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@@ -98,4 +98,72 @@
```
──────────────────────────────────────────────
End – zero concrete values, zero implementation bias.
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.