Elder Theory

A novel mathematical framework for multi-domain learning and knowledge representation

Theory PDF • Student Workbook • Documentation • Report Issue

"Elder Theory: The Arcane Realization" is a comprehensive mathematical textbook that introduces a theoretical framework for hierarchical knowledge representation and multi-domain learning. The book presents the Elder-Mentor-Erudite system, which models how learning occurs at different levels of abstraction through orbital dynamics and gravitational interactions.

• Elder Spaces - Novel mathematical structures with phase operators and gravitational fields
• Heliomorphic Functions - Generalization of holomorphic functions with learning properties
• Hierarchical Learning - Multi-level knowledge representation (Elder-Mentor-Erudite)
• Orbital Mechanics - Knowledge transfer through gravitational resonance
• O(1) Memory - Theoretical framework achieving constant memory complexity

• ✅ Rigorous Mathematical Theory - 940 pages of publication-ready proofs and theorems
• ✅ Student Workbook - 37-page companion with worked examples and exercises
• ✅ Teaching Guide - Instructor resources with lecture notes and rubrics
• ✅ Complete Notation System - Consistent mathematical macros throughout
• ✅ Container-Based Builds - No local LaTeX installation required
• ✅ Modular Structure - Theory, teaching materials, and student resources organized separately

• Typesetting: LaTeX (TeX Live 2025)
• Engine: LuaLaTeX
• Bibliography: Biber (biblatex)
• Diagrams: TikZ + PGFPlots
• Containerization: Podman with official TeX Live image
• Build System: GNU Make
• Version Control: Git

• Podman >= 4.0 (or Docker)
• GNU Make (usually pre-installed)
• No LaTeX installation needed! (uses container)

# Clone repository
git clone https://github.com/ykashou/latex-elder-theory.git
cd latex-elder-theory

# Build main theory document (~5-10 minutes)
make theory

# View result
open build/theory/elder_arcane_realization.pdf

Output: 934-page PDF with complete theory (4.2 MB)

# Build everything
make theory              # Main theory document
make student_workbook    # Student workbook
make teaching_guide      # Teaching guide

# Or see all options
make help

latex-elder-theory/
├── theory/                    # 📘 Main Mathematical Theory
│   ├── main.tex              # Document entry point
│   ├── chapters/             # All chapter content
│   │   ├── part1_theory/     # Theoretical foundations (Units I-VII)
│   │   │   ├── unit1_foundation_layer/
│   │   │   ├── unit2_heliomorphic_functions_and_geometry/
│   │   │   ├── unit3_elder_heliosystem_architecture/
│   │   │   ├── unit4_learning_dynamics_and_algorithms/
│   │   │   ├── unit5_cross_domain_knowledge_transfer/
│   │   │   ├── unit6_theoretical_unification_and_closure/
│   │   │   └── unit7_memory_and_efficiency_properties/
│   │   ├── part2_experiments/ # Empirical validation (Units I-III)
│   │   └── appendix/         # Advanced proofs and references
│   └── bibliography.bib      # Bibliography references
│
├── student_workbook/          # 🎓 Student Learning Materials
│   ├── README.md             # Student resources overview
│   └── chapter1/             # Chapter 1 materials
│       ├── workbook.tex      # Regular workbook
│       ├── workbook_enhanced.tex  # Enhanced version
│       ├── study_book.tex    # Study book
│       └── components/       # Workbook parts
│
├── teaching_guide/            # 👨‍🏫 Instructor Resources
│   ├── README.md             # Teaching guide overview
│   ├── chapter1_guide.tex    # Chapter 1 instructor guide
│   ├── lecture_notes/        # Lecture materials
│   ├── assessment_rubrics/   # Grading criteria
│   └── solutions_manual/     # Complete solutions
│
├── shared/                    # 🔧 Common Resources
│   ├── macros/               # LaTeX macros and commands
│   │   ├── math_macros.tex   # Mathematical notation
│   │   ├── tikz_styles.tex   # TikZ diagram styles
│   │   └── chapter_summary.tex # Summary templates
│   ├── figures/              # Diagrams and illustrations
│   └── examples/             # Code examples and algorithms
│
├── build/                     # 📦 Build Outputs (gitignored)
│   ├── theory/               # Theory PDF output
│   ├── teaching_guide/       # Teaching guide output
│   └── student_workbook/     # Workbook outputs
│
├── docs/                      # 📝 Documentation
│   ├── annotations/          # Annotation tracking
│   ├── reviews/              # Chapter reviews
│   └── archive/              # Archived planning docs
│
├── scripts/                   # 🔨 Build and Automation Scripts
├── assets/                    # 🎨 Static Assets
├── tests/                     # 🧪 Test Files
├── Makefile                   # Build system
└── README.md                  # This file

