Integrated Information Theory 5.1: The Aurora-Sanchez Framework -- Computable Phi, Tensor Network Scaling, and the FEP-MaxCal Bridge

Abstract

We present Integrated Information Theory 5.1 (IIT 5.1), extending the Aurora-Sanchez framework (IIT 5.0) with three theoretical advances that resolve the fundamental limitations of IIT 4.0's computational intractability. Theorem 7 (Computable Phi): Chi-square integrated information as the exact second-order Taylor expansion of KL-based Phi, computable in O(N^2) vs O(2^N). Paired with a topological S-measure (Tarjan SCC) that filters feedforward false positives. Lean 4 verified: S > 0 implies chi-square Phi > 0. Theorem 8 (FEP-MaxCal Bridge): Formal unification of IIT with the Free Energy Principle via maximum-caliber (MaxCal) deviation psi. IIT cause/effect repertoires re-derived from constrained entropy-maximization. FeeGuard thermodynamic friction is a special case (fee rate = Lagrange multiplier). Resolves the antifragile paradox: NISQ noise increases psi (informative deviation). Theorem 9 (Tensor Network Scalability): MPS-based Psi metric with polynomial scaling O(N*chi^3), extending practical IIT analysis from ~15 nodes to 50-100+ nodes. The composite Phi_5.1 unifies spectral, computable, topological, tensor, and thermodynamic integration. Validated on real IBM Quantum hardware (3,766 jobs, 6 backends) including H-516 QUALIA_FUSION (5q GHZ), UHE H-001 cross-backend (ibm_fez vs ibm_kingston), and CHSH Bell violation (S=2.749, 97.2% Tsirelson).