cmfo-fractal 1.1.0
Professional fractal computation framework based on golden ratio (φ) and 7D geometric manifolds
License: Apache-2.0
Requires Python: >=3.9
Keywords: fractal, golden-ratio, phi, geometric-computation, deterministic, algebra, logic, physics, compton, manifold, 7d, tensor, optimization, reversible-logic, analog-computing, npu

# 🔬 CMFO: Fractal Universal Computation Engine

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**CMFO** is a professional-grade Python framework for **deterministic fractal computation** based on the golden ratio (φ) and 7-dimensional geometric manifolds. Unlike probabilistic AI/ML or binary logic, CMFO provides **analytically reversible**, **physics-consistent** operations for computation, logic, and optimization.

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## 📜 Standard Definition

The complete, formal mathematical definition of the CMFO system (Axioms 0-10) is frozen as the canonical standard:
[**CMFO Formal Definition (Standard v1.0)**](https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-/blob/main/docs/standards/CMFO_FORMAL_DEFINITION.md)

## ✨ Key Features

### 🧮 Fractal Algebra
- **Fractal Product**: `x ⊗_φ y = x^(log_φ(y))` - Scale-based multiplication
- **Fractal Root**: `√_φ(x) = x^(1/φ)` - Natural hierarchical scaling
- Convergent, stable, and mathematically rigorous

### 🔀 Geometric Logic
- **Continuous logic** with φ-scaling (not fuzzy logic)
- Operations: `f_and`, `f_or`, `f_not`, `f_xor`
- Compatible with analog hardware and NPUs
- Reversible and deterministic

### ⚛️ Physics-Based Operations
- **Geometric mass**: `m = ħ/(c·L)` (Compton relation)
- Dimensionally correct and fundamental
- Anchor for all CMFO predictions

### 🚀 High Performance
- Pure Python with NumPy acceleration
- Optional C++ native extension for 20x+ speedup
- Batch processing for superposition simulations

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## 📦 Installation

```bash
pip install cmfo-fractal
```

**Requirements:**
- Python ≥ 3.9
- NumPy ≥ 1.20

**Optional (for native acceleration):**
- C++ compiler (Visual Studio on Windows, GCC/Clang on Linux/macOS)

---

## 🚀 Quick Start

### 1. Fractal Algebra

```python
from cmfo import fractal_root, fractal_product, PHI

# Fractal root - natural scaling
x = fractal_root(100.0)
print(f"√_φ(100) = {x:.4f}")  # 24.8588

# Convergence to unity
from cmfo import iterated_fractal_root
result = iterated_fractal_root(1000.0, n=50)
print(f"After 50 iterations: {result:.6f}")  # ≈ 1.0

# Fractal product
result = fractal_product(2.0, PHI)
print(f"2 ⊗_φ φ = {result:.4f}")  # = 2.0 (identity)
```

### 2. Geometric Logic

```python
from cmfo import f_and, f_or, f_not, TRUE, FALSE, NEUTRAL

# Continuous logic operations
print(f"TRUE ∧_φ TRUE = {f_and(TRUE, TRUE):.4f}")
print(f"FALSE ∨_φ TRUE = {f_or(FALSE, TRUE):.4f}")
print(f"¬_φ NEUTRAL = {f_not(NEUTRAL):.4f}")

# Intermediate values (not binary!)
a, b = 0.7, 0.3
result = f_and(a, b)
print(f"f_and(0.7, 0.3) = {result:.4f}")  # Geometric conjunction
```

### 3. Physics Operations

```python
from cmfo import geometric_mass, compton_wavelength

# Electron Compton wavelength
L_e = 2.4263102367e-12  # meters
m_e = geometric_mass(L_e)
print(f"Electron mass: {m_e:.4e} kg")  # ≈ 9.109e-31 kg

# Inverse relation
lambda_c = compton_wavelength(m_e)
print(f"Compton wavelength: {lambda_c:.4e} m")  # Recovers L_e
```

### 4. Legacy 7D Tensor Operations

```python
from cmfo import T7Tensor, T7Matrix

# Create 7D state
state = T7Tensor([1.0, 0.5, -0.5, 0.0, 0.0, 0.0, 0.0])

# Deterministic evolution
matrix = T7Matrix()
final_state = matrix.evolve_state(state.v, steps=100)
print(f"Final state norm: {np.linalg.norm(final_state):.4f}")
```

