Phi-prime Stage 1: Instrument Validation for a Structural Integration Measure of Transformer Attention Mechanisms

This pre-registration documents Stage 1 of the Phi-prime instrument validation study. Phi-prime (Φ′) is a CKA-based measure of integration irreducibility in transformer attention mechanisms, quantifying the degree to which a layer's full multi-head attention output cannot be approximated by any single head. Stage 1 tests whether Φ′ is a valid instrument: internally consistent, stable across surface-form variation, independent of sequence length, and capable of discriminating between structurally distinct input types in GPT-2. This is a mechanistic interpretability study; it makes no claims about consciousness. Companion papers: Paper A (Φ′ methods, targeting the interpretability community) and Paper B (theoretical motivation). Author: Christopher Daley.