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Finite Experiments Can Certify Integrated Information: Identifiability and Limits

This paper investigates when mechanism-level quantities like integrated information (phi) can be identified from finite, partial, and noisy interventions. Using stochastic networks of four and five units, the authors show that behavior alone can be silent, while internal recordings can separate mechanisms within a few trials. They also identify precision floors and sharp edges that limit certification, yet prove that one-sided lower bounds can be certified from about 10^7 controlled transitions with controlled error probability.