Update bounded_chaos.md

bounded_chaos.md

@@ -99,3 +99,71 @@
 
 ──────────────────────────────────────────────  
 End – zero concrete values, zero implementation bias.
+
+---
+
+──────────────────────────────────────────────  
+Θ-Framework – **bounded_chaos(θ.bound, θ.verify)**  
+──────────────────────────────────────────────  
+
+### 1.  **Core Axiom**  
+```
+valid(S, θ)  ≜  θ.bound(|S|) ∧ θ.verify(θ.sig, S)
+```
+
+### 2.  **Primitive Definitions**  
+
+| **Primitive** | **Type** | **Minimal Axiom** |
+|---------------|----------|-------------------|
+| `θ.bound` | function | `∀x ∈ ℕ, θ.bound(x) ∈ {true, false}` and `∃M: ∀x>M, θ.bound(x)=false` |
+| `θ.verify` | predicate | `∀(pk, msg, sig), θ.verify(pk, msg, sig) ⇒ sig authentic` |
+
+### 3.  **Usage Framework**  
+
+1. **Instantiate**  
+   • Provide concrete `θ.bound` (e.g., Fibonacci ceiling, energy budget, subnet split).  
+   • Provide concrete `θ.verify` (e.g., Ed25519, Schnorr, lattice-based).  
+
+2. **Deploy**  
+   • Embed `θ.bound` in code, hardware, or network rule.  
+   • Embed `θ.verify` in signature check.  
+
+3. **Protect**  
+   • Patent abstract claims on the **pair** `(θ.bound, θ.verify)`.  
+
+──────────────────────────────────────────────  
+End – two primitives, universal application.
+
+---
+
+──────────────────────────────────────────────  
+Θ-Framework – **Two-Primitive Specification**  
+──────────────────────────────────────────────  
+
+### 1.  **Core Axiom**  
+```
+valid(S, θ)  ≜  θ.bound(|S|) ∧ θ.verify(θ.sig, S)
+```
+
+### 2.  **Primitive Definitions**  
+
+| **Primitive** | **Type** | **Minimal Axiom** |
+|---------------|----------|-------------------|
+| `θ.bound` | function | `∀x ∈ ℕ, θ.bound(x) ∈ {true, false}` and `∃M: ∀x>M, θ.bound(x)=false` |
+| `θ.verify` | predicate | `∀(pk, msg, sig), θ.verify(pk, msg, sig) ⇒ sig authentic` |
+
+### 3.  **Usage Framework**  
+
+1. **Instantiate**  
+   • Provide concrete `θ.bound` (e.g., Fibonacci ceiling, energy budget, subnet split).  
+   • Provide concrete `θ.verify` (e.g., Ed25519, Schnorr, lattice-based).  
+
+2. **Deploy**  
+   • Embed `θ.bound` in code, hardware, or network rule.  
+   • Embed `θ.verify` in signature check.  
+
+3. **Protect**  
+   • Patent abstract claims on the **pair** `(θ.bound, θ.verify)`.  
+
+──────────────────────────────────────────────  
+End – two primitives, universal application.