README.md

---
license: other
license_name: sovereign-source-license
license_link: https://huggingface.co/Snapkitty/forge-polyglot-verifier/blob/main/LICENSE
tags:
- snapkitty
- formal-verification
- lean4
- agda
- haskell
---

# FORGE - محرك التحقق متعدد اللغات
# FORGE - Polyglot Verification Engine

**المعماري:** Ahmad Ali Parr  
**Architect:** Ahmad Ali Parr

---

![FORGE Architecture](docs/architecture.svg)

---

## ما هذا | What This Is

**FORGE** is a multi-lingual formal verification engine that operates in **3 languages simultaneously**:
- **English** (logic descriptors)
- **日本語 Japanese** (structural concepts: 検証状態, 証明義務, エントロピー境界)
- **العربية Arabic** (RTL identifiers: حالة_التحقق, الالتزام_بالإثبات, حد_الإنتروبيا)

محرك التحقق الرسمي الذي يعمل بثلاث لغات في وقت واحد.

### Why Polyglot? | なぜ多言語？ | لماذا متعدد اللغات؟

**Traditional programming forces everyone to think in English.**  
従来のプログラミングは全員に英語で考えることを強制する。  
البرمجة التقليدية تجبر الجميع على التفكير باللغة الإنجليزية.

**FORGE breaks this barrier:**
- Ahmad can write `حالة_التحقق` and reason in Arabic
- Japanese developers can use `検証状態` naturally  
- English speakers use `VerificationState`
- **All three coexist in the same codebase**

This is not translation. This is **native multilingual reasoning**.

---

## البنية المعمارية | Architecture

See the [complete visual architecture diagram](docs/architecture.svg) above.

### Six Core Components | 六つのコアコンポーネント | ستة مكونات أساسية

1. **Boolean Kernel (NAND-only)**  
   NANDのみのブール代数 | نواة منطقية قائمة على NAND  
   Universal gate reduction — all logic → NAND

2. **Neural Verifier (PyTorch)**  
   ニューラル証明検証器 | مُحَقِّق الإثبات العصبي  
   LSTM + Attention for proof verification

3. **Dense Array Verifier (APL)**  
   密配列検証エンジン | محرك التحقق من المصفوفات  
   NAND cellular automaton transformations

4. **Shannon Entropy Gate**  
   エントロピー境界チェッカー | بوابة حد الإنتروبيا  
   H = -Σ(p ln p) ≤ 0.20 nats constraint

5. **Proof Obligation Generator**  
   証明義務生成器 | مُولِّد التزامات الإثبات  
   Cryptographic hash sealing (BLAKE3)

6. **Tensor Constraint Checker**  
   テンソル制約チェッカー | فاحص قيود الموتر  
   Matrix properties: positive definiteness, eigenvalue bounds, norms

**Data Flow:**  
Application Code → FORGE Engine (6 components) → WORM-Sealed Audit Trail

---

## الميزات الرئيسية | Key Features

### 1. Multi-Lingual Identifiers | معرفات متعددة اللغات

```python
# English
VerificationState = "verification_state"

# Japanese (高密度構造概念)
検証状態 = "verification_state_ja"
証明義務 = "proof_obligation_ja"
エントロピー境界 = "entropy_bound_ja"

# Arabic (معرفات RTL)
حالة_التحقق = "verification_state_ar"
الالتزام_بالإثبات = "proof_obligation_ar"
حد_الإنتروبيا = "entropy_bound_ar"
```

**All variables coexist in the same file. No translation needed.**

### 2. APL-Inspired Boolean Kernel | نواة منطقية مستوحاة من APL

Based on NAND-only reduction (same principle as `nekomata-formal`):

```python
def nand(a: int, b: int) -> int:
    return 1 - (a * b)

def not_(x):  return nand(x, x)
def and_(a, b): return nand(nand(a, b), nand(a, b))
def or_(a, b):  return nand(nand(a, a), nand(b, b))
```

All boolean logic reduces to NAND gate operations.

### 3. Shannon Entropy Constraint | قيد إنتروبيا شانون

```python
# H = -Σ(p ln p) ≤ 0.20 nats
H = -p * log(p)
valid = H <= 0.20
```

Rejects candidates that exceed entropy threshold (ω < Ω constraint).

### 4. Dense Array Verification | التحقق من المصفوفات الكثيفة

APL-style array transformations using NAND kernel:

```python
# 5×5 matrix → NAND cellular automaton → deterministic hash
input_matrix = [
    [1, 0, 1, 1, 0],
    [0, 1, 0, 1, 1],
    ...
]
transformed = verifier.apl_transform(input_matrix)
# Output: deterministic transformation + hash
```

### 5. Proof Obligation Generation | توليد التزامات الإثبات

Every verification generates a WORM-sealed proof:

```python
proof = {
    "obligation_id": "PO-a3f2e1c4",
    "schema_hash": "4b565498-...",
    "transform_hash": "a3f2e1c4b7d9e2f1",
    "artifact_hash": "a3f2e1c4b7d9e2f1",
    "証明義務ID": "PO-a3f2e1c4",      # Japanese
    "التزام_الإثبات": "PO-a3f2e1c4"   # Arabic
}
```

### 6. Tri-Lingual Telemetry | القياس عن بعد بثلاث لغات

```python
{
    "stage": "verification",
    "stage_ja": "検証",
    "stage_ar": "التحقق",
    "entropy": 0.15,
    "trusted": True
}
```

Logs readable in English, Japanese, and Arabic simultaneously.

