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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