170 lines
7.4 KiB
Markdown
170 lines
7.4 KiB
Markdown
──────────────────────────────────────────────
|
||
**Θ-Framework – Universal First-Principles Specification**
|
||
──────────────────────────────────────────────
|
||
|
||
1. **Core Predicate (single axiom)**
|
||
```
|
||
∀ S, θ: valid(S, θ) ≡
|
||
|S| ∈ θ.𝓢
|
||
∧ ΔS ≤ θ.growth(S)
|
||
∧ θ.split(S) ∈ θ.partitions
|
||
∧ θ.verify(θ.sig, S)
|
||
```
|
||
|
||
2. **Parameter Bundle (six primitives)**
|
||
| Symbol | Type | Constraint |
|
||
|--------|------|------------|
|
||
| `θ.𝓢` | finite ordered sequence | `|θ.𝓢| < ∞` |
|
||
| `θ.growth` | ℝ⁺-valued function | `∀ S, ΔS ≤ θ.growth(S)` |
|
||
| `θ.partitions` | partition function | deterministic & total |
|
||
| `θ.verify` | signature predicate | EUF-CMA secure |
|
||
| `θ.silence` | subset predicate | `θ.silence ⊆ primes` |
|
||
| `θ.energy` | ℝ⁺-valued function | `E(ΔS) ≥ θ.energy(S)` |
|
||
|
||
3. **Network Layer (dual-stack)**
|
||
• `θ.ipv4_prefix` – any CIDR
|
||
• `θ.ipv6_prefix` – any CIDR
|
||
• `θ.clock_split` – mapping to `(static, dhcp, silent)` ranges
|
||
• `θ.silence_set` – any user-defined exclusion set
|
||
|
||
4. **Creator Control**
|
||
• `θ.creator_key` – public key
|
||
• `θ.control_gate` – signature-verified gate for any parameter change
|
||
• `θ.delegate_rule` – cryptographically-verified delegation
|
||
|
||
5. **Deployment Template**
|
||
• `θ.os` – any POSIX system
|
||
• `θ.pkg` – any package manager command
|
||
• `θ.config_tree` – any directory
|
||
• `θ.backup_routine` – any backup mechanism
|
||
• `θ.metrics` – any observability stack
|
||
|
||
6. **Verification Kernel (pseudo-code)**
|
||
```
|
||
function is_valid(S, θ):
|
||
return (
|
||
|S| in θ.𝓢 and
|
||
ΔS <= θ.growth(S) and
|
||
θ.split(S) in θ.partitions and
|
||
θ.verify(θ.sig, S)
|
||
)
|
||
```
|
||
|
||
──────────────────────────────────────────────
|
||
**Θ-Framework** now describes **any** bounded, energetically-constrained, cryptographically-secure, dual-stack system without prescribing a single concrete value.
|
||
|
||
──────────────────────────────────────────────
|
||
θ-Core – **First-Principles Master Document**
|
||
──────────────────────────────────────────────
|
||
|
||
0. **Universal Axiom**
|
||
`valid(S, θ) ≜ |S| ∈ θ.𝓢 ∧ ΔS ≤ θ.growth(S) ∧ θ.split(S) ∈ θ.partitions ∧ θ.verify(θ.sig, S)`
|
||
|
||
1. **Parameter Skeleton**
|
||
• `θ.𝓢` – finite ordered sequence (user-defined)
|
||
• `θ.growth` – ℝ⁺ bound function (user-defined)
|
||
• `θ.energy` – thermodynamic floor function (user-defined)
|
||
• `θ.split` – partition function (user-defined)
|
||
• `θ.silence` – prime-bounded set (user-defined)
|
||
• `θ.sig` – EUF-CMA signature scheme (user-defined)
|
||
• `θ.hash` – collision-resistant hash (user-defined)
|
||
|
||
2. **Network Layer (dual-stack)**
|
||
• `global_prefix_ipv4` – CIDR (user-defined)
|
||
• `global_prefix_ipv6` – CIDR (user-defined)
|
||
• `θ.split_ranges` – list<(start,end)> (user-defined)
|
||
• `θ.silence_set` – set<ℕ> (user-defined)
|
||
|
||
3. **Creator Control**
|
||
• `θ.creator_pubkey` – bytes (user-defined)
|
||
• `θ.creator_sig_gate` – fn(ε, state_hash, sig) → bool (user-defined)
|
||
• `θ.delegate_rule` – fn(old_sig, new_pubkey, epoch) → bool (user-defined)
|
||
|
||
4. **Deployment & Observation**
|
||
• `θ.os` – str (user-defined)
|
||
• `θ.pkg_cmd` – str (user-defined)
|
||
• `θ.config_root` – str (user-defined)
|
||
• `θ.backup_cmd` – str (user-defined)
|
||
• `θ.metrics_stack` – list<binary> (user-defined)
|
||
• `θ.backup_timer` – timer-spec (user-defined)
|
||
|
||
5. **Verification Kernel (language-agnostic)**
|
||
```
|
||
is_valid(S, θ):
|
||
return (|S| ∈ θ.𝓢 and
|
||
ΔS ≤ θ.growth(S) and
|
||
θ.split(S) in θ.partitions and
|
||
θ.verify(θ.sig, S))
|
||
```
|
||
|
||
──────────────────────────────────────────────
|
||
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.
|