# Canonical Formula Index: Sovereign Informatic Manifold

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.

## 1. Unified Cognitive Load Equation
The total cognitive load ($L_{total}$) of any semantic atom is the sum of its information-theoretic components.

$$L_{total} = L_{intrinsic} + L_{extraneous} + L_{germane} + L_{routing} + L_{memory}$$

Where:
- $L_I$: Core algorithmic complexity.
- $L_E$: Noise, repulsion signals, and status-inverted masks (ICP).
- $L_G$: Semantic utility and knowledge-integration Work.
- $L_R$: Network propagation and addressing overhead.
- $L_M$: Substrate persistence and cache-locality demand.

## 2. Infohazard Containment Protocol (ICP)
The ICP governs adversarial warding and detection-escalation.

### 2.1 Detection Level ($D_L$)
$$D_L(L_E) = \begin{cases} 
0 & \text{if } L_E < 1.0 \text{ (Quiescent)} \\ 
1 & \text{if } 1.0 \le L_E < 5.0 \text{ (Peripheral)} \\ 
2 & \text{if } 5.0 \le L_E < 10.0 \text{ (Investigative)} \\ 
3 & \text{if } L_E \ge 10.0 \text{ (Adversarial)} 
\end{cases}$$

### 2.2 Repulsion Mode ($M_R$)
$$M_R(D_L, C) = \text{Mode}(D_L) \text{ s.t. } M_R = \text{Radioactive} \implies C = 0$$
*(Where $C$ is the Deterrence Invariant: 1 = Locked, 0 = Armed.)*

## 3. AngrySphinx Difficulty Scaling
Difficulty ($H$) escalates in response to high-intensity adversarial pressure ($L_E > T_{L3}$).

$$H_{t+1} = H_t + \max(0, \delta \cdot (L_E - 10.0))$$
*(Default $\delta = 0.5$ in Q16.16.)*

## 4. SSMS Cycle Balancing (Heat Masking)
Total machine cycles ($C_{total}$) used to mask real computational work behind adversarial noise.

$$C_{total} = C_{work} + (L_E \times K_{mode}) \times \gamma$$
*(Where $\gamma$ is the physical thermal jitter key and $K_{mode}$ is the repulsion-mode density factor.)*

## 5. Metric-Coupled Convergence (MCC)
The efficiency metric for the Sovereign Informatic Manifold.

$$\eta = \frac{L_{germane}}{\sum L_{total}} + \Delta \text{Energy}_{manifold}$$

---
**Document Status**: `CANONICAL` / `VERIFIED`
**Ground Truth Reference**: `SemanticsCli.lean` / `SabotagePrevention.lean`