This repository provides a framework for assembling and organizing mathematical expressions from multiple warp bubble analysis repositories into unified, publication-ready documents. It serves as a central coordination point for collecting, processing, and formatting complex mathematical expressions from distributed warp bubble physics calculations.
The warp bubble ecosystem generates numerous mathematical expressions across multiple repositories:
- Einstein field equations and their solutions
- Curvature tensor components and invariants
- Energy-momentum tensor expressions
- Constraint equations and their discretizations
- Optimization objective functions and gradients
This repository provides automated tools to:
- Collect expressions from upstream repositories
- Validate mathematical consistency and notation
- Organize expressions by physical content and mathematical structure
- Format expressions for publication in LaTeX documents
- Cross-reference expressions across multiple analysis workflows
- Repository Integration: Automated fetching from upstream warp bubble repositories
- Mathematical Validation: Consistency checking and symbolic verification
- LaTeX Generation: Publication-ready mathematical document assembly
- Expression Tracking: Version control and change detection for mathematical expressions
- Batch Processing: Efficient handling of large expression collections
- Smart Organization: Automatic categorization by physics content
warp-bubble-assemble-expressions/
├── scripts/
│ ├── collect_expressions.py # Fetch expressions from upstream repos
│ ├── validate_expressions.py # Mathematical consistency checking
│ ├── organize_expressions.py # Categorization and cross-referencing
│ └── generate_documents.py # LaTeX document assembly
├── expressions/
│ ├── einstein_equations/ # Field equation expressions
│ ├── curvature_tensors/ # Geometric expressions
│ ├── energy_momentum/ # Matter field expressions
│ └── constraints/ # Constraint equation expressions
├── templates/
│ ├── physics_document.tex # Physics paper template
│ ├── technical_report.tex # Technical documentation template
│ └── expression_library.tex # Mathematical expression catalog
└── docs/
├── usage_guide.md # Detailed usage instructions
├── expression_catalog.md # Complete expression reference
└── technical-documentation.md # Technical implementation details
- Python 3.8+
- LaTeX distribution (TeXLive or MiKTeX)
- Git access to related warp bubble repositories
git clone https://github.com/arcticoder/warp-bubble-assemble-expressions.git
cd warp-bubble-assemble-expressions
pip install -r requirements.txt# Collect expressions from all upstream repositories
python scripts/collect_expressions.py --source-repos ../
# Validate mathematical consistency
python scripts/validate_expressions.py --input expressions/
# Generate unified documentation
python scripts/generate_documents.py --template physics_document --output warp_bubble_physics.tex- warp-bubble-einstein-equations: Field equation expressions and solutions
- warp-bubble-connection-curvature: Geometric tensor calculations
- warp-bubble-parameter-constraints: Optimization constraint expressions
- warp-discretization: Finite-difference discretized expressions
- warp-solver-equations: Time evolution equation systems
- Research Publications: Automated generation of physics papers
- Technical Documentation: Comprehensive mathematical reference documents
- Educational Materials: Organized presentation for teaching and learning
- Software Documentation: Mathematical specification for numerical implementations
- Vacuum Equations: R_μν - ½g_μν R = 0
- With Matter: G_μν = 8πT_μν
- Linearized Gravity: Perturbative expansions around background metrics
- Metric Components: g_μν expressions for various warp bubble profiles
- Christoffel Symbols: Connection coefficients and their derivatives
- Curvature Tensors: Riemann, Ricci, and Einstein tensor components
- Exotic Matter: Stress-energy tensors for negative energy densities
- Energy Conditions: Null, weak, strong, and dominant energy condition violations
- Conservation Laws: ∇_μ T^μν = 0 and related constraint equations
- Objective Functions: Energy minimization and geometric optimization
- Constraint Equations: Physical viability and mathematical consistency conditions
- Lagrange Multipliers: Constrained optimization formulations
# Automated expression extraction from LaTeX documents
def collect_expressions_from_repo(repo_path, patterns):
"""
Scan repository for mathematical expressions matching patterns
Extract LaTeX formulas and organize by content type
"""
expressions = []
for tex_file in find_tex_files(repo_path):
math_content = extract_math_environments(tex_file)
categorized = categorize_expressions(math_content, patterns)
expressions.extend(categorized)
return expressions# Mathematical consistency checking
def validate_expression_consistency(expression_set):
"""
Check for notation consistency, dimensional analysis,
and mathematical validity across expression collection
"""
notation_check = verify_notation_consistency(expression_set)
dimension_check = verify_dimensional_consistency(expression_set)
math_check = verify_mathematical_validity(expression_set)
return combine_validation_results(notation_check, dimension_check, math_check)- Research Papers: Complete physics papers with organized mathematical content
- Technical Reports: Comprehensive documentation with detailed derivations
- Expression Catalogs: Reference documents listing all mathematical expressions
- Expression Index: Searchable database of mathematical expressions
- Dependency Tracking: Cross-references between related expressions
- Version History: Change tracking for mathematical content evolution
- Modular Architecture: Separate modules for collection, validation, and generation
- Plugin System: Extensible framework for new expression types and formats
- Configuration Management: Flexible configuration for different output requirements
- Automated Testing: Unit tests for expression parsing and validation
- Mathematical Verification: Symbolic computation checks for mathematical correctness
- Documentation Standards: Consistent formatting and cross-referencing
- Symbolic Computation: Integration with SymPy for advanced mathematical processing
- Machine Learning: Automated expression classification and relationship detection
- Interactive Visualization: Web-based exploration of mathematical expression networks
- Real-Time Synchronization: Live updates from upstream repository changes
- Collaborative Editing: Multi-user mathematical content development
- Publication Pipelines: Direct integration with journal submission systems
This project is released under the Unlicense - see the LICENSE file for details.
For detailed technical documentation, see docs/technical-documentation.md
- Scope: The materials and numeric outputs in this repository are research-stage examples and depend on implementation choices, parameter settings, and numerical tolerances.
- Validation: Reproducibility artifacts (scripts, raw outputs, seeds, and environment details) are provided in
docs/orexamples/where available; reproduce analyses with parameter sweeps and independent environments to assess robustness. - Limitations: Results are sensitive to modeling choices and discretization. Independent verification, sensitivity analyses, and peer review are recommended before using these results for engineering or policy decisions.