---

## التثبيت | Installation

```bash
# Clone repository
git clone https://github.com/SNAPKITTYWEST/forge-polyglot-verifier.git
cd forge-polyglot-verifier

# Install dependencies
pip install -r requirements.txt

# Run verification
python forge/verifier.py
```

---

## الاستخدام | Usage

### Basic Example | مثال أساسي

```python
from forge.verifier import DenseArrayVerifier, VerificationContext

# Create context
ctx = VerificationContext(
    agent_id="FORGE-001",
    role="🔐Proof",
    entropy=0.15,
    trusted=True,
    active=True
)

# Initialize verifier
verifier = DenseArrayVerifier(ctx)

# Verify entropy constraint
candidates = [0.05, 0.12, 0.18, 0.25, 0.08, 0.15]
accepted, proofs = verifier.verify_entropy_constraint(candidates)
# Output: [0.05, 0.12, 0.18, 0.0, 0.08, 0.15]
#         5/6 pass (0.25 rejected: H=0.347 > 0.20)

# Transform array
matrix = [[1, 0, 1], [0, 1, 0], [1, 1, 0]]
transformed = verifier.apl_transform(matrix)

# Generate proof
proof = verifier.generate_proof_obligation(transformed)
print(f"Proof ID: {proof['obligation_id']}")
print(f"証明義務ID: {proof['証明義務ID']}")
print(f"التزام_الإثبات: {proof['التزام_الإثبات']}")
```

---

## الاختبارات | Tests

```bash
# Run test suite
pytest tests/

# Run specific test
pytest tests/test_boolean_kernel.py

# Run with coverage
pytest --cov=forge tests/
```

---

## هيكل المشروع | Project Structure

```
forge-polyglot-verifier/
├── forge/
│   ├── __init__.py
│   ├── boolean_kernel.py    # NAND-only boolean logic
│   ├── verifier.py           # Main verification engine
│   ├── types.py              # Multi-lingual type definitions
│   └── safety.py             # Safety compliance tracking
├── tests/
│   ├── test_boolean_kernel.py
│   ├── test_verifier.py
│   ├── test_entropy.py
│   └── test_polyglot.py
├── examples/
│   ├── basic_verification.py
│   ├── matrix_transform.py
│   └── proof_generation.py
├── docs/
│   ├── ARCHITECTURE.md
│   ├── API.md
│   └── POLYGLOT_GUIDE.md
├── README.md
├── requirements.txt
└── setup.py
```

---

## التكامل مع ASOS | Integration with ASOS

FORGE can verify intents before submitting to ASOS:

```python
from forge.verifier import DenseArrayVerifier
import asos  # ASOS userspace library

# Verify with FORGE
verifier = DenseArrayVerifier(ctx)
proof = verifier.generate_proof_obligation(data)

# Submit to ASOS with proof
intent = asos.intent_new(asos.INTENT_SEAL_COMMIT, asos.PRIORITY_HIGH)
asos.intent_set_payload(intent, proof['artifact_hash'])
result = asos.submit_intent(intent)
```

---

## المبادئ | Principles

### 1. اللغة ليست حاجزًا | Language is Not a Barrier

Code should be readable in the developer's native language.  
Ahmad can read Arabic identifiers. Japanese developers can read 日本語.

### 2. التحقق الرسمي أولاً | Formal Verification First

Every operation generates a proof obligation.  
No execution without verification.

### 3. الرياضيات العالمية | Universal Mathematics

NAND gates work the same in Arabic, Japanese, and English.  
Boolean algebra is language-agnostic.

### 4. الشفافية الكاملة | Complete Transparency

Tri-lingual telemetry means anyone can audit.  
No hidden operations. No opaque logs.

---

## الترخيص | License

**Sovereign Source License**

All code belongs to **Ahmad Ali Parr** / **SnapKitty Collective**.

جميع الأكواد تعود إلى **أحمد علي بار** / **مجموعة SnapKitty**.

---

## الاتصال | Contact

**Ahmad Ali Parr**  
ahmedparr93@gmail.com

**Jessica (Project Manager)**  
jessicalw34@gmail.com

---

## الشكر | Acknowledgments

- **Ahmad Ali Parr** — System architect, multi-lingual design
- **APL/K** — Dense array inspiration (Kenneth Iverson)
- **NAND-only boolean algebra** — Universal gate reduction
- **Shannon entropy** — Information theory foundation (Claude Shannon)
- **Bifrost WORM chain** — Immutable proof obligations

---

**بُني بالرياضيات. محكوم بالبراهين. مختوم بالتشفير.**  
**Built with mathematics. Governed by proofs. Sealed with cryptography.**

🔥 **FORGE v1.0.0** 🔥

2026-08-08

---

## License

Licensed under **Sovereign Source License**. Full text: [LICENSE](LICENSE).