Lattice Gauge Symmetry Breaking and Integrated Information Share Partition-Lattice Order — E8 Intelligence Research

FINDING: Symmetry breaking in lattice gauge theory and parity/time-reversal operations share the same partition-lattice order structure that Tononi's integrated information (Φ) requires; consciousness formalisms are being mapped onto the same lattice-QCD machinery used for chiral symmetry breaking. | MATH: Key objects — (1) Parity operator P: x→−x, P²=1, eigenvalues ±1; time-reversal T antiunitary, T²=(−1)^{2j} for spin-j (Kramers degeneracy when 2j odd). (2) Lattice QCD partition function Z = ∫DU Dψ̄Dψ e^{−S[U,ψ]}, with chiral condensate ⟨ψ̄ψ⟩ ≠ 0 breaking SU(N_f)_L×SU(N_f)_R → SU(N_f)_V. (3) Tononi Φ: Φ = min over partitions of effective information; IIT 3.0 uses Φ = min_{P∈Partitions} [I(X;M) − I(X^{1};M^{1}) − I(X^{2};M^{2})]. (4) Algorithmic-information reformulation (arXiv:1405.0126): Φ_AIT defined via Kolmogorov complexity K, Φ ≈ K(system) − K(parts) − K(interactions), avoiding lossy-integration paradox. | CONNECTION: Partition lattice (Boolean lattice B_n of subsets, ordered by Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com