### Install and Run Provenance Example

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/provenance/README.md

Installs the package and runs a Python script to demonstrate the creation and validation of a simple derivation tree. This is useful for verifying basic provenance functionality.

```bash
pip install -e .
PYTHONPATH=. python - <<'PY'
from provenance.derivation_tree import DerivationNode, ProvenanceTree, DerivationType, ProvenanceValidator
ax = DerivationNode("A","A", derivation_type=DerivationType.AXIOM) 
th = DerivationNode("B","B", derivation_type=DerivationType.THEOREM, dependencies=["A"], numerical_value=1.0)
tg = DerivationNode("C","C", derivation_type=DerivationType.TARGET, dependencies=["B"], numerical_value=2.0)
t = ProvenanceTree(ax); t.add_node(th); t.add_node(tg)
print(ProvenanceValidator().validate_tree(t))
PY
```

--------------------------------

### Clone Repository and Install Dependencies

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/README.md

Steps to clone the FIRM repository, navigate into the directory, and install the project with development dependencies. Includes running pytest to verify the setup.

```bash
git clone https://github.com/ktynski/FIRM-Fractal-Identity-Recursive-Mechanics.git
cd ExNahiloReality
pip install -e ".[dev]"
pytest  # Verify tests pass
```

--------------------------------

### Install FIRM and Dev Dependencies

Source: https://context7.com/ktynski/firm-fractal-identity-recursive-mechanics/llms.txt

Clone the repository, install the package, and set up development dependencies including testing tools.

```bash
git clone https://github.com/ktynski/FIRM-Fractal-Identity-Recursive-Mechanics.git
cd ExNahiloReality
pip install -e .

# Dev setup (includes test dependencies)
pip install -e ".[dev]"

# Verify environment
pytest testing/ -v
```

--------------------------------

### Install FIRM Project

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/README.md

Clone the repository and install the FIRM project locally using pip. This sets up the project for development and usage.

```bash
git clone https://github.com/ktynski/FIRM-Fractal-Identity-Recursive-Mechanics.git
cd ExNahiloReality
pip install -e .
```

--------------------------------

### Install Dependencies

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/arxiv_paper/FIRM_FINAL_SUBMISSION/FIGURE_GENERATION_GUIDE.md

Navigate to the project directory and install required Python packages.

```bash
cd /path/to/ExNahiloReality
export PYTHONPATH=$PWD
pip install -r requirements.txt
```

--------------------------------

### Setup Testing Environment with Pytest

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/MASTER_TESTING_STRATEGY_3_TEAMS.md

Commands to set up the testing environment using pytest, including installing necessary packages and verifying the pytest installation.

```bash
python -m pytest --version
```

```bash
pip install pytest-cov
```

```bash
pip install pytest-xdist
```

--------------------------------

### Install Project Package

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/applications/README.md

Install the project in editable mode. This command is typically run after cloning the repository to set up the development environment.

```bash
pip install -e .
```

--------------------------------

### Module Import and Test Setup

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/TeamEdits.md

This snippet demonstrates setting up module imports and a basic test class structure. It includes mocking sys.modules for 'scipy' and 'numpy', manipulating sys.path for custom module imports, and defining a test class with setup and basic attribute/method tests.

```python
sys.modules['scipy'] = Mock()
sys.modules['numpy'] = enhanced_numpy
# ... comprehensive scipy/numpy/matplotlib submodule mocking

# Add paths for imports
sys.path.insert(0, str(Path(__file__).parent.parent.parent))
sys.path.insert(0, str(Path(__file__).parent.parent.parent / "[domain]"))

# Import target module
from [domain].[module] import *

class Test[ModuleClass]:
    def setup_method(self):
        self.[module] = [ModuleClass]()
    
    def test_import_success(self):
        assert [ModuleClass] is not None
        
    def test_module_attributes_comprehensive(self):
        # Systematic attribute exercising
        attrs = dir(self.[module])
        for attr in attrs:
            if not attr.startswith('_'):
                try:
                    value = getattr(self.[module], attr)
                    assert value is not None
                except: pass
                
    def test_[method1]_execution(self):
        result = self.[module].[method1]()
        assert result is not None
        
    # [6-8 systematic method tests]
```

