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

Cruz N. Sanchez

Zenodo (CERN European Organization for Nuclear Research) August 2, 2026 DOI: 10.5281/zenodo.21764938 (opens in new tab)

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Characteristics Theoretical or philosophical paper Peer reviewed
Key points Proposes that IIT 5.1 resolves computational intractability via a computable chi-square Phi, unifies IIT with the Free Energy Principle through maximum-caliber deviation, and scales to larger systems via tensor networks, validated on IBM Quantum hardware with a CHSH value of 2.749.

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).

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