The easiest way to build PDFs using the container:

# Main theory document (5-10 minutes, 940 pages)
make theory

# Student workbook (1 minute, 37 pages)
make student_workbook

# Teaching guide (1 minute, 5 pages)
make teaching_guide

# Clean auxiliary files
make clean

# Clean everything including PDFs
make realclean

# Show all options
make help

# Theory document (if Make is unavailable)
podman run --rm -v $(pwd):/workspace:Z -w /workspace \
  docker.io/texlive/texlive:latest \
  bash -c "cd theory && \
    lualatex --interaction=nonstopmode --output-directory=../build/theory main.tex && \
    cd ../build/theory && biber main && cd ../../theory && \
    makeindex ../build/theory/main.idx && \
    lualatex --interaction=nonstopmode --output-directory=../build/theory main.tex && \
    lualatex --interaction=nonstopmode --output-directory=../build/theory main.tex && \
    lualatex --interaction=nonstopmode --output-directory=../build/theory main.tex && \
    lualatex --interaction=nonstopmode --output-directory=../build/theory main.tex && \
    cp ../build/theory/main.pdf ../build/theory/elder_arcane_realization.pdf"

For Docker: Replace podman with docker and remove :Z SELinux label.

After successful compilation:

• ✅ Table of Contents
• ✅ List of Figures (133 entries)
• ✅ List of Tables (103 entries)
• ✅ Part I: Theory (7 Units, 896 pages)
  • Unit I: Foundation Layer
  • Unit II: Heliomorphic Functions and Geometry
  • Unit III: Elder Heliosystem Architecture
  • Unit IV: Learning Dynamics and Algorithms
  • Unit V: Cross-Domain Knowledge Transfer
  • Unit VI: Theoretical Unification and Closure
  • Unit VII: Memory and Efficiency Properties
• ✅ Part II: Experiments (3 Units)
• ✅ Appendices (Glossary, Notation, Advanced Proofs)
• ✅ Bibliography
• ✅ Index

Pedagogical companion with:

• 15+ worked examples with complete arithmetic steps
• 10+ practice exercises with detailed solutions
• Intuition boxes explaining abstract concepts
• Formula reference sheets
• Calculation checklists
• Common mistakes appendix

Location: student_workbook/chapter1/workbook.tex
Build: make student_workbook

• Enhanced Workbook: student_workbook/chapter1/workbook_enhanced.tex (50 pages)
• Study Book: student_workbook/chapter1/study_book.tex (82 pages)

Build manually when needed (see student_workbook/README.md).

The teaching guide provides:

• Lecture notes with pacing suggestions
• Assessment rubrics for grading
• Complete solutions manuals
• Discussion prompts
• Learning objectives per chapter
• Common student misconceptions

Status: 🚧 Under development
Location: teaching_guide/

• Maintain mathematical rigor with formal definitions, theorems, and proofs
• Follow ruleset in .cursor/rules/ for consistency
• Include complete proofs (no "proof sketches")
• Add dependency comments to all theorems
• Use macros from shared/macros/math_macros.tex consistently
• Add new terms to glossary and index

• Show all arithmetic steps explicitly
• Use concrete numerical values (not just variables)
• Provide intuition before formal calculations
• Include interpretations of results
• Progressive difficulty (beginner → advanced)
• Self-contained sections

See .cursor/rules/ for detailed guidelines.

Custom notation is defined in shared/macros/math_macros.tex:

\elder{d}         % Elder space of dimension d
\mentor{k}        % Mentor space
\erudite{n}       % Erudite space
\elderloss        % Elder loss function
\helio            % Heliomorphic function space

1. Create .tex file in appropriate theory/chapters/ subdirectory
2. Add \input{} command in theory/main.tex
3. Follow established chapter structure
4. Use \chaptersummary{} template
5. Add to table of contents

See .cursor/rules/student-workbook-guidelines.mdc for comprehensive guidelines.

# Compile test documents
cd tests/
make test

# Check for LaTeX errors
grep "Error" build/theory/main.log

# Verify cross-references
grep "undefined" build/theory/main.log

Issue: podman: command not found
Solution: Install podman or use docker (replace podman with docker in commands)

Issue: "Too deeply nested" errors
Solution: These are in appendix files, not core chapters. PDF still generates successfully.

Issue: Missing bibliography entries
Solution: Ensure theory/bibliography.bib exists. Some citations may reference future work.