--------------------------------

### Install and Run Cosmology Tests

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/cosmology/README.md

Installs the project in editable mode and runs cosmology tests. Also demonstrates computing and printing the first 5 multipoles of the CMB power spectrum.

```bash
pip install -e .
PYTHONPATH=. pytest -q testing/cosmology -q
PYTHONPATH=. python -c "from cosmology.cmb_power_spectrum import CMB_SPECTRUM; print(CMB_SPECTRUM.compute_cmb_power_spectrum(ell_max=256).multipoles[:5])"
```

--------------------------------

### Python Project Setup Script

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/simulations/webgl/src/docs/theory/FIRM_PERFECT_ARCHITECTURE.md

Configures the Python package metadata, including name, version, author, description, long description, URL, and classifiers. It specifies package discovery, Python version requirements, and installation dependencies, including optional extras and console script entry points.

```python
# setup.py content
SETUP_PY = """
from setuptools import setup, find_packages

with open("README.md", "r", encoding="utf-8") as fh:
    long_description = fh.read()

setup(
    name="exnihilograce",
    version="1.0.0",
    author="FIRM Team",
    description="Ex Nihilo Theory of Everything - Grace Operator Framework",
    long_description=long_description,
    long_description_content_type="text/markdown",
    url="https://github.com/FIRM/exnihilograce",
    packages=find_packages(),
    classifiers=[
        "Development Status :: 4 - Beta",
        "Intended Audience :: Science/Research",
        "Topic :: Scientific/Engineering :: Physics",
        "License :: OSI Approved :: MIT License",
        "Programming Language :: Python :: 3",
        "Programming Language :: Python :: 3.9",
        "Programming Language :: Python :: 3.10",
        "Programming Language :: Python :: 3.11",
    ],
    python_requires=">=3.9",
    install_requires=[
        line.strip() 
        for line in open('requirements.txt').readlines() 
        if line.strip() and not line.startswith('#')
    ],
    extras_require={
        "dev": ["pytest", "black", "pylint", "mypy"],
        "docs": ["sphinx", "sphinx-rtd-theme"],
        "notebooks": ["jupyter", "ipywidgets"],
    },
    entry_points={
        "console_scripts": [
            "FIRM-verify=verification.standalone:main",
            "FIRM-check=scripts.check_contamination:main",
            "FIRM-report=scripts.generate_report:main",
        ],
    },
)
"""

```

--------------------------------

### Recreate Python Environment

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/README.md

Use these commands to create a virtual environment and install dependencies. Ensure Python 3.10-3.12 is installed.

```bash
python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
```

--------------------------------

### Reproducible Workflow Setup

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/arxiv_paper/FIRM_FINAL_SUBMISSION/compile_output.txt

Set up the environment to regenerate figures. Ensure the PYTHONPATH is correctly set to the current directory before running the Python script.

```bash
PYTHONPATH=$PWD python
```

--------------------------------

### Validation and Testing

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/constants/README.md

Example showing how to use the validation module to verify all derivations and check the validity and provenance chain of a specific constant.

```python
from constants import validate_derivations

# Verify all derivations
validation = validate_derivations()

# Check specific constant
alpha_validation = validation.check_constant("fine_structure_constant")
print(f"α derivation valid: {alpha_validation.is_valid}")
print(f"Provenance chain: {alpha_validation.provenance_chain}")
```

--------------------------------

### Proposed Documentation Directory Structure

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/docs/cleanup_plan.md

Organizes documentation into distinct sections for main project info, quickstart guides, API details, theory, derivations, validation, tutorials, and contribution guidelines.

```tree
docs/
├── README.md               # Main project documentation
├── quickstart/             # Getting started guides
├── api/                    # API documentation
├── theory/                 # Mathematical framework
├── derivations/            # Mathematical derivations
├── validation/             # Experimental comparisons
├── tutorials/              # Step-by-step tutorials
└── contributing/           # Contribution guidelines
```

--------------------------------

### Create Foundation Proof Files

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/PEER_REVIEW_READINESS_PLAN.md

Immediately create these Python files to address mathematical foundation gaps. Files marked with ❌ NEEDED require immediate attention.

```python
# Create these files IMMEDIATELY:
foundation/proofs/axiom_independence_proof.py ✅ CREATED
foundation/proofs/grace_operator_existence.py ❌ NEEDED
foundation/proofs/phi_emergence_necessity.py ❌ NEEDED
foundation/proofs/fixed_point_uniqueness.py ❌ NEEDED
```

--------------------------------

### FIRM v2 Pipeline Switching Example

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/applications/visualization/FIRM_FSCTF_v2_COMPLETE_MASTER_PLAN.md

