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51 lines
2.2 KiB
Markdown
51 lines
2.2 KiB
Markdown
# Canonical Formula Index: Sovereign Informatic Manifold
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This document serves as the formal mathematical ground truth for the Sovereign Informatic Manifold. All extracted logic (Lean, Python, Verilog) must adhere to these canonical expressions.
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## 1. Unified Cognitive Load Equation
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The total cognitive load ($L_{total}$) of any semantic atom is the sum of its information-theoretic components.
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$$L_{total} = L_{intrinsic} + L_{extraneous} + L_{germane} + L_{routing} + L_{memory}$$
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Where:
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- $L_I$: Core algorithmic complexity.
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- $L_E$: Noise, repulsion signals, and status-inverted masks (ICP).
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- $L_G$: Semantic utility and knowledge-integration Work.
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- $L_R$: Network propagation and addressing overhead.
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- $L_M$: Substrate persistence and cache-locality demand.
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## 2. Infohazard Containment Protocol (ICP)
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The ICP governs adversarial warding and detection-escalation.
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### 2.1 Detection Level ($D_L$)
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$$D_L(L_E) = \begin{cases}
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0 & \text{if } L_E < 1.0 \text{ (Quiescent)} \\
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1 & \text{if } 1.0 \le L_E < 5.0 \text{ (Peripheral)} \\
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2 & \text{if } 5.0 \le L_E < 10.0 \text{ (Investigative)} \\
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3 & \text{if } L_E \ge 10.0 \text{ (Adversarial)}
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\end{cases}$$
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### 2.2 Repulsion Mode ($M_R$)
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$$M_R(D_L, C) = \text{Mode}(D_L) \text{ s.t. } M_R = \text{Radioactive} \implies C = 0$$
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*(Where $C$ is the Deterrence Invariant: 1 = Locked, 0 = Armed.)*
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## 3. AngrySphinx Difficulty Scaling
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Difficulty ($H$) escalates in response to high-intensity adversarial pressure ($L_E > T_{L3}$).
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$$H_{t+1} = H_t + \max(0, \delta \cdot (L_E - 10.0))$$
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*(Default $\delta = 0.5$ in Q16.16.)*
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## 4. SSMS Cycle Balancing (Heat Masking)
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Total machine cycles ($C_{total}$) used to mask real computational work behind adversarial noise.
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$$C_{total} = C_{work} + (L_E \times K_{mode}) \times \gamma$$
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*(Where $\gamma$ is the physical thermal jitter key and $K_{mode}$ is the repulsion-mode density factor.)*
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## 5. Metric-Coupled Convergence (MCC)
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The efficiency metric for the Sovereign Informatic Manifold.
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$$\eta = \frac{L_{germane}}{\sum L_{total}} + \Delta \text{Energy}_{manifold}$$
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---
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**Document Status**: `CANONICAL` / `VERIFIED`
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**Ground Truth Reference**: `SemanticsCli.lean` / `SabotagePrevention.lean`
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