Operationalisation Independence in the Consciousness Gradient Index: Evidence That the Integration-Differentiation Framework Survives Measurement Choice

The Consciousness Gradient Index (CGI = sqrt(phi x rho) x 10) defines consciousness as the geometric mean of integration (phi) and differentiation (rho). A systematic audit of five independent CGI pipelines reveals that the framework produces valid results across multiple operationalisations of phi and rho, including theta coherence, alpha coherence, transfer entropy, information-theoretic synergy, and spectral entropy. Each operationalisation was developed for a different empirical context (sleep-wake discrimination, pharmacological sedation tracking, finegrained sleep staging), and each produces significant effects in its target domain. Critically, no single operationalisation succeeds in all contexts: theta coherence discriminates sleep from wake but fails to track propofol sedation; alpha coherence tracks propofol but produces inverted sleepstage ordering when used naively; information-theoretic synergy resolves all five sleep stages but fails on propofol sedation; and the alpha-coherence pipeline that tracks propofol produces inverted results on sleep data, completing a symmetric double dissociation. This pattern — where the theoretical framework generalises but the measurement must adapt — is characteristic of fundamental scientific quantities such as force, entropy, and coherence, all of which require domain-specific operationalisation while maintaining theoretical universality. We argue that operationalisation independence constitutes evidence for the underlying construct validity of the integration-differentiation framework.