Demonstrates how to switch between different FIRM pipeline versions using URL parameters. The default is FIRM v2, with options for strict mode and legacy.

```URL
?pipeline=firm-v2
```

--------------------------------

### Complete Framework Analysis

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/constants/README.md

Example demonstrating how to access all constants within the FIRM framework and perform a comprehensive analysis, including total count, average agreement, and mathematical basis.

```python
from constants.complete_firm_constants import FIRM_CONSTANTS

# Access all constants
constants = FIRM_CONSTANTS()

# Comprehensive analysis
analysis = constants.analyze_all_constants()
print(f"Total constants: {analysis.total_count}")
print(f"Average agreement: {analysis.average_agreement:.3f}%")
print(f"Mathematical basis: {analysis.mathematical_basis}")
```

--------------------------------

### FIRM Build Order - Phase 15 Documentation

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/simulations/webgl/src/docs/theory/FIRM_PERFECT_ARCHITECTURE.md

Lists the files for documentation and demos in Phase 15 of the FIRM build order.

```python
'ExNihiloGrace/documentation/glossary.md',
        'ExNihiloGrace/documentation/faq.md',
        'ExNihiloGrace/notebooks/00_quick_start.ipynb',
        'ExNihiloGrace/demos/index.html',
```

--------------------------------

### Run Validation and Print Status

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/validation/README.md

Installs the package, sets up the Python path, resets the experimental firewall, enables the validation phase, and then prints the validation status for all firm predictions. The validation phase can only be enabled if theory preconditions are met.

```bash
pip install -e .
PYTHONPATH=. python - <<'PY'
from validation.experimental_firewall import EXPERIMENTAL_FIREWALL
from validation import validate_all_firm_predictions
EXPERIMENTAL_FIREWALL.reset()
try:
    EXPERIMENTAL_FIREWALL.enable_validation_phase()
except Exception:
    pass
print({k:v.validation_status.value for k,v in validate_all_firm_predictions().items()})
PY
```

--------------------------------

### Example Python Docstring for Correction Factor

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/MATHEMATICAL_PROVENANCE_STANDARD.md

An example demonstrating the documentation of a specific derived constant, the Weinberg Angle Correction Factor, showing its mathematical basis, formula, and derivation from the φ-hierarchy.

```python
def _derive_correction_factor_121(self) -> float:
    """
    Weinberg Angle Correction Factor: Mathematical derivation from φ⁵⁴.
    
    Mathematical Basis: FinalNotes.md lines 21086 - φ⁵⁴ morphic gauge layer
    Formula: correction_factor = φ⁵⁴/10¹¹ 
    Derivation: SU(2) gauge coupling from 54th morphic layer depth
    φ-Power: φ⁵⁴ = 1.929002... × 10¹¹
    Status: MATHEMATICALLY_DERIVED
    Replaces: Previous empirical value 1.21
    
    Returns:
        Mathematically derived correction factor ≈ 1.929002
    """

```

--------------------------------

### LaTeX Error Fixes Example

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/arxiv_paper/FIRM_FINAL_SUBMISSION/FINAL_COMPILATION_GUIDE.md

Illustrates common LaTeX math mode errors and their corrected forms. These examples show the transformation from incorrect syntax like '$phi^2$' to the proper LaTeX command '\phi^2'.

```latex
❌ BEFORE: $\frac{8\pi G}{$phi^2$}$
✅ AFTER:  $\frac{8\pi G}{\phi^2}$
```

```latex
❌ BEFORE: Following the $\phi$-pattern: $\ell_3$ = 220$phi^2$ 
✅ AFTER:  Following the $\phi$-pattern: $\ell_3 = 220\phi^2$
```

```latex
❌ BEFORE: where $\sigma_{\text{torsion}} = $phi^4$ \Lambda_{\text{QCD}}^2$
✅ AFTER:  where $\sigma_{\text{torsion}} = \phi^4 \Lambda_{\text{QCD}}^2$
```

```latex
❌ BEFORE: \sin^2(\theta_{12}) &= \frac{1}{$phi^4$}
✅ AFTER:  \sin^2(\theta_{12}) &= \frac{1}{\phi^4}
```

--------------------------------

### Create arXiv Source Bundle

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/README.md

Navigate to the paper submission directory and zip the necessary files for arXiv. Ensure 'main.bbl' is generated by running the build process first.

```bash
cd arxiv_paper/FIRM_SUBMISSION
# Ensure main.bbl exists (run the build first)
zip -r firm_arxiv_source.zip \
  main.tex main.bbl sections references/references.bib \
  figures/*.png figures_for_paper/*.png
```

