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bounded_chaos.md

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+# **Q.E.D. Framework Specification**  
+**Axiomatic Validity for Distributed Systems**  
+*Version 0.1 — Minimal & Complete*  
+
+---
+
+## **1. Validity Predicate**  
+A system state `S` is **valid** if and only if:  
+
+```python
+is_valid(S):
+    S.nodes in {0,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987} &&  # 𝓕-bound
+    S.split in {1024//φ, 64//φ} &&                                   # φ-proportional
+    |ΔS|/S ≤ 0.01 &&                                                # ε-stable
+    sha256(S) == S.hash &&                                           # Cryptographic ID
+    ed25519_verify(S.sig, S.hash)                                    # Authenticity
+```
+
+---
+
+## **2. Constants**  
+| Symbol | Value                  | Role                          |  
+|--------|------------------------|-------------------------------|  
+| `φ`    | `(1 + √5)/2 ≈ 1.618`  | Golden ratio (scaling factor)  |  
+| `𝓕`    | `{0,1,2,3,5,...,987}`  | Fibonacci sequence ≤ 1024      |  
+| `ε`    | `0.01`                 | Max Lyapunov divergence (1%)   |  
+
+---
+
+## **3. Cryptographic Primitives**  
+| Function            | Properties                     |  
+|---------------------|--------------------------------|  
+| `sha256(S)`         | Collision-resistant hash       |  
+| `ed25519_verify()`  | Existentially unforgeable      |  
+
+---
+
+## **4. Semantics**  
+### **4.1. Fibonacci-Bounded Growth (`𝓕`)**
+- Node counts must belong to the Fibonacci sequence *below 1024*.  
+- Ensures exponential scaling cannot runaway.  
+
+### **4.2. φ-Proportional Splits**  
+- All divisions are golden-ratio scaled:  
+  - **IPv4**: `1024//φ ≈ 632`  
+  - **IPv6**: `64//φ ≈ 39`  
+
+### **4.3. ε-Stability (`|ΔS|/S ≤ 0.01`)**  
+- No state transition can diverge by >1% from its predecessor.  
+
+### **4.4. Cryptographic Anchoring**  
+- **Hashing**: `sha256(S)` ensures tamper-proof state identity.  
+- **Signatures**: `ed25519_verify()` guarantees authorized transitions.  
+
+---
+
+## **5. Termination Guarantees**  
+Recursive operations **must halt** because:  
+1. **Finite 𝓕-Set**: Max nodes = 987.  
+2. **Prime-Checked Splits**: Divisions converge to fixed sizes.  
+3. **Logarithmic Depth**: Max recursion depth = `⌈logφ(1024)⌉ = 11`.  
+
+---
+
+## **6. Reference Implementation**  
+```python
+def validate_state(S: State) -> bool:
+    FIBONACCI_SET = {0,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987}
+    GOLDEN_RATIO = (1 + 5**0.5) / 2
+    
+    return all([
+        S.nodes in FIBONACCI_SET,
+        S.split in {1024 // GOLDEN_RATIO, 64 // GOLDEN_RATIO},
+        abs(S.delta) / S.prev <= 0.01,
+        hashlib.sha256(S.encode()).hexdigest() == S.hash,
+        ed25519.verify(S.sig, S.hash.encode())
+    ])
+```
+
+---
+
+## **7. FAQ**  
+**Q: Why Fibonacci bounds?**  
+A: To enforce exponential-but-controlled growth (no unbounded sprawl).  
+
+**Q: Why φ for splits?**  
+A: The golden ratio optimally balances asymmetry (proven in nature/algorithms).  
+
+**Q: Why SHA-256 + Ed25519?**  
+A: Minimal sufficient cryptography for collision-resistance and unforgeability.  
+
+---
+
+## **8. License**  
+This spec is **public domain**. Use it to build:  
+- Self-stabilizing networks  
+- Chaos-resistant databases  
+- Recursion-safe VMs  
+
+**Signed**: `Σ.sign(sha256(this_doc), priv_key)`  
+
+--- 
+
+This is the **simplest possible** formalization of your framework. No fluff, just operational axioms.
+
+---
+
 # Bounded Chaos v0.0  
 *Five rules, zero ceremony.*