Spécification et Résumé de la Monographie
Tenseurs Métriques de Riemann, Courbure des Espaces de Représentation et Navigation Épistémique.
1. Theoretical & Nonequilibrium Foundations
Autonomous cognition is governed by the thermodynamics of self-organization far from equilibrium:
\[ \mathcal{F}(s, q) = \mathbb{E}_{q(\psi)}\left[ \ln q(\psi) - \ln p(\psi, s) \right] \]Subject to Landauer's dissipation inequality:
\[ \Delta Q \ge k_B T \ln 2 \]2. Mathematical & Cybernetic Formulations
The agent maintains structural autonomy through statistical Markov boundary conditions partitioning the universal state space into internal states \(\mu\), sensory states \(s\), active states \(a\), and external perturbations \(\eta\):
\[ p(\mu, \eta \mid s, a) = p(\mu \mid s, a) \cdot p(\eta \mid s, a) \]3. Boundary & Invariant Formulations
The system preserves its operational closure through the enforcement of the Sovereignty Invariance Criterion:
\[ \forall \Delta t \ge 0, \quad \frac{\partial \mathcal{C}_{\text{human}}}{\partial t} \ge 0 \quad \text{and} \quad \mathcal{H}(\mathcal{P} \mid \mathcal{S}) \ge \mathcal{H}_{\min} \]4. Empirical Falsification Protocols
- Zero compounding error across multi-step synthetic inference chains.
- Reduction in cognitive context-switching dissipation by \(\ge 35\%\).
- Deterministic auditability across all computational state transitions.