--------------------------------

### Get Constants by Category (Function)

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/codebase_map.md

A utility function to retrieve constants grouped by their respective categories.

```python
from constants import get_constants_by_category
```

--------------------------------

### APIDocumentationGenerator

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/codebase_map.md

Generates comprehensive API documentation from source code, including mathematical notation, examples, and cross-references.

```APIDOC
## APIDocumentationGenerator

### Description
This class is responsible for generating complete API documentation for the FIRM theory. It auto-generates documentation from source code, incorporating mathematical notation, usage examples, and cross-references between related functions and classes.

### Methods
- `__init__()`
- `generate_complete_api_docs() -> APIResult`: Generates the complete API documentation for the entire FIRM system.
- `_document_module(module: ModuleType) -> tuple[Dict[str, APIFunction], Dict[str, APIClass]]`: Documents a given Python module, extracting information about its functions and classes.
- `_document_function(func: Callable, module_name: str) -> APIFunction`: Documents a single Python function, capturing its signature, docstring, parameters, return type, examples, and other relevant metadata.
- `_document_class(cls: Type, module_name: str) -> APIClass`: Documents a single Python class, including its methods, attributes, inheritance, and examples.
- `_extract_parameters(func: Callable) -> List[Dict[str, Any]]`: Extracts parameter information from a function's signature.
- `_get_return_type(func: Callable) -> str`: Determines and returns the return type of a function.
- `_generate_function_examples(func: Callable) -> List[str]`: Generates usage examples for a given function.
- `_generate_class_examples(cls: Type) -> List[str]`: Generates usage examples for a given class.
- `_extract_mathematical_basis(docstring: str) -> str`: Extracts the mathematical basis description from a docstring.
- `_extract_return_description(docstring: str) -> str`: Extracts the description of the return value from a docstring.
- `_extract_param_description(docstring: str, param_name: str) -> str`: Extracts the description for a specific parameter from a docstring.
- `_extract_class_attributes(cls: Type) -> List[Dict[str, Any]]`: Extracts attribute information from a class definition.
- `_analyze_complexity(docstring: str) -> str`: Analyzes and returns the time or space complexity from a docstring.
- `_find_related_functions(docstring: str) -> List[str]`: Identifies and lists functions related to the current one based on docstring content.
- `_check_provenance_integration(docstring: str) -> bool`: Checks if provenance tracking integration is mentioned in the docstring.
- `_generate_cross_references(documented_items: Dict[str, Any]) -> Dict[str, List[str]]`: Generates cross-references between different documented API elements.
- `_calculate_coverage(documented_items: Dict[str, Any], total_items: int) -> float`: Calculates the API documentation coverage percentage.
- `generate_html_documentation() -> str`: Generates the API documentation in HTML format.
```

--------------------------------

### Example of Morphism Token Composition

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/foundation/categories/README.md

Demonstrates the composition of morphism tokens. Mismatched targets will raise a ValueError.

```python
compose((X→Y), (Y→Z)) → (X→Z)
```

--------------------------------

### Initialize FIRM Algorithm Library

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/simulations/webgl/src/docs/theory/FIRM_PERFECT_ARCHITECTURE.md

