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THE EPISTEMIC HEXALOGUE · 卷 III

高维潜在拓扑与自主符号学

黎曼度量张量、表征空间的曲率与符号认识论导航。

专著规格与摘要

黎曼度量张量、表征空间的曲率与符号认识论导航。

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.