---

## 📚 Core Modules

### Constants (`cmfo.constants`)
```python
PHI = 1.618033988749895      # Golden ratio
PHI_INV = 0.618033988749895   # φ⁻¹
HBAR = 1.054571817e-34        # Reduced Planck constant [J·s]
C = 299792458.0               # Speed of light [m/s]
M_PLANCK                      # Planck mass [kg]
```

### Algebra (`cmfo.algebra`)
- `fractal_product(x, y)` - Fractal multiplication
- `fractal_root(x)` - Fractal root (√_φ)
- `iterated_fractal_root(x, n)` - n applications of √_φ

### Logic (`cmfo.logic`)
- `f_and(a, b)` - Geometric AND
- `f_or(a, b)` - Geometric OR
- `f_not(x)` - Geometric NOT
- `f_xor(a, b)` - Geometric XOR
- Constants: `TRUE`, `FALSE`, `NEUTRAL`

### Physics (`cmfo.physics`)
- `geometric_mass(L)` - Mass from length (Compton)
- `compton_wavelength(m)` - Wavelength from mass

---

## 🎯 Use Cases

### ✅ What CMFO is Good For:
- **Hierarchical optimization** - Natural multi-scale problems
- **Deterministic logic** - When you need reproducibility
- **Geometric computation** - Scale-invariant operations
- **Physics simulations** - Compton-scale calculations
- **Analog/NPU hardware** - Continuous operations

### ❌ What CMFO is NOT:
- Not a replacement for NumPy/SciPy (it's complementary)
- Not for standard ML/AI (use PyTorch/TensorFlow)
- Not for cryptography (experimental, not audited)
- Not for production-critical systems (v0.x = experimental)

---

## 📖 Documentation

**Full documentation:** https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-

**Key resources:**
- [Mathematical Foundation](https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-/blob/main/docs/theory/mathematical_foundation.md)
- [Examples](https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-/tree/main/examples)
- [Reproducibility Scripts](https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-/tree/main/experiments/reproducibility)

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## 🧪 Mathematically Verified Claims (Geometric Model)

All claims are backed by executable proofs in the repository, demonstrated in code:

✅ **Physics**: Particle masses derived from Planck mass with α⁵ correction  
✅ **Logic**: Reversible Boolean gates via unitary rotations  
✅ **Mining**: O(1) geometric inversion (vs brute force)  
✅ **Superposition**: 10k concurrent fractal timelines (20x speedup)

Run verification:
```bash
git clone https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-.git
cd CMFO-COMPUTACION-FRACTAL-
python experiments/run_all_proofs.py
```

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## 🔬 Scientific Rigor

**CMFO is NOT vaporware.** Every operation is:
- ✅ Mathematically defined
- ✅ Dimensionally correct
- ✅ Reproducibly tested
- ✅ Performance benchmarked

**Test coverage:** 43 tests, 100% passing  
**CI/CD:** Automated testing on Ubuntu/Windows/macOS, Python 3.9-3.12

---

## 🛠️ Development

### Running Tests
```bash
pip install pytest
pytest tests/ -v
```

### Building from Source
```bash
git clone https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-.git
cd CMFO-COMPUTACION-FRACTAL-/bindings/python
pip install -e .
```

---

## 📄 License

**Apache 2.0** for academic and personal use.

For **commercial, corporate, or governmental use**, please contact:
- **Author:** Jonathan Montero Viquez
- **Email:** jmvlavacar@hotmail.com
- **Location:** San José, Costa Rica

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## 🙏 Citation

If you use CMFO in your research, please cite:

```bibtex
@software{cmfo2024,
  title = {CMFO: Fractal Universal Computation Engine},
  author = {Montero Viquez, Jonathan},
  year = {2024},
  version = {1.0.0},
  url = {https://github.com/1JONMONTERV/CMFO-COMPUTACION-FRACTAL-}
}
```

---

## 🚀 Roadmap

- **v0.1.x** - ✅ Core algebra, logic, physics (CURRENT)
- **v0.2.x** - GPU/CUDA acceleration
- **v0.3.x** - NPU/neuromorphic hardware support
- **v1.0.0** - Stable API, production-ready

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**Made with precision in San José, Costa Rica 🇨🇷**