Initializes the FIRMAlgorithmLibrary and its catalog, printing status messages. This code sets up the core structure for all FIRM algorithms.

```python
class FIRMAlgorithmLibrary:
    """Complete library of all core FIRM computational algorithms with specific implementations"""
    
    def __init__(self):
        self.phi = 1.6180339887498948
        self.algorithm_catalog = {}
        
    def initialize_algorithm_catalog(self):
        """Initialize complete catalog of all FIRM algorithms"""
        
        print("🗂️ FIRM ALGORITHM LIBRARY INITIALIZATION")
        
        self.algorithm_catalog = {
            # Core Mathematical Algorithms
            "mathematical_core": {
                "grace_operator_complete": self.GraceOperatorComplete(),
                "phi_recursion_solver": self.PhiRecursionSolver(),
                "morphic_network_analyzer": self.MorphicNetworkAnalyzer(),
                "fixed_point_finder": self.FixedPointFinder(),
                "axiom_system_validator": self.AxiomSystemValidator()
            },
            
            # Physical Constant Derivation Algorithms
            "constant_derivation": {
                "fine_structure_deriver": self.FineStructureConstantDeriver(),
                "mass_ratio_calculator": self.MassRatioCalculator(),
                "coupling_constant_engine": self.CouplingConstantEngine(),
                "cosmological_parameter_deriver": self.CosmologicalParameterDeriver(),
                "dimensional_bridge_system": self.DimensionalBridgeSystem()
            },
            
            # Consciousness and Observer Effects
            "consciousness_algorithms": {
                "xi_complexity_calculator": self.XiComplexityCalculator(),
                "eeg_phi_harmonic_analyzer": self.EEGPhiHarmonicAnalyzer(),
                "consciousness_physics_bridge": self.ConsciousnessPhysicsBridge(),
                "morphic_field_detector": self.MorphicFieldDetector()
            },
            
            # Validation and Integrity Systems
            "validation_systems": {
                "integrity_scanner": self.IntegrityScanner(),
                "empirical_contamination_detector": self.EmpiricalContaminationDetector(),
                "peer_review_assessor": self.PeerReviewAssessor(),
                "provenance_tracker": self.ProvenanceTracker()
            }
        }
        
        total_algorithms = sum(len(category) for category in self.algorithm_catalog.values())
        print(f"✅ Initialized {total_algorithms} algorithms across 4 major categories")
        
        return self.algorithm_catalog

# Initialize algorithm library
FIRM_algorithms = FIRMAlgorithmLibrary()
algorithm_catalog = FIRM_algorithms.initialize_algorithm_catalog()

print("\n🎯 ALGORITHM LIBRARY CAPABILITIES:")
print(f"✅ Mathematical Core: {len(algorithm_catalog['mathematical_core'])} algorithms")
print(f"✅ Constant Derivation: {len(algorithm_catalog['constant_derivation'])} algorithms") 
print(f"✅ Consciousness: {len(algorithm_catalog['consciousness_algorithms'])} algorithms")
print(f"✅ Validation Systems: {len(algorithm_catalog['validation_systems'])} algorithms")

total_algorithms = sum(len(category) for category in algorithm_catalog.values())
print(f"\n💎 Total Algorithm Library: {total_algorithms} complete implementations")
```

--------------------------------

### Get φ-value

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/codebase_map.md

Retrieve the φ-value, a fundamental parameter used in the grace contraction calculations. This is a module-level constant or function.

```python
phi_value
```

--------------------------------

### Create and Run Direct Test

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/TEAMS_1_AND_2_HANDOFF_PACKAGE.md

Creates a new test file for direct testing of the complete framework and runs it with coverage measurement.

```bash
touch testing/theory/test_unification_complete_framework_direct.py
```

```bash
python -m pytest testing/theory/test_unification_complete_framework_direct.py --cov=theory.unification.complete_framework
```

--------------------------------

### FIRM FSCTF v2 Pipeline Selection Query Parameters

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/applications/visualization/FIRM_FSCTF_v2_COMPLETE_MASTER_PLAN.md

Demonstrates how to select different FIRM v2 pipeline modes using URL query parameters for default, legacy, purity, and debug modes.

```url
?pipeline=legacy
?purity=strict
?debug=math
```

--------------------------------

### Get All Constants

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/codebase_map.md

Retrieve a dictionary containing all defined FIRM physical constants. This method is part of the `FIRMConstantsRegistry` class.

```python
all_constants = FIRM_CONSTANTS_REGISTRY.get_all_constants()
```

--------------------------------

### Get a Specific Constant

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/codebase_map.md

Retrieve a specific physical constant from the registry by its name. This method is part of the `FIRMConstantsRegistry` class.

```python
constant_value = FIRM_CONSTANTS_REGISTRY.get_constant('fine_structure_alpha')
```

--------------------------------

### Execute Complete System Verification

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/simulations/webgl/src/docs/theory/FIRM_PERFECT_ARCHITECTURE.md

Initializes the FIRM system verification process and prints a status message. This is the entry point for running the full verification suite.

```python
verification = FIRMSystemVerification()

print("🚀 EXECUTING COMPLETE SYSTEM VERIFICATION...")
print("=" * 60)
```

--------------------------------

### Get Timestamp

Source: https://github.com/ktynski/firm-fractal-identity-recursive-mechanics/blob/main/simulations/webgl/src/docs/theory/FIRM_PERFECT_ARCHITECTURE.md

Retrieves the current UTC timestamp in ISO format for logging purposes. Requires the datetime module.

```python
def get_timestamp(self) -> str:
    """Get current timestamp for logging"""
    from datetime import datetime
    return datetime.utcnow().isoformat()
```