Compression-Aware Intelligence

Contradiction Density (CD):

$$CD = \frac{\text{Number of contradictions detected}}{\text{Total outputs evaluated}}$$

Coherence Delta (CoD):

$$CoD = \text{Coherence(before)} - \text{Coherence(after)}$$

Entropy Risk Score (ERS):

$$ERS = - \sum_i p_i \log(p_i)$$

Composite CAI Score:

$$CAI\_Score = \alpha \cdot CD + \beta \cdot CoD + \gamma \cdot ERS$$

CAI is about one thing: test stability across semantically equivalent but differently phrased prompts to detect internal model contradictions and compression failures. Brittleness arises when meaning-preserving transformations induce semantically incompatible internal states under compression, and hallucinations are the forced collapse of that incompatibility.