Node · Chain Position 158 of 346

FAITHFULNESS MEASUREMENT DOMAIN

**Faithfulness ($F_{\text{Faithfulness}}$):** Faithfulness is measurable as the temporal consistency of commitments—the degree to which an agent maintains coherence with stated principles, relationships, and promises across time.

Connections

Assumes

  • None

Enables

  • None
Physics Layer

The Faithfulness Operator

\hat{F}_{\text{Faithfulness}} = \frac{1}{T} \int_0^T \hat{U}^\dagger(t) \hat{B} \hat{U}(t) \cdot \hat{B}(0) \, dt

Where:

  • \hat{B} is the commitment-behavior alignment operator
  • \hat{U}(t) is the time evolution operator
  • The product measures correlation between current and initial alignment
Mathematical Layer

Formal Definition

Definition (Faithfulness Metric): Let \mathcal{A} be an agent with commitment set \mathcal{C} and behavior function B: \mathcal{C} \times \mathbb{R}_+ \to [0,1] measuring alignment. The Faithfulness metric is:

F_{\text{Faithfulness}}(\mathcal{A}) = \frac{1}{|\mathcal{C}|} \sum_{c \in \mathcal{C}} \frac{1}{T} \int_0^T \text{Corr}(B_c(t), B_c(0)) \, dt

Where \text{Corr} is the Pearson correlation coefficient.

Defeat Conditions

To Falsify This

  1. **Faithfulness Without Consistency:** Demonstrate genuine faithfulness in agents with erratic, inconsistent behavior. This would decouple faithfulness from temporal coherence.
  2. **Consistency Without Faithfulness:** Show agents with perfect behavioral consistency who are universally judged unfaithful. This would break the equivalence.
  3. **Faithfulness to Bad Commitments:** If faithfulness to evil commitments counts as the virtue, this creates a paradox. The resolution: faithfulness is measured relative to coherence-aligned commitments.
  4. **Faithfulness Independent of Time:** Prove that faithfulness has no temporal component and is purely about current state. This would eliminate the persistence requirement.