## Structure
+
+### Part I: Foundations
+- Finite Element Method (brief review)
+- Lagrange Basis Functions (deep dive)
+- Assembly and Solving
+- Contact Mechanics
+
+### Part II: Software Design
+- Type Stability and Performance
+- Zero-Allocation Design
+- Immutability and Composition
+- Field System Architecture
+
+### Part III: History and Vision
+- Strategic Mistakes (2015-2019)
+- Why JuliaFEM is Different
+- Contact Mechanics Focus
+- Laboratory Philosophy
+
+### Part IV: Research
+- Nodal Assembly (experimental)
+- Matrix-Free Methods
+- Automatic Differentiation
+- GPU Acceleration
+
+### Part V: The Journey
+- Personal Reflections
+- Lessons Learned
+- Future Directions
+- Open Questions
+
+## Reading Guide
+
+- **For Theory:** Start with Part I
+- **For Design Rationale:** Start with Part II
+- **For History:** Start with Part III
+- **For Research Ideas:** Start with Part IV
+- **For Philosophy:** Read Part V first, then everything else
+
+---
+
+**Start here:** [Mathematical Foundations](foundations.md) | [Strategic Mistakes](strategic_mistakes.md) | [Why JuliaFEM?](philosophy.md)