Linearizing Integrated Information Theory: S-Measure as a Computable Topological Alternative to IIT 4.0 via Local Taylor Expansion
Zenodo (CERN European Organization for Nuclear Research) June 25, 2026 Yuri N. Berdinsky, А. О. Шпаков
A new computable measure of integrated information, chi-square Phi, is derived as the exact second-order Taylor expansion of the Kullback-Leibler-based Phi from Integrated Information Theory (IIT). The linear term vanishes, yielding a closed-form quadratic functional computable in O(N²) time. Paired with an architectural S-measure using Tarjan's algorithm for cycle complexity, the combined metric is faithful to IIT to second order, specific to genuine causal integration (no false positives from feedforward trees), and computable in polynomial time O(N³). The topological bridge S>0 implying chi-square Phi>0 is machine-verified in Lean 4. This provides a practical, computable measure for real neural and artificial systems.