──────────────────────────────────────────────  
**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)
        )
    ```

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**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.