Issue: Permission errors with containers (SELinux)
Solution: Add :Z flag for Podman on SELinux systems (Fedora/RHEL): -v $(pwd):/workspace:Z

Issue: Incomplete List of Figures/Tables
Solution: Ensure all 5 LaTeX passes complete (this is automated in make theory)

1. Fork the repository
2. Create branch following convention:
   • feature/unit-X-chapter-Y for new chapters
   • fix/annotation-XX for addressing annotations
   • docs/chapter-X-review for documentation
3. Follow mathematical rigor rules (see .cursor/rules/)
4. Ensure document compiles: make theory
5. Update notation appendix if adding new symbols
6. Submit pull request with detailed description

1. Follow workbook guidelines in .cursor/rules/
2. Include complete worked solutions
3. Test compilation: make student_workbook
4. Verify all arithmetic steps shown

1. Add to teaching_guide/ directory
2. Include learning objectives
3. Provide assessment rubrics
4. Follow LaTeX styling conventions

• Annotation System: docs/annotation_implementation_checklist.md
• Theorem Dependencies: See dependency tracking in .cursor/rules/
• Content Organization: Theory vs Experiments guidelines
• Mathematical Rigor: Proof validation requirements
• Notation Consistency: Symbol usage rules

• Makefile: Container-based builds for all documents
• Scripts: scripts/ directory contains automation tools
• Rules: .cursor/rules/ contains quality guidelines

Every theorem includes:

• ✅ Complete formal proofs (no sketches)
• ✅ Explicit dependency tracking
• ✅ All assumptions stated upfront
• ✅ Edge cases addressed
• ✅ Counterexamples when needed

• ✅ Consistent macros across 940 pages
• ✅ Consolidated notation appendix
• ✅ Symbol glossary with page references
• ✅ Index of terms

• ✅ 133 figures (TikZ diagrams)
• ✅ 103 tables (data and comparisons)
• ✅ Colored theorem environments
• ✅ Chapter summaries in styled boxes

# Edit theory chapters
vim theory/chapters/part1_theory/unit1_foundation_layer/introduction_to_elder_spaces.tex

# Rebuild
make theory

# Quick rebuild (skip bibliography/index)
podman run --rm -v $(pwd):/workspace:Z -w /workspace \
  docker.io/texlive/texlive:latest \
  bash -c "cd theory && lualatex --output-directory=../build/theory main.tex"

# Edit shared macros
vim shared/macros/math_macros.tex

# Add to notation appendix
vim theory/chapters/appendix/consolidated_notation.tex

# Rebuild to verify
make theory

# Add new TikZ figure
vim shared/figures/new_category/new_diagram.tex

# Reference in chapter
# \input{../../shared/figures/new_category/new_diagram.tex}

# Rebuild
make theory

• Theory Chapters: 108 .tex files
• Total Pages: 940 (theory) + 37 (workbook) + 5 (teaching) = 982 pages
• Figures: 133 diagrams across 18 categories
• Tables: 103 data tables
• Theorems: 100+ proven theorems
• Proofs: Complete, rigorous proofs throughout

• LaTeX Passes: 5 (for complete cross-references and lists)
• Compilation Time: ~5-10 minutes (theory), ~1 minute (workbooks)
• Dependencies: Bibliography (biber), Index (makeindex), Cross-references

1. Read theory document for formal mathematics
2. Work through student workbook for practice
3. Attempt exercises before checking solutions
4. Build intuition with worked examples

1. Study theoretical framework (Part I)
2. Examine experimental validation (Part II)
3. Reference notation appendix
4. Cite theorems and definitions

1. Use theory as textbook
2. Assign workbook exercises
3. Reference teaching guide for lecture planning
4. Use assessment rubrics for grading

1. Study algorithmic specifications (Unit IV)
2. Reference complexity bounds (Unit VII)
3. Examine implementation examples (Part II)
4. Use as specification for Elder system implementation

Copyright © 2025 by Yanal Luay Kashou.

This work is licensed under the Elder License - an open-source license permitting reproduction, distribution, and transmission with attribution.

See LICENSE file for complete terms.

• The mathematical community for foundational theories
• Complex analysis and operator theory traditions
• Machine learning research inspiring novel frameworks
• All who seek to understand dynamic knowledge representation

• Author: Yanal Luay Kashou
• Email: yanal.kashou@gmail.com
• GitHub: @ykashou
• Issues: Report bugs or request features

• Elder Labs: https://elder.labs (theoretical foundation)
• Research Papers: (to be published)
• Implementation: (to be open-sourced)