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